Dispersion Interactions in QM/EFP

The dispersion energy term between quantum-mechanical (QM) and classical (represented by effective fragment potentials, EFP) subsystems is developed and implemented. A new formulation is based on long-range perturbation theory and uses dynamic polarizability tensors of the effective fragments and electric field integrals and orbital energies of the quantum-mechanical subsystem. No parametrization is involved. The accuracy of the QM–EFP dispersion energy is tested on a number of model systems; the average mean unsigned error is 0.8 kcal/mol or 13% with respect to the symmetry adapted perturbation theory on the S22 data set of noncovalent interactions. The computational cost of the dispersion energy computation is low compared to the self-consistent field calculation of the QM subsystem. The dispersion energy is sensitive to the level of theory employed for the QM part and to the electrostatic interactions in the system. The latter means that the dispersion interactions in the QM/EFP method are not purely two-body but have more complex many-body behavior

Accurate Potential Energy Curve for B₂. Ab Initio Elucidation of the Experimentally Elusive Ground State Rotation-Vibration Spectrum

The electron-deficient diatomic boron molecule has long puzzled scientists. As yet, the complete set of bound vibrational energy levels is far from being known, experimentally as well as theoretically. In the present ab initio study, all rotational–vibrational levels of the X ³Σ_g^– ground state are determined up to the dissociation limit with near-spectroscopic accuracy (<10 cm^–1). Two complete sets of bound vibrational levels for the ¹¹B₂ and ¹¹B-¹⁰B isotopomers, containing 38 and 37 levels, respectively, are reported. The results are based on a highly accurate potential energy curve, which also includes relativistic effects. The calculated set of all vibrational levels of the ¹¹B₂ isotopomer is compared with the few results derived from experiment [Bredohl, H.; Dubois, I.; Nzohabonayo, P. J. Mol. Spectrosc. 1982, 93, 281; Bredohl, H.; Dubois, I.; Melen, F. J. Mol. Spectrosc. 1987, 121, 128]. Theory agrees with experiment within 4.5 cm^–1 on average for the four vibrational level spacings that are so far known empirically. In addition, the present theoretical analysis suggests, however, that the transitions from higher electronic states to the ground state vibrational levels <i>v</i> = 12–15 deserve to be reanalyzed. Whereas previous experimental investigators considered them to originate from the <i>v</i>′ = 0 vibrational level of the upper state (2)³Σ_u^–, the present results make it likely that these transitions originate from a different upper state, namely the <i>v</i>′ = 16 or the <i>v</i>′ = 17 vibrational level of the (1)³Σ_u^– state. The ground state dissociation energy <i>D</i>₀ is predicted to be 23164 cm^–1

Correlation Energy Extrapolation by Many-Body Expansion

Accounting for electron correlation is required for high accuracy calculations of molecular energies. The full configuration interaction (CI) approach can fully capture the electron correlation within a given basis, but it does so at a computational expense that is impractical for all but the smallest chemical systems. In this work, a new methodology is presented to approximate configuration interaction calculations at a reduced computational expense and memory requirement, namely, the correlation energy extrapolation by many-body expansion (CEEMBE). This method combines a MBE approximation of the CI energy with an extrapolated correction obtained from CI calculations using subsets of the virtual orbitals. The extrapolation approach is inspired by, and analogous to, the method of correlation energy extrapolation by intrinsic scaling. Benchmark calculations of the new method are performed on diatomic fluorine and ozone. The method consistently achieves agreement with CI calculations to within a few mhartree and often achieves agreement to within ∼1 millihartree or less, while requiring significantly less computational resources

Identification and Characterization of Molecular Bonding Structures by ab initio Quasi-Atomic Orbital Analyses

The quasi-atomic analysis of <i>ab initio</i> electronic wave functions in full valence spaces, which was developed in preceding papers, yields oriented quasi-atomic orbitals in terms of which the <i>ab initio</i> molecular wave function and energy can be expressed. These oriented quasi-atomic orbitals are the rigorous <i>ab initio</i> counterparts to the conceptual bond forming atomic hybrid orbitals of qualitative chemical reasoning. In the present work, the quasi-atomic orbitals are identified as bonding orbitals, lone pair orbitals, radical orbitals, vacant orbitals and orbitals with intermediate character. A program determines the bonding characteristics of all quasi-atomic orbitals in a molecule on the basis of their occupations, bond orders, kinetic bond orders, hybridizations and local symmetries. These data are collected in a record and provide the information for a comprehensive understanding of the synergism that generates the bonding structure that holds the molecule together. Applications to a series of molecules exhibit the complete bonding structures that are embedded in their <i>ab initio</i> wave functions. For the strong bonds in a molecule, the quasi-atomic orbitals provide quantitative <i>ab initio</i> amplifications of the Lewis dot symbols. Beyond characterizing strong bonds, the quasi-atomic analysis also yields an understanding of the weak interactions, such as vicinal, hyperconjugative and radical stabilizations, which can make substantial contributions to the molecular bonding structure

Relativistic <i>ab Initio</i> Accurate Atomic Minimal Basis Sets: Quantitative LUMOs and Oriented Quasi-Atomic Orbitals for the Elements Li–Xe

Valence virtual orbitals (VVOs) are a quantitative and basis set independent method for extracting chemically meaningful lowest unoccupied molecular orbitals (LUMOs). The VVOs are formed based on a singular value decomposition (SVD) with respect to precomputed and internally stored <i>ab initio</i> accurate atomic minimal basis sets (AAMBS) for the atoms. The occupied molecular orbitals and VVOs together form a minimal basis set that can be transformed into orthogonal oriented quasi-atomic orbitals (OQUAOs) that provide a quantitative description of the bonding in a molecular environment. In the present work, relativistic AAMBS are developed that span the full valence orbital space. The impact of using full valence AAMBS for the formation of the VVOs and OQUAOs and the resulting bonding analysis is demonstrated with applications to the cuprous chloride, scandium monofluoride, and nickel silicide diatomic molecules