Car—Parrinello method

Specific solute-solvent interactions involving the first solvation shell only can be treated in detail by discrete solvent models. The various approaches like point charge models, siipennoleciilar calculations, quantum theories of reactions in solution, and their implementations in Monte Carlo methods and molecular dynamics simulations like the Car-Parrinello method are discussed elsewhere in this encyclopedia. Here only some points will be briefly mentioned that seem of relevance for later sections. 

While simulations reach into larger time spans, the inaccuracies of force fields become more apparent on the one hand properties based on free energies, which were never used for parametrization, are computed more accurately and discrepancies show up on the other hand longer simulations, particularly of proteins, show more subtle discrepancies that only appear after nanoseconds. Thus force fields are under constant revision as far as their parameters are concerned, and this process will continue. Unfortunately the form of the potentials is hardly considered and the refinement leads to an increasing number of distinct atom types with a proliferating number of parameters and a severe detoriation of transferability. The increased use of quantum mechanics to derive potentials will not really improve this situation ab initio quantum mechanics is not reliable enough on the level of kT, and on-the-fly use of quantum methods to derive forces, as in the Car-Parrinello method, is not likely to be applicable to very large systems in the foreseeable future. 

In the Car-Parrinello method [6] (and see, e.g., [24, 25, 16, 4]), the adiabatic time-dependent Born-Oppenheimer model is approximated by a fictitious Newtonian dynamics in which the electrons, represented by a set of... 

F. A. Bornemann and Ch. Schutte. A mathematical investigation of the Car-Parrinello method. Preprint SC 96-19, ZIB Berlin, 1996. To appear in Numer. Math. 

Secondly, the ultimate properties of polymers are of continuous interest. Ultimate properties are the properties of ideal, defect free, structures. So far, for polymer crystals the ultimate elastic modulus and the ultimate tensile strength have not been calculated at an appropriate level. In particular, convergence as a function of basis set size has not been demonstrated, and most calculations have been applied to a single isolated chain rather than a three-dimensional polymer crystal. Using the Car-Parrinello method, we have been able to achieve basis set convergence for the elastic modulus of a three-dimensional infinite polyethylene crystal. These results will also be fliscussed. 

The structure of the metallocene cation energy minimised with the Car-Parrinello method agrees well with the experimentally obtained crystal structures of related complexes. Typical features of the structure as obtained from X-ray diffraction on crystals of very similar neutral complexes (e.g., the dichlorides), such as small differences in distances between C atoms within a cyclopentadienyl (Cp) ring, as well as differences in distances between the C atoms of the Cp ring and the Zr atom, were revealed from the simulations. 

An alternative to the Car-Parrinello method is the following scheme, which separates the electronic and nuclear motions ... 

Although constrained dynamics is usually discussed in the context of the geometrically constrained system described above, the same techniques can have many other applications. For instance, constant-pressure and constant-temperature dynamics can be imposed by using constraint methods [33,34]. Car and Parrinello [35] describe the use of the extended Lagrangian to maintain constraints in the context of their ab initio MD method. (For more details on the Car-Parrinello method, refer to the excellent review by Gain and Pasquarrello [36].)... 

For comparison, we applied also a simplified LCAO-DFT method to get the conductivity by means of the Kubo-Greenwood formula. This method is a hybrid between ab initio and empirical methods and is described in detail in Ref. [12]. It allows a faster computation of the electronic properties and the consideration of larger supercells than the Car-Parrinello method. Within this scheme it is also possible to split the total DOS into fractions referring to the sodium and tin atoms, respectively, i.e. to get the partial densities-of-states. 

The Kohn-Sham theory made a dramatic impact in the field of ab initio molecular dynamics. In the 1985, Car and Parrinello38 introduced a new formalism to study dynamics of molecular systems in which the total energy functional defined as in the Kohn-Sham formalism proved to be instrumental for practical applications. In the Car-Parrinello method (CP), the equations of motion are based on a Lagrangian (Lcp) which includes fictitious degrees of freedom associated with the electronic state. It is defined as ... 

Bernhardt L. Trout, Car-Parrinello Methods in Chemical Engineering Their Scope and Potential R. A. van Santeen and X. Rozanska, Theory of Zeolite Catalysis... 

Here, we will first give an introduction to the basic ideas underlying the Car-Parrinello method, especially addressed to complete newcomers in the field. We will then try to outline some of the recent methodological extensions, with particular emphasis on aspects with potential interest for applications in medicinal chemistry. The power and limitations of these new modeling tools will be illustrated with few selected examples. 

The Car-Parrinello method is similar in spirit to the extended system methods [37] for constant temperature [38, 39] or constant pressure dynamics [40], Extensions of the original scheme to the canonical NVT-ensemble, the NPT-ensemble, or to variable cell constant-pressure dynamics [41] are hence in principle straightforward [42, 43]. The treatment of quantum effects on the ionic motion is also easily included in the framework of a path-integral formalism [44-47]. 

The basic idea underlying AIMD is to compute the forces acting on the nuclei by use of quantum mechanical DFT-based calculations. In the Car-Parrinello method [10], the electronic degrees of freedom (as described by the Kohn-Sham orbitals y/i(r)) are treated as dynamic classical variables. In this way, electronic-structure calculations are performed on-the-fly as the molecular dynamics trajectory is generated. Car and Parrinello specified system dynamics by postulating a classical Lagrangian ... 

Many available codes use this kind of approach in order to carry out AIMD simulations. In fact some codes are not even implemented with the Car - Parrinello methods (e.g., cp2k). About the advantages and disadvantages of BOMD over CPMD the interested reader is referred to the seminal book of Marx and Hutter (57). 

At several points in diis book, it has been emphasized that the prevalence of classical MC and MD simulations derives from die impracticality of carrying out fully QM dynamics. While diis is largely true, for systems of only modest size where short trajectories may be profitably analyzed, fully QM MD simulations using the so-called Car-Parrinello technique are a viable option (Car and Parrinello 1985). In its most widely used formulation, the Car-Parrinello method employs DFT as the electronic-structure method of choice. In... 

Bernhardt L. Trout, Car-Parrinello Methods in Chemical Engineering Their Scope and potential... 

The first strategy maintains the QM description of the solvent molecules but reduces their number and adopts a different description for other molecules (often adopting a continuum distribution) to take account of bulk effects in the calculation. These QM simulation methods, of which the first and most frequently used is the Car-Parrinello method [2], are in use since several years, and have largely passed the stage of benchmark examples. This strategy is the most satisfactory under the formal aspects we have at present, and will surely be employed more and more with increasing computer power, but will certainly not completely replace, in the foreseeable future, other strategies. 

In order to overcome the limitations of currently available empirical force field param-eterizations, we performed Car-Parrinello (CP) Molecular Dynamic simulations [36]. In the framework of DFT, the Car-Parrinello method is well recognized as a powerful tool to investigate the dynamical behaviour of chemical systems. This method is based on an extended Lagrangian MD scheme, where the potential energy surface is evaluated at the DFT level and both the electronic and nuclear degrees of freedom are propagated as dynamical variables. Moreover, the implementation of such MD scheme with localized basis sets for expanding the electronic wavefunctions has provided the chance to perform effective and reliable simulations of liquid systems with more accurate hybrid density functionals and nonperiodic boundary conditions [37]. Here we present the results of the CPMD/QM/PCM approach for the three nitroxide derivatives sketched above details on computational parameters can be found in specific papers [13]. 

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