The X(1)(2)Pi(3/2) and X(2)(2)Pi(1/2) Potential Energy Surfaces of FO

Consistent Second-Order Treatment of Spin-Orbit Coupling and Dynamic Correlation in Quasidegenerate N-Electron Valence Perturbation Theory

We present a formulation and implementation of second-order quasidegenerate N-electron valence perturbation theory (QDNEVPT2) that provides a balanced and accurate description of spin-orbit coupling and dynamic correlation effects in multiconfigurational electronic states. In our approach, the energies and wave functions of electronic states are computed by treating electron repulsion and spin-orbit coupling operators as equal perturbations to the nonrelativistic complete active-space wave functions, and their contributions are incorporated fully up to the second order. The spin-orbit effects are described using the Breit-Pauli (BP) or exact two-component Douglas-Kroll-Hess (DKH) Hamiltonians within spin-orbit mean-field approximation. The resulting second-order methods (BP2- and DKH2-QDNEVPT2) are capable of treating spin-orbit coupling effects in nearly degenerate electronic states by diagonalizing an effective Hamiltonian expanded in a compact non-relativistic basis. For a variety of atoms and small molecules across the entire periodic table, we demonstrate that DKH2-QDNEVPT2 is competitive in accuracy with variational two-component relativistic theories. BP2-QDNEVPT2 shows high accuracy for the second- and third-period elements, but its performance deteriorates for heavier atoms and molecules. We also consider the first-order spin-orbit QDNEVPT2 approximations (BP1- and DKH1-QDNEVPT2), among which DKH1-QDNEVPT2 is reliable but less accurate than DKH2-QDNEVPT2. Both DKH1- and DKH2-QDNEVPT2 hold promise as efficient and accurate electronic structure methods for treating electron correlation and spin-orbit coupling in a variety of applications.

Factors affecting the relation between stretching frequencies and bond lengths. Diatomic and polyatomic species without adjustable fitting parameters

In 76 sets of similar type bonds in species A2, AB, AB2, AB3, and AB4 the stretching frequency, ν, is related to the bond length, r, by ν=a/(rμ(1/2))-b, where μ is the reduced mass. The sets treated include all ground states for which spectroscopic date were found for stable molecules, free radicals, carbenes and other species with unsatisfied valences, both ionic and covalent. The linear correlation coefficients of each set are always greater than 0.998. The slopes a and intercepts b are defined by the data of each set and vary widely. They become congruent, but not exactly identical, when a is multiplied by the square root of the mean value of the number of electrons in the valence shell of the two bonded atoms, the electrons that become joined in the molecular orbitals formed upon bonding. No adjustable parameters are used. The number of bonds treated, over 300, is not as important as the fact that all species found were treated. The aim is not to add yet another parametric correlation to the many extant, but to better understand the relation between these two fundamental properties of chemical bonds.

Theoretical study on the ground electronic state of FO(+) and FO(-)

The equilibrium structures of the ground electronic states for molecular ions FO(+) and FO(-) have been calculated by using the multi-reference configuration interaction method in combination with the augmented correlation-consistent basis sets up through sextuple zeta quality. The equilibrium parameters, potential energy curves and spectroscopic constants are derived for both species. The extrapolation schemes are adopted to estimate the complete basis set limit. The corrections of core-valence correlation and relativistic effect are included to improve the accuracy of the calculations. The vibrational energy levels as well as rotational and centrifugal distortion constants of the ground electronic states for both systems are obtained by solving the radial Schrödinger equation of nuclear motion. The computations on neutral FO radical are also carried out to investigate the ionization potentials and the electron affinities.

Orbital-optimized density cumulant functional theory

In density cumulant functional theory (DCFT) the electronic energy is evaluated from the one-particle density matrix and two-particle density cumulant, circumventing the computation of the wavefunction. To achieve this, the one-particle density matrix is decomposed exactly into the mean-field (idempotent) and correlation components. While the latter can be entirely derived from the density cumulant, the former must be obtained by choosing a specific set of orbitals. In the original DCFT formulation [W. Kutzelnigg, J. Chem. Phys. 125, 171101 (2006)] the orbitals were determined by diagonalizing the effective Fock operator, which introduces partial orbital relaxation. Here we present a new orbital-optimized formulation of DCFT where the energy is variationally minimized with respect to orbital rotations. This introduces important energy contributions and significantly improves the description of the dynamic correlation. In addition, it greatly simplifies the computation of analytic gradients, for which expressions are also presented. We offer a perturbative analysis of the new orbital stationarity conditions and benchmark their performance for a variety of chemical systems.

High-accuracy extrapolated ab initio thermochemistry. III. Additional improvements and overview

Effects of increased basis-set size as well as a correlated treatment of the diagonal Born-Oppenheimer approximation are studied within the context of the high-accuracy extrapolated ab initio thermochemistry (HEAT) theoretical model chemistry. It is found that the addition of these ostensible improvements does little to increase the overall accuracy of HEAT for the determination of molecular atomization energies. Fortuitous cancellation of high-level effects is shown to give the overall HEAT strategy an accuracy that is, in fact, higher than most of its individual components. In addition, the issue of core-valence electron correlation separation is explored; it is found that approximate additive treatments of the two effects have limitations that are significant in the realm of <1 kJ mol(-1) theoretical thermochemistry.

Scaling Dynamical Correlation Energy from Density Functional Theory Correlation Functionals

The scaling of dynamical correlation energy in molecules obtained by the correlation functionals of density functional theory (DFT) is examined. The approach taken is very similar to the scaled external correlation method of Brown and Truhlar but is based on the observation that DFT correlation functionals, especially the LYP, appear to represent the dynamical portion of the correlation energy in molecules. We examine whether higher accuracy in atomization energies can be gained by scaling without significant deterioration of the structural and spectroscopic properties of the molecules using four DFT functionals (BLYP, OLYP, B3LYP, and O3LYP) on 19 molecules including the six molecule AE6 database, the latter being representative of a much larger, 109 molecule training set. We show that, with molecule specific scale factors, nearly perfect agreement with experiment can be achieved in atomization energies without increasing the average errors in other molecular properties relative to the DFT calculation. We further show that it is possible to find optimal scale factors which reduce the mean unsigned error per bond to levels comparable to those of some multilevel multicoefficient methods.

Direct versus resonances mediated F+OH collisions on a new 3A″ potential energy surface

A theoretical study of the F(2P) + OH(2Pi) --> HF(1Sigma+) + O(3P) reactive collisions is carried out on a new global potential energy surface (PES) of the ground 3A" adiabatic electronic state. The ab initio calculations are based on multireference configuration interaction calculations, using the aug-cc-pVTZ extended basis sets of Dunning et al. A functional representation of the PES shows no nominal barrier to reaction, contrary to previous results by others. Wave packet and quasiclassical trajectory calculations have been performed for this PES to study the F + OH(v = 0,j) reactive collision. The comparison was performed at fixed and constant values of the total angular momentum from 0 to 110 and relative translational energy up to 0.8 eV. The reaction presents a dynamical barrier, essentially due to the zero-point energy for the bending vibration near the saddle point. This determines two different reaction mechanisms. At energies higher than approximately 0.125 eV the reaction is direct, while below that value it is indirect and mediated by heavy-light-heavy resonances. Such resonances, also found in the simulations of the photodetachment spectrum of the triatomic anion, manifest themselves in the quasiclassical simulations, too, where they are associated to periodic orbits.

Accurate quantum-chemical prediction of enthalpies of formation of small molecules in the gas phase

The coupled-cluster approach, including single and double excitations and perturbative corrections for triple excitations, is capable of predicting molecular electronic energies and enthalpies of formation of small molecules in the gas phase with very high accuracy (specifically, with error bars less than 5 kJmol-1), provided that the electronic wavefunction is dominated by the Hartree-Fock configuration. This capability is illustrated by calculations on molecules containing O-H and O-F bonds, namely OH, FO, H2O, HOF, and F2O. To achieve this very high accuracy, it is imperative to account for electron-correlation effects in a quantitative manner, either by using explicitly correlated two-particle basis functions (R12 functions) or by extrapolating to the limit of a complete basis. Besides taking into account harmonic zero-point vibrational energies, it is also necessary to account for anharmonic corrections to the zero-point vibrational energies, to include the core orbitals into the coupled-cluster calculations, and to account for spin-orbit corrections and scalar relativistic effects. These additional corrections constitute small but significant contributions in the range of 1-4 kJmol-1 to the enthalpies of formation of the aforementioned molecules. The highly accurate coupled-cluster results, obtained by employing R12 functions and by including various corrections, are compared with standard Kohn-Sham density-functional calculations as well as with the Gaussian-2 and complete-basis-set model chemistries.