Converging high-level coupled-cluster energetics via adaptive selection of excitation manifolds driven by moment expansions.

A novel approach to rapidly converging high-level coupled-cluster (CC) energetics in an automated fashion is proposed. The key idea is an adaptive selection of excitation manifolds defining higher--than--two-body components of the cluster operator inspired by CC(P;Q) moment expansions. The usefulness of the resulting methodology is illustrated by molecular examples where the goal is to recover the electronic energies obtained using the CC method with a full treatment of singly, doubly, and triply excited clusters (CCSDT) when the noniterative triples corrections to CCSD fail.

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.

Femtosecond intramolecular rearrangement of the CH3NCS radical cation.

Strong-field ionization, involving tunnel ionization and electron rescattering, enables femtosecond time-resolved dynamics measurements of chemical reactions involving radical cations. Here, we compare the formation of CH3S+ following the strong-field ionization of the isomers CH3SCN and CH3NCS. The former involves the release of neutral CN, while the latter involves an intramolecular rearrangement. We find the intramolecular rearrangement takes place on a single picosecond timescale and exhibits vibrational coherence. Density functional theory and coupled-cluster calculations on the neutral and singly ionized species help us determine the driving force responsible for intramolecular rearrangement in CH3NCS. Our findings illustrate the complexity that accompanies radical cation chemistry following electron ionization and demonstrate a useful tool for understanding cation dynamics after ionization.

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.

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.

Steric effects in light-induced solvent proton abstraction.

The significance of solvent structural factors in the excited-state proton transfer (ESPT) reactions of Schiff bases with alcohols is reported here. We use the super photobase FR0-SB and a series of primary, secondary, and tertiary alcohol solvents to illustrate the steric issues associated with solvent to photobase proton transfer. Steady-state and time-resolved fluorescence data show that ESPT occurs readily for primary alcohols, with a probability proportional to the relative -OH concentration. For secondary alcohols, ESPT is greatly diminished, consistent with the barrier heights obtained using quantum chemistry calculations. ESPT is not observed in the tertiary alcohol. We explain ESPT using a model involving an intermediate hydrogen-bonded complex where the proton is "shared" by the Schiff base and the alcohol. The formation of this complex depends on the ability of the alcohol solvent to achieve spatial proximity to and alignment with the FR0-SB* imine lone pair stabilized by the solvent environment.

Isoenergetic two-photon excitation enhances solvent-to-solute excited-state proton transfer.

Two-photon excitation (TPE) is an attractive means for controlling chemistry in both space and time. Since isoenergetic one- and two-photon excitations (OPE and TPE) in non-centrosymmetric molecules are allowed to reach the same excited state, it is usually assumed that they produce similar excited-state reactivity. We compare the solvent-to-solute excited-state proton transfer of the super photobase FR0-SB following isoenergetic OPE and TPE. We find up to 62% increased reactivity following TPE compared to OPE. From steady-state spectroscopy, we rule out the involvement of different excited states and find that OPE and TPE spectra are identical in non-polar solvents but not in polar ones. We propose that differences in the matrix elements that contribute to the two-photon absorption cross sections lead to the observed enhanced isoenergetic reactivity, consistent with the predictions of our high-level coupled-cluster-based computational protocol. We find that polar solvent configurations favor greater dipole moment change between ground and excited states, which enters the probability for TPE as the absolute value squared. This, in turn, causes a difference in the Franck-Condon region reached via TPE compared to OPE. We conclude that a new method has been found for controlling chemical reactivity via the matrix elements that affect two-photon cross sections, which may be of great utility for spatial and temporal precision chemistry.

Optimization of the Reax force field for the lithium-oxygen system using a high fidelity charge model.

Studies using molecular dynamics (MD) have long struggled to simulate the failure modes of materials, predicting unrealistically high ductility and failing to capture brittle fracture. The primary cause of this shortcoming is an inadequate description of bond breaking. While reactive force fields such as ReaxFF show improvements compared to traditional force fields, the charge models used yield unphysical partial charges, especially during dissociation of ionic bonds. This flaw may be remedied by using the atom-condensed Kohn-Sham density functional theory (DFT) approximated to a second order (ACKS2) charge model for determining partial charges. In this work, we present a new ACKS2-enabled Reax force field for fracture simulations of lithium oxide systems, which was obtained by training against an extensive set of DFT, multireference configuration interaction (MRCI), and MRCI+Q reference data using genetic optimization techniques. This new force field significantly improves the bond breaking behavior, but still cannot fully capture the brittle fracture in MD simulations, suggesting more research is needed to improve simulation of brittle fracture.

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.

Application of the CC(P;Q) Hierarchy of Coupled-Cluster Methods to the Beryllium Dimer.

The performance of coupled-cluster approaches with higher-than-doubly excited clusters, including the CCSD(T), CCSD(2)T, CR-CC(2,3), CCSD(TQ), and CR-CC(2,4) corrections to CCSD, the active-space CCSDt, CCSDtq, and CCSDTq methods, and the CC(t;3), CC(t,q;3), CC(t,q;3,4), and CC(q;4) corrections to CCSDt, CCSDtq, and CCSDTq resulting from the CC(P;Q) formalism, in reproducing the CCSDT and CCSDTQ potential energy curves and vibrational term values characterizing Be2 in its electronic ground state is assessed. The correlation-consistent aug-cc-pVnZ and aug-cc-pCVnZ (n = T and Q) basis sets are employed. Among the CCSD-based corrections, the completely renormalized CR-CC(2,3) and CR-CC(2,4) approaches perform the best. The CC(t;3), CC(t,q;3), CC(t,q;3,4), and CC(q;4) methods, especially CC(t;3) and CC(q;4), outperform other employed approaches in reproducing the CCSDT and CCSDTQ data. Composite schemes combining the all-electron CCSDT calculations extrapolated to the complete basis set limit with the frozen-core CC(q;4) and CCSDTQ computations using the aug-cc-pVTZ basis to account for connected quadruple excitations reproduce the latest experimental vibrational spectrum of Be2 to within 4-5 cm-1, when the vibrational spacings are examined, with typical errors being below 1-2 cm-1. The resulting binding energies and equilibrium bond lengths agree with their experimentally derived counterparts to within ∼10 cm-1 and 0.01 Å.

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.

Economical Doubly Electron-Attached Equation-of-Motion Coupled-Cluster Methods with an Active-Space Treatment of Three-Particle-One-Hole and Four-Particle-Two-Hole Excitations.

The previously developed active-space doubly electron-attached (DEA) equation-of-motion (EOM) coupled-cluster (CC) method with up to four-particle-two-hole (4p-2h) excitations [Shen, J.; Piecuch, P. J. Chem. Phys. 2013, 138, 194102], which utilizes the idea of applying a linear electron-attaching operator to the CC ground state of an (N - 2)-electron closed-shell system to generate ground and excited states of the N-electron open-shell species of interest, has been extended to a considerably less expensive model, in which both 3p-1h and 4p-2h terms rather than 4p-2h contributions only are selected using active orbitals. As illustrated by the calculations involving low-lying singlet and triplet states of methylene, trimethylenemethane, cyclobutadiene, and cyclopentadienyl cation and bond breaking in F2, the proposed DEA-EOMCC method with the active-space treatment of 3p-1h and 4p-2h excitations and its lower-level counterpart neglecting 4p-2h contributions are capable of accurately reproducing the results obtained using their considerably more expensive parent counterparts with a full treatment of 3p-1h and full or active-space treatment of 4p-2h excitations.

Systematic design of active spaces for multi-reference calculations of singlet-triplet gaps of organic diradicals, with benchmarks against doubly electron-attached coupled-cluster data.

Singlet-triplet gaps in diradical organic π-systems are of interest in many applications. In this study, we calculate them in a series of molecules, including cyclobutadiene and its derivatives and cyclopentadienyl cation, by using correlated participating orbitals within the complete active space (CAS) and restricted active space (RAS) self-consistent field frameworks, followed by second-order perturbation theory (CASPT2 and RASPT2). These calculations are evaluated by comparison with the results of doubly electron-attached (DEA) equation-of-motion (EOM) coupled-cluster (CC) calculations with up to 4-particle-2-hole (4p-2h) excitations. We find active spaces that can accurately reproduce the DEA-EOMCC(4p-2h) data while being small enough to be applicable to larger organic diradicals.

Coupled-cluster interpretation of the photoelectron spectrum of Ag3 (.).

We use the scalar relativistic ionized equation-of-motion coupled-cluster (IP-EOMCC) approaches to investigate the photoelectron spectrum of Ag3 (-), examining the effects of basis set, number of correlated electrons, level of applied theory including up to 3-hole-2-particle terms, and geometry relaxation. By employing an IP-EOMCC-based extrapolation scheme, we are able to provide an accurate interpretation and complete assignment of peaks and other key features in the experimentally observed spectra, including electron binding energies as high as about 6.5 eV.

Communication: Coupled-cluster interpretation of the photoelectron spectrum of Au3⁻.

We use the scalar relativistic ionized equation-of-motion coupled-cluster approaches, correlating valence and semi-core electrons and including up to 3-hole-2-particle terms in the ionizing operator, to investigate the photoelectron spectrum of Au3⁻. We provide an accurate assignment of peaks and shoulders in the experimental photoelectron spectrum of Au3⁻ for the first time.

Electronic structure of the S1 state in methylcobalamin: insight from CASSCF/MC-XQDPT2, EOM-CCSD, and TD-DFT calculations.

The methylcobalamin cofactor (MeCbl), which is one of the biologically active forms of vitamin B12, has been the subject of many spectroscopic and theoretical investigations. Traditionally, the lowest-energy part of the photoabsorption spectrum of MeCbl (the so-called α/ß band) has been interpreted as an S0→S1 electronic transition dominated by π→π* excitations associated with the C=C stretching of the corrin ring. However, a more quantitative band-shape analysis of the α/ß spectral region, along with circular dichroism (CD), magnetic CD, and resonance Raman data, has revealed the presence of a second electronic transition that involves the Co-C(Me) bond weakening. Conversely, the lowest-energy excitations based on transient absorption spectroscopy measurements have been interpreted as metal-to-ligand charge transfer (MLCT) transitions. To resolve the existing controversy about the interpretation of the S1 state of MeCbl, calculations have been performed using two independent ab initio wavefunction-based methods. These include the modified variant of the second-order multiconfigurational quasi-degenerate perturbation theory (MC-XQDPT2), using complete active space self-consistent field orbitals, and the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) approach using restricted Hartree-Fock orbitals. It is shown that both ab initio methods provide a consistent description of the S1 state as having an MLCT character. In addition, the performance of different types of functionals, including hybrid (B3LYP, MPW1PW91, TPSSh), generalized-gradient-approximation-type (GGA-type) (BP86, BLYP, MPWPW91), meta-GGA (TPSS), and range-separated (CAM-B3LYP, LC-BLYP) approaches, has been examined and the results of the corresponding time-dependent density functional theory calculations have been benchmarked against the MC-XQDPT2 and EOM-CCSD data. The hybrid functionals support the interpretation in which the S1 state represents a π→π* transition localized on corrin, while pure GGA, meta-GGA, and LC-BLYP functionals produce results consistent with the MLCT assignment.

Aerobic oxidation of methanol to formic acid on Au8-: benchmark analysis based on completely renormalized coupled-cluster and density functional theory calculations.

The left-eigenstate completely renormalized coupled-cluster (CC) method with singles, doubles, and noniterative triples [CR-CC(2,3)] and a few representative density functional theory (DFT) approaches have been applied to methanol oxidation to formic acid on a Au8(-) cluster, which is a model for aerobic oxidations on gold nanoparticles. It is demonstrated that CR-CC(2,3) supports the previous exothermic reaction mechanism, placing the initial rate-determining transition state, which corresponds to hydrogen transfer from the methoxy species to the molecular oxygen, at about 20 kcal/mol above the reactants, less than 40 kcal/mol above the O2 and CH3O(-) species coadsorbed on Au8(-), and considerably above the remaining two transition states along the reaction pathway. The DFT calculations using the previously exploited M06 hybrid functional show reasonable agreement with CR-CC(2,3), but B3LYP offers additional improvements in the description of the relevant activation energies. Pure functionals, including M06-L, BP86, and TPSS, do not work well, significantly underestimating the activation barriers, but dispersion corrections, as in B97-D, bring the results closer to the M06 accuracy level.

Doubly electron-attached and doubly ionized equation-of-motion coupled-cluster methods with 4-particle-2-hole and 4-hole-2-particle excitations and their active-space extensions.

The full and active-space doubly electron-attached (DEA) and doubly ionized (DIP) equation-of-motion coupled-cluster (EOMCC) methods with up to 4-particle-2-hole (4p-2h) and 4-hole-2-particle (4h-2p) excitations are developed. By examining bond breaking in F2 and low-lying singlet and triplet states in the methylene, (HFH)(-), and trimethylenemethane biradicals, we demonstrate that the DEA- and DIP-EOMCC methods with an active-space treatment of 4p-2h and 4h-2p excitations reproduce the results of the analogous full calculations at the small fraction of the computer effort, while improving the DEA/DIP-EOMCC theories truncated at 3p-1h/3h-1p excitations.