A comparison of linear and nonlinear correlation factors for basis set limit Møller-Plesset second order binding energies and structures of He2, Be2, and Ne2

Accurate calculations of intermolecular interaction energies using explicitly correlated wave functions

Explicitly correlated second-order Møller-Plesset (MP2-F12) calculations of intermolecular interaction energies for the S22 benchmark set of Jurecka, Sponer, Cerný, and Hobza (Chem. Phys. Phys. Chem. 2006, 8, 1985) are presented and compared with standard MP2 results. The MP2 complete basis set limits are estimated using basis set extrapolation and augmented quadruple-zeta and quintuple-zeta basis sets. Already with augmented double-zeta basis sets the MP2-F12 interaction energies are found to be closer to the complete basis set limits than standard MP2 calculations with augmented quintuple-zeta basis sets. Various possible approximations in the MP2-F12 method are systematically tested. Best results are obtained with localized orbitals and the diagonal MP2-F12/C(D) ansatz. Hybrid approximations, in which some contributions of the auxiliary basis set are neglected and which considerably reduce the computational cost, have a negligible effect on the interaction energies. Also the orbital-invariant fixed-amplitude approximation of Ten-no leads to only slightly less accurate results. Preliminary results for the neon and benzene dimers, obtained with the recently proposed CCSD(T)-F12a approximation, indicate that the CCSD(T) basis set limits can also be very closely approached using augmented triple-zeta basis sets.

General orbital invariant MP2-F12 theory

A general form of orbital invariant explicitly correlated second-order closed-shell Moller-Plesset perturbation theory (MP2-F12) is derived, and compact working equations are presented. Many-electron integrals are avoided by resolution of the identity (RI) approximations using the complementary auxiliary basis set approach. A hierarchy of well defined levels of approximation is introduced, differing from the exact theory by the neglect of terms involving matrix elements over the Fock operator. The most accurate method is denoted as MP2-F12/3B. This assumes only that Fock matrix elements between occupied orbitals and orbitals outside the auxiliary basis set are negligible. For the chosen ansatz for the first-order wave function this is exact if the auxiliary basis is complete. In the next lower approximation it is assumed that the occupied orbital space is closed under action of the Fock operator [generalized Brillouin condition (GBC)]; this is equivalent to approximation 2B of Klopper and Samson [J. Chem. Phys. 116, 6397 (2002)]. Further approximations can be introduced by assuming the extended Brillouin condition (EBC) or by neglecting certain terms involving the exchange operator. A new approximation MP2-F12/3C, which is closely related to the MP2-R12/C method recently proposed by Kedzuch et al. [Int. J. Quantum Chem. 105, 929 (2005)] is described. In the limit of a complete RI basis this method is equivalent to MP2-F12/3B. The effect of the various approximations (GBC, EBC, and exchange) is tested by studying the convergence of the correlation energies with respect to the atomic orbital and auxiliary basis sets for 21 molecules. The accuracy of relative energies is demonstrated for 16 chemical reactions. Approximation 3C is found to perform equally well as the computationally more demanding approximation 3B. The reaction energies obtained with smaller basis sets are found to be most accurate if the orbital-variant diagonal Ansatz combined with localized orbitals is used for the first-order wave function. This unexpected result is attributed to geminal basis set superposition errors present in the formally more rigorous orbital invariant methods.

Dispersion interactions within the Piris natural orbital functional theory: The helium dimer

The authors have investigated the description of the dispersion interaction within the Piris natural orbital functional (PNOF) theory. The PNOF arises from an explicit antisymmetric approach for the two-particle cumulant in terms of two symmetric matrices, Delta and Lambda. The functional forms of these matrices are obtained from the generalization of the two-particle system expressions, except for the off-diagonal elements of Delta. The mean value theorem and the partial sum rule obtained for the off-diagonal elements of Delta provide a prescription for deriving practical functionals. In particular, the previous employed approximation {Jpp/2} for the mean values {Jp*} affords several molecular properties but it is incapable to account for dispersion effects. In this work, the authors analyze a new approach for Jp* obtained by factorization of the matrix Delta within the bounds on its off-diagonal elements imposed by the positivity conditions of the two-particle reduced density matrix. Additional terms for the matrix elements of Lambda proportional to the square root of the holes are again introduced to describe properly the occupation numbers of the lowest occupied levels. The authors have found that the cross products between weakly occupied orbitals must be removed from the functional form of Lambda to obtain a correct long-range asymptotic behavior. The PNOF is used to predict the binding energy as well as the equilibrium distance of the helium dimer. The results are compared with the full configuration-interaction calculations and the corresponding experimental data.

New implementation of second-order Møller-Plesset perturbation theory with an analytic Slater-type geminal

The author introduces a new method for the exchange commutator integrals in explicitly correlated Møller-Plesset second order perturbation theory. The method is well suited with an analytic Slater-type geminal correlation factor. He also explains the scheme for auxiliary integrals needed for the correlation factor. Based on different Ansätze, he analyzes the performance of the method on correlation energies and reaction enthalpies in detail.

Quintuple-ζ quality coupled-cluster correlation energies with triple-ζ basis sets

The explicitly-correlated coupled-cluster method CCSD(T)(R12) is extended to include F12 geminal basis functions that decay exponentially with the interelectronic distance and reproduce the form of the average Coulomb hole more accurately than linear-r(12). Equations derived using the Ansatz 2 strong orthogonality projector are presented. The convergence of the correlation energy with orbital basis set for the new CCSD(T)(F12) method is studied and found to be rapid, 98% of the basis set limit correlation energy is typically recovered using triple-zeta orbital basis sets. The performance for reaction enthalpies is assessed via a test set of 15 reactions involving 23 molecules. The title statement is found to hold equally true for total and relative correlation energies.