Handbook of Solvents - George Wypych - ChemTech - Ventech!

11.1 Theoretical treatment of solvent effects 667
s 1
s ⎤ 1
( ) ( ) ()
⎡ 0 0 + + −1
Etot = P H + H + G + G f
⎣
⎢ μν μν μν μν μν
⎦
⎥
− ε ZBA BZ+ Enn + Enes
[11.1.93]
2
2
where Enn is solute nuclear-nuclear repulsion and Enes is the solvation energy related to the
0 0
dispersion and repulsion between the solute and solvent, and cavity formation; Hμν and Gμν
are the one-electron and two-electron parts of the Fock matrix for the isolated solute, respectively,
and Pμν are the density matrix elements. The solvent perturbations to the corresponding
operators have been expressed as
and
s
H =−f
() ε
ZBA BL
+ + −1
μν μν
s ⎛
+ ⎞ −1
Gμν =−f()
ε ⎜∑PλσLλσ
⎟A
L
⎝λσ
, ⎠
μν
[11.1.94]
[11.1.95]
where A and B aretheNxNsquare matrices (N - number of atomic nuclei in the solute molecule)
with the elements defined by equations [11.1.90] and [11.1.92]. The matrices Lμν consist of the one-electron integrals [11.1.91]. The first and second derivatives needed for
the calculation of the molecular potential surfaces and the respective solvent effects on vibrational
spectra have been also supplied within the framework of GCOSMO approach. 53 A
semi-quantitative agreement between the computational and experimental results has been
obtained for the vibrational frequencies of acetone in water.
Several approaches have been developed to account for the electron correlation effects
on the solvation energy of both the ground and the excited states of the molecule in the solution.
A multiconfigurational self-consistent reaction field (MC SCRF) theory has been proposed
as based on the classical Onsager’s reaction field model. 55 Notably, the higher order
electrical moments of the solute molecule and the respective reaction field in the solvent
were taken into account within this method. Thus, the dielectric solvation energy of a solute
in a given state embedded into a linear isotropic medium has been calculated as the product
m
of the expectation values for the reaction field �R l � and the respective multipole charge mo-
m 55-58
ments �Ml � of the solute
where
and
1
∑
+
m
E el =−
l
2 lm ,
m
Ml ∑
k
R M
m
k l
( )
m
l
= ZS R − S
m
k l
[11.1.96]
[11.1.97]
m
m
R = f M
[11.1.98]
l
l