Transition dipole moment computation

ZINDO is an adaptation of INDO speciflcally for predicting electronic excitations. The proper acronym for ZINDO is INDO/S (spectroscopic INDO), but the ZINDO moniker is more commonly used. ZINDO has been fairly successful in modeling electronic excited states. Some of the codes incorporated in ZINDO include transition-dipole moment computation so that peak intensities as well as wave lengths can be computed. ZINDO generally does poorly for geometry optimization. 

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. 

The measurements are predicted computationally with orbital-based techniques that can compute transition dipole moments (and thus intensities) for transitions between electronic states. VCD is particularly difficult to predict due to the fact that the Born-Oppenheimer approximation is not valid for this property. Thus, there is a choice between using the wave functions computed with the Born-Oppenheimer approximation giving limited accuracy, or very computationally intensive exact computations. Further technical difficulties are encountered due to the gauge dependence of many techniques (dependence on the coordinate system origin). 

State averaging gives a wave function that describes the first few electronic states equally well. This is done by computing several states at once with the same orbitals. It also keeps the wave functions strictly orthogonal. This is necessary to accurately compute the transition dipole moments. 

Intensities for electronic transitions are computed as transition dipole moments between states. This is most accurate if the states are orthogonal. Some of the best results are obtained from the CIS, MCSCF, and ZINDO methods. The CASPT2 method can be very accurate, but it often requires some manual manipulation in order to obtain the correct configurations in the reference space. 

In a combined experimental/computational study, the vibrational spectra of the N9H and N7H tautomers of the parent purine have been investigated [99SA(A) 2329]. Solvent effects were estimated by SCRF calculations. Vertical transitions, transition dipole moments, and permanent dipole moments of several low-lying valence states of 2-aminopurine 146 were computed using the CIS and CASSCF methods [98JPC(A)526, 00JPC(A)1930]. While the first excited state of adenine is characterized by an n n transition, it is the transition for 146. The... 

Now to the problem of calculating the transition densities. We need these quantities in order to be able to compute transition properties like the transition dipole moment. When we use a common orthonormal set of molecular orbitals for both the electronic states, the formalism developed in chapter 3 can be applied. For a one-electron operator A the transition matrix element is obtained from the simple formula ... 

Computed using the transition dipole moment calculated at the CASSCF level. 

The influence of the polymer length on the computed spectra was studied for this model as well. It was found that for a transition dipole moment of between about 0.3 and 0.5 Debye (corresponding approximately to an amide I and a guanine C=0 stretching vibration, respectively), the computed VCD spectra are more or less inde-... 

The calculated frequency separation of the amide I exciton components are much larger for the NMR structure than for the X-ray structure, although in both cases identical values for the unperturbed amide I frequency (1665 cm 1), and for the transition dipole moment were used. Further, and it was assumed for computational simplici-... 

CASSCF wave functions with their own sets of optimized orbitals, which where then not orthogonal to each other. The CAS State interaction CASSI, method made it possible to compute efficiently first and second order transition density matrices for any type of CASSCF wave functions [16, 17]. The method is used to compute transition dipole moments in spectroscopy and also in applications where it is advantageous to use localized orbitals, for example in studies of charge transfer reactions [18]. Today, the same approach is used to construct and solve a spin-orbit Hamiltonian in a basis of CASSCF wave functions [19]. 

Assume that we have computed CASSCF wave function for two different electronic states. Now we want to compute transition properties, for example, the transition dipole moment. How can we do that. The two states will in general be described by two non-orthonormal sets of MOs, so the normal Slater rules cannot be applied. Let us start by considering the case where two electronic states fi and v are described by the same set of MOs. The transition matrix element for a one-electron operator A is then given by the simple expression ... 

In this presentation we have only considered single photon transitions since multi-photon transitions are not relevant to the atmosphere, however the time-dependent framework can easily be extended for this purpose. This requires computing the diabatic transition dipole moment for the multi-photon transitions. Furthermore, the couplings between the time-dependent external electric field and the molecular system would change. 

This technique was employed to monitor the B —> A transition of DNA as a function of the relative humidity (Pilet and Brahms, 1973 Pohle et al., 1984). The investigated bands are those which reflect the vibrations of the phosphate groups. As shown by Fig. 4.7-3, which presents the polarized infrared spectra of a salmon sperm DNA hydrated film with 93% RH (top, B form) and 58% RH (bottom, A form), the dichroism of the two phosphate bands changes. The B form of the antisymmetric PO2 stretching vibration around 1230 cm is non-dichroic, while that of the A form is perpendicular. The B form of the symmetric PO2 stretching vibration around 1090 cm is perpendicular, while that of the A form is parallel. A simple computation, for instance for the latter band, shows that the value of the angle between the transition dipole moment of this vibration and the double helical axis varies between 68 ° (B form) and 49 ° (A form). This parameter is an extremely sensitive indicator of a B A transition and may also be employed to show the inhibition of a B —> A transition by various classes of molecules, such as proteins (Liquier et al., 1977 Taillandier et al., 1979) or drugs (Fritzsche and Rupprecht, 1990). 

Prom these patterns, we compute both the position of the molecule and the orientation of its transition dipole moment (shown as yellow bars). Following the molecule in the circle, we can obtain the trajectory of this single... 

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