A Comprehensive Analysis in Terms of Molecule-Intrinsic Quasi- Atomic Orbitals. IV. Bond Breaking and Bond Forming along the Dissociative Reaction Path of Dioxetane

The quantitative analysis of molecular density matrices in terms of oriented quasi-atomic orbitals (QUAOs) is shown to yield detailed conceptual insight into the dissociation of dioxetane on the basis of ab initio wave functions. The QUAOs persist and can be followed throughout the reaction path. The kinetic bond orders and the orbital populations of the QUAOs quantitatively reveal the changes of the bonding interactions along the reaction path. At the transition state the OO bond is broken, and the molecule becomes a biradical. After the transition state the reaction path bifurcates. The minimum energy path gently descends from the transition state via a valley–ridge inflection point to a second saddle point, from which two new minimum energy paths lead to two equivalent formaldehyde dimers. The CC bond breaks, and the π-bonds of the formaldehyde fragments form in close vicinity of the second saddle point. The changes of the interactions in this region are elucidated by the analysis of the rearrangements of the QUAOs

A Comprehensive Analysis of Molecule-Intrinsic Quasi-Atomic, Bonding, and Correlating Orbitals. I. Hartree-Fock Wave Functions

Through a basis-set-independent web of localizing orbital-transformations, the electronic wave function of a molecule is expressed in terms of a set of orbitals that reveal the atomic structure and the bonding pattern of a molecule. The analysis is based on resolving the valence orbital space in terms of an internal space, which has minimal basis set dimensions, and an external space. In the internal space, oriented quasi-atomic orbitals and split-localized molecular orbitals are determined by new, fast localization methods. The density matrix between the oriented quasi-atomic orbitals as well as the locations of the split-localized orbitals exhibit atomic populations and inter-atomic bonding patterns. A correlation-adapted quasi-atomic basis is determined in the external orbital space. The general formulations are specified in detail for Hartree-Fock wave functions. Applications to specific molecules exemplify the general scheme

The transition from the open minimum to the ring minimum on the ground state and on the lowest excited state of like symmetry in ozone: A configuration interaction study

The metastable ring structure of the ozone 11A1 ground state, which theoretical calculations have shown to exist, has so far eluded experimental detection. An accurate prediction for the energy difference between this isomer and the lower open structure is therefore of interest, as is a prediction for the isomerization barrier between them, which results from interactions between the lowest two 1A1 states. In the present work, valence correlated energies of the 11A1 state and the 21A1 state were calculated at the 11A1 open minimum, the 11A1 ring minimum, the transition state between these two minima, the minimum of the 21A1 state, and the conical intersection between the two states. The geometries were determined at the full-valence multi-configuration self-consistent-field level. Configuration interaction (CI) expansions up to quadruple excitations were calculated with triple-zeta atomic basis sets. The CI expansions based on eight different reference configuration spaces were explored. To obtain some of the quadruple excitation energies, the method of Correlation Energy Extrapolation by Intrinsic Scaling was generalized to the simultaneous extrapolation for two states. This extrapolation method was shown to be very accurate. On the other hand, none of the CI expansions were found to have converged to millihartree (mh) accuracy at the quadruple excitation level. The data suggest that convergence to mh accuracy is probably attained at the sextuple excitation level. On the 11A1 state, the present calculations yield the estimates of (ring minimum—open minimum) ∼45–50 mh and (transition state—open minimum) ∼85–90 mh. For the (21A1–1A1) excitation energy, the estimate of ∼130–170 mh is found at the open minimum and 270–310 mh at the ring minimum. At the transition state, the difference (21A1–1A1) is found to be between 1 and 10 mh. The geometry of the transition state on the 11A1 surface and that of the minimum on the 21A1 surface nearly coincide. More accurate predictions of the energydifferences also require CI expansions to at least sextuple excitations with respect to the valence space. For every wave function considered, the omission of the correlations of the 2s oxygen orbitals, which is a widely used approximation, was found to cause errors of about ±10 mh with respect to theenergy differences

A Comprehensive Analysis in Terms of Molecule-Intrinsic, Quasi-Atomic Orbitals. II. Strongly Correlated MCSCF Wave Functions

A methodology is developed for the quantitative identification of the quasi-atomic orbitals that are embedded in a strongly correlated molecular wave function. The wave function is presumed to be generated from configurations in an internal orbital space whose dimension is equal to (or slightly larger) than that of the molecular minimal basis set. The quasi-atomic orbitals are found to have large overlaps with corresponding orbitals on the free atoms. They separate into bonding and nonbonding orbitals. From the bonding quasi-atomic orbitals, localized bonding and antibonding molecular orbitals are formed. The resolution of molecular density matrices in terms of these orbitals furnishes a basis for analyzing the interatomic bonding patterns in molecules and the changes in these bonding patterns along reaction paths. A new bond strength measure, the kinetic bond order, is introduced.Reprinted (adapted) with permission from Journal of Physical Chemistry A 119 (2015): 10360, doi:10.1021/acs.jpca.5b03399. Copyright 2015 American Chemical Society.</p

Quasi-Atomic Bond Analyses in the Sixth Period: I. Relativistic Accurate Atomic Minimal Basis Sets for the Elements Cesium to Radon

Full-valence relativistic accurate atomic minimal basis set (AAMBS) orbitals are developed for the sixth-row elements from cesium to radon, including the lanthanides. Saturated primitive atomic basis sets are developed and subsequently used to form the AAMBS orbitals. By virtue of the use of a saturated basis, properties computed based on the AAMBS orbitals are basis set independent. In molecules, the AAMBS orbitals can be used to construct valence virtual orbitals (VVOs) that provide chemically meaningful abinitio lowest unoccupied molecular orbitals (LUMOs) with basis set independent orbital energies. The optimized occupied molecular orbitals complemented with the VVOs form a set of full-valence molecular orbitals. They can be transformed into a set of oriented quasi-atomic orbitals (QUAOs) that provide information on intramolecular bonding via an intrinsic density analysis. In the present work, the development of the AAMBS for the sixth row is presented

Accurate Ab Initio Potential Energy Curve of F2. II. Core-valence Correlations, Relativistic Contributions, and Long-Range Interactions

The nonrelativistic, valence-shell-only-correlated ab initio potential energy curve of the F2molecule, which was reported in the preceding paper, is complemented by determining the energy contributions that arise from the electron correlations that involve the core electrons as well as the contributions that are due to spin-orbit coupling and scalar relativistic effects. The dissociation curve rises rather steeply toward the energy of the dissociated atoms because, at larger distances, the atomic quadrupole-quadrupole repulsion and spin-orbit coupling counteract the attractive contributions from incipient covalent binding and correlation forces including dispersion

The Virial Theorem and Covalent Bonding

A long-held view of the origin of covalent binding is based on the notion that electrostatic forces determine the stability of a system of charged particles and that, therefore, potential energy changes drive the stabilization of molecules. A key argument advanced for this conjecture is the rigorous validity of the virial theorem. Rigorous in-depth analyses have however shown that the energy lowering of covalent bonding is due to the wave mechanical drive of electrons to lower their kinetic energy through expansion. Since the virial theorem applies only to systems with Coulombic interaction potentials, its relevance as a foundation of the electrostatic view is tested here by calculations on analogues of the molecules H2+ and H2, where all 1/r interaction potentials are replaced by Gaussian-type potentials that yield one-electron “atoms” with realistic stability ranges. The virial theorem does not hold in these systems, but covalent bonds are found to form nonetheless, and the wave mechanical bonding analysis yields analogous results as in the case of the Coulombic potentials. Notably, the key driving feature is again the electron delocalization that lowers the interatomic kinetic energy component. A detailed discussion of the role of the virial theorem in the context of covalent binding is given

Quasi-Atomic Bond Analyses in the Sixth Period: II. Bond Analyses of Cerium Oxides

The role of the 4f orbitals in bonding is examined for the molecules cerium monoxide and cerium dioxide that have cerium formally in the +2 and +4 oxidation states, respectively. It is shown that the 4f orbitals are used primarily for polarization of the 5d orbitals when cerium is in the lower oxidation state, while the 4f orbitals play a significant role in chemical bonding via 5d/4f hybridization when cerium is in the +4 oxidation state