Dynamics studies

Boiton K and Nordhoim S 1996 A ciassicai moiecuiar dynamics study of the intramoiecuiar energy transfer of modei trans-stiibene Chem. Phys. 203 101-26... 

Straub J E, Borkovec M and Berne B J 1988 Molecular dynamics study of an isomerizing diatomic Lennard-Jones fluid J. Chem. Phys. 89 4833... 

Maynard A T, Wyatt R E and lung C 1995 A quantum dynamical study of CH overtones in fluoroform. 

Ma J, Bout D V and Berg M 1995 Solvation dynamics studied by ultrafast transient hole burning J. Moi. Liq. 65/66 301-4... 

Jesson B J, Foley M and Madden P A 1997 Thermal properties of the self-interstitlal In aluminum an ab initio molecular-dynamics study Pbys. Rev. B 55 4941-6... 

AokI M I and Tsumuraya K 1997 Ab initio molecular-dynamics study of pressure-induced glass-to-crystal transitions In the sodium system Pbys. Rev. B 56 2962-8... 

Parrinello M and Rahman A 1980 Crystal structure and pair potentials a molecular dynamics study Phys. Rev.L 45 1196-9... 

Truong T N 1997 Thermal rates of hydrogen exchange of methane with zeolite a direct ab initio dynamics study on the importance of quantum tunneling effects J. Rhys. Chem. B 101 2750... 

Goldanskii V I and Krupyanskii Y F 1989 Protein and protein-bound water dynamics studied by Rayleigh scattering of Mdssbauer radiation (RSMR) Q. Rev. Biophys. 22 39-92... 

Lutsko J F ef a/1989 Molecular-dynamic study of lattice-defect-nucleated melting in metals using an embedded-atom-method potential Phys. Rev. B 40 2841... 

To add non-adiabatic effects to semiclassical methods, it is necessary to allow the trajectories to sample the different surfaces in a way that simulates the population transfer between electronic states. This sampling is most commonly done by using surface hopping techniques or Ehrenfest dynamics. Recent reviews of these methods are found in [30-32]. Gaussian wavepacket methods have also been extended to include non-adiabatic effects [33,34]. Of particular interest here is the spawning method of Martinez, Ben-Nun, and Levine [35,36], which has been used already in a number of direct dynamics studies. 

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. 

To demonstrate the basic ideas of molecular dynamics calculations, we shall first examine its application to adiabatic systems. The theory of vibronic coupling and non-adiabatic effects will then be discussed to define the sorts of processes in which we are interested. The complications added to dynamics calculations by these effects will then be considered. Some details of the mathematical formalism are included in appendices. Finally, examples will be given of direct dynamics studies that show how well the systems of interest can at present be treated. 

A more comprehensive Gaussian wavepacket based method has been introduced by Martinez et al. [35,36,218]. Called the multiple spawning method, it has already been used in direct dynamics studies (see Section V.B), and shows much promise. It has also been applied to adiabatic problems in which tunneling plays a role [219], as well as the interaction of a... 

The present high cost of full CASSCF direct dynamics means that it is not possible to use such calculations to run large numbers of trajectories. As a result it cannot be used to build up experience of the types of effects to be found in dynamical studies of organic photochemistry, and in their interpretation. This problem can be remedied by performing calculations using the MMVB force field [63,64]. 

A more demanding dynamical study aimed to rationalize the product distribution in photochemical cycloaddition, looking at butadiene-butadiene [82]. A large number of products are possible, with two routes on the excited Si state leading back to channels on the ground state. The results are promising, as the MMVB dynamics find the major products found experimentally. They also... 

Full quantum wavepacket studies on large molecules are impossible. This is not only due to the scaling of the method (exponential with the number of degrees of freedom), but also due to the difficulties of obtaining accurate functions of the coupled PES, which are required as analytic functions. Direct dynamics studies of photochemical systems bypass this latter problem by calculating the PES on-the-fly as it is required, and only where it is required. This is an exciting new field, which requires a synthesis of two existing branches of theoretical chemistry—electronic structure theory (quantum chemistiy) and mixed nuclear dynamics methods (quantum-semiclassical). 

Rahman, A., Stillinger, F.H. Molecular dynamics study of liquid water. J. Chem. Phys. 55 (1971) 3336-3359. 

Tieleman, D.P., Berendsen, H.J.C. A molecular dynamics study of the pores formed by E. coli OmpF porin in a fully hydrated POPE bilayer. Biophys. J., in print (1998). 

Meier, R.J., Van Doremaele, H.J., larlori, S., Buda, F. Ab-initio molecular dynamics study of metallocene-catalysed ethylene polymerization. J. Amer. Chem. Soc. 116 (1994) 7274-7281. 

Mavri, J., Berendsen, H.J.C., Van Gunsteren, W.F. Influence of solvent on intramolecular proton transfer in hydrogen malonate. Molecular dynamics study of tunneling by density matrix evolution and nonequilibrium solvation. J. Phys. Chem. 97 (1993) 13469-13476. 

Izrailev et al., 1997] Izrailev, S., Stepaniants, S., Balsera, M., Oono, Y., and Schulten, K. Molecular dynamics study of unbinding of the avidin-biotin complex. Biophys. J. 72 (1997) 1568-1581... 

In molecular mechanics and molecular dynamics studies of proteins, assig-ment of standard, non-dynamical ionization states of protein titratable groups is a common practice. This assumption seems to be well justified because proton exchange times between protein and solution usually far exceed the time range of the MD simulations. We investigated to what extent the assumed protonation state of a protein influences its molecular dynamics trajectory, and how often our titration algorithm predicted ionization states identical to those imposed on the groups, when applied to a set of structures derived from a molecular dynamics trajectory [34]. As a model we took the bovine... 

Figiue 7.12 from Guillot B 1991. A Molecular Dynamics Study of the Infrared Spectrum of Water. The Journal of Chemical Physics 95 1543-1551. 

Fig. 7.12 Experimental and calculated infrared spectra for liquid water. The black dots are the experimental values. The thick curve is the classical profile produced by the molecular dynamics simulation. The thin curve is obtained by applying quantum corrections. (Figure redrawn from Guilbt B 1991. A Molecular Dynamics Study of the Infrared Spectrum of Water. Journal of Chemical Physics 95 1543-1551.)...

Leach A R and T E Klein 1995. A Molecular Dynamics Study of the Inhibitors of Dihydrofola Reductase by a Phenyl Triazine. Journal of Computational Chemistry 16 1378-1393. 

Catlow C R A1994. Molecular Dynamics Studies of Defects in Solids. In NATO ASI Series C 418 (Defects and Disorder in Crystalline and Amorphous Solids), pp. 357-373. 

Zhaiig X and C R A Callow 1992. Molecular Dynamics Study of Oxygen Diffusion in YBa2Cu306]9. Physical Review B46 457-462. 

Molecular dynamics studies are best done with a force field designed for that purpose. 

Both molecular dynamics studies and femtosecond laser spectroscopy results show that molecules with a sufficient amount of energy to react often vibrate until the nuclei follow a path that leads to the reaction coordinate. Dynamical calculations, called trajectory calculations, are an application of the molecular dynamics method that can be performed at semiempirical or ah initio levels of theory. See Chapter 19 for further details. 

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