Parrinello Approach

Use one of the methods of quantum chemistry to perform an electronic structure calculation. 

Note that these steps are equivalent to the force field-based method, but the forces are derived quantum mechanically. Accordingly, one can carry out simulations in the ground or electronically excited states as well as account for chemical reactions. 

Despite the theoretical feasibility of the scheme, it is quite limited from the computational point of view. The electronic structure calculations are carried out by matrix diagonalization, which is iteratively repeated until a self-consistent solution is found. Even for small systems, this procedure is time-consuming, and because it must be repeated for each atomic configuration during a simulation, it is easy to see that such calculations are impractical. A way out was found by Car and Parrinello.  

The Car-Parrinello (CP) approach is an extended energy minimization and MD scheme in which electronic degrees of freedom are treated explicitly on an equal footing with nuclear coordinates. Below we outline the conceptual scheme of the method and refer the interested reader elsewhere for a comprehensive discussion.  

Let us describe the electronic state of a system by a set of one-electron wavefunctions (orbitals) (()i c() , which are represented by expansion over some basis functions as in Eq. [4]. Formally, one may consider the set of coefficients c% = C as a set of coordinates that specifies the position of the orbital i 

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Remler D K and Madden P A 1990 Molecular dynamics without effective potentials via the Car-Parrinello approach Mol. Phys. 70 921-66... 

Regarding mechanical properties of polymers, the efficiency of the Car-Parrinello approach has enabled us to evaluate the ultimate Young s modulus of orthorhombic polyethylene, and demonstrate basis set convergence for that property. 

The Car-Parrinello approach combines an electronic structure method with a classical molecular dynamics scheme and thus unifies two major fields of computational chemistry, which have hitherto been essentially orthogonal. Through this unification a... 

The major drawback for employing the Car-Parrinello approach in dynamics simulations is that since a variational wavefunction is required, the electronic energy should in principle be minimized before the forces on the atoms are calculated. This greatly increases the amount of computer time required at each step of the simulation. Furthermore, the energies calculated with the electronic structure methods currently used in this approach are not exceptionally accurate. For example, it is well established that potential energy barriers, which are of importance to chemical reactivity, often require sophisticated methods to be accurately determined. Nonetheless, the Tirst-principles calculation of the forces during the dynamics is an appealing idea, and will continue to be developed as computer resources expand. 

The ideas outlined above, which have subsequently led to the development of computer programs such as CASTEP, are clearly very important as they have opened up the possibility of carrying out quite accurate and realistic calculations on solids, particularly those containing heavy elements, and molecules adsorbed on solids, due to the great amount of computer time saved by adopting the Car and Parrinello approach. 

Rentier DK, PA Madden (1990) Molecular-Dynamics without Effective Potentials Via the Car-Parrinello Approach. Mol. Phys. 70 (6) 921—966... 

Cucinotta et studied the equilibrium between the keto and enol tautomers of acetone, cf. Fig. 5, both in vacuum and in an aqueous solution. They used parameter-free, electronic-structure calculations for a periodically repeated supercell (see section IIB) with the Car-Parrinello approach (see, e.g., ref. 1). In static calculations for solely the acetone molecule they found a total-energy difference between the enol and keto forms of 11.8 kcal/mol. The barrier between the two forms was found to be around 58 kcal/mol (Fig. 5). 

Computational advances which have led to pseudopotential methods becoming efficient are Fast Fourier Transfoms and the approach of Car and Parrinello in which wavefunction coefficients are treated as d5mamical variables. Parts of the calculations on periodic systems are easier to calculate in real space and others in reciprocal space. Fourier transforms are needed to convert between the two spaces. The introduction of Fast Fourier Transforms substantially reduced the computational costs of this conversion. The key feature of the Car-Parrinello approach is the use of minimisation rather than diagonalisation of the Kohn-Sham equations to reach the ground state. 

We also expect that more studies will use MD and the Car-Parrinello approach, while the share of studies based solely on energy minimization and cluster approximations will diminish. It seems reasonable to expect that some of the difficulties encountered with embedding will be solved in the next couple of years. If this becomes true, one might expect that embedding, in fierce competition with the Car-Parrinello approach, will be used extensively in studies on zeolite catalysis. For embedding to become a success, it will be necessary to develop force fields that are compatible with the quantum chemistry model that is used in the description of the catalytic site. Such a compatibility seems possible only if these force fields allow for polarization. 

There are of course methods which attempt to tackle these problems in their complexity, and avoid some of the approximations we have described we quote, as an outstanding example, the Car-Parrinello approach (Car and Parrinello, 1985), that in recent extensions has aimed to give a coherent QM description of such models (Laasonen et al., 1993 Fois et al., 1994). However, these approaches are still in their infancy, and it is advisable to look at other models for liquids and chemical reactions in solutions. 

R. Vuilleumier Density Functional Theory based Ab Initio Molecular Dynamics Using the Gar-Parrinello Approach, Lect. Notes Phys. 703, 223—285 (2006)... 

D. Sebastiani and U. Rothlisberger (2003) Advances in Density Functional Based Modelling Techniques Recent Extensions of the Car-Parrinello Approach. In Medicinal Quantum, Chemistry, eds. P. Carloni and F. Alber Wiley-VCH, Weinheim. Methods and Principles in Medicinal Chemistry, pp. 5-40... 

An elegant way of carrying out AIMD is the Car-Parrinello approach [20,21], in which the dynamics of the nuclei as well as the temporal evolution of the electronic wave function are described by Newtonian equations of motion. Using massively parallel computers, this approach allows the direct simulation of up to a few... 

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