Showing papers in "International Journal of Quantum Chemistry in 1983"
TL;DR: The idea of representing the ground state (and perhaps some of the excited states as well) of atomic, molecular, and solid state systems in terms of the diagonal part of the one-body reduced density matrix ρ(x) is an old one as discussed by the authors.
Abstract: The idea of trying to represent the ground state (and perhaps some of the excited states as well) of atomic, molecular, and solid state systems in terms of the diagonal part of the one-body reduced density matrix ρ(x) is an old one. It goes back at least to the work of Thomas [1] and Fermi [2] in 1927. In 1964 the idea was conceptually extended by Hohenberg and Kohn (HK) [3]. Since then many variations on the theme have been introduced. As the present article is not meant to be a review, I shall not attempt to list the papers in the field. Some recent examples of applications are Refs. 4 and 5. Some recent examples of theoretical papers which will play a role here are Refs. 6–12. A bibliography can be found in the recent review article of Bamzai and Deb [13].
1,088 citations
TL;DR: In this article, the LCAO Hamiltonian is decomposed into terms having different physical meaning and significance: (i) sum of effective atomic Hamiltonians; (ii) electrostatic interactions in the point-charge approximation; (iii) the electrostatic effects connected with the deviation of the actual charge distribution from the pointlike one; (iv) two-center overlap effects; and (v) finite basis (counterpoise) correction terms related to the individual atoms.
Abstract: An analysis of the LCAO Hamiltonian is performed in terms of a “mixed” formulation of the second quantization for nonorthogonal orbitals, compressing the different interactions to one- and two-center terms as far as possible by performing appropriate projections. For this purpose an operator of atomic charge is also introduced, the expectation values of which are the Mulliken gross atomic populations on the individual atoms. The LCAO Hamiltonian is decomposed into terms having different physical meaning and significance: (i) sum of effective atomic Hamiltonians; (ii) the electrostatic interactions in the point-charge approximation; (iii) the electrostatic effects connected with the deviation of the actual charge distribution from the pointlike one; (iv) two-center overlap effects; (v) finite basis (“counterpoise”) correction terms related to the individual atoms; and (vi) similar finite basis correction terms with respect to the two-center interactions. Only terms of types (i) to (iv), containing no three- or four-center integrals, are considered as having physical significance. Based on the analysis of the Hamiltonian, an energy partitioning scheme is developed, and explicit expressions are given for one- and two-center (and basis extension) components of the SCF energy. The approach is also applied to the problem of intermolecular interactions, and an explicit formula is given permitting calculation of the “counterpoise” part of the supermolecule energy by properly taking into account that it depends not only on the extension of the basis, but also on the occupation of the additional orbitals in the intervening molecule—a factor completely overlooked in the usual scheme of calculations.
229 citations
TL;DR: In this article, the authors examined the short-range behavior of the spherically averaged Hartree-Fock exchange charge density by performing a simple Taylor expansion and constructed a theoretical model that generates gradient correction terms to the local density approximation for the exchange energy of an inhomogeneous electron gas.
Abstract: We examine the short-range behavior of the spherically averaged Hartree–Fock exchange charge density by performing a simple Taylor expansion. On the basis of this expansion, a theoretical model is constructed that generates gradient correction terms to the local density approximation for the exchange energy of an inhomogeneous electron gas. In particular, we derive the Xαβ exchange energy functional and a theoretical value for the parameter β. Our value for β agrees well with previous empirical estimates, and with empirical calculations in the present work.
225 citations
TL;DR: In this article, an approximate multireference CI method is presented to reduce the number of variational parameters by grouping together configurations with the same internal parts and freezing their relative weights by the use of perturbation theory.
Abstract: An approximate multireference CI method is presented. By grouping together configurations with the same internal parts and freezing their relative weights by the use of perturbation theory, the number of variational parameters is drastically reduced. The loss of correlation energy is shown to be usually less than 2%, and the timing is less than one ordinary CI iteration. Examples from calculations on some states of the nitrogen atom and nitrogen molecule are given. The basis set convergence for the lowest excitation energy in the atom is very slow. Less than 50% of the correlation effect is obtained at the s, p, d limit. After the inclusion of ƒ functions this value is improved to 83%. The dissociation energies of the molecule also show slow basis set convergence with errors of 0.5 eV even after addition of ƒ functions. The bond distances are, howeever, accurately reproduced with errors of less than 0.005 A for all the states. A qualitative discussion of predissociation in the a1Πg and B3Πgstates caused by spin–orbit interaction with the 5Σg+ state, is finally presented. Rapidly oscillating lifetimes between the different vibrational states are predicted.
206 citations
TL;DR: An overview of band structure calculations on the fourth and fifth group transition metal monocarbides, mononitrides, and monoxides, published since the review article by Calais as mentioned in this paper, is given here.
Abstract: An overview is given here of band structure calculations on the fourth and fifth group transition metal monocarbides, mononitrides, and monoxides, published since the review article by Calais [J.-L. Calais, Adv. Phys. 26, 847 (1977)]. Furthermore, the relations of three categories of experimental properties, which allow insight into the electronic structure of the above mentioned compounds, and the results of band structure calculations are discussed. Theoretical predictions are compared with experimental findings. The considered experimental properties are valence band photoemission spectra, valence band x-ray emission spectra, and optical properties.
153 citations
TL;DR: The coupled-cluster single and double excitation model (CCSD) is applied to an energy path for the insertion of Be into H2 and compared to the full configuration interaction (FCI) and full valence-multiconfiguration self-consistent field (FV-MCSCF) results as mentioned in this paper.
Abstract: The coupled-cluster single and double excitation model (CCSD) is applied to an energy path for the insertion of Be into H2 and compared to the full configuration interaction (FCI) and full valence–multiconfiguration self-consistent field (FV–MCSCF) results. This model problem is a severe test of a single-reference-function correlated method since two configurations are heavily weighted in the FCI description. CCSD is demonstrated to describe the FCI results using a single reference function which, however, changes orbital characteristics along the sampling path. In this case CCSD gives excellent agreement with the FCI results.
133 citations
TL;DR: In this article, the chemical bonding in the interesting class of refractory transition metal compounds is illustrated for TiC, TiN, and TiO. The electron densities corresponding to the occupied valence states are obtained from the LAPW calculations.
Abstract: The chemical bonding in the interesting class of refractory transition metal compounds is illustrated for TiC, TiN, and TiO. Self-consistent augmented plane wave (APW) calculations are already available for these compounds. Using the respective potentials we have repeated the band calculations on a finer k grid with the linearized APW method to obtain accurate densities of states (DOS). These DOS can be divided into local partial contributions to characterize the bonding. Further information can be obtained from a decomposition of the metal dDOS into t2g and eg symmetry components. These partial local DOS are compared with the LCAO counterpart and give a first picture of the chemical bonding in these compounds. The electron densities corresponding to the occupied valence states are obtained from the LAPW calculations. They provide further insight into characteristic trends in the series from TiC to TiO: around the nonmetal site the density shows increasing localization; around the metal site the deviation from spherical symmetry changes from eg to t2g. These effects can be traced back to the three types of valence bands. Electron density plots of characteristic band states (all energies of a selected k point in the Brillouin zone) will be shown. These plots can describe the different types of bonding occurring in these systems.
107 citations
97 citations
TL;DR: In this article, the Hartree-Fock relation between the kinetic and the exchange energy density was used for the direct calculation of electron density ρ (r) in many-electron systems.
Abstract: A new density-functional equation is suggested for the direct calculation of electron density ρ (r) in many-electron systems. This employs a kinetic energy functional T 2 + f(r)T 0 , where T 2 is the original Weizsacker correction, T 0 is the Thomas-Fermi term, and f(r) is a correction factor that depends on both r and the number of electrons N. Using the Hartree-Fock relation between the kinetic and the exchange energy density, and a nonlocal approximation to the latter, the kinetic energy-density functional is written (in a.u.) t[ρ]=1/4∇ 2 ρ+1/8(∇ρ. ∇ρ)/ρ+C k f(r)ρ 5/3 , where C k =2/10(3π 2 ) 2/3 . Incorporating the above expression in the total energy density functional and minimizing the latter subject to N representability conditions for ρ(r) result in an Euler-Lagrange nonlinear second-order differential equation [-1/2∇ 2 + ν nuc (r) + ν cou (r) + ν XC (r) +5/3C k g(r)ρ 2/3 ] Φ(r)= μΦ(r) where μ is the chemical potential, we have ρ(r) = |(r)| 2 , and g(r) is related to f(r). Numerical solutions of the above equation for Ne, Ar, Kr, and Xe, by modeling f(r) and g(r) as simple sums over Gaussians, show excellent agreement with the corresponding Hartree-Fock ground-state densities and energies, indicating that this is likely to be a promising method for calculating fairly accurate electron densities in atoms and molecules.
94 citations
TL;DR: In this article, a new method for separating differently transmitted components of spin-spin coupling constants is introduced which is suitable when couplings are calculated using the coupled Hartree-Fock (CHF) approximation via the polarization propagator.
Abstract: A new method for separating differently transmitted components of spin-spin coupling constants is introduced which is suitable when couplings are calculated using the coupled Hartree-Fock (CHF) approximation via the polarization propagator. Contributions transmitted through different electronic subsystems are found choosing different subsets of orbitals with their corresponding virtual spaces for their description. Examples for two different channels of transmission are given, which are very well known among NMR spectroscopists, namely, components transmitted via a-electron systems, and “through-space” interactions. In the first case a set of canonical orbitals is chosen, while in the latter noncanonical ones are used. For both cases, numerical results are given within the INDO approximation. These results are compared with others obtained previously by means of the partially restricted molecular orbitals approach. The possibility of using this method of inner projections of the polarization propagator in decomposing other second orther properties is suggested.
78 citations
TL;DR: In this paper, a two-dimensional fully numerical relaxation approach for the electronic Schrodinger equation of linear molecules is presented for the lowest σ, π, δ, and ϕ states of H and HeH2+.
Abstract: A two-dimensional fully numerical relaxation approach is presented for the electronic Schrodinger equation of linear molecules. The method is tested on the lowest σ, π, δ, and ϕ states of H and HeH2+. About 10-figure accuracy is obtained for the orbital energies. Seven-point numerical formulas are given for first and second derivatives.
TL;DR: In this article, a modified scheme for SCF interaction energy decomposition has been proposed where the nonphysical basis set superposition error (BSSE) has been corrected by means of the counterpoise method.
Abstract: A modified scheme for SCF interaction energy decomposition has been proposed where the nonphysical basis set superposition error (BSSE) has been corrected by means of the counterpoise method. A new procedure to separate the exchange and induction energy terms free of nonphysical BSSE has been tested in the case of the H2O dimer. The first order BSSE appears to be non-negligible for strong hydrogen bonded complexes. In addition the scheme allows separation of the long-controversial charge-transfer contribution within the induction term, which has been considerably overestimated in previous studies.
TL;DR: In this article, the authors employ a localized orbital formulation in order to analyze the results in terms of local and charge-transfer excitations in the random phase approximation (RPA).
Abstract: The computational considerations involved in calculating ordinary and rotatory intensities and electronic excitation energies in the random phase approximation (RPA) are examined. We employ a localized orbital formulation in order to analyze the results in terms of local and charge-transfer excitations. Occupied orbitals are localized by the Foster–Boys procedure. The virtual space is transformed into a localized “valence” set that maximizes dipole strengths with the occupied counterparts, and a delocalized remainder. The two-electron integral transformation is performed with an efficient algorithm, based on Diercksen's, that generates only the particle–hole-type integrals required in the RPA. The lowest solutions of the RPA equations are obtained iteratively using a modification of the Davidson-Liu simultaneous vector expansion method. This allows the inclusion of the entire set of particle–hole states supported by a basis set of up to 102 orbitals. Calculations at this level give better excitation energies and intensities than SDCI methods, at substantial savings in computational effort. Comparative timings, computed results and analysis in terms of localized orbitals are given for planar and distorted ethylene using extended atomic orbital bases including diffuse functions. The results for planar ethylene are in excellent agreement with experiment.
TL;DR: In this paper, the problem of bond length alternation in cyclic polyene models as described by the Pariser-Parr-Pople π-electron Hamiltonian, together with an empirical quasi harmonic σ-core potential is investigated using the unrestricted Hartree-Fock wave function employing different spatial orbitals for different spins.
Abstract: The problem of bond length alternation in cyclic polyene models as described by the Pariser–Parr–Pople π-electron Hamiltonian, together with an empirical quasi harmonic σ-core potential is investigated using the unrestricted Hartree–Fock wave function employing different spatial orbitals for different spins. It is shown that in contrast to the restricted Hartree–Fock method, which favors bond alternation in large cyclic polyenes, the unrestricted Hartree–Fock method stabilizes the symmetric structures with equidistant internuclear separation. An assessment of the amount of correlation error recovered by the unrestricted Hartree–Fock procedure is examined and the qualitatively different behavior of the cyclic polyene models when described by restricted and unrestricted Hartree–Fock wave functions is discussed from this viewpoint.
TL;DR: Two-dimensional fully numerical solutions of the Hartree-Fock problem are reported for the singlet ground states of H−, He, H2, and HeH+ as discussed by the authors.
Abstract: Two-dimensional fully numerical solutions of the Hartree–Fock problem are reported for the singlet ground states of H−, He, H2, and HeH+. The H2 energy at R = 1.4 a.u. is −1.13362957 a.u.
TL;DR: In this article, a triple-valence basis set augmented by polarization functions on oxygens and the central proton was used to compute the transfer barrier in a number of systems.
Abstract: Proton transfers in a number of systems are investigated using ab initio molecular orbital methods. Calculations are carried out with several different basis sets ranging in size from 4–31G to 6–311G**. Electron correlation is included using Moller–Plesset (MP) perturbation theory to second and third orders. Enlargements of the basis set invariably lead to higher energy barriers to proton transfer, while substantial reductions result from inclusion of correlation effects. Application to (HOHOH)− of third-order MP theory with a triple-valence basis set augmented by polarization functions on oxygens and the central proton, denoted MP3/6–311G*(*), leads to excellent agreement with the results of Roos et al. whose calculations involved an extensive CI treatment with a large basis set. For equivalent hydrogen bond lengths, the transfer barrier in the cation (H2OHOH2)+ is nearly identical to that for the (HOHOH)− anion while the barrier in (H3NHNH3)+ is somewhat smaller. The reduction of the SCF barrier height resulting from inclusion of correlation is greater for (O2H3)− than for the above cations. The lowest energy structure of (O2H5)+ contains a symmetric hydrogen bond in which the proton is located midway between the two oxygens whereas asymmetric H bonds are found in the equilibrium geometries of (N2H7)+ and (S2H5)+. The difference in energy between the symmetric and asymmetric configurations of (O2H3)− is extremely small.
TL;DR: In this paper, the non-degenerate finite-order many-body perturbation theory is applied to simple model systems in which the degree of quasidegeneracy can be continuously varied over a wide range.
Abstract: The nondegenerate finite-order many-body perturbation theory is applied to simple model systems in which the degree of quasidegeneracy can be continuously varied over a wide range Three ab initio minimum basis set models involving four hydrogen atoms in various spatial arrangements are considered The results are compared with the exact full configuration-interaction approach, double-excitation configuration-interaction and the coupled-pair many-electron theory
TL;DR: In this article, the authors propose a more general definition of the concept of stabilization energy, namely /b SE/= Delta /b H/sub a/- Sigma /b N/sub AB//b E //sub AB/, where Delta is the heat of atomization of the species under consideration and the /b E//sub AB /'s are standard bond energy terms derived from the heats of atomisation of reference compounds.
Abstract: In the framework of the theoretical approach of the structure and reactivity of chemical intermediates the authors reexamine the concept of stability which is widely used by the experimentalists often without specifying its true meaning. The authors propose a more general definition of the concept of stabilization energy, namely /b SE/= Delta /b H//sub a/- Sigma /b N//sub AB//b E //sub AB/, where Delta /b H//sub a/ is the heat of atomization of the species under consideration and the /b E//sub AB /'s are standard bond energy terms derived from the heats of atomization of reference compounds. Using experimental heats of formation or semiempirical ones deduced from theoretical heats of reaction of appropriate isodesmic processes, the authors have calculated the stabilization energies of various types of chemical species: saturated, unsaturated and conjugated molecules, free radicals, carbocations, and carbanions. The results obtained can be rationalized in terms of steric hindrance, angular strain, polar interactions, electron delocalization, and substituent effects. Moreover, they have shown that heats of hydrogenation and bond dissociation energies do not provide accurate information on the thermodynamic stabilization of unsaturated compounds and free radicals, respectively. Among other applications the concept of stabilization energy allowed them to propose a detailed classification of free radicals and to rationalize their reactivity.
TL;DR: From theoretical considerations, three types of coherent excitations of biological systems have been suggested: (i) vibrations of membranes and proteins with frequencies above 109 Hz; (ii) near static excitation of a highly polar metastable state; and (iii) low frequency periodic enzyme reactions as discussed by the authors.
Abstract: From theoretical considerations, three types of coherent excitations of biological systems have been suggested: (i) vibrations of membranes and of proteins with frequencies above 109 Hz; (ii) near static excitation of a highly polar metastable state; and (iii) low frequency periodic enzyme reactions. Recent experimental evidence is discussed.
TL;DR: In this paper, the Hartree-Fock problem was used to test the quality of the basis sets used for the atomic helium Hartree Fock problem and the results indicated that momentum space properties are more poorly predicted than position space ones.
Abstract: The expectation values 〈rk〉 (−2 ⩽ k ⩽ 4, k = 10), values of the charge density ρ(r) at selected points, and coefficients in the MacLaurin expansion of ρ(r) are used to test the quality of 71 orbital basis sets used for the atomic helium Hartree–Fock problem. These tests in position space are complementary to the momentum space tests previously carried out [Int. J. Quantum Chem. 21, 419 (1982)]. Information theoretic measures with respect to either or both position and momentum space properties are subsequently defined and the orbitals are ranked accordingly. These measures indicate that, for a given orbital, momentum space properties are more poorly predicted than position space ones. Moreover an improvement in the virial ratio does not necessarily lead to a more balanced orbital with respect to position and momentum space properties. Basis sets containing Slater-type orbitals are again found to be rather accurate. The exponentially damped rational function is confirmed to be the outstanding two-parameter unconventional orbital.
TL;DR: In this paper, Moller-Plesset-type perturbation theory is applied to calculate electron correlation effects in infinite, periodic, metallic, and semiconducting polymers, and a very efficient version of the method using optimally localized Wannier functions has been worked out.
Abstract: Moller–Plesset-type perturbation theory is applied to calculate electron correlation effects in infinite, periodic, metallic, and semiconducting polymers. Different possible choices of the zeroth-order Hamiltonian (symmetry adapted Hartree–Fock, spin-, and charge-density waves), the influence of the size of the atomic basis sets, lattice and conduction band sums are investigated. In the case of semiconducting systems a very efficient version of the method using optimally localized Wannier functions has been worked out. Applications include model calculations for infinite atomic hydrogen chains, the investigation of the role of correlation effects in the bond alternation and metal-insulator phase transition in polyene, different one-and many-particle effects contributing to the single-particle gap in polyene, and the calculation of correlated quasiparticle band structures using the electronic polaron model.
TL;DR: In this paper, different methods for the calculation of the electron correlation contribution to atomic and molecular properties are analyzed and evaluated, based on the self-consistent solution of the external perturbation problem.
Abstract: Different methods for the calculation of the electron correlation contribution to atomic and molecular properties are analyzed and evaluated. The methods based on the self-consistent solution of the external perturbation problem are shown to offer several formal and computational advantages. The analysis of the correlation perturbation series for properties of many-electron systems indicates the importance of the appropriate treatment of unlinked diagrammatic contributions. In particular, the standard limited configuration interaction scheme based on single and double substitutions in the reference function may significantly suffer from the erratic treatment of unlinked clusters and needs to be corrected appropriately. The basis set choice for the calculation of highly accurate values of properties is also discussed. In order to circumvent the dimensionality problem the use of basis sets with explicit dependence on the external perturbation strength is recommended and methods for their choice and optimization are presented. A particular attention is paid to the many-body perturbation theory involving singly and doubly substituted intermediate states and based on the coupled Hartree–Fock solution for the one-electron perturbation problem. Different computational aspects of this method are discussed and compared with other techniques currently in use.
TL;DR: In this article, the expressions needed in INDO calculations for compounds containing 4f elements were derived and an INDO program suitable for lanthanoid compounds was written and tested, and the electronic structure of LnF3 and paramagnetic shift of NMR spectra of lnF were studied.
Abstract: Expressions needed in INDO calculations for compounds containing 4f elements were derived and an INDO program suitable for lanthanoid compounds was written and tested. Electronic structure of LnF3 and paramagnetic shift of NMR spectra of LnF were studied.
TL;DR: In this paper, the authors reviewed recent progress in multiconfiguration time-dependent Hartree-Fock (MC-TDHF) theory, and the generality of a formalism first put forward by Moccia [Int. J. Quantum Chemistry 8, 293 (1974)] is emphasized, and illustrative applications are discussed.
Abstract: Recent progress in multiconfiguration time-dependent Hartree–Fock (MC–TDHF) theory is reviewed. The generality of a formalism first put forward by Moccia [Int. J. Quantum Chemistry 8, 293 (1974)] is emphasized, and illustrative applications are discussed. A calculation of the frequency-dependent electric-dipole polarizability of the helium atom shows that even with a modest amount of CI, it is possible to achieve an accuracy comparable to that obtained by use of Hylleraas-type wave functions.
TL;DR: Three different algorithms for the calculations of many center electron-repulsion integrals are discussed, all of which are considered to be economic in terms of the number of arithmetic operations.
Abstract: Three different algorithms for the calculations of many center electron-repulsion integrals are discussed, all of which are considered to be economic in terms of the number of arithmetic operations. The common features of the algorithms are as follows: Cartesian Gaussian functions are used, integrals are calculated by blocks (a block being defined as the set of integrals obtainable from four given exponents on four given centers), and functions may be adopted to r(3). Adaptation to molecular point group symmetry is not considered. Tables are given showing the minimum number of operations for a selection of block types allowing one to identify the theoretically most economic, and the corresponding salient features. Comments concerning the computer implementations are also given both on scalar and vector processors. In particular, the Cyber 205 is considered, a vector processor on which the authors have implemented what they believe to be the most efficient algorithm. 19 references.
TL;DR: In this paper, the effects of adding ligands, exchanging hydrogens with methyl groups, and comparing nickel and palladium were studied using large scale contracted CI calculations, and four different models were treated, namely, NiH 2, PdH2, Ni(CH3)2, and Pd(H2O)2H2.
Abstract: Theoretical models for reductive elimination from transition metal containing molecules have been studied using large scale contracted CI calculations. Four different models were treated, namely, NiH2, PdH2, Ni(CH3)2, and Pd(H2O)2H2, in order to study the effects of adding ligands, exchanging hydrogens with methyl groups, and comparing nickel and palladium. The most interesting result already appeared for the simplest system NiH2. A closed-shell-type 1A1 state with a small bond angle of only 57° is bound compared to Ni and H2 with only a very small barrier for formation. The bond distance is short, shorter than in NiH, and the d orbitals are strongly involved in the binding. The hydrogen atoms bind both to nickel and to each other. With methyl groups rather than hydrogens, this double sided bonding situation is destroyed and Ni(CH3)2 has a negative binding energy with the carbon bonds pointing towards nickel. For PdH2 only a weakly bound complex between an essentially unchanged H2 and Pd was found. The bond distance is very long. Adding H2O ligands to Pd shortens the bond distance and significantly opens up the bond angle. The methods used in the investigation and the chemical implications of the results are discussed.
TL;DR: In this paper, a set of characteristic operators is proposed for decomposition of p-particle Hermitian operators to constitute irreducible components of the unitary group D = FDp, q = 0,1,2, p.
Abstract: A set of characteristic operators {F} is proposed for performing the decomposition of p-particle Hermitian operators {Dp} to constitute irreducible components {D} of the unitary group D = FDp, q = 0,1,2,…,p. For a deeper expolration of the properties of the characteristic operators, a few theorems are presented. As an illustration, the expected values for symmetric p-particle Hermitian operators are obtained as a number of terms having invariant group-theoretical meaning.
TL;DR: The applicability of the finite-order many-body perturbation theory to the electron correlation problem in extended one-dimensional systems is examined in this paper, where the second-order perturbations to the correlation energy are obtained with three different partitionings of the Hamiltonian (Huckel, M⊘ller-Plesset, and Epstein-Nesbet).
Abstract: The applicability of the finite-order many-body perturbation theory to the electron correlation problem in extended one-dimensional systems is examined. The cyclic polyenes CNHN, N = 4ν + 2, ν = 1, 2, …, with the DNh geometry as described by both the Pariser–Parr–Pople and Hubbard Hamiltonians, are employed to model the metallic-like one-dimensional systems. The second-order perturbation theory contributions to the correlation energy are obtained with three different partitionings of the Hamiltonian (Huckel, M⊘ller–Plesset, and Epstein–Nesbet). The third- and fourth-order contributions are also calculated in special cases. A comparison with other methods is given wherever available. For the Hubbard Hamiltonian the asymptotic behavior of the perturbation theory expansion is examined numerically. It is shown that the finite-order perturbation expansion can provide reliable results for the correlation energy of one-dimensional systems even in the correlation region which corresponds to the spectroscopically determined physical value of the coupling constant.
TL;DR: In this paper, the electron density and the molecular electrostatic potential of β-carbolines were studied using ab initioSTO-3G wave functions using a previous model built with monoamine oxidase substrates and irreversible inhibitors.
Abstract: The electron density and the molecular electrostatic potential of the β-carbolines are studied using ab initioSTO-3G wave functions. The analysis was done from the point of view of a previous model built with monoamine oxidase substrates and irreversible inhibitors. The results confirm the usefulness of the model and make it possible to propose new precision to the molecular electrostatic potential patterns needed to have monoamine oxidase inhibitory activity.
TL;DR: In this article, a self-consistent field approximation allowing for a change of coordinates is applied to a model of two coupled oscillators considered by Davis and Heller [J. Chem. Phys. 75, 246 (1981)].
Abstract: A self-consistent field approximation allowing for a change of coordinates is applied to a model of two coupled oscillators considered by Davis and Heller [J. Chem. Phys. 75, 246 (1981)]. The model accounts well for the unsymmetrical nonstationary states involved in the quantum dynamical tunneling phenomenon.