Molecules centrifugal distortions

It has been shown that for bent, symmetric triatomic molecules centrifugal distortion constants can provide force constants with precisions ranging from 0.1 to 1 percent and accuracies ranging from 1 to 10 percent. A final question about combining infrared spectra with centrifugal distortion data to give the force field is worth considering. There are four approaches to this, and the merits of each will now be discussed. 

In a nonrigid rotating diatomic molecule, centrifugal distortion will elongate the bond as the rotational frequency increases. To accurately fit the energy levels, a correction term must be added to Eq. (1.55)... 

Actually, symmetrical tetrahedral molecules like methane do have extremely small dipole moments, caused by centrifugal distortion effects these moments are so small that they can be ignored for all practical purposes. For CH4, p is 5.4 x 10 D Ozier, I. Phys. Rev. Lett., 1971, 27, 1329 Rosenberg, A. Ozier, I. Kudian, A.K. J. Chem. Phys., 1972, 57, 568. 

The dipole moment is a fundamental property of a molecule (or any dipole unit) in which two opposite charges are separated by a distance . This entity is commonly measured in debye units (symbolized by D), equal to 3.33564 X 10 coulomb-meters, in SI units). Since the net dipole moment of a molecule is equal to the vectorial sum of the individual bond moments, the dipole moment provides valuable information on the structure and electrical properties of that molecule. The dipole moment can be determined by use of the Debye equation for total polarization. Examples of dipole moments (in the gas phase) are water (1.854 D), ammonia (1.471 D), nitromethane (3.46 D), imidazole (3.8 D), toluene (0.375 D), and pyrimidine (2.334 D). Even symmetrical molecules will have a small, but measurable dipole moment, due to centrifugal distortion effects. Methane " for example, has a value of about 5.4 X 10 D. 

Over the last years we have explored several advanced techniques for high-resolution rotational coherence spectroscopy (RCS [1]) in order to study the structures of molecules and clusters in the gas phase [2]. We have provided spectroscopic examples demonstrating (i) mass-selectivity (Fig. 1, [3]), (ii) that the rotational constants of the ground and electronic excited states can be obtained independently with high precision (lO MO"5, [4]), (iii) that the transition dipole moment alignment, (iv) centrifugal distortion constants, and (v) information on the polarizability tensor can be obtained (Fig.l, [5]). Here we review results pertaining to points (i), (ii), (iv) and (v) [2,3,5],... 

Up to this point, the molecule has been considered to be a rigid rotor, but the work in Chapter 4 on diatomics shows that we must add corrections for rotation-vibration interaction and centrifugal distortion. For a polyatomic molecule, there are several normal modes of vibration, each with its own vibrational quantum number (see Chapter 6). By analogy to (4.75), we write for polyatomic molecules... 

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. 

Absorption of microwave radiation to excite molecular rotation is allowed only if the molecule has a permanent dipole moment. This restriction is less severe than it may sound, however, because centrifugal distortion can disturb the molecular symmetry enough to allow weak absorption, especially in transitions between the higher rotational states which may appear in the far IR (c. 100cm-1). Microwave spectroscopy can provide a wealth of other molecular data, mostly of interest to physical chemists rather than inorganic chemists. Because of the ways in which molecular rotation is affected by vibration, it is possible to obtain vibrational frequencies from pure rotational spectra, often more accurately than is possible by direct vibrational spectroscopy. 

Modified thermal (Bates 1983) or phase space (Herbst 1985c) calculations of radiative association rates indicate, as expected, an inverse temperature dependence and a direct dependence on the complexity of the reaction partners. Thus, if theory is to be believed, the importance of radiative association is enhanced by complex molecules reacting in cold clouds. Let us consider two important examples in the synthesis of interstellar methane (Huntress and Mitchell 1979). Although methane can only be observed with difficulty via radioastronomical methods (by centrifugal distortion induced rotational transitions) because it does not possess a permanent dipole moment, its synthesis is an important one because methane is a precursor to more complex hydrocarbons which can be and have been detected. This synthesis can proceed via the following series of normal and radiative association reactions, most of which have been studied in the laboratory ... 

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. 

It is now possible to determine precise rotational spectra for hydrogen bonded molecules of moderate size and with even very small stabilization energies. Rotational constants, centrifugal distortion constants, electric dipole moments and nuclear hyperfine interactions have been measured for a considerable number of dimers using various microwave and molecular beam techniques. 

The evaluation of the matrix elements of these centrifugal distortion corrections appears rather daunting. However, they can be derived quite simply by matrix multiplication. We have already constructed the matrix representations of the two operators involved for a molecule in a 2n state. Since the operator in equation (8.422) consists of... 

As mentioned above, the small mass of OH leads to a pronounced centrifugal distortion of its rotational and spin energy levels. The description of these effects has already been given earlier in section 8.5.4(d), where the exphcit matrix elements for a molecule in a 2n state were given. 

We have made explicit the fact that this term is evaluated in the molecule-fixed axis system (with q = 0). The first term was introduced previously in equation (9.104) but the second term is less familiar it represents a centrifugal distortion correction to the spin-spin interaction but was not, in fact, included in the analysis of the CH spectrum so we shall not discuss it further here. 

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