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  • Articles  (3,341)
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  • 1995-1999  (956)
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  • 1
    Electronic Resource
    Electronic Resource
    Minimum Time Control of Flexible Spacecraft by Hamilton's Principle (1997)
    Springer
    Meccanica 32 (1997), S. 555-565 
    Details
    ISSN: 1572-9648
    Keywords: Spacecraft dynamics ; Optimal control ; Hamilton principle ; Vibrations (structures)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Modern space vehicles structure requisites are getting more and more stringent and complex as mission tasks become more sophisticated. This leads to the necessity of developing analysis methods that take into account structure flexibility and the need of reducing manoeuvre time as much as possible. In this work, a method based on the Hamilton Principle in its weak mixed form is developed, in which co-ordinates derivatives do not appear, but only their virtual variations. The proposed formulation is able to take into account system flexibility and saturation constraints on control torques and forces. A non-linear variational condition is obtained, which can be solved by means of a time-finite-element technique to give the minimum-time solutions of the control problem. The solutions for slewing manoeuvres are given, along with a new solution of the distributed optimal control problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004204510722
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  • 2
    Electronic Resource
    Electronic Resource
    Optimal control of the chemotherapy of HIV (1997)
    Springer
    Journal of mathematical biology 35 (1997), S. 775-792 
    Details
    ISSN: 1432-1416
    Keywords: Key words: Chemotherapy ; HIV ; Optimal control ; Ordinary differential equation system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract.  Using an existing ordinary differential equation model which describes the interaction of the immune system with the human immunodeficiency virus (HIV), we introduce chemotherapy in an early treatment setting through a dynamic treatment and then solve for an optimal chemotherapy strategy. The control represents the percentage of effect the chemotherapy has on the viral production. Using an objective function based on a combination of maximizing benefit based on T cell counts and minimizing the systemic cost of chemotherapy (based on high drug dose/strength), we solve for the optimal control in the optimality system composed of four ordinary differential equations and four adjoint ordinary differential equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002850050076
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  • 3
    Electronic Resource
    Electronic Resource
    Optimal control for a tandem network of queues with blocking (1997)
    Springer
    Acta mathematicae applicatae sinica 13 (1997), S. 425-437 
    Details
    ISSN: 1618-3932
    Keywords: Optimal control ; tandem queueing system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a two-station tandem queue with no intermediate buffer. Jobs at the first station may be blocked when the following station is occupied by another job. The objective is to control the arrival and departure processes, subject to some capacity limits, so that an expected discounted profit function is maximized. We prove that the optimal control policy is of a threshold type, and the characterization of the threshold is provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02009552
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  • 4
    Electronic Resource
    Electronic Resource
    The linear quadratic optimal control problem for linear descriptor systems with variable coefficients (1997)
    Springer
    Mathematics of control, signals, and systems 10 (1997), S. 247-264 
    Details
    ISSN: 1435-568X
    Keywords: Descriptor systems ; Differential algebraic equations ; Optimal control ; Strangeness index ; Riccati differential-algebraic equations ; Euler-Lagrange equations ; Linear feedback
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics , Technology
    Notes: Abstract We study linear quadratic optimal control problems for linear variable coefficient descriptor systems. Generalization from the case of standard control problems leads to several difficulties. We discuss a behavioral approach that solves some of these difficulties. Furthermore, an analysis of general rectangular systems is given and generalized Euler-Lagrange equations and Riccati differential algebraic equations are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01211506
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  • 5
    Electronic Resource
    Electronic Resource
    Quadratic control problems (1975)
    Springer
    Journal of optimization theory and applications 17 (1975), S. 1-42 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; calculus of variations ; quadratic control problems ; linear spaces ; conjugate points ; focal points ; Bolza problem ; Hilbert space techniques
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The present paper is concerned with the study of quadratic control problems on linear spaces. In particular, we are concerned with the conditions under which a quadratic criterion function is positive on certain linear spaces. This involves the elementary theory of conjugate and focal points, the existence of a conjugate system with a nonvanishing determinant, and the existence of extremal fields. The results given are in part a translation into control language of known theory for the problem of Bolza. The method used is based on the Hilbert space techniques developed earlier by the author.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933915
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  • 6
    Electronic Resource
    Electronic Resource
    On the existence of optimal controls (1975)
    Springer
    Journal of optimization theory and applications 17 (1975), S. 273-278 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; existence theorems ; control theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Using a recent result due to Berkovitz, we prove the existence of an optimal control in a broad class of problems, under relatively mild conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933880
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  • 7
    Electronic Resource
    Electronic Resource
    Remarks on bang-bang control in a Hilbert space (1977)
    Springer
    Journal of optimization theory and applications 21 (1977), S. 51-57 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; linear systems ; linear-quadratic problems ; bang-bang control ; Hilbert spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The control of a linear system, whose performance index is the sum of a linear term and a quadratic term, is considered. A necessary and sufficient condition is given for the optimal control to be bang-bang, and this is used to extend and clarify the results of Refs. 1–2. As an illustration, an application to an elliptic boundary-value problem is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932543
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  • 8
    Electronic Resource
    Electronic Resource
    Forward differential dynamic programming (1977)
    Springer
    Journal of optimization theory and applications 21 (1977), S. 487-504 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; forward dynamic programming ; differential dynamic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The dynamic programming formulation of the forward principle of optimality in the solution of optimal control problems results in a partial differential equation with initial boundary condition whose solution is independent of terminal cost and terminal constraints. Based on this property, two computational algorithms are described. The first-order algorithm with minimum computer storage requirements uses only integration of a system of differential equations with specified initial conditions and numerical minimization in finite-dimensional space. The second-order algorithm is based on the differential dynamic programming approach. Either of the two algorithms may be used for problems with nondifferentiable terminal cost or terminal constraints, and the solution of problems with complicated terminal conditions (e.g., with free terminal time) is greatly simplified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933093
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  • 9
    Electronic Resource
    Electronic Resource
    On the optimal control of a single-server queueing system: Reply (1978)
    Springer
    Journal of optimization theory and applications 26 (1978), S. 463-464 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; queueing systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This comment replies to a criticism due to Klein and Gruver (Ref. 1) of our earlier paper (Ref. 2) on the application of control theory to a queueing system. The criticism concerns the state-space diagram and the table which we inadvertently gave for the terminal-reward problem, albeit incorrectly labeled, rather than for the free-endpoint problem considered in our paper. We show that the solution given by Klein and Gruver is itself incorrect and nonoptimal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933467
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  • 10
    Electronic Resource
    Electronic Resource
    Sequential gradient-restoration algorithm for optimal control problems with general boundary conditions (1978)
    Springer
    Journal of optimization theory and applications 26 (1978), S. 395-425 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; numerical methods ; computing methods ; gradient methods ; gradient-restoration algorithms ; sequential gradient-restoration algorithms ; general boundary conditions ; nondifferential constraints ; bounded control ; bounded state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper considers the numerical solution of two classes of optimal control problems, called Problem P1 and Problem P2 for easy identification. Problem P1 involves a functionalI subject to differential constraints and general boundary conditions. It consists of finding the statex(t), the controlu(t), and the parameter π so that the functionalI is minimized, while the constraints and the boundary conditions are satisfied to a predetermined accuracy. Problem P2 extends Problem P1 to include nondifferential constraints to be satisfied everywhere along the interval of integration. Algorithms are developed for both Problem P1 and Problem P2. The approach taken is a sequence of two-phase cycles, composed of a gradient phase and a restoration phase. The gradient phase involves one iteration and is designed to decrease the value of the functional, while the constraints are satisfied to first order. The restoration phase involves one or more iterations and is designed to force constraint satisfaction to a predetermined accuracy, while the norm squared of the variations of the control, the parameter, and the missing components of the initial state is minimized. The principal property of both algorithms is that they produce a sequence of feasible suboptimal solutions: the functions obtained at the end of each cycle satisfy the constraints to a predetermined accuracy. Therefore, the values of the functionalI corresponding to any two elements of the sequence are comparable. The stepsize of the gradient phase is determined by a one-dimensional search on the augmented functionalJ, while the stepsize of the restoration phase is obtained by a one-dimensional search on the constraint errorP. The gradient stepsize and the restoration stepsize are chosen so that the restoration phase preserves the descent property of the gradient phase. Therefore, the value of the functionalI at the end of any complete gradient-restoration cycle is smaller than the value of the same functional at the beginning of that cycle. The algorithms presented here differ from those of Refs. 1 and 2, in that it is not required that the state vector be given at the initial point. Instead, the initial conditions can be absolutely general. In analogy with Refs. 1 and 2, the present algorithms are capable of handling general final conditions; therefore, they are suited for the solution of optimal control problems with general boundary conditions. Their importance lies in the fact that many optimal control problems involve initial conditions of the type considered here. Six numerical examples are presented in order to illustrate the performance of the algorithms associated with Problem P1 and Problem P2. The numerical results show the feasibility as well as the convergence characteristics of these algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933463
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  • 11
    Electronic Resource
    Electronic Resource
    On the optimal control problem of a single-server queueing system (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 317-325 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; queueing theory ; phase type distributions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a single-server queueing system (with a finite waiting room) with phase type arrivals and exponential service times, an optimal control for the service rate is derived. This generalizes the result of Scott and Jefferson for theM/M/1/1 queueing model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935227
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  • 12
    Electronic Resource
    Electronic Resource
    Realistic feedback control of two interconnected turbogenerators (1984)
    Springer
    Journal of optimization theory and applications 42 (1984), S. 103-141 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; realistic feedback control ; interconnected turbogenerators ; torque and voltage control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the optimal control of a system with two identical interconnected turbogenerators, which are connected to an infinite bus, is considered. The alternators are controlled through a linear feedback of the state variables. The feedback parameters are obtained by solving a nonlinear, two-point boundary-value problem. The values obtained for these parameters depend on the strength and duration of the disturbance, since the model is nonlinear, contrary to the usual feedback control of a linear model. In contrast to the model used in Ref. 1, the model used here includes the transfer function of the governors, the turbines, and the voltage regulators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934135
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  • 13
    Electronic Resource
    Electronic Resource
    Convergence of a strong variational algorithm for relaxed controls involving a class of hyperbolic systems (1984)
    Springer
    Journal of optimization theory and applications 42 (1984), S. 467-485 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; hyperbolic partial differential equations ; Darboux boundary conditions ; strong variational algorithm ; convergence ; relaxed control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a class of optimal control problems involving linear hyperbolic partial differential equations with Darboux boundary conditions. A strong variational algorithm has been obtained for solving this class of optimal control problems in a previous paper by the third and the first authors. It was also shown that anyL ∞ accumulation points of control sequences generated by the algorithm satisfy a necessary condition for optimality. Since such accumulation points need not exist, it is shown in this paper that the control sequences generated by the algorithm always have accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed control problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935327
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  • 14
    Electronic Resource
    Electronic Resource
    Necessary and sufficient conditions for optimal control of quasilinear partial differential systems (1984)
    Springer
    Journal of optimization theory and applications 43 (1984), S. 89-101 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; distributed-parameter systems ; control of partial differential equations ; sufficiency conditions ; Green's formula
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract First-order necessary and sufficient conditions are obtained for the following quasilinear distributed-parameter optimal control problem: $$max\left\{ {J(u) = \int_\Omega {F(x,u,t) d\omega + } \int_{\partial \Omega } {G(x,t) \cdot d\sigma } } \right\},$$ subject to the partial differential equation $$A(t)x = f(x,u,t),$$ wheret,u,G are vectors andx,F are scalars. Use is made of then-dimensional Green's theorem and the adjoint problem of the equation. The second integral in the objective function is a generalized surface integral. Use of then-dimensional Green's theorem allows simple generalization of single-parameter methods. Sufficiency is proved under a concavity assumption for the maximized Hamiltonian $$H^\circ (x,\lambda ,t) = \max \{ H(x,u,\lambda ,t):u\varepsilon K\} $$ .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934748
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  • 15
    Electronic Resource
    Electronic Resource
    Use of Augmented Lagrangian Methods for the Optimal Control of Obstacle Problems (1997)
    Springer
    Journal of optimization theory and applications 95 (1997), S. 101-126 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; Lagrange multipliers ; augmented Lagrangians ; variational inequalities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate optimal control problems governed by variational inequalities involving constraints on the control, and more precisely the example of the obstacle problem. In this paper, we discuss some augmented Lagrangian algorithms to compute the solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022635428708
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  • 16
    Electronic Resource
    Electronic Resource
    Coupled hartree-fock calculation of static and shielding factors for open shell atomic systems (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 1-8 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this paper a calculation of the static quadrupole polarizabilities and the shielding factors of the atoms and ions of the 2p open shell systems is presented. A fully coupled Hartree-Fock method using the Roothaan formalism is adopted. Calculations have been done for the ground as well as for some valence excited states. An antishielding effect is observed for all the atoms and ions under study.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090102
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  • 17
    Electronic Resource
    Electronic Resource
    A new integral transform basis function (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 67-74 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new integral transform function: \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm exp }\left({{\rm - }\zeta {\rm r}} \right)\int_0^\infty {s(n)r^n dn} $$\end{document} where s(n) is a positive definite shape function, is proposed and investigated. A test on H2+ shows that it does not suffer from the inadequacies of earlier integral transform functions, of the form: \documentclass{article}\pagestyle{empty}\begin{document}$$ r^n \int_0^\infty {c(\zeta ){\rm exp}({{-}\xi r})d\zeta } $$\end{document} where c(ζ) is a positive definite shape function.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090108
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  • 18
    Electronic Resource
    Electronic Resource
    Dispersion relations and spectral densities (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 103-117 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Weyl's eigenvalue theory for ordinary second-order differential equations is discussed for the case of a continuous spectrum. It is demonstrated that the spectral density function obtained from a suitably averaged Green's function, equal to the Weinstein function, can be directly related to the Weyl-Titchmarsh m-function. The explicit connections with scattering theory are derived and it is found that the Weyl and Jost solutions are proportional; the proportionality factor being the reciprocal value of the latter at the origin. The physical interpretation of the complex poles of the spectral density is discussed in relation to Gamow's exponentially growing functions. The advantage of using a formulation that allows for a “perturbation” of boundary conditions is pointed out.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090111
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  • 19
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    Electronic Resource
    Combined CI-HY studies of atomic states. II. Compact wave functions for the be ground stateResearch supported by a grant from the National Science Foundation. (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 149-156 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Combined CI-HY method techniques have been employed in obtaining a 57-term CI-HY wave function with an energy of -14.66632 a.u. A method due to Brown has been adopted for obtaining this wave function and various shorter expansions. A 44-term expansion with an energy of -14.66606 a.u. is analyzed in terms of various pair effects, and qualitative arguments are presented for understanding these effects.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090115
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  • 20
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    Møller-Plesset theory for atomic ground state energies (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 229-236 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Mø-Plesset theory, in which electron correlation energy is calculated by perturbation techniques, is used in second order to calculate energies of the ground states of atoms up to neon. The unrestricted Hartree-Fock (UHF) Hamiltonian is used as the unperturbed system and the technique is then described as unrestricted Mø-Plesset to second order (UMP2). Use of large Gaussian basis sets suggests that the limiting UMP2 energies with a complete basis of s, p, and d functions account for 75-84% of the correlation energy. Preliminary estimates of the contributions of basis functions with higher angular quantum numbers indicate that full UMP2 limits give even more accurate total energies.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090204
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  • 21
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    Electronic Resource
    Smooth interpolation, Fourier transformation, and two-center overlap integrals for numerical atomic orbitals (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 789-795 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A smooth interpolation method for the calculation of Fourier transforms of numerical atomic orbitals is presented and the method is used to calculate two-center overlap integrals. Examples applying various definitions of smoothness are given.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090504
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  • 22
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    A variational principle for transition and density matrices and approximations to the equations-of-motion (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 825-834 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A general variational principle for transition and density matrices is proposed. The principle is closely related to Rowe's variational treatment of the equations-of-motion method. It permits the simultaneous construction of coupled approximations for two eigenstates, and it is a straightforward extension of the usual variational method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090507
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  • 23
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    The electronic structure of molecules having arbitrary boundaries (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 887-900 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this paper we discuss an extension of the standard multiple scattered wave method for molecular electronic structure calculations to the case of arbitrarily shaped molecules. A general theory is presented where the difficulties arising from the matching problem across an arbitrary boundary are avoided. The secular equation to determine the energy spectrum is obtained and the wave functions are calculated in all regions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090511
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  • 24
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    Masthead (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975) 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090601
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  • 25
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    Operator formalism for forming ket vectors under some constraints (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 969-973 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Reformulation, generalization, and application of Löwdin's symmetric orthonormalization, of orthogonalization of two sets of vectors, and of McWeeny's variational method of a density matrix, etc., by means of an operator for forming ket vectors on which are imposed some conditions, are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090604
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  • 26
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    Orbit-orbit molecular integrals over Gaussian orbitals (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 1055-1067 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Analytical formulas are derived for integrals of the orbit-orbit operator in the Breit-Pauli Hamiltonian. The present method differs from an earlier one in the introduction of a new auxiliary function Gn(a) which is an integral of Shavitt's Fm(t) function. A method for its evaluation is discussed and some numerical examples are given.
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    Spin projections for even electron systems (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 1109-1112 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new method is presented for obtaining the spin eigenfunctions of 2n electron systems in the spin state S and MS = 0. Using a modified Young operator the function for the state S, MS ( = S) of the system is first projected out. The projected function is then symmetrized over the last n particles and the weight lowering operator Š-S is then applied to it, resulting in a projection of the state S, 0. To within a multiplicative factor, the resulting function is identical with the one resulting from the vector coupling methods.
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    Square well model and the functional form for the resonance integral (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 379-381 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090212
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    Corrections to coupled Hartree-Fock theory: the rearrangement effect (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 385-392 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this communication we discuss a method of incorporating corrections to the coupled Hartree-Fock (CHF) formalism by introducing the so-called “rearrangement effect.” In this we take account of the relaxation of the core orbitals when excitations from a starting Hartree-Fock wave function occur. The magnitude of this correction numerically is found to be quite significant for the polarizabilities of two-electron atomic systems, results for which are reported.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/qua.560090302
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    Resolvent technique and Padé approximants in configuration interaction calculations (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 431-443 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A perturbation approach based on resolvent technique and Padé approximants is proposed. The eigenvalue of interest is part of a solution of two nonlinear algebraic equations. The nonlinear equations are arrived at by considering two different expression of the expectation value of the resolvent of an outer projection of the Hamiltonian. The first expression is based on the spectral resolution of the resolvent, and the second one is obtained by a power series expansion analogous to that applied in the derivation of the energy expression in the Brillouin-Wigner perturbation theory. The truncated power series is extrapolated by Padé approximants of type II. The method is tested on a CI calculation of the energy of the lowest 1Σ state of the B2 molecule.
    Additional Material: 2 Tab.
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    Variational bounds on transition probabilities (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 479-487 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Complementary variational functionals are derived which impose upper and lower bounds on transition probabilities. These functionals are used to yield bounds in terms of sets of sum rules, and illustrative calculations are presented for hydrogen, helium and krypton atoms.
    Additional Material: 2 Tab.
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    Dynamical screening by Σ-electrons in π-electron transitions: Treatment in the equations-of-motion method (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 505-516 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Dynamical screening in π-electron systems is studied by the equations of motion method. By using a partitioning technique on the equations of motion we can obtain simple expressions for the effect of dynamical screening directly on the transition energies and transition moments in π-electron systems. These results are used to study the effect of such screening in the N → V transition in ethylene. This procedure can be used to extend the equations-of-motion method to larger π-electron systems.
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    Announcements (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 557-557 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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    URL: http://dx.doi.org/10.1002/qua.560090319
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    Alternant molecular orbitals (amo's) for some organic semiconductors: Ion radical salts from 7, 7, 8, 8-tetracyanoquinodimethane (TCNQ) and chloranil/ para-phenylenediamine (PDC) charge transfer complex (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 1087-1095 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We report an attempt of ab initio computation for the ground-state wave-function of a few organic semiconductors (namely TCNQ salts and the PDC charge transfer complex) for which we show that electrical conduction appears to look strongly like that of a band-gap semiconductor.
    Additional Material: 2 Tab.
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    URL: http://dx.doi.org/10.1002/qua.560090614
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    Lattice dynamics with second-neighbor interactions. III. Green's matrix (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 189-211 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The theory of pth-order singular differential equations is adaptable to the study of the system of recurrence relations occurring in the problem of a one-dimensional chain with pth-neighbor interactions. By using Green's formula, a mapping is defined between the space Vn of eigenvectors to the dynamical matrix and the symplectic space V2p of boundary conditions for the recurrence equations. The properties of the resolvent are obtained from an analysis of the solutions of a system of inhomogeneous equations and Green's matrix is constructed for the case of standard Sturm-Liouvilletype boundary conditions. The Weyl surface is discussed and its properties used for the construction of square summable sequences which in turn can be employed in expansion formulas. The generalization of Weyl's m-function in the second-order case (p = 1) becomes for p ≥ 2 a p × p matrix M(λ), where λ is a complex parameter. The imaginary part Im {M(λ)} is related to the spectral properties and serves as basis for the discussion of different concepts of spectral density for the normal modes of lattice dynamical problems. An important practical result is the equation M = -Ψa-1Φa valid in the limit point case, generalizing the corresponding second-order formula.
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    Electrostatic corrections to extended Hückel theory (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 271-276 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An electrostatic correction to the energy of the EH method is deduced from the Hartree energy. A recent correction, due to Anderson and Hoffmann, is easily deduced as a particular case. Some calculations show how the correction can improve the description of stretching problems by EH calculations but poor results are obtained in bending and torsion problems.
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    A basis set investigation for the oxygen 1s ionization potential in H2O (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 317-324 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The basis set dependency of the core ionization potential of water was investigated for atomic optimized Cartesian Gaussian basis sets. Basis set parameters optimized for oxygen yielded better IP's than basis set parameters optimized for fluorine. Not much was gained by using different parameters for the ground state and for the 1s hole state.
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    A numerical integration scheme for iterative calculations on atomic systems (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 325-339 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A recursive numerical integration scheme based on the method of Clenshaw and Curtis is proposed for the efficient implementation of the variation-iteration procedure for the computation of approximate energies and wave functions for atomic systems. Extensive numerical tests are carried out to assess the accuracy and efficiency of the method and inaccuracies in some earlier calculations are pointed out.
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    Clebsch-Gordan coefficients for chains of groups of interest in quantum chemistry. II. The chain SU(2) ⊃ D′∞ ⊃ D′4 ⊃ D′2 (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 359-379 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The formalism described in the first paper of this series is applied to the chain SU(2) ⊃ D′∞ ⊃ D′4 ⊃ D′2, the covering of SO(3) ⊃ D∞ ⊃ D4 ⊃ D2. The state vectors (|αJaΓγ) adapted to each link of the chain under consideration and the corresponding coupling coefficients \documentclass{article}\pagestyle{empty}\begin{document}$ f\left( {\begin{array}{*{20}c} {J_1 } & {J_2 } & J \\ {a_1 \Gamma _1 \gamma _1 } & {a_2 \Gamma _2 \gamma _2 } & {a\Gamma \gamma } \\ \end{array}} \right) $\end{document} are given in analytical form. The material reported here is very convenient for a quantum-mechanical description of molecular and nuclear systems with linear, tetragonal, or orthorhombic symmetry. In this respect, we present an outline for its applications to the electronic and vibrational-rotational spectroscopy of molecular aggregates and to the rotational spectroscopy of molecules or nuclei. In addition, we briefly show how the material may simplify the second-order non-Lie subgroup type approach to the representation theory of SU(2).
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    Using group (or Loge) functions to explore the transferability of chemical bonds (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 415-425 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The transferability of bonds in a set of small molecules has been explored. The molecular wave-functions have been calculated from the group (or loge) function method, via a construction based on Gaussian functions. The transferability is very good and the effect of lone pairs on adjacent bonds has been analysed. Furthermore, a very simple procedure has been proposed to estimate the frontiers of the bonds.
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    The energetic effects of p, d, and f Gaussian polarization functions on closed-shell AHn oxygen and sulfur hydrides (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 441-450 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A series of LCAO-MO-SCF calculations, using various basis sets of Gaussian-type functions, has been made in order to study the effects of p, d, and f polarization functions for a 10-electron isoelectronic series of oxygen hydrides and for an 18-electron isoelectronic series of sulfur hydrides. Conclusions from these results suggest that meaningful proton affinities cannot be calculated without the inclusion of a d function on the heavy atom and a p function on the hydrogen atoms.
    Additional Material: 2 Ill.
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    Masthead (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977) 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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    URL: http://dx.doi.org/10.1002/qua.560110401
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    Applications of an optimization technique in submolecular biologyThis paper was presented at the International Symposium on Atomic, Molecular, and Solid State Theory and Quantum Biology held at Sanibel Island, Florida, U.S.A. in January, 1974. (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 393-402 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Some applications of an optimization technique due to Levenberg in theoretical submolecular biology are described. This technique has proved a very useful tool for the generation of three-dimensional structures of molecules having cyclic components or other constrained regions. The generated molecular structures provide the starting point for quantum chemical calculations of great value in solving problems of biological interest. The mechanism of transport of alkali metal cations by valinomycin is one such example and this paper describes briefly how various conformations of valinomycin were obtained using the optimization technique. A variant of the same method has been suggested as a new technique for the detection of topographical similarities between apparently dissimilar molecules which are substrates for the same enzyme or receptor site. The technique is illustrated with a comparison of a tricyclic antidepressant with norepinephrine both of which have been postulated to compete for a common receptor site in the “amine pump” of peripheral adrenergic nerve cell membranes. Another area in which the optimization technique has proved useful is in developing an optimum separable localized bond function method designed for rigorous calculations on large saturated molecules. This method is briefly described.
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    Ab initio calculation of the electronic structure of TCNQ and its ions (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 459-471 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Ab initio SCF-LCAO-MO calculations have been performed for TCNQ and its positive and negative ions in various electronic states. A basis set consisting of 412 primitive Gaussian type orbitals contracted to 180 was used in the investigation. The electron density distribution in TCNQ and the negative ions, and the redistribution upon ionization has been illustrated by plotting difference density contour maps. The quinone structure of the neutral TCNQ system undergoes a transformation to a benzenoid structure when electrons are added. Electronic transitions, ionization potentials and electron affinities have also been calculated.
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    Spin-projected EHF method. II. The equations for successive optimization of the orbitals in the many-electron case (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 517-526 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The extended Hartree-Fock equations of the spin-projected scheme are derived in a form suitable for the construction of a surely convergent method of solution using successive optimization of the individual orbitals. The derivation is based on a specific form of the generalized Brillouin theorem.
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    Two-parameter ω-technique for MO calculations (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 759-766 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A two-parameter ω-technique for MO calculations is proposed. The parameters ω and ω′ are chosen empirically to obtain a good agreement between calculated and observed bond lengths. The method amounts to an inclusion of the effect of nearest-neighbour electronic repulsion integrals into the conventional ω-technique.
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    The convex structure of electrons (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 907-916 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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    URL: http://dx.doi.org/10.1002/qua.560110604
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    A linear combination of molecular orbital formalism (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 1001-1004 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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    URL: http://dx.doi.org/10.1002/qua.560110612
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    Quantum science. Methods and structure. Edited by J.-L. Calais, O. Goscinski, J. Linderberg, and Y. Öhm. Plenum Press, New York, 1976. 595 pages. Price: $49.50 (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 1043-1043 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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    URL: http://dx.doi.org/10.1002/qua.560110617
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    Energy of interaction of two hydrogen atoms using contracted Gaussian type valence-bond wavefunctions (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 1113-1129 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Valence-bond type wavefunctions based on contracted Gaussian atomic orbitals afford an adequate description of the potential of the ground 1Σg+ state of H2 for a wide range of internuclear separations. Semiempirical techniques for scaling the potential curve are evaluated. An efficient method for optimizing non-linear variables in the wavefunctions is explored.
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    Floating spherical gaussian orbital open-shell calculations on the four-electron H4 system (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 593-608 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Floating spherical Gaussian orbital (FSGO) open-shell calculations have been made to determine the potential energy surface of planar square and rectangular arrangements of the four-electron system H4. This surface is discussed in relation to the bimolecular isotope exchange reaction H2+D2-→ 2HD. The changes in energy and geometry accompanying the coplanar approach of two hydrogen molecules interacting chemically have also been investigated. Calculations on the electronic energies of planar T-shaped and kite arrangements of H4 of various sizes show that it is unlikely that these configurations can serve as transition states for the exchange reaction. However, the energy curve for linear configurations of H4 (H—H—H … H), calculated as a function of the H3 … H distance with the symmetric linear H3 (H-H-H) unit fixed at the internuclear distance of 1.9080 a.u., is found to have a deep minimum (-1.9176 a.u.) at an r(H3 … H) distance of 1.5846 a.u. The overall results suggest that the following mechanism for the exchange reaction, H2+H2→H2+H+H→H3+H→H+H2+ H→H2+H2 could be advantageous as it requires a barrier height of 0.1604 a.u. which is significantly lower than that calculated from the saddle point energy (0.1950 a.u.). However, the problem of reconciling this with the experimental activation energy of 0.0685 a.u. still remains.
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    Determination of excitation energies and transition moments in a second order polarization propagator approach. Application to the Be atom and the CH+ molecule (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 655-670 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Excitation energies and transition moments have been determined from a second order polarization propagator and the effect of including energy shifted denominators has been investigated. Results for Be and CH+ show a change of 2-5% for the transition moments and of 0-20% for the singlet excitation energies in a second order approach compared to a first order (time-dependent Hartree-Fock) approximation. Both Be and CH+ are triplet unstable in the time-dependent Hartree-Fock approximation. The triplet instability is removed for Be but not for CH+ in a second order polarization propagator approach.
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    URL: http://dx.doi.org/10.1002/qua.560120406
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    A weakly bound, quantum-mechanical buridan's ass (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 759-763 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The spherical limit of a single particle in the field of three nuclei is shown to exhibit a variety of phenomena associated with the stability of the various extrema involved. Some consequences with respect to the general problem of detecting broken symmetry solutions of variational problems are pointed out.
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    Preface (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 895-895 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560110602
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    An application of the Brillouin-Löwdin perturbation expansion: Lower bounds to the energy eigenvalues of the rigid rotator in an electric field (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 931-941 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: One of the variants of Löwdin's partitioning technique that makes use of a Brillouin-type perturbation expansion for the study of lower bounds to the eigenvalues of a Hamiltonian has not been applied to any practical quantum mechanical problem so far. To illustrate how powerful this method can be, an application is made to the rigid rotator in an electric field, which has already been studied by Choi and Smith using the bracketing function of an intermediate Hamiltonian. It turns out that for a given order of the basis set of the Bazley space the Brillouin-Löwdin perturbation expansion gives closer bounds than the method of Choi and Smith, except for the case l = m, where the procedures can be shown to be mathematically equivalent. Especially for high l - m the number of basis functions needed to attain the same accuracy is by far larger for the method of Choi and Smith than for the Brillouin-Löwdin method.
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    Exact eigenvalues for the Coulomb potential with cut-off (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 991-1000 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The solution of the quantum-mechanical one-particle problem involving a Coulomb potential with a cut-off contains Whittaker functions, difficult to evaluate individually. However, the energy expression involves a ratio of two contiguous Whittaker functions, and the entire ratio is easily expressed as a convergent continued fraction. Representative energy eigenvalues are calculated, correcting the errors due to an earlier Bessel function approximation by Wannier.
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    A simplified model for the predissociation of diatomic molecules (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 391-410 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A model consisting of a harmonic oscillator well and a repulsive inverse square potential, coupled by a delta function, is solved. We find the S-function for this case and study its poles as a function of the coupling strength. These poles show how the harmonic levels shift and broaden as the two potential curves couple and predissociation occurs. A “new state” is found when the energy threshold is just below the first excited state of the harmonic oscillator.
    Additional Material: 11 Ill.
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    Optimum scaling in a Monte Carlo method for quantum chemistry (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 455-456 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560130315
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    Thermodynamics of the DNA helix-coil transition (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 499-507 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The thermodynamics of the DNA helix-coil transition is studied, starting from the thermodynamical potential difference between the states helix and coil; this potential difference is understood as the difference in free energies. With only three parameters obtained from experimental data different quantities of the T2 phage DNA molecule are calculated. It is observed that the phase transition is of second order.
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    Applications of MO theory in organic chemistry (Progress in Theoretical Organic Chemistry, Vol. 2). I. G. Csizmadia, Ed. Elsevier Scientific Publishing Company, Amsterdam and New York, 1976. Price: $69.50, 626 pp. (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 563-563 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560130410
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    Masthead (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978) 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560130501
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    An efficient procedure to evaluate long-range coulombic interactions within the framework of the LCAO-CO method for infinite polymers (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 605-617 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A very efficient and exact method for calculating the long-range effects in polymers is reported. The method is based on the multipole expansion within the Fock operator, and exact summation up to infinity is carried out. Only a small number of one-electron integrals have to be considered, while in the traditional approach one has to compute a large number of two-electron integrals. Results on LiH model polymer have been obtained with a remarkable accuracy within a negligible computing time.
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    On the approximation of potential-energy functions for two-center systems (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 641-677 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Let E(R) be a potential-energy function for a neutral or ionic diatom in the Born-Oppenheimer approximation. Then the approximation of E(R) for 0 〈 R 〈 ∞ starting from finite and typically small sets of given information is considered. The approach is based on the fact that the scaled potential curves F(R) = R2E(R) derive from an eigenvalue problem which depends linearly on R. The nature of the curves F(R) is examined in detail. The results include the discovery of various approximants, some of which display rigorous bounding properties and others, closely related, whose behavior with respect to the approximated function appears to be predictable.
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    Approximate exchange perturbation study of intermolecular interactions in molecular complexes (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 679-692 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In an attempt to rationalize and improve an approximate exchange perturbation scheme related to the model of Murrell et al., more accurate approximations are introduced eliminating the use of empirical parameters. The total interaction energy has been evaluated as the sum of additive electrostatic, exchange, charge transfer, and dispersion contributions. It is proven that the assumption of intramolecular ZDO approximation is equivalent to the use of the Mulliken formula for intermolecular intergrals in the region of small overlap. It is also shown that the use of exact two-center resonance integrals and atomic multipole expansion leads to a substantial improvement of results. The method has been applied to calculation of interaction energies of some model hydrogen-bonded complexes of water, hydrogen fluoride, adenine, thymine, guanine, and cytosine using approximate all-valence wave functions.
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    Density matrix methods in orbital optimization for MCSCF calculations (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 769-775 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The problem considered is that of selecting the finite orbital basis which will minimize the energy in a given size CI calculation. (1) A one-body operator is defined which has as eigenfunctions the desired optimal basis. The operator is defined in terms of the basis which leads to a self-consistency problem of Hartree-Fock type. (2) A method of successive orbital rotations is defined which is shown to have desirable convergence properties.
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    Announcement (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 380-380 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560110217
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    Announcement (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 160-160 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560130115
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    Maximum and minimum overlap, localized, and hybrid orbitals for atoms and molecules by means of orthonormality-constrained variation (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 199-206 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown that application of the orthonormality-constrained variation method to the absolute squares of three kinds of overlap integrals leads to eigenvalue equations and of which the eigenvectors belonging to maximum (minimum) eigenvalues are the maximum (minimum) overlap, localized, and hybrid orbitals. In the eigenvalue equations, coupling operators similar to those used in SCF theory are found to occur. Connection of the maximum orbitals to a many-shell model, a simple MO theory, and Löwdin's orthonormalization is also discussed.
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    CNDO calculation of polarizabilities including polarization functions in the basis set (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 235-238 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Electric polarizabilities are calculated by solving the first- and second-order perturbation equations through a variational procedure. Satisfactory numerical results are obtained for a number of molecules using the CNDO approximation with an extended basis set.
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    URL: http://dx.doi.org/10.1002/qua.560130209
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    Mathematical basis of approximate MO theories: Origin of mulliken's magic formula (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 209-212 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The mathematical basis for the Ruedenberg's and Mulliken's approximations is given in a general framework.
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    URL: http://dx.doi.org/10.1002/qua.560140208
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    Energy band structure of (SN)x chain: Unrestricted Hartree-Fock and charge density wave solutionsSupported by RC of Slovenia (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 239-243 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The ab initio Hartree-Fock crystal orbital method is used for the calculation of the energy band structure of a one-dimensional model of (SN)x. Two energy band structures are described corresponding to the self-consistent spin density wave (SDW) and the self-consistent charge density wave (CDW) solution, respectively.
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    A comparative study of multiple scattering calculations on CrF63- (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 367-374 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The multiple scattering molecular orbital method, with different choices of sphere radii and local exchange, is applied to the cluster CrF63-. The orbital energies are almost always in the same order but uniformly moved up or down the energy scale depending on which parameters are used. Charge densities are only slightly dependent on the parameters. A method to avoid interaction with Rydberg-like states is suggested.
    Additional Material: 1 Ill.
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    Quantum-mechanical theory for transport across biological membranes (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 411-428 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A general quantum-mechanical description of molecular transport across biological membranes has been developed. The one-dimensional Schrödinger equation for the motion of ions and molecules across the biological membrane has been solved using reasonable potential barriers. Two types of potential profiles for such transports have been considered: a flat barrier proposed by Hall et al. for lipids and an oscillatory potential proposed by Lauger for lipids and by us in this paper for intrinsic proteins. The general behavior of the transmission coefficient as a function of energy and the variation of the permeability as a function of structural changes in the membrane have been discussed. Finally, the importance and areas of applicability of such a theory have been pointed out.
    Additional Material: 11 Ill.
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    Introduction (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. III 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560140402
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    Vers une nouvelle interprétation de la liaison chimique? (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 483-497 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Le découpage de la densité électronique totale dans une molécule, en contributions provenant des diverses orbitales, permet de définir des régions orbitalaires de caractère conventionnel dont la charge totale est égale à la somme des populations de Mulliken des orbitales constituant les diverses régions. La fluctuation relative de la charge de ces régions s'exprime simplement en fonction des populations de Mulliken et des indices de liaisons. Cette analyse de la densité dans des molécules variées (saturées ou conjuguées) permet de retrouver les liaisons chimiques de la graphie classique comme correspondant à des régions orbitalaires de charge voisine de 2 et présentant une fluctuation relative fiable (≤0, 10). Compte tenu du caractère dynamique que contient la notion de liaison, les résultats obtenus trouveraient une interprétation simple dans l'espace des phases. L'impuissance de la Mécanique quantique de donner une description dans cet espace expliquerait l'impossibilité de déduire de calculs quantiques la notion měme de liaison chimique.
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    Dependence of the electrostatic molecular potential upon the basis set and the method of calculation of the wave function. Case of the ground 3A1(π → π*) and 1A1(π → π*) states of formaldehyde (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 537-552 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The dependence of the molecular electrostatic potential V on the method of calculating the wave function and on the basis set has been examined for three electronic states of H2CO. The calculations analyzed here refer to two different basis sets: a minimal set and a split-valence shell set, both supplemented with diffuse p orbitals. The methods of calculation include the SCF procedure (for the ground state), CI procedures of increasing complexity, which practically reach their asymptotic limits, and, for the excited states, simpler methods (rigid orbital excitation, complete CI of single excitations, electron-hole potential methods). It appears that in the ground state the two bases give equivalent descriptions of V when the CI process reaches the asymptotic limit and that the SCF descriptions approximate fairly well the more accurate ones. For the 3A1(π → π*) state the conclusions on the two basis sets are similar and, in addition, it is shown that a simple method (EHP) gives an approximation of V that reproduces the essential features of the complete CI calculations. The inadequacy of both basis sets for the representation of the 1A1(π → π*) state turns out to be evident. A discussion is presented concerning the possibility of adopting the calculation of V as an auxiliary tool to compare the accuracy of different descriptions of the same electronic state.
    Additional Material: 10 Ill.
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    Total cross section of the SF6 molecule for elastic electron scattering (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 597-603 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A multiple scattering method is used for determining the total cross section of elastic electron scattering for the SF6 molecule in the energy range 10-60 eV.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/qua.560130504
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    Applicaition of the statistical method in the theory of intermolecular interactions (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 627-634 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The approximate way of calculating the supermolecular density applied in the Gordon and Kim method is examined. If the supermolecular density is approximated by a sum of the subsystem densities, the results for the individual contributions to the interaction energy (kinetic, potential) appear to be incorrect as compared with those obtained in the SCF approach and in first-order perturbation theory. However, a considerable improvement of the statistical results is obtained if a more suitably calculated supermolecular density is used. All calculations have been carried out for the He2 system.
    Additional Material: 4 Tab.
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    Fifth conference on reduced density matrices (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 693-695 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560130602
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    Reduced-density-matrix theory and algebraic structures (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 719-730 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A survey of our recent work on algebraic structures and reduced-density-matrix theory is presented. Our approach leads to a method of classifying reduced density matrices and generalizes the notion of open and closed shells in many-body theory.
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    Reduced hamiltonian orbitals. II. Optimal orbital basis sets for the many-electron problem (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 777-790 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Optimal orbital exponents are approximated by minimization of the reduced Hamiltonian orbital ground state energy. They appear to be as good as and are obtained at much less expense than the values derived by the usual SCF exponent optimization scheme. Partitioning of energy into 0-energy, 1-energy, and 2-energy (Absar and Coleman, Int. J. Quant. Chem. 10, 319 (1976); Chem. Phys. Lett. 39, 60 (1976)) is used to study the variation in the electronic energy surface upon variation of orbital exponents. The 1-energy operator, the natural orbitals of which are the reduced Hamiltonian orbitals, is compared with the SCF operator.
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    Representable reference density matrices applied to the graphical description of the Coulomb hole in the 1s2(2p)2 1S state of the B+ ion (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 13 (1978), S. 791-799 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Representable reference density matrices are applied to the graphical description of the Coulomb hole in a CI wave function for the first excited 1S state of the four-electron boron ion B+. It is found that a satisfactory picture of the Coulomb hole emerges only when the symmetry of the correlated wave function is recognized in the construction of the reference full-density matrix.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/qua.560130610
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    Ab initio molecular orbital calculations of the cobalt porphine complex. I. LCAO SCF MO calculation of low-spin, high-spin, and π-ionized states of Co-porphine (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 13-27 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Ab initio LCAO SCF MO calculations are carried out on planar Co-porphine with a basis set of roughly double zeta quality for Co and N and of single zeta quality for C and H. The net charge on Co and N and the overlap population between them are 1.78, -0.57, and 0.06, respectively, in the 2A1g, state, which is known to be the ground state by experiment. The bonding in this complex is thus largely ionic. The first and second calculated ionization potentials are 6.51 and 6.77 eV, respectively, and are in reasonable agreement with the observed ionization potentials of 6.44 and 6.62 eV for Ni-tetraphenylporphine. CI calculations within the framework of the ligand field theory are also performed. The calculated order of the five lowest states is 4B2g ≈ 4Eg, 4A2g, 2A1g, 4Eg from below and is not in agreement with the semiempirical order of 2A1g ≈ 4B2G, 4A2g, 2Eg, 4Eg determined by Lin.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560140103
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    Ab-initio and approximately rigorous calculations on small, medium, and large systems (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 1005-1015 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We have explored two areas of approximately rigorous calculations for computing nonempirical wave functions for heavy and/or large molecules orders of magnitude faster than with conventional ab-initio methods but with the same chemical accuracy.First, we have developed and used a series of programs (starting from our new fast sets of ab-initio Gaussian SCF and SCF-CI programs) incorporating ab-initio effective core model potentials (MOD-POT) which allow one to treat only the valence electrons explicitly, plus a charge conserving integral prescreening, which cuts down significantly on the number of integrals that have to be calculated, stored, or processed for a large molecule. We have named this latter procedure VRDDO (variable retention of diatomic differential overlap). With these MODPOT and MODPOT/VRDDO methods we have explored a variety of small, medium, and large systems ranging from electron affinities of atoms through to molecules of biological interest and large boron hydrides. The results compared to ab-initio SCF or SCF/CI calcuations are very good, usually within 0.001 to 0.002 a.u. for orbital energies and gross atomic populations (GAPS) and even better along potential energy curves.Secondly, we have explored the use of the MS-Xα method for less conventional molecules and properties than those for which it is customarily employed.
    Additional Material: 6 Tab.
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    URL: http://dx.doi.org/10.1002/qua.560110613
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    The AMO method at small internuclear distances (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 11-17 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The AMO function of the hydrogen molecule ψ = ψc + η ψi, where ψc is the covalent part and ψi the ionic part, is investigated for small internuclear distances R. We found η → -1 as R →,-1 as R → 0, contrary to the intuitively expected limit η → 1. However, near R = 0 an analytical expression of ψ is derived, showing that ψ reduces to the helium ground state as R → 0. We have proved that the empirical concept „covalent and ionic character“ should be replaced by the symmetry argument in the case of small R.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/qua.560120103
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  • 86
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    Biorthonormal basis sets and the interaction between one-electron atoms (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 191-207 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The properties of biorthonormal sets and their use in quantum chemistry are discussed. A theoretical description of the interaction between one-electron atoms is presented. The description is based on a single orbital per electron but is otherwise complete. Structurally simple relations are derived for the energy of interaction, and theoretical justifications for the London equation and the diatomics-in-molecules method are presented. Some comments on the stability of spin-coupling-optimized methods are made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560140207
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    Determination of the charge distribution in nonmetallic crystals. I. Theory and application to tetrahedrally coordinated solids (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 181-190 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A SCF method using localized molecular orbitals which are built up on hybrid atomic orbitals is proposed to obtain the charges in infinite crystals. Hybrid orbitals are built up on a minimal STO basis set. The formalism has been adapted in order to take into account the periodicity of the system and its infinite size by introducing the Madelung constant. The total energy is given by an infinite sum of terms each corresponding to the energy of a bond in the crystal field. Minimizing this bond energy with respect to eigenvectors it is straightforward to obtain the electronic charges, whence the polarity, i.e., the ionicity, of bonds. In this first paper, we study and discuss the polarity of bonds in zincblende and wurtzite-type compounds built up on first and second row elements. Our values are coherent between themselves and in agreement with other authors' results. The connection with electronegativity and polarizability is discussed.
    Additional Material: 1 Tab.
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    URL: http://dx.doi.org/10.1002/qua.560140206
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    Iterative hypervirial-scaling method for obtaining wave functions and eigenvalues (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 231-237 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A procedure to improve trial wave functions is given in terms of the off-diagonal hypervirial theorem. This procedure is closely related to the optimum scaling method which is valid for the diagonal hypervirial theorem. The second excited state of the one-dimensional oscillator model is employed as an example, and improved wave functions and expectation values are calculated. The results are compared with previous values based on the diagonal hypervirial theorem.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/qua.560140302
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    Orbital optimization techniques: Comparative study in a semiempirical framework (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 289-297 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this paper, MC-SCF and CI methods have been explored for the calculation of ground- and excited-state energies of some aromatic heterocycles in the PPP framework. A new algorithm for solving the orbital equations in MC-SCF theory has been suggested and its performance has been compared with the conventional gradient optimization technique. Energies of first few transitions have been calculated and compared with rather extensive CI results.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/qua.560140307
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    Heuristic intermolecular potential function for the methane-water interaction based on ab initio quantum-mechanical calculations (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 319-327 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An analytical potential function for the pairwise interaction of methane and water is reported. The function is representative of 225 ab initio quantum-mechanical calculations of the intermolecular interaction using 6-31G self-consistent-field molecular-orbital theory. The statistical parameters of the curve fitting are given and isoenergy contour maps of the interaction energy are presented and discussed.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/qua.560140310
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    Intermolecular interactions: From diatomics to biopolymers. B. Pullman, ed. John Wiley & Sons Inc., New York, 1978. Price: $48.50, 447 pp (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 341-341 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560140314
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    Complex scaling transformations in stationary and scattering problemsTalk presented at the 1978 Sanibel Symposium (Florida). (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 353-359 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We review the methods and some applications of complex scaling transformation as well as some goals that now seem accessible using this technique in atomic and molecular physics.
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    URL: http://dx.doi.org/10.1002/qua.560140404
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    Complex coordinates and the Stark effect (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 393-418 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The theories of the dilatation, r → r eiθ, and translation, x → x + iq, transformations as related to the Stark problem are reviewed, and new results obtained. Results for the hydrogen atom n = 1 and n = 2 levels and the 1P0, 2s2p H- shape resonance in dc fields are presented, and the extension to the ac Stark effect made. Spectral estimates are made using the technique of the numerical range and via discussion of several model problems, using both coordinate rotation and coordinate translation.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/qua.560140408
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    Time dependence, complex scaling, and the calculation of resonances in many-electron systems (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 457-513 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The theory of this paper deals with certain aspects of the formal properties of atomic and molecular highly excited nonstationary states and the problem of calculating their wave functions, energies, and widths. The conceptual framework is a decay theory based on the consistent definition and calculation of the t = 0 localized state, |Ψ. Given this framework, the following topics are treated: (a) The variational calculation of Ψ0 and E0 using a previously published theory that generalized the projection operator approach to many-electron systems. (b) The exact definition of the resonance energy. (c) The possibility of bound states in the continuum. (d) The relation of Ψ0 to the resonance (Gamow) function Ψ and of the Hamiltonian to the rotated Hamiltonian H(θ) based on the notion of perturbation of boundary conditions in the asymptotic region. (e) The variational calculation of real and complex energies employing matrix elements of H and H2 with square-integrable and resonance functions. (f) The mathematical structure of the time evolution of |Ψ0〉 and the possibility of observing nonexponential decays in certain autoionizing states that are very close to the ionization threshold. (g) A many-body theory of atomic and molecular resonances that employs the coordinate rotation method.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/qua.560140411
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    Some aspects of the model potential method (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 623-634 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The theoretical justification of the model potential method is studied in some detail. The correct equations within the framework of Roothaan's open-shell scheme are derived and the approximations necessary to get a workable method are discussed. Analysis of the local part of the model potential suggests a new analytical form for it. The new expression is theoretically more consistent than the original one, and it can be determined in a more straightforward way. A basis set approximation, which is particularly suitable for approximate evaluation of two-electron integrals when only valence orbitals are involved, is discussed and tested with encouraging results. The ideas are tested on the Fe and I atoms.
    Additional Material: 7 Tab.
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    URL: http://dx.doi.org/10.1002/qua.560140509
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    Polarization model representation of hydrogen fluoride for use in gas- and condensed-phase studies (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 649-657 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The polarization model, originally developed to describe deformable and ionizable water molecules, has been extended to hydrogen fluoride. Since electronic polarization is explicitly included, the interaction energy in aggregates of molecules (with or without ions) is nonadditive. The model properly describes the structure of (HF)2, including off-axis bending of the proton acceptor molecule. Calculations are presented to illustrate elementary gas-phase reactions involving proton transfer between HF and F-, and H2F+ and F-.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560140512
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    Universal basis sets and transferability of integralsPresented at the American Conference on Theoretical Chemistry, Boulder, Colorado, June 25-30, 1978. (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 635-639 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The concept of a universal basis set for electronic structure calculation is illustrated by presenting results obtained when basis sets are transferred from one atom to another. A single Slater-orbital basis set, consisting of nine 1s and six 2p functions, produces Hartree-Fock total energies and orbital energies in good agreement with the most accurate calculations of these energies obtained using different basis sets individually optimized for each atom. Transferability of integrals is a natural consequence of the use of the same basis set for each atom in a molecule.
    Additional Material: 3 Tab.
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    URL: http://dx.doi.org/10.1002/qua.560140510
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    Half-projected Hartree-Fock model for computing potential-energy surfaces (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 641-648 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The possible uses of the half-projected Hartree-Fock (HPHF) scheme for computing potential-energy surfaces for both singlet and triplet states are investigated. For that purpose, a new procedure based on the simultaneous solution of two eigenvalue equations is presented for calculating the HPHF function. Applications are given in the cases of the singlet ground state and lowest triplet state of the lithium molecule. In both cases, the HPHF scheme is found to yield the correct general shape of the curves. The features of these curves are discussed. Finally, it is concluded that the HPHF model seems to be useful as a tool for determining potential-energy surfaces, especially in the cases of large molecules where more sophisticated methods are unmanageable.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/qua.560140511
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    Interpretation of electron spectra. III. Spectra of formamide, studied with HAM/3 (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 737-740 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The molecular spectra of formamide (HCONH2) are interpreted by the use of the new semiempirical method HAM/3. Very good agreement with experiments can be obtained for the calculation of all valence ionization energies as well as for the (negative) electron affinity. In addition, the calculated excitation energies allow an unambiguous interpretation of the UV spectrum, for which previously different ordering of the triplet 3ππ* and 3nπ* transitions have been suggested.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/qua.560140605
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    Preface (1983)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. v 
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560230102
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