Dipole derivative

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. ... 

The second term in the above expansion of the transition dipole matrix element Za 3 if i/3Ra (Ra - Ra,e) can become important to analyze when the first term ifi(Re) vanishes (e.g., for reasons of symmetry). This dipole derivative term, when substituted into the integral over vibrational coordinates gives... 

General expressions for the force constants and dipole derivatives of molecules are derived, and the problems arising from their practical application are reviewed. Great emphasis is placed on the use of the Hartree-Fock function as an approximate wavefunction, and a number... 

At this level of theory, the calculated equilibrium bond length is 110.47 pm, and the dipole moment changes sign around which may explain why one has to work so hard to achieve agreement with experiment. The dipole derivative can be found by numerical methods from the data points. 

One of the most familiar uses of dipole derivatives is the calculation of infrared intensities. To relate the intensity of a transition between states with vibrational wavefunctions i/r and jfyi it is necessary to evaluate the transition dipole moment... 

For a vibrating molecule to absorb radiation from an incident IR beam at the frequency of a particular normal mode it must be situated at a position of finite intensity and with an orientation such that there is a finite component of the dipole derivative du /dQ in the direction of the electric vector of the radiation field, where duj is the change of dipole for the change of normal mode coordinate dQ. At a... 

To be precise, this expression employs the so-called double-harmonic approximation, where cubic and higher force constants as well as second and higher dipole derivatives are ignored. This approximation is common to all current implementations of calculating IR and Raman intensities. For details see Amos, 1987. 

Infrared spectra are straightforward to predict theoretically, demanding development of a force field (FF) to determine frequencies and dipole derivatives for intensities. These parameters were initially obtained using empirically fitted force constants and simple models for transition dipoles (Krimm and Bandekar, 1986 Torii and Tasumi, 1996). 

With quantum-mechanical methods, the second derivatives of the energy could be used directly for the FF and atomic polar tensors (APT) for the dipole derivatives. Both are standardly computed in most quantum-chemistry programs but for accurate results, moderately large basis sets and/or some accommodation for correlation interaction is needed. Until recently, this has restricted most ab initio studies to modest-sized molecules. 

Figure 1. Bottom panel OH stretch frequencies, to , for water clusters and the surrounding point charges, versus electric field ) (in atomic units). The solid line is the best quadratic fit. Top panel Dipole derivative, / ], (relative to the gas phase value) for water clusters and the surrounding point charges, versus electric field ). The solid line is the best linear fit.

A number of researchers [15, 38 40, 43, 113, 124 126, 128, 146] have used mixed quantum/classical models, mostly as described in Section III.A, to calculate vibrational line shapes for this system, and several are in fair agreement with experiment. Here we describe our latest work involving approaches discussed in Section III.C. Our theoretical line shapes are calculated as briefly described in previous sections and in published work [98]. From an MD simulation of SPC/E heavy water, we determine the electric field on each putative H atom. We then use electric field maps to determine the transition frequency and dipole derivative. The orientational contribution to mp(t) we... 

In a recent experimental study involving the temperature dependences of the IR and Raman line shapes, Loparo et al. [14] confirmed that non-Condon effects are important in experimental (and theoretical ) line shapes, and they found a frequency dependence to the dipole derivative that is qualitatively similar to the form used in our work. 

Another very important consequence due to the reflection rale described here is that only those fundamental vibrations of adsorbed species which have a finite value of the dipole derivative perpendicular to the surface can undergo interaction with the radiation. Consider a simple case of a diatomic molecule adsorbed on the surface (Fig. 6.25). When this molecule lies on the surface, its dipole moment is parallel to the... 

A related strategy was used to prepare D-allosamine (134). Cycloaddition of the dipole derived from nitroacetal (129) to (S )-vinyl dioxolane (74) afforded a mixture of erythro/threo isoxazolines 130 131 (Scheme 6.72). The erythro isoxazoline was subjected to hydroxylation as described above, to give 4-hydroxyisoxazoline 132 with high diastereoselectivity. Lithium aluminium hydride reduction furnished a single diastereomer of aminodiol 133, which could be deprotected to give the hydrochloride salt of D-allosamine (134) (141). 

Electric dipoles derived from covalent linkages... 

The oscillator strength (dipole derivative) associated with the C-0 stretching mode for bridge-bonded CO is of the order of... 

The IETS intensities for the methyl group vibrations of this species are shown in Fig. 9. The theoretical predictions of Kirtley and Hall (34) using KSH, and taking methyl group dipole derivatives from infrared measurements of ethane, assuming the C-S bond normal vs parallel to the interface, are also shown in Fig. 9. Note that for an orientation with the C-S bond normal, the symmetric C-H modes ( 2 and 9 ), which have net dipoles parallel to the C-S bond, are favored over the anti-symmetric modes ( 4,7, and 11), which have net dipole moments perpendicular to the C-S bond, but that for the C-S bond parallel to the surface the situation is reversed. The better, although by no means perfect, agreement between theory and experiment for the C-S bond normal tends to support the proposed orientation of Hall and Hansma. 

Figure 9. Experimental and theoretical (KSH) IETS intensities for the methyl group vibrations of methyl sulfonate ions on alumina. The theoretical curves assume dipole derivatives from IR measurements of C2He, and compares the predictions for the C—S bond normal vs. parallel to the interface. The relatively better fit for C-S normal supports the proposed orientation of Hall and Hansma.

E3 - energy obtained by association of water dipols derived from dehydration according to E] and E2 ... 

An example of enantioselective 1,3-dipolar cycloaddition of ethyl diazopyruvate to 2,3-dihydrofuran, catalyzed by a chiral ruthenium-PyBox complex, to provide a tetrahydrofurofuran was reported (Equation 125). However, the adduct 240 was only obtained in 74% ee, and its absolute configuration not determined <2004SL2573, 2005HCA1010>. As shown in Equation (126), 2,3-dihydrofuran also participated in 1,3-dipolar cycloaddition with dipoles derived from aziridines under Sc(OTf)3-catalyzed conditions, forming rfr-fused furopyrrolidines <2001TL9089>. 

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