Car-Parrinello scheme

A key feature of the Car-Parrinello proposal was the use of molecular dynamics a simulated annealing to search for the values of the basis set coefficients that minimise I electronic energy. In this sense, their approach provides an alternative to the traditioi matrix diagonalisation methods. In the Car-Parrinello scheme, equations of motion ... 

One prominent example of rods with a soft interaction is Gay-Berne particles. Recently, elastic properties were calculated [89,90]. Using the classical Car-Parrinello scheme, the interactions between charged rods have been considered [91]. Concerning phase transitions, the sohd-fluid equihbria for hard dumbbells that interact additionally with a quadrupolar force was considered [92], as was the nematic-isotropic transition in a fluid of dipolar hard spherocylinders [93]. The influence of an additional attraction on the phase behavior of hard spherocylinders was considered by Bolhuis et al. [94]. The gelation transition typical for clays was found in a system of infinitely thin disks carrying point quadrupoles [95,96]. In confined hquid-crystalline films tilted molecular layers form near each wall [97]. Chakrabarti has found simulation evidence of critical behavior of the isotropic-nematic phase transition in a porous medium [98]. 

Most of the current implementations employ the original Car-Parrinello scheme based on DFT. The system is treated within periodic boundary conditions (PBC) and the Kohn-Sham (KS) one-electron orbitals are expanded in a basis set of plane waves (with wave vectors Gm) [48-50] ... 

If not mentioned otherwise, all the calculations presented in the next sections use the original Car-Parrinello scheme based on (gradient-corrected) density functional theory in the framework of a pseudo potential approach and a basis set of plane waves. 

Overlap of Cnuciear ) ud Ce/ec(w), as shown in Figure 9a, leads to rapid energy exchange between nuclear coordinates and electronic parameters in the Car-Parrinello scheme. If Ce ec(w) extends to very high frequencies, as shown in Figure 9b, the required time step becomes prohibitively small. The ideal situation is shown in Figure 9c. 

The purpose of this chapter will be to review the fundamentals of ab initio MD. We will consider here Density Functional Theory based ab initio MD, in particular in its Car-Parrinello version. We will start by introducing the basics of Density Functional Theory and the Kohn-Sham method, as the method chosen to perform electronic structure calculation. This will be followed by a rapid discussion on plane wave basis sets to solve the Kohn-Sham equations, including pseudopotentials for the core electrons. Then we will discuss the critical point of ab initio MD, i.e. coupling the electronic structure calculation to the ionic dynamics, using either the Born-Oppenheimer or the Car-Parrinello schemes. Finally, we will extend this presentation to the calculation of some electronic properties, in particular polarization through the modern theory of polarization in periodic systems. 

The value of the mass is a free parameter, that can be tuned in order to obtain a smooth evolution of the s. Within a Car-Parrinello scheme [49] an important requirement is the adiabatic separation with respect to the electronic degrees of freedom. Since the extra term in the Hamiltonian introduces... 

In recent years, there have been many attempts to combine the best of both worlds. Continuum solvent models (reaction field and variations thereof) are very popular now in quantum chemistry but they do not solve all problems, since the environment is treated in a static mean-field approximation. The Car-Parrinello method has found its way into chemistry and it is probably the most rigorous of the methods presently feasible. However, its computational cost allows only the study of systems of a few dozen atoms for periods of a few dozen picoseconds. Semiempirical cluster calculations on chromophores in solvent structures obtained from classical Monte Carlo calculations are discussed in the contribution of Coutinho and Canuto in this volume. In the present article, we describe our attempts with so-called hybrid or quantum-mechanical/molecular-mechanical (QM/MM) methods. These concentrate on the part of the system which is of primary interest (the reactants or the electronically excited solute, say) and treat it by semiempirical quantum chemistry. The rest of the system (solvent, surface, outer part of enzyme) is described by a classical force field. With this, we hope to incorporate the essential influence of the in itself uninteresting environment on the dynamics of the primary system. The approach lacks the rigour of the Car-Parrinello scheme but it allows us to surround a primary system of up to a few dozen atoms by an environment of several ten thousand atoms and run the whole system for several hundred thousand time steps which is equivalent to several hundred picoseconds. 

Recently, a simplified quantum mechanical molecular dynamics scheme, [i.e., tight-binding molecular dynamics (TBMD)] has been developed [13-16] which bridges the gap between classical-potential simulations and the Car-Parrinello scheme. In the same spirit as the Car-Parrinello scheme, TBMD incorporates electronic structure effects into molecular dynamics through an empirical tight-binding Hamiltonian... 

The Car-Parrinello scheme for minimization of the electronic wave functions involves an orthogonalization step, the computational expense of which increases as the square of the number of bands (Payne et al. 1992). Therefore, to increase the speed, unoccupied states are typically not included in this process. For systems such as insulators and semiconductors, their exclusion does not pose a problem because the electronic ground state is often easily found from linear combinations of lowest occupancy initial states. In the converged wave function then, unoccupied states are not... 

The intricacies of QM/MM methods lie in the challenge of finding an appropriate treatment for the coupling between QM and MM regions as described by the term V qm/mm- Special care has to be taken that the QM/MM interface is described in an accurate and consistent way, in particular in combination with the Car-Parrinello scheme. Several mixed QM/MM Car-Parrinello methods have been implemented. In the fiilly Hamiltonian coupling scheme developed, bonds between QM and MM part of the system are treated with specifically designed pseudopotentials, whereas the remaining... 

Biological systems can be treated at various different levels within a Car-Parrinello approach. One possibility is to use intelligently designed cluster models of the active site. Currently, systems of typically a few himdred atoms can be treated at the full quantum level. In addition, a static external field that captures the electrostatic field of the surrounding protein can be introduced. A common procedure is to parameterize the external electrostatic field in terms of point charges from empirical protein force fields. The most comprehensive approach for the treatment of biological systems within a Car-Parrinello framework are mixed quantum/classical QM/MM simulations. In these hybrid simulations, the reactive part of the system is treated within a standard Car-Parrinello scheme, whereas the surroimding protein is described with an empirically derived force field. In this way, electrostatic as well as steric and mechanic effects of the environment can be taken explicitly into account. 

A general and alternative approach can be proposed in order to establish the number of topological constraints ndx, T, P) for any thermodynamic condition using Molecular Dynamics (MD). In both MD s versions, classical or First Principles (FPMD) using the Car-Parrinello scheme, Newton s equation of motion is solved for a system of N atoms or ions, representing a given material. Forces are either evaluated from a model interaction potential which has been fitted to recover some materials properties, or directly calculated from the electronic density in case of a quantum mechanical treatment using density functional theory (DFT). 

---