terms of electron kinetic energy, electron-nucleus attraction, and electron-electron
repulsion. With a basis set {f 1 ,f 2 ,...} (e.g.Section 5.2.3.6), a Fock matrix is
constructed with elementshfi|H|^fji(Dirac notation,Section 4.4.1.2). The usual
SCF procedure (Section 5.2.3.6.5) gives a wavefunction and energy for the solvated
molecule. The wavefunction can be used to calculate the usual properties, like
dipole moment and spectra [ 24 ]. Particularly relevant to solute–solvent interactions
is the fact that the charge distributionr(r) of the solute molecule (Eq.8.2) polarizes
the solvent continuum of the cavity wall, which in turn altersr(r), and so on.
Because of the polarization of the cavity wall these methods are calledpolarized
continuum methods, PCM, and since the final interaction energy must be calculated
iteratively, in this context the SCF procedure is calleda self-consistent reaction
field, SCRF, calculation. SCRF calculations have been implemented in ab initio,
semiempirical and DFT calculations. Variations on the PCM method are IPCM,
isodensity PCM, which simplifies the calculation by using a vacuum isodensity
charge surface [ 25 ], and CPCM, a PCM implementation of the conductor-like
screening model [ 20 , 26 ]. The conductor-like screening model, COSMO, simplified
the calculation by using a conducting medium (einfinite) and introducing the
solvent dielectric constant as a correction factor [ 27 ]. COSMO-RS (real solvents),
an improved version, dispensed with the dielectric constant, which Klamt and
coworkers distrust in the microscopic context, by eschewing solvent-specific para-
meters and a continuous solvent medium (although it still seems to be regarded as
being in the spirit of continuum methods) and applying statistical thermodynamics
to solute–solvent fragment surface interactions. COSMO-RS uses surface charges
for both solute and solvent and empirical parameters, eight general ones and two for
each atom, rather than for each solvent [ 28 , 29 ]. COSMO-RS calculations are
effective at reproducing thermodynamic and other properties of solutions, as may
be seen by examining the numerous papers since 1993 by A. Klamt or Klamt and
coworkers; further information is available from the company COSMOlogic and
Klamt’s book [ 30 ]. All these continuum methods are very fast when used, as is
usually the case, with gas phase geometries followed by single-point calculations in
solvent. The free energy of solvation is usually the most relevant energy quantity
sought; the keywords for obtaining this depend on the program.
We will look at two important processes which have been studied by implicit
solvation techniques:
1.The SN2 reaction in solution.We saw above the application of microsolvation
to SN2 reactions ([ 14 , 15 ]). Let us now look at the chloride ion-chloromethane
SN2 reaction in water, as studied by a continuum method. Figure8.2shows a
calculated reaction profile (potential energy surface) from a continuum solvent
study of the SN2 attack of chloride ion on chloromethane (methyl chloride) in
water. Calculations were by the author using B3LYP/6-31+G* (plus or diffuse
functions in the basis set are considered to be very important where anions are
involved:Section 5.3.3) with the continuum solvent method SM8 [ 22 ] as
implemented in Spartan [ 31 ]; some of the data for Fig.8.2are given in Table8.1.
Using as the reaction coordinaterthe “deviation” from the transition state C–Cl
8.1 Solvation 527