Density matrix nonadiabatic

A rather general method of the calculation of the tunneling taking account of the dissipation was given in Ref. 82. The cases of rather strong dissipation were considered in Refs. 81 and 82, where it was assumed that a thermodynamical equilibrium in the initial potential well exists. The case of extremely weak friction has been considered using the equations for the density matrix in Ref. 83. A quantum analogue of the Focker-Planck equation for the adiabatic and nonadiabatic processes in condensed media was obtained in Refs. 105 and 106. 

The Cl of the adiabatic PESs is a common phenomenon in molecules [11-13], The singular nonadiabatic coupling (NAC) associated with Cl is the origin of ultrafast non-Born-Oppenheimer transitions. For a number of years, the effects of Cl on IC (or other nonadiabatic processes) have been much discussed and numerous PESs with CIs have been obtained [11, 12] for qualitative discussion. Actual numerical calculations of IC rates are still missing. In this chapter, we shall calculate IC rate with 2-dependent nonadiabatic coupling for the pyrazine molecule as an example to show how to deal with the IC process with the effect of CL Recently, Suzuki et al. have researched the nn state lifetimes for pyrazine in the fs time-resolved pump-probe experiments [13]. The population and coherence dynamics are often involved in such fs photophysical processes. The density matrix method is ideal to describe these types of ultrafast processes and fs time-resolved pump-probe experiments [14-19]. 

Yet, some theoretical problems are left to be discussed to seek for the ultimate and idealistic features as a nonadiabatic-transition theory Although a trajectory thus hopping plural times converges to run on an adiabatic potential surface asymptotically, the off-diagonal density matrix element Pij t) does not vanish practically, as in the original SET. This is ascribed to an incomplete treatment of the nuclear-electronic entanglement. This issue, often referred to as the problem of decoherence, is originated from the nuclear wavepacket bifurcation due to different slopes of potential surfaces, which will be discussed more precisely below. 

Wang et al have proposed a density matrix based TDDFT method in both real time and frequency domains to calculate the dynamic hyperpolarizabilities. Illustrations carried out using local density approximation on small compounds (CO, HF, HCl, and LiF) have shown the good agreement between the two methods. In addition, in the real time domain scheme, it has been found that the external field should be turned on slowly to prevent nonadiabatic efiects. 

In the antiadiabatic state, for particular k and proper q values, nonadiabatic prefactors under summation symbol in (27.9) can be large. The prefactors, i.e. coefficients of P-dependent transformation matrix (27.8c), reflect influence of nuclear kinetic energy on electronic structure. At the dominance of these contributions (antiadiabatic state), strong increase in localization of charge density appears at distorted site-positions for x equal to (mi —d ) and m2 + d2). It induces (or increases) inter-site polarization of charge density distribution. 

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