Fast and Accurate Quantum Mechanical Modeling of Large Molecular Systems Using Small Basis Set Hartree–Fock Methods Corrected with Atom-Centered Potentials

Abstract

There has been significant interest in developing fast and accurate quantum mechanical methods for modeling large molecular systems. In this work, by utilizing a machine learning regression technique, we have developed new low-cost quantum mechanical approaches to model large molecular systems. The developed approaches rely on using one-electron Gaussian-type functions called atom-centered potentials (ACPs) to correct for the basis set incompleteness and the lack of correlation effects in the underlying minimal or small basis set Hartree−Fock (HF) methods. In particular, ACPs are proposed for ten elements common in organic and bioorganic chemistry (H, B, C, N, O, F, Si, P, S, and Cl) and four different base methods: two minimal basis sets (MINIs and MINIX) plus a double-ζ basis set (6-31G*) in combination with dispersion-corrected HF (HF-D3/MINIs, HF-D3/MINIX, HF-D3/6-31G*) and the HF-3c method. The new ACPs are trained on a very large set (73 832 data points) of noncovalent properties (interaction and conformational energies) and validated additionally on a set of 32 048 data points. All reference data are of complete basis set coupled-cluster quality, mostly CCSD(T)/CBS. The proposed ACP-corrected methods are shown to give errors in the tenths of a kcal/mol range for noncovalent interaction energies and up to 2 kcal/mol for molecular conformational energies. More importantly, the average errors are similar in the training and validation sets, confirming the robustness and applicability of these methods outside the boundaries of the training set. In addition, the performance of the new ACP-corrected methods is similar to complete basis set density functional theory (DFT) but at a cost that is orders of magnitude lower, and the proposed ACPs can be used in any computational chemistry program that supports effective-core potentials without modification. It is also shown that ACPs improve the description of covalent and noncovalent bond geometries of the underlying methods and that the improvement brought about by the application of the ACPs is directly related to the number of atoms to which they are applied, allowing the treatment of systems containing some atoms for which ACPs are not available. Overall, the ACP-corrected methods proposed in this work constitute an alternative accurate, economical, and reliable quantum mechanical approach to describe the geometries, interaction energies, and conformational energies of systems with hundreds to thousands of atoms.

Best‐Practice DFT Protocols for Basic Molecular Computational Chemistry**

“…[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 counterpoise 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 be 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.…”

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

“…The ACP development procedure employed in this article has been described in detail in our earlier studies. − , We summarize it here for convenience. The mathematical form of an ACP is: where δ V l α ( r ) = V l α ( r ) – V local α ( r ), α represents an atom, r is the distance, and | Y lm ⟩⟨ Y lm | are projection operators using real spherical harmonics based on atom α with l angular momentum quantum numbers and m magnetic quantum numbers.…”

“…The total number of ACP energy terms was 1102. This way of generating the ACP energy terms and carrying out the fitting procedure is identical to our previous studies. − ,, Least absolute shrinkage and selection operator (LASSO) regression − is employed to solve the regularized least-squares fitting problem. The advantage of LASSO is that it automatically selects the best subset of ACP energy terms and discards the others by assigning a zero coefficient to them.…”

“… a Defined as the difference between the energy of the complex and the sum of the monomer energies. A negative interaction energy indicates that the complex is more stable than the separated monomers. b The reference data were recalculated using DLPNO-CCSD­(T)/CBS (see ref ). c Comprises noncovalently bound dimer complexes where at least one of the monomers is negatively charged. d The reference data were calculated at the CCSD­(T)/CBS level using the same extrapolation method as in ref . e Defined as the difference between the energy of a particular conformer and a lower-energy conformer of the same molecule. f Comprises negatively charged conformers. g Defined as the difference between the sum of energies of reactants minus that of products or vice-versa. h The forward barrier height is the energy difference between the transition state and reactant(s) or prereaction complex; the reverse barrier height is the energy difference between the transition state and product(s) or postreaction complex. i The reference data were recalculated using DLPNO-CCSD­(T)/CBS with the same extrapolation method as in ref . j The barrier heights are relative to the pre- or postreaction complexes for forward and reverse barriers, respectively. k The barrier heights are relative to the isolated reactant(s) or product(s) for forward and reverse barriers, respectively. l Defined as the difference between the energy of a molecule and its radical fragments formed by cleavage of a particular bond. m Includes molecular deformation energies, isomerization energies, and total atomization energies. Molecular deformation energy is the difference between the energy of a molecule deformed along a particular normal mode and the energy of the same molecule at equilibrium.…”

“…In this way, ACPs can be used to efficiently mitigate the shortcomings of double-ζ basis set DFT methods, because the use of ACPs incurs only a ca. 10% increase in the computational cost relative to the uncorrected method.…”