A comprehensive analysis of molecule-intrinsic quasi-atomic, bonding, and correlating orbitals. I. Hartree-Fock wave functions

West, Aaron C.; Schmidt, Michael W.; Gordon, Mark S.; Ruedenberg, Klaus

doi:10.1063/1.4840776

Cited by 95 publications

(208 citation statements)

References 90 publications

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“…23 Typical representative examples of these quasi-atomic orbitals are displayed in Figure 11. The upper set of panels in the figure display the quasi-atomic orbitals found on the left atom of the N 2 molecule.…”

Section: The Molecules B 2 C 2 N 2 O 2 Fmentioning

confidence: 99%

Covalent bonds are created by the drive of electron waves to lower their kinetic energy through expansion

Schmidt

Ivanic

Ruedenberg

2014

The Journal of Chemical Physics

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153

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An analysis based on the variation principle shows that in the molecules H 2 + , H 2 , B 2 , C 2 , N 2 , O 2 , F 2 , covalent bonding is driven by the attenuation of the kinetic energy that results from the delocalization of the electronic wave function. For molecular geometries around the equilibrium distance, two features of the wave function contribute to this delocalization: (i) Superposition of atomic orbitals extends the electronic wave function from one atom to two or more atoms; (ii) intra-atomic contraction of the atomic orbitals further increases the inter-atomic delocalization. The inter-atomic kinetic energy lowering that (perhaps counter-intuitively) is a consequence of the intra-atomic contractions drives these contractions (which per se would increase the energy). Since the contractions necessarily encompass both, the intra-atomic kinetic and potential energy changes (which add to a positive total), the fact that the intra-atomic potential energy change renders the total potential binding energy negative does not alter the fact that it is the kinetic delocalization energy that drives the bond formation. © 2014 AIP Publishing LLC. [http://dx

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Section: The Molecules B 2 C 2 N 2 O 2 Fmentioning

confidence: 99%

Covalent bonds are created by the drive of electron waves to lower their kinetic energy through expansion

Schmidt

Ivanic

Ruedenberg

2014

The Journal of Chemical Physics

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153

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“…Section II presents the equations for VVO generation in a simpler form than a decade ago, 4 since the present paper is not concerned with the closely related atom localized orbitals known as QUAMBOs 4 and QUAOs. 5,6 Section III describes the characteristics and applications of VVOs. The VVOs are shown to be nearly independent of the quantitative basis set in which a calculation is performed, in their shape and in their energy.…”

Section: Introductionmentioning

confidence: 99%

Valence Virtual Orbitals: An Unambiguous ab Initio Quantification of the LUMO Concept

2015

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Many chemical concepts hinge on the notion of an orbital called the lowest unoccupied molecular orbital, or LUMO. This hypothetical orbital and the much more concrete highest occupied molecular orbital (HOMO) constitute the two "frontier orbitals", which rationalize a great deal of chemistry. A viable LUMO candidate should have a sensible energy value, a realistic shape with amplitude on those atoms where electron attachment or reduction or excitation processes occur, and often an antibonding correspondence to one of the highest occupied MOs. Unfortunately, today's quantum chemistry calculations do not yield useful empty orbitals. Instead, the empty canonical orbitals form a large sea of orbitals, where the interesting valence antibonds are scrambled with the basis set's polarization and diffuse augmentations. The LUMO is thus lost within a continuum associated with a detached electron, as well as many Rydberg excited states. A suitable alternative to the canonical orbitals is proposed, namely, the valence virtual orbitals. VVOs are found by a simple algorithm based on singular value decomposition, which allows for the extraction of all valence-like orbitals from the large empty canonical orbital space. VVOs are found to be nearly independent of the working basis set. ABSTRACT: Many chemical concepts hinge on the notion of an orbital called the lowest unoccupied molecular orbital, or LUMO. This hypothetical orbital and the much more concrete highest occupied molecular orbital (HOMO) constitute the two "frontier orbitals", which rationalize a great deal of chemistry. A viable LUMO candidate should have a sensible energy value, a realistic shape with amplitude on those atoms where electron attachment or reduction or excitation processes occur, and often an antibonding correspondence to one of the highest occupied MOs. Unfortunately, today's quantum chemistry calculations do not yield useful empty orbitals. Instead, the empty canonical orbitals form a large sea of orbitals, where the interesting valence antibonds are scrambled with the basis set's polarization and diffuse augmentations. The LUMO is thus lost within a continuum associated with a detached electron, as well as many Rydberg excited states. A suitable alternative to the canonical orbitals is proposed, namely, the valence virtual orbitals. VVOs are found by a simple algorithm based on singular value decomposition, which allows for the extraction of all valence-like orbitals from the large empty canonical orbital space. VVOs are found to be nearly independent of the working basis set. The utility of VVOs is demonstrated for construction of qualitative MO diagrams, for prediction of valence excited states, and as starting orbitals for more sophisticated calculations. This suggests that VVOs are a suitable realization of the LUMO, LUMO + 1, ... concept. VVO generation requires no expert knowledge, as the number of VVOs sought is found by counting s-block atoms as having only a valence s orbital, transition metals as having valence s and d, and main ...

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“…The resolution is expected to shed light on the qualitative and quantitative synergisms between the various physical interactions that cause bond-forming energy lowerings and, thereby, to provide insights into the bonding patterns of molecules. The first of the preceding papers 1 dealt with Hartree−Fock wave function. In the second paper, 2 the analysis was extended to strongly correlated wave functions.…”

Section: Introductionmentioning

confidence: 99%

A Comprehensive Analysis in Terms of Molecule-Intrinsic, Quasi-Atomic Orbitals. III. The Covalent Bonding Structure of Urea

et al. 2015

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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.

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A comprehensive analysis of molecule-intrinsic quasi-atomic, bonding, and correlating orbitals. I. Hartree-Fock wave functions

Cited by 95 publications

References 90 publications

Covalent bonds are created by the drive of electron waves to lower their kinetic energy through expansion

Covalent bonds are created by the drive of electron waves to lower their kinetic energy through expansion

Valence Virtual Orbitals: An Unambiguous ab Initio Quantification of the LUMO Concept

A Comprehensive Analysis in Terms of Molecule-Intrinsic, Quasi-Atomic Orbitals. III. The Covalent Bonding Structure of Urea

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