However, even for a small molecule such as HgCO, determination of the rotational constants in the v = 1 levels of all the vibrations presents considerable difficulties. In larger molecules it may be possible to determine only Aq, Bq and Cq. In such cases the simplest way to determine the structure is to ignore the differences from A, and Cg and make sufficient isotopic substitutions to give a complete, but approximate, structure, called the Tq structure. [Pg.133]

The second temi is used to allow for centrifugal stretching and is usually small but is needed for accurate work. The quantity B is called the rotation constant for the state. In a rigid rotator picture it would have the value [Pg.1140]

Measurement and assignment of the rotational spectmm of a diatomic or other linear molecule result in a value of the rotational constant. In general, this will be Bq, which relates [Pg.131]

The method of combination differences applied to the P and R branches gives the lower state rotational constants B", or B" and D", just as in a A transition, from Equation (6.29) or Equation (6.32). These branches also give rotational constants B, or B and D, relating to the upper components of the 77 state, from Equation (6.30) or Equation (6.33). The constants B, or B and D, relating to the lower components of the state, may be obtained from the Q branch. The value of q can be obtained from B and B. [Pg.260]

As in diatomic molecules the structure of greatest importance is the equilibrium structure, but one rotational constant can give, at most, only one structural parameter. In a non-linear but planar molecule the out-of-plane principal moment of inertia 4 is related to the other two by [Pg.132]

From the following wavenumbers of the P and R branches of the 1-0 infrared vibrational band of H Cl obtain values for the rotational constants Bq, Bi and B, the band centre coq, the vibration-rotation interaction constant a and the intemuclear distance r. Given that the band centre of the 2-0 band is at 4128.6 cm determine cOg and, using this value, the force constant k. [Pg.195]

Hollenstein H, Marquardt R, Quack M and Suhm M A 1994 Dipole moment function and equilibrium structure of methane In an analytical, anharmonic nine-dimenslonal potential surface related to experimental rotational constants and transition moments by quantum Monte Carlo calculations J. Chem. Phys. 101 3588-602 [Pg.1091]

The separation of individual lines within the Q branch is small, causing the branch to stand out as more intense than the rest of the band. This appearance is typical of all Q branches in infrared spectra because of the similarity of the rotational constants in the upper and lower states of the transition. [Pg.178]

The use of the symbols F J) and B for quantities which may have dimensions of frequency or wavenumber is unfortunate, but the symbolism is used so commonly that there seems little prospect of change. In Equations (5.11) and (5.12) the quantity B is known as the rotational constant. Its determination by spectroscopic means results in determination of intemuclear distances and represents a very powerful structural technique. [Pg.106]

The illustration of various types of vibronic transitions in Figure 7.18 suggests that we can use the method of combination differences to obtain the separations of vibrational levels from observed transition wavenumbers. This method was introduced in Section 6.1.4.1 and was applied to obtaining rotational constants for two combining vibrational states. The method works on the simple principle that, if two transitions have an upper level in common, their wavenumber difference is a function of lower state parameters only, and vice versa if they have a lower level in common. [Pg.250]

Since the form of the electronic wave functions depends also on the coordinate p (in the usual, parametric way), the matrix elements (21) are functions of it too. Thus it looks at first sight as if a lot of cumbersome computations of derivatives of the electronic wave functions have to be carried out. In this case, however, nature was merciful the matrix elements in (21) enter the Hamiltonian matrix weighted with the rotational constant A, which tends to infinity when the molecule reaches linear geometry. This means that only the form of the wave functions, that is, of the matrix elements in (21), in the p 0 limit are really needed. In the above mentioned one-elecbon approximation [Pg.486]

Van der Waals complexes can be observed spectroscopically by a variety of different teclmiques, including microwave, infrared and ultraviolet/visible spectroscopy. Their existence is perhaps the simplest and most direct demonstration that there are attractive forces between stable molecules. Indeed the spectroscopic properties of Van der Waals complexes provide one of the most detailed sources of infonnation available on intennolecular forces, especially in the region around the potential minimum. The measured rotational constants of Van der Waals complexes provide infonnation on intennolecular distances and orientations, and the frequencies of bending and stretching vibrations provide infonnation on how easily the complex can be distorted from its equilibrium confonnation. In favourable cases, the whole of the potential well can be mapped out from spectroscopic data. [Pg.2439]

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