Resonance Theory Reboot
Frank Weinhold
Theoretical Chemistry Institute and Department of Chemistry, University of
Wisconsin-Madison, Madison WI 53706 (weinhold@chem.wisc.edu)
Natural Resonance Theory (NRT) is an extension of Natural Bond Orbital (NBO) theory that reformulates Pauling’s traditional resonance-theoretic conceptions in terms of the 1st -order reduced density matrix Γ(1) and associated “natural” (maximumoccupancy) properties as first enunciated by P.-O. Löwdin. Although the original formulation of NRT has proven quite successful in chemical applications to smaller molecules, it often suffers from the ineptness of available non-linear solvers for the variational optimization of resonance weightings. This bottleneck has now been bypassed with recognition that NRT variational optimization can be reformulated as a Gram-type convex quadratic programming (QP) problem. The QPNRT solver (a primary feature of the newly released NBO 7.0 program) thereby opens up resonancetheoretic description to a broad new range of chemical applications, including the highly delocalized metallic-like limit in which no single “parent” Lewis structure is evident. The new NRT implementation also allows efficient evaluation of a new family of “resonance NBOs” (RNBOs) that provide a far-reaching extension of familiar Natural Localized Molecular Orbitals (NLMOs) and achieve strict compliance with Pople’s criterion for uniform applicability over every point or path of a potential energy surface. We illustrate “re-booted” NRT resonance weightings, bond orders, and graphical RNBO depictions for a variety of near-equilibrium and reactive chemical species, demonstrating their broad usefulness for elucidating details of reaction mechanism or other structural and spectroscopic properties in a chemically intuitive manner.
E. D. Glendening and F. Weinhold, “Natural Resonance Theory of Chemical Reactivity, with Application to Intramolecular Claisen Rearrangement,” Tetrahedron 74, 4799-4804 (2018).
E. D. Glendening and F. Weinhold, “Resonance Natural Bond Orbitals: Efficient SemiLocalized Orbitals for Computing and Visualizing Reactive Chemical Processes,” J. Chem. Theor. Comput. (in press).
E. D. Glendening, J. K. Badenhoop, A. E. Reed, J. E. Carpenter, J. A. Bohmann, C. M. Morales, P. Karafiloglou, C. R. Landis, and F. Weinhold, NBO 7.0: Natural Bond Orbital Analysis Programs, Theoretical Chemistry Institute, U. Wisconsin, Madison (2018).