Showing papers in "International Journal of Quantum Chemistry in 1988"

Three-dimensional numerical integration for electronic structure calculations

Abstract: Two three-dimensional numerical schemes are presented for molecular integrands such as matrix alements of one-electron operators occuring in the Fock operator and expectation values of one-electron operators describing molecular properties. The schemes are based on a judicious partitioning of space so that product-Gauss integration rules can be used in each region. Convergence with the number of integration points is such that very high accuracy (8–10 digits) may be obtained with obtained with a modest number of points. The use of point group symmetry to reduce the required number of points is discussed. Examples are given for overlap, nuclear potential, and electric field gradient integrals.

A progress report on the status of the COLUMBUS MRCI program system

Abstract: The COLUMBUS program system is a collection of Fortran programs for performing general multireference single- and double-excitation configuration interaction (MRSDCI) wave function optimization based on the graphical unitary group approach. The program system also includes integral generation, SCF and MCSCF orbital optimization, integral transformation, and wave function analysis programs. The original program system was written in 1980 to 1981. Since that time, it has evolved into one of the most popular MRSDCI program systems used in the computational chemistry community. The discussion of this evolution will include the exploitation of efficient matrix-matrix and matrix-vector product computational kernels, the use of generally contracted symmetry-adapted orbital basis sets, general Hamiltonian diagonalization procedures, energy-based internal walk selection, flexible DRT specification, improved coupling-coefficient evaluation methods, coupled-pair functional and multireference CPF capabilities, and density matrix construction. The numerous versions of the program system that are maintained at different sites and on different computers are now in the process of being merged. The source code for this combined version will be made available to the computational chemistry community. The source code for a specific computer may be generated from the source code for another computer by a single pass through a simple filter utility that is included with the program system. The directly supported computers will initially include various models of VAX, Cray, FPS, IBM, CDC, and ETA machines with the addition of other machines shortly thereafter. The ongoing developments of the COLUMBUS system that are discussed include a new method for computing analytic energy gradients for MRSDCI wave functions. This effective-density-matrix based method avoids the “coupled perturbed MCSCF” solutions for each coordinate direction, avoids the transformation of any derivative-integral quantities from the AO to the MO basis, avoids the transformation of the coupling coefficients from the MO to the AO basis, allows a subset of the MCSCF doubly occupied orbitals to be frozen in the CI wave function, and allows the MRSDCI wave function to be generated from general reference CSFs that are not necessarily related to the MCSCF expansion CSFs.

A coupled‐cluster method for quasidegenerate states

Abstract: A size-extensive, multireferences coupled-cluster method for studies of quasidegenerate states based on the Jeziorski–Monkhorst [16] ansatz for the cluster operator (Ω = ∑ePj, where the sum is extended over the configurations spanning the model space), is presented and applied in pilot calculations. The method is referred to as multireference coupled electron-pair method (MR CEPM), because it is assumed that the individual cluster operators can be approximated by their two-body parts, i.e., Tj ≈ Tj(2). The linear version of this method (MR L-CEPM) is also discussed. Both methods are applied to two simple model systems: (1) a minimum basis set model involving eight hydrogen atoms in various spacial arrangements for which the degree of quasidegeneracy can be continuously varied; (2) a model involving the C2ν insertion of Be into H2. For the first time in multireference coupled-cluster calculations, the nonlinear parts of the equations are completely accounted for. The MR CEPM results are very encouraging for strongly quasidegenerate states. The MR L-CEPM results are slightly below the accurate (FCI) values.

A spin‐free form of valence bond theory

Abstract: Classical valence bond theory is recast in a spin-free form which provides a practicable route to ab initio calculations of molecular electronic structure. The approach is simple and direct and requires only efficient algorithms for the generation and processing of permutations and the handling of Rumer diagrams: it makes modest demands on computing power and pilot calculations have indeed been performed entirely within the fast memory of a personal computer, which should be sufficient for dealing with systems possessing up to 10 electrons outside a closed shell. Simple applications confirm the conclusion of Cooper et al. [1] that, by using strongly overlapping orbitals, a small number of classical (nonpolar) structures can give results close to those obtained in a “full CI” calculation.

Molecular hardness and softness parameters and their use in chemistry

Abstract: The semiempirical Atoms-in-a-Molecule (AIM) hardness matrix, η, is defined, using the usual finite difference formula, ηii = Ii – Ai, for the diagonal AIM hardness and the Ohno formula, ηij = 1/(a2 + R)1/2, for the off-diagonal AIM hardness. The Ohno formula is shown to exhibit the correct asymptotic behavior and satisfies the relevant stability criterion. The normal displacements in the AIM electron populations are examined for pyrrole and N-methyl pyrrole, and their relation to the polarization channels is briefly discussed. The new AIM hardness matrix is also tested by comparing the predicted global hardnesses with the corresponding experimental finite difference data for selected diatomics and triatomics. Finally implications of the hardness combination rules are examined and the corresponding softness combination rules are used to calculate the regional and global softnesses of selected molecules. We examine how the regional softnesses reflect known trends in selectivity of protonation of five membered heterocycles, and comment on the signs of the AIM fukui function and the Hard-Soft-Acids-and-Bases principle.

Modified all-valence INDO/spd method for ground and excited state properties of isolated molecules and molecular complexes

Abstract: A new semiempirical all-valence method, GRINDOL (Ghost and Rydberg INDO), based on the INDO approximation, is described. Linderberg–Seamans relation (extended to the d and Rydberg orbitals) for the resonance integrals and a new semitheoretical expression for the core-core repulsion term and energy correction including basis-set superposition error (intermolecular as well as intramolecular) has been applied. The proposed method enables calculation of ground and excited state properties. The ground state results (including intermolecular interactions) as well as the spectral properties are in reasonable agreement with relevant experimental (or ab initio) studies for isolated molecules, molecular complexes, and transition metal compounds. The method contains only one adjustable parameter, all two-center integrals and terms are only basis-set dependent. The one-center integrals are evaluated from the respective atomic terms.

The use of symmetry in reciprocal space integrations. Asymmetric units and weighting factors for numerical integration procedures in any crystal symmetry

Abstract: A systematic collection of spatial domains for reciprocal space integrations is derived for all possible crystal symmetries. This set can be used as a simpler alternative to the conventional Brillouin zones. The analysis is restricted to integrations where the function in the integrand satisfies inversion symmetry in k space. In this case only 24 different spatial domains have to be defined in order to allow for k space integrations in the 230 different crystal symmetries. A graphic representation of the asymmetric unit for each of the 24 integration domains is given. Special positions and the associated weighting factors required for numerical integrations in theoretical solid-state approaches are tabulated.

A combined density functional and configuration interaction method

Abstract: Correlation energies are divided into two parts. One contribution is given by a configuration interaction calculation in the space of the natural orbitals with occupation numbers larger than an arbitrary threshold u. The remaining part is obtained from a u-dependent functional of the electronic density. Representative examples (for which the existing spin-density functionals fail) are (1) the correlation energies in the He and Be series and (2) the contribution of the correlation energy to the dissociation energy of the first-row dimers. It is shown that even for large values of v the errors remain on the order of 0.01 hartree.

Calculation of harmonic frequencies and harmonic force fields by the hartree‐fock‐slater method

Abstract: Results are presented from Hartree-Fock-Slater (HFS) calculations on harmonic frequencies and force constants of H2O, H2S, NH3, PH3, CH4, SiH4, and C2H4. Both frequencies and force constants were calculated by a numerical (finite difference) differentiation of analytical energy gradients. It is shown by a comparison with experimental data and results from ab initio Hartree-Fock (HF) calculations that the HFS-method provides harmonic frequencies and force constants in at least as good agreement with experiment as the HF-scheme.

Viewing the born model for ion hydration through a microscope

Abstract: The hydration-free energy, energy, and entropy of monovalent ions are calculated using the extended RISM integral equation theory and computer simulations. Plots of these thermodynamic quantities against 1/R, where R is the Lennard–Jones radius, lie on two distinct curves corresponding to cations and anions. This result is attributed to differences in the microscopic structure of solvent surrounding the ions. Charge distribution functions are used to analyze solvent structure. It is found that the modified Born formula proposed by the Latimer et al. gives good agreement with the RISM results for the energy and the free energy, but not for the entropy. A microscopic interpretation of Latimer formula is attempted in light of the statistical mechanical theory.

A practical solution to the “unknown normalization” problem

Abstract: We analyze the theoretical basis of a procedure to determine an unknown normalization factor in discretized wave functions, which we have successfully used in a series of calculations of resonance widths for atomic and molecular systems. By reducing this determination to that of a suitable interpolation function for the energy eigenvalues, the problem is easily solved when atomic basis sets are chosen according to simple rules. Illustrations of our procedure are presented for atomic, molecular, and model systems; renormalized wave functions are compared with the exact ones for these model systems. The resulting method of renormalized continuum wave functions has a wide range of application in the study of long-lived quasibound states (predissociation, autoionization, photoionization, unimolecular reactions, etc.).

On characterization of three-dimensional structures†

Abstract: Molecular descriptors currently used in structure–property–activity studies are based on molecular graphs rather than on a structure as a three-dimensional object. Here we suggest a way to amend graph-theoretic invariants with additional geometric information, thereby providing new molecular descriptors for possible use in quantitative structure–activity correlations. In the approach we assume molecular structures embedded on a regular grid. As an illustration we consider first chains of different length embedded on graphite-like lattice. Subsequently, we consider all possible conformations of hexatriene. Although the cases considered here relate to graphite-like lattice, the approach is general and applies to embedings of molecules on three-dimensional lattices, or, in general, to molecules of arbitrary spatial conformations.

A survey of optimization procedures for stable structures and transition states

Abstract: We examine a variety of methods for obtaining the stable geometry of molecules and the transition states of simple systems and summarize some of our findings. We find the most efficient methods for optimizing structure to be those based on calculated gradients and estimated second derivative (Hessian) matrices, the later obtained either from the Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton update method or from approximations to the coupled perturbed Hartree–Fock method. For uncovering transition states we find particularly useful a variety of the augmented Hessian theory used to uncover regions of the potential energy hypersurface with one and only one negative eigenvalue of the Hessian matrix characterizing the catchment region of the transition state. Once this region is found we minimize the norm of the gradient vector to catch the nearest extreme point of the surface. Examples of these procedures are given.

Partial fourth order electron propagator theory

Abstract: Third order diagonal self-energies are augmented with fourth order terms that are easily determined from by-products of a third order calculation. Comparisons are made with the outer valence approximation, a method for estimating fourth and higher order terms. The number of operations needed for all of these procedures is less than the number required for the limited two electron integral transformation. Improved one-electron reduced density matrices are another useful by-product of these calculations. The present methods are applied to calculating the ionization energies and dipole moments of the anions F−, OH−, NH, Cl−, SH−, PH2−, and CN−. The basis sets used in these calculations have been shown to be sufficiently flexible in a variety of calculations.

Inclusion of relativistic effects into ZDO methods. III. A. Quasi‐relativistic INDO/1 version

Abstract: The quasi-relativistic CNDO/1 method for molecular orbital calculations has been extended to the INDO/1 version where all monocentric repulsion integrals are taken into account. This version has been applied to calculate molecular geometries of MXn-type molecules, with the central atom belonging to from the second to seventh period. Properties of hypothetical superheavy elements (Z = 110–117) have been predicted. Transition metal complexes of the MCl-type (M = Ni, Pd, Pt, and ePt) have been investigated from the point of view of spin-state and configuration stability.

A Crystal Orbital approach for two‐ and three‐dimensional solids on the basis of CNDO/INDO Hamiltonians. Basis equations

Abstract: A Hartree–Fock (HF) self-consistent field (SCF) crystal orbital (CO) formalism for two- and three-dimensional (2D/3D) solids on the basis of semiempirical CNDO/INDO (complete neglect of differential overlap; intermediate neglect of differential overlap) Hamiltonians is presented. The employed SCF variants allow for the treatment of atomic species up to bromine under the inclusion of the first (i.e., 3d) transition metal series. Band structure investigations of 2D and 3D materials containing more than 30 atoms per unit cell are feasible by the present SCF HF CO formalism. The theoretical background of the computational scheme is given in this contribution. Special emphasis is placed on physically reliable truncation criteria for the lattice sums, the adaptation of the crystal symmetry in k space, as well as the suitable choice of domains in Brillouin zone (BZ) integrations required in the determination of charge-density matrices. The capability and limitations of the semiempirical SCF HF CO approach is demonstrated for some simpler solids by comparing the present computational results with those of ab initio CO schemes as well as conventional numerical methods in soid-state theory. The employed model solids are graphite and BN (2D and 3D networks for both solids) as well as diamond, silicon, germanium, and TiS2.

Multireference many‐body perturbation theory

Abstract: The multireference many-body perturbation theory (MBPT) method is presented pedagogically. The distinctions between complete and incomplete model spaces are discussed. All second- and third-order diagrams for the diagonal and off-diagonal elements of the effective Hamiltonian matrix are presented in a compact form for complete and incomplete model spaces, including a new treatment of the renormalization diagrams. Illustrative numerical results are presented for the excitation energies of C2H4 using an incomplete single excitation model space, and for a study of FH potential energy surfaces with several different sizes of reference space.

Electronic structure of the phosphonitrilic trimer—role of d orbitals in chemical bonding

Abstract: Ab initio molecular orbital calculations were performed on a series of phosphazene trimer molecules to elucidate the electronic structure of these systems. The role of the d orbitals was analyzed from comparison of the molecular orbital contour calculations performed both with and without d orbitals in a split valence basis set description. The results indicate that, although the major geometric aspects of these systems can be described without invoking the use of d orbitals, these orbitals are essential to properly describe the electronic structure. The d orbital involvement in out-of-plane π bonding contains elements of both the classical Craig, Paddock, and Mitchell [1–3] and Dewar et al. [4] bonding schemes; the d orbital effects on in-plane bonding modes are also substantial. The charge distribution in these systems is best described as a zwitterionic form, because a significant amount of charge accumulates on the ring nitrogens.

On the abinitio calculation of d-d spectra in transition-metal compounds - the importance of relaxed charge-transfer states

Abstract: By calculations on CuCl, CuBr, and NiO clusters it is shown that a first-order configuration interaction (CI) calculation significantly improves the d-d and charge transfer (CT) spectra of ionic transition metal compounds. The first-order CI introduces delocalization (covalency) effects in the dn states, thus increasing the effective ligand-field splitting which is always underestimated at the Hartree–Fock (HF) level. It is demonstrated that this HF + first-order CI treatment is strongly related to a valence bond model. In this model the delocalization is introduced by explicit interactions with relaxed CT states. After account has been taken of the physically very different atomic correlation effects, a very good agreement with experimental d-d spectra is obtained, using only a small cluster. The effect of first-order CI on CT states is to account for hole localization and polarization effects which lead to reductions in the CT excitation energies in the order of 2–3 eV.

Dependence of MO shapes on a continuous measure of delocalization

Abstract: Whereas localization of orbitals has long been a tool for a semiclassical interpretation of chemical properties, it is in fact electron delocalization that is a fundamental property of quantum mechanical molecules. A mathematically well-defined measure is suggested for the degree of delocalization of molecular orbitals. It is shown that an orbital set of maximum delocalization exists for which the degree of delocalization depends on the charge distribution of the molecule. Hartree-Fock canonical orbitals are definitely more localized than the most uniformaly distributed MO's giving an equivalent description of the molecule. The changes in the geometrical shape of molecular orbitals are studied passing (quasi-) continuously from the strongly localized description towards the most delocalized picture. In the case of charge-inhomogeneities even the most delocalized orbitals remain rather compact. The degree of maximum delocalization may be correlated with chemical properties such as reactivity. The shape distortion of MO's under the perturbing effect of other ions and small molecules is investigated in several examples.

The role of hydrophobicity in the Ames test. The correlation of the mutagenicity of nitropolycyclic hydrocarbons with partition coefficients and molecular orbital indices

Abstract: A set of 20 nitropolycyclic aromatic hydrocarbons, whose mutagenicity has been determined in the Ames test, has been studied using octanol-water partition coefficients (P) as a measure of relative hydrophobicity and molecular orbital energies to account for variation in their electronic characteristics. A good structure-activity relationship was found using log P and ϵLUMO. The latter were taken from the results of ab initio calculations performed by Maynard, Pedersen, Posner, and McKinney [7] and were also calculated by the MNDO method. The dependence of mutagenicity on hydrophobicity was found to be similar to that observed for triazenes [2]. ϵLUMO values calculated by MNDO and STO-3G were found to be strongly correlated, and the role of hydrophobicity in correlating mutagenicity was not significantly affected by the molecular orbital model employed.

Long distance electron transfer

Abstract: Quantum mechanical models to treat long distance electron transfer are being developed. The model is based on the theory of R.A. Marcus. Our contribution is in the calculation of the electron coupling factor k. Estimations of the latter number, as well as the bond and solvent relaxation energies, λi and λo, respectively, are necessary to be able to calculate the rate constant for a reaction of the conductivity in an electric field. k may be approximately calculated from orbital energy differences at avoided crossings between orbitals localized in different parts of the system. A novel spectroscopic NDO method is suggested in which one may include any atom of the periodic table. Another problem discussed is the inclusion of electronic relaxation effects of the solvent or protein in the calculation. Applications are made to systems where metal ions are connected by organic bridges of different kinds such as dipyridine with coplanar and perpendicular pyridyl groups. As expected the electronic factor depends strongly on the conformation of the bridge. A strong conformational dependence is also obtained for a saturated bridge of the type NH2 · (CH2)n · NH2. In another study we use an α helix as a bridge between two metal ions. If one glycine in this α-helix is substituted by phenylalanine the electronic factor increases by factors of 1.5–10. It is suggested, however, that larger enhancement factors are possible if an aromatic group is positioned in a favorable way. The CNDO/S method is used to study the charge separation process in a bichromophoric molecule and in the reaction center (RC) of Rhodopseudomonas viridis. In those cases where the electronic coupling is large enough for the charge transfer states to be seen in the spectrum, the calculated results agree well with the experimental ones, but suggest a novel assignment. The CNDO/S results verify that electron transfer is possible through saturated spacers. In the special pair of RC the S1 state is calculated at approximately the correct position. Like the ground state, it has a delocalized character.

Molecular conformations and molecular shape: A discrete characterization of continua of van der Waals surfaces

Abstract: A characterization of molecular model surfaces is proposed. It is based on a graph associated with the van der Waals surface, defined by the detailed information on the interpenetration of van der Waals spheres of the constituent atoms. This “van der Waals graph” describes the three-dimensional body of the molecule, and it does not coincide in general with the less informative bond graph obtainable from the molecular skeleton. The description in terms of the graph reveals clearly the changes in molecular shape induced by conformational rearrangements. The nuclear configurations can be classified by the graph associated with the molecular surface, and the graph-theoretical analysis provides a rigorous partitioning of the configurational space based on shape properties.

A comparative study of the bonding in different halides of iridium

Abstract: X-ray photoelectron spectroscopy and multiple scattering Xα calculations have been applied to a series of iridium halide complexes in order to corroborate the nature of the bondings inherent in this class of compounds. Our results seem to substantiate contentiously that higher oxidation states of iridium favor the formation of covalent bonds. This conclusion is based on the observation that (1) successive bombardment of the iridium species by Ar ions almost definitely leads to a configuration in which iridium is bound to at most one halide ion, and (2) the theoretical charge per ligand ion approaches systematically a value of {1−} in the limit as the formal oxidation state of iridium approaches {1+}. The theoretical results are further arthenticated by the fact that the experimental ionization energy of the Ir(4f) level in the different iridium halide complexes studied is seen to decrease as a result of exposure to Ar ions.

Natural energy orbitals and the one-particle Green's function

Abstract: It is shown how the properties of the one-particle Green's function lead naturally to the definition of the so-called natural energy orbitals. These orbitals allow the fully correlated total energy of a system to be written in Hartree–Fock-like fashion and might therefore provide a bridge between sophisticated correlated wave functions and approximate theories of chemical structure and reactivity based on a Hartree–Fock-like energy expression. Moreover these orbitals form the basis for a self-consistent scheme to calculate the one-particle Green's function. The relation between these natural energy orbitals and the extended Koopmans' theorem is considered. Finally it is shown that the exactness of the lowest extended Koopmans' ionization potential implies the linear independence of the corresponding Dyson orbital from all other Dyson orbitals.

Vibrational frequencies and assignments for some isotopomers of urcail using a scaled ab initio force field

Abstract: Vibrational frequencies and IR band intensities for 18 isotopomers of uracil, including deuterated 15N and 18O species, have been calculated using the scaled ab initio force field of Ref. 1. The results obtained are compared with available experimental data, and a number of refinements in former assignments are proposed. The good agreement between the calculated and experimental frequencies confirms the reliability of the scaled quantum mechanical-force field.

Geometry optimization using local-density functional methods: Numerical aspects

Abstract: The need to perform a numerical integration of the exchange-correlation functional because of its non-analyticity severely complicates the accurate application of local-density functional methods to molecules and clusters. The optimal choice of grid points for this integration and the estimation of the error made by the choice are subtle considerations. In particular, because the position and/or weighting of each grid point must change when the nuclear positions change, these errors are most noticeable when different geometries are compared. We have determined a method of grid point selection and weighting that reduces these errors. We have also determined a simple method of estimating the extent of the error made in the particular density of points used for the grid. These results are illustrated for a selection of small molecules.

The chain build‐up procedure in computing the structures of biologically active polypeptides and proteins

Abstract: The chain-buildup method is presented for sampling the low energy conformations of polypeptides and enzyme-substrate complexes. This method circumvents the multiple minimum problem. It is shown that the method can compute structures in agreement with experiment.

Continuum electrostatics and hydration phenomena

Abstract: A formalism for a computational treatment of the polarization of a solvent and polar solutes immersed in it is presented. The solvent is modeled as a continuum dielectric. Polarization effects are represented by a polarization charge density at the dielectric boundaries and by induced dipoles at the polarizable atoms. Applications of this formalism with nonpolarizable atoms have led to excellent agreement between the calculated and experimental hydration enthalpies of a variety of polar molecules. A problem of the choice of the charge distribution of the solute is addressed in calculations of the solution dipole moment and hydration enthalpy of polarizable molecule of water in solution. Experimental values of these properties were well reproduced in calculations starting with point charges fitted to the vacuum dipole moment of the water molecule. Tests calculations for spherical models and for a 13-residue peptide show good convergence of the computational method. It is shown in calculations on simplified models that a change in the exposure of a charged side chain can lead to large changes in the potential inside protein measured at a fixed distance from the charge and at the same depth from the protein surface. Calculations performed for the C-peptide of the ribonuclease suggest that the differential screening of partial charges can reverse the sign of the vacuum potential of the helix dipole.