Car-Parrinello calculations

Ab initio molecular-dynamics simulations, introduced by Car and Par-rinello [112], have the ambition to model biological systems in laboratoryrelevant conditions, i.e., either in solution or in solid phase (see, e.g., [113-115]). Recently, Carloni et al. [116] applied this method to a study of the first hydrolysis step of cisplatin. They were able to reproduce satisfactorily the free energy of activation and provided a model for the transition state. Their preliminary results, which include a model of the transition state for the chelation step of the reaction between the diaqua form of cisplatin, cA-[Pt(NH3)2(H20)2]2+, and d(GpG), seem to indicate that ab initio modeling of substitution reactions on heavy-metal centers may become possible in the near future. The main drawback of Car-Parrinello calculations - their considerable computer-time cost - can be expected to abate in the next years... 

The downside to the power of Car-Parrinello calculations is that they are computationally costly. Typically, the largest systems that can be treated are of the order of 100 atoms, and the time scale of the simulations is of the order of picoseconds. The purposes of Car-Parrinello simulations generally fall under three main categories (i) simulations as a means of optimization to determine structural properties, (ii) direct simulations of processes occurring over short time scales, and (iii) simulations to sample equilibrium properties. 

Figure 7. Car-Parrinello calculated envelope for the OH stretching mode in picolinic acid N-oxide in the solid state, according to Ref [32].

Figure 1.18 Geometries of the three lowest isomers of Nag as obtained from Car-Parrinello calculations [34, 47]...

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. 

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. 

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]. 

The QM/MM and ab initio methodologies have just begun to be applied to challenging problems involving ion channels [73] and proton motion through them [74]. Reference [73] utilizes Hartree-Fock and DFT calculations on the KcsA channel to illustrate that classical force fields can fail to include polarization effects properly due to the interaction of ions with the protein, and protein residues with each other. Reference [74] employs a QM/MM technique developed in conjunction with Car-Parrinello ab initio simulations [75] to model proton and hydroxide ion motion in aquaporins. Due to the large system size, the time scale for these simulations was relatively short (lOps), but the influences of key residues and macrodipoles on the short time motions of the ions could be examined. 

Quantum chemical methods are well established, accepted and of high potential for investigation of inorganic reaction mechanisms, especially if they can be applied as a fruitful interplay between theory and experiment. In the case of solvent exchange reactions their major deficiency is the limited possibility of including solvent effects. We demonstrated that with recent DFT-and ab initio methods, reaction mechanisms can be successfully explored. To obtain an idea about solvent effects, implicit solvent models can be used in the calculations, when their limitations are kept in mind. In future, more powerful computers will be available and will allow more sophisticated calculations to be performed. This will enable scientists to treat solvent molecules explicitly by ab initio molecular dynamics (e.g., Car-Parrinello simulations). The application of such methods will in turn complement the quantum chemical toolbox for the exploration of solvent and ligand exchange reactions. 

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 ... 

The study of the enantioselective hydrosilylation reaction was performed with a series of combined quantum mechanics/molecular mechanics (QM/MM) calculations [26, 30] within the computational scheme of ab initio (AIMD) (Car-Parrinello) [62] molecular dynamics. The AIMD approach has been described in a number of excellent reviews [63-66], AIMD as well as hybrid QM/MM-AIMD calculations [26, 47] were performed with the ab initio molecular dynamics program CPMD [67] based on a pseudopotential framework, a plane wave basis set, and periodic boundary conditions. We have recently developed an interface to the CPMD package in which the coupling with a molecular mechanics force field has been implemented [26, 68],... 

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 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... 

In fact these calculations did not treat the time scales correctly because they generally fixed most features of the atomic structure of solvent and then calculated the resulting electronic structure, for fixed potential drop across the interface. (A recent calculation [34] that takes more detailed account of the electronic structure of the electrode than these early calculations also suffers from this defect.) In fact, of course, in the Bom-Oppenheimer approximation, the electronic structure should be recalculated for each atomic configuration in an ensemble of atomic configurations that follow the Bom-Oppenheimer surface. This became possible with Car-Parrinello... 

---