Electronic-state chaos, intramolecular electronic energy redistribution, and chemical bonding in persisting multidimensional nonadiabatic systems

Abstract

We study the chaotic, huge fluctuation of electronic state, resultant intramolecular energy redistribution, and strong chemical bonding surviving the fluctuation with exceedingly long lifetimes of highly excited boron clusters. Those excited states constitute densely quasi-degenerate state manifolds. The huge fluctuation is induced by persisting multidimensional nonadiabatic transitions among the states in the manifold. We clarify the mechanism of their coexistence and its physical significance. In doing so, we concentrate on two theoretical aspects. One is quantum chaos and energy randomization, which are to be directly extracted from the properties of the total electronic wavefunctions. The present dynamical chaos takes place through frequent transitions from adiabatic states to others, thereby making it very rare for the system to find dissociation channels. This phenomenon leads to the concept of what we call intramolecular nonadiabatic electronic-energy redistribution, which is an electronic-state generaliztion of the notion of intramolecular vibrational energy redistribution. The other aspect is about the peculiar chemical bonding. We investigate it with the energy natural orbitals (ENOs) to see what kind of theoretical structures lie behind the huge fluctuation. The ENO energy levels representing the highly excited states under study appear to have four robust layers. We show that the energy layers responsible for chaotic dynamics and those for chemical bonding are widely separated from each other, and only when an event of what we call “inter-layer crossing” happens to burst can the destruction of these robust energy layers occur, resulting in molecular dissociation. This crossing event happens only rarely because of the large energy gaps between the ENO layers. It is shown that the layers of high energy composed of complex-valued ENOs induce the turbulent flow of electrons and electronic-energy in the cluster. In addition, the random and fast time-oscillations of those high energy ENOs serve as a random force on the nuclear dynamics, which can work to prevent a concentration of high nuclear kinetic energy in the dissociation channels.

Sonification of molecular electronic energy density and its dynamics

“…The last example is taken from an ab initio MD dynamics simulation of molecular dissociation in the densely quasidegenerate electronic state manifold of B 12 clusters. 26,27 The many vacancies in the 2p orbital valence space of the boron atoms give rise to the highly quasi-degenerate manifold of excited states, and for balance between their rough representation and computation-intensive dynamics, we choose to use the STO-3G minimum basis set for molecular orbital determination and conguration interaction singles and doubles from the highest occupied molecular orbital (HOMO) and HOMO−1 (MO 29 and 30) to all virtual orbitals for the excited states description. The number of conguration state functions included in the calculation is 1891.…”

“…The excited states in such highly degenerate manifolds are generally of very long lifetime as discussed in a previous paper, due to what we call the intramolecular nonadiabatic electronic-energy redistribution (INER). 27 Therefore, in order to study the dissociation dynamics for B 12 → B 11 + B, we need to find or intentionally prepare a moment right before a dissociation. Fig.…”

“…7 shows the time-variation of 60 ENOs on the occasion of such a dissociation, which starts at about 30 fs in the graph. Despite a very wild diffusive electronic wavepacket state in the Hilbert space, 27 we find a very clear layer structure composed of 4 bands to exist before dissociation: the core layer (panel(c) in Fig. 7 ) composed of ENOs 1 through 12 of the lowest energy; the valence layer in panel (b) from ENOs 13 to 28; the half-occupied layer of ENOs 29 and 30 (panel (a), the lower part); and the flowing layer from ENOs 31 to 60 (panel (a), the upper band).…”