Handbook of Solvents - George Wypych - ChemTech - Ventech!

674 Mati Karelson
Table 11.1.5. The INDO/CI calculated solvatochromic shifts Δν (from the gas phase to
cyclohexane) of some aromatic compounds and the respective experimental data in
low polarity solvents (cm -1 ) 81
Compound Transition Δν (calc) Δν (exp)
Benzene
1
B2u -316 -209 a
Naphthalene
1
Lb(x)
1
Lb(y)
-332
-879
-300 b ; -275 a
-950 b ; -902 a
Chrysene
Azulene
1 Lb( 1 B u)
1 La( 1 B u)
1 Bb( 1 B u)
1 Lb(y)
1 La(x)
1 Kb(y)
1 Bb(x)
a in n-pentane, b in cyclohexane, c in 2-chloropropane
-243
-733
-1666
+162
-288
-446
-1475
-252 a
-1030 a
-1620 a
+164 c
-333 c
-285 c
-1650 c
The equation [11.1.130] has been used within the semiempirical quantum-chemical
INDO/CI formalism to calculate the solvent shifts of some aromatic compounds in cyclohexane.
81 The results compare favorably with the experimental data for some nonpolar solvents
(cf. Table 11.1.5).
11.1.5 SUPERMOLECULE APPROACH TO THE INTERMOLECULAR
INTERACTIONS IN CONDENSED MEDIA
The supermolecule approach to the calculation of solute-solvent interaction energies is
based on the discrete molecular representation of the solvent. The supermolecule can be
treated quantum-mechanically as a complex consisting of the central solute molecule and
the surrounding closest solvent molecules. This supermolecule complex can be treated individually
or as submerged into the dielectric continuum. 82 In the last case, some continuum
theory (SCRF, PCM) is applied to the supermolecule complex consisting of the solute molecule
and the solvent molecules in its first coordination sphere. 83-86 Therefore, the
short-range solute-solvent electron correlation, dispersion and exchange-repulsion interactions
are taken into account explicitly at the quantum level of theory as the electrons and nuclei
both from the solute and solvent are included explicitly in the respective Schrödinger
equation. The long-range electrostatic polarization of the solvent outside the first coordination
sphere is, however, treated according to the dielectric continuum theory. Thus, the energy
of solvation of a solute molecule can be expressed as follows:
S
E = Ψ � ( )
Ψ − Ψ � ( 0) Ψ −n
Ψ � ( 0)
H H H Ψ
sol SM SM
SM SM M SM SM S SM
[11.1.131]
where � (S)
H SM is the Hamiltonian for the supermolecule in the solution, and H� (0)
M and H� (0)
S are
the Hamiltonians for the isolated solute and the solvent molecules, respectively. In the last
equation, n denotes the number of the solvent molecules applied in the supermolecule, ΨSM is the total wavefunction of the supermolecule immersed into dielectric medium, and ΨM and ΨS are the wavefunctions for isolated solute and solvent molecules, respectively.