Rotation parameter

FIGURE 6.2 The amide or peptide bond planes are joined by the tetrahedral bonds of the ff-carbon. The rotation parameters are p and Ip. The conformation shown corresponds to clockwise rotation as viewed from Starting from 0°, a rotation of 180° in the clockwise direction ( + 180°) is equivalent to a rotation of 180° in the counterclockwise direction (—180°). (truing G s)... 

The isotope effects of reactions of HD + ions with He, Ne, Ar, and Kr over an energy range from 3 to 20 e.v. are discussed. The results are interpreted in terms of a stripping model for ion-molecule reactions. The technique of wave vector analysis, which has been successful in nuclear stripping reactions, is used. The method is primarily classical, but it incorporates the vibrational and rotational properties of molecule-ions which may be important. Preliminary calculations indicate that this model is relatively insensitive to the vibrational factors of the molecule-ion but depends strongly on rotational parameters. 

At that point, it should also be kept in mind that the values of bond lengths and angles are not directly accessible from experiments but are indirectly determined so as to reproduce the rotational constants which are themselves deduced from microwave experiments. Thus, comparison are always subject to some controversy since there is no biunivoque correspondence between the geometry and the rotational parameters. 

Molecular electronic spectroscopy can provide information on vibrational parameters (frequencies and force constants), rotational parameters (moments of inertia and therefore molecular geometries), electronic excitation energies, ionization potentials, and dissociation energies for ground and excited electronic states. Moreover, a knowledge of excited electronic states is important in understanding the course of photochemically induced reactions. 

The first term in this expression is the zeroth order energy E(0,0). The two next terms gives the first derivatives with respect to the parameters Ty (equation (3 37)) and SK0 (equation (3 42)). We obtain the following result for the Erst derivative with respect to the orbital rotation parameters ... 

The direct solution for the rotation parameters S and T from (4 16) is not very practical if the MC expansion is large, due to the complications in computing matrix elements over the orthogonal complement space IK>, defined by equation (3 41). An M2 transformation is needed to obtain h(cc)... 

The state rotation parameters S are obtained from the variations of the individual Cl coefficients as S = C SCq, but the number of parameters in 5Cq is M, while the number of linearly independent parameters in S is only M-l. This redundancy in 5C0 can be removed by adding one row to equation... 

In CASSCF calculations only the rotation parameters Tit, T, and Tto have to be used, where i represents an inactive orbital, t an active orbital, and a an external orbital. Motivate ... 

Table 12.4. Rotation parameters n or m, real (A, A), and complex (p, r) quaternion parameters, and the Cayley-Klein parameters a, b for the operators R D3.

Table 14.5. Rotation parameters

My aim has been to give in these tables only the most commonly required information. For character tables for n > 6, Cartesian tensor bases of rank 3, spinor bases, rotation parameters, tables of projective factors, Clebsch-Gordan coefficients, direct product... 

Typically, Hund s case (b)161 applies to molecules with A = 0, to which spin-orbit effects do not contribute in first order. For states with a nonzero A value and a rotational parameter Bv of the same order-of-magnitdue as the spin-orbit parameter Av, rotational coupling cannot be neglected. In this case, it... 

Where X is an antisymmetric matrix containing the independent (orthogonal) rotation parameters. Expanding the energy in X about the origin... 

Bond lengths (A) Bond angles (°) Rotational parameters (MHz)... 

In a similar manner, there is a second-order contribution to the spin-rotation parameter which arises from the cross-term between the spin orbit coupling and the... 

In other words, each of the parameters is the sum of a first-order and a second-order contribution. We have met equation (7.126) for the effective rotational constant operator before, in an earlier section, where we pointed out that the second-order contribution Ba> is very much smaller than BiV) and that these two contributions have a different reducedmass dependence. It is importantto realise thatthis is not generally true. Indeed, except for molecules with very light atoms such as H2, the second-order contribution to the spin-rotation parameter is usually very much larger in magnitude than the first-order contribution. The same is also often true for the spin-spin coupling parameter /.. The reduced mass dependences of the two contributions to the spin-rotation parameter y are different from each other and quite complicated. However, Brown and Watson [17] were able to show the rather remarkable result that when one takes the first- and second-order contributions together as in equation (7.127), the reduced mass dependence of the resultant parameter y(R) is simply /u-1. 

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