Solutes-solvent interaction energies

Fig. 3. Functions in the integrand of the partition function formula Eq. (6). The lower solid curve labeled Pq AU/kT) is the probability distribution of solute-solvent interaction energies sampled from the uncoupled ensemble of solvent configurations. The dashed curve is the product of this distribution with the exponential Boltzmann factor, e AJJ/kT r the upper solid curve. See Eqs. (5) and (6).

To make an accurate FEP calculation, a good description of the system is required. This means that the parameters for the chosen force field must reproduce the dynamic behaviour of both species correctly. A realistic description of the environment, e.g. size of water box, and the treatment of the solute-solvent interaction energy is also required. The majority of the parameters can usually be taken from the standard atom types of a force field. The electrostatic description of the species at both ends of the perturbation is, however, the key to a good simulation of many systems. This is also the part that usually requires tailoring to the system of interest. Most force fields require atom centered charges obtained by fitting to the molecular electrostatic potential (MEP), usually over the van der Waals surface. Most authors in the studies discussed above used RHF/6-31G or higher methods to obtain the MEP. 

The physical interpretation of these equations is that when the solute polarizes the solvent to lower the solute-solvent interaction energy by an amount Gss,half the gain in free energy is canceled by the work in polarizing the solvent, which raises its own internal energy. 

The solvent polarization contribution (third term of Eq (81)), may be obtained from the fundamental theorem of the RF theory, relating the electrostatic solute-solvent interaction energy and the solvent polarization contribution [2,3,7,14] ... 

Wi(y) can be a function of the solute-solvent interaction energy, the orientation, the distance, etc. Wi(y) is usually chosen as an inverted power of the distance r between the solute and the g solvent molecule 1/r, 1/r2 or even l/(r2+ C), C being a given constant [31]. 

In solution or vapor phase growth, the strength of the solute-solvent interaction energies, namely the species and types of solvent component and transport agent. 

Even if crystals grow from the same aqueous solution, there are differences in Habitus. NaC103 crystals, for example, grow easily as polyhedral crystals, whereas NH Cl crystals always grow as dendrites, and NaCl crystals appear as hopper crystals. If Pb or Mn ions are added, cubic crystals of NaCl bounded by flat 100 faces may be obtained quite easily, but if NaCl is grown in pure solution all crystals take a hopper form, unless great care is taken to keep the supersaturation very low. These differences occur because the solute-solvent interaction energies, and, as a result, the values of Ap,/kT and A/x/kT, are different for different crystals. 

The reasons why we have Habitus variation for vapor and solution phases, and for different solvents when the crystals grow from the solution phase, can therefore be understood in terms of the factor of steps because of the different solute-solvent interaction energies. 

Since the edge free energies, y, are different for the vapor and solution phases, and particularly for solute-solvent interaction energies, the same crystal species will exhibit different Tracht and Habitus in different ambient phases and different solvents. If impurities are present in the system, this affects y and the advancing rates of steps. There are two opposite cases in impurity effects, and, depending on the interface state, some will promote growth, whereas others will suppress growth. 

An early crossover to the hydrodynamics takes place when the solute-solvent interaction energy is changed along with the solute-solvent size ratio. This early crossover is found to be due to the nonvanishing contribution from the density mode for increased solute-solvent interaction. This density mode contribution leads to a faster decrease of the microscopic contribution to the diffusion and thus an early crossover to the hydrodynamic picture. 

The nature of the solvent is introduced by the factor kP = k L, where, according to Liptay s theory,70 71 the solvent polarity function L depends on e and n of the solvent as well as on the polarizability a of the solute. Following a proposal66,67 by Bakhshiev, a can be approximated by setting a, = 0.5r], eventually yielding70,71 for the total solute-solvent interaction energy W after solvent relaxation (with k ks Ars = k = const) ... 

Since solvatochromic parameters are derived from direct measurements of the energy resulting from intermolecular interaction, they can be used to predict solubility, which is determined by solute-solute, solvent-solvent, and solute-solvent interaction energies. For nonself-associated liquid aliphatic compounds with a weak or nonhydrogen-bond donor (Taft etal., 1985 Kamlet etal., 1986), the solubility in water at 29S was related to molar volunWjf, hydrogen-bond basicity j and polarity/polarizability (jf) by a linear solvation energy relationship (LSER) as in Equation 3.55 ... 

In the standard continuum solvation model, exemplified by the Polarizable Continuum Model (PCM) we developed in Pisa [9], the solute-solvent interaction energies are described by four Qx operators, each having a clearly defined physical nature. Each term gives a contribution to the solvation energy which has the nature of a free energy. The free energy of M in solution is thus defined as the sum of these four terms, supplemented by a fifth describing contributions due to thermal motions of the molecular framework ... 

This functional is also physically motivated as it expresses the balance of two terms a favorable (negative) solute-solvent interaction energy and an unfavorable (positive) solvent-solvent interaction. At equilibrium the second term is equal to half of the first as expected also from basic electrostatic arguments. 

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