Rotational Constants. Internuclear Distance

Constants of the ground state and the v = 1 vibrational state were measured using a tunable IR diode laser in the range of the fundamental vibration band and the Zeeman modulation of the absorption lines. The true values depend on the unobserved state. From line positions, only effective B values, defined as B (2ri3 ) = Bv(1 + Bv/A) (A = fine structure constant, see p. 68) can be deduced [1,4], from which the following constants were derived [4] taking A = -177.3cm i [1]  

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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. 

From precise wavelength measurements of the fluorescence spectrum (which may be performed e. g. by interferometric methods accurate values for the molecular constants can be obtained since the wavelength differences of subsequent lines in the fluorescence progression yield the energy separation of adjacent vibrational and rotational levels as a function of v . From these spectroscopically deduced molecular constants, the internuclear distance can be calculated A special computer programm developed by Zare ) allows the potential curve to be constructed from the measured constants and, if the observed fluorescence progression... 

The fifth term in (4.67) represents an interaction between vibration and rotation, and ae is called a vibration-rotation coupling constant. [Do not confuse ae with a in (4.26).] As the vibrational quantum number increases, the average internuclear distance increases, because of the anharmonicity of the potential-energy curve (Fig. 4.4). This increases the effective moment of inertia, and therefore decreases the rotational energy. We can define a mean rotational constant Bv for states with vibrational quantum number v by... 

Electronic Energies, Rotational Constants, and Internuclear Distances of Linear Triatomic Nonhydride Radicals... 

Pure rotational spectroscopy in the microwave or far IR regions joins electron diffraction as one of the two principal methods for the accurate determination of structural parameters of molecules in the gas phase. The relative merits of the two techniques should therefore be summarised. Microwave spectroscopy usually requires sample partial pressures some two orders of magnitude greater than those needed for electron diffraction, which limits its applicability where substances of low volatility are under scrutiny. Compared with electron diffraction, microwave spectra yield fewer experimental parameters more parameters can be obtained by resort to isotopic substitution, because the replacement of, say, 160 by lsO will affect the rotational constants (unless the O atom is at the centre of the molecule, where the rotational axes coincide) without significantly changing the structural parameters. The microwave spectrum of a very complex molecule of low symmetry may defy complete analysis. But the microwave lines are much sharper than the peaks in the radial distribution function obtained by electron diffraction, so that for a fairly simple molecule whose structure can be determined completely, microwave spectroscopy yields more accurate parameters. Thus internuclear distances can often be measured with uncertainties of the order of 0.001 pm, compared with (at best) 0.1 pm with electron diffraction. If the sample is a mixture of gaseous species (perhaps two or more isomers in equilibrium), it may be possible to unravel the lines due to the different components in the microwave spectrum, but such resolution is more difficult to accomplish with electron diffraction. 

Rotational constants depend on internuclear distances. High-energy electrons (40-60keV) interact primarily with the Coulomb potential of the nuclei, which leads also to internuclear distances in an ED experiment. X-ray crystallography, however, probes the electron density in the molecule and thus measures distances between maxima of this electron density. Comparison between data obtained by X-ray and by neutron diffraction... 

The two terms in afl, equation (26), also have a physical interpretation. The first arises from the second derivative of the effective rotational constant in the hamiltonian with respect to the internuclear distance, by first-order perturbation theory i.e. it arises from the third term in square brackets in the expansion (22) and from the fact that there is a mean square displacement in q in the zeroth-order model given by... 

The spin-rotation and nuclear hyperfine structure of the N = 0 and 1 rotational levels is shown in figure 10.41, together with the observed transitions. The spectra of CN radicals in both v = 0 and v = l were observed, and the molecular constants determined are listed in table 10.7. The final column of table 10.7 shows the equilibrium values of certain parameters and also the internuclear distance. The final row gives a value for the... 

The values of p and T can now be used for the statistical mechanical calculations. In order to calculate the rotational characteristic temperature t with Eq. (20), use the literature value for the rotational constant Bo = 0.037315 cm [or calculate Bo from the internuclear distance in the molecule, rg = 0.2667 nm, with Eqs. (17) to (19)]. From the literature value of the molecular vibrational frequency in the gas phase, Tg = 213.3 cm , calculate the vibrational characteristic temperature vu, with Eq. (22). From the phonon dispersion data in Table 1, calculate the 12 vibrational characteristic temperatures , -. 

The equilibrium internuclear separation (r ) of HgO(g) is estimated from the corresponding quantity for PbO(g) and comparison of Hg-X and Pb-X bond distances for cases in which values of both distances are known. The rotational constant 8 is calculated from r. The fundamental vibrational frequency (d is estimated from Guggenhelmer s relation for multiple bonded molecules ( ). 

As mentioned in the previous papers, spectroscopy (sp) and electron diffraction (ed) have their own merits and demerits and, in many cases, a combined use of them should result in the most accurate structure for free molecules. The connections among the structural parameters determined by the ed and sp methods are shown in Table 1. Information about geometry comes from the bonded and non-bonded internuclear distances determined by ED and also from the rotational constants determined by sp. One has to test in the first place whether these values are consistent with each other. One of the experimental examinations is shown in Figure 1.t For BF3, the discrepancies between the measured ed intensities (dots) and those calculated from the rotational constants B0 (measured by Ginn etaL by high-resolution infrared spectroscopy), with corrections for vibrational effects, are well within the estimated limits of experimental error. The rz (B-F) distances determined by ed and sp independently are 1311 0.0012 A and 13113 ... 

Vibrational-rotational molecular constants, and structural quantities (harmonic force constant, k, and equilibrium internuclear distance, Re) derived from these constants are listed in Table 1.1 for the electronic ground states of three... 

This table lists the leading spectroscopic constants and equilibrium internuclear distance in the ground electronic state for selected diatomic molecules. The constants are those describing the vibrational and rotational energy through the expressions ... 

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

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