Reaction Energetics for the Abstraction Process C₂H₃ + H₂ → C₂H₄ + H

The fundamentally important combustion reaction of vinyl radical with hydrogen has been studied in the laboratory by at least five experimental groups. Herein, the reaction C₂H₃ + H₂ → C₂H₄ + H has been examined using focal-point analysis. Molecular energies were determined from extrapolations to the complete basis-set limit using correlation-consistent basis sets (cc-pVTZ, cc-pVQZ, and cc-pV5Z) and coupled-cluster theory with single and double excitations (CCSD), perturbative triples [CCSD(T)], full triples [CCSDT], and perturbative quadruples [CCSDT(Q)]. Reference geometries were optimized at the all-electron CCSD(T)/cc-pCVQZ level. Computed energies were also corrected for relativistic effects and the Born–Oppenheimer approximation. The activation energy for hydrogen abstraction is predicted to be 9.65 kcal mol^–1, and the overall reaction is predicted to be exothermic by 5.65 kcal mol^–1. Natural resonance theory (NRT) analysis was performed to verify the reaction pathway and describe bond-breaking and bond-forming events along the reaction coordinate

Structural Distortions Accompanying Noncovalent Interactions: Methane–Water, the Simplest C–H Hydrogen Bond

Neglect of fragment structural distortions resulting from noncovalent interactions is a common practice when examining a potential energy surface (PES). Herein, we make quantitative predictions concerning the magnitude of such distortions in the methane–water system. Coupled cluster methods up to perturbative quadruples [CCSDT­(Q)] were used in the structural optimizations to the complete basis set limit (using up to cc-pV6Z basis sets). Our results show that the interaction energy differences between the fully optimized and nonoptimized structures are on the order of 0.02 kcal mol^–1. These findings imply that scanning the PES of a very weakly bound noncovalent system, while neglecting intramolecular distortions, is a reasonable approximation for points other than the minima

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 <i>N</i>-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 <i>N</i>-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

Simulation of the VUV Absorption Spectra of Oxygenates and Hydrocarbons: A Joint Theoretical–Experimental Study

Vacuum UV absorption spectroscopy is regularly used to provide unambiguous identification of a target species, insight into the electronic structure of molecules, and quantitative species concentrations. As molecules of interest have become more complex, theoretical spectra have been used in tandem with laboratory spectroscopic analysis or as a replacement when experimental data is unavailable. However, it is difficult to determine which theoretical methodologies can best simulate experiment. This study examined the performance of EOM-CCSD and 10 TD-DFT functionals (B3LYP, BH&HLYP, BMK, CAM-B3LYP, HSE, M06-2X, M11, PBE0, ωB97X-D, and X3LYP) to produce reliable vacuum UV absorption spectra for 19 small oxygenates and hydrocarbons using vertical excitation energies. The simulated spectra were analyzed against experiment using both a qualitative analysis and quantitative metrics, including cosine similarity, relative integral change, mean signed error, and mean absolute error. Based on our ranking system, it was determined that M06-2X was consistently the top performing TD-DFT method with BMK, CAM-B3LYP, and ωB97X-D also producing reliable spectra for these small combustion species

Simulation of the VUV Absorption Spectra of Oxygenates and Hydrocarbons: A Joint Theoretical–Experimental Study

Vacuum UV absorption spectroscopy is regularly used to provide unambiguous identification of a target species, insight into the electronic structure of molecules, and quantitative species concentrations. As molecules of interest have become more complex, theoretical spectra have been used in tandem with laboratory spectroscopic analysis or as a replacement when experimental data is unavailable. However, it is difficult to determine which theoretical methodologies can best simulate experiment. This study examined the performance of EOM-CCSD and 10 TD-DFT functionals (B3LYP, BH&HLYP, BMK, CAM-B3LYP, HSE, M06-2X, M11, PBE0, ωB97X-D, and X3LYP) to produce reliable vacuum UV absorption spectra for 19 small oxygenates and hydrocarbons using vertical excitation energies. The simulated spectra were analyzed against experiment using both a qualitative analysis and quantitative metrics, including cosine similarity, relative integral change, mean signed error, and mean absolute error. Based on our ranking system, it was determined that M06-2X was consistently the top performing TD-DFT method with BMK, CAM-B3LYP, and ωB97X-D also producing reliable spectra for these small combustion species

Psi4NumPy: An Interactive Quantum Chemistry Programming Environment for Reference Implementations and Rapid Development

<div> <div> <div> <p><i>Psi4NumPy</i> demonstrates the use of efficient computational kernels from the open- source <i>Psi4</i> program through the popular <i>NumPy</i> library for linear algebra in Python to facilitate the rapid development of clear, understandable Python computer code for new quantum chemical methods, while maintaining a relatively low execution time. Using these tools, reference implementations have been created for a number of methods, including self-consistent field (SCF), SCF response, many-body perturbation theory, coupled-cluster theory, configuration interaction, and symmetry-adapted perturbation theory. Further, several reference codes have been integrated into Jupyter notebooks, allowing background and explanatory information to be associated with the imple- mentation. <i>Psi4NumPy</i> tools and associated reference implementations can lower the barrier for future development of quantum chemistry methods. These implementa- tions also demonstrate the power of the hybrid C++/Python programming approach employed by the <i>Psi4</i> program. </p> </div> </div> </div