Diabatic models with transferrable parameters for generalized chemical reactions

Abstract

Abstract. Diabatic models applied to adiabatic electron-transfer theory yield many equations involving just a few parameters that connect ground-state geometries and vibration frequencies to excited-state transition energies and vibration frequencies to the rate constants for electrontransfer reactions, utilizing properties of the conical-intersection seam linking the ground and excited states through the Pseudo Jahn-Teller effect. We review how such simplicity in basic understanding can also be obtained for general chemical reactions. The key feature that must be recognized is that electron-transfer (or hole transfer) processes typically involve one electron (hole) moving between two orbitals, whereas general reactions typically involve two electrons or even four electrons for processes in aromatic molecules. Each additional moving electron leads to new high-energy but interrelated conical-intersection seams that distort the shape of the critical lowest-energy seam. Recognizing this feature shows how conicalintersection descriptors can be transferred between systems, and how general chemical reactions can be compared using the same set of simple parameters. Mathematical relationships are presented depicting how different conical-intersection seams relate to each other, showing that complex problems can be reduced into an effective interaction between the ground-state and a critical excited state to provide the first semi-quantitative implementation of Shaik's "twin state" concept. Applications are made (i) demonstrating why the chemistry of the firstrow elements is qualitatively so different to that of the second and later rows, (ii) deducing the bond-length alternation in hypothetical cyclohexatriene from the observed UV spectroscopy of benzene, (iii) demonstrating that commonly used procedures for modelling surface hopping based on inclusion of only the first-derivative correction to the Born-Oppenheimer approximation are valid in no region of the chemical parameter space, and (iv), demonstrating the types of chemical reactions that may be suitable for exploitation as a chemical qubit in some quantum information processor. IntroductionThough chemical reactions involve complicated restructuring of the electronic and nuclear configuration and dynamics, it can be useful to use the simplification of envisaging reactions as occurring along a single reaction coordinate. This basic concept forms the conceptual framework of Transition-State Theory and much of modern chemistry. Modern electronic-structure calculation methods can predict wide ranges of properties to within the accuracy of experimental measurements, capturing all chemical and spectroscopic features of the system, but such approaches rarely provide insight into why processes occur and have to be repeated for each small system variation. Diabatic models can be used to interpret these calculations, however, revealing the chemical features controlling the process. Basically, simple forms, called diabatic surfaces, are used to describe the reactants and pro...

Bond angle variations in XH3[X = N, P, As, Sb, Bi]: the critical role of Rydberg orbitals exposed using a diabatic state model

“…53,54 For the ammonia inversion reaction, the NH symmetric bonding ( A ), nonbonding (n), and symmetric antibonding (* A ) orbitals are specified by valence-bond theory, neglecting the degenerate bonding ( E ) and antibonding (* E ) valence orbitals, whilst for benzene the doubly degenerate HOMO and LUMO orbitals are required. For ammonia, we have found that  A is only weakly involved and so can be ignored in the simplest diabatic approach, 52 justifying this usual and qualitatively very successful practice. 51,55 The n to * A interaction thus generates 3 electronic states (the ground state g, the n* A singly excited state s, and the n* A ,n* A doubly excited state d), all of which are coupled together by the same strong vibronic coupling.…”

“…A similar but more complex scenario arises also for benzene for which 7 coupled electronic states are implicated. 52 Having established the importance of including all states in quantitative analyses, we also showed that such complex 20 descriptions can be reduced to effective two-state models. This makes available the wide range of results developed for electrontransfer theory and widely applied historically to more general problems, except that now the two-state model parameters become renormalized in a property-dependent fashion.…”

“…51 Recently, we overcame the fundamental limitation concerning simple diabatic descriptions by demonstrating that diabatic models for electron-transfer fundamentally differ from typical chemical processes as they involve radical species rather than closed-shell ones. 52 The consequence of this is that more than one electronic excited state can be made by exciting electrons between the critical occupied and virtual orbitals involved in the chemical process. Identifying these critical orbitals is the initial challenge facing diabatic analyses, with those specified by Valence-Bond theory being a good starting point.…”

“…This makes available the wide range of results developed for electrontransfer theory and widely applied historically to more general problems, except that now the two-state model parameters become renormalized in a property-dependent fashion. 52 This 25 explains why previous generalized 2-state diabatic approaches have failed to be universal as different parameters are required to describe say the ground-state structure and the excited-state manifold. Using our modified theory it is possible, for example, to deduce diabatic C-C and C=C bond lengths of 1.53 Å and 1.31 30 Å, respectively, based on the observed value in benzene (1.41 Å) and excited-state spectral data only; similarly, we showed that, in crude calculations ignoring Rydberg states, it is possible to deduce the equilibrium bond angle and well depth for NH 3 inversion from spectroscopic data obtained at the planar geometry only.…”

“…Using our modified theory it is possible, for example, to deduce diabatic C-C and C=C bond lengths of 1.53 Å and 1.31 30 Å, respectively, based on the observed value in benzene (1.41 Å) and excited-state spectral data only; similarly, we showed that, in crude calculations ignoring Rydberg states, it is possible to deduce the equilibrium bond angle and well depth for NH 3 inversion from spectroscopic data obtained at the planar geometry only. 52 Conversely, it is possible to estimate spectroscopic transition energies knowing only the shape of the ground-state potential-energy surface, and herein we analyze the latest fulldimensional experimentally derived [56][57][58][59] and theoretical 60 surfaces as well as those produced from high quality calculations.…”