General orbital invariant MP2-F12 theory

Abstract

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.

Gas-phase spectra of MgO molecules: a possible connection from gas-phase molecules to planet formation

“…Coupled cluster theory (Crawford & Schaefer III 2000;Shavitt & Bartlett 2009) at the singles, doubles, and perturbative triples [CCSD(T)] level (Raghavachari et al 1989) as well as the explicitly correlated second-order Møller-Plesset perturbation theory MP2-F12 levels (Raghavachari et al 1989;Møller & Plesset 1934;Werner, Adler & Manby 2007;Hill & Peterson 2010) are utilized to determine the spectroscopic properties of the magnesium oxide clusters. The CCSD(T) method used to calculate the spectroscopic data in this work is regarded as the "gold standard" of quantum chemistry (Helgaker et al 2004).…”

Gaussian basis sets for molecular applications

“…where V and B contain the many-electron integrals approximated by the RI, [91] and RI ref is a very large reference set of functions. [214] The resulting OptRI ABSs are compact and produce negligible RI errors compared to the basis set incompleteness error of the underlying OBS, both for correlation and relative energies.…”

“…The approach of Peterson and coworkers to producing basis sets for use with explicitly correlated methods mirrors the original cc work of Dunning as correlation consistent groupings were determined by plotting the incremental contribution of individual functions to the total correlation energy at the explicitly correlated second-order Møller-Plesset perturbation theory level (MP2-F12, [91,92] where F12 denotes a nonlinear correlation factor). [93] A comparison of the incremental correlation energy contributions at the MP2 and MP2-F12 levels made it obvious that higher angular momentum functions are much less important in explicitly correlated calculations, meaning only DZ-QZ sets were developed.…”

Accurate quantum chemical energies for tetrapeptide conformations: why MP2 data with an insufficient basis set should be handled with caution

“…We investigate here the MP2-F12 method, 19 which achieves a faster convergence to the CBS limit than conventional MP2. For the present systems, this can already be seen at the double-z level: MP2-F12/VDZ-F12 20 yields relative energies comparable to MP2/CBS (see Table 1).…”