Energy-Screened Many-Body Expansion: A Practical Yet Accurate Fragmentation Method for Quantum Chemistry

Abstract

We introduce an implementation of the truncated many-body expansion, MBE(n), in which the n-body corrections are screened using the effective fragment potential force field, and only those that exceed a specified energy threshold are computed at a quantum-mechanical level of theory. This energy-screened MBE(n) approach is tested at the n = 3 level for a sequence of water clusters, (H 2 O) N=6−34 . A threshold of 0.25 kJ/mol eliminates more than 80% of the subsystem electronic structure calculations and is even more efficacious in that respect than is distance-based screening. Even so, the energyscreened MBE(3) method is faithful to a full-system quantum chemistry calculation to within 1−2 kJ/mol/monomer, even in good quality basis sets such as aug-cc-pVTZ. These errors can be reduced by means of a two-layer approach that involves a Hartree−Fock calculation for the entire cluster. Such a correction proves to be necessary in order to obtain accurate relative energies for conformational isomers of (H 2 O) 20 , but the cost of a full-system Hartree−Fock calculation remains smaller than the cost of three-body subsystem calculations at correlated levels of theory. At the level of second-order Møller− Plesset perturbation theory (MP2), a screened MBE(3) calculation plus a full-system Hartree−Fock calculation is less expensive than a full-system MP2 calculation starting at N = 12 water molecules. This is true even if all MBE(3) subsystem calculations are performed on a single 40-core compute node, i.e., without significant parallelization. Energy-screened MBE(n) thus provides a fragment-based method that is accurate, stable in large basis sets, and low in cost, even when the latter is measured in aggregate computer time.

Analytic first and second derivatives of the energy in the fragment molecular orbital method combined with molecular mechanics

“…Deviations of the vibrational frequencies from 20 Å, envir = MM) for (A) formate (envir = MM); (B) DMEDAH (envir = MM); (C) Trp‐6 (envir = MM); (D) formate (envir = none); (E) DMEDAH (envir = none); and (F) Trp‐6 (envir = none). Formate and DMEDAH are computed in an ionic liquid cluster; Trp‐6 is computed in solvated Trp‐cage…”

“…[10,11] One way to accomplish the scaling reduction is provided by fragmentation approaches. [12][13][14][15][16][17][18][19][20][21] Some of them have analytic second derivatives developed. [22][23][24][25][26] Delocalized low frequencies are hard to estimate accurately without anharmonic corrections [27] because the frequencies and corrections may have a similar magnitude.…”

Frozen‐density embedding‐based many‐body expansions

“…Water clusters present a challenging test case for the MBE because of the large many-body polarization effects that need to be captured. [38,44,72,[77][78][79][80] Here, we consider water clusters extracted from the crystal structure of ice I h. [81,82] First, we use a water pentamer, (H 2 O) 5 , in which the central water molecule is surrounded by four water molecules in a pseudo-tetrahedral environment (see Figure 1A). Second, we consider an (H 2 O) 17 cluster, in which a second shell of water molecules has been added to the pentamer, that is, each of the surrounding water molecules in the pentamer is now coordinated to three additional water molecules that complete its pseudo-tetrahedral environment (see Figure 1B).…”

Frozen-Density Embedding Based Many-Body Expansions

“…Water clusters present a challenging test case for the MBE because of the large many-body polarization effects that need to be captured [38,44,72,[77][78][79][80]. Here, we consider water clusters extracted from the crystal structure of ice I h [81,82].…”