Measuring vectors, vibration-rotation

Photodissociation dynamics [89,90] is one of the most active fields of current research into chemical physics. As well as the scalar attributes of product state distributions, vector correlations between the dissociating parent molecule and its photofragments are now being explored [91-93]. The majority of studies have used one or more visible or ultraviolet photons to excite the molecule to a dissociative electronically excited state, and following dissociation the vibrational, rotational, translational, and fine-structure distributions of the fragments have been measured using a variety of pump-probe laser-based detection techniques (for recent examples see references 94-100). Vibrationally mediated photodissociation, in which one photon... 

The shape of the vibration-rotation bands in infrared absorption and Raman scattering experiments on diatomic molecules dissolved in a host fluid have been used to determine2,15 the autocorrelation functions unit vector pointing along the molecular axis and P2(x) is the Legendre polynomial of index 2. These correlation functions measure the rate of rotational reorientation of the molecule in the host fluid. The observed temperature- and density-dependence of these functions yields a great deal of information about reorientation in solids, liquids, and gases. These correlation functions have been successfully evaluated on the basis of molecular models.15... 

In Equation 12.6 p, is the permanent dipole moment, h is Planck s constant, I the moment of inertia, j the angular momentum quantum number, and M and K the projection of the angular momentum on the electric field vector or axis of symmetry of the molecule, respectively. Obviously if the electric field strength is known, and the j state is reliably identified (this can be done using the Stark shift itself) it is possible to determine the dipole moment precisely. The high sensitivity of the method enables one to measure differences in dipole moments between isotopes and/or between ground and excited vibrational states (and in favorable cases dipole differences between rotational states). Dipole measurements precise to 0.001 D, or better, for moments in the range 0.5-2D are typical (Table 12.1). 

Up to now we have exclusively considered the scalar properties of the photodissociation products, namely the vibrational and rotational state distributions of diatomic fragments, i.e., the energy that goes into the various degrees of freedom. Although the complete analysis of final state distributions reveals a lot of information about the bond breaking and the forces in the exit channel, it does not completely specify the dissociation process. Photodissociation is by its very nature an anisotropic process — the polarization of the electric field Eo defines a unique direction relative to which all vectors describing both the parent molecule and the products can be measured. These are ... 

Generally in molecular beam studies, both beams have comparable velocities and intersect one another at 90°, and thus the CM velocity vector points at a wide angle intermediate between the two beams. Measurement of the displacement of the laboratory angular distribution of products from the centre-of-mass vector enables an estimate of the velocity of the products to be derived. Reaction products have been velocity analysed (e.g. see refs. 8 and 231) and the results support the view that the product relative translational energy is usually within ca. 1 kcal mole of the reactant relative translational energy. Most of the alkali metal reactions studied to date are exothermic, thus the products must be internally excited. It is believed [8] that, for most reactions, the internal excitation consists mainly of vibrational excitation however, the partition of the vibrational energy between, for example, KI and CH3 is as yet unknown. There are a few exceptions, e.g. the K + HBr reaction where KBr is rotationally excited rather than vibrationally excited [8], and the... 

The curve formed by connecting the tips of the E vectors along the z axis gives a helix. The sense of rotation is reversed in helices corresponding to right- and left-circular radiations. The difference between infrared absorptions for right- and left-circular infrared radiations is called infrared circular dichroism or vibrational circular dichroism (VCD). Measurements of VCD are described in Chapter 22. 

In these studies, not only rotational and vibrational states of products should be detected, but also the distribition of the velocity of the separation of products. Either time-of-flight mass spectroscopy, or the LIE method with a high spectral resolution is used for this purpose. When LIF is used, the Doppler contour of the line in the excitation spectrum is measured. Since atoms with different velocity vectors, according to the Doppler effect, absorb (emit) the light in different manners, this reflects the shape of the line in the excitation spectrum. Therefore, using the experimentally determined contour of the line in the excitation spectrum, one can obtain information about the values and direction of the velocity of the separation of products. 

---