Rotational and Vibrational Constants

Rotational and Spin-Rotation Coupling Constants. Centrifugal Distortion Constants 

The IR absorption spectrum of the quasi-linear NHj ion (showing large amplitudes of the bending vibration) was analyzed applying an asymmetric top formalism. Due to the 

The antisymmetric stretching vibration in the electronic ground state X Bi, V3 = 3359.932(2) cm , was obtained from an IR absorption spectrum [1]. Additional vibrational frequencies of NH2 in the three lowest electronic states were determined from photoelectron spectra (PES) of NH2(X Bi) [6]. Vibrational frequencies of NH2 and Isotopomers (in cm ) from experiments (see data collections [7 to 9]) and ab initio calculations are listed in the following table  

The force constant due to stretch, ke=1520 N/m, was determined from an ab initio-calculated energy curve at re = 1.07 A [13]. 

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Table 4.1 lists rotational and vibrational constants for some diatomic-molecule states. The most extensive compilation of such data is Bourcier. 

A remarkably large proportion of the constants in the effective Hamiltonian were determined from the analysis of the FIR laser magnetic resonance spectrum, supplemented by data from other spectroscopic regions which allowed equilibrium values of some of the constants to be determined. The following rotational and vibrational constants are listed by Nelis, Beaton, Evenson and Brown [76] (in cm-1) ... 

Rotational and vibrational constants are based on the microwave studies of Clouser and Gordy (12,). Earlier microwave data of Honig et al. ( ) and electric resonance data of Lee et al. ( ) are in excellent agreement. Infrared spectra of Rice and Klemperer (15) yield 6 = 261 6 cm" which is in good agreement. The constants were adjusted to a natural isotopic composition of... 

The ground state vibrational constants have not been determined experimentally. O Hare (8) computed Hartree-Fock total energies for the ground states of NF, SiF, PF, and SF and derived spectroscopic constants for each monofluoride by a Dunham analysis. He adjusted the computed values for SF for differences found between calculated and experimental data for the other three monofluorides. We adopt his predicted vibrational constants along with his computed value for a. We do not include the rotational and vibrational constants (4, 5) for the A state since they have a negligible effect. 

The rotational and vibrational constants are those selected by Rosen (9). The ground state is treated as two distinct levels because of the splitting of the ground state as expressed by the spin coupling constant (A = 142.83 cm" ). This approximation gives slightly biased results at lower temperatures which are allowed for in the 0.05 cal K" mol" error assigned to 3 (298.15 K). 

The B-X transition has been reported by Jenkins and de Laszlo (1 ). The rotational and vibrational constants are derived from... 

Table 8. Rotational and vibrational constants (cm 1) in the electronic and stretching mode g.s. of C3...

The analysis of purely rotational, rotational-vibrational, and electronic spectra (cf. pp. 23/30) gave rotational and vibrational constants for the electronic ground state and various excited states of PH and PD. The more accurate values were obtained, of course, by IR Fourier transform and laser spectroscopy as compared to the conventional UV-visible spectroscopic methods (conventional IR spectroscopy has never been applied to PH). 

PH, PD. Ground State X Rotational and Vibrational Constants, Internuclear Distance. B, D, tte, cOe, cOeXe in cm" re in A three standard deviation in parentheses. 

Rotational and Vibrational Constants. Internuclear Distance. Experimental results are available for the ground state X 211 and the excited state A 2A, which have been obtained from rotational analyses of the UV-visible A-X system. Rotational constants Be or Bq, ae, Ye, Dq, vibrational constants cOe, cOgXe, or AG1/2, and internuclear distances re or ro are given in Table 4. 

PH+. Theoretical Rotational and Vibrational Constants and Internuclear Distances. Be, Bq, a, cOe, cOeXe in crrr rg in A. 

Thus once the spectroscopic rotational and vibrational constants are known for a pair of isotopic molecules it is possible to calculate the partition function ratio of a pair of isotopic molecules... 

The values in the following table for the molar heat capacity C°, entropy S°, Gibbs free energy function (G°-H298)/T, in caTmor K and for the enthalpy H°-H298 kcal/mol are taken from the JANAF Tables [1], where they were calculated in intervals of 100 K up to T = 6000K for the ideal gas at latm on the basis of estimated rotational and vibrational constants (see pp. 71/3) and of a electronic ground state ... 

Such an expression involves the assumption that the rotational and vibrational constants are identical for all three electronic states. To avoid such an assumption separate treatment of each of the states would be needed.)... 

Therefore many rotational states are populated at room temperature. Table 11.2 gives rotational and vibrational constants for several small molecules. 

TABLE 9.1 Ground state molecular rotational and vibrational constants for selected diatomic molecules. Values for the vibrational constants are based on varying numbers of anharmonic terms. In this table Dq is the v = 0 rotational distortion constant. Missing values indicate the constant was not measured in the corresponding experiment... 

Any homonuclear diatomic molecule has no permanent dipole moment and therefore no allowed rotational spectrum. Because the dipole moment remains zero as the bond stretches, homonuclear diatomics also have no allowed vibrational spectrum. Only electronic spectroscopy in homonuclear diatomics is allowed by electric dipole selection rules, and high precision measurements of the rotational and vibrational constants in molecules as simple as H2 and N2 can be quite difficult. 

Geometry optimization for determining rg and evaluating the rotational and vibrational constants are included in numerous quantum-chemical ab initio calculations on NH. These are essentially the same studies that are quoted in the next section on potential energy functions (see table on p. 55). Further references may be found in the bibliographies on quantum-chemical calculations given on p. 31. 

NH, ND in the States X and a A. Rotational and Vibrational Constants from Purely Rotational and Rotational-Vibrational Spectra in the Far IR and IR. 

Rotational and vibrational constants in cm equilibrium internuclear distance r in A. 

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