Optimization to Locate Molecular Structure

for each molecule i, the summation of all forces acting on it is computed and its equation of motion  

With the increased availability of software (e.g., DISCOVER in CERIUS by Materials Studio, ETOMICA Kofke and Mihalick, 2002) and faster computers, these simulations are being carried out more routinely for the estimation of thermophysical and transport properties, as well as for the calculation of phase equilibria. The estimates are tuned to match experimental data by adjusting the energy and size parameters. 

In Monte-Carlo simulations, the energy of the molecular system is minimized by randomly moving the molecules in accordance with a desired probability distribution. After each move, the energy of each molecule is computed. When the total energy is reduced, the move is accepted and the molecules are redistributed. Moves are continued until equilibrium is achieved. As for molecular dynamics simulations, potential functions are provided. After convergence, the thermophysical properties, at equilibrium, are computed by averaging. Monte-Carlo methods, which are particularly effective for the calculation of thermophysical properties, including phase equilibria, are considered in detail by Rowley (1994). 

Molecular structure design relies on accurate property estimation methods. When sufficiently accurate, the atoms and groups in the molecular structure are adjusted to minimize the sum of the squares of the differences between the property estimates and the specified values  

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Optimization to Locate Molecular Structure 51 Using the objective function in Eq. (2.6), with relative differences, the nonlinear [nogram is ... 

Optimization to Locate Molecular Structure 55 TTie group contributions for use in the above equations from Joback and Reid (1987) are ... 

Know how to apply optimization methods to locate molecular structures having the desired properties. 

As mentioned before, the investigation of a PES involves the location of the important critical points (intermediates, transition structures), the geometry optimization of the molecular structures corresponding to these critical points, and their characterization by means of the eigenvalues of the Hessian matrix. 

Geometry optimizations usually attempt to locate minima on the potential energy surface, thereby predicting equilibrium structures of molecular systems. Optimizations can also locate transition structures. However, in this chapter we will focus primarily on optimizing to minima. Optimizations to minima are also called minimizations. 

The material system is a Langmuir-Blodgett film of the S enantiomer of a chiral polymer deposited on a glass substrate. The polymer is a poly(isocyanide)30 functionalized with a nonlinear optical chromophore (see Figure 9.14). In this particular system the optical nonlinearity and chirality are present on two different levels of the molecular structure. The chirality of the polymer is located in the helical backbone whereas the nonlinearity is present in the attached chromophores. Hence, this opens the possibility to optimize both properties independently. 

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