Mixed-state trajectory

The mixed-state character of a trajectory outside a non-adiabatic region is a serious weakness of the method. As the time-dependent wave function does not... 

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

Figure 15. Snapshots of the two frontier excited-state natural orbitals (computed using the HF-OA-CAS(4/4) S wavefunction) of the excited-state trajectory of cyclobutene shown in Fig. 13. Left panels Before the onset of disrotatory motion, the excited-state wavefunction can be described using a single determinant with one electron in a tt-like orbital (4>a) and one in a 7t -like orbital (4>b). Middle panels During the disrotatory motion the simplest description of the electronic wavefunction requires two determinants. In one determinant both electrons are in the (j)a orbital, and in the other they are both in the (j)b orbital. Both orbitals (<()a and 4>b) show significant cj—it mixing, which is a consequence of the significant disrotatory motion. Right panels When the disrotatory motion is completed, the excited-state wavefunction is described by a single determinant in which both electrons are in the <()b orbital. Note how the shape of the orbitals changes as the initial bonds are broken and the two new tc bonds are formed.

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. 

For the case of intramolecular energy transfer from excited vibrational states, a mixed quantum-classical treatment was given by Gerber et al. already in 1982 [101]. These authors used a time-dependent self-consistent field (TDSCF) approximation. In the classical limit of TDSCF averages over wave functions are replaced by averages over bundles of trajectories, each obtained by SCF methods. 

In a mixed quantum-classical simulation such as a mean-field-trajectory or a surface-hopping calculation, the population probability of the diabatic state v[/ t) is given as the quasiclassical average over the squared modulus of the diabatic electronic coefficients dk t) defined in Eq. (27). This yields... 

---