Relaxation dynamics through a conical intersection: Quantum and quantum–classical studies

Abstract

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Ultrafast dynamics with the exact factorization

“…In more general terms, we can say that the numerically-exact solution of the molecular TDSE is prohibitive already for small molecules like H 2 . Nonetheless, techniques able to deal with the quantum mechanical evolution of nuclear wavepackets [19,20] including the effect of multiple electronic states can access up to few tens of nuclear degrees of freedom, but the potential energy surfaces and their couplings have to be pre-computed (or even expressed in analytical forms). In approaches such as the multi-configurational time-dependent Hartree (MCTDH) method [65][66][67][68][69], up to hundreds, or even thousands, nuclear degrees of freedom can be handled, however, the potential energy surfaces need to be pre-computed and expressed as sums of single-particle functions (and often, the majority of the degrees of freedom are harmonic oscillators that mimic the effect of a bath).…”

“…However, we only describe the critical points of such derivation, since the details can be found in Refs. [19,43,44,49].…”

“…It is worth mentioning here that the norm of the electronic wavefunction is preserved along the dynamics by Eqs. (19), i.e., m |C α m (t)| 2 = 1 ∀ t, α. The off-diagonal contributions in Eq.…”

“…( 14) used to propagate CT-MQC trajectories contains the vector potential, and its total time derivative has to be computed to give an explicit expression of the force in terms of electronic coefficients and the other electronic properties introduced in Eqs. (19). The final expression in given in Sect.…”

“…The theoretical description of nonequilibrium processes at the microscopic scale poses continuous challenges in many fields, such as molecular and chemical physics, condensed matter physics, and theoretical chemistry. Theory needs to be able to describe purely quantum effects such as electronic transitions [1][2][3][4][5][6][7][8][9], (de)coherence [10][11][12][13][14][15], interferences [16,17], energy relaxation [18][19][20], or phase transitions [21,22], that are often the result of complex interactions between electrons and nuclei on ultrafast time scales and of the non-perturbative effect of time-dependent external fields. While quantum mechanics is the key to unravel these processes, actual applications and studies relying on computational methods require the introduction of approximations.…”