Molecular orientation calculation

Fig. 2.9 Planar stack of three dielectric layers used for molecular orientation calculation. Reproduction by permission from [51].

There is, of course, a mass of rather direct evidence on orientation at the liquid-vapor interface, much of which is at least implicit in this chapter and in Chapter IV. The methods of statistical mechanics are applicable to the calculation of surface orientation of assymmetric molecules, usually by introducing an angular dependence to the inter-molecular potential function (see Refs. 67, 68, 77 as examples). Widom has applied a mean-held approximation to a lattice model to predict the tendency of AB molecules to adsorb and orient perpendicular to the interface between phases of AA and BB [78]. In the case of water, a molecular dynamics calculation concluded that the surface dipole density corresponded to a tendency for surface-OH groups to point toward the vapor phase [79]. 

Molecular mechanics methods have been used particularly for simulating surface-liquid interactions. Molecular mechanics calculations are called effective potential function calculations in the solid-state literature. Monte Carlo methods are useful for determining what orientation the solvent will take near a surface. Molecular dynamics can be used to model surface reactions and adsorption if the force held is parameterized correctly. 

The ESR spectrum of C6H6 " trapped in CFCI3 at 15 K is shown in Figure la and agrees with that reported previously [18]. The principal values of the hyperfine coupling were obtained from previous ESR and ENDOR measurements [17, 18]. The best agreement with experiment was obtained with the axes oriented as in Table 4. In the latter study, the simulated ENDOR spectra were insensitive to the orientation of the tensor axes, however, and the assignment was made on the basis of molecular orbital calculations [9]. The tensor data are reproduced here for convenience (see Table 4). 

Fig. 13 Results from the quantum calculations on the duplex sequence 5 -GAGG-3. In a, the sodium ions and their solvating water molecules are located at positions near the phosphate anions of the DNA backbone. In b, one sodium ion is moved from near a phosphate anion to N-7 of a guanine, which molecular dynamics calculations show to be a preferred site. The balloons represent the hole density on the GAGG sequences with the two different sodium ion orientations. The radical cation clearly changes its average location with movement of the sodium ion...

The ° mn coefficients are the mean values of the generalized spherical harmonics calculated over the distribution of orientation and are called order parameters. These are the quantities that are measurable experimentally and their determination allows the evaluation of the degree of molecular orientation. Since the different characterization techniques are sensitive to specific energy transitions and/or involve different physical processes, each technique allows the determination of certain D mn parameters as described in the following sections. These techniques often provide information about the orientation of a certain physical quantity (a vector or a tensor) linked to the molecules and not directly to that of the structural unit itself. To convert the distribution of orientation of the measured physical quantity into that of the structural unit, the Legendre addition theorem should be used [1,2]. An example of its application is given for IR spectroscopy in Section 4. 

For the ideal case where all the structural units have an identical orientational direction (i.e., a Dirac distribution), the angle of molecular orientation 90 can be calculated from the value of (P2) by... 

In addition to the [4+2] cycloaddition, intramolecular [2+2] photocycloaddition was also successfully used as a main procedure in the synthesis of (i)-ginkgolide B <00JA8453>. The studies on the model reactions and molecular mechanics calculation show that the stereochemistry of the substituents at C6 and C8 should influence severely the reaction diastereoselectivity. When syn-diastereomer 41 is subjected to irradiation the reaction gives a single diastereomer 42 in a quantitative yield since two substituents at C6 and C8 would be in pseudo-equatorial orientation in the chair-like transition state. 

Takeuchi and coworkers prepared a series of methyl and phenyl substituted germacy-clohexanes to evaluate conformational preferences of these substituents (Scheme 17)35,36. Based on analysis of 13C NMR spectra and molecular mechanics calculations, they concluded that a C-methyl prefers the equatorial orientation by ca 1.4 kcal mol 1 but the Ge-methyl substituent actually shows a slight intrinsic preference for the axial orientation (Figure 9). A similar conclusion was reached for the Ge-phenyl substituent. 

The curves 1 in Figs. 4.6a and b show the functions Fr and FA calculated by formulae (4.3.35) and (4.3.38) for the case of normal molecular orientations (e Oz) and plotted versus the argument AQ/( +AQ). The dimensionless argument and functions of this kind normalized with respect to the sum of the resonance and the band widths were introduced so as to depict their behavior in both limiting cases, ACl rj and Af2 77. The deviation of the solid lines from the dotted ones indicates to which degree the one-parameter approximation defined by Eq. (4.3.38) differs from the realistic dispersion law. As seen, this approximation shows excellent adequacy, but for the region AQ r/, where the asymptotic behavior of the approximation (4.3.38) and Eq. (4.3.35) are as follows ... 

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