Showing papers in "International Journal of Quantum Chemistry in 1984"

A linear response, coupled‐cluster theory for excitation energy

Abstract: Expressions for static and dynamic properties in coupled-cluster (CC) theory are derived. In the static case, using diagrammatic techniques, it is shown how consideration of orbital relaxation effects in the theory introduces higher-order correlation effects. For the dynamic case, excitation energy expressions are obtained without consideration of orbital relaxation effects and shown to be equivalent to an equation of motion (EOM) approach subject to a coupled-cluster ground-state wave function and an excitation operator consisting of single and double excitations. Illustrative applications for excited states of ethylene are reported.

Bond order and valence: Relations to Mulliken's population analysis

Abstract: Discussion de plusieurs proprietes de nouvelles definitions des indices de liaison et des indices de valence, donnes a l'aide de la matrice P et de la matrice S de recouvrement d'orbitales atomiques

Basis set expansion of the dirac operator without variational collapse

Abstract: The eigenstates of the matrix representation of the Dirac operator for c → ∞ do not approach their nonrelativistic counterparts in the same basis. This wrong “Schrodinger limit” is shown to be the main reason for the phenomenon known as “variational collapse.” After a short review of existing proposals to overcome the “variational collapse,” a systematic study of the possible ways to avoid it is given. All discussed approaches are analyzed in terms of various criteria that one wants to fulfill. The most promising approach consists of a free-particle Foldy–Wouthuysen (FW) transformation on operator level and a back transformation on matrix level (approaches C2 and C3). This implies a modification of the free-electron part of the matrix representation of the Dirac operator and leads to the correct Schrodinger limit (and if one wishes even the correct Pauli limit) in the same basis (and to the exact results for a complete basis). The potential energy is unchanged, which makes the application to n -electron systems straightforward. Projection of the Dirac operator to positive energy states does not remove the variational collapse unless this is done in a very special way.

Analytical gradients for the coupled-cluster method†

Abstract: A nondiagrammatic formulation of the analytical first derivative of the coupled-cluster (CC) energy with respect to nuclear position is presented and some features of an efficient computational method to calculate this derivative are described. Since neither the orbitals nor the configuration expansion coefficients are variationally determined, in the most general case derivatives of both are necessary in computing the gradient. This requires the initial solution of the coupled perturbed Hartree-Forck (CPHF) equations and seems to mandate the solution of a linear matrix equation ZT(1) = X for first-order corrections to the CC coefficients. However, if only the analytic gradient is desired a simpler non-perturbation-dependent set of equations can be solved instead. This and the first-order character of the linear matrix equation makes the application of an analytic gradient technique to the CC method feasible.

Foundations of the relativistic theory of many‐electron bound states

Abstract: Most of the existing calculations of relativistic effects in many-electron atoms or molecules are based on the Dirac–Coulomb Hamiltonian HDC. However, because the electron–electron interaction mixes positive- and negative-energy states, the operator HDC has no normalizable eigenfunctions. This fact undermines the quantum-theoretic rationale for the Dirac–Hartree–Fock (DHF) equations and therefore that of the relativistic configuration-interaction (RCI) and multiconfiguration Dirac–Fock (MCDF) methods. An approach to this problem based on quantum electrodynamics is reviewed. It leads to a configuration-space Hamilton H which involves positive-energy projection operators dependent on an external potential U; identification of U with the nuclear potential Vext corresponds to use of the Furry bound-state interaction picture. It is shown that the RCI method can be reinterpreted as an approximation scheme for finding eigenvalues of a Hamiltonian H, with U identified as the DHF potential; the theoretical interpretation of the MCDF method needs further clarification. It is emphasized that if U differs from Vext one must consider the effects of virtual-pair creation by the difference potential δU = Vext − U; an approximate formula for the level-shift arising from δU is derived. Some ideas for dealing with the technical problems introduced by the projection operators are discussed and relativistic virial theorems are given. Finally, a possible scheme for adapting current MCDF methods to Hamiltonians involving projection operators is described.

Motion of a particle in a ring-shaped potential: an approach via a nonbijective canonical transformation

Abstract: The problem of a particle in the three-dimensional ring-shaped potential ησ2(2a0/r − ηa/r2 sin2 θ)e0 introduced by Hartmann is transformed into the problem of a coupled pair two-dimensional harmonic oscillators with inverse quadratic potentials by using a nonbijective canonical transformation, viz., the Kustaanheimo–Stiefel transformation. The energy E of the levels for the ring-shaped potential is obtained in a straightforward way from the one for the two-dimensional potential — (4Eρ2 + η2σ2a e0/ρ2).

A second-quantization approach to the analytical evaluation of response properties for perturbation-dependent basis sets

Abstract: A general theory for response properties is presented which is applicable to perturbations affecting the molecular basis set, notably nuclear derivatives. A perturbation-independent Fock space is introduced, and the necessary reorthonormalization of a truncated basis set after a perturbation is explicitly incorporated in the Hamiltonian. Explicit formulas for MCSCF first- and second-order properties are presented, and some computational aspects are briefly discussed. A brief comparison with previous results is given.

Relativistic calculations of dissociation energies and related properties

Abstract: Methods of calculation of potential energy curves or surfaces, including dissociation energies, bond distances, and vibration frequencies, are discussed as well as recently obtained results for several molecules. The ab initio relativistic methods involve the derivation of shape-consistent effective potentials from Dirac-Fock atomic calculations. These effective potentials are averaged and differenced with respect to spin with the differences, p/sub 3/2/-p/sub 1/2/, etc., yielding spin-orbit operators. The molecular calculations are then set up in a familiar manner through the SCF stage using spin-averaged effective potentials. The final stage is a configuration-interaction calculation including the spin-orbit terms as well as the electron repulsion terms. Calculations that have been made for several low-lying excited states as well as the ground state for Au/sub 2/, TlH, Tl/sub 2/, Sn/sub 2/, and Pb/sub 2/ are reviewed. Good agreement is obtained with spectroscopic data and a number of interesting predictions are made. 36 references, 8 figures, 2 tables.

Diagrammatic valence‐bond theory for finite model Hamiltonians

Abstract: Valence bond (VB) diagrams form a complete basis for model Hamiltonians that conserve total spin, S, and have one valence state, φ p , per site. Hubbard and Pariser-Parr-Pople (PPP) models illustrate ionic problems, with zero, one, or two electrons in each φ p , while isotropic Heisenberg models illustrate spin problems, with only purely covalent VB diagrams. The difficulty of nonorthogonal VB diagrams is by-passed by exploiting the finite dimensionality of the complete basis and working with unsymmetric sparse matrices. We introduce efficient bit manipulations for generating, storing, and handling VB diagrams as integers and describe a new coordinate relaxation method for the ground and lowest excited states of unsymmetric sparse matrices. Antiferromagnetic spin-½ Heisenberg rings and chains of N≤20 spins, or 2 N spin functions, are solved in C 2 symmetry as illustrative examples. The lowest S=1 and 0 excitations are related to domain walls, or spin solitons, and studied for alternations corresponding to polyacetylene. VB diagrams with arbitrary S and nonneighbor interactions are constructed for both spin and ionic problems, thus extending diagrammatic VB theory to other topologies.

Self‐consistent Dirac–Slater calculations for molecules and embedded clusters

Abstract: The basis of self-consistent local density theory used in the fully relativistic Dirac–Slater model is briefly reviewed. Moment-polarized extensions of theory are developed to treat open-shell systems by lifting the pair-wise Kramers degeneracy. The discrete variational method is used to calculate one-electron energies and charge and magnetization densities of a series of rare-earth trihalides. The theoretical binding energies compare very well with recent gas-phase photoelectron spectra of Berkowitz et al. The von Barth–Hedin exchange and correlation potential produces energies which are significantly better, compared to simpler exchange-only models. Embedded molecular cluster studies on actinide compounds are reported, with particular emphasis on the AcO2 dioxides. Single-particle energy densities of states (DOS) and magnetization DOS are presented, along with an analysis of effective atomic configurations in the solid. Trends in these quantities with actinide atomic number are noted. In contrast to the semicore nature of rare-earth 4f electrons, the actinide 5f levels are seen to be active participants in bonding interactions.

Fitting electron densities of molecules

Abstract: Compact, convenient expressions for the electron density are derived using a fitting functional. Results are given for H2O, CH4, HF, NH3, and PH3, and show the accuracy obtainable using differing numbers of functions on each center. The definition of an atomic charge using these expressions is discussed and it is shown that the Bader virial-partitioning definition, in which the density is integrated over a volume around each nucleus, leads to convergent results.

Anisotropic electronic intracule densities for diatomics

Abstract: The electronic intracule density, a three-dimensional contraction of the spinless electron pair density, is the probability density function for an interelectronic vector. A computationally efficient algorithm for the evaluation of the basic two-electron intracule integral for GTOs is presented. In order to provide an initial understanding of the topography of intracule distributions, anisotropic intracule densities for the X1Σ ground states of the H2 and N2 molecules are reported and analyzed.

Effective basis sets for calculations of exchange‐repulsion energy

Abstract: Usefulness of different Gaussian basis sets for reproducing the “tail” region of the SCF wavefunctions employed in calculations of the exchange-repulsion effect is investigated for the model He-He interaction. It has been shown that extension of the monomer-centered basis set in the scheme of regularized even-tempered basis sets [M. W. Schmidt and K. Ruedenberg, J. Chem. Phys. 71, 3951 (1979)] can be more efficient than augmentation of the fully energy-optimized basis set with diffuse basis functions. It has been also found that Landshoff term vanishes and the “tail” region is well reproduced if monomer wavefunctions are calculated with the basis set of the dimer.

Relativistic atomic structure theory: Some recent work†

Abstract: Recent developments in relativistic atomic structure have been more in terms of program improvement than in fundamental theory. Some comments on both aspects of this work are illustrated by a description of two different recent applications. In the first, we study the contribution of the interaction of relativity and correlation to the 2 3S−2 3P0,1,2 intervals in heliumlike ions, whose theoretical estimation is important for testing QED. The study of satellite structure in the Kβ x-ray emission spectrum of Ar illustrates a quite different use of the program packages developed at Oxford for investigating configuration interaction. The use of shake theory to predict the initial states, populated along with the primary vacancy giving rise to the diagram line, gives a satellite line intensity distribution which agrees very well with recent experimental spectra.

Quantum chemical studies on zeolites and silica

Abstract: After mentioning differences in CO and SiO bonding and different structural types of silicates, the conclusion that interactions between external partners and surfaces of silica and zeolites are mostly dominated by van der Waals forces is discussed. Consequently, the theoretical treatment includes (i) selection of appropriate cluster models, (ii) application of nonempirical quantum chemical methods for obtaining interaction potentials, and (iii) statistical thermodynamic evaluation of adsorption characteristics. As examples vibrational frequencies of H2O and NH3 adsorbed on cationic sites, the interaction of conjugated hydrocarbons with Na+ sites, and the interaction of H2O with various sites on silica and zeolite surfaces are considered.

Coupled-cluster method with optimized reference state

Abstract: We propose a variant of the coupled-cluster (CC) method in which spin orbitals of the reference Slater determinant are optimized in a self-consistent way This approach is a reformulation of the Brueckner–Hartree–Fock (BHF) method used in nuclear physics and known also as the exact SCF method We discuss the use of the reference-state determinants built of HF, natural, and Brueckner spin orbitals, with relations among them investigated in terms of the many-body perturbation theory (MBPT) It is shown that the Brueckner spin orbitals emerge as a convenient basis set in the coupled-cluster method and equations that determine these spin orbitals are found The Brueckner spin orbitals can be calculated as eigenvectors of a certain Hermitian one-electron operator which has a form of the Hartree–Fock operator plus a “correlation potential” depending linearly on two- and three- electron cluster amplitudes The usual decoupling scheme in the coupled-cluster method leads to a hierarchy of approximations; in the first nontrivial one the three-electron cluster amplitudes are neglected, and the two-electron ones are determined by solving Cižek's CPMET equations We also analyze the problem of spatial, spin, and time-reversal symmertry in the CC and BHF methods If (and only if) the reference-state determinant belongs to a one-dimensional representation of a certain symmetry subgroup of the system, the CC operator and the BHF one-electron operator are invariant with respect to this subgroup Thus the restricted (entirely symmetry-adapted) version of the BHF method can be formulated only for the closed-shell systems This is done for the above-mentioned approximate BHF method We discuss also the usefulness of the BHF method in application to extended metallic systems

Theoretical investigations of the electronic states of porphyrins. II: Normal and hyper phosphorus porphyrins

Abstract: Ab initio methods have been used to calculate the ground and excited states of “normal” and “hyper” porphyrins. Perturbation theory and CI methods were used to determine differential ground and excited-state correlation effects for [Pv(P)F2]+ and [PIII(P)]+. A comparison is made to the INDO/S/CI predicted wavefunctions and spectra and to the experimental spectra of closely related molecules. The “hyper” [PIII(P)]+ calculations show some very low energy electronic transitions which provide an explanation for an anomalous “red” band in the spectrum and for the lack of fluorescence. Ab initio calculations also predict that (1) the lowest energy 1A1 state is a two-configuration wavefunction which can be described as a diradical, (2) the two lowest-energy singlet excited states are double excitations from the closed shell SCF configuration, and (3) a 3B2 state is very close in energy to the lowest 1A1 state.

Parallelism in quantum chemistry: Hydrogen bond study in DNA base pairs as an example

Abstract: We present results on the energetics of the hydrogen bridges for the Guanine–Cytosine pair obtained in a DNA fragment consisting of three stacked base pairs in the B-DNA conformation. The wave function computations on the 87 atom system are all-electron ab initio SCF-MO computations obtained with a basis set of 1032 primitive gaussian functions contracted to 315. Even if the results are only preliminary, one can tentatively advance conclusions relative to the molecular field effect of stacked base-pairs on the potential energy surface for a hydrogen bond. These computations have been performed with a modified version of our molecular program, which uses an IBM 4341 host and six to ten attached array processors (FPS-164) in parallel. The strategy to convert the program from sequential to parallel is briefly outlined and comparisons with our parallel system are made with a present-day “vector” super-computer. From these studies, we conclude that if one adopts the “parallel” approach presented and tested here, much larger chemical systems than previously are now amenable to all-electron ab initio computations.

Fourier transforms of atomic orbitals. I. Reduction to four-dimensional harmonics and quadratic transformations

Abstract: A general expression for the Fourier transform of the basis functions of exponential class has been derived. Particular cases of Slater functions, hydrogen-like functions, Shull and Lowdin functions, Shavitt, Filter, and Steinborn functions have been considered. In many particular cases the Fourier transforms have been shown to reveal some important special properties (reduction to four-dimensional harmonics, quadratic transformations, etc.) which considerably simplify the mathematical treatment of these functions and lead to new possibilities in the development of calculation methods for multicenter integrals.

Remarks on the concept of an atom in a molecule and on charge transfer between atoms on molecule formation

Abstract: Density functional theory provides a natural and rigorous definition of an atom in a molecule in its ground state: The molecular electron density is the sum of atomic densities, the atoms have the same chemical potential as does the molecule, and the atoms are minimally promoted from their ground states. These atoms in general are not spherical, and in general they bear nonintegral charges. Charge transfer on molecule formation is thereby uniquely defined. Calculations by Palke and by Guse are reviewed, in which the hydrogen atom is identified in the hydrogen molecule.

Relativistic band structure calculations

Abstract: The inclusion of relativistic effects in band theory is discussed. Examples showing how these affect optical properties, Fermi surface properties, and cohesive properties are shown. With respect to the latter, it is pointed out that the mass–velocity and Darwin shifts are most important, whereas the SO coupling can be omitted since it does not shift the bands (quenching of angular momentum). The band theoretical aspects are presented in the terminology of the LMTO-ASA method which offers a physical transparent picture of the formation of bands. The volume and energy dependences of the spin-orbit splittings are explained in this picture. As examples are considered calculations for W, Xe, Au, and the copper halides.

Ab initio and pseudopotential calculations on the singlet and triplet states of the disilyne isomers

Abstract: Ab initioSCF as well as pseudopotential calculations were performed for determining equilibrium structures and relative stabilities of several disilyne isomers. For the singlet state there are only two structures, the bridged and the silavinylidene carbene, which correspond to minima on the energy hypersurface. The most stable of the six isomeric structures investigated is the bridged conformer in the 1A1 electronic state, followed by the silavinylidene carbene in the 1A1 and 3A2 electronic states. Inclusion of electron correlation by MRD-CI calculations has no qualitative influence on the relative stabilities found in the SCF calculations.

Direct MRCI method for the calculation of relativistic many-electron wavefunctions. I. General formalism

Abstract: The formalism of a quasi- or full-relativistic multireference CI method has been developed and implemented. The scheme is appropriate for the calculation of molecular systems in which the relativistic effects are of the same order of magnitude as the correlation contributions. In this contribution some important symmetry aspects of a relativistic many-electron wave function are discussed and the consequences for the CI matrix structure are shown. An efficient CI strategy in the form of a direct CI is presented, which avoids the construction of the whole CI matrix. Based on a determinantal expansion of molecular spinor products, the individual one- and two-electron molecular integrals are processed, and the molecular symmetry is easily accounted for by a proper linear combination of Slater determinants in the CI starting vector. For an efficient CI organization some powerful techniques of the graphical unitary group approach have been transferred to the relativistic case.

Nonempirical approach to structure–activity studies†

Abstract: After a brief review of empirical and nonempirical schemes used in the study of molecular properties, the difficulties associated with structure–activity correlations are outlined. Part of the difficulty originates with the lack of precise definition of a structure. An analogy is made with similarly vague concepts of structural chemistry—the notion of aromaticity. This follows with the description of a characterization of structures by selected graph invariants. In particular we consider the count of weighted paths derived from suitable weighting of the individual bonds in a structure. We adopted the weighting factors (mn)−1/2 introduced originally for the definition of the connectivity index. The approach thus combines some features of the very successful connectivity index with features of path sequences, found very useful in comparative studies of related compounds. As an illustration of the combined approach we consider a set of some 40 therapeutically active substances, studied previously by others, and derive their clustering (classification) which is solely based on the count of weighted paths and is devoid of any empirical parametrization.

On a semiclassical interpretation of inter- and intramolecular interactions

Abstract: The semiclassical models considered here are composed by charge distributions coming from ab initio quantum-mechanical calculations on actual molecular systems. These charge distributions interact with one another according to the laws of classical electrostatics. This article describes some results of a systematic examination of the performances of this model in a variety of cases, with the aim of putting in evidence the usefulness and the limits of this inherently approximate representation of chemical interactions. Intermolecular interactions are examined first; the test cases are interactions of neutral molecules with H+, Li+, and C1−, and the formation of H-bonded complexes. Attention is paid mainly to the energetics of the processes; each interacting molecule is considered as a unique entity and classical molecular reactivity indexes (electrostatic potential V, polarization term P) are introduced to compute the interaction energy, to interpret the details of the interaction process, and then to elaborate on less expensive computational procedures. Intramolecular interactions are considered. Attention is paid to the question of defining chemical groups starting from SCF molecular wavefunctions. The transferability and conservation degree of groups derived from localized orbitals of actual molecules is examined in detail, taking as tests their ability to reproduce charge distribution, one-electron observables, and energy. The effect of classical fields on these groups is then examined, taking into consideration external fields originated either by a point charge or by a solvent, and internal fields deriving from substitution of chemical groups. The intergroup analysis is then extended to the case of bimolecular reaction acts by considering the whole system as a supermolecule. Approximate computational procedures able to reproduce the main features of these interactions are proposed and tested. All through the article the performances of the classical models are compared with ab initioSCF calculations (mainly of low or intermediate quality).

Fine and hyperfine structure of the two lowest bound states of Be− and their first two ionization thresholds

Abstract: The two lowest bound excited states of the Be− ion, 1s2 2s2p24P and 1s2 2p34S0, and their respective thresholds, Be 1s2 2s2p 3P0 and Be 1s2 2p23P, and the thresholds of these, Be+ 1s2 2s and Be+ 1s2 2p, have been examined using many-body methods. Here, we present the electron affinities (EAs) or ionization potentials, fine and hyperfine structure, and the electric dipole transition probabilities associated with these states and compare them with existing theory and experiment when available. Based on our new EA, a suggestion is made as to why no negative ion transition has yet been seen in the laboratory.

Unitary group approach to the many‐electron problem. III. Matrix elements of spin‐dependent Hamiltonians

Abstract: This is the final paper in a series of three directed toward the evaluation of spin-dependent Hamiltonians. In this paper we derive the reduced matrix elements of the U(2n) generators in a basis symmetry adapted to the subgroup U(n) × U(2) (i.e., spin-orbit basis), for the representations appropriate to many-electron systems. This enables a direct evaluation of the matrix elements of spin-dependent Hamiltonians in the spin-orbit basis. An alternative (indirect) method, which employs the use of U(2n) U(n) × U(2) subduction coefficients, is also discussed.

First principles charge transfer exciton theory of the UV spectrum of DNA

Abstract: The Slater–Koster resolvent formalism of exciton theory, as proposed originally by Takeuti, has been applied to calculate charge transfer exciton states and to investigate hypochromism in polynucleotides. As a first step, spatially well localized ab initio Wannier functions (WFS) are calculated at the Hartree–Fock level using a two-phase (inter- and intramolecular) localization procedure for the Fourier transformation of the Bloch functions. The single particle energies, entering the Green's function of the polymer, are corrected for electron correlation effects with the help of second order Moller–Plesset (MP) perturbation theory. The interelectronic matrix elements, used in the MP calculation as well as in solving the resolvent problem for the excitons, are calculated in terms of the WFS. Singlet- and triplet-excitonic dispersions, oscillator strengths, the possible affects of ions, hydration, and aperiodicity on the exciton spectrum are discussed.

Degeneracy and coupled-cluster approaches

Abstract: Problems which arise in the application of closed-shell coupled-cluster approaches to quasidegenerate or almost degenerate situations are discussed and the basic classification of quasidegeneracy types is outlined. Recent coupled-cluster results obtained for the cyclic polyene model, particularly in the strongly correlated limit, are briefly discussed and the unexpected features of approximate and localized coupled-pair approaches are pointed out.