Resonance Theory Reboot

Abstract

What is now called "resonance theory" has a long and conflicted history. We first sketch the early roots of resonance theory, its heritage of diverse physics and chemistry conceptions, and its subsequent rise to reigning chemical bonding paradigm of the mid-20th century. We then outline the alternative "natural" pathway to localized Lewis-and resonance-structural conceptions that was initiated in the 1950s, given semi-empirical formulation in the 1970s, recast in ab initio form in the 1980s, and successfully generalized to multi-structural "natural resonance theory" (NRT) form in the 1990s. Although earlier numerical applications were often frustrated by the ineptness of then-available numerical solvers, the NRT variational problem was recently shown to be amenable to highly efficient convex programming methods that yield provably optimal resonance weightings at a small fraction of previous computational costs. Such convexity-based algorithms now allow a full "reboot" of NRT methodology for tackling a broad range of chemical applications, including the many familiar resonance phenomena of organic and biochemistry as well as the still broader range of resonance attraction effects in the inorganic domain. We illustrate these advances for prototype chemical applications, including (i) stable near-equilibrium species, where resonance mixing typically provides only small corrections to a dominant Lewisstructural picture, (ii) reactive transition-state species, where strong resonance mixing of reactant and product bonding patterns is inherent, (iii) coordinative and related supramolecular interactions of the inorganic domain, where sub-integer resonance bond orders are the essential origin of intermolecular attraction, and (iv) exotic longbonding and metallic delocalization phenomena, where no single "parent" Lewis-structural pattern gains pre-eminent weighting in the overall resonance hybrid.

Charge-Shift Bonding in Xenon Hydrides: An NBO/NRT Investigation on HXeY···HX (Y = Cl, Br, I; X = OH, Cl, Br, I, CCH, CN) via H-Xe Blue-Shift Phenomena

“…More studies are on the way to answer such a question and to generalize CS bonding models. We believe that more surprise will be gained via NBO/NRT methods, in particular, new-type NBO-based NRT methods on analyses for larger CS bonding species (Glendening et al, 2019).…”

NBO/NRT Two-State Theory of Bond-Shift Spectral Excitation

“…For notational convenience, we denote each such (Ω i (L) ) 2 → (Ω j (NL) ) 2 delocalization as the “i→j*” correction to the idealized Ψ (NLS) , with associated energy lowering Δ E i →j* . Each i→j* interaction can also be associated with a corresponding resonance-structural bonding pattern ( Figure 1 ) whose weighting ( w i j* ) can be quantified by NRT analysis [ 13 , 14 , 15 ].…”

“…Resonance-type aspects (ii), (iii) of electronic bond shifts can be further quantified with the descriptors of natural resonance theory (NRT) [ 13 , 14 , 15 ], particularly the fractional bond orders { b AB } and resonance weightings { w R } that allow continuous tracing of a bond shift from one limit to another along a reactive pathway. Such resonance-type NBO/NRT bond shifts of n N -π* CO or π CC -π* CC type are well-known to profoundly influence the structural, reactive, and spectroscopic properties of amides or polyenes, respectively.…”

Vibrational spectroscopic and Hirshfeld surface analysis of N,N'-(azanediylbis(2,1-phenylene))bis(2-chloropropanamide)

“…Using the PAVF 1.0 program, the performance of the used method was quantitatively characterized [47]. The population analysis has also been performed by the natural bond orbital method [48] at B3LYP, BLYP, B3PW91, mPW1PW91 and HF/6-31G(d,p) and 6-311G(d,p) level of theory using the natural bond orbital (NBO) program [49] under the Gaussian 16W program package.…”