The use of elementary reaction coordinates in the search for conical intersections

Abstract

A method to locate conical intersections between the ground-state potential surface and the first electronically excited states of polyatomic molecules is described. It is an extension of the Longuet-Higgins sign-change theorem and uses reaction coordinates of elementary reactions as the starting point of the analysis. It is shown that the complete molecular landscape [1] can be partitioned into 2-D domains, each bordered by a Longuet-Higgins loop formed from reaction coordinates of elementary reactions. A domain may contain a conical intersection and if it does, it contains only one (the uniqueness theorem), whose energy is higher than the neighboring minima or transition states. The method can be helped by symmetry, but applies also to systems having no symmetry elements. It is demonstrated for some simple cases. The presence of a conical intersection is manifested by the nature of ground-state thermal reactions, as shown for instance by the fact that the transition state in the ring opening of the cyclopropyl radical is nonsymmetric.

Assessment of approximate computational methods for conical intersections and branching plane vectors in organic molecules

“…The S 0 /S 1 intersections in these systems, see Figure 3, originate from crossings between the electronic states that correspond to the homolytic (diradical) and heterolytic (charge transfer, CT) breaking of the π -bond. 4,22,[108][109][110] These CIs can be classified as twisted-pyramidalized (tw-pyr, for brevity) or as twisted-bond_length_alternating (tw-BLA) depending on the relative preference for the two bond-breaking mechanisms; the tw-pyr CIs are typical of molecules with dominant homolytic bond breaking, while the tw-BLA CIs occur in molecules for which both π -bond breaking processes are nearly isoenergetic. 22,108 Another type of CIs commonly occurring in organic molecules can be vaguely classified as n/π CIs that originate from the crossing between an electron configuration (n 2 π * 0 ) with a doubly occupied lone pair and a singly excited (n 1 π * 1 ) configuration.…”

“…7,118 The twpyr MECI (see Figure 3) arises from a crossing between the PESs of the electronic states for homolytic and heterolytic π -bond breaking. 20,22,73,108,109 The heterolytic π -bond breaking process is much less favorable than the homolytic one. 20,22 According to a previously proposed rule, 20, 22 the tw-pyr MECI occurs in the proximity of a ground-state conformation that corresponds to heterolytic π -bond breaking and features strong pyramidalization to stabilize the shift of the π electron pair toward one of the carbon atoms.…”

Toward Separation of Nuclear Spin Isomers with Coherent Light

“…Also of interest is the energy regime that nears or surpasses the conical intersection between the ground and excited electronic states of fulvene, where the influence of the nuclear spin on the nonadiabatic dynamics will enrich the problem. [24][25][26] In general, the efficiency of the present approach will depend on the times, the ortho-and para-species need for passing through the conical intersection. Finally, in the present study, we used simple Gaussian pulses to separate ortho-and para-fulvene.…”

“…Figure 1 b shows a sketch of the potential energy for the ground and first excited electronic states of fulvene. [24][25][26] Assume an ensemble of molecules which forms an incoherent mixture of para-and ortho-fulvene: the torsional ground state will be symmetric for para-fulvene (solid line) and antisymmetric for ortho-fulvene (dashed line). The potential barrier in the ground electronic state is sufficiently high so that the two eigenfunctions are practically degenerate.…”

Progress and Challenges in the Calculation of Electronic Excited States

“…Further help can be provided with the intuitive method provided by Zilberg and coworkers that, based on the Longuet-Higgins phase change theorem, is able to predict the location of CoIns between (typically) the ground and the first electronic state. [234,235] According to the topography, CoIns can be classified into sloped (Figure 6 b) and peaked (Figure 6 c). [222] A sloped crossing is characterized by two approximately parallel gradients and two minima of the respective crossing states lying on the same side of the crossing.…”