Compressed representation of dispersion interactions and long-range electronic correlations

Abstract

The description of electron correlation in quantum chemistry often relies on multiindex quantities. Here, we examine a compressed representation of the long-range part of electron correlation, that is associated with dispersion interactions. For this purpose, we perform CCSD computations on localized orbitals, then extract the portion of CCSD amplitudes corresponding to dispersion energies. Using singular value decomposition, we uncover that a very compressed representation of the amplitudes is possible in terms of occupied-virtual geminal pairs located on each monomer. These geminals provide an accurate description of dispersion energies at medium and long distances. The corresponding virtual orbitals are examined by further singular value decompositions of the geminals. We connect each component of the virtual space to the multipole expansion of dispersion energies. Our results are robust with respect to basis set change and hold for systems as large as the benzene-methane dimer.This compressed representation of dispersion energies paves the way to practical and accurate approximations for dispersion, for example in local correlation methods. a) j

Compressed intramolecular dispersion interactions

“…(subject to the same restrictions given on fragments A and B above). Since MP2 amplitudes are known to over estimate dispersion energies in the basis set limit 28,29 , the t ab ij amplitudes in equation 2 can be substituted with the more accurate CCSD amplitudes, similar to previous studies on the energy decomposition of the full exchangedispersion terms [30][31][32][33] and the previous SVD analysis of dimers 25 (see ref. 25 for more details).…”

“…The analysis of the compressibility of dispersion interactions between two monomers follows the method described in our previous work 25 . First, we choose a suitable tensor describing dispersion interactions, for example the CCSD T 2 amplitudes.…”

“…Since our interest usually lies in truncations of the virtual space, we restrict our analysis to matrix V . By transforming the significant columns of this matrix to the Atomic Orbital basis, we obtain and plot the most important virtual orbitals involved in the excitation processes giving rise to dispersion interactions 25 .…”

“…The correlation energy can be computed as the product of the CCSD amplitudes (decomposed as singular values and vectors) with the two-electron integrals. To the first order, the decay behavior of the singular values and the corresponding integrals will be the same 25 . Thus, the decay of the correlation energy will be the square of the singular values' decay, i.e., if singular values decay as R −3 , then the energy should decay as R −6 .…”

“…) between dimers can be greatly compressed to as few as three virtual orbitals per occupied orbital 25 . This result fulfills the prediction made by Pulay in his first paper on local correlation ideas 26 .…”