ManyHF: A pragmatic automated method of finding lower-energy Hartree–Fock solutions for potential energy surface development

Abstract

Developing global, high-dimensional potential energy surfaces (PESs) is a formidable task. Beside the challenges of PES fitting and fitting set generation, one also has to choose an electronic structure method capable of delivering accurate potential energy values for all geometries in the fitting set, even in regions far from equilibrium. Such regions are often plagued by Hartree-Fock (HF) convergence issues, and even if convergence is achieved, self-consistent field (SCF) procedures that are used to obtain HF solutions offer no guarantee that the solution found is the lowest-energy solution. We present a study of the reactant regions of CH 3 OH + OH⋅, C 2 H 6 + F⋅, and CH 3 NH 2 + Cl⋅, where the SCF procedure often converges to a higher-energy state or fails to converge, resulting in erratic post-HF energies and regions where no energy is obtained, both of which are major obstacles for PES development. We introduce a pragmatic method for automatically finding better HF solutions (dubbed ManyHF) and present evidence that it may extend the applicability of single-reference methods to some systems previously thought to require multireference methods.

Full-dimensional potential energy surface development and dynamics for the HBr + C2H5 → Br(2P3/2) + C2H6 reaction

“…27 It is important to note that, in regions far from equilibrium, in our case, the reactant and product regions of HBr + C 2 H 5 → Br + C 2 H 6 , one is often plagued by Hartree-Fock (HF) convergence issues, and even if convergence is achieved, self-consistent field procedures that are used to obtain HF solutions offer no guarantee that the solution found is the lowest-energy solution, resulting in erratic post-HF energies and regions where no energy is obtained. 25 Therefore, here we use the ManyHF method recently developed in our group for automatically finding better HF solutions to compute all the energies in this work. First, five different Kohn-Sham DFT computations, an ordinary ROHF/AVDZ calculation, and an MCSCF calculation started from the final orbitals of the ordinary ROHF/AVDZ were performed, leading to the first seven ROHF/AVDZ primary candidates for the best HF solution.…”

“…In addition, the reactants and products are randomly scattered around each other in the range of 3–8 Å (for three product channels: hydrogen-abstraction, methyl-substitution, hydrogen-substitution). At these initial geometries single-point quantum chemical computations are performed at the ManyHF-based 25 RMP2/aug-cc-pVDZ 26 (aug-cc-pVDZ-PP for Br atom) level of theory using the MOLPRO program package. 27 It is important to note that, in regions far from equilibrium, in our case, the reactant and product regions of HBr + C 2 H 5 → Br + C 2 H 6 , one is often plagued by Hartree–Fock (HF) convergence issues, and even if convergence is achieved, self-consistent field procedures that are used to obtain HF solutions offer no guarantee that the solution found is the lowest-energy solution, resulting in erratic post-HF energies and regions where no energy is obtained.…”

“…Finally, the lowest energy solution among the primary and secondary candidates is then used as the reference wavefunction for the desired correlation method. 25 The data set is then cut by excluding the geometries with higher than 100 kcal mol −1 relative energy with respect to the global minimum of the set. After the cut the initial data set consists of 6313 geometries, and is used to start the PES development with the ROBOSURFER program package 28 developed in our group.…”

Neural Network Based ∆-Machine learning approach efficiently brings the DFT potential energy surface to the CCSD(T) quality: a case for the OH + CH3OH reaction

“…60 Tests show this method also works well for the title reaction. As shown in Figure S2, the recently proposed manyHF method 67 may fail while our proposed method works well.…”

“…Another difficulty is the single reference method, UCCSD(T)-F12a, may result in some discontinuity along some dimensions, as the title system is of multi-reference in nature. 67 Although carefully selected Hartee-Fock (HF) orbitals can delete the discontinuity, as proposed by us for the OH + HO2 system, 60 a single-point energy calculation at the level of UCCSD(T)-F12a/AVTZ [68][69][70] still takes 30 ~ 70 minutes with 8 cores of a computational node with Intel Xeon CPU E5-2682 v4 @ 2.50GHz. It is expensive to determine the energies of 10 5 ~10 6 points directly at the UCCSD(T)-F12a/AVTZ level.…”