Dynamic mean field density functional

Fraaije, J.G.E.M., Van Vlimmeren, B.A.C., Maurits, N.M., Postma, M., Evers, O.A., Hoffmann, C., Altevogt, P., Goldbeck-Wood, G. The dynamic mean-field density functional method and its application to the mesoscopic dynamics of quenched block copolymer melts. J. Chem. Phys. 106 (1997) 4260-4269. 

DYNAMIC MEAN-FIELD DENSITY FUNCTIONAL METHOD... 

The dynamic mean-field density functional method is similar to DPD in practice, but not in its mathematical formulation. This method is built around the density functional theory of coarse-grained systems. The actual simulation is a... 

In dynamic mean field density functional theory, the dynamics of the polymer melt under simple steady shear is described by the time evolution of density fields p/. The dynamics is governed by a diffusion-convection equation with sheared periodic boundary conditions and can readily be extended with (second order) reaction terms in the following manner ... 

Finally a method which shows promise for the future is d5mamic mean field theory. Dynamical mean field theory uses an approximation to the local spectral density functional (rather than energy density functional) and a set of correlated local orbitals. For solids this local description is combined with a periodic description such as DFT using EDA to provide a method of dealing with both localised and delocalised electrons." Anisimov et applied this method to the photo-... 

The two basic sampling methods used for such studies are (1) Monte Carlo calculations, which allow one to obtain, among other properties, adsorption energies and preferred locations for the adsorbed species, and (2) molecular dynamics simulations, which provide dynamical information such as diffusion coefficients. Both methods require repeated calculation of the energy of the system, and accordingly this is still an area dominated by force field calculations. A few studies have been performed by means of density functional calculations, as exemplified by Haase, Sauer, and Hutter, but these calculations require at present substantial computer power. 

The static and dynamic mean-field equations are derived, for a given energy-density functional, by variation with respect to the single-particle wave functions Ritz variational principle of minimal energy yields the static mean-field equations,... 

Abbreviations MD, molecular dynamics TST, transition state theory EM, energy minimization MSD, mean square displacement PFG-NMR, pulsed field gradient nuclear magnetic resonance VAF, velocity autocorrelation function RDF, radial distribution function MEP, minimum energy path MC, Monte Carlo GC-MC, grand canonical Monte Carlo CB-MC, configurational-bias Monte Carlo MM, molecular mechanics QM, quantum mechanics FLF, Hartree-Fock DFT, density functional theory BSSE, basis set superposition error DME, dimethyl ether MTG, methanol to gasoline. 

Thus, we see that in order to obtain the mean field equations of motion, the density matrix of the entire system is assumed to factor into a product of subsystem and environmental contributions with neglect of correlations. The quantum dynamics then evolves as a pure state wave function depending on the coordinates evolving in the mean field generated by the quantum density. As we have seen in the previous sections, these approximations are not valid and no simple representation of the quantum-classical dynamics is possible in terms of single effective trajectories. Consequently, in contrast to claims made in the literature [54], quantum-classical Liouville dynamics is not equivalent to mean field dynamics. 

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