Infinite‐order functional for nonlinear parameters optimization in explicitly correlated coupled cluster theory

Abstract

ABSTRACT:Coupled cluster (CC) calculations with Gaussian geminals rely heavily on extensive optimizations of nonlinear parameters (exponents and positions) defining the geminal basis functions. As the CC method is not a variational theory, it provides no functional for such an optimization. The nonlinear parameters must therefore be supplied by some other theory, giving pair functions that can be expected to be close to those of the CC method. The conventional approach thus far was to use the secondorder many-body perturbation theory with Møller-Plesset partition of the Hamiltonian (MP2) for this purpose and to minimize the corresponding Hylleraas-type functional. We present a new functional, which goes beyond the second order, and can be applied in situations when the Møller-Plesset theory converges slowly. This functional does take a partial account of infinite-order terms in the MP theory, but neglects the interpair coupling in the spirit of the independent electron pair approximation approach. The pair functions minimizing this new functional include the most important infinite-order contributions from the point of view of the MP theory and are much closer to the CC pair functions than the first-order ones. The nonlinear parameters obtained using this infinite-order functional are then better suited for coupled cluster calculations than those obtained using the MP2 functional. The effectiveness of the new functional is demonstrated by performing coupled cluster doubles (CCD) calculations for the Be atom and Li Ϫ ion. The obtained energies are much better than those based on the MP2

Theory and application of explicitly correlated Gaussians

“…In most cases, the MP2-optimized bases lead to satisfactory convergence of the coupled-cluster energies. Recently, a new, infinite-order functional was presented (Przybytek, Jeziorski, and Szalewicz, 2009), which can be used in cases where post-MP2 contributions to the CCD or CCSD energies are large.…”

Correlation energies for many-electron atoms with explicitly correlated Slater functions

“…For larger basis sets it becomes oscillatory and finally diverges. This [60]. e re-optimised 400-term GTG expansion (infinite-order functional), Ref.…”

“…f 400-term GTG expansion (infinite-order functional), Ref. [60]. change in the behaviour usually occurred for n a and Ω for which the number of basis functions exceeded 400, and prevented us from generating more accurate results.…”

“…The corresponding results for helium atom and lithium cation/anion are also provided, together with data from Refs. [58][59][60] which used to be the most accurate results available in the literature. The uncertainty of the present data (≈ 1 pE h ) constitutes an improvement of roughly 5 orders of magnitude compared with previous works.…”

On the large interelectronic distance behavior of the correlation factor for explicitly correlated wave functions

“…Thus, the pair functions were not represented with a single, universal correlation factor. Massive optimizations of thousands of nonlinear parameters defining the Gaussian geminals (γ i and orbital exponents) made these calculations very time-consuming, limiting applications of this approach to very small systems like Be, Li − , LiH, He 2 , Ne, or H 2 O [31][32][33][34][35] .…”