Onsager dipole model

Note that systems having a dipole moment of 0 will not exhibit solvent effects for the Onsager SCRF model, and therefore Onsager model (SCRF=Dipole) calculations performed on them will give the same results as for the gas phase. This is an inherent limitation of the Onsager approach. 

Continuum models of solvation treat the solute microscopically, and the surrounding solvent macroscopically, according to the above principles. The simplest treatment is the Onsager (1936) model, where aspirin in solution would be modelled according to Figure 15.4. The solute is embedded in a spherical cavity, whose radius can be estimated by calculating the molecular volume. A dipole in the solute molecule induces polarization in the solvent continuum, which in turn interacts with the solute dipole, leading to stabilization. 

The salient features of quantum formulation of Onsager reaction field model (dipole model) is described here. In this method, the reaction field is treated as perturbation to the Hamiltonian of the isolated molecule. If H0 is the Hamiltonian of the isolated molecule and HR[ is the reaction field [21], the Hamiltonian of the whole system (Hlol) is represented as... 

The energy curves in Figure 22 are closely related to the Marcus-Hush theory for electron transfer. The formalism we employ emphasizes a dipole model for the solute solvent interaction, i.e., an Onsager cavity model. However, a Born charge model based on ion solvation as something in between [135] would be essentially equivalent because we do not attempt to calculate Bop and Bor but rather determine them empirically. 

The key differences between the PCM and the Onsager s model are that the PCM makes use of molecular-shaped cavities (instead of spherical cavities) and that in the PCM the solvent-solute interaction is not simply reduced to the dipole term. In addition, the PCM is a quantum mechanical approach, i.e. the solute is described by means of its electronic wavefunction. Similarly to classical approaches, the basis of the PCM approach to the local field relies on the assumption that the effective field experienced by the molecule in the cavity can be seen as the sum of a reaction field term and a cavity field term. The reaction field is connected to the response (polarization) of the dielectric to the solute charge distribution, whereas the cavity field depends on the polarization of the dielectric induced by the applied field once the cavity has been created. In the PCM, cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly describe the response of the molecular solutes to the Maxwell field in the liquid, both static E and dynamic E, [8,47,48] (see also the contribution by Cammi and Mennucci). 

In contrast, the Onsager—Kirkwood model provides a polarizability in polar liquids larger than that in vapors.21 This is a result of the increase of the dipole moment by the strong electric field, which is generated when a molecule with a permanent dipole moment is introduced in a polarizable medium (Onsager), and the correlation between the orientations of neighboring molecules (Kirkwood).21... 

As emphasized, the Born—Kirkwood—Onsager (BKO) approach includes only the solute s monopole and dipole interaction with the continuum. That is, the full classical multipolar expansion of the total solute charge distribution is truncated at the dipole term. This simplification of the electronic distribution fails most visibly for neutral molecules whose dipole moments vanish as a result of symmetry. A distributed monopole or distributed dipole model is more... 

The charge distribution of the molecule can be represented either as atom-centred partial charges or as a multipole expansion. For a neutral molecule, the lowest order approximation considers only the dipole moment. This may be a quite poor approximation, and fails completely for symmetric molecules that do not have a dipole moment. For obtaining converged results, it is often necessarily to extend the expansion up to order six or more, i.e. including dipole, quadrupole, octupole, etc., moments. Furthermore, only for small and symmetric molecules can the approximation of a spherical or ellipsoidal cavity be considered realistic. The use of the Bom/ Onsager/Kirkwood models should therefore only be considered as a rough estimate of the solvent effects, and quantitative results can rarely be obtained. 

The cavity size in the Bom/Onsager/Kirkwood models strongly influences the calculated stabilization. Unfortunately, there is no consensus on how to choose the cavity radius. In some cases, the molecular volume is calculated from the experimental density of the solvent and the cavity radius is defined by equating the cavity volume to the molecular volume. Alternatively, the cavity size may be derived from the (experimental) dielectric constant and the calculated dipole moment and polarizability. In any case, the underlying assumption of these models is that the molecule is roughly spherical or ellipsoidal, which is only generally true for small compact molecules. 

The point-dipole approximation used by Onsager is not essential higher multipole moments have been progressively included in the models with spherical or ellipsoidal shapes. Important progress has been the introduction of quantum mechanical descriptions of the solute. This change created new ways of using Onsager s model. 

With these and other results it seems abundantly clear that calculations however refined for point dipole models lead to values of g considerably larger than that of water and a fortiori of normal polar liquids which as discussed in 2 2 are moderately well described by Onsager s equation This might be called an experimentalist s assessment That of theorists seems to be embodied in such statements ad We now know that the Onsager model seriously underestimates (30) and breakdown of Onsager s theory (31) To the writer these are true in the sense of calculations for point dipoles but beg the question of why Onsager s equation for a point dipole in continuum model works as well as it does ... 

At = 1 Eq. (3.4) becomes an analog of the Onsager dipole energy (a model of the reactive field)... 

The Onsager model describes the system as a molecule with a multipole moment inside of a spherical cavity surrounded by a continuum dielectric. In some programs, only a dipole moment is used so the calculation fails for molecules with a zero dipole moment. Results with the Onsager model and HF calculations are usually qualitatively correct. The accuracy increases significantly with the use of MP2 or hybrid DFT functionals. This is not the most accurate method available, but it is stable and fast. This makes the Onsager model a viable alternative when PCM calculations fail. 

A variety of methodologies have been implemented for the reaction field. The basic equation for the dielectric continuum model is the Poisson-Laplace equation, by which the electrostatic field in a cavity with an arbitrary shape and size is calculated, although some methods do not satisfy the equation. Because the solute s electronic strucmre and the reaction field depend on each other, a nonlinear equation (modified Schrddinger equation) has to be solved in an iterative manner. In practice this is achieved by modifying the electronic Hamiltonian or Fock operator, which is defined through the shape and size of the cavity and the description of the solute s electronic distribution. If one takes a dipole moment approximation for the solute s electronic distribution and a spherical cavity (Onsager s reaction field), the interaction can be derived rather easily and an analytical expression of theFock operator is obtained. However, such an expression is not feasible for an arbitrary electronic distribution in an arbitrary cavity fitted to the molecular shape. In this case the Fock operator is very complicated and has to be prepared by a numerical procedure. 

The simplest SCRF model is the Onsager reaction field model. In this method, the solute occupies a fixed spherical cavity of radius Oq within the solvent field. A dipole in the molecule will induce a dipole in the medium, and the electric field applied by the solvent dipole will in turn interact with the molecular dipole, leading to net stabilization. 

We ran an SCRF single point energy calculation for gauche dichloroethane conformers in cyclohexane (e=2.0), using the Onsager model at the Hartree-Fock and MP2 levels of theory (flfl=3.65) and using the IPCM model at the B3LYP level. The 6-31+G(d) basis set was used for all jobs. We also ran gas phase calculations for both conformations at the same model chemistries, and an IPCM calculation for the trans conformation (SCRF=Dipole calculations are not necessary for the trans conformation since it has no dipole moment). 

Remember that the trans form of dichloroethane has no dipole moment, so it is not necessary to compute its energy in solution with the Onsager model. 

One drawback of the original Onsager model is that molecules that have no dipole moment do not show any stabilization. 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

The spherical cavity, dipole only, SCRF model is known as the OnMger model.The Kirkwood model s refers to a general multipole expansion, if the cavity is ellipsoidal the Kirkwood—Westheimer model arise." A fixed dipole moment of yr in the Onsager model gives rise to an energy stabilization. 

FL, and the difference in dipole moments determined from the plot is 2.36 D if the Onsager radius is 0.33 nm [53]. The Onsager cavity radius was obtained from molecular models where the molar volumes were calculated by CAChe WS 5.0 computer program. The simplest method to estimate the cavity radius is to assume a = (3y/47r) 3, where V is the volume of the solute. 

Of course, there are some uncertainties in this procedure, as the Onsager model describes the structures of solution and a solute only approximately. It can be noted that there is a good opportunity to calculate dipole moments, exactly, their ratio, in the simpler way using the relative shifts of absorption, and fluorescence spectra. As follows from (16) and (17), dividing them by proper parts we may obtain the following relation ... 

In the Onsager s SCRF model, the solute is placed in a cavity immersed in a continuous medium with a dielectric constant e. The molecular dipole of the solute induces a dipole in the solvent, which in turn interacts with the molecular dipole, leading to a net stabilization effect. 

Dielectric constants are determined for pure liquid dimethylsiloxane oligomers. Mean-square dipole moments, calculated from the Onsager equation, are in good agreement with predicted values based on the RIS model (S 117) with neighbor dependence and chain conformational energies obtained in an independent analysis of the random-coil dimensions of such chains. In addition, the observed temperature coefficients of are in qualitative agreement with calculated results. 

On the basis of an Onsager cavity (23) model of dielectrics applied to a polar solute with an intrinsic dipole movement /xr° in its rth electronic state, Mazurenko gives an equation for the orientational free energy of the solute molecule in a pure polar solvent environment, which can be identified as equivalent to u/jlpe chem, thus 2... 

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