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  • 1
    Electronic Resource
    Electronic Resource
    A nonorthogonal approach to perfect pairing (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 5633-5638 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present an alternative formulation of perfect pairing (PP) aimed at giving a more faithful representation of the valence correlation energy of an arbitrary molecule. In the new theory, the occupied and virtual orbitals are nonorthogonal amongst themselves but orthogonal to each other. Whereas for the fully orthogonal version of PP one has the number of pairs equal to the number of occupied orbitals, the current formulation allows for an arbitrary number of pairs built from redundant orbitals. We propose setting the number of pairs equal to the number of valence orbitals in the molecule. Preliminary results indicate that the redundant formulation gives qualitatively improved results for delocalized systems such as benzene, while maintaining the attractive features of PP for localized systems. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481138
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  • 2
    Electronic Resource
    Electronic Resource
    Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O4+ (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 4171-4181 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We describe an alternative procedure for obtaining approximate Brueckner orbitals in ab initio electronic structure theory. Whereas approximate Brueckner orbitals have traditionally been obtained by mixing the orbitals until the coefficients of singly substituted determinants in the many-electron wave function become zero, we remove singly substituted determinants at the outset and obtain orbitals which minimize the total electronic energy. Such orbitals may be described as variational Brueckner orbitals. These two procedures yield the same set of exact Brueckner orbitals in the full configuration interaction limit but differ for truncated wave functions. We consider the simplest variant of this approach in the context of coupled-cluster theory, optimizing orbitals for the coupled-cluster doubles (CCD) model. An efficient new method is presented for solving the coupled equations defining the energy, doubles amplitudes, and orbital mixing parameters. Results for several small molecules indicate nearly identical performance between the traditional Brueckner CCD method and the variational Brueckner orbital CCD approach. However, variational Brueckner orbitals offer certain advantages: they simplify analytic gradients by removing the need to solve the coupled-perturbed Brueckner coupled-cluster equations for the orbital response, and their straightforward extensions for inactive orbitals suggests possible uses in size-extensive models of nondynamical electron correlation. Application to O4+ demonstrates the utility of variational Brueckner orbitals in symmetry breaking cases. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477023
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  • 3
    Electronic Resource
    Electronic Resource
    Periodic boundary conditions and the fast multipole method (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 10131-10140 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The seminal work of Nijboer and De Wette [Physica 23, 309 (1957)] enables the calculation of lattice sums of spherical harmonics, but has long been overlooked. In this article, their central result is recast in a simplified form suitable for modern multipole algorithms that employ the solid harmonics. This formulation makes possible the imposition of periodic boundary conditions within modern versions of the fast multipole method, and other fast N-body methods. The distinction between the extrinsic values obtained with the lattice sums M of the multipole interaction tensors, and the intrinsic values associated with Taylor's expansion of the Ewald formulas, is made. The central constants, M, are computed to 32 digit accuracy using extended precision arithmetic. Timings and corresponding errors obtained with a periodic version of the fast multipole method are presented for particle numbers spanning [103,106], and a range of expansion orders. A qualitative comparison is made between the present implementation, other periodic versions of the fast multipole method, and fast Ewald methods. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.474150
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  • 4
    Electronic Resource
    Electronic Resource
    Polarized atomic orbitals for self-consistent field electronic structure calculations (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 9085-9095 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a new self-consistent field approach which, given a large "secondary" basis set of atomic orbitals, variationally optimizes molecular orbitals in terms of a small "primary" basis set of distorted atomic orbitals, which are simultaneously optimized. If the primary basis is taken as a minimal basis, the resulting functions are termed polarized atomic orbitals (PAO's) because they are valence (or core) atomic orbitals which have distorted or polarized in an optimal way for their molecular environment. The PAO's derive their flexibility from the fact that they are formed from atom-centered linear-combinations of the larger set of secondary atomic orbitals. The variational conditions satisfied by PAO's are defined, and an iterative method for performing a PAO-SCF calculation is introduced. We compare the PAO-SCF approach against full SCF calculations for the energies, dipoles, and molecular geometries of various molecules. The PAO's are potentially useful for studying large systems that are currently intractable with larger than minimal basis sets, as well as offering potential interpretative benefits relative to calculations in extended basis sets. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.475199
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  • 5
    Electronic Resource
    Electronic Resource
    Ab Initio Calculations of Singlet and Triplet Excited States of Chlorine Nitrate and Nitric Acid (1995)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 99 (1995), S. 3493-3502 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/j100011a015
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  • 6
    Electronic Resource
    Electronic Resource
    Closely approximating second-order Møller–Plesset perturbation theory with a local triatomics in molecules model (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 3592-3601 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new ansatz for local electron correlation is introduced, which truncates double substitutions subject to a triatomics in molecules (TRIM) criterion. TRIM includes all double substitutions in which one occupied-virtual substitution is atomic while the other substitution can be nonlocal (a cubic number, before cutoffs). With an additional approximation, the TRIM second-order Møller–Plesset perturbation theory (MP2) model can be noniteratively solved; this is the model that is implemented. Results are shown for absolute energies of alkane and polyene chains, rotational barriers of substituted ethylenes and benzenes, and association energies of the water and neon dimers. Over 99.7% of the untruncated MP2 energy is recovered for the test cases, and the relative energies of small systems are in error by less than 0.1 kcal/mol. By contrast, a diatomics in molecules (DIM) truncation recovers about 95% of the full MP2 energy, and yields errors several times larger for relative energies. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.480512
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  • 7
    Electronic Resource
    Electronic Resource
    Linear and sublinear scaling formation of Hartree–Fock-type exchange matrices (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 1663-1669 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a new method (LinK) to form the exact exchange matrix, as needed in Hartree–Fock and hybrid density functional theory calculations, with an effort capable of scaling only linearly with molecular size. It preserves the highly optimized structure of conventional direct self-consistent field (SCF) methods with only negligible prescreening overhead and does not impose predefined decay properties. Our LinK method leads to very early advantages as compared to conventional methods for systems with larger band gaps. Due to negligible screening overhead it is also competitive with conventional SCF schemes both for small molecules and systems with small band gaps. For the formation of an exchange-type matrix in coupled perturbed SCF theory our LinK method can exhibit sublinear scaling, or more precisely, independence of the computational effort from molecular size. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.476741
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  • 8
    Electronic Resource
    Electronic Resource
    Size-consistent wave functions for nondynamical correlation energy: The valence active space optimized orbital coupled-cluster doubles model (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 10669-10678 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The nondynamical correlation energy may be defined as the difference between full configuration interaction within the space of all valence orbitals and a single determinant of molecular orbitals (Hartree–Fock theory). In order to describe bond breaking, diradicals, and other electronic structure problems where Hartree–Fock theory fails, a reliable description of nondynamical correlation is essential as a starting point. Unfortunately, the exact calculation of nondynamical correlation energy, as defined above, involves computational complexity that grows exponentially with molecular size and is thus unfeasible beyond systems of just two or three heavy atoms. We introduce a new hierarchy of feasible approximations to the nondynamical correlation energy based on coupled-cluster theory with variationally optimized orbitals. The simplest member of this hierarchy involves connected double excitations within the variationally optimized valence active space and may be denoted as VOO-CCD, or VOD. VOO-CCD is size-consistent, has computational complexity proportional to the sixth power of molecule size, and is expected to accurately approximate the nondynamical correlation energy in such cases as single bond dissociation, diradicals, and anti-ferromagnetic coupling. We report details of our implementation of VOO-CCD and illustrate that it does indeed accurately recover the nondynamical correlation energy for challenging multireference problems such as the torsion of ethylene and chemical bond breaking. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477764
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  • 9
    Electronic Resource
    Electronic Resource
    Electronic structure of large systems: Coping with small gaps using the energy renormalization group method (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 10159-10168 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A newly developed energy renormalization-group method for electronic structure of large systems with small Fermi gaps within a tight-binding framework is presented in detail. A telescopic series of nested Hilbert spaces is constructed, having exponentially decreasing dimensions and electrons, for which the Hamiltonian matrices have exponentially converging energy ranges focusing to the Fermi level and in which the contribution to the density matrix is a sparse contribution. The computational effort scales near linearly with system size even when the density matrix is highly nonlocal. This is illustrated by calculations on a model metal, a small radius carbon-nanotube and a two-dimensional puckered sheet polysilane semiconductor. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477709
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  • 10
    Electronic Resource
    Electronic Resource
    A tensor formulation of many-electron theory in a nonorthogonal single-particle basis (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 616-625 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We apply tensor methods to formulate theories of electron correlation in nonorthogonal basis sets. The resulting equations are manifestly invariant to nonorthogonal basis transformations, between functions spanning either the occupied or virtual subspaces of the one-particle Hilbert space. The tensor approach is readily employed in either first or second quantization. As examples, second-order Møller–Plesset perturbation theory, and coupled cluster theory with single and double substitutions, including noniterative triples, are recast using the tensor formalism. This gives equations which are invariant to larger classes of transformations than existing expressions. Procedures for truncating these equations are discussed. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.475423
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