Showing papers in "International Journal of Quantum Chemistry in 1991"

A general treatment of vibration‐rotation coordinates for triatomic molecules

Abstract: An exact, within the Born-Oppenheimer approximation, body-fixed Hamiltonian for the nuclear motions of a triatomic system is presented. This Hamiltonian is expressed in terms of two arbitrarily defined internal distances and the angle between them. The body-fixed axis system is related to these coordinates in a general fashion. Problems with singularities and the domain of the Hamiltonian are discussed using specific examples of axis embedding. A number of commonly used coordinate systems including Jacobi, bond-length-bond-angle, and Radau coordinates are special cases of this Hamiltonian. Sample calculations on the HzS molecule are presented using all these and other coordinate systems. The possibility of using this Hamiltonian for reactive scattering calculations is also discussed.

Ab initio relativistic effective potentials with spin‐orbit operators. VI. Fr through Pu

Abstract: Ab initio averaged relativistic effective core potentials (AREP), spin-orbit (so) operators, and valence basis sets are reported for the elements Fr through Pu in the form of expansions in Gaussian-type functions. Gaussian basis sets with expansion coefficients for the low-energy states of each atom are given. Atomic orbital energies calculated under the j-j coupling scheme within the self-consistent field approximation and employing the AREP's in their unaveraged form (REP's) agree to within 10% of orbital energies due to numerical all-electron Dirac-Fock calculations

Nonadiabatic molecular dynamics

Abstract: Molecular dynamics simulation of mixed quantum-classical systems, in situations where the quantal degrees of freedom undergo transitions among states, poses a number of challenging problems. Among the difficulties are bifurcation of trajectories that evolve into different quantum states and proper treatment of quantum coherence. In this article we outline the problems and contrast the ways in which they are addressed by current methods for nonadiabatic molecular dynamics. In the course of this comparison we present a new result, the relationship between the velocity adjustment in the “surface hopping” method and the “Pechukas force,” as well as some new reflections on an old result, oscillatory yields in ion-surface scattering.

An intermediate neglect of differential overlap model for second-row transition metal species

Abstract: An intermediate neglect of differential overlap (INDO) model for elements of the second transition series is described. Values of exponents for the radial portion of the Slater basis atomic orbitals, the orbital ionization energies, and the beta (or bonding) parameters for these elements are reported. Use of the model to investigate equilibrium geometries, relative energy ordering of geometric isomers, spectroscopic transition energies, energy ordering of state wave functions of different symmetry, trends in dipole moments, and equilibrium stretching frequencies is reported. The results indicate that the INDO method is capable of yielding quality results for species containing atoms of the second transition series.

The prism algorithm for two-electron integrals

Abstract: A new approach to the evaluation of two-electron repulsion integrals over contracted Gaussian basis functions is developed. The new scheme encompasses 20 distinct, but interrelated, paths from simple shell-quartet parameters to the target integrals, and, for any given integral class, the path requiring the fewest floating-point operations (FLOPS) is that used. Both theoretical (FLOP counting) and practical (CPU timing) measures indicate that the method represents a substantial improvement over the HGP algorithm.

Portable tools and applications for parallel computers

Abstract: A distributed-memory model is adopted for the development of parallel ab initio codes with an emphasis on portability as well as efficiency. A highly portable message-passingtoolkit (inspired by the Argonne ACRF PARMACS) is described. Examples and results of its use are presented

Two‐electron repulsion integrals over Gaussian s functions

Abstract: We present an efficient scheme to evaluate the [0] (m) integrals that arise in many ab initio quantum chemical two-electron integral algorithms. The total number of floating-point operations (FLOPS) required by the scheme has been carefully minimized, both for cases where multipole expansions of the integrals are admissable and for cases where this is not so. The algorithm is based on the use of a modified Chebyshev interpolation formula to compute the function exp(-T) and the integral F m (T)=f 0 1 u 2m exp(-Tu 2 ) du very cheaply

Perturbation theory calculations of intermolecular interaction energies

Abstract: Intermolecular interactions play an essential role in determining the structure and conformation of biomolecules, in particular, in aqueous solutions. With the recent development of computer capabilities, it is now possible to calculate the interactions of biologically relevant molecules using the standard self-consistent field approximation. For most systems, this approximation is not sufficient and the correlation component of the interaction energy must be included. Unfortunately, the supermolecular method, which is mostly used to calculate the intermolecular interactions at the correlated level, is plagued by the basis-set superposition error and does not provide any physical interpretation of the interaction energy. An alterative approach is to use the symmetry-adapted (exchange) perturbation theory developed by us. This theory is free from the basis-set superposition error, provides a clear physical picture of the interaction energy, and involves less computational effort than does a standard many-body perturbation theory calculation of equivalent order. We have developed a system of ab initio computer codes performing calculations for arbitrary molecules. For small systems—where the accuracy could be tested—our results are in excellent agreement with experiment. Large-scale calculations performed for systems such as (H2O)2, (HF)2, and uracil…water demonstrate the high efficiency and accuracy of our method.

Spin‐orbit (core) and core potential integrals

Abstract: Molecular integral formulas and corresponding computational algorithms are developed for the relativistic spin-orbit and core potential operators that are obtained from atomic relativistic calculations by means of the effective core potential procedure. Much use is made of earlier work on core potential integrals by McMurchie and Davidson. The resulting computer code has been made part of the ARGOS (Argonne, Ohio State) program from the COLUMBUS suite of programs, which computes the needed integrals over symmetry-adapted combinations of generally contacted Gaussian atomic orbitals

Kinetic balance in contracted basis sets for relativistic calculations

Abstract: A demonstration of kinetic balance failure in heavily contracted basis sets is given. Other possible methods of constructing small component basis sets for 4-component relativistic calculations are discussed. The position of the additional negative energy levels in extended balance calculations in some recent many-electron calculations is examined.

Improved quadrature methods for three‐center nuclear attraction integrals with exponential‐type basis functions

Abstract: The numerical properties of a two-dimensional integral representation [J. Grotendorst and E.O. Steinborn, Phys. Rev. A 38, 3857 (1988)] of the three-center nuclear attraction integral with a special class of exponential-type orbitals (ETO'S), the B functions [E. Filter and E.O. Steinborn, Phys. Rev. A 18, 1 (1978)] are examined. B functions span the space of ETO'S. The commonly occurring ETO'S can be expressed in terms of simple finite sums of B functions. Hence, molecular integrals for other ETO'S, like the more common Slater-type orbitals, may be found as finite linear combinations of integrals with B functions. The main advantage of B functions is the simplicity of their Fourier transform that makes the derivation of relatively simple general formulas for molecular integrals with the Fourier transform method possible. The integrand of the integral representation mentioned above shows sharp peaks causing, in the case of highly asymmetric charge distributions, slow convergence of the quadrature method used by Grotendorst and Steinborn. New quadrature schemes are presented that use quadrature rules based on Mobius transformations. These rules are well suited for the numerical quadrature of functions that possess a sharp peak at or near a single boundary of integration [H.H.H. Homeier and E.O. Steinborn, J. Comput. Phys., 87, 61 (1990)]. Numerical results are presented that illustrate the fact that convergence of the new quadrature schemes is about a factor two faster in case of highly asymmetric charge distributions.

Non‐local relation between kinetic and exchange energy densities in Hartree–Fock theory

Abstract: A non-local generalization K(r, r‘) of the kinetic energy t(r) such that t(r) = JK(r, r‘) dr’ is defined using the idempotency property of the Hartree-Fock first-order density matrix. This is, in turn, related by means of an explicit differential equation to the non-local exchange energy densityX(r, r‘). The relationship is illustrated for a couple of examples: with the Fermi-hole in a uniform electron gas, of importance in the local density version of density functional theory, and with inhomogeneous electron systems.

Energy deposition mechanisms and biochemical aspects of DNA strand breaks by ionizing radiation

Abstract: A theoretical model based on physical, chemical, and biochemical mechanisms has been presented to evaluate the yields of DNA strand breaks (single and double) as a function of linear energy transfer (LET) or −dE/dx. Energetic heavy charged particles are considered explicitly to provide a general theory for low- as well as for high-LET radiation. There are three main features of the calculation: (a) track structure considerations for the energy deposition pattern, (b) three-dimensional structure of DNA molecules to provide information on the exact location of damage, and (c) a Monte-Carlo scheme to simulate the diffusion processes of water radicals. To avoid the complexities of a cellular medium, an aqueous solution of DNA is considered in the calculation. When the results of the calculations are compared with experimental measurements of the yields of strand breaks in mammalian DNA (exposed in a cellular complex), reasonable agreement is obtained. However, only those experimental data have been compared where there were no enzyme repair processes. The method of calculation has also been extended to study breaks in higher-order structures of DNA molecules such as chromatin. Specific limitations of the present model have been pointed out for making further improvements.

The generalized Slater–Condon rules

Abstract: By relating the blocking structure of the relevant matrix of overlap-integrals to its cofactors, the Slater–Condon rules for the evaluation of an element of a matrix representation of an electronic Hamiltonian in a Slater determinant basis are generalized to the case where not all orbitals are orthogonal. This yields a set of 33 rules, which allows for an efficient implementation of the valence bond theory.

On the solution of coupled-cluster equations in the fully correlated limit of cyclic polyene model

Abstract: It is shown that the exact pair-cluster coefficients corresponding to the fully correlated limit of cyclic polyene model satisfy the equations of the approximate coupled-pair theory with quadruples (ACPQ) approach, but do not represent any solution of the standard coupled-cluster method with doubles (CCD) equations. Implications of this result for the performance of various coupled-cluster (CC) approaches, when applied to cyclic polyene model, are discussed.

Approximate noninteracting kinetic energy functionals from a nonuniform scaling requirement

Abstract: We have recently proven an inequality for the exact noninteracting kinetic energy density functional . It is known that the gradient expansion through fourth order, T[n], violates this inequality. Toward improving TsGE[n], we have constructed two new functionals, Ts1[n] and Ts2[n], by keeping the zeroth and second orders in TsGE[n] and replacing the fourth order with two simple terms, respectively, so that these new functionals satisfy the inequality. Numerical tests are presented for Ts1[n], Ts2[n], and TsGE[n] and for the gradient expansion through second order. Hartree–Fock and hydrogenic atomic densities are employed.

Electronic aspects of LADH catalytic mechanism

Abstract: Electronic aspects of the catalytic mechanism of liver alcohol dehydrogenase (LADH) are studied with the help of ab initio analytical gradient SCF MO methods. Three points are considered: (i) role of the catalytic zinc; (ii) geometry and electronic structure of the transition state for the hydride transfer reactions; and (iii) factors affecting the energy gap for the hydride transfer step, namely, substrate binding to zinc, reaction field, and serine 48 effects on the potential energy profile. The coordination sphere of the catalytic zinc has been modeled with an ammonia molecule and two SH− groups; complexes with CH3O−, CH3OH, and CH2O have been studied; a (6, 2, 2, 2, 1/6, 2, 1/3, 2) basis set has been used for Zn++; a (5, 2, 1, 1/3, 2) was used for oxygen, carbon, and sulfur; and a (3, 1) was used for hydrogen atoms. The hydride step was studied with two model systems: pyridinium cation/1,4-dihydropyridine coupled to the CH3O−/CH2O reaction, and cyclopropenyl cation/cyclopropene coupled to the CH3O−/CH2O system. For the latter, the role of Ser48 has been studied at the supermolecule level. The calculation on the hydride transfer step has been done at a 4–31G basis set level. The results obtained shed new light on the sources of catalytic activity of liver alcohol dehydrogenases.

A BSSE-free SCF algorithm for intermolecular interactions

Abstract: A very simple modification of the usual (∼N 4 ) SCF procedure is proposed, permitting the exclusion of basis set superposition errors (BSSE) in problems of intermolecular interactions. No a posteriori corrections are required. The results of this «CHA/F method» are numerically close to those of the Boys-Bernardi correction scheme but are free from the «overcompensation» characteristic of the latter at smaller distances

A density functional for the correlation energy, deduced in the framework of the correlation factor approach

Abstract: An approximate density functional is deduced from a wave function within the correlation factor method. The new functional does not include terms depending on the gradient of the density, but shows the simplicity of local density functionals without spin polarization. However, it includes correctly the inhomogeneity effects and, also, the nonlocal nature of an electronic system. The approach adopted here stresses the goodness of the expression taken by Colle and Salvetti for building a correlation factor and, at the same time, allows us to gain light on the nature of the deficiencies of those functionals obtained, up to now, from the perspective of the Hohenberg and Kohn theorem.

Higher analytic derivatives. I. A new implementation for the third derivative of the SCF energy

Abstract: This is the first of a series of papers on the ab initio calculation of the second, third, and fourth derivatives of the energy with respect to nuclear coordinates. The knowledge of these derivatives yields anharmonic spectroscopic constants. Here, we present efficient formulae for the analytic evaluation of these derivatives for closed-shell SCF wave functions. We discuss our implementation of the third derivative formula, in particular the integral and vectorization procedures. Applications are reported for H 2 S, CHOF and HCCF

Analysis of coupled cluster and quadratic configuration interaction theory in terms of sixth-order perturbation theory

Abstract: The energy at sixth-order Mnller-Plesset (MP6) perturbation theory is given and dissected into 36 sizeconsistent energy contributions resulting from single (S), double ( D), triple (T ), quadruple (Q), pentuple (P), and hextuple (H) excitations. It is shown that MP6 is an O(N9) method, but less costly approximations to MP~ are possible. MP~ is used to analyze and compare coupled cluster (cc ) and quadratic configuration interaction (QCI) methods, namely CCD, CCSD, CCSD(T), CCSD(TQ), CCSDT, CCSDT(Q), CCSDT(QQ), QCISD, QCISD(T), and QCISD(TQ). For larger molecules and molecules with distinct T contributions, CCSD is significantly better than QCISD because CCSD covers a relatively large number of T contributions and in particular T,T coupling effects at sixth order. Differences between the two methods become larger at higher orders of perturbation theory. If T and Q excitations are included in QcisD and CCSD in a noniterative way-thus leading to QCISD(T ), CCSD(T ), QCISD(TQ), and ccsD(TQ)-then differences between QCI and cc decrease. Hence, if a given molecular problem depends on the inclusion Of T effects, improved calculational results will be obtained in the following order: MP4(SDTQ) < QCISD(T) < CCSD(T) < QCISD(TQ), CCSD(TQ) < CCSDT. None of the methods investigated is correct in sixth order. Only ifCCsDT is extended to CCSDT(QPH), which is also an O(N9) method, are all MF6 energy contributions then covered.

An examination of the effects of basis set and charge transfer in hydrogen-bonded dimers with a constrained Hartree–Fock method

Abstract: Constrained Hartree–Fock methods in which orbitals are constructed from strictly local nonorthogonal subsets of the molecule's atomic orbital basis have been known for over a decade. These methods have been principally used to generate localized molecular orbitals and interpret intramolecular interactions. In this paper, constrained Hartree–Fock results from basis sets ranging from minimal to extensive are presented for hydrogen-bonded dimers in which individual molecular orbitals are constructed from atomic orbitals belonging to individual monomers. These calculations eliminate both basis set superposition errors (BSSE) as well as charge transfer between monomers. This allows one to examine the effects of basis sets on the electrostatic and polarization components to the energy unmasked from BSSE. The charge transfer components are also isolated by comparing results to unconstrained calculations near the Hartree–Fock limit, where BSSE is vanishingly small. Finally, at moderate intermolecular separations when charge transfer becomes negligible, the constrained results are compared to both counterpoise-corrected and unconstrained calculations.

Dirac-Fock self-consistent field method for closed-shell molecules with kinetic balance and finite nuclear size

Abstract: We present a general method of implementing the kinetic balance condition within the Dirac-Fock (DF) self-consistent field (SCF) formalism for closed-shell molecular structure. We review the steps leading to the derivation of DF SCF equations for closed-shell molecules, particularly as formulated by Matsuoka et al. In the present approach, the large component of the molecular spinors are expanded in terms of atomic basis spinors of spherical-type Gaussian functions, with the small component related to the large component by the kinetic balance condition. It is shown that imposing the kinetic balance condition on geometric Gaussian-type basis functions allows us to obtain the Fock matrix elements, involving both the large and the small components, form the standard nonrelativistic Cartesian-type matrix elements. By using properties of orthogonal polynomials, the solid spherical harmonics are expressed in Cartesian form, thus providing a general basis for transformation of one- and two-electron-matrix elements, obtained from a Cartesian Gaussian-type basis, to a spherical Gaussian-type basis. The advantages of using kinetically balanced geometric Gaussian-type basis functions in molecular DF calculations including finite-size nucleus effects are emphasized. For the sake of completeness, we have added in an appendix corrections to the nuclear attraction matrix elements for the finite-size nucleus already derived by Matsuoka.

Collision-induced emission of O2(b1Σ a1Δg) in the gas phase†

Abstract: In flow tube studies of the quenching of O2(b1Σ), broad band emission of O2(b):M collision complexes was found to appear under the discrete rotational lines of the 0–0 band of the b1Σ a1Δg electric quadrupole transition at higher oxygen pressures and on addition of foreign gases. Bimolecular rate constants for the collision-induced emission processes have been derived from the ratio of the intensities of the discrete lines and the continuum as well as from low-resolution measurements of the relative intensities of the b a and b X bands as a function of O2 and added gas pressure. They range from ≈10−21 cm3 s−1 for He to ≈4 × 10−19 cm3 s−1 for PCl3 vapor.

Dipole moments, transition moments, oscillator strengths, radiative lifetimes, and overtone intensities for CH and CH+ as computed by quasi-degenerate many-body perturbation theory

Abstract: The correlated, size-consistent, ab initio effective valence-shell dipole operator (μv) method is used to calculate dipole moments and transition dipole moments of the CH molecule and transition dipole moments of the CH+ ion as a function of internuclear distance. The dipole and transition dipole moments computed here compare well with those of other accurate ab initio methods. The transition dipole moments are then used to calculate oscillator strengths and radiative lifetimes for the A X and B A transitions of the CH+ ion and the A X transition of the CH molecule. Comparisons are made with the best available theoretical and experimental lifetimes. Finally, the CH ground-state dipole moment function is used to evaluate overtone intensities and to examine simple models of the CH overtone intensities in polyatomic molecules.

Second-order polarization propagator calculations of dynamic dipole polarizabilities and C6 coefficients

Abstract: The frequency-dependent dipole polarizability, α(E), is calculated using the second-order polarization propagator approximation (SOPPA). We have shown how to express α(E) as a function of E 2 and thus obtained a form of α(E) that can be used to compute C 6 -coefficients without invoking complex arithmetic. For He we find that SOPPA recovers a large fraction of the correlation contribution for all frequencies, whereas for H 2 where the correlation contributions are much smaller and also basis set-dependent, we find a less definite trend of SOPPA relative to RPA

Abinitio methods for large systems

Abstract: Methods for calculations on extended systems are proposed, in which long-range Coulombic interactions are treated classically. The basic mode of description for the system is still in a quantum mechanical language, involving wave functions, Hamiltonians, etc. The electron density in a large molecular system is divided into suitable fragments, and the electrostatic potential generated by such a fragment at some distance away from it is then expressed by a generalized multipole expansion relative to a single point in space, conveniently taken as the center of charge distribution for that fragment. The computational effort required for evaluating the interactions involving those multipoles is modest and scales favorably (quadratically) with the size of the system. The remaining interactions, which need to be treated with conventional methods, i.e., with explicit one- and two-electron integrals, scale only linearly with size in extended systems. An important characteristic of the approach is that, while the approximations and shortcuts introduced have a clear physical origin, they can bc justified on strict numerical grounds, such that calculated energies and other properties are identical to those obtained with conventional methods.

Ab initio SCF calculations on [V10O28]6−: A benchmark for the classical calculation and processing of molecular integrals on large Gaussian basis sets

Abstract: A vector efficient implementation of the McMurchie and Davidson algorithm for the calculation of one- and two-electron molecular integrals is presented, as available in the Cray version of the ASTERIX program system. The implementation and performance of a vector-oriented strategy for the generation and processing of the P supermatrix is also discussed

Multidimensional wave-packet analysis : splitting method for time-resolved property determination

Abstract: The splitting method is an approach for preventing unphysical behavior of a wave-packet at the edges of its coordinate space representation grid. We examine here the possibilities and limits of using this method to perform time-resolved analysis of the products of molecular processes.