Semiempirical direct dynamics

Semiempirical direct dynamics was used to study trimethylene s unimo-lecular dynamics and the thermal stereomutation of cyclopropane.The semiempirical model used in these simulations is AMI with specific reaction parameters (SRPs see discussion of semiempirical electronic structure theory in the section on BO direct dynamics) chosen to fit the CASSCF PES. In choosing the SRPs, the AMI barrier for propene formation was lowered by... 

Direct dynamics attempts to break this bottleneck in the study of MD, retaining the accuracy of the full electronic PES without the need for an analytic fit of data. The first studies in this field used semiclassical methods with semiempirical [66,67] or simple Hartree-Fock [68] wave functions to heat the electrons. These first studies used what is called BO dynamics, evaluating the PES at each step from the elech onic wave function obtained by solution of the electronic structure problem. An alternative, the Ehrenfest dynamics method, is to propagate the electronic wave function at the same time as the nuclei. Although early direct dynamics studies using this method [69-71] restricted themselves to adiabatic problems, the method can incorporate non-adiabatic effects directly in the electionic wave function. 

Jones et al. [144,214] used direct dynamics with semiempirical electronic wave functions to study electron transfer in cyclic polyene radical cations. Semiempirical methods have the advantage that they are cheap, and so a number of trajectories can be run for up to 50 atoms. Accuracy is of course sacrificed in comparison to CASSCF techniques, but for many organic molecules semiempirical methods are known to perform adequately. 

In fact, the distinction between two-step and direct dynamics is rather fuzzy. The basic issue is what kind and amount of preliminary work is needed before starting a dynamical calculation. Direct ab initio dynamics [90,97-101] requires a minimum of preparation some tests to choose basis sets and other options may suffice. For large systems, however, fully ab initio calculations are impractical, and one has to resort to QM/MM or PCM approaches but then, a host of empirical parameters are introduced, which may need some readjustement to avoid artefacts and to improve the accuracy before starting the dynamical calculations. The same holds for the semiempirical methods in order to represent at best the excited states, one has to re-parameterize the hamiltonian. In particular, our FOMO-SCF-CI method [56-58] differs considerably from the normal SCF or SCF+CIS procedures, so that the standard parameters need to be modified. However, the parameter sets are fairly transferable, and their optimization can be limited to the atoms belonging to the chromophore. In the two-step strategies one fits the ab... 

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

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-... 

One difficulty with straight direct dynamics is that the large number of electronic structure calculations required tends to mitigate against employing high levels of theory. Thus, for example, some direct dynamics calculations have employed minimum basis sets [32d] and semiempirical molecular orbital theory [7b]. 

Direct dynamics was first applied by Wang and Karplus in a study of the CH2 + H2 CH4 reaction. The CNDO semiempirical electronic structure theory was used for this calculation. Two years later, Warshel and... 

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 integrals in Eqs. [15] and [17] are evaluated by solving the time-independent Schrodinger equation. Depending on the system size and accuracy requirement, ab initio, DFT or semiempirical methods can be used to solve the Schrodinger equation and determine the system s potential energy surface. The quantum mechanical methods are described in the previous two sections and are not repeated in this section. The direct dynamics calculation is performed with this potential energy surface. 

B. C. Garrett, A. D. Isaacson, A. Gonzalez-Lafont, S. N. Rai, G. C. Hancock, T. Joseph, and D. G. Truhlar, Comput. Phys. Commun., 75,143 (1993). MORATE A Program for Direct Dynamics Calculations of Chemical Reaction Rates by Semiempirical Molecular Orbital Theory. 

Election nuclear dynamics theory is a direct nonadiababc dynamics approach to molecular processes and uses an electi onic basis of atomic orbitals attached to dynamical centers, whose positions and momenta are dynamical variables. Although computationally intensive, this approach is general and has a systematic hierarchy of approximations when applied in an ab initio fashion. It can also be applied with semiempirical treatment of electronic degrees of freedom [4]. It is important to recognize that the reactants in this approach are not forced to follow a certain reaction path but for a given set of initial conditions the entire system evolves in time in a completely dynamical manner dictated by the inteiparbcle interactions. 

Once a PES has been computed, it is often fitted to an analytic function. This is done because there are many ways to analyze analytic functions that require much less computation time than working directly with ah initio calculations. For example, the reaction can be modeled as a molecular dynamics simulation showing the vibrational motion and reaction trajectories as described in Chapter 19. Another technique is to fit ah initio results to a semiempirical model designed for the purpose of describing PES s. 

Equation (4-5) can be directly utilized in statistical mechanical Monte Carlo and molecular dynamics simulations by choosing an appropriate QM model, balancing computational efficiency and accuracy, and MM force fields for biomacromolecules and the solvent water. Our group has extensively explored various QM/MM methods using different quantum models, ranging from semiempirical methods to ab initio molecular orbital and valence bond theories to density functional theory, applied to a wide range of applications in chemistry and biology. Some of these studies have been discussed before and they are not emphasized in this article. We focus on developments that have not been often discussed. 

Na3F2 cluster, direct molecular dynamics, semiempirical studies, 415 Near-adiabatic limit, molecular systems,... 

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