Born-Oppenheimer direct dynamics

Lipeng Sun and William L. Hase, Born-Oppenheimer Direct Dynamics Classical Trajectory Simulations. 

We wanted to extend this approach to include dynamical effects on line shapes. As discussed earlier, for this approach one needs a trajectory co t) for the transition frequency for a single chromophore. One could extract a water cluster around the HOD molecule at every time step in an MD simulation and then perform an ab initio calculation, but this would entail millions of such calculations, which is not feasible. Within the Born Oppenheimer approximation the OH stretch potential is a functional of the nuclear coordinates of all the bath atoms, as is the OH transition frequency. Of course we do not know the functional. Suppose that the transition frequency is (approximately) a function of a one or more collective coordinates of these nuclear positions. A priori we do not know which collective coordinates to choose, or what the function is. We explored several such possibilities, and one collective coordinate that worked reasonably well was simply the electric field from all the bath atoms (assuming the point charges as assigned in the simulation potential) on the H atom of the HOD molecule, in the direction of the OH bond. 

Eq. (21), which directly reflects the non-Born-Oppenheimer dynamics of the system. Assuming that the system is initially prepared at x = 3 in the diabatic state /2), the corresponding initial distribution pg mainly overlaps with orbits A and C, since at x = 3 these orbits do occupy the state /2). Similarly, excitation of /i) mainly overlaps with orbits of type B, which at x = 3 occupy the state /i) (see Fig. 32). In a first approximation, the electronic population probability P t) may therefore be calculated by including these orbits in the... 

Sun, L. Hase, W. L. Born-Oppenheimer direct dynamics classical trajectory simnla-tions, Rev. Comput. Chem. 2003,19, 79-146. 

Two methods, identified as Car-Parinello [113] and Born-Oppenheimer [114], have been advanced for performing direct dynamics simulations. For the former, the motions of the electrons are determined simultaneously as the nuclear classical equations of motion are integrated, to determine the change in the electronic wave function as the nuclei move. For the second method the electronic wave function is optimized during the numerical integration of the classical trajectory. 

At present, reaction path methods represent the best approach for utilizing ab initio electronic structure theory directly in chemical reaction dynamics. To study reaction dynamics we need to evaluate accurately the Born-Oppenheimer molecular potential energy surface. Our experience suggests that chemical reaction may take place within in a restricted range of molecular configurations (i.e., there is a defined mechanism for the reaction). Hence we may not need to know the PES everywhere. Reaction path methods provide a means of evaluating the PES for the most relevant molecular geometries and in a form that we can use directly in dynamical calculations. 

It has been shown that in the limit of ultrashort laser pulses the stimulated-emission pump-probe signal is proportional to the population probability of the initially excited diabatic state [Tf)) Eq. (59) and Refs. 7, 99 and 141. As has been emphasized in Chapter 9, the electronic population probability P2 t) represents a key quantity in the discussion of internal-conversion processes, as it directly reflects the non-Born-Oppenheimer dynamics (in the absence of vibronic coupling, P2 t) = const ). It is therefore interesting to investigate to what extent this intramolecular quantity can be measured in a realistic pump-probe experiment with finite laser pulses. It is clear from Eq. (33) that the detection of P2(t) is facilitated if a probe pulse is employed that stimulates a major part of the excited-state vibrational levels into the electronic ground state, that is, the probe laser should be tuned to the maximum of the emission band. Figure 4(a) compares the diabatic population probability P2(t) with a cut of the stimulated-emission spectrum for uj2 3.4 eV, i.e. at the center of the red-shifted emission band. Apart from the first 20 fs, where the probe laser is not resonant with the emission [cf Fig. 2(b)], the pump-probe signal is seen to capture the overall time evolution of electronic population probability. Pump-probe experiments thus have the potential to directly monitor electronic populations and thus non-Born-Oppenheimer dynamics in real time. ... 

Ab initio molecular dynamics methods can roughly be divided into two classifications Born-Oppenheimer Molecular Dynamics and Car-Parrinello Molecular Dynamics . In both simulations, the wavefunction is propagated with the changes in the nuclear coordinates. In the Born-Oppenheimer MD approach, the forces on each of ions are explicitly calculated at each MD time step. As such, the system directly follows the Bom-Oppenheimer surface. The primary drawback of the Born-Oppenheimer MD approach relates to the fact that time-intensive electronic structure calculations must be converged... 

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