Electronic dephasing of polyatomic molecules interacting with mixed quantum-classical media

Abstract

This paper offers an expedient, efficient, and unique treatment of multimode quantum subsystems (polyatomic molecules) interacting with a classical environment in which the time evolution of the coupling term is governed by the algebraic rules of statistical mechanics in mixed quantum-classical systems developed by Kapral and Nielsen [S. Nielsen, R. Kapral, and G. Ciccotti, J. Chem. Phys., 2001, 115, 5805]. This unique time evolution of the coupling term is neither quantal nor classical but rather something different that relies heavily on Wigner transform, thereby leading to non-Newtonian mechanics. As such, an argument is presented that the approach provided herein for treating polyatomic molecular systems in a mixed quantum-classical environment is new and different as opposed to the many other schemes of semiclassical dynamics that are normally employed to study such systems. The merits of expediency and efficiency of the herein mixed quantum-classical dynamics calculations emanate from avoiding using integrals for time evolutions, and, instead, employing matrix mechanics whereby LU decomposition and singular value decomposition (SVD) numerical techniques are utilized for diagonalization. An electronic 2-level subsystem interacting with a classical bath through the spin-boson model to render accurate pure electronic dephasing in multimode molecular systems by eliminating the unphysical asymmetry in the line shape of the zero-phonon line (ZPL) exhibited by other models is exploited. This work has a superior advantage over the single-mode spin-boson model, published previously, whereby a multitude of types of vibrational modes (slow, fast, or both) of the quantum subsystem may readily be handled using different spectral densities. The spin-boson model used here is a composite system made up of a quantum subsystem, i.e., a subsystem bilinearly coupled to a multidimensional harmonic oscillator (representing the intermediate quantum vibrational modes between the electronic subsystem and the bath), interacting with a classical bath, where the coupling term is governed by the mixed quantum-classical Liouville equation. A multidimensional coherent-state approach is employed to deal with the time evolution of the quantum subsystem. A closed-form expression of linear and nonlinear optical electronic transition dipole moment time correlation functions in mixed quantum-classical dissipative media is derived. Pure electronic dephasing is probed using the aforementioned approach. Linear absorption spectra and 4-wave mixing signals (e.g., photon echo and pump–probe) are calculated showing a reasonable thermal broadening, temporal decay, and accurate pure dephasing.