Quartic distortion constant

Centrifugal distortion constants are not of prime importance in the determination of molecular stmcture, but it may be necessary to determine them in order to interpret an observed speetmm. To determine a quartic distortion constant it is generally necessary to have very precise data, preferably over a good range of the quantum numbers (7, and also K for a symmetric top). Otherwise, there is no partieular difficulty in obtaining reliable values for Dj and Djx for a symmetrie top, or D for a linear molecule. ) has very little influence on the form of the speetmm for a symmetric top, and is correspondingly difficult to determine. 

Watson has shown that of the six quartic distortion constants (7) only five combinations are generally determinable from the spectra (one exception is nearly spherical tops such as SO2F2). Furthermore, only seven combinations of the ten sextic constants 0) and only nine combinations of the fifteen octic constants (L) can be obtained from the spectra. Watson proposed two sets of constraints ... 

The conclusion is that if the spectrum can be analysed in terms of equations (3)—(7), then the force constants can be determined. The bond length re can be determined from the equilibrium rotational constant Bc then the quadratic force constant /3 can be determined either from the harmonic wavenumber centrifugal distortion constant De then the cubic force constant /3 can be determined from aB and finally the quartic force constant /4 can be determined from x. It is necessary to determine the force constants in this order since in each case we depend upon already knowing the preceding constants of lower order. The values of re,f2,f3, and /4 calculated in this way for a number of diatomic molecules are shown in Table 2. 

The quartic centrifugal distortion constant Ak shows a great isotopic shift. An isotopic ratio was therefore approximated for the respective higher order constant 0k by the 1.5th power of the Ak ratio. 

Tables in the present chapter contain in their upper part data on the spin-rotation interaction constants e q (q = Inertial axes a, b, c) and In their lower part data on the rotational constants A, B, and C. Methods of measurement, references, and remarks are the same for either constant. The quartic (A, 8 and A, 5) and sextic (O, (p) centrifugal distortion constants listed In the first table (for the electronic ground state of PHg) are defined by the A-reduced form (asymmetric reduction) of the respective Hamiltonian for spin-rotation Interaction and rotation [1 to 3]. Abbreviations used in the tables are MW for microwave absorption, EL AB for electronic absorption, LMR for laser magnetic resonance, FIR for far IR, IMF for Intermodulated fluorescence.

Quartic centrifugal distortion constants CaPyS, Dj, Die, Djic,. . . Harmonic force field, i.e., harmonic frequencies and normal coordinates... 

Higher order terms for rotation (sextic centrifugal distortion constants Hk, Hkn. H k, Hn. k, hpjK. h vi plus the eigth-power term Lk) and spin-rotation coupling (quartic centrifugal... 

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... 

Figure 8 Comparison of observed ( ) and calculated (—) variations of the quartic centrifugal distortion constant Ajk with the ring-puckering quantum number v for methylene cyclobutane. Reproduced with permission from Charro ME, Lopez JC, Alonso JL, Wlodarczak G and Demaison J (1993) The rotational spectrum of methylene cyclobutane. Journal of Molecular Spectroscopy 62 67.

Bg = equilibrium rotational constant = rotational constant in the Vj vibrational mode = rotational constant D, d= quartic centrifugal distortion constants Go v) = vibrational term value when the energy levels are referred to the ground state as zero H, h = sextic distorsion constants = Boltzmann... 

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