Solvent-induced dipole moments

Table 3-8. Average solvent-induced dipole moments in the N, Z and V states for 81° twist angle...

Finally, we address the application of the ASEP/MD methodology to the smdy of electronic transitions. Here, we can consider two situations depending on the description, implicit or explicit, of the solvent electronic polarization. If one uses an implicit description of this component then it is only necessary to perform the calculation of the different excited states in presence of the solvent charge distribution obtained during the ASEP/MD procedure. If, on the contrary, we explicitly include the contribution of this component then it is necessary to perform an additional self-consistent process. Using the solvent structure and solute geometry obtained in the first self-consistent process, we couple the quanmm mechanical solute and the electron polarization of the solvent. The process finishes when the solute charge distribution and the solvent induced dipole moments become mutually equilibrated. 

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). 

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... 

Separation of Electronic and Nuclear Motions. The polarizabilities of the ground state and the excited state can follow an electronic transition, and the same is true of the induced dipole moments in the solvent since these involve the motions of electrons only. However, the solvent dipoles cannot reorganize during such a transition and the electric field which acts on the solute remains unchanged. It is therefore necessary to separate the solvent polarity functions into an orientation polarization and an induction polarization. The total polarization depends on the static dielectric constant Z), the induction polarization depends on the square of the refractive index n2, and the orientation polarization depends on the difference between the relevant functions of D and of n2 this separation between electronic and nuclear motions will appear in the equations of solvation energies and solvatochromic shifts. 

Dispersion Interactions. Last but not least in the range of solute-solvent electrostatic interactions come the dispersion forces which depend on the polarizabilities of the molecules. Any atom or molecule—non-polar or polar—has a small fluctuating dipole moment as the electrons move around the nuclei. These instantaneous dipoles induce dipole moments in all other polarizable molecules, so that the interaction energy is proportional to the product of the average polarizabilities aM and as of the solute and solvent molecules... 

From Fig. 9.1.1, it is clear that the polarization of the solvent will tend to enhance the electrical asymmetry of the molecule, i.e., enhance the molecular dipole moment. The resulting dipole moment p is then the permanent dipole plus an induced dipole moment ... 

The OWB equations obtained in this semiclassical scheme analyse the effective polarizabilities in term of solvent effects on the polarizabilities of the isolated molecules. Three main effects arise due to (a) a contribution from the static reaction field which results in a solute polarizability, different from that of the isolated molecules, (b) a coupling between the induced dipole moments and the dielectric medium, represented by the reaction field factors FR n, (c) the boundary of the cavity which modifies the cavity field with respect the macroscopic field in the medium (the Maxwell field) and this effect is represented by the cavity field factors /c,n. 

Support to these assumptions has recently come from the analysis of the coupling between electrostatic and dispersion-repulsion contributions to the solvation of a series of neutral solutes in different solvents [31]. It has been found that the explicit inclusion of both electrostatic and dispersion-repulsion forces have little effect on both the electrostatic component of the solvation free energy and the induced dipole moment, as can be noted from inspection of the data reported in Table 3.1. These results therefore support the separate calculation of electrostatic and dispersion-repulsion components of the solvation free energy, as generally adopted in QM-SCRF continuum models. 

In Eq. (1-6), E) , vcnt refers to the total solvent electric field and it contains a sum of contributions from the point charges and the induced dipole moments in the MM part of the system. Such a field (and hence the induced dipole) depends on all other induced dipole moments in the solvent. This means that Eq. (1-6) must be solved iteratively within each SCF iteration. As an alternative, Eq. (1-6) may be reformulated into a matrix equation... 

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. 

The statistical average over the electronic degrees of freedom in Eq. [15] is equivalent, in the Drude model, to integration over the induced dipole moments pg and py. The Hamiltonian H, is quadratic in the induced dipoles, and the trace can be calculated exactly as a functional integral over the fluctuating fields pg and The resulting solute-solvent interaction energy... 

The LSER approach relates a bulk property, P, to molecular parameters thought to account for cavity formation, dipole moment/polarizability, and hydrogen-bonding effects at the molecular level. The cavity term models the energy needed to provide a solute molecule-sized cavity in the solvent. The dipole moment/polarizability terms model dipole and induced dipole interactions between solute and solvent these can be viewed as related to dispersion interactions. The hydrogen-bonding terms model HBA basicity and EIBD acidity interactions. 

We have shown above how the reaction field model can be used to estimate solute-solvent interactions in the absence of external fields. Now we introduce effective polarizabilities that connect the Fourier components of the induced dipole moment (33) with the macroscopic fields in the medium. In the linear case, the Fourier component / induced by an external optical field can be represented by the product of the macroscopic field amplitude " and an effective first-order polarizability a(-tu w) using (93). 

The orientation of liquid crystalline solutions of polypeptides is caused by the permanent dipole moment of the molecular cluster in an ekctric field when in a hi dielectric solvent, and by the induced dipole moment of the molecular du r in a magnetic field, irrespective of the solvent used. The maximum induced dqtote moment of the mdecular duster is about 2.4x10 ... 

In order to extend the above treatment to the metal solution interface, one must consider the effect of the solvent molecules adsorbed on the metal on the electronic overspill. Because the solvent molecules are polarizable, an induced dipole moment is established in the solvent monolayer, which acts to reduce the extent of overspill. As a result, the dipolar potential due to the metal is reduced by a factor corresponding to the optical permittivity of the monolayer, Sop. Recalling that this dipole potential is designated as one has at the PZC... 

A proper solvated electron is a particle localized in the potential well of a polar medium, the well being created by the interaction of electron charge with the permanent and induced dipole moments of the nearest as well as remote neighbours. This notion of the nature of a solvated electron, based on the idea that the Landau-Pekar theory initially advanced for solid bodies can be applied also to liquid systems, was advanced in 1948 since then considerable efforts have been made to develop it and verify it experimentally. In most liquid systems, localization of an electron is followed by the formation of a cavity where most of the density of the solvated electrons is concentrated. The cavity is surrounded by the orientated dipoles of the solvent. Usually, the radius of this cavity equals about 3-3.5 A which conforms to a solvated-electron molar volume of 70-100 cm . This is the reason why solutions with large concentrations of solvated electrons have a lower density. 

Many groups have investigated the suitability of various solvents for use in LM systems and have attempted to describe the relationship between solvent characteristics and transport properties [93-96]. Of all solvent properties, dielectric constant seems to be most predictable in its effect on transport [92]. For solvents, such as the halocarbons, transport usually decreases with increasing dielectric constants [93]. Figure 2.10 shows this trend for alkali metals binding by dicyclohexano-18-crown-6 in a number of alcohols. This trend holds true for many simple systems, but it breaks down under more complex conditions. Solvent donor number, molecule size, solvent viscosity, carrier solubility in the solvent, permanent and induced dipole moments, and heats of vaporization are important [94]. 

A polarisable apolar molecule can be represented by a dielectric sphere of radius a and relative permittivity 8, bearing no diarge distribution vdiidi can produce singularities for r g a. An ion or polar molecule situated in the vidnity of this sphere give rise to an induced dipole moment in and hence to an electrostatic field around the dielectric sphere. The solvent around the apolar molecule is considered as a homogeneous medium of relative permittivity s. 

Solvent oscillators are localised but their induced dipole moments increase with molecular size. On this basis we expect dispersion forces to be greater between picrate and methanol than between picrate and water. This accounts for the change in equilibrium constant of the reaction... 

When the free electrostatic charge in phase a turns to zero, = 0 and = X . The surface potential of a liquid phase is dictated by a certain interfacial orientation of solvent dipoles and other molecules with inherent and induced dipole moments, and also of ions and surface-active solute molecules. For solid phases, it is associated with the electronic gas, which expands beyond the lattice (and also causes the formation of a dipolar layer) other reasons are also possible. 

---