Integral-Direct Hartree-Fock and Møller-Plesset Perturbation Theory for Periodic Systems with Density Fitting: Application to the Benzene Crystal

Adsorption and vibrational spectroscopy of CO on the surface of MgO from periodic local coupled-cluster theory

The adsorption of CO on the surface of MgO has long been a model problem in surface chemistry. Here, we report periodic Gaussian-based calculations for this problem using second-order perturbation theory (MP2) and coupled-cluster theory with single and double excitations (CCSD) and perturbative triple excitations [CCSD(T)], with the latter two performed using a recently developed extension of the local natural orbital approximation to problems with periodic boundary conditions. The low cost of periodic local correlation calculations allows us to calculate the full CCSD(T) binding curve of CO approaching the surface of MgO (and thus the adsorption energy) and the two-dimensional potential energy surface (PES) as a function of the distance from the surface and the CO stretching coordinate. From the PES, we obtain the fundamental vibrational frequency of CO on MgO, whose shift from the gas phase value is a common experimental probe of surface adsorption. We find that CCSD(T) correctly predicts a positive frequency shift upon adsorption of +14.7 cm-1, in excellent agreement with the experimental shift of +14.3 cm-1. We use our CCSD(T) results to assess the accuracy of MP2, CCSD, and several density functional theory (DFT) approximations, including exchange correlation functionals and dispersion corrections. We find that MP2 and CCSD yield reasonable binding energies and frequency shifts, whereas many DFT calculations overestimate the magnitude of the adsorption energy by 5-15 kJ mol-1 and predict a negative frequency shift of about -20 cm-1, which we attribute to self-interaction-induced delocalization errors that are mildly ameliorated with hybrid functionals. Our findings highlight the accuracy and computational efficiency of the periodic local correlation for the simulation of surface chemistry with accurate wavefunction methods.

Massively parallel implementation of gradients within the random phase approximation: Application to the polymorphs of benzene

The Random-Phase approximation (RPA) provides an appealing framework for semi-local density functional theory. In its Resolution-of-the-Identity (RI) approach, it is a very accurate and more cost-effective method than most other wavefunction-based correlation methods. For widespread applications, efficient implementations of nuclear gradients for structure optimizations and data sampling of machine learning approaches are required. We report a well scaling implementation of RI-RPA nuclear gradients on massively parallel computers. The approach is applied to two polymorphs of the benzene crystal obtaining very good cohesive and relative energies. Different correction and extrapolation schemes are investigated for further improvement of the results and estimations of error bars.

Can Spin-Component Scaled MP2 Achieve kJ/mol Accuracy for Cohesive Energies of Molecular Crystals?

Attaining kJ/mol accuracy in cohesive energy for molecular crystals is a persistent challenge in computational materials science. In this study, we evaluate second-order Møller-Plesset perturbation theory (MP2) and its spin-component scaled models for calculating cohesive energies for 23 molecular crystals (X23 data set). Using periodic boundary conditions and Brillouin zone sampling, we converge results to the thermodynamic and complete basis set limits, achieving an accuracy of about 2 kJ/mol (0.5 kcal/mol), which is rarely achieved in previous MP2 calculations for molecular crystals. When compared to experimental data, our results have a mean absolute error of 12.9 kJ/mol, comparable to Density Functional Theory with the PBE functional and TS dispersion correction. By separately scaling the opposite-spin and same-spin correlation energy components, using predetermined parameters, we reduce the mean absolute error to 9.5 kJ/mol. Further fine-tuning of these scaling parameters specifically for the X23 data set brings the mean absolute error down to 7.5 kJ/mol.

Even Faster Exact Exchange for Solids via Tensor Hypercontraction

Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting) approximation to periodic hybrid DFT calculations with Gaussian-type orbitals using the Gaussian plane wave approach. This is done to lower the computational scaling with respect to the number of basis functions (N) and k-points (Nk) at a fixed system size. Additionally, we propose an algorithm to fit only occupied orbital products via THC (i.e., a set of points, NISDF) to further reduce computation time and memory usage. This algorithm has linear scaling cost with k-points, no explicit dependence of NISDF on basis set size, and overall cubic scaling with unit cell size. Significant speedups and reduced memory usage may be obtained for moderately sized k-point meshes, with additional gains for large k-point meshes. Adequate accuracy can be obtained using THC-oo-K for self-consistent calculations. We perform illustrative hybrid density function theory calculations on the benzene crystal in the basis set and thermodynamic limits to highlight the utility of this algorithm.

Exact exchange with range-separated algorithm for thermodynamic limit of periodic Hartree-Fock theory

The expensive cost of computing exact exchange in periodic systems limits the application range of density functional theory with hybrid functionals. To reduce the computational cost of exact change, we present a range-separated algorithm to compute electron repulsion integrals for Gaussian-type crystal basis. The algorithm splits the full-range Coulomb interactions into short-range and long-range parts, which are, respectively, computed in real and reciprocal space. This approach significantly reduces the overall computational cost, as integrals can be efficiently computed in both regions. The algorithm can efficiently handle large numbers of k points with limited central processing unit (CPU) and memory resources. As a demonstration, we performed an all-electron k-point Hartree-Fock calculation for LiH crystal with one million Gaussian basis functions, which was completed on a desktop computer in 1400 CPU hours.

Faster Exact Exchange for Solids via occ-RI-K: Application to Combinatorially Optimized Range-Separated Hybrid Functionals for Simple Solids with Pseudopotentials Near the Basis Set Limit

In this work, we developed and showcased the occ-RI-K algorithm to compute the exact exchange contribution in density functional calculations of solids near the basis set limit. Within the Gaussian planewave (GPW) density fitting, our algorithm achieves a 1-2 orders of magnitude speedup compared to conventional GPW algorithms. Since our algorithm is well suited for simulations with large basis sets, we applied it to 12 hybrid density functionals with pseudopotentials and a large uncontracted basis set to assess their performance on band gaps of 25 simple solids near the basis set limit. The largest calculation performed in this work involves 16 electrons and 350 basis functions in the unit cell utilizing a 6 × 6 × 6 k-mesh. With 20-27% exact exchange, global hybrid functionals (B3LYP, PBE0, revPBE0, B97-3, SCAN0) perform similarly with a root-mean-square deviation (RMSD) of 0.61-0.77 eV, while other global hybrid functionals such as M06-2X (2.02 eV) and MN15 (1.05 eV) show higher RMSD due to their increased fraction of exact exchange. A short-range hybrid functional, HSE achieves a similar RMSD (0.76 eV) but shows a notable underestimation of band gaps due to the complete lack of long-range exchange. We found that two combinatorially optimized range-separated hybrid functionals, ωB97X-rV (3.94 eV) and ωB97M-rV (3.40 eV), and the two other range-separated hybrid functionals, CAM-B3LYP (2.41 eV) and CAM-QTP01 (4.16 eV), significantly overestimate the band gap because of their high fraction of long-range exact exchange. Given the failure of ωB97X-rV and ωB97M-rV, we have yet to find a density functional that offers consistent performance for both molecules and solids. Our algorithm development and density functional assessment will serve as a stepping stone toward developing more accurate hybrid functionals and applying them to practical applications.