Rotational correction terms

Structural parameters, symmetry coordinates and rotational correction terms to dipole moment derivatives for H2CO ... 

Eventually, qiplying Eq. (3.11) separately for each synunetiy vibrational coordinate we obtain the rotational correction term matrix Rg (in units of D/A or D/rad)... 

These quantities are given in Table 3.2 as well. The same procedure can be followed in the case of odier X2CY molecules with X = D, F, Cl, Br and Y = O, S. The rotation-free isotope is created by setting the X-masses equal to zero. Application of the zero-mass approach in evaluating rotational correction terms to polarizability derivatives will be illustrated with an example in die second part of the book. 

The method was introduced by Van Straten and Smit [34] in order to overcome problems arising with the zero-mass approach for certain types of molecules. For bent X2Y and pyramidal X3 Y molecules the creation of an isotope with zero X-masses results in indefinite Pp elements, thus hampering the evaluation of rotational correction terms [34], No such problems are encountered following die procedure of Van Straten and Smit. It will be illustrated with several examples. 

Structural parameters, definition of symmetry coordinates and rotational correction terms for 1,1,1-trifluoroethane... 

The hypothetical isotope method is aimed at calculating absolute rotational correction terms. An alternative mediod for evaluating relative rotational corrections in a series of isotopically related molecules was proposed by Escribano, del Rio and Orza [71], The formalism of diis rproach will be briefly presented in the second part of the book. 

In die third equation of the set (3.47) the term -0.05 Ip is the rotational correction term. It should be noted that for H2O the inverse electro-optic problem is entirely defined, simply because of the very small size of the molecule and its symmetry allowing the OH bond moment to be evaluated firom the permanent dipole moment. Obviously, in molecules where at least two non-equivalent bonds are present, experimental determination of the bond moments is not possible and certain assumptions have to be made. 

With the addition of the Ppp term the atomic polar tensor matrix becomes mass independent since it refers to a space-fixed coordinate system. Thus, the transformation of measured infrared intensities of different isotopic species of a molecule widi identical symmetry will result in proximately the same Px mahix, within the experimental uncertainties. This is an important feature of the atomic polar tensor representation of infrared band intensities. The troublesome problem of rotational correction terms is treated in a straightforward and general way. The treatment, however, introduces some difficulties in the physical interpretation of the elements of atomic polar tensors. These will be discussed later in conjunction with some examples of calculations. 

R is 3 x(3N-6) array containing rotational correction terms [Eq. (3.5)]. Both sides of Eq. (4.126) are free of rotational contributions and form complete sets for each symmetiy class. The elements of P), are then easily calculated. A requirement exists diat the axes of the reference Cartesian system are oriented in accordance widi molecular symmetry. 

Experimental intensity data, reference Cartesian system, internal coordinates, force fields and L matrices for methyl chloride are the same as given in section m.C. Bond displacement coordinates are defined in Fig. 4.6. Rotational corrections to the dipole moment derivatives with respect to symmetry coordinates are evaluated using the heavy isotope method [34]. The rotational correction terms are given in Table 4.8. To illustrate the calculations in more detail the entire V matrix of methyl chloride is presented in Table 4.9. To remove die rotational terms fi om the sets of linear equations for symmetiy... 

The transfer of intensity parameters between molecules for quantitative intensity predictions encounters various problems that need care l consideration. As already emphasized in tius section, due to the very high sensitivity of intensities to structural changes transferability properties of intensity parameters are expected to be much less pronounced compared to other molecular quantities. Secondly, certain parameters will be dependent on the particular site symmetry of the chemical bonds or atoms considered. Additional complications can arise if rotational correction terms are to be calculated. Predictions by transfer of parameters should, therefore, only be attempted for closely related molecules, such as homologous series. Bond polar parameters have been used in predicting intensities in intiared spectra in fluorinated methanes [144], alltylacetylenes [145] and medium-size n-alkanes [143]. In Fig. 4.8 the predicted infrared spectra of different conformers of n-pentane using bond polar parameters from n-butane are presented [143]. In more quantitative terms the predicted intensities are compared with the experimental values in Table 4.12. As can be seen from Table 4.12, the agreement between calculated and observed intensities is quite satisfactory. 

Cartesian reference systems, geometric parameters and symmetiy coordinates for H2O and NH3 are given in Chapter 3. Dipole moment derivatives with respect to symmetiy coordinates for H2O, evaluated in analyzing experimental absolute infrared intensities, are also presented there. dp/dSj dipole moment derivatives for ammonia used in the present calculations were taken from Ref. [147] and are presented in Table 4.13. The signs of these quantities have been fixed with the aid of ab initio MO calculations [147]. Elements of the respective matrices for both molecules were evaluated by employing the heavy isotope mediod [34], weighting the respective heavy atoms by a factor of 1000. The rotational correction terms for ammonia are tabulated in Table 3.3. The Rs matrix for H2O has the following form (in D A l or D rad )... 

Rotational correction terms to polarizability derivatives for the three molecules obtained by following the procedure described above are given in Tables 9.2, 9.3 and 9.4, respectively. 

Symmetry coordinates and rotational correction terms to polarizability derivatives with respect to symmetry coordinates for acetonitrile (Reprinted from Ref [2S ] widi permission of John Wiley Sons, Ltd., Copyright (1993] John Wil Sons, Ltd.)... 

It should be pointed out that if a non-rotating (hypothetical-mass) isotope is chosen as a reference molecule, the procedure proposed could be used for calculating the absolute rotational correction terms to polarizability derivatives. 

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