Dipole moment symmetry rule

Other linear molecules (acetylene, CjHj, for example) have similarly described vibrational spectra either stretching vibrations or bending vibrations. It is only when a molecule becomes nonlinear that additional complexities arise. Unfortunately, most molecules are nonlinear. Fortunately, similar rough descriptions of the vibrations can be applied. Also fortunately, symmetry considerations combine with the change-in-dipole-moment selection rule to limit the number of IR-active vibrational motions of large, symmetric molecules. The next few sections will illustrate some of the procedures used to simplify our understanding of molecular vibrations. 

Qualitatively, the selection rule for IR absorption for a given mode is that the symmetry of qT ) " must he the same as qT ). Qiianii-talivcly, the transition dipole moment is proportion al to tlie dipole derivative with respect to a given normal mode dp/di. ... 

Another related issue is the computation of the intensities of the peaks in the spectrum. Peak intensities depend on the probability that a particular wavelength photon will be absorbed or Raman-scattered. These probabilities can be computed from the wave function by computing the transition dipole moments. This gives relative peak intensities since the calculation does not include the density of the substance. Some types of transitions turn out to have a zero probability due to the molecules symmetry or the spin of the electrons. This is where spectroscopic selection rules come from. Ah initio methods are the preferred way of computing intensities. Although intensities can be computed using semiempirical methods, they tend to give rather poor accuracy results for many chemical systems. 

Excited states formed by light absorption are governed by (dipole) selection rules. Two selection rules derive from parity and spin considerations. Atoms and molecules with a center of symmetry must have wavefunctions that are either symmetric (g) or antisymmetric (u). Since the dipole moment operator is of odd parity, allowed transitions must relate states of different parity thus, u—g is allowed, but not u—u or g—g. Similarly, allowed transitions must connect states of the same multiplicity—that is, singlet—singlet, triplet-triplet, and so on. The parity selection rule is strictly obeyed for atoms and molecules of high symmetry. In molecules of low symmetry, it tends to break down gradually however,... 

The selection rule for Raman spectroscopy requires a change in the induced dipole moment or polarizability of the molecule, and so it is a complementary technique to infrared which requires a change in the permanent dipole moment. For molecules having a center of inversion, all Raman-active bands are infrared inactive and vice versa. As the symmetry of the molecule is lowered, the coincidences between Raman-active and infrared-... 

One of the most useful features of a QM model is its ability to provide information about the molecular charge distribution. It is a general rule of thumb that even very low quality QM methods tend to give reasonable charge distributions. For neutral molecules, the dominant moment in the overall charge distribution is the usually dipole moment (unless symmetry renders the dipole moment zero). For a 125-molecule test set including H, C, N, O, F, Al, Si, P, S, Cl, Br, and I functionality, Stewart found mean unsigned errors in dipole moments... 

For a symmetric top, symmetry requires the dipole moment to lie along the symmetry axis, so that two of the three principal-axis components of d must vanish. In deriving the symmetric-top wave functions in Section 5.5, we assumed that the c axis was the symmetry axis hence to use the eigenfunctions (5.68) to find the selection rules, we must take da = db — 0, dcJ= 0. For a symmetric top, we thus must evaluate only the three integrals IXOc, lYoc anc Azof The three relevant direction cosines are given in (6.64) and Problem 5.15 they are independent of x- Since the integral... 

Symmetric tops with no dipole moment have no microwave spectrum. For example, planar symmetric-top molecules have a C axis and a ak symmetry plane such molecules cannot have a dipole moment. Thus benzene has no microwave spectrum. For a symmetric top with a permanent electric dipole moment, the selection rules for pure-rotation transitions are... 

On pjge W the argument is made ihat a molecule with a center of symmetry, i, cannot have a molecular dipole moment. Prove this same rule using a molecule with a cenier of symmetry and summing up the individual bond moments. 

Both infrared (IR) and Raman spectroscopy have selection rules based on the symmetry of the molecule. Any molecular vibration that results in a change of dipole moment is infrared active. For a vibration to be Raman active, there must be a change of polarizability of the molecule as the transition occurs. It is thus possible to determine which modes will be IR active, Raman active, both, or neither from the symmetry of the molecule (see Chapter 3). In general, these two modes of spectroscopy are complementary specifically, if a molecule has a center of symmetry, no [R active vibration is also Raman active. 

Selection rules also arise on considering the point-group symmetry of tfo(Qeq). In the case of electric dipole radiation the perturbation Y, which describes the interaction with the radiation field, may be expressed in terms of the x, y, z components of the dipole moment operator r. The operators (t) transform as the x, y, or z components of r. 

The selection rules for the Raman effect are quite different from those for IR spectroscopy. The mechanism involves interaction between the incident radiation and the fluctuating polarisability of the molecule, in contrast to the fluctuating dipole moment in IR absorption. The dipole moment is a vector quantity, and can be resolved into components along three Cartesian axes. The polarisability is a tensor quantity, whose components can be written as products of Cartesian axes. For a molecule having no symmetry at all, or having only a plane of symmetry, all... 

A well-known selection rule concerning centrosymmetric systems (those with a center of inversion) is the Laporte s rule. For such systems, states are either g (even) or u (odd). Laporte s rule states that only transitions between g and u states are allowed i.e., transitions between two g states and those between two u states are forbidden. With the foregoing discussion, this rule can now be easily proved. For centrosymmetric molecules, the three components of the dipole moment vector are all u. For g g transitions, the overall symmetry... 

Step 4. For a vibrational mode to be infrared (IR) active, it must bring about a change in the molecule s dipole moment. Since the symmetry species of the dipole moment s components are the same as rx, ry, and 1, a normal mode having the same symmetry as Ix, Ey, or 1 will be infrared active. The argument employed here is very similar to that used in the derivation of the selection rules for electric dipole transitions (Section 7.1.3). So, of the six vibrations of NH3, all are infrared active, and they comprise four normal modes with distinct fundamental frequencies. 

Looking at all the examples in Figure 4.18 suggests that molecular symmetry can be used to formulate a rule which will tell us whether any molecule has a non-zero dipole moment. 

Group Theory for Non-Rigid Molecule (NRG), permits us to classify the torsional wave-functions according to the irreducible representations of the symmetry group of the molecule. As it is well known, the scalar product of (119) does not vanish when the direct products of the irreducible representations, under which 4, and / transform, contain at least one of the components of the dipole moments variation. Thus, when symmetry properties of these components are known, Selection Rules may be established. 

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