Dipole moment rotating

It is important to note that this is half of the pair potential that is expected for the interaction of an ion with a molecule having a permanent dipole moment (rotating) similarly aligned [V(r) = —aE2, compare with Equation (34) in Section 2.4.1]. Since some energy is taken up in polarizing a molecule to induce a dipole moment rather than having a permanent dipole moment, it is reasonable that a weaker pair potential is obtained for the interactions between ions and induced non-polar molecules. 

As the hydrogen molecule has no permanent dipole moment, rotational transitions are inactive in the infrared, but not necessarily in Raman (see Section 2.2). However, as the molecule is composed of two indistinguishable fermions, the nuclear spins are correlated to the symmetry of the rotational states. According to the Pauli... 

Although a diatomic molecule can produce only one vibration, this number increases with the number of atoms making up the molecule. For a molecule of N atoms, 3N-6 vibrations are possible. That corresponds to 3N degrees of freedom from which are subtracted 3 translational movements and 3 rotational movements for the overall molecule for which the energy is not quantified and corresponds to thermal energy. In reality, this number is most often reduced because of symmetry. Additionally, for a vibration to be active in the infrared, it must be accompanied by a variation in the molecule s dipole moment. 

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... 

Liu K, Brown M G and Saykally R J 1997 Terahertz laser vibration rotation tunneling spectroscopy and dipole moment of a cage form of the water hexamer J. Phys. Chem. A 101 8995-9010... 

The polarization properties of single-molecule fluorescence excitation spectra have been explored and utilized to detennine botli tlie molecular transition dipole moment orientation and tlie deptli of single pentacene molecules in a /7-teriDhenyl crystal, taking into account tlie rotation of tlie polarization of tlie excitation light by tlie birefringent... 

For linear moleeules, the vibrationally averaged dipole moment pave lies along the moleeular axis henee its orientation in the lab-fixed eoordinate system ean be speeified in terms of the same angles (0 and ([)) that are used to deseribe the rotational funetions Yl,m (0,(1)). Therefore, the three eomponents of the <(l)ir Pave I (1)6 integral ean be written as ... 

For molecules that are non-linear and whose rotational wavefunctions are given in terms of the spherical or symmetric top functions D l,m,K, the dipole moment Pave can have components along any or all three of the molecule s internal coordinates (e.g., the three molecule-fixed coordinates that describe the orientation of the principal axes of the moment of inertia tensor). For a spherical top molecule, Pavel vanishes, so El transitions do not occur. 

The result of all of the vibrational modes contributions to la (3 J-/3Ra) is a vector p-trans that is termed the vibrational "transition dipole" moment. This is a vector with components along, in principle, all three of the internal axes of the molecule. For each particular vibrational transition (i.e., each particular X and Xf) its orientation in space depends only on the orientation of the molecule it is thus said to be locked to the molecule s coordinate frame. As such, its orientation relative to the lab-fixed coordinates (which is needed to effect a derivation of rotational selection rules as was done earlier in this Chapter) can be described much as was done above for the vibrationally averaged dipole moment that arises in purely rotational transitions. There are, however, important differences in detail. In particular. 

Because of point 2, rotational microwave and millimetre wave spectroscopy are powerllil techniques for determining dipole moments. However, the direction of the dipole moment cannot be determined. In the case of 0=C=S, for which /r = 0.715 21 0.000 20 D [(2.3857 0.0007) x 10 ° C m], a simple electronegativity argument leads to the correct conclusion - that the oxygen end of the molecule is the negative end of the dipole. However, in CO, the value of 0.112 D (3.74 x 10 C m) is so small that only accurate electronic stmcture calculations can be relied upon to conclude correctly that the carbon end is the negative one. 

Although these molecules form much the largest group we shall take up the smallest space in considering their rotational spectra. The reason for this is that there are no closed formulae for their rotational term values. Instead, these term values can be determined accurately only by a matrix diagonalization for each value of J, which remains a good quantum number. The selection mle A/ = 0, 1 applies and the molecule must have a permanent dipole moment. 

As well as resulting in rotational constants for the two vibrational states involved, such a specttum also yields the dipole moment in each state. 

CFlBrClF (bromochlorofluoromethane) dipole moment, 99ff enantiomers, 79 symmetry elements, 79ff CF12F2 (difluoromethane) cartesian axes, 89 symmetry elements, 77, 83 CF13F (methyl fluoride) dipole moment, 116 symmetry elements, 74, 83 C Fl3F (methyl fluoride) vibration-rotation band, 178... 

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