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

Abstract

Articles you may be interested inExplicitly correlated coupled-cluster theory using cusp conditions. I. Perturbation analysis of coupled-cluster singles and doubles (CCSD-F12)Explicitly correlated coupled-cluster singles and doubles method based on complete diagrammatic equations Explicitly correlated coupled cluster F12 theory with single and double excitations Improvement of the coupled-cluster singles and doubles method via scaling same-and opposite-spin components of the double excitation correlation energy A comparative assessment of the perturbative and renormalized coupled cluster theories with a noniterative treatment of triple excitations for thermochemical kinetics, including a study of basis set and core correlation effectsThe coupled cluster method with single and double excitations has been formulated in a basis set independent language of first quantization. In this formulation the excitation operators are represented in terms of one-and two-electron cluster functions satisfying a set of integrodifferential equations and the strong orthogonality conditions. These equations are solved iteratively by minimizing appropriate Hylleraas-type functionals. During the iteration process correlation energies of up to fourth order in the Mo "ller-Plesset perturbation operator are extracted. A slight modification of the coupled cluster equations leads to an explicitly correlated formulation of the configuration interaction theory. The method was tested in applications to two-and four-electron systems: He, Li ϩ , H 2 , Be, Li Ϫ , and LiH. The two-electron cluster functions were expanded using explicitly correlated Gaussian geminal bases optimized in the lowest order of perturbation theory. Most of the correlation energies computed at various levels of the coupled cluster and perturbation theory represent the most accurate values to date.

Theory and application of explicitly correlated Gaussians

“…Later the formalism was extended to the CCSD level of theory, with benchmark results reported for some two-electron (He, Li þ , H 2 ) and four-electron (Be, Li À , LiH) systems (Bukowski, Jeziorski, and Szalewicz, 1999).…”

Accurate ab initio potential energy curve of F2. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method

“…[79][80][81][82][83][84][85][86][87][88] Hylleraas 89 was the first to show that this problem can be greatly alleviated by the explicit inclusion of the interelectronic distance in the wavefunctions for He and H 2 . More recently, a number of authors have succeeded in adapting this approach to the general case of many-electron systems, [90][91][92][93][94][95][96][97] notwithstanding nontrivial algorithmic complexities. These methods yield indeed very accurate energies, but studies of potential energy surfaces are as yet rare.…”

New Transcorrelated Method Improving the Feasibility of Explicitly Correlated Calculations

“…Especially, Szalewicz and coworkers have used GTG successfully for accurate calculations of correlation energies in their series of papers [4,5]. Although the function form is not suitable from the viewpoint of the cusp condition, the methods with GTGs have demonstrated the efficiency [6,7] to give correlation energies to µHartree accuracy, as shown in the recent result of Cencek and Rychlewski [8]. This situation is comprehensible by evaluating the motion of pair-electrons in three-dimension, i.e.…”