Molecular potential surfaces

Mandelshtam V A and Moiseyev N 1996 Complex scaling of ab initio molecular potential surfaces J. Chem. Phys. 104 6192... 

Energy minimization methods that exploit information about the second derivative of the potential are quite effective in the structural refinement of proteins. That is, in the process of X-ray structural determination one sometimes obtains bad steric interactions that can easily be relaxed by a small number of energy minimization cycles. The type of relaxation that can be obtained by energy minimization procedures is illustrated in Fig. 4.4. In fact, one can combine the potential U r) with the function which is usually optimized in X-ray structure determination (the R factor ) and minimize the sum of these functions (Ref. 4) by a conjugated gradient method, thus satisfying both the X-ray electron density constraints and steric constraint dictated by the molecular potential surface. 

The MM3 force field4 was developed in order to correct for some of the basic limitations and flows in MM2 by providing a better description of the molecular potential surface in terms of the potential functions and the parameters. One major outcome of the improved force field is the omission of lone pairs on nitrogen and oxygen since the reason for their inclusion in MM2 was no longer pertinent. This allows for a realistic... 

Johansson, A., Kollman, P., and Rothenberg, S., An application of the functional Boys-Bernardi counterpoise method to molecular potential surfaces, Theor. Chim. Acta 29, 167-172 (1973). 

While the model employed in the present work provides a reasonable picture of a unimolecular reaction involving a large molecule in solution, other ingredients not considered here may play a role in some systems. The possible role played by intramolecular friction (nonlinear coupling between the reaction coordinate and other nonreactive modes near the barrier) has been discussed in Section IV. Also, the dependence of the molecular potential surface, in particular the activation barrier on the molecule-solvent interaction, may dominate in some cases the observed solvent effect on the rate. Such may be the case (see Section VIII) in a polar solvent when the reaction involves a change in the molecular dipole moment (such as a charge transfer reaction). 

A. Johansson, P. Kollman, and S. Rothenberg, Theor. Chim. Acta, 29, 167 (1973). An Application of the Functional Boys-Bernardi Counterpoise Method to Molecular Potential Surfaces. 

Sellers, H., Pulay, P. The adiabatic correction to molecular potential surfaces in the SCF approximation, Chem. Phys. Lett. 1984,103,463-5. 

Most calculations on chemical systems within the scheme just mentioned are model calculations in the sense that they are performed on very simple chemical systems and are intended to serve as a model for a large class of similar systems. Consequently, it is also important to develop qualitative models of the topology and energetics of potential surfaces so that one may interpolate between experimental data that may be available, since only a small number of model situations may be explored with detailed numerical computations. Such qualitative theoretical models need to be formulated so that a numerical calculation of the characteristics of a molecular potential surface can be analysed a posteriori within a quantitative model and the results of this analysis carried forward to other systems in a qualitative way. The familiar Woodward-Hoffmann approach (based on Hiickel theory) and the frontier orbital method have the difficulty that they cannot be us to analyse the results of a molecular structure computation based upon an extensive configuration-interaction (Cl) expansion. Thus, one must begin to reformulate such qualitative models within the sophisticated models that are now routinely used to perform molecular structure computations. 

Normal-mode vibrational frequencies (see Normal Modes) are then obtained in order to confirm that the equilibrium structures are minima on the relevant molecular potential surfaces. Local minima have no imaginary frequencies. The theoretical harmonic vibrational frequencies are also used to determine zero-point vibrational energies (ZPEs) and to correct calculated thermochemical data to 298 K (see below). Since... 

For the case y = 0.9 a = 0.961261), U(x) is shown in Figure 6. This model potential has many features generic to molecular potential surfaces, in particular... 

R. T Pack, Van der Waals coefficients through Cg for atom-linear molecule interactions. I. C02 noble gas systems, J. Chem. Phys. 64 1659 (1976) G, A. Parker, R. L. Snow, and R. T Pack, Inter-molecular potential surfaces from electron gas methods, I. 

Figure 2 Molecular potential surface of thiophen in a plane parallel to the molecule at a distance of 1.74 A (dotted lines) and electron density map for the highest occupied orbital (full lines)...

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