Watson rotational Hamiltonians

Contact Transformation for the Effective Hamiltonian.—The vibration-rotation hamiltonian of a polyatomic molecule, expressed in terms of normal co-ordinates, has been discussed in particular by Wilson, Decius, and Cross,24 and by Watson.27- 28 It is given by the following expression for a non-linearf polyatomic molecule, to be compared with equation (17) for a diatomic molecule ... 

We wish to add that Martin and Bratoz330 also considered a case (c) corresponding to almost rigid complex. The treatment of the dynamics in the case (c) does not differ from the standard treatment of rotations and vibrations in rigid molecules with the Watson s Hamiltonian for nuclear motions. 

Watson JKG (1968) Simplification of themolecular vibration-rotation Hamiltonian. Mol Phys 15 479-490... 

Another complication arises from the fact that the rotational constants are usually obtained as effective fitting parameters of a reduced rotational Hamiltonian [14]. Not only do the numerical values of the rotational constants depend on the exact form of the reduced Hamiltonian, they also contain small contributions from quartic and higher order centrifugal distortion terms. Watson [14] has proposed to always determine the so-called determinable combinations of these constants. The values of these combinations are independent of the form of the reduction, although they still contain small contributions from the distortion terms. Up to the quartic centrifugal distortion terms, the determinable combinations of the rotational constants are... 

The effective form for the spin-rotation Hamiltonian is given by Brown and Watson (1977) as... 

Watson, J.K.G. Simplification of the molecular vibration-rotation Hamiltonian, Mol. Phys. 1968, 5, 479-90. 

In zeroth order one then obtains the Born-Oppenheimer nuclear Hamiltonian, Eq. (2.12), whereas going to second order gives an effective vibration-rotational Hamiltonian for the electronic ground state (Watson, 1973 Bunker and Moss, 1977 Watson, 1980 Herman and Ogilvie, 1998)... 

The analysis of the rotational spectrum of an asymmetric molecule in the vibrational state ui,... vj,... v u-6 normally allows the determination of the constants listed in this table. All rotating molecules show the influence of molecular deformation (centrifugal distortion, c.d.) in their spectra. The theory of centrifugal distortion was first developed by Kivelson and Wilson [52Kiv]. The rotational Hamiltonian in cylindrical tensor form has been given by Watson [77 Wat] in terms of the angular momentum operators J, J/and as follows ... 

The rotational part is a standard Watson-type Hamiltonian in the S -reduction and the T representatioa The rotational part of the energy difference has been expressed as [04Mul, 03Chr]... 

Previous fully quantum mechanical studies of predissociation phenomena in triatomic molecules do not, to our knowledge, use a Hamiltonian that has a non-zero total angular momentum. Tennyson et al[43, 44, 45, 46, 47, 48, 49, 50, 51] solve the same equations as we do but have not yet, to our knowledge, treated any predissociation problems. The adiabatic rotation approximation method of Carter and Bowman[52] plus a complex C2 modification have, on the other hand, been used to compute rovibrational energies and widths in the HCO[53, 54] and HOCl[55, 56, 57] molecules. This method is based upon the the Wilson and Howard[58], Darling and Dennison[59] and Watson[60] formalism. It is less transparent but the exact formalism in refs.[58, 59, 60] is equivalent to the one presented here and in ref [43]. While both we and Tennyson et al[43] include the exact Hamiltonian in our formalism the latter authors 152] use an approximate method which they have analysed and motivated. 

Watson [77Watl, 77Wat2] has given the relationships between the parameters in the A and S reduced Hamiltonians. It is thus possible to estimate the parameters for the alternative reduction from those determined in a particular fit to experimental data. Note that the values determined for the rotational constants also depend on the reduction employed. 

Constants for deuterated phosphanes are presented In Table 7. The constants of PHJD (prolate asymmetric top) and PHDa (oblate asymmetric top) result from an analysis of their rotational spectra (see Table 15, p. 187) through Watson s [25] asymmetric rotor Hamiltonian in its S reduction [2]. Linear combinations of rotational constants of PHgD (A-C, 2B-A-C) were obtained by fitting them to Q-branch transitions [34]. 

Rotational and centrifugal distortion constants for Watson s A-reduced Hamiltonian [96Kis2]. 

Two new bands — in-phase (ui) and out-of-phase (I ls) antisymmetric CH2 stretching vibrations of allyl radical have been obtained in the slit jet discharge spectrometer, as the sample spectra shown in the top panel of Fig. 5.18. The data have been successfully analyzed with a Watson asymmetric rotor Hamiltonian, yielding precise band origins and rotational constants for both bands. The high quality of least squares fits to ground state combination differences indicates that the rotational level structure in the lower state is well behaved, while the reduced quality of fits to the vibrational transitions, on the other hand, suggest the presence of Coriolis mediated rotational perturbations in the upper state. Due to sub-Doppler resolution (Ai/ 70 MHz) in the slit jet expansion. 

Rotational and Centrifugal Distortion Constants. The rotational constants of gaseous NH2 were obtained by fitting the rovibrational bands of the high-resolution IR spectrum to a Watson-type S-reduced Hamiltonian. The results in cm for the ground state of the ion are Ao = 23.0508 0.0019, Bo = 13.0684 0.0015, Cq = 8.11463 0.00048, Dj = 0.001082 0.000022, Djk=-0.00381 0.00012, Dk = 0.02065 0.00013, Di =-0.000492 0.000014, and 2= -0.0000461 0.0000054. The corresponding values for the v l and the Va = 1 states and the estimated equilibrium rotational constants of the ground state are also listed. The analysis was restricted to quartic distortion terms, because the inclusion of sextic terms did not result in a better fit of the bands. The Hamiltonian used does not include the effects of the rotational interactions which are noticeable in some bands [2]. Rotational constants... 

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