Molecular interactions dispersion coefficients

The effect of molecular interactions on the distribution coefficient of a solute has already been mentioned in Chapter 1. Molecular interactions are the direct effect of intermolecular forces between the solute and solvent molecules and the nature of these molecular forces will now be discussed in some detail. There are basically four types of molecular forces that can control the distribution coefficient of a solute between two phases. They are chemical forces, ionic forces, polar forces and dispersive forces. Hydrogen bonding is another type of molecular force that has been proposed, but for simplicity in this discussion, hydrogen bonding will be considered as the result of very strong polar forces. These four types of molecular forces that can occur between the solute and the two phases are those that the analyst must modify by choice of the phase system to achieve the necessary separation. Consequently, each type of molecular force enjoins some discussion. 

Here, is the distance between atoms i andj, C(/ is a dispersion coefficient for atoms i andj, which can be calculated directly from tabulated properties of the individual atoms, and /dampF y) is a damping function to avoid unphysical behavior of the dispersion term for small distances. The only empirical parameter in this expression is S, a scaling factor that is applied uniformly to all pairs of atoms. In applications of DFT-D, this scaling factor has been estimated separately for each functional of interest by optimizing its value with respect to collections of molecular complexes in which dispersion interactions are important. There are no fundamental barriers to applying the ideas of DFT-D within plane-wave DFT calculations. In the work by Neumann and Perrin mentioned above, they showed that adding dispersion corrections to forces... 

The set of coefficients (s, p, a, b, constant) obtained from fitting experimental Kjat values for olive oil, as well as for some other organic solvents, are summarized in Table 6.2. These constants clearly quantify the importance of the individual inter-molecular interactions for each solvent. For example, n-hexadecane has nonzero s and p coefficients, representing this solvent s ability to interact via dispersive and polarizability mechanisms. But the a and b coefficients are zero, consistent with our expectation from hexadecane s structure that hydrogen bonding is impossible for this hydrocarbon. At the other extreme in polarity, methanol has nonzero coefficients for all of the terms, demonstrating this solvent s capability to interact via all mechanisms. 

It has been shown that the free energy of adhesion can be positive, negative, or zero, implying that van der Waals interactions can be attractive as well as repulsive [130,133,134]. While Eq. (14) can, strictly speaking, be expected to hold only for systems that interact by means of dispersion forces only, there are no restrictions on Eq. (15). Since this equation describes very well the fundamental patterns of the behavior of particles, including macromolecules, independent of the type of molecular interactions present, it was found to be convenient to define an "effective Hamaker coefficient that reflects the free energy of adhesion [130],... 

In this way, for each H atom, the calculated dipole pseudospectra a, si] i = 1,2, , N of Table 4.2 can be used to obtain better and better values for the C6 London dispersion coefficient for the H—H interaction a molecular (two-centre) quantity C6 can be evaluated in terms of atomic (one-centre), nonobservable, quantities, a, (a alone is useless). The coupling between the different components of the polarizabilities occurs through the denominator in the London formula (4.19), so that we cannot sum over i or / to get the full, observable,12 aA oraB. 

Magnasco, V. and Figari, G. (2009) Reduced dipole pseudospectra for the accurate tabulation of Cg dispersion coefficients. Theoret. Chem. Acc., 123, 257-263. Magnasco, V., Figari, G., and Costa, C. (1988) Long-range coefficients for molecular interactions. J. Mol. Struct. Tbeochem, 164, 49-66. 

Methods to compute the interaction energy of a cluster of atoms and molecules have been developed at different levels of sophistication. The development of quantum chemical methods and computers has permitted us to accurately model the interaction energy of assembhes of molecules. During the last decades, Anthony Stone has played a prominent role in the endeavour of accurately modelling molecular properties and interactions from quantum chemistry. The IMPT theory, models of distributed multipoles, distributed polarizabilities, distributed dispersion coefficients, anisotropic repulsion, developed by Stone and collaborators, allow us to build accurate interaction potentials from quantiun chemistry. 

The theoretical treatments of Ajg discussed here were motivated by the question of the effects of molecular weight dispersion on measured second virial coefficients. Once Ajf Mjy Mj ) is available it is obvious in principle how to obtain A 2 or. 4 2 for any desired form of distribution. Detailed calculations using the hard-spherelike interaction model with the familiar Schulz-Zimm distribution indicate that the ratio of virial coefficients increase wi out limit with the... 

Where FCl is the solute gas-liquid partition coefficient, r is the tendency of the solvent to interact through k- and n-electron pairs (Lewis basicity), s the contribution from dipole-dipole and dipole-induced dipole interactions (in molecular solvents), a is the hydrogen bond basicity of the solvent, b is its hydrogen bond acidity and I is how well the solvent will separate members of a homologous series, with contributions from solvent cavity formation and dispersion interactions. 

The coefficients Cn may be derived from the (imaginary) frequency dependent polarizabilities summed over the entire frequency range [46]. If one employs only dipole polarizabilities the dispersion expansion is truncated at the leading term, with n = 6. In the current EFP2 code, an estimate is used for the n = 8 term, in addition to the explicitly derived n = 6 term. Rather than express a molecular C as a sum over atomic interaction terms, the EFP2 dispersion is expressed in terms of LMO-LMO... 

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