Handbook of Solvents - George Wypych - ChemTech - Ventech!

718 Ranieri Urbani and Attilio Cesàro
The free energy of dispersion, G disp, in equation [12.2.2] takes into account both attractive
and repulsive non-bonding interactions and is expressed as a combination of the London
dispersion equation and Born-type repulsion: 51
II u v −6
Gdisp =−0.
327Nvαuα
v ruv
[12.2.5]
I + I
u v
where:
α molecular polarizability
I ionization potential
Nv nearest-neighbor solvent molecules
Nv is the number of molecules surrounding the solute molecule in a given conformation and
is calculated from the following equation: 52
( 2 )
3 N
N =
⎡
3
a + a −a
⎤⎛4π
⎜ u
v ⎣⎢ u v ⎦⎥⎜
⎝ 3Vv
A
⎞
⎟
⎠
3
where:
Vv solvent molar volume
NA Avogadro number
In order to elucidate the effect of different solvents on the conformation, the energy
differences between conformers in a given solvent are more relevant than the absolute solvation
energies in each solvent. In particular, it is important that the perturbation effect on
the detailed shape in the low energy regions of the conformational map. Figure 12.2.8
shows the free-energy of solvation and energy contributions for the maltose dimer as a function
of ψ calculated at ϕ=-30° and refers to the energy of the (-30°, 180°) conformer for two
solvents, water and DMSO (Figure 12.2.8 a and b, respectively). In this section, the cavity
term is a complex function of the size of the maltose molecule, as determined by the spatial
orientation of the two glucose residues. The cavity energy is, by definition, always unfavorable;
the more expanded the conformers, which are usually located in the low energy region
of the map (around ψ=0° for maltose), the larger the Gcav due to the size of larger cavities to
be created in the solvent.
The electrostatic free-energy, Gel, increases with the dipole and quadrupole moments
of solute molecule and decreases with the radius of the cavity. On the other hand, the dipole
moment μ is a function of dihedrals ϕ and ψ and for maltose has two large maxima around
(ϕ, ψ)=(-40°,0°) and (180°, 140°) which is in agreement with the major contributions of Gel shown in Figure 12.2.8. The electrostatic free-energy (eq. [12.2.4]) is also dependent on the
solvent dielectric constant and increases in passing from DMSO (ε=46.68 debye) to water
(ε=78.30 debye) at 25°C. The dispersion term (eq. [12.2.5]) makes a significant contribution
(-20 to -70 kJ·mol -1 ) to the absolute value of solvation free-energy but the angular dependence
is very small giving an almost equal contribution to the energy of conformers.
In an early paper 53 it was shown that, in the comparative cases of cellobiose and maltose,
the probability distribution of conformers (Figure 12.2.9) is affected by the presence of
the solvent, changing the shape of the function from one solvent to another. The minimum
of the maltose map goes from (-20°,-30°) to (-10°,-20°) in water and DMSO, while that of
cellobiose map goes from (0°, 50°) to (-30°, -20°) in both solvents. 53 These solvent perturbations
(apparently small) on the conformational energies have a great effect on the proba-