Body-fixed axis complexes

Satchler" and YjK(0,(j)) is a spherical harmonic involving the angular coordinates of the diatomic molecule in the body-fixed axis system. Physically, the end-over-end angular momentum of the complex cannot have any body-fixed projection along R, so that the K quantum numbers appearing in the rotation matrix element and in the spherical harmonic must be the same. 

The coordinate system needed for an atom-nonlinear molecule complex is a straightforward generalisation of that for an atom-diatom complex. The body-fixed axis system is defined as before, with Euler angles (a,, 0) specifying the orientation of R. However, it is now necessary to define an axis system (x y z) fixed in the monomer the relationship of these axes to the body-fixed axes is specified by Euler angles (0,, x)- md 0 describe the orientation of the z axis, and x describes rotations about the 2 axis. 

The coordinate system needed for a trimeric system in this approximation is a straightforward generalisation of that for an atom-diatqm complex. The R vector is now defined as running from the HX centre of mass to the midpoint of the Ar2 pair, and forms the axis of a body-fixed axis system. An additional vector, p, runs between the two Ar atoms. The body-fixed x axis is perpendicular to R and coplanar with p. The relationship between the body-fixed and the space-fixed axes now requires three Euler angles Once again, the... 

In conjunction with data on Ar-H20 from the near IR, however, these ambiguities can be resolved. For H2O in a cold jet, complex formation only of the lowest para Ar-H20 (correlating with para Oqo water) and ortho Ar-H20 states (correlating to ortho Iq water) will be appreciable. The (2j+l) degenerate ortho Iq H2O states will be split by interaction with the Ar induced anisotropy to yield states which can be characterized approximately by the projection of the internal rotor angular momentum onto the body fixed axis of the complex (i.e. 2 and II), provided that the splittings are small with respect to the rotational spacings in free water. Note that this K is not the same as the projection of j onto the body fixed axis (k ) of the water monomer, which is a very poor quantum... 

In the present work, we must carry out transformations of the dipole moment functions analogous to those descrihed for triatomic molecules in Refs. [18,19]. Our approach to this problem is completely different from that made in Refs. [18,19]. We do not transform analytical expressions for the body-fixed dipole moment components (/Zy, fiy, fi ). Instead we obtain, at each calculated ab initio point, discrete values of the dipole moment components fi, fiy, fif) in the xyz axis system, and we fit parameterized, analytical functions of our chosen vibrational coordinates (see below) through these values. This approach has the disadvantage that we must carry out a separate fitting for each isotopomer of a molecule Different isotopomers with the same geometrical structure have different xyz axis systems (because the Eckart and Sayvetz conditions depend on the nuclear masses) and therefore different dipole moment components (/Z, fiy, fij. We resort to the approach of transforming the dipole moment at each ab initio point because the direct transformation of analytical expressions for the body-fixed dipole moment components (/Zy, fiyi, fi i) is not practicable for a four-atomic molecule. The fact that the four-atomic molecule has six vibrational coordinates causes a huge increase in the complexity of the transformations relative to that encountered for the triatomic molecules (with three vibrational coordinates) treated in Refs. [18,19]. 

In a complex with more than one argon atom, we use the body-fixed system of axes illustrated in Fig. 2 for Hg- Ar2. The z axis is chosen along the R vector joining the mercury atom to the center of mass of the argons the x axis lies in the plane defined by the z axis and the first argon atom Ar(i). The quantization axis is the body-fixed z axis. The corresponding atomic basis set is denoted by L, A,5,E) or for Hund s case (c). For the Hg—Ar(ife)... 

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