Rotational spectra centrifugal distortion

In sections 2.2 through 2.5 the diamagnetic molecules are ordered according to the type of their respective spectrum as follows Diatomic molecules (2.2), linear molecules (2.3), symmetric top molecules (2.4), and asymmetric top molecules (2,5). Molecules which are asymmetric only due to isotopic substitution are listed together with their parent species in 2.4. The tables include rotational constants, centrifugal distortion constants, rotation-vibration interaction constants, and 1-type doubling constants. Some additional molecular constants obtained by microwave type methods have been listed as well. References to publications concerning the molecular structure are cited separately. 

The out-of-plane bending fundamental V4 (near 926 cm" ) was recorded at high resolution in the infrared spectrum of HBF2 [8]. Rotational and centrifugal distortion constants were obtained for the two isotopic species H BF2 and H BF2 in both the ground and 4 levels the position of the Vg fundamental of was estimated to be 1099 cm from rotational... 

Once quantum chemistry has provided all the information required, that is, rotational and centrifugal distortion constants and, if the case, hyperfine parameters as well as line intensities, a graphical simulation of the rotational spectrum can be performed. The latter requires the knowledge of the experimental technique involved. For example, if the frequency modulation with second harmonic detection is performed, then the second derivative of the natural spectrum is obtained (as seen in Figure 6.2). The graphical representation of the computed spectrum can then be... 

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... 

Evidence for a significant contribution from the ionic form [BX] + - -Y in a gas-phase complex B- XY was first deduced from the spectroscopic constants of H3N- -ClF, as obtained by analysis of its rotational spectrum [63]. In particular, the value ka = 34.3 N m 1 of the intermolecular stretching force constant (obtained from the centrifugal distortion constant Dj in the man-... 

Stoicheff investigated the pure rotational Raman spectrum of CS2. The first few lines could not be observed because of the width of the exciting line. The average values of the Stokes and anti-Stokes shifts for the first few observable lines (accurate to 0.02 cm-1) are Ap = 4.96, 5.87, 6.76, 7.64, and 8.50 cm-1, (a) Calculate the C=S bond length in carbon disulfide. (Assume centrifugal distortion is negligible. The rotational Raman selection rule for linear molecules in 2 electronic states is AJ = 0, 2.) (b) Is this an R0 or Re value (c) Predict the shift for the 7 = 0—>2 transition. 

Figure 2. Temperature-analysis plot for rotational Raman scattering from Ot in an Hr-Ot premixed flame. The experimental spectrum is in Figure 5 of Ref. 1. All data are corrected for centrifugal distortion (---), analysis without consid-...

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 coefficients B, D, H, etc., are determined from an analysis of the experimental spectrum it is rarely necessary to go beyond the cubic term, except when very high J values are involved. The parameters D, 77, etc., are known as the centrifugal distortion corrections to the rotational kinetic energy. 

In order to assign the Zeeman patterns for the three lowest rotational levels quantitatively, one must determine the spacings between the rotational levels, and the values of g/and gr-In the simplest model which neglects centrifugal distortion, the rotation spacings are simply B0. /(./ + 1) this approximation was used by Brown and Uehara [10], who used the rotational constant B0 = 21295 MHz obtained by Saito [12] from pure microwave rotational spectroscopy (see later in the next chapter). The values of the g-factors were found to be g L = 0.999 82, gr = —(1.35) x 10-4. Note that because of the off-diagonal matrix elements (9.6), the Zeeman matrices (one for each value of Mj) are actually infinite in size and must be truncated at some point to achieve the desired level of accuracy. In subsequent work Miller [14] observed the spectrum of A33 SO in natural abundance 33 S has a nuclear spin of 3/2 and from the hyperfine structure Miller was able to determine the magnetic hyperfine constant a (see below for the definition of this constant). 

The analysis of the spectrum was accomplished using a case (a) basis, with the addition of two nuclear spins, I and h, for 63Cu and 19F respectively. The basis functions therefore take the form A S, E J, 72, I, F, h- F, Mp), and leaving aside nuclear spin interactions, the theory follows closely the same path as that already described for 3n CO in chapters 9 and 10. The effective Hamiltonian is the sum of terms representing the spin orbit, rotational, spin-rotation, spin-spin and centrifugal distortion contributions and is written [56] ... 

In the analysis of the spectrum, which involved high values of TV, it was found necessary to include centrifugal distortion corrections to both the electron spin rotation and nuclear dipolar constants, i.e. 

As 1 is a nonpolar symmetric top with symmetry, it should have no pure rotational spectrum, but it acquires a small dipole moment by partial isotopic substitution or through centrifugal distortion. In recent analyses of gas-phase data, rotational constants from earlier IR and Raman spectroscopic studies, and those for cyclopropane-1,1- /2 and for an excited state of the v, C—C stretching vibration were utilized Anharmonicity constants for the C—C and C—H bonds were determined in both works. It is the parameters, then from the equilibrium structure, that can be derived and compared from both the ED and the MW data by appropriate vibrational corrections. Variations due to different representations of molecular geometry are of the same magnitude as stated uncertainties. The parameters from experiment agree satisfactorily with the results of high-level theoretical calculations (Table 1). 

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