The accuracy of molecular bond lengths computed by multireference electronic structure methods

Prediction Challenge: Simulating Rydberg photoexcited cyclobutanone with surface hopping dynamics based on different electronic structure methods

This research examines the nonadiabatic dynamics of cyclobutanone after excitation into the n → 3s Rydberg S2 state. It stems from our contribution to the Special Topic of the Journal of Chemical Physics to test the predictive capability of computational chemistry against unseen experimental data. Decoherence-corrected fewest-switches surface hopping was used to simulate nonadiabatic dynamics with full and approximated nonadiabatic couplings. Several simulation sets were computed with different electronic structure methods, including a multiconfigurational wavefunction [multiconfigurational self-consistent field (MCSCF)] specially built to describe dissociative channels, multireference semiempirical approach, time-dependent density functional theory, algebraic diagrammatic construction, and coupled cluster. MCSCF dynamics predicts a slow deactivation of the S2 state (10 ps), followed by an ultrafast population transfer from S1 to S0 (<100 fs). CO elimination (C3 channel) dominates over C2H4 formation (C2 channel). These findings radically differ from the other methods, which predicted S2 lifetimes 10-250 times shorter and C2 channel predominance. These results suggest that routine electronic structure methods may hold low predictive power for the outcome of nonadiabatic dynamics.

Optimized Structural Data at the Complete Basis Set Limit via Successive Quadratic Minimizations

Two variants of a successive quadratic minimization method (SQM and c-SQM) are suggested to calculate the structural properties of molecular systems at the complete basis set (CBS) limit. When applied to H₃⁺, H₂O, CH₂O, SH₂, and SO₂, they revealed CBS/(x₁, x₂) structural parameters that significantly surpass the raw ones calculated at the x₂ basis set level. Such a performance has also been verified for the intricate case of the water dimer. Because the c-SQM method is system specific, thus showing somewhat enhanced results relative to the general SQM protocol, it can be of higher cost depending on the level of calibration used. Yet, it hardly surpasses the general quality of the results obtained with the cost-effective SQM method. Since the number of cycles required to reach convergence is relatively small, both schemes are simple to use and easily adaptable to any of the existing extrapolation schemes for the Hartree-Fock and correlation energies.

The generality of the GUGA MRCI approach in COLUMBUS for treating complex quantum chemistry

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.

Representations of Shavitt Graphs Within the Graphical Unitary Group Approach

The Shavitt graph is a visual representation of a distinct row table (DRT) within the graphical unitary group approach. The DRT is a compact representation of the entire configuration state function expansion space within a molecular electronic structure calculation. Each node of the graph is associated with an integer triple (a _k ,b _k ,c _k ). These integers may be mapped to other quantum numbers, including the number of orbitals, number of electrons, and spin quantum number, and used to display Shavitt graphs in various ways that emphasize different aspects of the expansion space or that reveal different aspects of computed wave functions. The features of several graph density plots are discussed, including electron-hole symmetries and the bonding-antibonding wave function character. © 2019 Wiley Periodicals, Inc.

Small Alcohols Revisited: CCSD(T) Relative Potential Energies for the Minima, First- and Second-Order Saddle Points, and Torsion-Coupled Surfaces

The elucidation of conformations and relative potential energies (rPEs) of small molecules has a long history across a diverse range of fields. Periodically, it is helpful to revisit what conformations have been investigated and to provide a consistent theoretical framework for which clear comparisons can be made. In this paper, we compute the minima, first- and second-order saddle points, and torsion-coupled surfaces for methanol, ethanol, propan-2-ol, and propanol using consistent high-level MP2 and CCSD(T) methods. While for certain molecules more rigorous methods were employed, the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pV5Z theory level was used throughout to provide relative energies of all minima and first-order saddle points. The rPE surfaces were uniformly computed at the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ level. To the best of our knowledge, this represents the most extensive study for alcohols of this kind, revealing some new aspects. Especially for propanol, we report several new conformations that were previously not investigated. Moreover, two metrics are included in our analysis that quantify how the selected surfaces are similar to one another and hence improve our understanding of the relationship between these alcohols.

Analytic Energy Gradients for Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Theory

Analytic energy gradients are presented for a variational two-electron reduced-density-matrix (2-RDM)-driven complete active space self-consistent field (CASSCF) method. The active-space 2-RDM is determined using a semidefinite programing (SDP) algorithm built upon an augmented Lagrangian formalism. Expressions for analytic gradients are simplified by the fact that the Lagrangian is stationary with respect to variations in both the primal and the dual solutions to the SDP problem. Orbital response contributions to the gradient are identical to those that arise in conventional CASSCF methods in which the electronic structure of the active space is described by a full configuration interaction (CI) wave function. We explore the relative performance of variational 2-RDM (v2RDM)- and CI-driven CASSCF for the equilibrium geometries of 20 small molecules. When enforcing two-particle N-representability conditions, full-valence v2RDM-CASSCF-optimized bond lengths display a mean unsigned error of 0.0060 Å and a maximum unsigned error of 0.0265 Å, relative to those obtained from full-valence CI-CASSCF. When enforcing partial three-particle N-representability conditions, the mean and maximum unsigned errors are reduced to only 0.0006 and 0.0054 Å, respectively. For these same molecules, full-valence v2RDM-CASSCF bond lengths computed in the cc-pVQZ basis set deviate from experimentally determined ones on average by 0.017 and 0.011 Å when enforcing two- and three-particle conditions, respectively, whereas CI-CASSCF displays an average deviation of 0.010 Å. The v2RDM-CASSCF approach with two-particle conditions is also applied to the equilibrium geometry of pentacene; optimized bond lengths deviate from those derived from experiment, on average, by 0.015 Å when using a cc-pVDZ basis set and a (22e,22o) active space.

Analytic gradients for density cumulant functional theory: the DCFT-06 model

Density cumulant functional theory (DCFT) is one of a number of nascent electron correlation methods that are derived from reduced density matrices and cumulants thereof, instead of the wavefunction. Deriving properties from the density cumulant naturally yields methods that are size extensive and size consistent. In this work, we derive expressions for the analytic gradient, with respect to an external perturbation, for the DCFT-06 variant of density cumulant functional theory. Despite the fact that the DCFT-06 energy functional is stationary with respect to the density cumulant, the analytic gradients of the energy require the solution of perturbation-independent equations for both orbital and cumulant response. These two sets of linear response equations are coupled in nature and are solved iteratively with the solution of orbital and cumulant response equations each macroiteration, exhibiting rapid convergence. The gradients are implemented and benchmarked against coupled cluster theory with single and double excitations (CCSD) and CCSD with perturbative triple excitations [CCSD(T)], as well as accurate empirically corrected experimental data, for a test set comprising 15 small molecules. For most of the test cases, results from DCFT-06 are closer to CCSD(T) and empirical data than those from CCSD. Although the total energy and analytic gradient have the same asymptotic scaling, the present experience shows that the computational cost of the gradient is significantly lower.