Quantifying Intramolecular Basis Set Superposition Errors

Abstract

We show that medium-sized Gaussian basis sets lead to significant intramolecular basis set superposition errors at Hartree–Fock and density functional levels of theory, with artificial stabilization of compact over extended conformations for a 186 atom deca-peptide. Errors of ∼80 and ∼10 kJ/mol are observed, with polarized double zeta and polarized triple zeta quality basis sets, respectively. Two different procedures for taking the basis set superposition error into account are tested. While both reduce the error, it appears that polarized quadruple zeta basis sets are required to reduce the error below a few kJ/mol. Alternatively, the basis set superposition error can be eliminated using multiresolution methods based on Multiwavelets.

Basis Set Superposition Errors Are Partly Basis Set Imbalances

“…25 We have recently quantified intramolecular BSSE for a 186-atom peptide and shown that quadruple-ζ quality basis sets are required to reduce the BSSE to below 1 kJ/ mol with Hartree−Fock (HF) and density functional theory (DFT) methods. 29 Although an overestimation of the attractive interaction energy is the most commonly observed effect, Mentel for the Be dimer is underestimated by medium-sized basis sets and that the CP correction here leads to an even larger underestimation. 30 A similar observation has been made by Alvarez-Idaboy and Galano for the Ar dimer.…”

“…A valence bond approach can be used to estimate intramolecular BSSE but cannot account for charge-transfer effects . We have recently quantified intramolecular BSSE for a 186-atom peptide and shown that quadruple-ζ quality basis sets are required to reduce the BSSE to below 1 kJ/mol with Hartree–Fock (HF) and density functional theory (DFT) methods …”

VAMPyR—A high-level Python library for mathematical operations in a multiwavelet representation

“…The resulting representations, denoted f_n and df_n, are fully described by their mathematical definitions in Eqs. (7) and (9), respectively. 42 Figures 2 and 3 In Fig.…”

“…In particular, multiwavelets have recently been employed within the field of quantum chemistry to overcome some of the known drawbacks of traditional atomic orbital (AO)-based calculations. [1][2][3][4][5][6][7][8][9] The code that pioneered this approach is M-A-D-N-E-S-S, 10 followed by our own code, MRChem. 11 To date, they are the only two codes available for quantum chemistry calculations using multiwavelets.…”

Benchmarking Correlation-Consistent Basis Sets for Frequency-Dependent Polarizabilities with Multiresolution Analysis

“…MRA allows for a numerical solution of ground state and response properties − with guaranteed accuracy and speed. Recent results , demonstrate that for large molecules the MRA approach can be faster than Gaussian bases beyond low precision. Several previous studies have employed MRA to provide reference-quality quantum chemistry data − including evaluation of the aug-pc4 basis set for computation of DFT static polarizabilities on a set of 124 open and closed-shell systems. − …”