Mixed state dynamics

The MMVB force field has also been used with Ehrenfest dynamics to propagate trajectories using mixed-state forces [84]. The motivation for this is... 

Quantum chemical methods, exemplified by CASSCF and other MCSCF methods, have now evolved to an extent where it is possible to routinely treat accurately the excited electronic states of molecules containing a number of atoms. Mixed nuclear dynamics, such as swarm of trajectory based surface hopping or Ehrenfest dynamics, or the Gaussian wavepacket based multiple spawning method, use an approximate representation of the nuclear wavepacket based on classical trajectories. They are thus able to use the infoiination from quantum chemistry calculations required for the propagation of the nuclei in the form of forces. These methods seem able to reproduce, at least qualitatively, the dynamics of non-adiabatic systems. Test calculations have now been run using duect dynamics, and these show that even a small number of trajectories is able to produce useful mechanistic infomiation about the photochemistry of a system. In some cases it is even possible to extract some quantitative information. 

Takahashi and Umezawa introduced thermofield dynamics (TFD), a canonical formalism, for finite temperature theory (Y. Takahashi et.al., 1975 1996 1982 1993). TFD keeps the analogy with the zero-temperature field theory by describing thermal state, a mixed state, as a thermal... 

Because the mapping approach treats electronic and nuclear dynamics on the same dynamical footing, its classical limit can be employed to study the phase-space properties of a nonadiabatic system. With this end in mind, we adopt a onemode two-state spin-boson system (Model IVa), which is mapped on a classical system with two degrees of freedom (DoF). Studying various Poincare surfaces of section, a detailed phase-space analysis of the problem is given, showing that the model exhibits mixed classical dynamics [123]. Furthermore, a number of periodic orbits (i.e., solutions of the classical equation of motion that return to their initial conditions) of the nonadiabatic system are identified and discussed [125]. It is shown that these vibronic periodic orbits can be used to analyze the nonadiabatic quantum dynamics [126]. Finally, a three-mode model of nonadiabatic photoisomerization (Model III) is employed to demonstrate the applicability of the concept of vibronic periodic orbits to multidimensional dynamics [127]. 

Lett., 293, 259 (1998). Mixed State On the Fly Nonadiabatic Dynamics The Role of the Conical Intersection Topology. 

A systematic route to achieve a mixed quantum classical description of EET may start with the partial Wigner representation p(R,P t) of the total density operator referring to the CC solvent system. R and P represent the set of all involved nuclear coordinates and momenta, respectively. However, p(R,P t) remains an operator in the space of electronic CC states (here 4>o and the different first order of the -expansion one can change to electronic matrix elements. Focusing on singly excited state dynamics we have to consider pmn( It, / /,) = 4>m p R, P t) 4>n) which obeys the following equation... 

We will briefly discuss the molecular dynamics results obtained for two systems—protein-like and random-block copolymer melts— described by a Yukawa-type potential with (i) attractive A-A interactions (saa < 0, bb = sab = 0) and with (ii) short-range repulsive interactions between unlike units (sab > 0, aa = bb = 0). The mixtures contain a large number of different components, i.e., different chemical sequences. Each system is in a randomly mixing state at the athermal condition (eap = 0). As the attractive (repulsive) interactions increase, i.e., the temperature decreases, the systems relax to new equilibrium morphologies. 

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