Potential energy surface Monte-Carlo sampling

Geometry optimization of the proposed mimetic is included as part of the design analysis to ensure the feasibility of the desired molecular conformation. MM and semiempirical quantum mechanical methods have been used most extensively for these purposes. Conformational analysis of the proposed mimetic allows the determination of an energy profile for the molecule under consideration. This has been used by researchers to assess where the desired conformation for the mimetic resides on the molecular potential energy surface. Monte Carlo, MD, and distance geometry-based conformational search techniques have been employed extensively to sample conformational space. Computational methods that attempt to approximate the efifects of aqueous solvation on the conformational profile of the mimetic are being used more frequently as part of these efforts. 

Figure 5.16 Comparison of the experimentai HF vibrationai state distribution, points (normalized to unity at the most probable final state), and the results of trajectory computations (based on an ab initio potential energy surface) for the very exoerg ic reaction H + FCI -> HF + Cl, open points. The error bars shown for the trajectory results are due to the Monte Carlo sampling [adapted from R. Says etaL, Phys. Chem. Chem. Phys. 2, 523 (2000) experimental results o from D. Brandt and J. C. Polanyi, Chem. Phys. 35, 23 (1978) and A from K. Tamagake and D. W. Setser,...

Most of the details of the trajectory calculations are the same as described previously. All of the calculations are quasiclassical, i.e,y the vibrational and rotational action variables are restricted to have the correct quantized values at the start of the collision but, except for this and the final-state analysis after the collision, the internuclear motion is purely classical under the influence of the quantum mechanical potential energy surface.The only initial states considered were para-hydrogen states, i.e., states with even rotational quantum numbers. As will be indicated, some runs are for a given initial vibration-rotation state while other runs are for vibration-rotation states selected by Monte Carlo methods from the distribution of quantized states that has the desired temperature. Similarly, the relative translational energy is sometimes fixed for a run while for other runs a random selection is made from a predetermined distribution characteristic of a temperature. In the latter case importance sampling is sometimes used to improve the convergence of the calculated quantities such as the... 

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