Valence Correlation Energy Research Articles

Basis-set convergence in correlated calculations on Ne, N 2, and H 2O

Valence and all-electron correlation energies of Ne, N 2, and H 2O at fixed experimental geometries are computed at the levels of second-order perturbation theory (MP2) and coupled cluster theory with singles and doubles excitations (CCSD), and singles and doubles excitations with a perturbative triples correction (CCSD(T)). Correlation-consistent polarized valence and core-valence basis sets up to sextuple zeta quality are employed. Guided by basis-set limits established by r ij -dependent methods, a number of extrapolation schemes for use with the correlation-consistent basis sets are investigated. Among the schemes considered here, a linear least-squares procedure applied to the quintuple and sextuple zeta results yields the most accurate extrapolations.

Benchmark calculations with correlated molecular wave functions. X. Comparison with “exact” MP2 calculations on Ne, HF, H2O, and N2

The convergence of the MP2 valence correlation energy and pair energies for the correlation consistent basis sets has been investigated. Ne, HF, H2O, and N2 were studied. For all of these molecules, accurate MP2 correlation and pair energies are available from the recent MP2-R12 calculations of W. Klopper [J. Chem. Phys. 102, 6168 (1995)]. The magnitudes of the calculated MP2 valence correlation and pair energies are found to increase systematically with increasing basis set size, with the cc-pV6Z basis set yielding 97.4%–98.3% of the MP2 valence correlation energy. A detailed analysis of the results for Ne reveals that the error due to truncation of the radial functions in the cc-pV6Z set is comparable to that due to neglect of higher angular momentum functions. Procedures for extrapolating the results to the complete basis set limit have also been investigated.

On the accuracy of valence correlation energies in pseudopotential calculations

Total valence correlation energies of X5+, X+, X, X−, and X2 (X=F,Cl,Br,I) have been calculated with the coupled-cluster method for the all-electron and the pseudopotential case using large uncontracted basis sets containing up to g-type functions. The overestimation of valence correlation energies due to the modified nodal structure of the pseudo-orbitals is discussed. The errors are found to be less than 10% in all cases of chemical interest and reduce to 2 mH or less in correlation contributions to ionization potentials, electron affinities or binding energies.

Valence correlation energies from pseudopotential calculations

Total valence correlation energies of first-row atoms, their anions and cations as well as their homonuclear dimers have been determined in all-electron and [He]-core pseudopotential calculations using the coupled-cluster method and large uncontracted basis sets containing up to g-type functions. The inaccuracies mainly caused by the pseudo-orbital transformation of the 2s valence orbitals are discussed. The relative errors in total valence correlation energies are found to be 6% at most. Correlation contributions to excitation energies, ionization potentials, electron affinities or binding energies are accurate with absolute errors of 0.1 eV or less.

Ground State Properties of Hg2. 2. A Quantum Monte Carlo Study

We have carried out variational and pure diffusion quantum Monte Carlo calculations for the Hg atom and the Hg2 molecule. In the case of the Hg atom we have calculated valence correlation energies for relativistic and nonrelativistic 20-valence-electron pseudopotentials. The results are compared with those of conventional ab initio methods. For the Hg2 molecule we have used a 2-valence-electron pseudopotential together with a core-polarization potential. The resulting ground state potential energy curve agrees well with curves derived from configuration interaction calculations. Jastrow factors were found to be an efficient method to describe electron correlation in these systems.

The use of systematic sequences of wave functions for estimating the complete basis set, full configuration interaction limit in water

An assortment of 1- and 2-electron water properties were extracted from a systematic sequence of wave functions. The regularity inherent in this sequence permitted simple exponential fits of the resulting energies and, in many cases, the properties. To the extent the exponential fit accurately reflects the asymptotic convergence of a specific property, it provides an estimate of the complete basis set, full configuration interaction (CI) limiting value at a reduced computational expense. As a consequence of the vast reduction in the number of configurations that must be treated variationally, the proposed scheme may make possible improved estimates of the complete basis set, full CI limit beyond what could be obtained from explicit computations. In order to judge the accuracy of the procedure, we have carried out the highest level ab initio calculations to date on water, recovering in excess of 96% of the estimated valence correlation energy.

Atomic valence correlation energies from ab initio model potential calculations

Ab initio model potential calculations on X −, X, and X + (XF, Cl, Br, and I) using CISD wavefunctions have been performed in order to test a recent conclusion on the irrelevance of the valence orbital internal nodes in the values of atomic valence correlation energies. The results show that the ab initio model potential orbitals, showing the correct nodal structure, provide valence correlation energies much closer to the corresponding all-electron values than nodeless pseudo-orbitals do.

Relativistic effective potential quantum Monte Carlo simulations for Ne

We have carried out benchmark relativistic effective potential quantum Monte Carlo calculations for Ne. The resulting energy from the fixed-node diffusion QMC simulations was −34.960(3) a.u., as compared to the Hartree–Fock value of −34.647 a.u., giving a valence correlation energy of 0.313(3) a.u. This is in excellent agreement with previous work, and we believe accounts for 98% to 100% of the total valence correlation energy. We detect no significant error due to the effective potential approximation, and in particular, the nodeless pseudoorbitals in the 2s shell. We observed no difficulties related to the use of the conventional effective potentials in fixed-node QMC simulations.

Large atomic core—core correlation effects

The effects of core—valence and core—core correlation on valence ionization potentials (IP) and excitation energies of Ca +, neutral Sc and Sc 2+ are studied. Core—valence correlation has a large effect, particularly on 3d excitations, but results in overestimated (by up to 0.8 eV) IPs. Core—core correlation reduces the effect of core—valence correlation and may reduce the computed IP by as much as 1 eV compared with the core—valence CI result. Computing only the valence and core—valence correlation energy while excluding the core—core contribution in molecules containing Ca and Sc is thus not advisable.

Pseudopotential calculations on the ground state of the alkaline-earth monohydride ions

The ground state potential energy curves of alkaline-earth monohydride ions have been investigated. A pseudopotential formalism including a corepolarization potential has been used. For the valence correlation energy a local spin density functional with corrections for self interaction has been employed. Dissociation energies, bond lengths and vibrational frequencies are reported, and so are the vertical and adiabatic ionization potentials of the alkali and alkaline-earth monohydrides, which were obtained using the same theoretical model. A discussion and a comparison with other values, both theoretical and experimental, are also included.

Ground state properties of alkali and alkaline–earth hydrides

The ground state potential energy curves of alkali (LiH to CsH) and alkaline–earth monohydrides (BeH to BaH) have been calculated. A pseudopotential formalism including a core-polarization potential has been used. For the valence correlation energy, two different methods, the local spin-density functional and the configuration interaction with single and double excitations, have been employed. Dissociation energies, bond lengths, vibrational frequencies, anharmonicity constants, and dipole moments are reported. The agreement with experimental values, where available, is very good. A discussion and a comparison with other theoretical values, at different levels of approximation, are also included.

Dynamic correlation for MCSCF wave functions: An effective potential method

A method is suggested which allows the inclusion of dynamic correlation into CASSCF calculations. An effective Coulomb hole potential is added to the Hamiltonian. The potential has a simple form, which allows its implementation into existing LCAO programs using Gaussian integral packages. The parameters appearing in the potential are determined by fitting to empirical valence correlation energies for first row atoms. Calculations of ionization energies and electron affinities show considerable improvement compared to the MCSCF values. Test calculations on three molecules give the following results, H2∶ re=0.745 (0.741) A, De=4.62 (4.75) eV; N2∶ re=1.099 (1.098) A, De= 10.42 (9.91) eV; O2∶ re=1.198 (1.207) A, De=4.73 (5.21) eV. Experimental values within parenthesis.

Potential energy surfaces of HgH 2

Potential energy surfaces for HgH 2 have been calculated using a non-empirical relativistic effective core potential incorporating configuration interaction by means of the CIPSI algorithm. Core valence polarization and correlation energy are included via a perturbative treatment. Spin-orbit coupling is introduced through an effective Hamiltonian. These theoretical results are used to discuss the experimental results of Breckenridge, Jouvet and Soep for the reaction Hg( 3P 1) + H 2 → HgH( 2Σ +)+H.

A full CI treatment of Ne atom - a benchmark calculation performed on the NAS CRAY 2

Full CI calculations are performed for Ne atom using Gaussian basis sets of up to triple-zeta plus double polarization quality. The total valence correlation energy through double, triple, quadruple and octuple excitations is compared for eight different basis sets. These results are expected to be an important benchmark for calibrating methods for estimating the importance of higher excitations.

Electron affinities of the alkali dimers: Na2, K2, and Rb2

Ab initio calculations on the ground states of the alkali dimers, Na2, K2, and Rb2, and their anions are reported. The calculations employ large Gaussian basis sets and account for nearly all of the valence correlation energy. The calculated atomic electron affinities are within 0.02 eV of experiment and the calculated adiabatic electron affinities for Na2, K2, and Rb2 are, respectively, 0.470, 0.512, and 0.513 eV.

A study of potential curve crossing in X-Ar complexes (X=Mg, Ca, Sr, Ba)

Semiempirical pseudopotentials which are determined by fitting to experimental term values of Mg+, Ca+, Sr+, Ba+and Ar7+, are tested for ground and various excited states of the corresponding neutral atoms, using a spin-density functional approximation for valence correlation energies. Experimental triplet excitation energies are reproduced with an average error of 0.1 eV. The method is then applied to study adiabatic level crossing between ground and excited states in X-Ar complexes (X=Mg, Ca, Sr, Ba). Estimates of deactivation energies are given and are compared with results from deactivation cross section measurements.

Theoretical analysis of the cycloaddition of ethylene

The cycloaddition of ethylene is theoretically analyzed for portions of the excited singlet and triplet hypersurfaces using a combination of semi-empirical and intermediate level ab initio techniques. The semi-empirical UHF calculations on the addition of triplet ethylene and methyl radical to ethylene showed that these two reactions have comparable theoretical parameters, including activation energies, spin transfer and spin polarization at the transition state. For the 2S + 2S excited singlet state surfaces, the results of both the ab initio and semi-empirical calculations are qualitatively the same and correspond to the classical ideas generated from orbital symmetry rules. At the ab initio level the results are quantitatively poor, partially due to the use of an intermediate level configuration interaction treatment. In particular, it was not possible to obtain other than a small fraction of the total estimated valence correlation energy in cyclobutane. The configuration interaction problem for both ab initio and semi-empirical calculations is discussed in detail.

Triple and quadruple excitations and the valence correlation energies of small molecules

The contribution of triply-excited states and quadruply-excited states to the valence correlation energy is investigated for a number of atoms and molecules using the diagrammatic many-body perturbation theory. The importance of triple excitations in accurate calculations is demonstrated.

Correlation effects in the isomeric cyanides: HNC↔HCN, LiNC↔gLiCN, and BNC↔gBCN

Correlated values of the isomerization energy and barrier for the HNC→HCN reaction are obtained from many-body perturbation theory, including the effects of quadruple excitations. Extended basis sets of better-than-triple-zeta plus double-polarization quality are used, as well as basis sets including counterpoise and bond-centered orbitals. The best of these basis sets is sufficient to account for 84% of the valence correlation energy of HCN. These studies predict an isomerization energy for the HNC→HCN rearrangement to be −15±2 kcal/mole, in disagreement with a recent experimental value of −10.3±1. kcal/mole. Correlated isomerization energies of LiCN→LiNC and BCN→BNC are obtained in bases of double-zeta plus polarization quality. In all cases, correlation stabilizes the cyanide isomer more than the isocyanide. Trends in the series R–NC⇄RCN for R=H, Li, and B are discussed.

The cyclic ozone isomer

Analysis of basis set effects in large correlated wave function calculations is undertaken in relation to the energy separation of the cyclic (D3h) and open (C2v) forms of ozone. The present calculations attain some 60% of the valence correlation energy of ozone with the largest bases, superseding a number of recent investigations of the D3h−C2v separation. The conclusion is reached that these species are isomers corresponding to different local minima on the ground state surface, below the ozone dissociation limit. The energy separation of these species is narrowed down to 40–88 kJ/mol, with the likeliest value, 50±kJ/mol, emerging from the present calculations (’’doulbe zeta plus polarization’’ is in error ∼25 kJ/mol). The formation and implications of the secondary D3h ozone isomer are briefly discussed.