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Unrestricted absolutely localized molecular orbitals for energy decomposition analysis: Theory and applications to intermolecular interactions involving radicals
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10.1063/1.4798224
/content/aip/journal/jcp/138/13/10.1063/1.4798224
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/13/10.1063/1.4798224

Figures

Image of FIG. 1.
FIG. 1.

Alkyl Radical ALMO EDA Results: Unfavorable terms, such as geometric distortion are placed on the bottom of a double bar and grow to the left (negative). On the top bar, favorable terms such as polarization grow to the right (positive). By construction, the binding energy can then be read as the length of the bar to the right. Charge transfer is of much greater importance in systems involving molecular cations and, among those, for systems including a radical.

Image of FIG. 2.
FIG. 2.

Variational Charge Transfer (E V-CT; kJ/mol) Plotted Against the Inverse of the Interfragment Orbital Energy Gap (eV; ionization potential of alkyl species less the electron affinity of the cation): Data are for alkyl systems containing molecular cations. The proportionality of energy denominators to energy lowerings shown by the linear relationships echoes the physicality of traditional perturbative treatments of orbital interactions. Groupings are motivated by steric considerations, and the relative slopes can be explained by the greater proton affinity of ammonia.

Image of FIG. 3.
FIG. 3.

Alkyl COVP Results: All interactions are favorable, and the direction of growth from the zero line indicates the directionality of the charge transfer. Energy contributions to the left of zero involve COVPs with the acceptor orbital on the alkyl species while those on the right correspond to charge donation to the cation. Contributions from orbital interactions in the alpha space are denoted with warm colors and those in the beta space with cool colors to facilitate the recognition of symmetry or asymmetry with respect to spin. Each color indicates a different occupied-virtual orbital pair's energy contribution. Additionally, the total length of the bar indicates the magnitude of the charge transfer energy lowering calculated by perturbation theory. Notice that, in the alkali cation cases, donation is negligible while, for systems containing H3O+ and , charge transfer is primarily to the cation, symmetric with respect to spin for closed shell cases and primarily from the higher energy alpha HOMO of the alkyl species for the open shell cases.

Image of FIG. 4.
FIG. 4.

Representative COVP Images for Alkyl Systems: The most important COVPs in the alpha and beta spaces for the interaction of hydronium with the t-butyl radical ((CH3)3C) and its closed shell analog ((CH3)3CH). The charge transfer energy lowering (kJ/mol) associated with each orbital pair is also shown. The virtual (acceptor) orbital of the pair is depicted as a mesh isosurface while that for the occupied (donor) orbital is represented with a translucent isosurface. The charge transfer interaction with the radical is reminiscent of chemical bonding with the alpha space charge transfer occurring from a higher energy orbital on the t-butyl radical than the beta space charge transfer.

Image of FIG. 5.
FIG. 5.

E POL(kJ/mol) Plotted Against E Bind(kJ/mol) for Alkyl Systems: Grouping is by alkyl species for steric reasons. There is a strong linear relationship between polarization and E Bind, which encapsulates the overall degree of interaction, within steric groupings. Additionally, within radical/closed shell categories, there is an inverse relationship between the slopes and the respective alkyl intrafragment orbital gaps (cf. text).

Image of FIG. 6.
FIG. 6.

Aryl Radical EDA Results: Unfavorable terms, such as geometric distortion are placed on the bottom of a double bar and grow to the left (negative). On the top bar, favorable terms such as polarization grow to the right (positive). By construction, the binding energy can then be read as the length of the bar to the right. Notice the considerable shift toward dependence on frozen interactions rather than charge transfer when a species is oriented on the side rather than on top and also the very similar binding energy for water in the two orientations despite the considerably different character of interaction.

Image of FIG. 7.
FIG. 7.

Aryl Radical COVP Results: All interactions are favorable, and the direction of growth from zero indicates the directionality of the charge transfer. Energy contributions to the left of zero involve COVPs with the acceptor orbital on the aryl radical cation species while those on the right correspond to charge donation to the nucleophile. Contributions from orbital interactions in the alpha space are denoted with warm colors and those in the beta space with cool colors to facilitate the recognition of symmetry or asymmetry with respect to spin. Each color indicates a different occupied-virtual orbital pair's energy contribution. Additionally, the total length of the bar indicates the magnitude of the charge transfer energy lowering calculated by perturbation theory. Charge transfer is primarily from the nucleophile to the electron deficient aryl radical cation and, for on-top systems, in the beta space as the radical has a lower-lying beta LUMO accessible in that orientations. Charge transfer is diminished for side-on systems but largely symmetric with respect to spin due to poor overlap with the low-lying beta orbital.

Image of FIG. 8.
FIG. 8.

E V-CT(kJ/mol) Plotted Against the Inverse of the Interfragment Orbital Energy Gap (eV; IP of nucleophile less IP of benzene): Data are for systems containing the aryl radical cation and on-top oriented nucleophile. The equation is of the form E V-CT = a/Gap; a = −84.7 kJ eV/mol, the accurate fit demonstrates the consistency of the ALMO V-CT term with a perturbation theory understanding of orbital interactions based on isolated species. Minimal error in the fit was incurred by forcing the physically meaningful zero intercept.

Image of FIG. 9.
FIG. 9.

E POL(kJ/mol) Plotted Against E Bind(kJ/mol) for All Aryl Radical Cation Systems. All nucleophiles and orientations considered in this work are included. All systems are included in a single fit because the species with the smallest intrafragment orbital energy gap is in all cases the aryl radical cation and because steric concerns are fairly uniform. The fairly accurate fit despite the diversity of systems reaffirms the interpretation and strong physical content of the ALMO polarization term.

Image of FIG. 10.
FIG. 10.

E V-CT(kJ/mol) Plotted Against E FRZ(kJ/mol) for all Aryl Radical Cation Systems. All nucleophiles and orientations considered in this work are included. The linear correlation demonstrates the origin of the unfavorable Frozen interaction terms for these systems: core-core and exchange interactions resulting from close proximity needed for improved orbital overlap.

Image of FIG. 11.
FIG. 11.

The Ratio (Top:Side) of the E V-CT, E POL, and E Bind Contributions Plotted Against IP(eV): Systems shown are those with both an on-top and a side-on structure. This plot shows the considerable shift toward dependence on charge transfer interactions as IP decreases toward that of benzene (9.24 eV) when going from side-on to on-top orientation. The top:side ratio for E POL increases for smaller interfragment orbital energy gaps because of the closer contacts. These close contacts are brought about by the potential for energetically attractive orbital interactions and introduce a stronger perturbation for intramolecular mixings. The E POL ratio increases more slowly than that for E V-CT, and that for E Bind increases even more slowly because of the unfavorable frozen interactions incurred by the closer approach of the species.

Image of FIG. 12.
FIG. 12.

Representative COVP Images for Aryl Radical Cation Systems: The most important COVPs in the alpha and beta spaces for the interaction of water with the benzene radical cation in both the on-top and side-on orientations. The charge transfer energy lowering (kJ/mol) associated with each orbital pair is also shown. The virtual (acceptor) orbital of the pair is depicted as a mesh isosurface while that for the occupied (donor) orbital is represented with a translucent isosurface. For the side case, charge transfer is roughly symmetric with respect to spin and primarily into a C–H σ* orbital on the aryl radical cation. For the top case, charge transfer is from a lone pair orbital on water into a somewhat localized π orbital on the aryl radical cation. In the beta space, this acceptor orbital has one fewer node (lower energy) and thus leads to greater energy lowering.

Tables

Generic image for table
Table I.

Alkyl Radical ALMO EDA Results: EDA terms (kJ/mol) for systems containing an alkane or alkyl radical and a cation, either alkali or molecular. Note that the pairs H3O+/Na+ and /K+ are of comparable size, so one should expect comparable electrostatic interactions; however, FRZ and POL terms are noticeably larger in magnitude for the systems with molecular cations due to the closer interaction brought about by the charge transfer interactions exclusive to the molecular systems.

Generic image for table
Table II.

Aryl Radical ALMO EDA Results: EDA terms (kJ/mol) and nucleophile Ionization Potentials (IP) 64 for systems containing the benzene radical cation and a nucleophile in the given orientation, on-top or side-on. Note, for on-top orientations, the erratic dependence of the total binding energy on nucleophile IP but nearly monotonic dependence of V-CT on the same quantity. The IP of benzene and thus the Electron Affinity (EA) of the aryl radical cation acceptor is 9.24 eV. 64

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2013-04-05
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Unrestricted absolutely localized molecular orbitals for energy decomposition analysis: Theory and applications to intermolecular interactions involving radicals
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/13/10.1063/1.4798224
10.1063/1.4798224
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