Showing papers on "Full configuration interaction published in 1995"

Different forms of the zeroth-order Hamiltonian in second-order perturbation theory with a complete active space self-consistent field reference function

Abstract: A new one-particle zeroth-order Hamiltonian is proposed for perturbation theory with a complete active space self-consistent field (CASSCF) reference function. With the new partitioning of the Hamiltonian, reference functions dominated by a closed-shell configuration, on one hand, and an open-shell configuration, on the other hand, are treated in similar and balanced ways. This leads to a better description of excitation energies and dissociation energies. The new zeroth-order Hamiltonian has been tested on CH2, SiH2, NH2, CH3, N2, NO, and O2, for which full configuration interaction (FCI) results are available. Further, excitation energies and dissociation energies for the N2 molecule have been compared to corresponding multireference (MR) CI results. Finally, the dissociation energies for a large number of benchmark molecules containing first-row atoms (the “G1” test) have been compared to experimental data. The computed excitation energies compare very well with the corresponding FCI and MRCI values. In most cases the errors are well below 1 kcal/mol. The dissociation energies, on the other hand, are in general improved in the new treatment but have a tendency to be overestimated when compared to other more accurate methods.

Estimating full configuration interaction limits from a Monte Carlo selection of the expansion space

Abstract: Full configuration interaction (FCI) calculations are useful as benchmarks for approximate techniques used in quantum chemistry: they are indeed the desired goal for all energy and wave function calculations in that they are the best solution to the Schrodinger equation within a finite basis Ansatz. Application of the method is limited due to the rapid increase in the number of configurations as the basis set size is increased. Many means have been applied to limit the number of terms in the expansion with the best known method being the singles and doubles expansion CI(SD). A Monte Carlo algorithm is proposed here whereby a CI expansion is allowed to expand by randomly including new terms which interact with those terms already present in the expansion. Solution of the variational problem is then performed for these randomly chosen configurations and a selection criterium for the resulting CI coefficients is applied. Repeated application of this method allows for estimates of the FCI energy. Calculations...

Benchmark full configuration interaction calculations on the helium dimer

Abstract: Full configuration interaction calculations are presented for the helium dimer employing large basis sets Using the best basis, which contains up to h‐type basis functions and several closely spaced sets of bond functions, the interaction energy was calculated for a variety of internuclear distances in the range 40 to 120 bohr The best calculated values for the He2 interaction energy are −10947 K at 56 bohr (the van der Waals minimum) and +29490 K at 40 bohr (on the repulsive wall) The interaction energy at 40 bohr differs significantly from the most recent semiempirical potential of Aziz and Slaman [J Chem Phys 94, 8047 (1991)], indicating that this potential is too attractive around 40 bohr Using a more generally accessible basis, containing only up to f‐type basis functions and only one set of bond functions, the interaction energy was calculated to be −10903 K at 56 bohr and +29496 K at 40 bohr These results show that functions of higher than f symmetry and bond functions distributed over several centers are necessary for obtaining highly accurate results, particularly at the van der Waals minimum Our results may be used to benchmark more approximate methods The CCSD(T) method is estimated to underestimate the full CI interaction energy by 033 K at 56 bohr and by 20 K at 40 bohr

Breaking bonds with the state-selective multireference coupled-cluster method employing the single-reference formalism

Abstract: The state‐selective (SS) multireference coupled‐cluster (CC) method exploiting the single‐reference (SR) formalism [P. Piecuch, N. Oliphant, and L. Adamowicz, J. Chem. Phys. 99, 1875 (1993)] is applied to BH and H2O at equilibrium and displaced geometries. Different selections of active spaces are considered. Comparison with the SR CC approaches involving single and double (CCSD), single, double, and triple (CCSDT) and single, double, triple, and quadruple (CCSDTQ) excitations, and with the full configuration interaction method, indicates remarkable stability and accuracy of the SS CC results for difficult bond breaking cases. For the first time, the ab initio SS CC calculations include the most complete SS CCSD(TQ) approximation, which emerges through selection of the most essential clusters appearing in the full SR CCSDTQ theory.

Application of complete space multireference many‐body perturbation theory to N2: Dependence on reference space and H0

Abstract: We study the wide latitude available in choosing the reference space and the zeroth order Hamiltonian H0 for complete reference space multireference perturbation theory. This effective Hamiltonian Heff method employs a general one‐body form of H0 which is varied by using different molecular orbitals and orbital energies. An energy gap is imposed between the zeroth order reference and secondary space states by forcing the valence orbitals to be degenerate. The forced valence orbital degeneracy removes the occurrence of detrimentally small perturbation energy denominators. Extensive computations are provided for the nitrogen molecule, where calculated ground state spectroscopic constants are compared with full configuration interaction computations and calculated vertical excitation energies are compared with multireference coupled cluster computations. It is demonstrated that the forced reference space degeneracy can lead to certain perturbation denominators becoming too small for practical convergence. Th...

Ab initio potential energy surfaces for the two lowest 1A′ states of H+3

Abstract: Three‐dimensional potential energy surfaces of H+3 in the two lowest 1A′ electronic states have been calculated by the full configuration interaction method with a [8s6p2d1f] Gaussian‐type basis set. The features of the avoided crossing of two surfaces as well as the energy minimum of the 1A′ ground state have been produced by the potential calculation at 680 different spatial geometries. These surfaces should be useful for the detailed studies of charge transfer and chemical reaction in the H+ and H2 collisions.

On the singlet–triplet separation in methylene: A critical comparison of single‐ versus two‐determinant (generalized valence bond) coupled cluster theory

Abstract: We present a critical comparison of the performance of the single‐ vs two‐determinant‐reference coupled cluster method, including its generalized valence bond version, for the classic multireference problem of the singlet–triplet separation in methylene. After demonstrating excellent agreement between the two‐determinant coupled cluster method with single and double excitations and the full configuration interaction method for a double zeta polarization (DZP) basis, we adopt an extended atomic natural orbital basis and obtain harmonic frequencies for the two states to give T0=10.30 kcal mol−1 and 8.86 kcal mol−1, respectively, for the single‐ and two‐ determinant‐reference coupled cluster results, compared to the experimental value, 8.998±0.014 kcal mol−1. Adding triples, the corresponding single‐reference value is 9.35 kcal mol−1. We also consider stretched geometries of CH2 as a stringent test of our approach. Comparisons are made between the two‐determinant coupled cluster values, including the single ...

A new grid-based method for the direct computation of excited molecular vibrational states: test application to formaldehyde

Abstract: A new method is presented for the direct computation of excited vibrational energy levels of molecules. The method combines the advantages of grid-based approaches to molecular dynamics problems with those of the Davidson diagonalization technique, which has found widespread usage in molecular electronic structure theory. It permits the direct computation of a prespecified vibrational state without the need to compute all lower lying levels. The wavefunctions used in the present test applications are extremely accurate and are the vibrational analogues of “full configuration interaction (CI)” wavefunctions in electronic structure theory. The method is applicable to large problems in that it requires the storage of only a few vectors, between six and eleven in the examples given, and no large matrices need to be retained. The theory of the new method is presented, first for the case of a single degree of vibrational freedom and then for the general case. Test results are given both for a diatomic model system and for a realistic ab initio potential energy surface computed for the formaldehyde molecule. The method is expected to provide a starting point for the development of future techniques for computing highly accurate vibrational wavefunctions for much larger molecules. As with all grid-based methods, no matrix elements of the potential need to be evaluated. The value of the potential is required only at the grid points of the multidimensional grid in coordinate space.

Full Configuration Interaction Molecular Dynamics of Na2 and Na3

Abstract: We extend our ab initio molecular dynamics methods to more exact wave functions, including complete active space multiconfiguration self-consistent-field (CASSCF) and full configuration interaction (full CI) wave functions. These extensions are critical for describing properly the dynamics of bond formation/ dissociation and isomerization, as we illustrate here by examining the bond dissociatiordformation of Naz and the isomerization (“pseudorotation”) of Na3 with full CI dynamics. Equivalencing of all three atoms of Na3 is found to proceedfirst via facile inversions through linear structures, which occur more often than conventional pseudorotation (via obtuse to acute to obtuse isosceles triangles).

State-selective multi-reference coupled-cluster theory employing the single-reference formalism : application to an excited state of h8

Abstract: The state‐selective (SS) multi‐reference (MR) coupled‐cluster (CC) method exploiting the single‐reference (SR) formalism [P. Piecuch, N. Oliphant, and L. Adamowicz, J. Chem. Phys. 99, 1875 (1993)] is applied to the first excited totally symmetric singlet state of a prototype molecular system composed of eight hydrogen atoms. Minimum basis set is employed and various geometries are considered. The SS CC energies are compared with the results of the state‐universal (SU) MR CC calculations involving single and double excitations (CCSD) as well as with the exact energies obtained using the full configuration interaction method. Comparison is also made with the results of the standard SR CCSD calculations. In both nondegenerate and quasidegenerate regions, our SS CC theory truncated at double excitations [SS CCSD(TQ) method] provides much better description of the first excited state than the genuine multi‐determinantal SU CCSD formalism.

Consistent treatment of correlation effects in molecular dissociation studies using randomly chosen configurations

Abstract: A means of performing configuration interaction calculations by randomly generating expansion vectors has recently been proposed and referred to as Monte Carlo configuration interaction (MCCI). To check the ability of the approach to accurately describe molecular dissociation, a comparison with benchmark full configuration interaction (FCI) calculations is presented. The results of the comparison indicate that the MCCI approach can consistently treat correlation effects in molecular dissociation studies.

A geometry optimization benchmark using highly correlated wavefunctions (FCI and MRD-CI)

Abstract: Full configuration interaction (FCI) geometry optimizations have been performed for the X3B1, a1A1, b1B1 and c1A1 electronic states of CH2, the X2B1 and A2A1 electronic states of NH2 and the X1A′1 electronic state of BH3 using a DZP basis set. The results are compared with those obtained using the MRD-CI method at different levels of theoretical treatment. The agreement between the geometrical parameters optimized with the FCI and MRD-CI methods is very good.

On the convergence of MBPT and CC nuclear magnetic shielding constants of BH toward the full CI limit

Abstract: The performance of many-body perturbation theory (MBPT) and coupled-cluster (CC) methods in the calculation of nuclear magnetic shielding constants for BH is analyzed by comparison with results from full configuration interaction (FCI) calculations. Low-order MBPT computations are shown to be inadequate for BH, while the coupled-cluster ansatz, in particular, in its singles and doubles (CCSD) approximation, provides an efficient treatment of electron correlation, overestimating correlation effects to the 11B shielding by only 3-4 ppm (1.5%). Based on this comparison, CCSD calculations with large atomic natural orbital (ANO) basis sets are used to estimate accurate theoretical values for the isotropic and anisotropic shielding constants of BH. © 1995 John Wiley & Sons, Inc.

A πCI approach to the study of correlation effects on the nonlinear‐optical properties in organic π‐conjugated systems

Abstract: A π‐electron method which allows for the systematic inclusion of configuration interaction of any order has been developed for the computation of electronic and optical properties of conjugated molecules. It has been used to study the effect of electron correlation on these properties in all trans finite polyenes of up to 16 carbon atoms. For smaller molecules it has been possible to carry out a complete set of CI calculations, from singly excited (SCI) to full configuration interaction (FCI). For the larger molecules the SCI and doubly excited CI (SDCI) calculations have been performed. The program permits the execution of a configuration interaction calculation of any order, n, in which all configurations involving the excitation of 1,2,...,n electrons from the occupied π‐orbitals of the Hartree–Fock ground‐state to the virtual π‐orbitals are included. The set of π‐orbitals is extracted from the ground state obtained from an all valence‐electron, complete neglect of differential overlap (CNDO) calculation. The configurations are represented by binary integers so that their generation and storage is very rapid and efficient. The nonlinear optical properties have been computed mainly by the correction vector method but in some cases the sum‐over‐states (SOS) method has also been used to study the evolution of the THG coefficient as virtual states of increasing energy are added. The results obtained for the finite polyenes are found to be in very good agreement with both experimental and other theoretical values in literature. The results clearly show the effect of electron correlation, which is found to affect the electronic and optical properties of these systems both qualitatively and quantitatively.

Local quantum chemistry: The local space approximation for Møller–Plesset perturbation theory

Abstract: The local space approximation is an accurate technique for describing a relatively small cluster embedded within an extended system. It has previously been developed for the Hartree-Fock, local density functional, configuration interaction, and coupled cluster electronic structure methods. Here it is extended to Moller-Plesset perturbation theory. © 1995 John Wiley & Sons, Inc.

Benchmark full configuration interaction calculations on N2

Abstract: Valence Full Configuration Interaction (FCI) calculations are reported for the N2 molecule with a 4s3p triple-zeta basis set at different distances. The size of the FCI space is more than 225 000 000 symmetry-adapted Slater determinants. The computation requires about 1400 s of c.p.u. time per iteration on a CRAY C90, and is one of the largest FCI calculations ever converged. Our results, as is in general the case for FCI computations, can be used to test the performance of approximated methods used to study electronic correlation in molecules.

Spectral density distribution of an N‐electron Hamiltonian in a finite‐dimensional and spin‐adapted model space

Abstract: Expressions for moments of spectral density distribution of a many-electron Hamiltonian defined in a finite-dimensional, antisymmetric, and spin-adapted model space (as, e.g., a full configuration interaction space) are derived. The moments are expressed in terms of combinations of two-electron integrals corresponding to a symmetric (a two-electron singlet) and antisymmetric (two-electron triplet) two-electron wave functions. A diagrammatic approach based on Hugenholtz-type diagrams and leading to a simple and universal classification scheme of the terms appearing in the expression for a specific moment is proposed. 17 refs., 3 tabs.

Structure and properties of fractional charge molecular systems: quark molecular hydrogen ions

Abstract: The electronic structure of the hypothetical two-electron quark molecular ions associating a quark hydrogen atom Q with an ordinary hydrogen atom is investigated. The quark hydrogen atom is a system consisting of a nucleus of charge ZQ = 1 ± 1/3 or ZQ = 1 + 2/3 and an electron. Potential energy curves of the low lying singlet and triplet Σ+ and Π electronic states of the HQ quark hydrogen molecular ions are presented. Full configuration interaction expansions upon extended Gaussian-type orbital basis sets are employed. Rovibrational parameters are given. A comparison with the ‘ordinary’ hydrogen moleculule is made. Absorption spectra from the ground states and emission spectra from some low lying excited states are studied. The results show that hypothetical two-electron quark hydrogen molecular ions are stable. This study is intended as a contribution to an understanding of the physicochemical properties of fractional charge systems, and possibly as a suggestion for experimentalists involved in ...

Improving the second order reduced density matrix within the spin-adapted reduced hamiltonian theory. an application to the beh2 potential curve

Abstract: This paper describes the last improvement introduced to a method for determining in a direct form the second order reduced density matrix within the framework of the Spin-adapted Reduced Hamiltonian theory. The potential energy curve for the BeH 2 molecule is calculated and compared with the results obtained by the Hartree-Fock, perturbative Moller-Plesset and Full Configuration Interaction methods.

Determination of spectroscopic terms in the LS-coupling scheme: a full configuration interaction space approach

Abstract: This paper describes a procedure for determining the spectroscopic terms arising from an atomic or a linear molecular configuration. The method, based on a simple calculation of the dimensions of ( L^ 2 , L^ z )- and ( Ŝ 2 , Ŝ z )-adapted full configuration interaction spaces, reduces the conventional situations of equivalent, non-equivalent (or both) electron configurations to one unique case. Some practical examples are considered.