A unified diabatic description for electron transfer reactions, isomerization reactions, proton transfer reactions, and aromaticity

Abstract

While diabatic approaches are ubiquitous for the understanding of electron-transfer reactions and have been mooted as being of general relevance, alternate applications have not been able to unify the same wide range of observed spectroscopic and kinetic properties. The cause of this is identified as the fundamentally different orbital configurations involved: charge-transfer phenomena involve typically either 1 or 3 electrons in two orbitals whereas most reactions are typically closed shell. As a result, two vibrationally coupled electronic states depict charge-transfer scenarios whereas three coupled states arise for closed-shell reactions of non-degenerate molecules and seven states for the reactions implicated in the aromaticity of benzene. Previous diabatic treatments of closed-shell processes have considered only two arbitrarily chosen states as being critical, mapping these states to those for electron transfer. We show that such effective two-state diabatic models are feasible but involve renormalized electronic coupling and vibrational coupling parameters, with this renormalization being property dependent. With this caveat, diabatic models are shown to provide excellent descriptions of the spectroscopy and kinetics of the ammonia inversion reaction, proton transfer in N2H7(+), and aromaticity in benzene. This allows for the development of a single simple theory that can semi-quantitatively describe all of these chemical phenomena, as well as of course electron-transfer reactions. It forms a basis for understanding many technologically relevant aspects of chemical reactions, condensed-matter physics, chemical quantum entanglement, nanotechnology, and natural or artificial solar energy capture and conversion.

Communication: Exciton analysis in time-dependent density functional theory: How functionals shape excited-state characters

“…Finally, the computed excited-state properties open a new route for property-based diabatization schemes. [43][44][45] S.A.M. acknowledges funding of the Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences and Landesgraduiertenförderung BadenWürttemberg.…”

Diabatic models with transferrable parameters for generalized chemical reactions

“…It also forms the basis for understanding of primary charge separation in natural and artificial solar-energy harvesting systems used in plants, bacteria, organic photovoltaics and artificial photosynthesis, as well as the reverse process, light emission in organic light-emitting diodes. A critical feature of the approach is that it leads to very many analytical or numerically exactly-solvable relationships linking system properties, as recently summarized in a number of contexts [28,[43][44][45][46]. Exemplary in Hush's description of intervalence compounds is that he showed how from measurement of the visible absorption spectrum of the dye Prussian blue, it was possible to deduce kinetics parameters critical to the understanding of the charge conductivity of the material [5].…”

“…In this review, we present a fundamental feature only just recognized [28] as a defining element of molecular potential-energy surfaces. Utilizing it, diabatic models can be produced for many types of chemical processes that involve transferrable parameters-parameters whose values depict wideranging properties, parameters who values can be transferred between systems.…”

“…Applications of this formalism to understanding why the chemistry of first-row elements is so different to that of later row ones, to understanding aromaticity, to designing chemical quantum computers, and to understanding the basics of Born-Oppenheimer breakdown and non-adiabatic chemical processes. In terms of understanding general Born-Oppenheimer breakdown, the onedimensional model described herein obviously cannot deal with processes involving direct conical intersections, but analogues are drawn to known fully general mathematical results coming from the field of Catastrophe Theory [80][81][82][83] The reason that parameters previously derived for general chemical reactions cannot be transferred between properties or between systems is that the effect of the number of electrons involved in the chemical processes was not taken into account analytically within the models [28]. This means that the effect of varying electron number gets treated implicitly rather than explicitly, modifying the values of deduced parameters.…”

“…Closely related are the polaron models from solid-state physics [13][14] and the Rashba spin Hamiltonian [15], but a different approach from the field of spectroscopy has been the Pseudo-JahnTeller effect (PJTE) developed by Bersuker and others [16][17][18][19][20] that focuses on spectroscopic states as "reactants" and "products" coupled through Herzberg-Teller [21] vibronic coupling [22][23][24][25]. At the basic level, these approaches are all equivalent [26], and can remain so even after extension to include multiple nuclear motions [27] (as is required to describe processes involving conical intersections) or multiple electronic states [28], but the convenience with which they may be applied to different problems varies.The basic model is sketched in figure 1, as it is usually presented in adiabatic electron-transfer theory relevant to general chemical reactivity. In simple cases involving symmetric isomerization reactions, only 3 parameters are often sufficient to describe complex Born-Oppenheimer ground and excited electronic states, increasing to 4 parameters to include any reaction asymmetry.…”