Showing papers in "International Journal of Quantum Chemistry in 1996"

Relativistic regular two-component Hamiltonians.

Abstract: It is shown how the regularized two-component relativistic Hamiltonians of Heully et al. and Chang, Pelissier, and Durand can be viewed as arising from a perturbation expansion that unlike the Pauli expansion remains regular even for singular attractive Coulomb potentials. The performance of these approximate Hamiltonians is tested in the framework of the local density approximation and the relation of their spectrum to that of the Dirac Hamiltonian is discussed. The circumstances under which the current approximations are superior to the Pauli Hamiltonian are analyzed. Finally, it shown how the Hamiltonians could be used within the context of conventional Hartree-Fock theory. © 1996 John Wiley & Sons, Inc.

Calculations of molecules, clusters, and solids with a simplified LCAO-DFT-LDA scheme

Abstract: A simplified LCAO-DFT-LDA scheme for calculations of structure and electronic structure of large molecules, clusters, and solids is presented. Forces on the atoms are calculated in a semiempirical way considering the electronic states. The small computational effort of this treatment allows one to perform molecular dynamics (MD) simulations of molecules and clusters up to a few hundred atoms as well as corresponding simulations of condensed systems within the Born-Oppenheimer approximation. The accuracy of the method is illustrated by the results of calculations for a series of small molecules and clusters. © 1996 John Wiley & Sons, Inc.

Application of localized molecular orbitals to the solution of semiempirical self-consistent field equations

Abstract: When conventional matrix algebra is used to solve the semiempirical self-consistent field equations for large systems, the time required rises as the third power of the size of the system. A consequence of this is that self-consistent calculations of large systems such as enzymes are impractical. By using localized molecular orbitals instead of matrix methods, the time required for these systems can be made almost proportional to the size of the system. In partial geometry optimizations, the time required depends only upon the size of the fragment being optimized and is almost independent of the size of the whole system. © 1996 John Wiley & Sons, Inc.

Comparison shopping for a gradient-corrected density functional

Abstract: mGradient corrections to the local spin density (LSD) approximation for the exchangecorrelation energy are making density functional theory as useful in quantum chemistry as it is in solid-state physics. But which of the many gradient-corrected density functionals should be preferred a priori? We make a graphical comparison of the gradient dependencies of some popular approximations, discussing the exact formal conditions which each obeys and identifying which conditions seem most important. For the exchange energy, there is little formal or practical reason to choose among the Perdew-Wang 86, Becke 88, or Perdew-Wang 91 functionals. But, for the correlation energy, the best formal properties are displayed by the nonempirical rw91 correlation functional. Furthermore, the real-space foundation of rw91 yields an insight into the character of the gradient expansion which suggests that rw91 should work especially well for solids. Indeed, while improving dissociation energies over LSD, rw91 remains the most "local" of the gradient-corrected exchange-correlation functionals and, thus, the least likely to overcorrect the subtle errors of LSD for solids. To show that our analysis of spin-unpolarized functionals is sufficient, we also compute spin-polarization energies for atoms, finding ~w91 values only slightly more negative than SD values. Wiley & Sons, Inc. 0 1996 John

Atomic shell structure and electron numbers

Abstract: rn The electron localization function (ELF) was calculated for the atoms Li to Sr The ELF maxima reveal the atomic shell structure for all these atoms The shells are separated from each other by ELF minima The integration of the electron density in a shell gives electron numbers For the valence shell those are in good agreement with the ones expected from the Periodic Table of Elements 0 1996 John Wiley & Sons, Inc

Calculation of intramolecular force fields from second‐derivative tensors

Abstract: A practical procedure (FUERZA) to obtain internal force constants from Cartesian second derivatives (Hessians) is presented and discussed. It allows a systematic analysis of pair atomic interactions in a molecular system, and it is fully invariant to the choice of internal coordinates of the molecule. Force constants for bonds or for any pair of atoms in general are defined by means of the eigenanalysis of their pair interaction matrix. Force constants for the angles are obtained from their corresponding two-pair interaction matrices of the two bonds or distances forming the angle, and the dihedral force constants are similarly obtained using their corresponding three-pair interaction matrices. © 1996 John Wiley & Sons, Inc.

DNA base amino groups and their role in molecular interactions: Ab initio and preliminary density functional theory calculations

Abstract: Interactions of DNA bases frequently involve the DNA base amino groups. In contrast to the empirical force fields, the ab initio calculations predict nonplanar DNA base amino groups. The same conclusion also follows from the density functional theory (DFT) calculations. Both local and nonlocal density approximations were used. Optimized geometries of two other molecules with nonplanar amino groups (aniline, formamidine) are presented for comparison. The influence of nonplanar DNA base amino groups on the conformational variability of DNA is discussed. © 1996 John Wiley & Sons, Inc.

Comparison of perturbative and multiconfigurational electron propagator methods

Abstract: Ionization energies below 20 eV of 10 molecules calculated with electron propagator techniques employing Hartree-Fock orbitals and multiconfigurational self-consistent field orbitals are compared. Diagonal and nondiagonal self-energy approximations are used in the perturbative formalism. Three diagonal methods based on second- and third-order self-energy terms, all known as the outer valence Green's function, are discussed. A procedure for selecting the most reliable of these three versions for a given calculation is tested. Results with a polarized, triple ζ basis produce root mean square errors with respect to experiment of approximately 0.3 eV. Use of the selection procedure has a slight influence on the quality of the results. A related, nondiagonal method, known as ADC(3), performs infinite-order summations on several types of self-energy contributions, is complete through third-order, and produces similar accuracy. These results are compared to ionization energies calculated with the multiconfigurational spin-tensor electron propagator method. Complete active space wave functions or close approximations constitute the reference states. Simple field operators and transfer operators pertaining to the active space define the operator manifold. With the same basis sets, these methods produce ionization energies with accuracy that is comparable to that of the perturbative techniques. © 1996 John Wiley & Sons, Inc.

Modification of the Roothaan equations to exclude BSSE from molecular interaction calculations

Abstract: The Roothaan equations have been modified to compute molecular interactions between weakly bonded systems at the SCF level of theory without the basis set superposition error (BSSE). The increase in complication with respect to the usual SCF algorithm is negligible. Calculation of the SCF energy on large systems, such as nucleic acid pairs, does not pose any computational problem. At the same time, it is shown that a modest change in basis-set quality from 3-21G to 6-31G changes the binding energy by about 50% when computed according to standard SCF “supermolecule” techniques, while remaining practically constant when computed without introducing BSSE. Bader analysis shows that the amount of charge transferred between the interacting units is of the same order of magnitude when performed on standard SCF wave functions and those computed using the new method. The large difference between the corresponding computed energies is thus ascribed to the BSSE. © 1996 John Wiley & Sons, Inc.

Enzyme mechanisms with hybrid quantum and molecular mechanical potentials.i. theoretical considerations

Abstract: The application of hybrid quantum mechanical and molecular mechanical (QM/MM) potentials to the study of chemical reactions in enzymes is outlined. The discussion is general and addresses the difficulties encountered in an enzyme QM/MM study. First, general criteria for determining whether a particular enzyme is an appropriate candidate for a QM/MM approach are outlined. Methods for obtaining starting structures are detailed. The importance of choosing appropriate levels of ab initio or semiempirical theory is emphasized. Approaches for interfacing the QM and MM regions are briefly discussed, with greater detail given to describing our CHARMM-GAMESS interface. Techniques for partitioning the system into QM and MM regions are explored. Link atom placement, as distant from reacting atoms as possible within the confines of computational efficiency, is examined in some detail. Methods for determining reaction paths are also discussed. © 1996 John Wiley & Sons, Inc.

Structural homeomorphism between the electron density and the virial field

Abstract: The virial field V(r) is defined by the local statement of the quantum mechanical virial theorem, as the trace of the Schrodinger stress tensor. This field defines the electronic potential energy density of an electron at r and integrates to minus twice the electronic kinetic energy. It is the most short-ranged description possible of the local electronic potential energy and it exhibits the same transferable behavior over bounded regions of real space (corresponding to the functional groups of chemistry) as does ρ(r). This article establishes a structural homeomorphism between −V(r) and ρ(r), showing that the two fields are homeomorphic over all of the nuclear configuration space. The stable or unstable structure defined by the gradient vector field Δρ(r; X) for any configuration X of the nuclei can be placed in a one-to-one correspondence with a structure defined by the field −ΔV(r; X′). In particular, a molecular graph for ρ(r) defining a molecular structure is mirrored by a corresponding virial graph for V(r) and the lines of maximum density linking bonded nuclei in the former field are matched by a set of lines of maximally negative potential energy density in the latter. The homeomorphism is also geometrically faithful, an equilibrium geometry in general, exhibiting equivalent structures in the two fields. The demonstration that the virial field, whose integrated value equals twice the total energy, is essentially just a locally scaled version of the electron density is suggestive of possible new approaches in density functional theory. © 1996 John Wiley & Sons, Inc.

A test of the new “integrated MO + MM” (IMOMM) method for the conformational energy of ethane and n‐butane

Abstract: Test calculations of the newly developed “Integrated Molecular Orbital + Molecular Mechanics” (IMOMM) method were performed for the optimized equilibrium and transition structures and energies of ethane and n-butane. In this method, the total energy of a large molecular system is expressed as a sum of the MO energy of the small “model” system and a modified MM energy of the “real” system, and full geometry optimization is carried out using the gradient of this total energy. Various schemes of partition of the system into the MO part and the MM part, including some not intended in the original design of the method, were examined and compared with the pure ab initio MO and the pure MM results. In most reasonable partition schemes, the IMOMM method can reproduce the pure ab initio and the pure MM geometries and energies quite well. © 1996 John Wiley & Sons, Inc.

The Wiener polynomial of a graph

Abstract: rn The Wiener index is a graphical invariant that has found extensive application in chemistry. We define a generating function, which we call the Wiener polynomial, whose derivative is a q-analog of the Wiener index. We study some of the elementary properties of this polynomial and compute it for some common graphs. We then find a formula for the Wiener polynomial of a dendrimer, a certain highly regular tree of interest to chemists, and show that it is unimodal. Finally, we point out a connection with the Poincar6 polynomial of a finite Coxeter group. 0 1996 John Wiley & Sons, Inc.

The calculation of NMR shielding tensors based on density functional theory and the frozen‐core approximation

Abstract: The application of the frozen-core approximation to the calculation of the shielding tensor of nuclear magnetic resonance (NMR) spectroscopy is discussed and an implementation is presented. A complete formulation of the shielding calculation within the frozen-core approximation is given, both in general terms and for the special case of density functional theory (DFT) and “gauge including atomic orbitals” (GIAOs). The practical implementation is validated by a detailed discussion of the consequences of the approximation. The general conclusion is drawn that the frozen-core approximation is a useful tool for shielding calculations—if the valence space is increased to contain at least the ns, np, (n − 1)p, (n − 1)d (fourth period and higher) shells, where n is the number of the given period in the periodic table of elements. The new method is applied to 77Se shieldings and chemical shifts for a small number of compounds. The agreement between theory and experiment is good for relative shifts, whereas calculated absolute shieldings are generally too small by about 300–400 ppm. This difference is attributed to the relativistic contraction of the core density at the selenium atom that had been explicitly incorporated into the experimental absolute shielding scale. © 1996 John Wiley & Sons, Inc.

Molecular polarization potential maps of the nucleic acid bases

Abstract: Ab initio calculations at the SCF level were carried out to compute the polarization potential map NM of the nucleic acid bases: cytosine, thymine, uracil, adedine, and guanine For this purpose, the Dunning`s 9s5p basis set contracted to a split-valence, was selected to perform the calculations The molecular polarization potential (MPP) at each point was evaluated by the difference between the interaction energy of the molecule with a unit point charge and the molecular electrostatic potential (MEP) at that point MEPS and MPPS for the different molecules were computed with a density of 5 points/{Angstrom}{sup 2} on the van der Waals surface of each molecule, defined using the van der Waals radii Due to the symmetry of the molecules, only half the points were computed The total number of points calculated was 558 for cytosine, 621 for thymine, 526 for uracil, 666 for adenine, and 699 for guanine The results of these calculations are analyzed in terms of their implications on the molecular interactions between pairs of nucleic acid bases 23 refs, 5 figs, 1 tab

Ring currents in aromatic hydrocarbons

Abstract: Coupled Hartree-Fock theory is used to compute and map the current density induced in planar hydrocarbons by an external magnetic field. Results of useful accuracy can be obtained with modest (6-31G**) basis sets by employing a continuous gauge transformation. Maps are presented and discussed for benzene, naphthalene, anthracene, tetracene, pentacene, heptacene, and biphenylene. © 1996 John Wiley & Sons, Inc.

Hybrid classical quantum force field for modeling very large molecules

Abstract: A coherent computational scheme on a very large molecule in which the subsystem that undergoes the most important electronic changes is treated by a semiempirical quantum chemical method, though the rest of the molecule is described by a classical force field, has been proposed recently The continuity between the two subsystems is obtained by a strictly localized bond orbital, which is assumed to have transferable properties determined on model molecules The computation of the forces acting on the atoms is now operating, giving rise to a hybrid classical quantum force field (CQFF) which allows full energy minimization and modeling chemical changes in large biomolecules As an illustrative example, we study the short hydrogen bonds and the proton-exchange process in the histidine-aspartic acid system of the catalytic triad of human neutrophil elastase The CQFF approach reproduces the crystallographic data quite well, in opposition to a classical force field The method also offers the possibility of switching off the electrostatic interaction between the quantum and the classical subsystems, allowing us to analyze the various components of the perturbation exerted by the macromolecule in the reactive part Molecular dynamics confirm a fast proton exchange between the three possible energy wells The method appears to be quite powerful and applicable to other cases of chemical interest such as surface reactivity of nonmetallic solids © 1996 John Wiley & Sons, Inc

STOP: A slater‐type orbital package for molecular electronic structure determination

Abstract: A general ab initio package using Slater-type atomic orbitals is presented. This package, called STOP, uses the one-center two-range expansion method to evaluate the multicenter electronic integrals. Thoroughly optimized numerical techniques, in particular, convergence accelerators and suitable Gauss quadratures, are used in the algorithms which provide accurate numerical values for all these integrals. STOP thus provides wavefunctions for general molecular structures at the self-consistent field level for the first time over a Slater-type orbital basis. © 1996 John Wiley & Sons, Inc.

Note on the generation of Gaussian bases for pseudopotential calculations

Abstract: We present a technique to generate Cartesian Gaussian bases for electronic configuration and cross-section calculations on molecules. The technique is specially useful for pseudopotential work, when the bases cannot be tabulated because they depend on the specific choice of the pseudopotential. © 1996 John Wiley & Sons, Inc.

Attempts toward a pair density functional theory

Abstract: A generalized density functional theory (DFT) is proposed based on a generalized Hohenberg-Kohn theorem with the pair density as the key quantity and the kinetic energy as a universal functional of the pair density. It is assumed that there exists an effective interaction potential which, via the corresponding two-particle (2P) Schrodinger equation, generates 2P orbitals (geminals) from which follows the pair density, just as in the conventional DFT the density follows from 1P orbitals (as the solutions of an effective 1P Schrodinger equation). According to three different representations (natural spectral resolutions) of the pair density or the cumulant pair densities in terms of geminals, three versions of a pair DFT (PDFT) are formally sketched. Also considered are the relation between electron correlation and particle-number fluctuations in fragments of the system and the use of the pair density for an estimation of such fluctuations. © 1996 John Wiley & Sons, Inc.

Basis sets for ab initio periodic Hartree—Fock studies of zeolite/adsorbate interactions: He, Ne, and Ar in silica sodalite

Abstract: Silica sodalite is an ideal model system to establish base-line computer requirements of ab initio periodic Hartree-Fock (PHF) calculations of zeolites. In this article, the authors investigate the effect of various basis sets on the structural and electronic properties of bulk silica sodalite. They also study the interaction of He, Ne, and Ar with the sodalite cage. This work shows that basis-set superposition errors (BSSE) in calculations using STO-3G and 6-21G(*) basis sets are as large as the interaction energies, leading to poor confidence in the results. To cure this problem, the authors present high-quality basis sets for si, O, He, Ne, and Ar, optimized for use with PHF methods, and demonstrate that the new basis set greatly reduces BSSE. The theoretical barriers for transfer of the rare gases between sodalite cages are 5.6, 13.2, and 62.1 kcal/mol for He, Ne, and Ar. 27 refs., 6 figs., 8 tabs.

Calculation of bond dissociation energies for oxygen containing molecules by ab initio and density functional theory methods

Abstract: Two ab initio (ROHF and MP2), one local (SVWN), four hybrid (BHandH, BHandHLYP, Becke3LYP, and Becke3P86), and two nonlocal (BLYP and BP86) density functional theory (DFT) methods are used for calculating the dissociation energies of molecules that contain H(SINGLE BOND)O, O(SINGLE BOND)O and O(SINGLE BOND)C bonds. The sensitivity to the basis set of the prediction of bond dissociation energies with DFT methods was tested with Becke3LYP on the H(SINGLE BOND)O dissociation energy of water. The 6–31 + G(d) methods are chosen as the smallest basis set which produces reasonable results. The calculated values for all other ab initio and DFT methods were performed with these basis sets and then compared with the experimental data. The suitability of DFT methods for computing reliable bond dissociation energies of oxygen containing molecules is discussed. © 1996 John Wiley & Sons, Inc.

Density functional calculations of difluorodiazete structures with Gaussian-orbital-type approach

Abstract: The comparison of local nonlocal and hybrid DFT methods with RHF, MP2, CCSD, and CPF ab initio methods in generating geometries and relative energies of cis- and trans-difluorodiazete, SVWN, BLYP, BP86, BECKE3LYP, and BECKE3P86 DFT methods with 6-311 + g(2d) and 6-311 + + g(3df) basis sets. The geometries generated with RHF ab initio models are quite different from experimental values and energy evaluation prefers the wrong isomer. The hybrid methods give superior geometries while energies evaluated with nonlocal DFT methods are better than the one obtained with MP2 or CCDS ab initio methods. The results suggest DFT as the method of choice of studying similar systems. © 1996 John Wiley & Sons, Inc.

Interatomic potential for theX1?+g state of Be2

Abstract: An extended geminal model has been applied to determine the interatomic potential for the X1Σ+g state Be2. By adopting a [11s, 9p, 6d, 4f, 2g] contracted Gaussian-type basis, the following potential minimum parameters are obtained: Re = 4.67 a.u. (4.63 a.u.) and De = 3.70 mH (3.82 ± 0.05 mH), experimental values in parentheses. A calculation with a nuclei-centered [9s, 7p, 4d, 2f, 1g] GTO basis plus two sets of bond-type function, each set comprising diffuse (2s, 2p, 2d, 2f, 1g) GTOs, yielded −3.79 mH as the value of the potential at R = 4.63 a.u. On the basis of an error analysis the best theoretical estimate of the binding energy is determined to be 3.83 ± 0.08 mH. The calculated value for the fundamental vibrational frequency is v01 = 224.7 cm−1 (exp. = 224 ± 3 cm). © 1996 John Wiley & Sons, Inc.

Direct reaction field force field: A consistent way to connect and combine quantum-chemical and classical descriptions of molecules

Abstract: The direct reaction field (DRF) force field gives a classical description of intermolecular interactions based on ab initio quantum-chemical descriptions of matter. The parameters of the DRF force field model molecular electrostatic and response properties, which are represented by distributed charges and dipole polarizabilities. The advantage of the DRF force field is that it can be combined transparently with quantum-chemical descriptions of a part of a large system, such as a molecule in solution or an active site in a protein. In this study, the theoretical basis for the derivation of the parameters is reviewed, paying special attention to the four interaction components: electrostatic, induction, dispersion, and repulsion. The ability of the force field to provide reliable intermolecular interactions is assessed, both in its mixed quantum-chemical-classical and fully classical usage. Specifically, the description of the water dimer and the solvation of water in water is scrutinized and seen to perform well. The force field is also applied to systems of a very different nature, viz. the benzene dimer and substituted-benzene dimers, as well as the acetonitrile and tetrachloromethane dimers. Finally, the solvation of a number of polar solutes in water is investigated. It is found that as far as the interaction energy is concerned, the DRF force field provides a reliable embedding scheme for molecular environments. The calculation of thermodynamic properties, such as solvation energy, requires better sampling of phase space than applied here. (C) 1996 John Wiley & Sons, Inc.

Comparative study of DFT methods applied to small titanium oxygen compounds

Abstract: The performance of a number of different local and nonlocal density functional theory (DFT) methods has been investigated for some small titanium-oxygen systems. Equilibrium geometries, ionization potentials, dipole moments, atomization energies, and harm