Direction of transition dipoles

Reflection-absorption (RA) or grazing-angle spectroscopy, is a very useful technique that gives information about the direction of transition dipoles in a sample. Figure 3 present an optical setup for a grazing-angle experiment (22). 

Fig. 4. The anatomy of a p-like state . Two isodensity contour maps (+ 0.01 and + 0.03 a.u." ) of the same LUMO orbital are shown side by side. Unlike the p-Uke orbitals in one-electron models, LUMO states in MQC MD-DFT and CIS models have the lobes pushed outwards between the first and the second solvation shells, with < 20% of the spin density residing inside the cavity. This results in considerable firagmentation of the diffuse part of the wavefunction. The O 2p orbitals are strongly polarized, with opposite signs of the orbitals attained by water molecules on the opposite sides of the cavity in the direction of transition dipole moment.

Fig. 9.20 Comparison of the IR spectrum of neat pyridine recorded in the transmission mode with the SNiFTiRS spectrum for the configuration Au(llO) electrode/0.001 M pyridine soiution in D20/ZnSe hemispherical window, recorded using the sample potential 2 = 0.4 V and the reference potential , =-0.75 V (SCE). Inset shows directions of transition dipole moments of fli and fai bands in the IR spectrum of pyridine. Taken with permission from Refs. [36] and [40].

The signs of cross peaks indicate relative reorientation directions of transition dipoles and consequently their associated chemical groups. If the sign of a synchronous cross peak is positive, the corresponding pair of transition dipoles reorient in the same direction. If negative, on the other hand, the reorientation directions are perpendicular to each other. In Figure 1-10, mutually perpendicular reorientation of a pair of transition dipoles at wavenumbers A and C, as well as parallel reorientation for B and D, are observed. 

Atomic polar tensors, defined widi respect to an aibitraty Cartesian system, nn be transformed into quantities referring to a bond axis system using Eq. (4.22). If a molecule has sets of equivalent atmns the transfonnatiatomic polar tensors, provided the local refermce systems are chosen in a consistent way. With such representations it is clear that the number of independent atomic polar tensor elements is smaller for molecules with higher symmetiy. Decius and Mast [117] analyzed in detail the site symmetiy properties of atomic polar tensors exjnessed in tenns of bond axis system. The treatment covers molecules with sufficient symmetiy so that the directions of transitional dipole moments are uniquely determined. Molecules with symmetiy point grotq> G = C2h> Ci, C, Q and Ci are excluded from fire analysis. As already discussed, all elements of the Pq matrix for such molecules cannot be determined from experiment. 

We shall limit our presentation only to defining relations between different intensity parameters and atomic polar tensors [33,108]. There are two main reasons for diis. Atomic polar tensors are evaluated from experimental infiared intensities of symmetric molecules (the directions of transition dipoles are fixed by symmetry) without any fiirther assumptions or approximations to be made. Secondly, quantum mechanical estimates of infrared intensities are presently obtained from calculations by analytical differentiation atomic polar tensors. These quantities appear in die standard output of current ab initio program packages [153,154], Thus, most intensity parameters can be interconnected by defining their relations to atomic polar tensors. 

For an asymmetric top, the rotational quantum numbers undergo the same possible changes in vibration-rotation transitions as in pure-rotation transitions however, it is the direction of the change in the dipole moment, rather than the direction of the dipole moment, that is relevant. The... 

Fig. 1.5. Direction of the dipole moment d of an optical transition in a diatomic molecule (a), (c) parallel transition (b), (d) perpendicular transition (e) arbitrary orientation of the angular momentum J.

Since for each pair of dipoles we have many possible directions of transition moments, it is useful to rewrite (1.34) in a tensorial form using the dipole-dipole interaction tensor < >(m — n) ... 

The orientation of the dipole moment in the ground state of uracil (26 3° or 45 3° depending on the assumed direction of transition moment) and thymine (29 2°) has been determined from the influence of an electric field on the light absorption of the molecules in solution. 

Table 12. Effect of a gauge-origin shift on the B term for the five lowest dipole-allowed (singlet) transitions from the ground state XA of formaldehyde i CHjOi obtained at the CCSD/aug-cc-pVTZ level. The molecule is placed on the xz-plane with the C2 axis along and the center of mass (CM) as origin of the coordinate system. Direction of transition in parentheses and excitation energie.s in atomic units (from [70])...

Since all but one of the electrons in the given molecule remain unchanged in state as a result of electronic excitation, then only the wavefunctions involved directly in the electronic transition need be considered in defining the transition dipole moment. In the case of biological macromolecules and macromolecular assemblies, relevant wavefunctions usually correlate to lone pair orbitals, n, and ttItt molecular orbitals such that only two main types of transition dipole moment need be considered, which are ( jl n ) and (tt /2 tt ) respectively. The first of these transition dipole moments is in fact zero, consequently corresponding jx electronic transitions are known as weak, symmetry forbidden transitions. The second of these transition dipole moments is always non-zero and consequently corresponding tt TT transitio ns are known as a stro ng, symmetry allowed transitions. The symmetry allowed transitions are at least 100 times more intense than symmetry forbidden transitions. 

The optical anisotropy, as characterized by the difference between the absorption of IR light polarized in the directions parallel and perpendicular to the reference axis (i.e., the direction of applied strain), is known as the IR linear dichroism of the system. For a uniaxially oriented polymer system [10, 28-30], the dichroic difference, A/4(v) = y4 (v) - Ax v), is proportional to the average orientation, i.e., the second moment of the orientation distribution function, of transition dipoles (or electric-dipole transition moments) associated with the molecular vibration occurring at frequency v. If the average orientation of the transition dipoles absorbing light at frequency is in the direction parallel to the applied strain, the dichroic difference AA takes a positive value on the other hand, the IR dichroism becomes negative if the transition dipoles are perpendicularly oriented. 

Theoretical calculation can also be used to determine the direction of electric dipole transition moments of a chromophore within a complex system (e.g., for the use of exciton chirality method). Although TDDFT calculations could be used for this purpose," the DeVoe polarizability model has also been applied for various compounds, including supramolecular systems. ... 

---