Molecular-orbital-based machine learning for open-shell and multi-reference systems with kernel addition Gaussian process regression.

We introduce a novel machine learning strategy, kernel addition Gaussian process regression (KA-GPR), in molecular-orbital-based machine learning (MOB-ML) to learn the total correlation energies of general electronic structure theories for closed- and open-shell systems by introducing a machine learning strategy. The learning efficiency of MOB-ML(KA-GPR) is the same as the original MOB-ML method for the smallest criegee molecule, which is a closed-shell molecule with multi-reference characters. In addition, the prediction accuracies of different small free radicals could reach the chemical accuracy of 1 kcal/mol by training on one example structure. Accurate potential energy surfaces for the H10 chain (closed-shell) and water OH bond dissociation (open-shell) could also be generated by MOB-ML(KA-GPR). To explore the breadth of chemical systems that KA-GPR can describe, we further apply MOB-ML to accurately predict the large benchmark datasets for closed- (QM9, QM7b-T, and GDB-13-T) and open-shell (QMSpin) molecules.

Benchmarking the semi-stochastic CC(P;Q) approach for singlet-triplet gaps in biradicals.

We recently proposed a semi-stochastic approach to converging high-level coupled-cluster (CC) energetics, such as those obtained in the CC calculations with singles, doubles, and triples (CCSDT), in which the deterministic CC(P;Q) framework is merged with the stochastic configuration interaction Quantum Monte Carlo propagations [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017)]. In this work, we investigate the ability of the semi-stochastic CC(P;Q) methodology to recover the CCSDT energies of the lowest singlet and triplet states and the corresponding singlet-triplet gaps of biradical systems using methylene, (HFH)-, cyclobutadiene, cyclopentadienyl cation, and trimethylenemethane as examples.

Fast Near Ab Initio Potential Energy Surfaces Using Machine Learning.

A machine-learning based approach for evaluating potential energies for quantum mechanical studies of properties of the ground and excited vibrational states of small molecules is developed. This approach uses the molecular-orbital-based machine learning (MOB-ML) method to generate electronic energies with the accuracy of CCSD(T) calculations at the same cost as a Hartree-Fock calculation. To further reduce the computational cost of the potential energy evaluations without sacrificing the CCSD(T) level accuracy, GPU-accelerated Neural Network Potential Energy Surfaces (NN-PES) are trained to geometries and energies that are collected from small-scale Diffusion Monte Carlo (DMC) simulations, which are run using energies evaluated using the MOB-ML model. The combined NN+(MOB-ML) approach is used in variational calculations of the ground and low-lying vibrational excited states of water and in DMC calculations of the ground states of water, CH5+, and its deuterated analogues. For both of these molecules, comparisons are made to the results obtained using potentials that were fit to much larger sets of electronic energies than were required to train the MOB-ML models. The NN+(MOB-ML) approach is also used to obtain a potential surface for C2H5+, which is a carbocation with a nonclassical equilibrium structure for which there is currently no available potential surface. This potential is used to explore the CH stretching vibrations, focusing on those of the bridging hydrogen atom. For both CH5+ and C2H5+ the MOB-ML model is trained using geometries that were sampled from an AIMD trajectory, which was run at 350 K. By comparison, the structures sampled in the ground state calculations can have energies that are as much as ten times larger than those used to train the MOB-ML model. For water a higher temperature AIMD trajectory is needed to obtain accurate results due to the smaller thermal energy. A second MOB-ML model for C2H5+ was developed with additional higher energy structures in the training set. The two models are found to provide nearly identical descriptions of the ground state of C2H5+.

High-level coupled-cluster energetics by merging moment expansions with selected configuration interaction.

Inspired by our earlier semi-stochastic work aimed at converging high-level coupled-cluster (CC) energetics [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017) and J. E. Deustua, J. Shen, and P. Piecuch, J. Chem. Phys. 154, 124103 (2021)], we propose a novel form of the CC(P; Q) theory in which the stochastic Quantum Monte Carlo propagations, used to identify dominant higher-than-doubly excited determinants, are replaced by the selected configuration interaction (CI) approach using the perturbative selection made iteratively (CIPSI) algorithm. The advantages of the resulting CIPSI-driven CC(P; Q) methodology are illustrated by a few molecular examples, including the dissociation of F2 and the automerization of cyclobutadiene, where we recover the electronic energies corresponding to the CC calculations with a full treatment of singles, doubles, and triples based on the information extracted from compact CI wave functions originating from relatively inexpensive Hamiltonian diagonalizations.

Is Externally Corrected Coupled Cluster Always Better Than the Underlying Truncated Configuration Interaction?

The short answer to the question in the title is "no". We identify classes of truncated configuration interaction (CI) wave functions for which the externally corrected coupled-cluster (ec-CC) approach using the three-body (T3) and four-body (T4) components of the cluster operator extracted from CI does not improve the results of the underlying CI calculations. Implications of our analysis, illustrated by numerical examples, for the ec-CC computations using truncated and selected CI methods are discussed. We also introduce a novel ec-CC approach using the T3 and T4 amplitudes obtained with the selected CI scheme abbreviated as CIPSI, correcting the resulting energies for the missing T3 correlations not captured by CIPSI with the help of moment expansions similar to those employed in the completely renormalized CC methods.

High-level coupled-cluster energetics by Monte Carlo sampling and moment expansions: Further details and comparisons.

We recently proposed a novel approach to converging electronic energies equivalent to high-level coupled-cluster (CC) computations by combining the deterministic CC(P;Q) formalism with the stochastic configuration interaction (CI) and CC Quantum Monte Carlo (QMC) propagations. This article extends our initial study [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017)], which focused on recovering the energies obtained with the CC method with singles, doubles, and triples (CCSDT) using the information extracted from full CI QMC and CCSDT-MC, to the CIQMC approaches truncated at triples and quadruples. It also reports our first semi-stochastic CC(P;Q) calculations aimed at converging the energies that correspond to the CC method with singles, doubles, triples, and quadruples (CCSDTQ). The ability of the semi-stochastic CC(P;Q) formalism to recover the CCSDT and CCSDTQ energies, even when electronic quasi-degeneracies and triply and quadruply excited clusters become substantial, is illustrated by a few numerical examples, including the F-F bond breaking in F2, the automerization of cyclobutadiene, and the double dissociation of the water molecule.

The Ground State Electronic Energy of Benzene.

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground-state energy of the benzene molecule in a standard correlation-consistent basis set of double-ζ quality. As a broad international endeavor, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around -863 mEH. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 mEH), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.

Recent developments in the general atomic and molecular electronic structure system.

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree-Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized.

Accurate excited-state energetics by a combination of Monte Carlo sampling and equation-of-motion coupled-cluster computations.

The recently proposed idea of identifying the most important higher-than-doubly excited determinants in the ground-state coupled-cluster (CC) calculations through stochastic configuration interaction Quantum Monte Carlo propagations [J. E. Deustua et al., Phys. Rev. Lett. 119, 223003 (2017)] is extended to excited electronic states via the equation-of-motion (EOM) CC methodology. The advantages of the new approach are illustrated by calculations aimed at recovering the ground- and excited-state energies of the CH+ molecule at the equilibrium and stretched geometries resulting from the EOMCC calculations with a full treatment of singles, doubles, and triples.

Communication: Approaching exact quantum chemistry by cluster analysis of full configuration interaction quantum Monte Carlo wave functions.

We propose to accelerate convergence toward full configuration interaction (FCI) energetics by using the coupled-cluster approach, in which singly and doubly excited clusters, needed to determine the energy, are iterated in the presence of their three- and four-body counterparts extracted from FCI quantum Monte Carlo (FCIQMC) propagations. Preliminary calculations for the water molecule at the equilibrium and stretched geometries show that we can accurately extrapolate the FCI energetics based on the early stages of FCIQMC propagations.

Converging High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions.

We propose a new approach to the determination of accurate electronic energies that are equivalent to the results of high-level coupled-cluster (CC) calculations. The approach is based on merging the CC(P;Q) formalism, which corrects energies obtained with an arbitrary truncation in the cluster operator, with the stochastic configuration interaction and CC ideas. The advantages of the proposed methodology are illustrated by molecular examples, where the goal is to recover the energetics obtained in the CC calculations with a full treatment of singly, doubly, and triply excited clusters.