Direct dynamics calculations

Baldridge K K, Gordon M S, Steckler R and Truhlar D G 1989 Ab initio reaction paths and direct dynamics calculations J. Phys. Chem. 93 5107... 

The Helgaker-Chen algorithm results in very large steps being possible, and despite the extra cost of the required second derivatives, this is the method of choice for direct dynamics calculations. A number of systems have been treated, and a review of the method as applied to chemical reactions is given in [2]. 

Importantly for direct dynamics calculations, analytic gradients for MCSCF methods [124-126] are available in many standard quantum chemistiy packages. This is a big advantage as numerical gradients require many evaluations of the wave function. The evaluation of the non-Hellmann-Feynman forces is the major effort, and requires the solution of what are termed the coupled-perturbed MCSCF (CP-MCSCF) equations. The large memory requirements of these equations can be bypassed if a direct method is used [233]. Modem computer architectures and codes then make the evaluation of first and second derivatives relatively straightforward in this theoretical framework. 

Being able to ntn direct dynamics calculations will add an extra, important, tool to help chemists understand photochemical systems. This chapter has outlined the present standpoint of the theory and practice of such calculations showing that, although much work remains to be done, they are already bringing new insight to mechanistic studies of photochemistry. 

However, the direct dynamics calculations are computationally expensive, and cannot employ particularly high levels of electron correlation or large basis sets. If certain regions of the potential cannot be treated to within the required accuracy using a computationally affordable level of theory, the results may have unacceptably large errors. Nevertheless, direct dynamics calculations have played and will play a critical role in the discovery and analysis of competing pathways in chemical reactions. 

For both statistical and dynamical pathway branching, trajectory calculations are an indispensable tool, providing qualitative insight into the mechanisms and quantitative predictions of the branching ratios. For systems beyond four or five atoms, direct dynamics calculations will continue to play the leading theoretical role. In any case, predictions of reaction mechanisms based on examinations of the potential energy surface and/or statistical calculations based on stationary point properties should be viewed with caution. 

In order to investigate which model for the behavior of 8 is closer to being correct, our group provided Carpenter with an analytical expression, fit to our PES, so that Carpenter could perform semiclassical trajectory calculations on our PES. At the same time. Doubleday and Hase undertook direct dynamics calculations. As discussed in Chapter 21 in this volume, in the latter type of trajectory calculation the forces acting on a molecule at different points on a PES are found by performing electronic structure calculations. For this purpose. Doubleday and Hase used a reparameterized version of AMI that provided a PES, similar to those calculated by Getty and by Baldwin, Yamaguchi, and Schaefer. 

Both types of dynamics calculations gave the same type of results. The calculations found that the ratio of double-to-single methylene rotations is higher than the 1 1 ratio predicted by application of a TST model to the PES. Ratios of double-to-single rotations between 2.9 and 3.5 were obtained from the direct dynamics calculations of Doubleday et al., and a ratio of 4.7 was computed from the trajectory calculations performed by Carpenter and co-workers. ... 

Another advantage of making these direct dynamics calculations on sp metals is that, unlike the simplified model of copper, the full ip-metal simulations have realistic forces between the metal atoms, so that surface relaxations and, eventually, reconstructions can be studied. This was not done in the cadmium study just described, but one of us (SW) has recently explored the possibilities with a calculation of the relaxation of an aluminum surface. The calculation was done on a system consisting of 5 x 5 x 5 = 125 aluminum... 

Direct dynamics calculations using the PM3 method were carried out for reaction l.4 The trajectories starting from the TS between the biradical intermediate and norbornene (2, 3) with 2kcalmol 1 kinetic energy on the imaginary frequency mode together with zero-point energy (ZPE) on other real... 

Direct dynamics calculations were carried out with quasiclassical normalmode sampling from a canonical ensemble at 923 K (the experimental reaction temperature). Simulations initiated at the vicinity of TS for rearrangement of carbene 13 to 14 via oxirene 12, and 300 trajectories were obtained at DFT methods. The preliminary results reported in the manuscript showed that preferred formation of 15a over 15b by the ratio of 1.8 7.6 depends on the method used. The results were qualitatively consistent with the value of 2.5 deduced from the experiment. The non-unity ratio likely arises from the situation that two methyl groups in 14 are dynamically unequal on the carbene formation process. 

Gonzalez-Lafont, A. Truong, T. N. Truhlar, D. G. Direct dynamics calculations with neglect of diatomic differential overlap molecular orbital theory with specific reaction parameters, J. Phys. Chem. 1991, 95,4618-4627. 

Roberto-NetoO., CoitinoE. L., andTruhlar D. G. (1998) Duallevel direct dynamics calculations of deuterium and carbon-13 kinetic isotope effects for the reaction Cl + CH4. J. Phys. Chem. A 102, 4568-4578. 

Gonzalez-Lafont, A., Truong, T.N. and Truhlar, D.G. (1991) Direct Dynamics Calculations with Neglect of Diatomic Differential Overlap Molecular Orbital Theory with Specific Reaction Parameters, J. Phys. Chem. 95, 4618-4627. 

The most recent calculations on the tunneling dynamics of double proton transfer in formic acid dimer and benzoic acid dimers have been reported by Smedar-china et al. [20]. They used direct dynamics calculations to predict the tunneling splittings of both carboxylic dimers. 

However, based upon a direct dynamical calculation, which used a potential surface for benzoic acid dimer at a B3LYP/6-31 + G(d) level [20], Smedarchina et al. suggest that the hydrogen bonding is weaker in the excited state, in agreement with the experimentally observed increase in the intermolecular distance r [24]. 

A program for direct dynamics calculations of chemical reaction rates by semiempirical molecular orbital theory, Comput. Phys. Commun. 75, 143-159. 

Liu, Y.-P., Lu, D.-h., Gonzalez-Lafont, A., Truhlar, D. G., Garrett, B. C. (1993) Direct dynamics calculation of the kinetic isotope effect for an organic hydrogen-transfer... 

A promising recent development concerns the use of semiempirical NDDO methods with specific reaction parameters (NDDO-SRP) [144-147] in direct dynamics calculations. In these studies the parameters in the standard AMI method are carefully adjusted to optimize the potential surface for an individual reaction or a set of related reactions (typically allowing parameter variations up to 10% from the original values). When adjusting with respect to experimental data, NDDO-SRP is required to reproduce the exothermicity and the barrier (or rate constant) of the reaction investigated. Under these circumstances NDDO-SRP then predicts reasonable transition structures and force fields for the reaction which is consistent with previous experience [48,49]. Direct dynamics calculations on such NDDO-SRP surfaces have provided very encourag-... 

Ab Initio Reaction Paths and Direct Dynamics Calculations. 

M. Watanabe and W. P. Reinhardt, Phys. Rev. Lett., 65,3301 (1990). Direct Dynamical Calculation of Entropy and Free Energy by Adiabatic Switching. 

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