Small-Basis Set Density-Functional Theory Methods Corrected with Atom-Centered Potentials

Abstract

Density functional theory (DFT) is currently the most popular method for modeling noncovalent interactions and thermochemistry. The accurate calculation of noncovalent interaction energies, reaction energies, and barrier heights requires choosing an appropriate functional and, typically, a relatively large basis set. Deficiencies of the density-functional approximation and the use of a limited basis set are the leading sources of error in the calculation of noncovalent and thermochemical properties in molecular systems. In this article, we present three new DFT methods based on the BLYP, M06-2X, and CAM-B3LYP functionals in combination with the 6-31G* basis set and corrected with atom-centered potentials (ACPs). ACPs are one-electron potentials that have the same form as effective-core potentials, except they do not replace any electrons. The ACPs developed in this work are used to generate energy corrections to the underlying DFT/basis-set method such that the errors in predicted chemical properties are minimized while maintaining the low computational cost of the parent methods. ACPs were developed for the elements H, B, C, N, O, F, Si, P, S, and Cl. The ACP parameters were determined using an extensive training set of 118655 data points, mostly of complete basis set coupled-cluster level quality. The target molecular properties for the ACP-corrected methods include noncovalent interaction energies, molecular conformational energies, reaction energies, barrier heights, and bond separation energies. The ACPs were tested first on the training set and then on a validation set of 42567 additional data points. We show that the ACP-corrected methods can predict the target molecular properties with accuracy close to complete basis set wavefunction theory methods, but at a computational cost of double-ζ DFT methods. This makes the new BLYP/6-31G*-ACP, M06-2X/6-31G*-ACP, and CAM-B3LYP/ 6-31G*-ACP methods uniquely suited to the calculation of noncovalent, thermochemical, and kinetic properties in large molecular systems.

Bridging the gap between high-level quantum chemical methods and deep learning models

“…where U local is a local potential and U l are potentials associated with the angular momenta (l) of the occupied orbitals of each atom (A) for which the ACP is developed. The value of l max is taken to be one larger than the maximum l of the occupied atomic orbitals; this is the choice used in previous works [9][10][11][12][13]. The U l potentials are projected onto orbitals of specific angular momentum via the |l⟩⟨l| operators.…”

“…Our choice is motivated by the good performance of ωB97XD for reaction energies and barrier heights [8,26,27], and by cursory calculations on the BSE49 and BH9 sets with various functional and basis set combinations, as well as our own experience that ωB97XD performs well across a range of chemical properties. The choice of this particular functional is not very critical because ACP improves performance regardless of the choice of functional, basis set, and target molecular property [9][10][11]. The pcseg-1 basis set [28] was chosen because it was optimized for DFT calculations and is computationally efficient.…”

“…Previous efforts in ACP development were centered on the generation of general-purpose ACPs for Hartree-Fock (HF) and DFT methods with large fitting data sets (≈10 5 ) for non-covalent interactions and thermochemistry [9][10][11][12][13]. In contrast with our past work, this article focuses on demonstrating how ACPs developed for specific properties (BDEs, reaction energies, barrier heights, .…”

Best Practice DFT Protocols for Basic Molecular Computational Chemistry

“…For BSSE prone systems with clearly separated fragments with no inter-fragment covalent bonds, the so-called counter-poise correction can be applied to correct for BSSE. 112 An efficient alternative to this computationally demanding correction is provided by approximate, empirical correction schemes that are based on the molecular structure, such as the geometric counter-poise correction (gCP), or employ specially adapted effective core potentials 113 In contrast to the full counterpoise corrections, these are always applicable and computationally cheap, and thus can also employed to correct for the intramolecular BSSE. Such approximate counter-poise corrections can repair the most drastic effects of BSSE, e.g., in geometry optimizations with small basis sets.…”

Best Practice DFT Protocols for Basic Molecular Computational Chemistry

“…For BSSE prone systems with clearly separated fragments with no inter-fragment covalent bonds, the so-called counter-poise correction can be applied to correct for BSSE. 91 An efficient alternative to this computationally demanding correction is provided by approximate, empirical correction schemes that are based on the molecular structure, such as the geometric counter-poise correction (gCP), or employ specially adapted effective core potentials 92 In contrast to the full counterpoise corrections, these are always applicable and computationally cheap, and thus can also employed to correct for the intramolecular BSSE. Such approximate counterpoise corrections can repair the most drastic effects of BSSE, e.g., in geometry optimizations with small basis sets.…”