Intramolecular Vibrational Relaxation in Electronically Excited States

Abstract

A density matrix approach for describing intramolecular dynamics, with special application to vibrational relaxation in excited electronic states, is presented. We derive the master equations governing intramolecular transfer of excitation energy between the states in a zeroth-order basis defined by considering the excitation and detection conditions in the time-resolved experiments. It is shown that, in this formalism, the memory function plays a central role. We note that the form of intramolecular memory is determined by the importance of quantum mechanical mixing of the zeroth-order states. A distinction is made between the subsystems of states with strong and weak mixing properties; while the former account for quasiperiodic character of coherent motion, the latter display a Markovian behavior. The physical conditions fixing the relative importance of quasiperiodic and statistical dynamics in individual systems are discussed. In the application to time resolved intramolecular vibrational relaxation, special consideration is given to the nature of the initially excited doorway states and the intermode couplings. The symmetry restrictions and the possible role of rotational motion in vibrational relaxation are also discussed, before considering the recent results obtained by Zewail et al. with anthracene in the first excited singlet state.

Theoretical Treatments of Radiationless Transitions

“…In this section we shall obtain the equations of motion for both population and coherence of the system embedded in the heat bath, i.e. the generalized master equation (GME) 13 from the Liouville equation for the total system (i.e., the system plus the heat bath) where $ Hdenotes the Hamiltonian of the total system which can be written as…”

“…In the Markoff approximation, the memory kernel has the delta-function time dependent and in this case, Eq. (2-11) reduces to (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) where $ R is defined by (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) Here $ R describes the relaxation and dephasing of the system due to its couplings with the heat bath. L is given by…”

“…Notice that in ( $ $ ) , R av av s only vibrational relaxation is involved due to the coupling between the system and the heat bath, i.e. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) It follows that (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) Similarly we have (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) In the right-hand side of Eq. (3-13), the first term, the second term and the third term describe the dynamical behaviors of s av,av due to the vibronic coherence dynamics, non-adiabatic transitions 27 and vibrational relaxation, respectively.…”

“…Several cases can be considered. First if vibrational relaxation is much faster than electronic processes, then (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15) If the heat bath maintains thermal equilibrium, then s av,av is related to the Bolzmann distribution P av by s av,av (t) = s a (t)P av (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) where s a (t) represents the total population of the system in the electronic state. Similarly we have…”

Influence of large magnetic fields on non-radiative transitions from the A state of thiophosgene

“…The electronically excited singlet state, which initially may be prepared by laser where 6 and f denote the density operator and the damping operator, respectively. From this equation, we obtain the generalized master equations [34,35]:…”