Model Onsager

The Isodensity PCM (IPCM) model defines the cavity as an isodensity surface of the molecule. This isodensity is determined by an iterative process in which an SCF cycle is performed and converged using the current isodensity cavity. The resultant wavefunction is then used to compute an updated isodensity surface, and the cycle is repeated until the cavity shape no longer changes upon completion of the SCF. 

An isodensity surface is a very natural, intuitive shape for the cavity since it corresponds to the reactive shape of the molecule to as great a degree as is possible (rather than being a simpler, pre-defined shape such as a sphere or a set of overlapping spheres). 

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. 

238 Exploring Chemistry with Electronic Structure Methods 

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The Electrostatic Contribution to the Free Energy of Solvation The Born and Onsager Models... 

This can be solved analytically only for a few simplified systems. The Onsager model uses one of the known analytic solutions. 

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. 

Onions, dehydrated Onium Onium salts On-line databases On-line sampling ONO802, [64318-79-2] Onsager model Onychomycosis Onyx... 

Fig. 7. The field-dependence of the charge-generation efficiency of a 2.0- lm thick (0) a l.l-).tm thick ( ), and 1.8-).tm thick (A) fuUerene/PMPS film obtained with positive charging and 340-nm irradiation (A). The soHd lines are calculated from the Onsager model. The best-fit curve is obtained with Tq = 2.7 nm and = 0.85. Also plotted is the charge-generation efficiency of a fuUerene/PVK film (+) obtained with positive charging and 340-nm irradiation (B). The soHd lines are calculated from the Onsager model. The best-fit curve is obtained with = 1.9 nm and = 0.9 (13).

The initial election—hole separation distance, and the quantum yield, ( )q, are derived by fitting with the Onsager model. When the initial quantum yield,... 

Experimental Values of Charge-Generation Efficiencies. In this section the charge-generation efficiencies of many polymeric photoconductors are compared (Table 3). When the experimental data has been fitted to the Onsager model, the initial electron—hole separation distance,... 

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). 

A molecular volume calculation to estimate Oq for the Onsager model. 

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. 

As the plot of AE indicates, the energy difference between the two forms decreases in more polar solvents, and becomes nearly zero in acetonitrile. The left plot illustrates the fact that the IPCM model (at the B3LYP/6-31+G(d) level of theory) does a much better job of reproducing the observed solvent effect than the two Onsager SCRF models. In contrast, the Onsager model at the MP2 level treats the solvated systems more accurately than it does the gas phase system, leading to a poorer value for the solvent effect. ... 

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. 

Ab initio Simulating MeCN (the Onsager Model), semiempirical The COSMO Model, MOPAPC 93 keywords NSPA = 60, EPS = 35.9, TS, PRECISE. 

Both of these substitution pathways in MeCN solution have been simulated using the Onsager model (Tables IV and V). Whereas pathway b is favored in the gas phase, inclusion of solvent effects in the calculations causes pathway a to be energetically favored. Substitution of Cl via pathway a is now 1.6 kcal/mol more favorable. In addition, TS(X)/TS(Pyr) calculations (Scheme 15) for the OMe (40) and OSiMes (41) cations have been performed. TS(X) of both 40 and 41 remain significantly disfavored (+66.9 kcal/mol and +46.6 kcakmol, respectively), thus indicating that pathway b should be preferred in MeCN.Tliese calculations are in complete agreement with experimental observations. 

Using the Onsager model, the function Av-l(t) can be calculated for all time domains of dielectric relaxation of solvents measured experimentally for commonly used liquids (see, for example, [39]). Such simulations, for example, give for alcohols, at least, three different time components of spectral shift during relaxation, which are due to appropriate time domains of solvents relaxation. 

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 ... 

As the temperature is decreased, the chains become increasingly rigid zc then approaches 1 if we assume that there is only one fully ordered crystalline structure and Zconf for the liquid becomes smaller than 1. This means that, at this level of approximation, the disordered state becomes less favorable than the crystalline ground state. A first-order disorder-order phase transition is expected to occur under these conditions. Flory interpreted this phase transition as the spontaneous crystallization of bulk semiflexible polymers [12], However, since the intermolecular anisotropic repulsion essential in the Onsager model is not considered in the calculation, only the short-range intramolecular interaction is responsible for this phase transition. 

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