Direct dynamics simulations

Calculational estimates of the lifetimes of the trimethylene diradical " based on microcanonical variational unimolecular rate theory and direct dynamics simulations have been reported. The lifetimes derived from theory, 91 and 118 fs, are comparable to the experimental estimate, 120 20 fs. Similar lifetime estimates from theory for tetramethylene are comparable, or slightly below, the experimental value. ... 

Here r is the magnitude of the projection of the vector r — f2 between oxygens onto a plane parallel to the metal walls, and z and zz are the distances of oxygens 1 and 2 from the wall. Values of the parameters appear in Ref. 69, where the resulting oxygen densities from the classical and direct dynamics simulations are compared. While the densities are rather similar, the potential distributions are not, as emphasized above. 

The MP2/6-31G direct dynamics simulation study was later extended to cover the dynamics from the central barrier for the SN2 reaction of Cl I C2H5CI.104 The majority of the trajectories starting from the saddle point moved off the central barrier to form the Cl- C2H5CI complex. The results were different from those obtained previously for the CH3C1 reaction, in which extensive recrossing was observed. The reaction of C2H5CI was, in this sense, consistent with the prediction by the RRKM theory. However, some of the... 

A direct dynamics simulation of the. S N2 identity reaction of CD3C1 at the MP2/6-31G level of theory110 found that the dynamics of the trajectories from the transition state were inconsistent with both RRKM and transition state theory. 

Direct dynamics simulations, in which the methodology of classical trajectory simulations is coupled to electronic structure, have had and will continue to have an enormous impact on the use of computational chemistry to develop [111,112] the theory of unimolecular kinetics. In these simulations the derivatives of the potential, required for numerically integrating the classical trajectory, are obtained directly from electronic stmcture theory without the need for an analytic PES. Direct dynamics is particularly important for studying the unimolecular dynamics of molecules with many degrees of freedom, for which it is difficult to construct an accurate analytic PES. 

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. 

Direct dynamics has made it possible to investigate the unimolecular decomposition of a broad group of molecules for different excitation processes, to compare with experiment and determine fundamental information concerning intramolecular and unimolecular dynamics. Summarized in Table 15.1 are the unimolecular direct dynamics simulations performed by the Hase research group [117-129]. Some degree of non-RRKM behavior is present in each of the reactions. It would not have been possible to determine this level of understanding of the unimolecular dynamics of these reactions without access to direct dynamics. 

Table 15.1 Direct dynamics simulations of unimolecular decomposition...

Eventually, the DFT opens the possibility of direct dynamical simulations of chemical reactions via the combination of DFT with molecular dynamics [9], and moreover on the base of a real quantum molecular dynamics combined with DFT. But these concepts are beyond the scope of this book. 

Hase WL, Song K, Gordon MS (2003) Direct dynamics simulations. Comput Sci Eng 5 36-44... 

Meroueh O, Wang Y, Hase WL (2002) Direct dynamics simulations of collision- and surface-induced dissociation of N-protonated glycine. Shattering fragmentation. J Phys Chem A 106 9983-9992... 

Park K, Song K, Hase WL (2007) An ab initio direct dynamics simulation of protonated glycine surface-induced dissociation, hit J Mass Spectrom 265 326-336... 

This work prompted optimal control experiments on a large cyanine [88, 89], which confirmed that the branching ratio could be controlled by a pulse leading to excitation of the same skeletal deformations in the initial wavepacket (see Fig. 7.11). This control strategy was further validated in a quantum dynamics context with Gaussian-based direct dynamics simulations [90]. 

Two approaches have been advanced for performing direct dynamics simulations on a potential energy surface for a single electronic state. The Born-Oppenheimer (BO) direct dynamics approach is considered here. It bears a close resemblance to traditional classical trajectory simulations and electronic structure calculations. At each step of the trajectory integration the potential energy V(q) and gradient dV q)/dqi are obtained by optimizing the electronic wavefunction. 

Because the electronic energy Ee(q) in Eq. [8] and its derivatives must be calculated at each integration step of a classical trajectory, a direct dynamics simulation is usually very computationally intense. A standard numerical integration time step is /St = 10 " s. Thus, if a trajectory is integrated for 10 s, 10" evaluations of Eq. (8) are required for each trajectory. An ensemble for a trajectory simulation may be as small as 100 events, but even with such a small ensemble 10 " electronic structure calculations are required. Because of such computational demands, it is of interest to determine the lowest level of electronic structure theory and smallest basis set that gives an adequate representation for the system under study. In the following parts of this section, semiempirical and ab initio electronic structure theories and mixed electronic structure theory (quantum mechanical) and molecular mechanical (i.e. QM/MM) approaches for performing direct dynamics are surveyed. 

The relative compute times required for different ab initio methods are compared in Table 1 for the Cl 4- CH3CI Sn2 reaction." This comparison illustrates the utility of the MP2 method. Though it gives more accurate structures and energies than does HF, the MP2 calculations do not require appreciably more compute time that is, only approximately a factor of 3 more is needed for Cl + CH3CI. At the present time, a very high-level electronic structure theory such as CCSD(T) is not feasible for direct dynamics. Multiconfiguration ab initio methods are practical for direct dynamics simulations, as illustrated by the use of CASSCF in a recent study of the unimolecular dynamics of the cyclopropyl radical. ... 

As discussed above in the chapter introduction, either Newton s or Hamiltonian s equations may be numerically integrated for direct dynamics simulations. There is also a choice of coordinate representation, such as Cartesian, internal, " or instantaneous normal modes. Though potential... 

Direct dynamics simulations based on a high level of electronic structure theory, may be performed to study chemical events that occur in a short time. Thus, though a large amount of compute time is required for each integration step, only a small number of integration steps are required. High-level direct dynamics is practical for simulating the exit-channel dynamics of a chemical reaction from the transition state to products, since this is usually a direct... 

Table 2 Applications of Born-Oppenheimer Direct Dynamics Simulations ...

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