Low rank factorization of the Coulomb integrals for periodic coupled cluster theory

Abstract

We study a tensor hypercontraction decomposition of the Coulomb integrals of periodic systems where the integrals are factorized into a contraction of six matrices of which only two are distinct. We find that the Coulomb integrals can be well approximated in this form already with small matrices compared to the number of real space grid points. The cost of computing the matrices scales as O(N) using a regularized form of the alternating least squares algorithm. The studied factorization of the Coulomb integrals can be exploited to reduce the scaling of the computational cost of expensive tensor contractions appearing in the amplitude equations of coupled cluster methods with respect to system size. We apply the developed methodologies to calculate the adsorption energy of a single water molecule on a hexagonal boron nitride monolayer in a plane wave basis set and periodic boundary conditions.

Applying the Coupled-Cluster Ansatz to Solids and Surfaces in the Thermodynamic Limit

“…The same system has recently been studied using diffusion Monte Carlo (DMC), the random-phase approximation (RPA), and dispersion functionals [40,41], as well as molecular MP2 [42] and periodic coupled cluster theory [43], demonstrating the need for reliable methods that can account for long-range van der Waals interactions and also to provide benchmark data. Furthermore, the recent work of Al-Hamdani et al [40] illustrates the importance of long-range correlation effects that account for approximately 25% of the reference adsorption energy computed in a (4 × 4) unit cell of h-BN.…”

“…We observe a similar speed-up in convergence using RPA þ SOSEX-FS theory, illustrating the transferability of the proposed method. The water adsorption on the 32-atom h-BN sheet can also be studied using the more sophisticated CCSD theory [43]. CCSD with and without finite-size corrections yields an adsorption energy of 83 meV and 68 meV, respectively.…”

“…We believe that the ability to predict accurate benchmark results will help the entire electronic structure theory community to improve further upon computationally efficient ab initio theories and to help interpret experimental findings more reliably. To expand the scope of the proposed techniques even further, we will aim at combining them with explicit correlation and low-rank factorization methods [43][44][45].…”

Sampling Potential Energy Surfaces in the Condensed Phase with Many‐Body Electronic Structure Methods

“…With the PW basis, both MP2 and RPA energies and forces are available with k ‐point sampling in the VASP program . Related to VASP is the cc4s program featuring CC methods to computed electronic energies …”

“…With the PW basis, both MP2 [33,34] and RPAe nergies [11] and forces [35] are available with k-point samplingi nt he VASP program. [18,19] Relatedt o VASP is the cc4s program featuring CC methods [36] to computed electronic energies. [12] MP2 energies [37,38] andf orces [39][40][41] as well as RPAe nergies [38,42] with Gaussian basis sets are available( with RI and GPW techniques employed for the integral evaluation, RI-GPW) in the CP2K program.…”