Performance of small basis set Hartree–Fock methods for modeling non-covalent interactions

J. Chem. Theory Comput.

2022

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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.

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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

Prasad

J. Chem. Theory Comput.

2022

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“…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.…”

Section: Computational Detailsmentioning

confidence: 99%

“…We have shown in earlier studies that atom-centered potentials (ACPs) offer a useful way to mitigate the underlying shortcomings of HF and DFT methods. − ACPs are similar to one-electron effective-core potentials , (ECPs) in functional form, except ACPs do not replace any electrons. Sharing a form similar to ECPs allows ACPs to be used in any software package that implements the use of ECPs.…”

Section: Introductionmentioning

confidence: 99%

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

Prasad

J. Chem. Theory Comput.

2022

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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.

“…When used in conjunction with a minimal basis set, such as that of Huzinaga with scaled exponents (MINIs), HF is among the least expensive quantum mechanical methods available. However, HF/MINIs does not accurately capture intermolecular interactions, and even when corrected for dispersion it does not come close to chemical accuracy. − For example, HF-D3/MINIs, which uses Grimme’s D3 dispersion, has been shown to still suffer from significant basis set incompleteness error (BSIE) . The HF-3c , method improves upon HF/MINIs by using a tailor-made basis set derived from MINIs (MINIX) and three empirical corrections to account for dispersion (D3 with Becke-Johnson damping, D3BJ), , basis set superposition error (gCP), and short-range covalent overbinding (SRB): The last two terms in Equation mitigate BSIE.…”

Section: Introductionmentioning

confidence: 99%

Minimal Basis Set Hartree–Fock Corrected with Atom-Centered Potentials for Molecular Crystal Modeling and Crystal Structure Prediction

Tuca

2022

J. Chem. Inf. Model.

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Crystal structure prediction (CSP), determining the experimentally observable structure of a molecular crystal from the molecular diagram, is an important challenge with technologically relevant applications in materials manufacturing and drug design. For the purpose of screening the randomly generated candidate crystal structures, CSP protocols require energy ranking methods that are fast and can accurately capture the small energy differences between molecular crystals. In addition, a good ranking method should also produce accurate equilibrium geometries, both intramolecular and intermolecular. In this article, we explore the combination of minimal-basis-set Hartree–Fock (HF) with atom-centered potentials (ACPs) as a method for modeling the structure and energetics of molecular crystals. The ACPs are developed for the H, C, N, and O atoms and fitted to a set of reference data at the B86bPBE-XDM level in order to mitigate basis-set incompleteness and missing correlation. In particular, ACPs are developed in combination with two methods: HF-D3/MINIs and HF-3c. The application of ACPs greatly improves the performance of HF-D3/MINIs for lattice energies, crystal energy differences, energy-volume and energy-strain relations, and crystal geometries. In the case of HF-3c, the improvement in the crystal energy differences is much smaller than in HF-D3/MINIs, but lattice energies and particularly crystal geometries are considerably better when ACPs are used. The resulting methods may be useful for CSP but also for quick calculation of molecular crystal lattice energies and geometries.