Induced dipole moment, determination

The expression contains the van der Waals MM/MM energy given by E J/MM and the polarization term is the second term in Eq. (13-28) which depends explicitly on the induced dipole moments determined as... 

Accordingly, the modifications to the KS operator are twofold (i) a static contribution through the static multipole moments (here charges) of the solvent molecules and (ii) a dynamical contribution which depends linearly on the electronic polarizability of the environment and also depends on the electronic density of the QM region. Due to the latter fact we need within each SCF iteration to update the DFT/MM part of the KS operator with the set of induced dipole moments determined from Eq. (13-29). We emphasize that it is the dynamical contribution that gives rise to polarization of the MM subsystem by the QM subsystem. 

These can be determined experimentally to very high accuracy from the Stark effect and molecular beam studies. The experimental accuracy is far beyond the capabilities of ab initio studies. At the other extreme, the original route to these quantities was through studies of the dielectric polarization of species in solution, and there is currently interest in collision-induced dipole moments. In either case, the quantities deduced depend critically on the model used to interpret the experiment. 

On the other hand, electric dipolar moments of the solute molecules can be obtained with standard methods in ab initio molecular orbital calculations, whereas the induced dipole moments in solution are determined from differences between the values obtained in solution and in the gas phase. 

The relative changes in intensity of the vibronic bands in the pyrene fluorescence spectrum has its origin in the extent of vibronic coupling between the weakly allowed first excited state and the strongly allowed second excited state. Dipole-induced dipole interactions between the solvent and pyrene play a major role. The polarity of the solvent determines the extent to which an induced dipole moment is formed by vibrational distortions of the nuclear coordinates of pyrene (Karpovich and Blanchard, 1995). 

In order to relate the dressed state population dynamics to the more intuitive semiclassical picture of a laser-driven charge oscillation, we analyze the induced dipole moment n) t) and the interaction energy V)(0 of the dipole in the external field. To this end, we insert the solution of the TDSE (6.27) into the expansion of the wavefunction Eq. (6.24) and determine the time evolution of the charge density distribution p r, t) = -e r, f)P in space. Erom the density we calculate the expectation value of the dipole operator... 

At the next level of complexity, the polarity of solvent models, as made manifest by their atomic partial charges, can be augmented with a polarizability. This allows the solvent molecule to respond to its surroundings in a fashion conceptually similar to the electronic component of die solvent polarization described in Section 11.1.1. Typically a polarizability tensor a is assigned either to the solvent molecule as a whole or to individual atoms. Then, die induced dipole moment at each polarizable position can be determined from... 

Spectroscopic measurement. Specifically, if the induced dipole moment and interaction potential are known as functions of the intermolecular separation, molecular orientations, vibrational excitations, etc., an absorption spectrum can in principle be computed potential and dipole surface determine the spectra. With some caution, one may also turn this argument around and argue that the knowledge of the spectra and the interaction potential defines an induced dipole function. While direct inversion procedures for the purpose may be possible, none are presently known and the empirical induced dipole models usually assume an analytical function like Eqs. 4.1 and 4.3, or combinations of Eqs. 4.1 through 4.3, with parameters po, J o, <32, etc., to be chosen such that certain measured spectral moments or profiles are reproduced computationally. 

This section provides the fundamental equations for the quantum mechanical and molecular mechanical approach for determining the energies of molecules interacting with a structured environment. We can illustrate the QM/MM procedure as indicated in Figure 13-1 for a system where one part is described by quantum mechanics (QM) and the other part is described by classical mechanics or molecular mechanics (MM). The electrons and the nuclei of the QM system are treated separately at positions r7 and Rm, respectively. We represent the particles in the MM part by effective charges positioned at the atomic sites, Rs, and induced dipole moments located at (R ). 

The magnitude of the induced dipole moment that is produced when an indole molecule in its ground Sq and electronically excited Si states is polarized by the attachment of a hydrogen-bonded water molecule in the gas-phase complex indole-H20 have been determined as /i I(So) = 0.7 D atid /t I(Si) = 0.5 D <2005JCP1743011>. The permanent dipole moment values for the complex (/tlW(So) =4.4D and /tlW(Si) = 4.0 D) are substantially different from calculated values based on vector sums of the dipole moments of the component parts. The orientation of the induced moment is also significantly different in the two electronic states. 

In condensed media consisting of molecules, the intermolecular forces such as permanent and induced dipole interactions are generally small compared to intramolecular chemical binding forces. Therefore, the molecular identities and properties are conserved to a certain extent. They nevertheless differ significantly from those of an isolated molecule in the gas phase. Therefore, both in linear and non-linear optics the question arises of how to relate molecular to macroscopic properties. More specifically, how do the individual permanent and induced dipole moments of the molecules translate into the macroscopic polarization of the medium The main problem is to determine the local electric field acting on a molecule in a medium which differs from the average macroscopic field E (Maxwell field) in this medium. 

Since the intensity calculation can be reduced to calculating a and for deformed molecules, the availability of quantum chemical methods immediately led to attempts to employ them to determine vibrational intensities (Segal and Klein, 1967). The polarizability is the proportionality factor between the induced dipole moment and the inducing electric field. It is therefore necessary to use a perturbation treatment which takes the electric field into account. Two different approaches were explored the Finite... 

The polarization of the double layer has a number of typical consequences. One of these is that an induced dipole moment can be assigned to it. It is a vector (sec. 1.4.4b). The magnitude of this dipole moment is determined by the applied field, the shape, orientation and volume of the particles, Du and a few... 

Returning to the Induced dipole moment, this vector is determined with respect to both sign and magnitude by the variety of fluxes in the nonequilibrium double layer. Because of this, and because it is measurable (by dielectric spectroscopy), p, j is the most basic characteristic of non-equilibrium double layers. 

Dukhin, V.N. Shilov. Kinetic Aspects of Electrochemistry of Disperse Systems. Part II. Induced Dipole Moment and the Non-Equilibrium Double Layer of a Colloid Particle. Adu. Colloid Interface Sci. 13 (1980) 153. (Review on the determination and interpretation of induced dipole moments of various colloidal particles.)... 

Change in the dipole moment and polarizability upon electronic excitation was determined for various linear polyenes by adopting electric field-induced changes in the optical absorption spectrum [70]. Polyenes studied (Exhibit 2) were diphenylbutadiene (DPB 7), diphenylhexatriene (DPH 8), diphenyloctate-traene (DPO 9), diphenyldecapentaene (DPD 10), and all-tranj-retinal (3). Exhibit 2 describes the experimental values determined. It is proposed that (based on the results obtained) the excited state dipole moments determined on these polyene systems have a role to play in the mechanism of trans-cis photoisomerization. 

Here, for example, is the induced dipole moment along the x axis caused by the 0 (ground state) — j (excited state) electronic transition, y,n is the frequency of the 0 j transition, and v is the exciting frequency. Thus, it is readily seen that the character of the polarizability components such as a and is determined by... 

To determine the activity of the vibrations in the infrared and Raman spectra, the selection rule must be applied to each normal vibration. From a quantum mechanical point of view, a vibration is active in the infrared spectrum ij the dipole moment of the molecule is changed during the vibration, and is active in the Rarnan spectrum if the polarizability cf the molecule is changed during the vibration. As stated in Sec. I-l, the induced dipole moment P is rdated to the strength of the electric field E by the relation... 

---