Quantum mechanical potentials

Beyond the clusters, to microscopically model a reaction in solution, we need to include a very big number of solvent molecules in the system to represent the bulk. The problem stems from the fact that it is computationally impossible, with our current capabilities, to locate the transition state structure of the reaction on the complete quantum mechanical potential energy hypersurface, if all the degrees of freedom are explicitly included. Moreover, the effect of thermal statistical averaging should be incorporated. Then, classical mechanical computer simulation techniques (Monte Carlo or Molecular Dynamics) appear to be the most suitable procedures to attack the above problems. In short, and applied to the computer simulation of chemical reactions in solution, the Monte Carlo [18-21] technique is a numerical method in the frame of the classical Statistical Mechanics, which allows to generate a set of system configurations... 

Lasaga, A.C., and Gibbs, G.V., Quantum mechanical potential surfaces and calculations on minerals and molecular clusters, I. STO-3G and 6-31G results, Phys. Chem. Miner., 16, 29, 1988. 

Dr. McLaughl, D.L. Thompson, Ab-initio dynamics HeH+ -h H2 He -h (C2v) classical trajectories using a quantum-mechanical potential-energy surface, /. Chem. Phys. 59 (8) (1973) 4393-4405. 

Lasaga, A. C., and G. V. Gibbs (1987). Applications of quantum mechanical potential surfaces to mineral physics calculations. Phys. Chem. Mineral. 14, 107-17. 

M.J. Field, Global optimization using ab initio quantum mechanical potentials and simulated annealing of the classical Liouville equation, J. Chem. Phys. 103 (1995), 3621. 

A classical molecular dynamics trajectory is run using the quantum mechanical potential surface. Annealing periodically zeroes the kinetic energy. 

The quantum mechanical free energy barrier, A.g, can be evaluated by Feynman s path integral formulation [59], where each classical coordinate is replaced by a ring of quasiparticles that are subjected to the effective quantum mechanical potential... 

The centroid force -dV qJ/dq defined on the right-hand side of Eq. (3.11) is the quantum mechanical potential of mean force for the centroid, given by... 

Waldher, B., Kuta, J., Chen, S., Henson, N., Qark, A.E. ForceFit a code to fit classical force fields to quantum mechanical potential energy surfaces. J. Comp. Chem. 12, 2307—2316 (2010)... 

Exercise C.2 Consider case 3 of Exercise C.lb. Evaluate the gradient and the Hessian at c = 3.3, y = 1.8 and solve the Newton-Raphson equation of Exercise C.la for xi, yi). Comment on this. In practical cases, the quantum mechanical potential energy surface is not quadratic, especially for regions as far away from the neighborhood of the minimum as (jc, y) in this example. 

The pair potential functions for the description of the intermolecular interactions used in molecular simulations of aqueous systems can be grouped into two broad classes as far as their origin is concerned empirical and quantum mechanical potentials. In the first case, all parameters of a model are adjusted to fit experimental data for water from different sources, and thus necessarily incorporate effects of many-body interactions in some implicit average way. The second class of potentials, obtained from ab initio quantum mechanical calculations, represent purely the pair energy of the water dimer and they do not take into account any many-body effects. However, such potentials can be regarded as the first term in a systematic many-body expansion of the total quantum mechanical potential (dementi 1985 Famulari et al. 1998 Stem et al. 1999). 

However, despite of the great importance of quantum mechanical potentials from the purely theoretical point of view, simple effective two-body potential functions for water seem at present to be preferable for the extensive simulations of complex aqueous systems of geochemical interest. A very promising and powerful method of Car-Parrinello ah initio molecular dynamics, which completely eliminates the need for a potential interaction model in MD simulations (e.g., Fois et al. 1994 Tukerman et al. 1995, 1997) still remains computationally extremely demanding and limited to relatively small systems N < 100 and a total simulation time of a few picoseconds), which also presently limits its application for complex geochemical fluids. On the other hand, it may soon become a method of choice, if the current exponential growth of supercomputing power will continue in the near future. 

The general emphasis in force field development is towards transferrable force fields, where the functional form and the values of associated parameters can be used in a wide variety of molecules and crystals. As the parameters are developed empirically, transferability implies a degree of reliability and confidence that the parameters will work for crystals for which they were not specifically parameterised. In a recent development of the so-called tailor-made force field, it was pointed out that for the specific case of crystal structure prediction, the force field does not need to be transferable and that in fact there are some important advantages to having a force field derived specifically for the molecule of interest. Given sufficiently accurate information from quantum mechanical calculations, the tailor-made force field can be obtained by fitting to the quantum mechanical potential energy surface. Neumann defined a number of quantum mechanical data sets which represented both the non-bonded and bonded interactions in the crystal. The parameters of the force field were then optimised to fit these data sets. The quantum mechanical method chosen for the calculations was the DFT(d) method which will be described below. 

H. Liu and Y. Shi, /. Comput. Chem., 15,1311 (1994). Combined Mtdecular Mechanical and Quantum Mechanical Potential Smdy of a Nucleophilic Addition Reaction in Solution. 

---