Wave function direct molecular dynamics

Density functional theory, direct molecular dynamics, complete active space self-consistent field (CASSCF) technique, non-adiabatic systems, 404-411 Density operator, direct molecular dynamics, adiabatic systems, 375-377 Derivative couplings conical intersections, 569-570 direct molecular dynamics, vibronic coupling, conical intersections, 386-389 Determinantal wave function, electron nuclear dynamics (END), molecular systems, final-state analysis, 342-349 Diabatic representation ... 

Wigner rotation/adiabatic-to-diabatic transformation matrices, 92 Electronic structure theory, electron nuclear dynamics (END) structure and properties, 326-327 theoretical background, 324-325 time-dependent variational principle (TDVP), general nuclear dynamics, 334-337 Electronic wave function, permutational symmetry, 680-682 Electron nuclear dynamics (END) degenerate states chemistry, xii-xiii direct molecular dynamics, structure and properties, 327 molecular systems, 337-351 final-state analysis, 342-349 intramolecular electron transfer,... 

In this chapter, we look at the techniques known as direct, or on-the-fly, molecular dynamics and their application to non-adiabatic processes in photochemistry. In contrast to standard techniques that require a predefined potential energy surface (PES) over which the nuclei move, the PES is provided here by explicit evaluation of the electronic wave function for the states of interest. This makes the method very general and powerful, particularly for the study of polyatomic systems where the calculation of a multidimensional potential function is an impossible task. For a recent review of standard non-adiabatic dynamics methods using analytical PES functions see [1]. 

For translational motion, the velocity correlation function is particularly useful and, as we will show, can be utilized to provide a relationship between the echo amplitude and the molecular dynamics in the case of general modulation wave forms. Its Fourier spectrum is simply the selfdiffusion tensor (Lenk, 1977 Stepisnik, 1981) D (w), where a and /3 may take each of the Cartesian directions, x, y, z, that is. 

Fig. 22 Steady state incoherent intermediate scattering functions (z) measured in the vorticity direction as functions of accumulated strain jf for various shear rates y data from molecular dynamics simulations of a supercooled binary Lenard-Jones mixture below the glass transition ate taken from [91]. These collapse onto a yield scaling function at long times. The wavevector is q = 3.55/R (at the peak of Sq). The quiescent curve, shifted to agree with that at the highest y, shows ageing dynamics at longer times outside the plotted window. The apparent yielding master function from simulation is compared to those calculated in ISHSM for glassy states at or close to the transition (separation parameters s as labeled) and at nearby wave vectors (as labeled). ISHSM curves were chosen to match the plateau value fq, while strain parameters yc = 0.083 at = 0 solid line) and y, = 0.116 at e = 10 dashed line) were used from [45]...

Figure 8 shows the volume as a function of time for four overdriven single shock wave simulations in the [110] direction of a 25688 atom perfect Lennard-Jones face centered cubic crystal. Elastic compression is characterized by VjV 0.9 and plastic compression occurs for smaller volumes. As the shock speed decreases, the amount of time the molecular dynamics system spends in the elastically compressed state increases. This plot illustrates how the final thermodynamic state in the shock is a function of the simulation duration when slow chemical reactions or phase transitions occur. For example, on the 10-20 ps timescale, the 2.8 km/sec shock has an elastically compressed final state on the 100 ps timescale, this simulation has a plastically compressed final state. 

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