Coupled Electron Pair Approximation Research Articles

Size consistency in multi-reference double excitation CI calculations

The problem of size consistency in a multi-reference CI calculation is discussed using the method of quasi-degenerate many-body perturbation theory suggested by Brandow [1, 2]. The multi-reference form of linear coupled pair many-electron theory (CPMET), the coupled electron pair approximation (CEPA) and the Davidson correction are derived. It is shown that these methods are easily implemented in quantum chemical calculations.

CEPA calculations on open-shell molecules. I. Outline of the method

A systematic description of an open-shell CEPA-PNO (coupled electron pair approximation using pair natural orbitals) program based on spin-adapted PNO-configurations is given which is used for the calculation of correlation energies of open-shell molecular ground and excited states. This program is an extension of our previous closed-shell CEPA-PNO program and is designed to treat doublet, triplet and open-shell singlet states. Its characteristic features are: Inclusion of all singly and doubly substituted configurations belonging to the interacting space; direct determination of pair natural orbitals; matrix element generator for automatic construction of matrix elements for prototype configurations; CEPA estimate of the contributions of unlinked clusters of singles and doubles. Applications of the program to small molecules will appear in further papers of this series.

Recent computational developments with the self‐consistent electron pairs method and application to the stability of glycine conformers

AbstractSignificant improvements in calculational efficiency and capability with the self‐consistent electron pairs (SCEP) method has resulted from several new computational developments. A new procedure for constructing the important internal Coulomb and exchange operators has substantially reduced the preiteration time. A general scheme for utilizing molecular symmetry has been used to advantage in reducing the number of pair functions and external operators that must be found explicitly at each iteration. A projection operator tool has been implemented and found to be quite effective at minimizing the number of iterations required at some point on a potential energy surface when an SCEP wavefunction exists for some nearby point. These and other improvements in the program construction have yielded sizable reductions in time for some representative test cases, including water and a potential energy curve for formaldehyde. The new SCEP program also performs low‐order perturbation theory treatments and coupled electron pair approximation (CEPA) calculations using the same operator approach. The usefulness of the approach is demonstrated by very large scale calculations on the stability of the two interstellar glycine conformers. These calculations involve the variational treatment of 82,205 symmetry‐adapted singly and doubly substituted configurations involving 225 internal electron pairs.

An electron pair operator approach to coupled cluster wave functions. Application to He2, Be2, and Mg2 and comparison with CEPA methods

A method for obtaining coupled cluster expansions with double substitutions (CCD) utilizing the electron pair operator approach of self-consistent electron pair (SCEP) theory is presented. A fairly simple operator is developed in this method and its calculation increases the expense over a typical variational configuration expansion only moderately. With this method, large basis set calculations have been performed on the weakly interacting dimers He2, Be2, and Mg2. Comparison calculations have been performed with various types of coupled electron pair approximations (CEPA), which may be viewed as approximations to coupled cluster theory, and with modification of the internal orbitals in the CCD treatment.

Ab initio calculations including electron correlation for the minimum energy path of the (1A1) CH2+(1Σ)H2→ (1A1) CH4 insertion reaction

AbstractAb initio calculations on the SCF level and with the inclusion of valence shell electron correlation in the IEPA–PNO (independent electron pair approximation with pair natural orbitals), the PNO–CI (pair‐natural‐orbital configuration interaction) and the CEPA–PNO (coupled electron pair approximation with pair natural orbitals) schemes with Gaussian lobe functions of “double zeta quality” have been performed for the minimum energy path of the insertion of singlet (1A1) methylene to the (1Σ)H2 molecule to yield methane. The energy was minimized on the SCF level to all geometrical parameters for various values of the “approximate” reaction coordinate. The energy along the reaction path decreases monotonically without a barrier and the curves representing the total energy of the system as a function of approximate reaction coordinates obtained at different levels of approximations have the same shape. From the physical point of view three phases of the reaction can be distinguished (chemically two steps) with different geometrical arrangements and different internal geometries of the partners.

The dynamic Jahn–Teller effect in the electronic ground state of Li3. An a b i n i t i o calculation of the BO hypersurface and the lowest vibronic states of Li3

The lowest adiabatic potential energy hypersurface of Li3 is determined using the coupled electron pair approximation (CEPA). The GTO basis used accounts for at least 80% of the valence electron correlation energy. Our calculated binding and ionization energies (34 kcal/mole and 4.0 eV, respectively) are in good agreement with the experimental values of Wu [J. Chem. Phys. 65, 3181 (1976)] (41.5±4 kcal/mole and 4.35±0.2 eV, respectively). We show that vibronic coupling is essential in the electronic ground state of Li3, giving rise to a dynamic Jahn–Teller effect which is treated in a nonharmonic approximation. The lowest vibronic states of Li3 have been calculated by solving the two-dimensional Schrödinger equation for the E′×e′ Jahn–Teller case by a variational method. Vibrational probability densities are presented which allow the discussion of the ground state geometry of Li3. In contrast to previous work, an effective D3h geometry is proposed. This is supported by the calculated rotational energy levels, which can be interpreted as belonging to a symmetric top molecule with spectroscopic constants A=B=0.568 cm−1 and C=0.268 cm−1 (assuming three 7Li isotopes).

A PNO—CEPA calculation of the barrier height for the collinear atom exchange reaction Cl′ + HCl → Cl′H + Cl

Abstract A barrier height of 16.6 kcal mol−1 has been calculated for the collinear atom exchange reaction Cl′ +_HCL → Cl′H + Cl by means of the coupled electron pair approximation CEPA. The long-range attraction between the chlorine atoms has a non-negligible influence on the barrier height. The remaining correlation errors are estimated to reduce the barrier height by 10 to 15 kcal mol−1 to 2 to 7 kcal mol−1.

PNO-CI and PNO-CEPA studies of electron correlation effects

Dipole moments and static dipole polarizabilities are calculated for neon and the molecules HF, H2O, NH3, CH4 and CO from SCF and correlated wavefunctions. The construction of appropriate gaussian-type basis sets is discussed and the convergence of the correlation contributions to the polarizability is analysed. The effect of vibrational averaging is also investigated. The polarizabilities as obtained from the coupled electron pair approximation (CEPA) with the most extended basis sets differ from experimental values by less than 1·5 per cent in all cases. The calculated polarizability anisotropies appear to be correct to about 5–15 per cent. The correlation contributions to the polarizabilities are found to vary from 3 to 12 per cent.

PNO–CI and CEPA studies of electron correlation effects. III. Spectroscopic constants and dipole moment functions for the ground states of the first-row and second-row diatomic hydrides

A systematic investigation of the ground state potential curves and dipole moment functions has been performed for the diatomic hydrides LiH to HCl on the basis of variational configuration interaction wavefunctions PNO–CI and the coupled electron pair approximation CEPA. The basis sets of Gaussian-type orbitals are derived by simple rules from optimized atomic sets available in the literature. Between 95% (LiH) and 85% (HCl) of the valence shell correlation energies are accounted for in the CEPA calculations. Core–valence intershell correlation has been included for several members of each row, and its effect on the potential curves is analyzed. Comparison of the spectroscopic constants derived from the CEPA potential curves with experiment shows a high reliability of the theoretical values. The standard deviations over both rows are as follows: re:0.003 Å, ωe:14 cm−1, αe:0.005 cm−1, and ωexe:1.5 cm−1. The errors of the calculated dissociation energies go up to 0.3 eV but behave very regularly. They are believed to allow for predictions which are correct to about ±0.05 eV. The following new D0 values are recommended (empirical values in parenthesis): NH:3.40 (3.2±0.16); NaH:1.88 (2.05±0.2); MgH:1.23 (2.0±0.5); PH:3.02 (3.5±0.3). Various vibrational matrix elements have been calculated from the dipole moment curves. The μ0 values show errors of 0.02–0.04 D. The differences between diagonal elements as well as the transition elements for the first few levels deviate by only about 10% from the available experimental data.

PNO–CI (pair natural-orbital configuration interaction) and CEPA–PNO (coupled electron pair approximation with pair natural orbitals) calculations of molecular systems. III. The molecules MgH2, AlH3, SiH4, PH3 (planar and pyramidal), H2S, HCl, and the Ar atom

PNO–CI and CEPA–PNO calculations are performed for the molecules MgH2, AlH, AlH3, SiH4, PH3, H2S, HCl, and the Ar atom. Two types of Gaussian basis sets are used; both sets contain one p-set on H. The ’’small’’ set includes one d-set on the heavy atom, the ’’standard’’ basis two d-sets and one f-set. Both for MgH2 and Ar, a ’’large’’ and a ’’very large’’ basis are used as well, which contain additional polarization functions. The energy improvement due to the different polarization functions is analyzed. Hartree–Fock limits for the molecular energies are estimated. The computed valence shell correlation energies are analyzed in terms of quantities defined in part I, in particular in terms of the IEPA (independent electron pair) correlation energies εμIEPA and the error ΔEIEPA of the IEPA scheme. Both the valence shell interorbital pair correlation energies and the IEPA error are smaller in absolute value than those of the corresponding first row hydrides, provided that one uses the localized representation. MgH2, AlH3, and SiH4 are ’’good IEPA molecules’’, i.e., ‖ΔEIEPA‖ is unusually small for them. For Ar, calculations that include the L and M shell, and the K, L, and M shell correlation energy are reported. The best known variational energy of the Ar atom is obtained as −527.2592 a.u., the (nonvariational) CEPA energy being −527.2916 a.u. For the unknown molecules MgH2 and AlH3, binding energies, equilibrium geometries, and symmetric-stretching force constants are predicted. MgH2 has a binding energy of 104 kcal/mol referred to Mg+2H; it is hence expected to be unstable with respect to Mg+H2. The predicted binding energy of AlH3 is ? 205 kcal/mol referred to Al+3H. The inversion barrier of PH3 which amounts to ? 38 kcal/mol on SCF level is reduced by electron correlation to ? 35 kcal/mol.

PNO–CI (pair natural orbital configuration interaction) and CEPA–PNO (coupled electron pair approximation with pair natural orbitals) calculations of molecular systems. I. Outline of the method for closed-shell states

The methods of configuration interaction with double substitutions to pair natural orbitals (PNO−CI) and of the coupled electron pair approximation (CEPA) proposed by W. Meyer are improved by combination with a new scheme of the calculation of the pair natural orbitals (PNO) and an efficient iterative scheme for the diagonalization of the CI matrix. The relevant matrix elements for the closed shell case are tabulated, the quantities that are pertinent for an analysis of the correlation energy are defined, and the organization of the computer programs is described.

PNO-CI and CEPA studies of electron correlation effects

Ab initio calculations of the potential curves of low laying electronic states of OH are performed on the basis of a variational configuration interaction wavefunction (PNO-CI) and the coupled electron pair approximation (CEPA).