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  • 1
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 1531-1549 
    ISSN: 0170-4214
    Keywords: gratings ; Helmholtz equation ; high frequencies ; geometric theory of diffraction ; transition regions ; finite element method ; error estimates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new numerical method is derived for the calculation of high-frequency asymptotic expansions of the scalar wave scattered by curved periodic structures. Optimal error estimates for this method are established. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 2
    Electronic Resource
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 1637-1654 
    ISSN: 0170-4214
    Keywords: generalized Stokes equations ; incompressible flow ; least-squares ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we are concerned with a weighted least-squares finite element method for approximating the solution of boundary value problems for 2-D viscous incompressible flows. We consider the generalized Stokes equations with velocity boundary conditions. Introducing the auxiliary variables (stresses) of the velocity gradients and combining the divergence free condition with some compatibility conditions, we can recast the original second-order problem as a Petrovski-type first-order elliptic system (called velocity-stress-pressure formulation) in six equations and six unknowns together with Riemann-Hilbert-type boundary conditions. A weighted least-squares finite element method is proposed for solving this extended first-order problem. The finite element approximations are defined to be the minimizers of a weighted least-squares functional over the finite element subspaces of the H1 product space. With many advantageous features, the analysis also shows that, under suitable assumptions, the method achieves optimal order of convergence both in the L2-norm and in the H1-norm. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
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  • 3
    Electronic Resource
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 69-72 
    ISSN: 1069-8299
    Keywords: finite element method ; thermoplasticity ; internal dissipation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper, a simple modification of the internal dissipation term in coupled thermoplastic finite element equations is presented. A modified form of the heat capacity and the thermomechanical coupling matrices are derived. These modifications are based on a decomposition of the internal dissipation term into two parts, which depend on the total strain rate and the rate of temperature change, respectively.
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  • 4
    Electronic Resource
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 403-407 
    ISSN: 1069-8299
    Keywords: finite element method ; residual bending flexibility ; convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper I re-examine the mechanics of the residual bending flexibility correction and show that it is an extravariational trick.
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  • 5
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 373-381 
    ISSN: 1069-8299
    Keywords: finite element method ; mesh refinement ; adaptivity ; singularities near edges ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with several refinement techniques of finite element meshes for treating elliptic boundary value problems in domains with re-entrant edges and corners. A priori mesh grading is explained, and it is combined with the well-known adaptive finite element method. For two representative examples the numerically determined error norms are recorded, and the different strategies are compared.
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  • 6
    Electronic Resource
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 425-431 
    ISSN: 1069-8299
    Keywords: time integration ; finite element method ; least squares formulation ; multistep methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a formulation and analysis of three and four step least squares algorithms for first order IVPs. The three step algorithm is derived using cubic Lagrangian interpolation, and is found to be third order accurate but only conditionally stable. Fourth order Lagrangian interpolation is used to obtain a four step least squares scheme which is A0-stable but inconsistent.
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  • 7
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 483-495 
    ISSN: 1069-8299
    Keywords: finite element method ; solid modelling ; optimal interpolation ; a posteriori error estimation ; adaptive interpolation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of approximating functions is considered in a general domain in one and two dimensions using piecewise polynomial interpolation. An error estimator is proposed which shows how to adaptively determine the interpolation degree. Numerical examples are given.
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  • 8
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 581-594 
    ISSN: 1069-8299
    Keywords: acoustics ; finite element method ; error estimation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A posteriori error estimation has become very popular, mainly in linear elasticity. A robust implementation of the superconvergent patch recovery technique of O. C. Zienkiewicz and J. Z. Zhu is presented for acoustic finite element analyses: the original concepts are extended to complex variables, and both local and global behaviours of the recovery procedure and the error estimation are studied. The numerical tests confirm the improvement of the rates of convergence for the recovered solution and also show the reliability of the error estimator except at frequencies corresponding either to the analytical or to the finite element eigenfrequencies.
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  • 9
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 807-826 
    ISSN: 1069-8299
    Keywords: incompressible materials ; finite element method ; p-version ; elasticity ; stress extraction ; complementary energy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Direct methods for computing the pointwise stresses for nearly incompressible elastic materials fail to provide meaningful results when applied to the displacement formulation of the finite element method (FEM). A new extraction method for accurate computation of pointwise stresses for nearly incompressible elastic materials is presented. It is based on the complementary energy principle applied over a local domain in the postprocessing phase in conjunction with the p-version finite element solution. It is shown that accurate pointwise stresses are obtained, that the relative error in the pointwise stresses converges at a rate which is as fast as the relative error measured in the energy norm or faster, and importantly, the extracted stresses are virtually independent of Poisson's ratio. Numerical results for two problems, one having a smooth solution and the other containing a singular point, are provided.
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  • 10
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 873-884 
    ISSN: 1069-8299
    Keywords: thin-walled beam ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for computing the deformation of thin-walled beams with closed cross-section under warping torsional loading is presented. In comparison to the classical theory (Umanski), the hypothesis of no deformation of the contour of the cross-section of the beam is maintained and the assumption of no distortion of the cross-section plane is modified. The new approach gives better results than the classical theory when both are compared to a standard finite element technique (using shell elements). The central idea of the new approach lies in the usage of a new finite element called a macro-element, which is especially well suited for thin-walled beam computations.
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  • 11
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 193-198 
    ISSN: 1069-8299
    Keywords: finite element method ; software engineering ; object-oriented programming ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Making a finite element code easier to maintain is achieved by further modularizing it. Due to its two levels of modularity (of procedures and data), object-oriented programming is the method of choice. Its potential is investigated in two bottlenecks of finite element programming where so far it has not proved significantly more successful than classical Fortran programming. The first of these is the lack of adequate data structures between the analysis specifications and the basic objects of the finite element method, like the element and the node. This is solved by defining two classes of objects, namely problem and domain, with clearly differentiated specifications. The second gap deals with solving linear equation systems. Introducing an intermediate class UnassembledMatrix allows alternative storage/solving schemes to be implemented in a very flexible manner. © 1997 by John Wiley & Sons, Ltd.
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  • 12
    Electronic Resource
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 103-112 
    ISSN: 1069-8299
    Keywords: static reanalysis ; finite element method ; structural analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an exact structural static reanalysis method for locally modified structures. Through the introduction of structural rigid body motion eigenvectors, the generalized structural compliance matrix can be obtained and the original stiffness equation is transformed into a linear system of much lower order. The general solution of displacements can be expressed prior to any assignment of boundary conditions. For a structure with given boundary and loading conditions, the displacements can be obtained by solving this linear system. For locally modified structures, the structural compliance matrix can be adjusted quickly. This static reanalysis method can be used for structures with modifications on structural elements, boundary and loading conditions, either independently or in combination. Two test examples are provided in the paper to prove the efficiency of the method. © 1997 John Wiley & Sons, Ltd.
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  • 13
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 319-326 
    ISSN: 1069-8299
    Keywords: homogenization of periodic media ; masonry ; damage ; finite element method ; plane stress ; generalized plane strain ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Through the homogenization theory for periodic media, the macroscopic behaviour of masonry may be derived from the behaviour of its constitutive materials (brick and mortar). Such a procedure has been used by many authors but always in an approximate manner. In particular, masonry has been considered either as infinitely thin (two-dimensional media under plane stress), or as infinitely thick (two-dimensional media under generalized plane strain). In order to determine the range of validity of either assumption, the homogenization theory is here implemented in a rigorous way, i.e. taking into account the finite thickness of masonry. Both brick and mortar being assumed as subjected to isotropic damage, numerical computations show that the above-mentioned assumptions have little influence on the macroscopic elastic behaviour of masonry, but may significantly affect its non-linear response (ultimate load and mode of failure). © 1997 John Wiley & Sons, Ltd.
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  • 14
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 343-353 
    ISSN: 1069-8299
    Keywords: plate element ; finite element method ; reduced integration ; penalty number ; Lagrange and serendipity elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The serendipity (eight nodes) and Lagrange (nine nodes) plate elements following the Reissner-Mindlin irreducible formulation for the bending of plates are among the most popular in the finite element method. However, reduced integration on the shearing part of the stiffness matrix has to be performed in order to avoid locking of the mesh in the limit of thin plates, where numerical constraints are taking some degrees of freedom in order to be satisfied. This paper explains the competition between those constraints and the degrees of freedom, giving a mean to predict whether a mesh will lock or not. It also shows why the Lagrange element performs better than the serendipity element. Numerical results confirm this analysis. © 1997 John Wiley & Sons, Ltd.
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  • 15
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 355-372 
    ISSN: 1069-8299
    Keywords: differential quadrature method ; finite element method ; porosity distribution ; powder metallurgy ; sintering ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Viscous sintering of a porous ball with various initial distributions of porosity versus radius is considered. For the solution of the corresponding boundary-value problems of the evolution of porosity and flow velocity fields during sintering, the numerical algorithms based on the differential quadrature method (DQM) and an arbitrary Eulerian-Lagrangian version of the finite element method (FEM) (the permeable element method) are elaborated. A comparative analysis of the calculation results is carried out. The question of the influence of non-uniformity of porosity distribution on the localization of densification is discussed. © 1997 John Wiley & Sons, Ltd.
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  • 16
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 775-795 
    ISSN: 0029-5981
    Keywords: computational mechanics ; finite element method ; a posteriori error estimation ; finite elasticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Methods for a posteriori error estimation for finite element solutions are well established and widely used in engineering practice for linear boundary value problems. In contrast here we are concerned with finite elasticity and error estimation and adaptivity in this context. In the paper a brief outline of continuum theory of finite elasticity is first given. Using the residuals in the equilibrium conditions the discretization error of the finite element solution is estimated both locally and globally. The proposed error estimator is physically interpreted in the energy sense. We then present and discuss the convergence behaviour of the discretization error in uniformly and adaptively refined finite element sequences.
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  • 17
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 33-50 
    ISSN: 0029-5981
    Keywords: finite element method ; shape optimization ; sensitivity analysis ; forming process ; optimal design ; forging ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We suggest a shape optimization method for a non-linear and non-steady-state metal forming problem. It consists in optimizing the initial shape of the part as well as the shape of the preform tool during a two-step forging operation, for which the shape of the second operation is known. Shapes are described using spline functions and optimal parameter values of the splines are searched in order to produce, at the end of the forging sequence, a part with a prescribed geometric accuracy, optimal metallurgical properties and for a minimal production cost. The finite element method, including numerous remeshing operations, is used for the simulation of the process. We suggest using a least-squares-type algorithm for the unconstrained optimization method (based on external penalty) for which we describe the calculation of the derivatives of the objective function. We show that it can reduce to calculations which are equivalent to the derivative calculations of steady-state processes and to evolution equations. Therefore, the computational cost of such an optimization is quite reasonable, even for complex forging processes. Lastly, in order to reduce the errors due to the numerous remeshings during the simulation, we introduce error estimation and adaptive remeshing methods with respect to the calculation of derivatives.
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  • 18
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 3745-3774 
    ISSN: 0029-5981
    Keywords: Helmholtz equation ; finite element method ; error analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When applying numerical methods for the computation of stationary waves from the Helmholtz equation, one obtains ‘numerical waves’ that are dispersive also in non-dispersive media. The numerical wave displays a phase velocity that depends on the parameter k of the Helmholtz equation. In dispersion analysis, the phase difference between the exact and the numerical solutions is investigated. In this paper, the authors' recent result on the phase difference for one-dimensional problems is numerically evaluated and discussed in the context of other work directed to this topic. It is then shown that previous error estimates in H1-norm are of nondispersive character but hold for medium or high wavenumber on extremely refined mesh only. On the other hand, recently proven error estimates for constant resolution contain a pollution term. With certain assumptions on the exact solution, this term is of the order of the phase difference. Thus a link is established between the results of dispersion analysis and the results of numerical analysis. Throughout the paper, the presentation and discussion of theoretical results is accompanied by numerical evaluation of several model problems. Special attention is given to the performance of the Galerkin method with a higher order of polynomial approximation p(h-p-version).
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  • 19
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3049-3064 
    ISSN: 0029-5981
    Keywords: mold cooling ; injection molding ; finite element method ; three-dimensional ; Jacobi conjugate gradient ; matrix-free algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A methodology is presented to simulate the three-dimensional heat transfer within a mold during the injection molding process. The mold cooling analysis assists cooling channel design and paves the way for part shrinkage and warpage analysis. The transient temperature distributions in the mold and the polymer part are simultaneously computed by Galerkin Finite Element Method (GFEM) using a matrix-free Jacobi Conjugate Gradient (JCG) scheme. The numerical method presented here is efficient and has shown to require a fraction of the memory and computing time required by conventional methods. The matrix-free algorithm is initially validated using an injection mold designed to produce a plaque with a molded-in hole. Subsequently, the method is further applied to a representative automotive plastic component.
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  • 20
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 4039-4061 
    ISSN: 0029-5981
    Keywords: finite element method ; optimal mesh ; strategy ; refinement ; error estimation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Five Adaptive Modification Strategies (AMSs) are studied as means to obtain nearly optimal meshes using an adaptive finite element modelling system based on the h-version of the FEM. These strategies include the method traditionally seem in the literature as well as four additional methods. The five strategies are tested over five numerical examples, one of them producing convergence oscillations in one example. The principal characteristic of our system is that it permits the user to control certain parameters of the adaptive process, which contributes to an improvement in the results.
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  • 21
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    Communications in Numerical Methods in Engineering 14 (1998), S. 229-240 
    ISSN: 1069-8299
    Keywords: filling of thin section ; finite element method ; surface tension ; interface element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An interface element to model the pressure discontinuity due to surface tension when applied to the filling of a thin section cavity is presented. The equations used to form the element matrix for the interface element are the line integral form of the continuity and momentum equations. During the development of the finite element model, the pressure difference across the free surface due to surface tension is treated as an additional traction and is applied to all element sides which form the free surface. Simple numerical examples are then presented to illustrate the technique on the filling of a rectangular thin section cavity. © 1998 John Wiley & Sons, Ltd.
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  • 22
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    Communications in Numerical Methods in Engineering 13 (1997), S. 705-713 
    ISSN: 1069-8299
    Keywords: natural-modes ; finite element method ; model problem ; thermomechanical buckling ; computing statistics report ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We address here some computational aspects of the natural-mode finite element method (NM-FEM), a technique recently developed by the authors for the analysis of arbitrary composite shells. We consider in particular a model problem comprising a (45/-45/0/90)S cylindrical composite shell with 2398 degrees of freedom subjected to compressive load and temperature increase, and compute the first four critical loads and temperatures. For this problem a computational statistics report is obtained showing the breakdown of the CPU time in the various routines. It is observed that most of the computing time is spent on algebraic operations, suggesting computational efficiency and high potential for vectorization/parallelization. © 1997 John Wiley & Sons, Ltd.
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  • 23
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    Communications in Numerical Methods in Engineering 11 (1995), S. 105-115 
    ISSN: 1069-8299
    Keywords: finite element method ; conceptual diagrams ; error estimation ; postprocessing ; teaching ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The success of the finite element method depends on the highly systematic way the analysis is built up, which means that the structure of the theoretical description and the code is transferable between different applications. It is advisable to teach the subject in such a way that this fact is fully exploited. It is a fact that most FE calculations today do not contain a check of the accuracy/quality of the solution. In the teaching of the FE method nothing is more important than the basic knowledge and understanding of the properties and behaviour of the obtained FE solution. The paper deals with the methodology in presenting the method, by use of conceptual diagrams. It also discusses the interpretation of the results from a classical FE analysis and the extraction of high quality information. Finally, error estimation and postprocessing are discussed. The detailed description of the boundary conditions is lost in the FE solution. In the postprocessing stage they should be taken into account once more.
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  • 24
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    Communications in Numerical Methods in Engineering 14 (1998), S. 135-149 
    ISSN: 1069-8299
    Keywords: multiphase immiscible flow ; deforming porous media ; fully coupled ; soil displacements ; fluid pressures ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A fully coupled numerical model has been developed which describes multiphase fluid flow through soil: namely gas, water and a non-aqueous phase liquid (NAPL) in a deforming porous media for subsurface systems. A multiphase flow model, based on the two-phase flow model of Brooks and Corey, is presented to express the dependence of saturation and relative permeability on the capillary pressure. Non-linear saturation and relative permeability functions are incorporated into a Galerkin finite element model which is subsequently used to simulate multiphase immiscible fluid flow under saturated and unsaturated conditions in porous media. The governing partial differential equations, in terms of soil displacements and fluid pressures, which are coupled and non-linear, are solved by the finite element method. Numerical implementation of the formulation is discussed, and example problems demonstrate the model and solution procedure. © 1998 John Wiley & Sons, Ltd.
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  • 25
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    Communications in Numerical Methods in Engineering 14 (1998), S. 181-194 
    ISSN: 1069-8299
    Keywords: oscillating flow ; Keulegan-Carpenter number ; finite element method ; in-line force ; transverse force ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The results of a numerical study of the viscous oscillating flow around a circular cylinder at Reynolds number=200 and Keulegan-Carpenter number=20 are presented. The finite element method was used for the solution of the Navier-Stokes equations, in the formulation where the streamfunction and the vorticity are the field variables. The computation revealed a complicated flow pattern at which the flow is not periodic but switches between different modes at various oscillation cycles. The vortex shedding patterns occurring at different cycles were identified by means of numerical flow visualization. The traces of the hydrodynamic forces were derived from the solution, and the hydrodynamic coefficients of the in-line force were evaluated. © 1998 John Wiley & Sons, Ltd.
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  • 26
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    Communications in Numerical Methods in Engineering 11 (1995), S. 409-416 
    ISSN: 1069-8299
    Keywords: contact ; friction ; finite element method ; large deformation ; augmented Lagrangian method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper is devoted to the analysis of two- or three-dimensional contact problems with Coulomb friction and large deformation. The classical approach is based on two minimum principles or two variational inequalities: the first for unilateral contact and the second for friction. A coupled approach using only one principle or one inequality is presented. This new approach allows us to extend the notion of normality law to dissipative behaviours with a non-associated flow rule, such as surface friction. Non-differentiable contact potentials are regularized by means of the augmented Lagrangian method. Using the C++ language, an object-oriented finite element database is created, which allows us to implement the contact and friction in an existing code in a very simple and neat way. Numerical examples are carried out in many difficult cases such as shock absorber and three-dimensional contact. The numerical results prove that this approach is robust and efficient concerning numerical stability.
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  • 27
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    Communications in Numerical Methods in Engineering 11 (1995), S. 899-909 
    ISSN: 1069-8299
    Keywords: finite element method ; non-linear shell elements ; assumed strain approach ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A quadrilateral degenerated C0 shell element is presented which relies on extensible director kinematics and which incorporates unmodified three-dimensional constitutive models. It is shown that the direct interpolation of the extensible director field causes severe locking behaviour in the case of thin shell structures. An assumed strain interpolation is proposed to overcome the thin-shell defect. Due to this modification the shell element is able to accommodate large rotations without a rotation tensor, even for very thin shells. Several large deformation examples confirm that the developed shell element is competitive with more elaborate formulations which use rotational degrees of freedom.
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  • 28
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    Communications in Numerical Methods in Engineering 12 (1996), S. 77-83 
    ISSN: 1069-8299
    Keywords: eigenvalue extraction ; conjugate gradient method ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new conjugate gradient algorithm is presented for extracting eigenvalues from large systems of equations encountered in finite element analysis. The new algorithm involves applying the conjugate gradient method (CGM) to a static problem to generate an equivalent tridiagonal matrix used for eigenvalue computation. The eigenvalues of the tridiagonal matrix are then extracted using a QR factorization. The similarity of the new CGM with the Lanczos method is discussed regarding the need for matrix inversion and reorthogonalization. Several examples using the new method are presented to illustrate its performance.
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  • 29
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    Communications in Numerical Methods in Engineering 13 (1997), S. 999-1008 
    ISSN: 1069-8299
    Keywords: optimization ; sensitivity analysis ; constraint approximation ; non-linear analysis ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the finite element non-linear analysis of engineering problems combined with an optimization method, two techniques - a semi-analytical sensitivity method and bi-point constraint approximation - have been proposed. To validate the proposed methods, a raft foundation on a soil medium has been analysed and the results have been compared. From the numerical results, it has been found that, for non-linear analysis, the semi-analytical sensitivity method is more efficient than the finite difference method and the bi-point approximation gives results which compare favourably with the finite element results. © 1997 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 9-22 
    ISSN: 1069-8299
    Keywords: finite element method ; optimal control theory ; Navier-Stokes equations ; Lagrange multipliers ; adjacent equations ; Sakawa-Shindo method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This work presents control of vorticity for buoyancy-driven flows. The governing set of equations includes Navier-Stokes and heat transfer equations. The basic formulation for the control problem is derived using Lagrange multipliers and the Pontryagin minimum principle. Control values are found using the Sakawa-Shindo method. Control was accomplished using velocity components. Numerical examples present control of vorticity for Rayleigh-Bernard convection in an enclosed cavity for a wide range of Ra numbers. The current formulation proved reliable and fast. Optimal control was obtained and turned out to be adequate. © 1998 John Wiley & Sons, Ltd.
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    Communications in Numerical Methods in Engineering 14 (1998), S. 997-1012 
    ISSN: 1069-8299
    Keywords: potential flow ; finite element method ; wave resistance ; absorbing boundary condition ; free surface flow ; partial discretization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for computing ship wave resistance from a momentum flux balance is presented. It is based on computing the momentum flux carried by the gravity waves that exit the computational domain through the outlet plane. It can be shown that this method ensures a non-negative wave-resistance, in contrast with straightforward integration of the normal pressure forces. However, this calculation should be performed on a transverse plane located far behind the ship. Traditional Dawson-like methods add a numerical viscosity that dampens the wave pattern so that some amount of momentum flux is lost, and resulting in an error in the momentum balance. The flow field is computed, then, with a centred scheme with absorbing boundary conditions. Copyright © 1998 John Wiley & Sons, Ltd.
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  • 32
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    Communications in Numerical Methods in Engineering 14 (1998), S. 1119-1131 
    ISSN: 1069-8299
    Keywords: Reissner-Mindlin plate ; finite element method ; p version ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the finite element (FE) approximation of the Reissner-Mindlin (RM) plate model, and indicate how to design meshes that yield accurate results when the p/hp version of the standard FE method is used. These guidelines allow quantities of engineering interest to be predicted numerically with great confidence near the boundary. We illustrate this through numerical computations in the case when both boundary layers and corner singularities are present. Copyright © 1998 John Wiley & Sons, Ltd.
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  • 33
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    Communications in Numerical Methods in Engineering 11 (1995), S. 297-306 
    ISSN: 1069-8299
    Keywords: semi-analytic method ; dynamic response ; convolution ; variational principle ; series ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper a semi-analytic approach for solving dynamic response problems is developed which is based on Gurtin's convolution-type variational principle. A finite element discretization in the space domain and a series representation in the time domain are considered. This approach overcomes the shortcomings of existing methods yet utilizes their advantages for solving dynamic response problems. The example of a beam shows that this new approach is a very effective method in obtaining solutions for dynamic response problems. The paper also concentrates on utilizing time domain series for various boundary conditions, so that solutions calculated by this approach have a very high accuracy and efficiency.
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    Communications in Numerical Methods in Engineering 11 (1995), S. 727-733 
    ISSN: 1069-8299
    Keywords: eddy currents ; finite element method ; equivalence ; uniqueness ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new variational problem corresponding to a three-dimensional eddy-current boundary-value problem is treated in the paper. The equivalence between the variational problem and the boundary-value problem is proved, and so is the uniqueness of the solution. These form the foundation of the H - Ψ method.
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  • 35
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    Journal of Computational Chemistry 11 (1990) 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
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  • 36
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    Journal of Computational Chemistry 11 (1990), S. 1-18 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Counterpoise corrected ab initio calculations are reported for (H2O)2 and H2O-H2CO. Geometry searches were done in the moment-optimized basis DZP' at the SCF, MP2, and CEPA-1 levels of theory, followed by more accurate single-point calculations in basis ESPB, which includes bondfunctions to saturate the dispersion energy. The final equilibrium binding energies obtained are -4.7 ±0.3 kcal/mol for a near-linear (H2O)2 structure and -4.6 ±0.3 kcal/mol for a strongly bent HOH ‥ OCH2 structure. The energy difference between these systems is much smaller than in all previous ab initio work. Cyclic (C2h) and bifurcated (C2v) transition structures for (H2O)2 are located at 1.0 ±0.1 kcal/mol and 1.9 ±0.3 kcal/mol above the global minimum, respectively. A new partitioning scheme is presented that rigorously partitions the MP2 correlation interaction energy in intra and intermolecular (dispersion) contributions. These terms are large (up to 2 kcal/mol) but of opposite sign for most geometries studied and hence their overall effect upon the final structures is relatively small. The relative merits of the MP2 and CEPA-1 approaches are discussed are discussed and it is concluded that for economical reasons MP2 is to be preferred, especially for larger systems.
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    Journal of Computational Chemistry 11 (1990), S. 45-57 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A data compression method is presented that is generally applicable to first-order convergent iterative procedures that employ subspace expansions or extrapolations based on successive correction vectors. This method is based on the truncation of insignificant information in successive correction vectors. Although the correction vectors themselves may be severely truncated with the proposed approach, the final solution vector may be represented to arbitrary accuracy. A feature of the proposed method is that more slowly convergent iterative procedures allow the correction vectors to be more severely truncated without affecting the overall convergence rate. The method is implemented and applied to the iterative Davidson diagonalization method. If the compressed representation of the expansion vectors can be held in main computer memory, then a significant reduction in the I/O requirements is achieved.
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    Journal of Computational Chemistry 11 (1990), S. 67-75 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: By examining the displacement coordinate metric three modes of constrained optimization for large molecules and clusters are suggested. The first method corresponds to a conventional optimization using internal coordinates. The second mode has applications with respect to both internal and cartesian coordinates. The final mode is particularly interesting because it can result in computational savings. A mixture of both internal and cartesian coordinates is specified where these coordinates are usually a subset of the molecules or clusters total coordinate set. In the optimization only a subset of the energy derivatives need be evaluated reducing the computational effort associated with the gradient calculation.
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  • 39
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    Journal of Computational Chemistry 11 (1990), S. 82-87 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A finite-field method for the calculation of polarizabilities and hyperpolarizabilities is developed based on both an energy expansion and a dipole moment expansion. This procedure is implemented in the MOPAC semiempirical program. Values and components of the dipole moment (μ), polarizability (α), first hyperpolarizability (β), and second hyperpolarizability (γ) are calculated as an extension of the usual MOPAC run. Applications to benzene and substituted benzenes are shown as test cases utilizing both MNDO and AM1 Hamiltonians.
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    Journal of Computational Chemistry 11 (1990), S. 121-151 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A procedure has been developed for global energy minimization of surface loops of proteins in the presence of a fixed core. The ECEPP potential function has been modified to allow more accurate representations of hydrogen bond interactions and intrinsic torsional energies. A computationally efficient representation of hydration free energy has been introduced. A local minimization procedure has been developed that uses a cutoff distance, minimization with respect to subsets of degrees of freedom, analytical second derivatives, and distance constraints between rigid segments to achieve efficiency in applications to surface loops. Efficient procedures have been developed for deforming segments of the initial backbone structure and for removing overlaps. Global energy minimization of a surface loop is accomplished by generating a sequence (or a trajectory) of local minima, the component steps of which are generated by searching collections of local minima obtained by deforming seven-residue segments of the surface loop. The search at each component step consists of the following calculations: (1) A large collection of backbone structures is generated by deforming a seven-residue segment of the initial backbone structure. (2) A collection of low-energy backbone structures is generated by applying local energy minimization to the resulting collection of backbone structures (interactions involving side chains that will be searched in this component step are not included in the energy). (3) One low-energy side-chain structure is generated for each of the resulting low-energy backbone structures. (4) A collection of low-energy local minima is generated by applying local energy minimization to the resulting collection of structures. (5) The local minimum with the lowest energy is retained as the next point of the trajectory. Applications of our global search procedure to surface segments of bovine pancreatic trypsin inhibitor (BPTI) and bovine trypsin suggest that component-step searches are reasonably complete. The computational efficiency of component-step searches is such that trajectories consisting of about 10 component steps are feasible using an FPS-5200 array processor. Our procedure for global energy minimization of surface loops is being used to identify and correct problems with the potential function and to calculate protein structure using a combination of sequence homology and global energy minimization.
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  • 41
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    Journal of Computational Chemistry 11 (1990), S. 416-430 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A systematic analysis of the molecular electrostatic potential (MEP) is presented. This study has been performed with a twofold purpose: first, to study the MEP dependence with regard to the quality of the basis set used to compute the ab initio SCF wavefunction and second, to develop and to assess a new strategy for computing isoelectrostatic potential maps using the semiempirical MNDO wavefunction. The only differences between this procedure and the ab initio SCF MEP computation lie in the freezing of the inner electrons and in the origin of the first-order density matrix. The statistical analysis of MEPs computed for a large number of molecules from MNDO wavefunction and ab initio SCF wavefunctions obtained using STO-3G, 4-31G, 6-31G, 4-31G*, 6-31G*, and 6-31G** basis sets points out the ability of any wavefunction to reproduce the general topological characteristics of the MEP surfaces. Nevertheless, split-valence basis sets including polarization functions are necessary to obtain accurate MEP minimum energy values. MNDO wavefunction tends to overestimate the MEP minima depth by a constant factor and shows an excellent ability to reflect the relative variation of MEP minima energies derived from a rather sophisticated (6-31G*) basis set, lacking of the shortcomings detected in the semiempirical CNDO approximation.
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    Journal of Computational Chemistry 11 (1990), S. 487-492 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Expressions are derived for computing the kinetic energy of a peptide with fixed geometry, in terms of dihedral angles as generalized coordinates; other expressions required for the solution of Lagrange's equations are also presented. The peptide is regarded as held stationary at one end. We also outline the computations that are needed in calculating the components of the third derivative of a potential energy function that consists of a sum of pairwise interatomic interactions.
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    Journal of Computational Chemistry 11 (1990), S. 819-828 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Complexes of alkali and alkaline earth cations with organic compounds are modeled by describing ionligand interaction energies with pair potentials and intraligand as well as interligand energies with the MM2 potential. New pair potentials for the interaction of Li+, Na+, K+, Mg2+, and Ca2+ ions are derived on the basis of 30,000 ab initio interaction energy values with 70 selected model ligand molecules. Various problems of the combination of these two basically different potentials are discussed. An application for the K+ complex of 18-crown-6 is presented. For more flexible ligands the introduction of three-body correction terms of the pair potentials seems necessary.
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    Journal of Computational Chemistry 11 (1990), S. 924-929 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The geometry, electronic structure, and photoelectron spectra of Sb2 and Sb4 have been investigated employing the LCGTO-MP-LSD method. For both molecules the geometrical and spectroscopic constants computed using the VWN potential are in very good agreement with the available experimental data. The HeI photoelectron spectra were computed with different potentials (Xα, GL, HL, BH, and VWN). The calculated spectra are in excellent agreement with the experimental ones and the use of the VWN potential gives the most accurate results. The reliable results for molecules complement those for the Sb atom and show that the proposed LSD Model Potential is able to give an accurate description of the structural and spectroscopic properties of the title molecules.
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    Journal of Computational Chemistry 11 (1990), S. 958-971 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Intermolecular potential functions have been developed for use in computer simulations of alkyl ethers. The simple OPLS model was adopted and parameterized to yield good descriptions of bimolecular and ion-molecule complexes as well as to reproduce experimental thermodynamic properties of liquid ethers. The principal testing featured Monte Carlo statistical mechanics simulations for liquid dimethyl ether (DME), ethyl methyl ether (EME), diethyl ether (DEE), and tetrahydrofuran (THF). Average errors of 1-3% are obtained for the computed densities and heats of vaporization including results for THF at pressures up to 5000 atm. The torsional motion about the central C—O bonds in EME and DEE was included in the simulations using rotational potential functions fit to results of molecular mechanics (MM2) calculations. The liquid-state environment is found to have negligible effect on the conformational equilibria.
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    Journal of Computational Chemistry 11 (1990), S. 972-977 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A quadrature-point-driven implementation of the standard Rys polynomial method for computing two-electron repulsion integrals of gaussian basis functions has been found to be both concise and openended with respect to the angular momentum of the gaussian functions (i.e., s,p,d,f,g,…). These are important features in certain applications, such as molecular properties and property gradients.
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    Journal of Computational Chemistry 11 (1990), S. 994-1002 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Free energy perturbation calculations were performed to determine the free energy of binding associated with the presence of perhaps an unusual hydroxyl group in the transition state analog of nebularine, an inhibitor of the enzyme adenosine deaminase. The presence of a single hydroxyl group in this inhibitor has been found to contribute -9.8 kcal/mol to the free energy of binding, with a 108-fold increase in the binding affinity by the enzyme. In this work, we calculate the difference in solvation free energy for the 1,6-dihydropurine complex versus that of the 6-hydroxyl-1,6-dihydropurine complex to determine if this marked increase in binding affinity is attributed to an unusually hydrophobic hydroxyl group. The calculated ΔG associated for the solvation free energy is -11.8 kcal/mol. This large change in the solvation free energy suggests that this hydroxyl is instead unusually hydrophilic and that the difference in free energy of interaction for the two inhibitors to the enzyme must be at least ca. 20 kcal/mol. Although the crystal structure for adenosine deaminase is currently not known, we attempt to mimic the nature of the active site by constructing models which simulate the enzyme-inhibitor complex. We present a first attempt at determining the change in free energy of binding for a system in which structural data for the enzyme is incomplete. To do this, we construct what we believe is a minimal model of the binding between adenosine deaminase and an inhibitor. The active site is simulated as a single charged carboxyl group which can form a hydrogen bond with the hydroxyl group of the analog. Two different carboxyl anion models are used. In the first model, the association is modeled between an acetic acid anion and the modified inhibitor. The second model consists of a hydrophobic amino acid pocket with an interior Glu residue in the active site. From these models we calculate the change in free energy of association and the overall change in free energy of binding. We calculate the free energies of interaction both in the absence and presence of water. We conclude from this that the presence of a single suitably placed-CO-2 group probably cannot explain the binding effect of the-OH group and that additional interactions will be found in the adenosine deaminase active site.
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    Journal of Computational Chemistry 11 (1990), S. 1029-1037 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Pseudopotentials and valence basis sets to be used in calculations for organometallic compounds of zinc and magnesium have been tested in calculations for the M(CH3)n (M = Zn, Mg; n = 1,2) molecules. Valence correlation effects are treated at the SDCI and CEPA levels. The capability of a polarization potential on zinc to account for the valence shell contracting effect of core valence correlation is studied. Properties considered are geometries, force constants, Mulliken populations, ionization potentials, atomization, and binding energies. Differences in bonding between the two dimethyl compounds are discussed.
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    Journal of Computational Chemistry 11 (1990), S. 1094-1100 
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    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The acid-catalyzed hydrolysis mechanisms of maleamic (4-amino-4-oxo-2-butenoic) acids were studied using AM1 method. The reaction proceeded mainly in two steps: (1) nucleophilic attack of the undissociated carboxyl group on the adjacent aminocarbonyl carbon via a zwitterionic intermediate; and (2) the rate-determining proton transfer to form the zwitterionic tetrahedral intermediate. In each step, the hydration of water and hydronium ion molecules was important in stabilizing the polarized intermediates. The substituent effects at the amide moiety and the 2,3-positions of the maleamic acids were qualitatively estimated for each step.
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    Journal of Computational Chemistry 11 (1990) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
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    Journal of Computational Chemistry 11 (1990), S. 1139-1146 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A prescription for applying the method of molecular similarity calculations based on electrostatic potentials and fields is developed by consideration of a typical structure-activity series. Firm conclusions are drawn about the nature of the grid of points surrounding the molecules and about the choice of geometry, but options for point charges are less clearcut.
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    Journal of Computational Chemistry 11 (1990), S. 899-908 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: An expanded form of the Wiener number is suggested for characterization of molecular graphs and structure-property correlations. The simple, computer-oriented method for counting of the novel index is briefly discussed.
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    Journal of Computational Chemistry 11 (1990), S. 1193-1205 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A common requirement in conformational analysis is the identification of a molecule's lowest energy conformations. The application of the A* algorithm to this problem is examined. The algorithm uses heuristic information about the problem domain to direct the search and has been implemented in a system for performing automated conformational analysis. The method is detailed and sample results presented. Some limitations of the approach are identified.
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    Journal of Computational Chemistry 11 (1990), S. 1009-1016 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Heats of formation and net atomic charges of some 120 structures involving substituted phenols, anilines, and benzoic acids and the corresponding anions were calculated by MNDO, AM1, and PM3 semiempirical methods. The gas phase acidities of substituted phenols and anilines and the net atomic charges on the anionic heteroatoms of the corresponding anions have been successfully correlated with σ- constants. Moreover, good correlations with σ were found for the charges on the acidic hydrogens of substituted phenols and anilines. In contrast, the gas phase acidities of substituted benzoic acids and the charges on the anionic oxygens of the corresponding anions are better correlated with Taft σ° constants. Comparisons of these results with experimental data and ab initio theoretical calculations indicate that AM1 and PM3 methods are much better than MNDO in predicting the acidity of aromatic compounds.
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    Journal of Computational Chemistry 11 (1990), S. 1038-1046 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: We studied geometries and energies of complexes between water and neutral or protonated imidazole by ab initio molecular orbital calculations using the 4-31G basis set with and without the counterpoise correction. Positions of hydration sites and relative binding energies could be also estimated by using the electrostatic field map of imidazole as calculated by our bond increment method. The reliability of the calculations is confirmed by comparing the geometries of the imidazole-water complex to the experimental ones from the Cambridge Structural Database. These were obtained by X-ray diffraction studies on crystals with water bound to a molecule containing the imidazole fragment.
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  • 56
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    Journal of Computational Chemistry 11 (1990), S. 1061-1071 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A new method for the evaluation of metal complexes with molecular mechanics calculations is described. The method has been employed to determine the global minimum energy conformations of three seven-coordinate lanthanide complexes. The method searches the potential energy surface of the metal complexes for the global minimum structure using the recently reported Random Incremental Pulse Search (RIPS). The molecular mechanics calculations were performed using the MM2 metal-extended force field (MM2MX). This force field excludes 1-3 bending terms about the metal center and, instead, explicitly includes 1-3 nonbonded van der Waals interactions. This affords a model based mainly on steric interactions about the ligating atoms, and removes the necessity of specifying ligand-metal-ligand bond angles for seven-coordinate and higher metal complexes in which no preferred bond angle can be proficiently determined. The calculated minimum-energy structures were well known seven-coordinate conformations in all cases, and a comparison with X-ray crystallographic is presented.
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    Journal of Computational Chemistry 11 (1990), S. 1076-1079 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The method of approximation of the frozen molecular fragment (FMF) we derived has been applied to calculations of proton affinities. Results are in good agreement with experimental data and extended basis set calculations.
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  • 58
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    Journal of Computational Chemistry 11 (1990), S. 1087-1093 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Myelin basic protein (MBP) is the major extrinsic protein of the myelin sheath in the central nervous system. It is this protein that is destroyed in such demyelinating diseases as multiple sclerosis. We have examined the predicted structures of one segment of MBP using the molecular mechanics program ECEPP83 developed by Scheraga and co-workers as modified by Chuman, Momany, and Schafer. We have focused upon a segment, 87-118, containing the Pro-Pro-Pro sequence (residues 100-102), which has been predicted from standard algorithms to exist in a hairpin loop connecting anti-parallel beta-strands. Several local energy minima have been found and reported. Tripoline sequences are not rare in proteins, but their structure and function is still uncertain.
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  • 59
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    Journal of Computational Chemistry 11 (1990), S. 1101-1110 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Two new computational methods for the evaluation and partitioning of projected, planar, and averaged slab electron densities, implemented in the program PRODEN, are presented. The new algorithms for the projection, demarcation, and integration of electron densities are described and evaluated in terms of speed and numerical accuracy. Integrated Projected Populations are analyzed and some of the advantages and limitations of the methods are discussed.
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  • 60
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    Journal of Computational Chemistry 12 (1991), S. 175-179 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: This is a study of the effect of data structures and algorithms on parallelism and vectorization for the molecular dynamics package GROMOS. About 80% of the computing time (for the GROMOS benchmark) is spent on the nonbonded interactions, and an important issue is the method that is used for finding all pairs of atoms (actually atom groups) which are within a given cutoff radius of each other. Favored by the authors of GROMOS is the use of the (Verlet) neighbor list with direct calculation of all distances. Substantial restructuring of their code for the nonbonded interactions has resulted in a speedup of a factor 6.9 for the eight-processor Alliant FX/8 through the use of concurrent subroutine calls. Vectorization gave a further improvement of 30%. However, the direct calculation of all distances does not scale up linearly with the number of atoms. (Nor would neighbor lists be needed if cutoffs were abandoned in favor of such techniques as the fast multipole method). Therefore an alternative GROMOS subroutine that implements the “gridcell plus linked list” approach without a neighbor list was also rewritten and tested. This resulted in the discovery of an apparent flaw in an early study of the relative merits of the two algorithms. It is observed that actually the neighbor list version of GROMOS is not much faster.
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  • 61
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    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Conformational energies of different conformers have been calculated for a series of molecules using various molecular mechanics and semiempirical methods. The quality of the force fields has also been tested by calculating barriers to rotation about carbon-carbon bonds. The molecular mechanics force fields used are MM2(85), Sybyl 5.1, Sybyl 5.21, and ChemX, ver. Jan 89. The semiempirical methods used are AM1 and PM3. Molecules with different functional groups, for which good experimental data exist, have been selected. The semiempirical methods generally calculate barriers to rotation which are lower than the experimentally determined. The conformational energies for hydrocarbons are reasonably well reproduced by all tested methods although MM2(85) gives the quantitatively best agreement with experiments. For compounds containing oxygen, nitrogen and halogens MM2(85) gives results which are in best agreement with the experimentally determined values.
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  • 62
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    Journal of Computational Chemistry 12 (1991), S. 147-166 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The modeling program AMBER 3.0 was used to study the conformations adopted by the C8-substituted guanosine adduct of the carcinogen N-2-acetylaminofluorene (AAF), called dGuo-AAF. This conformational study was extended to the hexamer d(CGCGCG)2 in the Z form, modified by AAF at guanine G4 with the carcinogen situated at the helix exterior in two different orientations (named ZAAF-5′ and ZAAF-3′). Considering the importance of electrostatic interactions in case of charged molecules like nucleic acids, minimization and molecular dynamics (MD) were performed using different electrostatic parameters (dielectric functions and scale factors). For that purpose, a subroutine allowing the use of a sigmoidal distance-dependent dielectric function εcal has been added to the program. For dGuo-AAF, the results show a great importance of the starting conformation and of the force field parameters on the minimization and MD behaviors. For the AAF-modified Z-DNA, the results display a pronouned dependence on the choice of the set of electrostatic parameters as well. With the distance-dependent dielectric function ε = r, the force field parameters favor the formation of intramolecular H bonds, which can lead to important distortions of Z-DNA. The use of ε = 4r or ε = εcal attenuates effectively such a tendency, except in full MD simulations. The dielectric function εcal is computing intense, but often similar results are obtained with ε = 4r, especially with the use of the BELLY option. AAF appears to prefer the ZAAF-5′ conformation, i.e., with the fluorene ring stacking on the sugar phosphate backbone of the following 5′ C-G bases. Such a conformation is further stabilized by an intramolecular hydrogen bond between the amino group of the 3′ cytosine and the carbonyl group of AAF. The fluorene ring, although mobile around its long axis, does not flip-flop between its two main orientations, ZAAF-5′ and ZAAF-3′. The presence of the AAF does not prevent the ZI to ZII transitions. Whatever the electrostatic parameters, the presence or absence of AAF, the cytosine sugars stay in the C2′-endo pucker domain. In unmodified Z-DNA, the guanine sugars stay in the C3′-endo region, except for the terminal guanines which transit to the C2′endo region. In modified Z-DNA, the sugar of the modified guanine behaves as a terminal guanine sugar.
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    Journal of Computational Chemistry 12 (1991), S. 690-696 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: This article presents theoretical calculations on bond energies for the first-row diatomics C2, CN, CO, CF, N2, NO, NF, O2, FO, and F2, which vary in bond order from one to three. The atomic-centered basis functions are systematically augmented with bond functions (BFs), which range in composition from (sp) to 2(spd), to determine the basis set which yields a dissociation energy closest to the experimental De. A strong correlation is found to exist between the bond order and the number of BFs required in the optimum basis set. Based on these results, we are able to predict the optimum composition of the BF basis which should be added to a DZP-quality AO basis set for a case in which only the bond order is known. These optimized BF basis sets are shown in the accompanying article to give more accurate potential curves than larger basis sets without bond functions.
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    Journal of Computational Chemistry 12 (1991), S. 731-741 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The harmonic molecular force fields for the nucleic acid bases, cytosine, and guanine, that have been previously published by several investigators are tested by the calculation of the relative intensities of the in-plane modes in the ultraviolet resonance Raman (UVRR) effect from the two lowest lying absorption bands using a theoretical approach devised previously.1-3 Since only a fraction of the 2N - 3 in-plane vibrations of a molecule are active in the UVRR, the two criteria that are taken for the adjustment of the force constant are: (1) the closest possible agreement between the observed and calculated frequencies of the 2N - 3 in-plane vibrations, and (2) the closest possible agreement between the calculated and observed intensities of those few vibrations that are strongly active in the ultraviolet resonance Raman effect. In particular it is necessary that the force constants be adjusted to avoid the calculation of intense Raman lines with frequencies that are not observed in the UVRR spectrum. Using this criteria, a new force field has been developed that appears to give better agreement with the observed UVRR intensities than previously published ones. It is suggested that this calculation of the UVRR intensities can be used to refine molecular force fields in combination with other methods such as isotopic replacement currently in use to refine force constants.
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    Journal of Computational Chemistry 12 (1991), S. 839-843 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The calculated result obtained with MM2(87) for the rotation of the isopropyl group in 3-methyl-1-butene is not in agreement with experimental data. In order to reparametrize the Csp2-Csp3-Csp-Csp3 torsional angle, 3-methyl-1-butene and 1-butene have been studied by molecular mechanics (MM2(87)) and ab initio (MP2/6-31G* and MP3/6-31G*) calculations. The reparametrization of the torsional angle gives calculated results from MM2(87) in agreement with experimental data and ab initio calculations for both 3-methyl-1-butene and 1-butene. The calculated barriers for the rotation of alkyl groups in alkylbenzenes are improved with these new parameters.
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    Journal of Computational Chemistry 12 (1991), S. 880-884 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Vibrational spectra were obtained for the structurally similar compounds 2-methylbutyronitrile and 3-methyl-1-pentyne, and vibrational assignments were made with the aid of normal coordinate calculations. Molecular mechanics calculations were also made, and each compound was shown to exist as a mixture of three conformers, with the most stable conformer being the one with the two methyl groups trans to each other. Results of the calculations are given.
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    Journal of Computational Chemistry 12 (1991), S. 909-912 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Finite difference methods are becoming very popular for calculating electrostatic fields around molecules. Due to the large amount of computer memory required, grid spacings cannot be made extremely small in relation to the size of the van der Waals radii of the atoms. As a result, the calculations make a rather crude approximation to the molecular surface by defining grid line midpoints discontinuously as either interior or exterior. We present a method which “smoothes” the boundary, but more accurately models the potential from the analytic solution of the discontinuous dielectric problem and improves convergence in electrostatic energy calculations. In addition, a small improvement in convergence rate is observed.
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    Journal of Computational Chemistry 12 (1991), S. 868-871 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: An algorithm is presented for calculating the solvent accessible surface area of proteins using a three-dimensional grid. Since it requires only calculations based on single atomic positions, the algorithm is easy to be vectorized. It has been implemented on ST100 and may also be implemented on supercomputers like the CRAY or the CYBER. Results on several proteins indicate that its deviation from that of the Shrake-Rupley algorithm is very small while the computation time is much reduced.
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    Journal of Computational Chemistry 12 (1991), S. 885-890 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The use of principal components as a basis for a graphical procedure to analyze polar tensor data is proposed. Molecular orbital and experimental polar tensor data for all possible sign combinations of the ∂p/∂Qj of CHCl3 and CDCl3 are represented graphically as principal component scores facilitating sign selection for the ∂p/∂Qj. The graphs are particularly useful in analyzing an apparent conflict in ∂p/∂Qj sign choices based on the isotopic invariance criterion and molecular orbital results for the A1 symmetry species of these molecules. The numerical impacts of individual sign ambiguities for the ∂p/∂Qj on the polar tensor data are measured by the variances associated with the principal components. Assuming the ∂p/∂Qj sign sets with indeterminate signs provide replicated results for the polar tensor elements, their errors are estimated and compared with errors obtained previously by propagating intensity uncertainties through the polar tensor equations.
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    Journal of Computational Chemistry 12 (1991), S. 913-917 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A novel method to calculate electrostatic charges is proposed. Partial charges are fitted to reproduce the electrostatic potential of a distributed multipole series without explicitly evaluating electrostatic potentials. The calculation is economical and results in charges reflecting the symmetry properties of charge centers and being independent of molecular orientation.
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    Journal of Computational Chemistry 12 (1991), S. 1129-1133 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: MM2-87 calculations have been performed on C60 (buckminsterfullerence; footballene) and C70 with full energy minimization. The steric energies for C60 and C70 were computed to be 179.9 and 177.9 kcal/mol, respectively. The heats of formation for C60 is found to be more stable than C60. The two bond lengths for C60 were computed to be 1.393 and 1.444 Å. Eight different bond lengths were found for C70 ranging from 1.386 to 1.452 Å. Bond angles, dihedral angles, and moments of inertia are also reported for the compounds.
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    Journal of Computational Chemistry 12 (1991), S. 1065-1076 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The Metropolis Monte Carlo method has been added to the program FANTOM for energy refinement of polypeptides and proteins using a Newton-Raphson minimizer in torsion angle space. With this extension, different strategies for global minimization of the semiempirical energy function ECEPP/2 by various temperature schedules and restriction of conformational space were tested for locating local minimum conformations with low energy of the pentapeptide Met-enkephalin. In total, 1881 conformations below -10 kcal/mol were found. These conformations could be represented by 77 nonidentical conformations which were analysed for their pattern of hydrogen bonds, types of tight turn, pairwise root-mean-square-deviation (rmsd), Zimmermann codes and side chain conformations. All low energy conformations below -10.4 kcal/mol show strong similarity to the global minimum conformation in the backbone structure.
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    Journal of Computational Chemistry 12 (1991) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
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    Journal of Computational Chemistry 12 (1991), S. 1187-1197 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: We have developed a method for building up accurate electrostatic models for polypeptides, based on a distributed multipole representation of the SCF charge densities for the dipeptides (CH3.CO.NH.CHR.CO.NH.CH3) of the naturally occurring amino acids. It is based on the observation that each peptide residue has almost the correct formal charge (0, ±1). We find that the variations in the backbone charge distributions (excluding proline) with sidechain have a negligible effect on the predicted electrostatic potential around the residue. However changes in the atomic multipoles with the torsion angles (φ, ψ, χ) are more significant, and may need to be taken into account if electrostatic potential close to the residue is required to high accuracy. This type of DMA peptide library provides more accurate, more theoretically based, estimates of the electrostatic potential around polypeptides than current models.
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    Journal of Computational Chemistry 13 (1992), S. 478-491 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: An extensive conformational analysis of 3′-azido-3′-deoxythymidine (AZT) was performed at the semiempirical AM1 level with full relaxation of all geometric parameters and careful consideration of furan puckering and the rotational states of the thymine - furan, furan - azide, furan - methylene, and methylene - hydroxyl bonds. The search located 70 conformers, 21 of which have relative energies within 2.5 kcal/mol of the global minimum. Several geometric features, including various forms of hydrogen bonding, within this selected lowenergy subset were examined in terms of their relative contributions to the conformational states of AZT. Hydrogen bonding of thymine's position 2 carbonyl oxygen atom to the hydroxymethyl group (O2—;HO), which until recently has not been mentioned in the literature, is observed in a few low-energy AM1 conformations; however, this form is less favored at the AM1 level than the usually depicted modes involving the thymine moiety with the oxygen atoms of the hydroxyl and furan groups (H6—;OH and H6—Ofur, as observed in the two crystallographically independent structures), as well as that involving the hydroxyl hydrogen and furan oxygen atoms (OH—Ofur, which also has not been mentioned for AZT in the literature until recently). The AM1-optimized geometries agree more closely with nuclear magnetic resonance data than with crystallographic structures and bear little resemblance to molecular mechanics results. The present study shows no evidence of a single dominant conformation or single structural parameter that determines AZT's conformational states. In contrast to our previous analogous study of cGMP, this computational study of AZT does not show strong evidence of a syn conformation with hydrogen bonding involving the base.
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    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The potential energy surfaces of four cyclic alkanes have been examined using molecular mechanics, semiempirical, and ab initio methods to determine if they produce mutually consistent results and investigate the source of any errors between the methods. The C5 — C8 cyclic alkanes were chosen since these structures present a finite set of conformations and transition-state geometries and are still within the computational time and memory limits of the quantum mechanical approaches. We also examined several conformations of 1,2-dideoxyribose to determine the effect of heteroatoms on the results for the 5-membered ring. The molecular mechanics and ab initio calculations are consistent in the relative energies and geometries determined for the conformers of all ring systems. While the semiempirical calculations yielded geometries consistent with the other methods (except for 5-membered rings), the relative energies often deviated substantially. A decomposition analysis of the semiempirical and molecular mechanics energies revealed that the disparities are mainly due to errors in the 1-center energies of the semiempirical calculations. The 2-center bonding and nonbonding energies followed reasonable trends for the conformers. The core-repulsion function, however, is suspected of producing anomalies. A minimum in the attractive Gaussian of this term at 2.1 Å for H—H interactions partly explains the propensity of the 5-membered rings to optimize to near planarity (decreasing 1,2-diaxial hydrogen distances to 2.3 Å) and the underestimation of the relative energy of the boat structure of cyclohexane.
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    Journal of Computational Chemistry 13 (1992), S. 585-594 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: We have derived alternative expressions for computing the energies and forces associated with angle bending and torsional energy terms commonly used in molecular mechanics and molecular dynamics computer programs. Our expressions address the problems of singularities that are intrinsic in popular angle energy functions and that occur from other chain rule derivations of force expressions. Most chain rule derivations of expressions for Cartesian forces due to angle energies make use of relations such as \documentclass{article}\pagestyle{empty}\begin{document}$$ \frac{{\partial E}}{{\partial x}} = \frac{{\partial E}}{{\partial \phi }}\frac{{\partial \phi }}{{\partial \cos \phi }}\frac{{\partial \cos \phi }}{{\partial x}} $$\end{document} where φ is a bond or torsion angle, E(φ) is energy, and ∂/∂x represents a derivative with respect to some Cartesian coordinate. This expression leads to singularities from the middle term, -1/sin φ, when φ is 0 or π. This is a problem that prevents the use of torsional energy expressions that have phase angles, φ°, other than 0 or π, such as in E(φ) = κ[1 + cos(nφ - phsi;°)]. Our derivations make use of a different, but equivalent, form of the chain rule: \documentclass{article}\pagestyle{empty}\begin{document}$$ \frac{{\partial E}}{{\partial x}} = \frac{{\partial E}}{{\partial \phi }}\frac{{\partial \phi }}{{\partial x}} $$\end{document} This form still possesses singularities for the bond angle forces since the last factor is undefined when φ is 0 or π. However, the alternate form may be used to great advantage for the torsional angle forces where no such problem arises. The new expressions are necessary if one desires the use of torsional energy expressions with general phase angles. Even for energy expressions in common use, i.e., with phase angles of 0 or π, our force expressions are as computationally efficient as the standard ones. The new expressions are applicable to all molecular simulations that employ restrained, or phase-shifted, torsional angle energy expressions.
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    Journal of Computational Chemistry 13 (1992), S. 622-632 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Atomic monopoles are routinely determined through a least squares fit to molecular electrostatic potentials. We report studies of the variation in atomic monopoles with variation in conformation for the zwitterionic polar head group of lecithins, a common class of lipid. The monopole of one atom, a relatively buried carbon, varied by 1.3 electron units between different conformers. “Exterior” atoms, as seen previously, showed smaller changes in charge and smaller estimated standard deviations. The total charge of local groups of atoms varied less than the charge of individual atoms, indicating that shifts in charge occurred mostly between neighboring atoms. This effect might be reflected in the high correlations seen between charges of many neighboring atoms. These correlations, while present for many logical groupings of atoms (such as within methylene and methyl groups), are curiously absent between some bonded atoms. Monopoles were fit to multiple conformations simultaneously to provide a charge set that could optimally reproduce the electrostatic potential of all the conformers as a means of generating monopoles for molecular dynamics simulations or other studies where conformation varies. In some cases, the charges on chemically equivalent atoms (e.g., the hydrogen atoms in a methyl group) were different by more than their estimated error of fit. These studies lead to the suggestion that a minimum error in reported charges is on the order of 10%. All conformations show that the positive charge of the trimethylalkyl ammonium group is carried by the methyl hydrogens; the total charge on the nine hydrogens is over 2 electron units, counterbalanced by negative monopoles on the carbons. The presence of this diffuse cloud of substantial charge would appear to be a disindicator of the use of a “united” atoms approach for these methyl groups. The effects of the charge variation on intermolecular interactions is also examined.
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    Journal of Computational Chemistry 13 (1992) 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
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    Journal of Computational Chemistry 13 (1992), S. 722-729 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: An ab initio study of 3-chloro-, 3-hydroxy-, 3-mercapto-, and 3-amino-propanenitrile and 4-chloro-bu- tanenitrile was carried out at several levels of theory. The calculated stabilities and geometrical trends are interpreted in terms of the effects of intramolecular hydrogen bonds and anomeric interactions, and compared with available experimental data.
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    Journal of Computational Chemistry 13 (1992), S. 772-791 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Quantum mechanical (ab initio and semiempirical) and force field calculations are reported for representative torsion potentials in several tetrahydropyran derivatives. The overall agreement between the various methods is quite good except that the AMBER torsion profiles are sensitive to the choice of atomic point charges. Using electrostatic potential (ESP) derived atomic point charges determined with the STO-3G basis set we find that AMBER is able to match the best quantum mechanical results quite well. However, when the point charges are derived using the 6-31G* basis set we find that scaling the intramolecular electrostatic nonbond interactions is necessary. AM1 does not work very well for these compounds when compared to the ab initio methods and, therefore, should only be used in cases when ab initio calculations would be prohibitive. Based upon our results we feel that any force field that makes use of 6-31G* ESP derived atomic point charges will need to scale intramolecular interactions. Implications of scaling intramolecular interactions to the development of force fields based on 6-31G* ESP derived atomic point charges are discussed. © 1992 by John Wiley & Sons, Inc.
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  • 82
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    Journal of Computational Chemistry 13 (1992), S. 842-850 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The molecular electrostatic potential (MEP) distribution of anisole, chlorobenzene, and fluorobenzene obtained from STO-3G, 3-21G, and 6-31G* basis set ab initio and MNDO and AM1 semiempirical wave functions is investigated to explain the differences among the MEP features obtained for polychlorodibenzo-p-dioxins. The main topological features as well as the absoltue and relative minima location obtained from ab initio calculations are independent from the choice of the basis set. MNDO calculations are in good agreement with the ab initio ones in the case of anisole and fluorobenzene, while they incorrectly describe the MEP of chlorobenzene. The AM1 fails to localize the absolute minimum of fluorobenzene and does not find the minimum above the chlorobenzene chlorine atom. The poor agreement of both semiempirical methods with ab initio for any kind of chlorinated compounds is confirmed by results obtained for chloreothylene and chloroethane. We hypothesize that the main problem concerning these methods is that they freeze a too large amount of electrons in the atomic core of elements belonging to the second row, which makes for a wrong description of the core-valence electron interactions. Results obtained by modifying the AM1 parameters related to these interactions confirm our hypothesis. © 1992 by John Wiley & Sons, Inc.
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  • 83
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    Journal of Computational Chemistry 13 (1992), S. 874-882 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A numerical method for solving the approximate Schrödinger equation (SE) for a single internal motion is presented. In the SE the reduced moment of inertia I(φ) and potential energy V(φ) are expressed as functions of the torsional angle φ. Molecular examples include ethane, chloroethane, and 1,2-dichloroethane for which I(φ) and V(φ) have been derived from the HF/6-31G* optimized geometries and energies at φ increments of 30°. The resulting potential energy curves, energy levels, and wave functions are shown graphically. The calculated fundamental torsional frequencies are found to fall within 10 cm-1 of the experimental values. Approximations for the off-diagonal energy matrix elements, and numerical accuracy of torsional energy levels, are shown to be satisfactory. Attention is called to the computer programs developed for this work and their applications to torsional studies in relevant areas of spectroscopy, thermodynamics, and reaction rates. © 1992 by John Wiley & Sons, Inc.
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  • 84
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    Journal of Computational Chemistry 13 (1992), S. 912-918 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The electronegativities () of some 36 atoms/groups (including some 6 ionic ones) X are calculated from the atomic charges in the corresponding methyl species CH3X that were obtained by applying Bader's theory of atoms in molecules. The numerical values of the for the various groups studied are reasonable and correlate linearly with the two existing experimental scales for group electronegativity, Inamoto's i scale and the 1JCC (ortho-ipso) coupling constants in the monosubstituted benzenes, to satisfactory extents. The relations between the values and some “critical properties” of the various CH3X molecules considered are also studied. It is suggested that in a molecule PX, rP/R where rP is the distance of Bader's critical point on the bond PX of length R from the atom P or the binding atom of the group P can be a very good measure of the electronegativity of the atom/group X. © 1992 by John Wiley & Sons, Inc.
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  • 85
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    Journal of Computational Chemistry 13 (1992), S. 565-569 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Modifications to the distance geometry algorithm as embodied in the program DGEOM have been made to improve sampling capabilities. Specifically, torsion angle sampling replaces distance sampling for 1,4 atomic relationships and correlated distance sampling is disabled. The effects of these modifications are illustrated by comparing the different sets of conformations produced for butane. In addition, these changes are shown to increase the conformational sampling of two medium-sized rings, cycloheptadecane and caprylolactam. The current results for these molecules are compared to those of other conformational searching methods.
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  • 86
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    Journal of Computational Chemistry 13 (1992), S. 595-601 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A two-component Kramers' restricted Hartree-Fock method (KRHF) has been developed for the polyatomic molecules with closed shell configurations. The present KRHF program utilizes the relativistic effective core potentials with spin-orbit operators at the Hartree-Fock (HF) level and produces molecular spinors obeying the double group symmetry. The KRHF program enables the variational calculation of spin-orbit interactions at the HF level. KRHF calculations have been performed for the HX, X2, XY(X, Y = I, Br), and CH3I molecules. It is demonstrated that the orbital energies from KRHF calculations are useful for the interpretation of spin-orbit splittings in photoelectron spectra. In all molecules studied, bond lengths are only slightly expanded, harmonic vibrational frequencies are reduced, and bond energies are significantly decreased by the spin-orbit interactions.
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  • 87
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    Journal of Computational Chemistry 13 (1992), S. 614-621 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A computational chemistry study of the artificial redox enzyme synthesized by covalently attaching flavin to cyclodextrins explains some of its properties. Calculations indicate that the flavin moiety covalently attached to cyclodextrin is not within the cavity of cyclodextrin. This result is consistent with the UV-vis spectrum of the artificial enzyme. The calculations also indicate hydrogen bonds formed between the carbonyl groups of the catalytic functionality and the hydroxyl groups of cyclodextrin play a role in their most stable conformation. This explains the observed overall stability of these artificial enzymes compared to riboflavin. Electrostatic energies and solvation energies play a major role in the stability of the hosts and the orientation of guests included within the artificial enzymes. The rates of oxidation of various thiols catalyzed by the artificial enzyme can be explained by the relative distances between the sulfur atom of the substrates and C(4a) of the flavin moiety.
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    Journal of Computational Chemistry 13 (1992), S. 651-656 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The polynomial path is introduced for the calculation of liquid state free energies. The well-characterized SPC, TIP4P, and MCY water models were used to demonstrate its efficiency, as well as its range of applicability in conjunction with Monte Carlo computer simulations using thermodynamic integration based on Gaussian quadratures. The technique employed is compared with the slow-growth method (another variant of thermodynamic integration), the perturbation method, and the use of the grand-canonical ensemble.
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    Journal of Computational Chemistry 13 (1992), S. 675-680 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The free energy gradient or Hessian of a molecule interacting with a liquid represented by a dielectric continuum is derived in the self-consistent reaction field formalism. An ellipsoidal approximation of the cavity is proposed with an algorithm to automatically define the ellipsoid from the nuclear coordinates of the atoms. With this approximation, geometry optimization of the solvated molecule becomes very fast. This method has been implemented in some standard ab initio or semiempirical computational codes. As a first test of the method, full geometry optimization of formamide in a high dielectric constant medium reveals that the CPU time needed for one optimization cycle is less than 3% longer for a solvated species than for the corresponding free molecule.
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    Journal of Computational Chemistry 13 (1992), S. 718-721 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The geometry of acryloyl fluoride was optimized completely at the RHF/6-31G* level of theory at 10 points on the theoretical potential energy curve for internal rotation. The energies obtained were used to determine a six term cosine expansion of the torsional potential energy function. This function was then refined using the experimental torsional transition frequencies in the s-trans and s-cis wells in conjunction with the geometrical parameters optimized at the RHF/6-31G* level. The effective potential function obtained is compared with previous results. The necessity of accounting for relaxation of the geometry upon internal rotation is stressed. © 1992 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 13 (1992), S. 768-771 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Finite-difference Poisson-Boltzmann (FDPB) methods allow a fast and accurate calculations of the reaction field (charge-solvent) energies for molecular systems. Unfortunately, the energy in the FDPB calculations includes the self-energies and the finite-difference approximation to the Coulombic energies as well as the reaction field energy. A second finite-difference calculation, in a uniform dielectric, is therefore necesssary to eliminate these contributions. In this article we describe a rapid and accurate method to calculate the self energy and finite-difference Coulombic energies in a uniform dielectric thus eliminating the need for a second finite-difference calculation. The computational savings for this method range from a factor of 4 for a typical protein to a factor of 103 for small molecules. © 1992 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 13 (1992), S. 793-798 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Simulation data from an off-lattice polymer model are compared with data from the Rouse model. The polymer model is built of sequentially connected rigid monomer units that represent the amide planes of a protein backbone. The time propagation of the dynamics of the polymer model is performed by a Monte Carlo method. The elementary Monte Carlo steps correspond to local confomational changes in a window of three consecutive monomer units. The time autocorrelation functions of end-to-end distances from segments within the linear chain molecule are considered in detail. Both models exhibit a stretched exponential decay pattern. A comparison of the data from the Rouse model and the computer simulation provide an estimate of the time unit of 15 ps for a full scan of the algorithm for local conformational changes along the chain. With a conservative estimate of the parameters governing the Rouse model this time unit is four orders of magnitude longer than the elementary time step of a conventional computer simulation of polymer dynamics based upon the classical equations of motion for all atoms. © 1992 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 13 (1992), S. 838-841 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A bond and group equivalent scheme that allows the calculation of heats of formation for carboxylic acids and esters from ab initio 6-31G* energies has been developed. For a group of 16 compounds, the rms error for the calculated heats of formation was 0.64 kcal/mol. Heats of formation have been predicted for an additional seven compounds for which the experimental values are either unknown or suspect. © 1992 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 13 (1992), S. 830-837 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A semi-empirical NDDO method, generalized from a similar scheme at the CNDO/2 level developed previously, is presented to treat very large molecules. The extended molecular system is divided into a relatively small subsystem where substantial chemical changes take place and an environment remaining more-or-less unperturbed during the process. Expanding the wave function on an atomic hybrid basis an SCF procedure is performed for the subsystem in the field of the iteratively determined electronic distribution of the environment. A computer program has been written for the IBM RISC System/6000 530 computer and several test calculations were done for a variety of large classical molecules, like substituted aliphatic hydrocarbons, water oligomers, and a heptapeptide. Protonation energies, proton transfer potential curves, rotational barriers, atomic net charges, and HOMO and LUMO energies, as computed by the exact version of the NDDO method, are fairly well reproduced by our approximation if the subsystem is appropriately defined. © 1992 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 14 (1993) 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
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    Journal of Computational Chemistry 14 (1993), S. 237-245 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The affinity of a ligand for a receptor is usually expressed in terms of the dissociation constant (Ki) of the drug-receptor complex, conveniently measured by the inhibition of radioligand binding. However, a ligand can be an antagonist, a partial agonist, or a full agonist, a property largely independent of its receptor affinity. This property can be quantitated as intrinsic activity (1A), which can range from 0 for a full antagonist to 1 for a full agonist. Although quantitative structure-activity relationship (QSAR) methods have been applied to the prediction of receptor affinity with considerable success, the prediction of IA, even qualitatively, has rarely been attempted. Because most traditional QSAR methods are limited to congeneric series, and there are often major structural differences between agonists and antagonists, this lack of success in predicting IA is understandable. To overcome this limitation, we used the method of comparative molecular field analysis (CoMFA), which, unlike traditional Hansch analysis, permits the inclusion of structurally dissimilar compounds in a single QSAR model. A structurally diverse set of 5-hydroxytryptamine1A (5-HT1A) receptor ligands, with literature IA data (determined by the inhibition of 5-HT sensitive forskolin-stimulated adenylate cyclase), was used to develop a 3-D QSAR model correlating intrinsic activity with molecular structure properties of 5HT1A receptor ligands. This CoMFA model had a crossvalidated r2 of 0.481, five components and final conventional r2 of 0.943. The receptor model suggests that agonist and antagonist ligands can share parts of a common binding site on the receptor, with a primary agonist binding region that is also occupied by antagonists and a secondary binding site accommodating the excess bulk present in the sidechains of many antagonists and partial agonists. The CoMFA steric field graph clearly shows that agonists tend to be “flatter” (more coplanar) than antagonists, consistent with the difference between the 5-HT1A agonist and antagonist pharmacophores proposed by Hibert and coworkers. The CoMFA electrostatic field graph suggests that, in the region surrounding the essential protonated aliphatic amino group, the positive molecular electrostatic potential may be weaker in antagonists as compared to agonists. Together, the steric and electrostatic maps suggest that in the secondary binding site region increased hydrophobic binding may enhance antagonist activity. These results demonstrate that CoMFA is capable of generating a statistically crossvalidated 3-D QSAR model that can successfully distinguish between agonist and antagonist 5-HT1A ligands. To the best of our knowledge, this is the first time this or any other QSAR method has been successfully applied to the correlation of structure with IA rather than potency or affinity. The analysis has suggested various structural features associated with agonist and antagonist behaviors of 5-HT1A ligands and thus should assist in the future design of drugs that act via 5-HT1A receptors. © 1993 John Wiley & Sons, Inc.
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  • 97
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    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Four semiempirical methods (AM1, MNDO, PM3, and MINDO/3) are used to calculate the deformation angles of [n]paracyclophanes and their Dewar benzene isomers for n = 3… 10. The results obtained by all these methods are in good agreement with data from X-ray studies. We have determined the strain energies that, in both series of compounds, are due to two components: (1) the strain energy of deformation of the cycle (aromatic or Dewar Benzene skeletons) and (2) the strain energy of the oligomethylene chain. In [6]paracyclophane, the strain energy [SEring(MNDO) ≍ 32.9 kcal/mol] almost compensates the resonance energy (Eresonance ≈ 36 kcal/mol) so that its chemical properties are closer to alkenes than to benzenic compounds. To better reproduce the enthalpy of the valence isomerization [n]Dewar bezene → [n]paracyclophane, which is poorly calculated with these methods, a correction is proposed and the reaction enthalpy of [6]paracyclophane is estimated to be about ΔHr ≈ 15 ± 15 kcal/mol. It is found that MNDO and MINDO/3 need the smallest corrections, but MNDO leads to better geometries than MINDO/3. In conclusion, MNDO seems to be the best technique for further studies of these compounds. © 1992 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 13 (1992), S. 1089-1097 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Our recently proposed scheme for including aqueous solvation free energies in parameterized NDDO SCF models is extended to the Parameterized Model 3 semiempirical Hamiltonian. The solvation model takes accurate account of the hydrophobic effect for hydrocarbons, as well as electric polarization of the solvent, the free energy of cavitation, and dispersion interactions. Eight heteroatoms are included (along with H and C), and the new model is parameterized accurately for the water molecule itself, which allows meaningful treatments of specifically hydrogen bonded water molecules. The unphysical partial charges on nitrogen atoms predicted by the Parameterized Model 3 Hamiltonian limit the accuracy of the predicted solvation energies for some compounds containing nitrogen, but the model may be very useful for other systems, especially those for which PM3 is preferred over AM1 for the solute properties of the particular system under study. © 1992 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 13 (1992), S. 1119-1124 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The particular expression that relates the first Mori coefficients of the solvent particles with the solute particles as a function of their masses m1 and m2 is generalized to the case of the solute particle also having a different volume. The resulting density relationship, in terms of the mass factor M(m2) and coupling constants CD, is also valid for the second Mori coefficients and for two- and three-dimensional system. © 1992 by John Wiley & Sons, Inc.
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    Journal of Computational Chemistry 13 (1992), S. 1170-1170 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
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