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. 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 interatomic 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. © 2013 AIP Publishing LLC.

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 quasiatomic 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. Disciplines Chemistry CommentsReprinted (adapted) ABSTRACT: 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.

A general intrinsic energy resolution has been formulated for strongly correlated wave functions in the full molecular valence space and its subspaces. The information regarding the quasi-atomic organization of the molecular electronic structure is extracted from the molecular wave function without introducing any additional postulated model state wave functions. To this end, the molecular wave function is expressed in terms of quasi-atomic molecular orbitals, which maximize the overlap between subspaces of the molecular orbital space and the free-atom orbital spaces. As a result, the molecular wave function becomes the superposition of a wave function representing the juxtaposed nonbonded quasi-atoms and a wave function describing the interatomic electron migrations that create bonds through electron sharing. The juxtaposed nonbonded quasi-atoms are shown to consist of entangled quasi-atomic states from different atoms. The binding energy is resolved as a sum of contributions that are due to quasi-atom formation, quasiclassical electrostatic interactions, and interatomic interferences caused by electron sharing. The contributions are further resolved according to orbital interactions. The various transformations that generate the analysis are determined by criteria that are independent of the working orbital basis used for calculating the molecular wave function. The theoretical formulation of the resolution is quantitatively validated by an application to the C molecule.

The quasi-atomic analysis of ab initio electronic wave functions in full valence spaces, which was developed in preceding papers, yields oriented quasi-atomic orbitals in terms of which the ab initio molecular wave function and energy can be expressed. These oriented quasi-atomic orbitals are the rigorous ab initio 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 ab initio wave functions. For the strong bonds in a molecule, the quasi-atomic orbitals provide quantitative ab initio 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.

The analysis of molecular electron density matrices in terms of quasi-atomic orbitals, which was developed in previous investigations, is quantitatively exemplified by a detailed application to the urea molecule. The analysis is found to identify strong and weak covalent bonding interactions as well as intramolecular charge transfers. It yields a qualitative as well as quantitative ab initio description of the bonding structure of this molecule, which raises questions regarding some traditional rationalizations. Disciplines Chemistry CommentsReprinted (adapted) ABSTRACT: The analysis of molecular electron density matrices in terms of quasi-atomic orbitals, which was developed in previous investigations, is quantitatively exemplified by a detailed application to the urea molecule. The analysis is found to identify strong and weak covalent bonding interactions as well as intramolecular charge transfers. It yields a qualitative as well as quantitative ab initio description of the bonding structure of this molecule, which raises questions regarding some traditional rationalizations.

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. ABSTRACT: 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.

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The O((3)P) + C(2)H(4) reaction provides a crucial, initial understanding of hydrocarbon combustion. In this work, the lowest-lying triplet potential energy surface is extensively explored at the multiconfiguration self-consistent field (MCSCF) and MRMP2 levels with a preliminary surface crossing investigation; and in cases that additional dynamical correlation is necessary, MR-AQCC stationary points are also determined. In particular, a careful determination of the active space along the intrinsic reaction pathway is necessary; and in some cases, more than one active space must be explored for computational feasibility. The resulting triplet potential energy surface geometries mostly agree with geometries from methods using single determinant references. However, although the selected multireference methods lead to energetics that agree well, only qualitative agreement was found with the energetics from the single determinant reference methods. Challenges and areas of further exploration are discussed.