George D. Purvis

A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples

The coupled‐cluster singles and doubles model (CCSD) is derived algebraically, presenting the full set of equations for a general reference function explicitly in spin–orbital form. The computational implementation of the CCSD model, which involves cubic and quartic terms, is discussed and results are reported and compared with full CI calculations for H2O and BeH2. We demonstrate that the CCSD exponential ansatz sums higher‐order correlation effects efficiently even for BeH2, near its transition state geometry where quasidegeneracy efforts are quite large, recovering 98% of the full CI correlation energy. For H2O, CCSD plus the fourth‐order triple excitation correction agrees with the full CI energy to 0.5 kcal/mol. Comparisons with low‐order models provide estimates of the effect of the higher‐order terms T1T2, T21T2, T31, and T41 on the correlation energy.

Molecular Applications of Coupled Cluster and Many-Body Perturbation Methods

A series of molecular applications of many-body perturbation theory (MBPT) and the coupled-cluster doubles (CCD) model are described. Even though these methods have been available for sometime, only recently have large scale, MBPT molecular calculations become available. In the case of CCD, the results presented here are among the first obtained from a general purpose ab initio program. The intention of this paper is to present an overview of the current state of the many-body approach to ground state properties of molecules. The properties studied are correlation energies, including contributions from single, double, and quadruple excitations diagrams in fourth-and higher-order; dissociation energies; potential energy surfaces; and molecular polarizabilities and hyperpolarizabilities. Examples are taken from studies of a variety of molecules including HF, H2O, HCO, C6H6, B2H6, CO2, and N2. In many cases, it is found that quantitatively accurate dissociation energies, geometries, and force constants can be obtained. In an illustration of the X1Σg+ potential energy curve of N2, it is shown that a single UHF or RHF reference function MBPT/CCD approach is inadequate at some internuclear separation.

The quartic force field of H2O determined by many‐body methods that include quadruple excitation effects

Many‐body perturbation theory (MBPT) and coupled cluster methods are employed in an investigation of the potential energy surface of H2O in the vicinity of its equilibrium geometry. The basis set of 39 Slater‐type orbitals is the same as that previously used in a configuration interaction study (limited to all single and double excitations, SD‐CI) of this surface, and is capable of accounting for 80% of the total correlation energy of the molecule. Detailed comparisons among the results of the various methods are presented, with particular reference to the role of size extensivity in providing a reliable model for the prediction of the shape of the surface. The predicted quartic force field obtained by the coupled cluster doubles (CCD) and by several MBPT models is in very good agreement with experiment. The inclusion of quadruple excitations, which account for about 5% of the correlation energy, is found to have a significant effect on the shape of the surface, bringing the predicted force field into sub...

Atomic and molecular electronic spectra and properties from the electron propagator

Decoupling in terms of the superoperator formalism according to Pickup and Goscinski is employed to find tractable forms of the self‐energy operator leading to direct calculation of the electron propagator or Greens function. This is applied to the calculation of photoelectron line spectra, ground state total energies, and electronic properties of atoms and molecules. Numerical results for the helium atom and the nitrogen molecule are reported.

The reduced linear equation method in coupled cluster theory.

A numerical procedure for efficiently solving large systems of linear equations is presented. The approach, termed the reduced linear equation (RLE) method, is illustrated by solving the systems of linear equations that arise in linearized versions of coupled‐cluster theory. The nonlinear coupled‐cluster equations are also treated with the RLE by assuming an approximate linearization of the nonlinear terms. Very efficient convergence for linear systems and good convergence for nonlinear equations are found for a number of examples that manifest some degeneracy. These include the Be atom, H2 at large separation, and the N2 molecule. The RLE method is compared to the conventional iterative procedure and to Pade approximants. The relationship between the projection method and least square methods for reducing systems of equations is discussed.

Comparison of MBPT and coupled-cluster methods with full CI. Importance of triplet excitation and infinite summations☆

Abstract Results from full fourth-order perturbation theory [SDTQ MBPT(4)], and the coupled-cluster single- and double-excitation model (CCSD). are compared with recent full CI results for BH, HF, NH3, and H2O. For H2O, studies include large symmetric displacements of the OH bonds, which offer a severe test for any single-reference MBPT/CC method. In every case. CCSD plus fourth-order triple-excitation terms provide agreement with the full CI to

The potential energy curve for the X1Σg+ state of Mg2 calculated with many‐body perturbation theory

The ground state potential curve for the van der waals molecule, Mg2, is calculated by adding to the Hartree–Fock potential curve those many‐body perturbation theory (MBPT) correlation corrections which arise from double excitation type diagrams through fourth order (DE–MBPT). The fourth‐order binding energy is shown to be unaffected by higher order double excitation diagrams. The DE–MBPT potential curve is compared to the fourth‐order Rayleigh–Schrodinger perturbation theory (RSPT) approximation of the double excitation configuration interaction (DECI) potential curve. The DE–MBPT curve is found to be in much better agreement with experiment. Since the only difference between the MBPT equation and the RSPT equation is the size‐inconsistent E2Δ renormalization term contained in the double CI and its fourth‐order RSPT approximation, the importance of having a size‐consistent model for molecular binding is demonstrated. The inclusion of additional correlation effects, due to the fourth‐order EPV rearrangeme...

Electron propagator calculations of the photoelectron spectrum for open shell molecules with applications to the oxygen molecule

An approximate self−energy for the electron propagator is derived using the Grand Canonical averaging procedure for open shell molecules. The connection between the overlap amplitudes and the photoionization cross section is discussed. A direct pole and residue search is employed to solve the Dyson equation with a second order self−energy for the oxygen molecule, yielding a theoretical photoelectron spectrum in good agreement with experimental x−ray induced spectra.

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.

Higher‐order decoupling of the electron propagator

The decoupling of the electron propagator in the superoperator formalism is extended to include a description of processes corresponding to simultaneous electron ionization (or electron attachment) and double excitation, observed in electron spectrometry, by including products of five spin–orbital field operators in the inner projection basis. Although the terms thus introduced are fourth order in the electron interaction, an argument based on the self‐consistent solution of the second‐order equations suggests that these fourth‐order terms are more important than the third‐order terms. The argument is substantiated by numerical applications to the neon atom. A calculation using third‐order shifts is compared with a calculation using the suggested fourth‐order terms, but without third‐order terms.