Coupled-Cluster Density-Based Many-Body Expansion

While CCSD(T) is often considered the “gold standard” of computational chemistry, the scaling of its computational cost as N7 limits its applicability for large and complex molecular systems. In this work, we apply the density-based many-body expansion [Int. J. Quantum Chem.2020, 120, e26228] in combination with CCSD(T). The accuracy of this approach is assessed for neutral, protonated, and deprotonated water hexamers, as well as (H2O)16 and (H2O)17 clusters. For the neutral water clusters, we find that already with a density-based two-body expansion, we are able to approximate the supermolecular CCSD(T) energies within chemical accuracy (4 kJ/mol). This surpasses the accuracy that is achieved with a conventional, energy-based three-body expansion. We show that this accuracy can be maintained even when approximating the electron densities using Hartree–Fock instead of using coupled-cluster densities. The density-based many-body expansion thus offers a simple, resource-efficient, and highly parallelizable approach that makes CCSD(T)-quality calculations feasible where they would otherwise be prohibitively expensive.

This Supporting Information contains interaction energies for the calculations presented in the results section of the main article.The total interaction of a system E super int,tot describes the interaction between the subsystems.It is defined as Herein, E is the energy of an isolated subsystem, i.e. a monomer, and E super tot is the total energy of the full system in a supermolecular calculation at the considered level of theory.For (H 2 O) 16 and (H 2 O) 17 , the latter values have been taken from Ref. [1].
Within the energy-based MBE scheme discussed in the paper, the sum of isolated monomer I is equivalent to the one-body expansion E eb-MBE( 1) tot . The other interaction energies at the different orders n of the MBE are approximations of this total interaction energy and defined analogously as and Errors, as presented in the main text, can be calculated as differences between the approximated total interaction energies and the exact value for E super int,tot .Results achieved with various methods as applied to the neutral water hexamers are presented in tables S1 to S4.
Our other test systems are presented only with the preferred combination of CCSD(T) energies and HF densities.They can be found in tables S5 to S8. ) and the density-based MBE of order n (E ).The calculations for the reference energies and the energy-based MBE energies are done with HF/aug-cc-pVTZ.The density-based energies start from the energy-based MBE energies and use HF/aug-cc-pVTZ densities and PBE/PW91k for the corrections.) and the density-based MBE of order n (E ).The calculations for the reference energies and the energy-based MBE energies are done with CCSD(T)/aug-cc-pVTZ.The density-based energies start from the energy-based MBE energies and use OO-CCD/aug-cc-pVTZ orbital-densities and PBE/PW91k for the corrections.).The calculations for the reference energies and the energy-based MBE energies are done with CCSD(T)/aug-cc-pVTZ.The densitybased energies start from the energy-based MBE energies and use HF/aug-cc-pVTZ orbital-densities and PBE/PW91k for the corrections.) and the density-based MBE of order n (E ).The calculations for the reference energies and the energy-based MBE energies are done with CCSD(T)/augcc-pVTZ.The density-based energies start from the energy-based MBE energies and use HF/aug-cc-pVTZ orbital-densities and PBE/PW91k for the corrections.) and the density-based MBE of order n (E ).The calculations for the reference energies and the energy-based MBE energies are done with CCSD(T)/augcc-pVTZ.The density-based energies start from the energy-based MBE energies and use HF/aug-cc-pVTZ orbital-densities and PBE/PW91k for the corrections.).The calculations for the reference energies and the energy-based MBE energies are done with CCSD(T)/aug-cc-pVTZ.The density-based energies start from the energy-based MBE energies and use HF/aug-cc-pVTZ orbital-densities and PBE/PW91k for the corrections.).The calculations for the reference energies and the energy-based MBE energies are done with CCSD(T)/aug-cc-pVTZ.The density-based energies start from the energy-based MBE energies and use HF/aug-cc-pVTZ orbital-densities and PBE/PW91k for the corrections.

Table S3 :
tot Total interaction energies in kJ/mol calculated for the neutral water hexamers (H 2 O) 6 from: the full calculation of the cluster (E super int,tot ), the energy-based MBE of order n (E tot TableS4: Total interaction energies in kJ/mol calculated for the neutral water hexamers (H 2 O) 6 from: the full calculation of the cluster (E super int,tot ), the energy-based MBE of order n (E

Table S5 :
tot Total interaction energies in kJ/mol calculated for the protonated water hexamers (H 3 O + )-(H 2 O) 5 from: the full calculation of the cluster (E super int,tot ), the energy-based MBE of order n (E

Table S6 :
tot Total interaction energies in kJ/mol calculated for the deprotonated water hexamers (OH − )-(H 2 O) 5 from: the full calculation of the cluster (E super int,tot ), the energy-based MBE of order n (E

Table S7 :
tot Total interaction energies in kJ/mol calculated for the water 16mers (H 2 O) 16 from: the full calculation of the cluster (E super int,tot ), the energy-based MBE of order n (E

Table S8 :
Total interaction energies in kJ/mol calculated for the water 17mers (H 2 O) 17 from: the full calculation of the cluster (E super int,tot ), the energy-based MBE of order n (E