Dynamic DFT method

Dynamic DFT method is usitally used to model the dynamic behavior of polymer systems and has been implemented in the software package Mesodyn TM from Accelrys [41]. The DFT models the behavior of polymer fluids by combining Gaussian mean-field statistics with a TDGL model for the time evolution of conserved order parameters. However, in contrast to traditional phenomenological free-energy expan-... 

The projector augmented-wave (PAW) DFT method was invented by Blochl to generalize both the pseudopotential and the LAPW DFT teclmiques [M]- PAW, however, provides all-electron one-particle wavefiinctions not accessible with the pseudopotential approach. The central idea of the PAW is to express the all-electron quantities in tenns of a pseudo-wavefiinction (easily expanded in plane waves) tenn that describes mterstitial contributions well, and one-centre corrections expanded in tenns of atom-centred fiinctions, that allow for the recovery of the all-electron quantities. The LAPW method is a special case of the PAW method and the pseudopotential fonnalism is obtained by an approximation. Comparisons of the PAW method to other all-electron methods show an accuracy similar to the FLAPW results and an efficiency comparable to plane wave pseudopotential calculations [, ]. PAW is also fonnulated to carry out DFT dynamics, where the forces on nuclei and wavefiinctions are calculated from the PAW wavefiinctions. (Another all-electron DFT molecular dynamics teclmique using a mixed-basis approach is applied in [84].)... 

To use direct dynamics for the study of non-adiabatic systems it is necessary to be able to efficiently and accurately calculate electronic wave functions for excited states. In recent years, density functional theory (DFT) has been gaining ground over traditional Hartree-Fock based SCF calculations for the treatment of the ground state of large molecules. Recent advances mean that so-called time-dependent DFT methods are now also being applied to excited states. Even so, at present, the best general methods for the treatment of the photochemistry of polyatomic organic molecules are MCSCF methods, of which the CASSCF method is particularly powerful. 

In this chapter, a short introduction to DFT and to its implementation in the so-called ab initio molecular dynamics (AIMD) method will be given first. Then, focusing mainly on our own work, applications of DFT to such fields as the definition of structure-activity relationships (SAR) of bioactive compounds, the interpretation of the mechanism of enzyme-catalyzed reactions, and the study of the physicochemical properties of transition metal complexes will be reviewed. Where possible, a case study will be examined, and other applications will be described in less detail. 

In the following text we present a very short synopsis both of the DFT approach and the ab initio molecular dynamics (AIMD) method that can by no means be considered as an introduction to the use of the computational tools based on them. The interested reader will find exhaustive treatment of these arguments elsewhere in this book (Chapter 1). 

The first way has been followed in what has become known as Car-Parrinello molecular dynamics (CPMD) (9). A solute and 60-90 solvent molecules are considered to represent the system, and the QM calculations are performed with density functionals, usually of generalised gradient approximation type (GGA), such as the Becke-Lee-Young-Parr (BLYP) (10) or the Perdew-Burke-Enzerhofer (PBE) (11,12) functionals. It is clear that the semiempirical character of concurrent density functional theory (DFT) methods and the use of these simple functionals imply a number of error sources and do not really provide a method-inherent control procedure to test the reliability of results. Recently it has been shown that these functionals even do not enable a correct description of the solvent water itself, as at ambient temperature they will describe water not as liquid but as supercooled system... 

It is, however, for the transition metals themselves that DFT has proven to be a tremendous improvement over HF and post-HF methods, particularly for cases where tlie metal atom is coordinatively unsaturated. The narrow separation between filled and empty d-block orbitals typically leads to enormous non-dynamical correlation problems with an HF treatment, and DFT is much less prone to analogous problems. Even in cases of a saturated coordination sphere, DFT methods typically significantly ouqierform HF or MP2. Jonas and Thiel (1995) used the BP86 functional to compute geometries for the neutral hexacarbonyl complexes of Cr, Mo, and W, the pentacarbonyl complexes of Fe, Ru, and Os, and the tetracarbonyl... 

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. 

Semiempirical methods - based on approximate solutions of the Schrodinger equation with appeal to fitting to experiment (i.e. using parameterization) Density functional theory (DFT) methods - based on approximate solutions of the Schrodinger equation, bypassing the wavefunction that is a central feature of ab initio and semiempirical methods Molecular dynamics methods study molecules in motion. 

The vinylcyclopropane rearrangement has been studied using a variety of semiempirical methods [59,60], including a study of the reaction dynamics at the AMI level [61], Recently, both possible pathways have been studied using various MO and DFT methods [62], The results for the two possible pathways are shown in Table 6. 

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