Atomic and molecular correlation energies with explicitly correlated Gaussian geminals. II. Perturbation treatment through third order for He, Be, H2, and LiH

Abstract

Third-order correlation energies for He, Be, H2, and LiH were calculated using highly accurate first-order pair functions obtained recently by us [J. Chem. Phys. 78, 1420 (1983)] with a novel second-order energy functional and a large basis set of explicitly correlated Gaussian geminals. Since these strong orthogonality projection, no new types of integrals appear as compared to the second-order treatment. Consequently, the third-order calculation does not require much more time than the second-order one. For He and Be atoms, the calculated third-order energies agree very well with the most accurate results obtained using the partial-wave expansion and extrapolation techniques. We estimate that our third-order energies are accurate up to within a fraction of 1%. The sum of the calculated values of the second- and third-order energies represents 97.5%, 90.4%, 94.4%, and 95.0% of the experimental correlation energy for He, Be, H2, and LiH, respectively.

Gaussian geminals in explicitly correlated coupled cluster theory including single and double excitations

“…Sensitivity of the CCSD-GTG method to the quality of the occupied Hartree-Fock orbitals turned out to be similar to that observed for the previously investigated MBPT and CCD approaches, 38,46,48 i.e., the relative error of the CCSD correlation energy resulting from the SCF basis set incompleteness is comparable to the relative error of the SCF energy. It is easy to saturate the correlation energy with respect to the orbital basis in which the one-electron cluster functions are expanded.…”

“…60 In the case of the H 2 molecule the present results are much better than those obtained in earlier GTG calculations employing smaller bases. 38,41,43,46,48 However, our CCSD energy is still 15 hartree off the accurate result. This relatively low accuracy when compared with direct RayleighRitz variational calculations 24 employing a similar number of basis functions has two reasons.…”

“…This functional allowed the use of much larger and better optimized geminal expansions and, in consequence, led to the second-and thirdorder energies of He, H 2 , Be and LiH that were the most accurate at that time. 46,48 The CCD-GTG energies have been computed for two-and four-electron systems, 38,49 as well as for the Ne atom 47 in geminal bases optimized at the secondorder level of MBPT. These calculations benefited from the use of a very efficient approximate strong orthogonality procedure introduced in Ref.…”

Theory and application of explicitly correlated Gaussians

“…Early applications were restricted to small basis sets because of the computationally expensive direct treatment of the strong orthogonality problem. The introduction of the more efficient weakorthogonality second-order energy functional (Szalewicz et al, 1982) resulted in MP2 (Szalewicz et al, 1983a) and MP3 energies (Szalewicz et al, 1983b) of He, Be, H 2 , and LiH that were the most accurate ones at that time. This approach was also applied to ten-electron systems: the Ne atom (Wenzel et al, 1986) and the water molecule (Bukowski et al, 1995).…”

Application of pair correlation theory to positronium compounds

“…Szalewicz et al have developed weak orthogonality ͑WO͒ techniques. [33][34][35][36][37][38] The WO techniques are very useful for use of explicitly correlated functions, where many-electron integrals due to strong orthogonality ͑SO͒ projector disappear. Kutzelnigg et al have developed a technique which reduces a many-electron integral to a sum of products of two-electron integrals by an incomplete set insertion.…”