bond lengthr¼rC–Cl"2.426) makes the graph symmetrical about the energy
axis, as it should be presented for this identity reaction. The energies are room
temperature enthalpies relative to a state of little Cl"/CH 3 Cl interaction (rC–Cl¼
25 A ̊,r¼22.574 A ̊). The calculations were done as a series of constrained
geometry optimizations with fixed Cl"/C distance; the transition state (imagi-
nary frequency 470icm"^1 ; C–Cl 2.426 A ̊) was calculated without constraints.
These results are in accord with the accepted mechanism for the SN2 reaction in
water: a smooth, one-step process with no intermediates [ 32 ]. This calculation
agrees with a valence bond-calculated profile and activation energy (109 kJ mol"^1
[ 33 ]), and with molecular dynamics activation energies (113 kJ mol"^1 [ 34 , 35 ]; those
are free energies and the 101 kJ mol"^1 of Fig. 1 is an enthalpy, but the difference
is not expected to be large here (Section 5.5.2.1a). The experimental free energy
of activation is 111 kJ mol"^1 [ 36 ]. The respectable quantitative agreement with
experiment for our modest computational level is gratifying, but for us the salient
point is the smooth one-step profile: we now contrast this with the gas phase
reaction.
Compare Fig.8.2with Fig.8.3, this latter being the calculated reaction profile for
the SN2 attack of chloride ion on chloromethane in thegasphase; otherwise, the
calculation was implemented as for the water continuum calculation of Fig.8.2.
Some of the data for Fig.8.3are given in Table8.2. In the gas phase calculation,
as Cl"approaches CH 3 Cl the energy falls, rather than rises, until a “complex”, a
somewhat vague word in chemistry, sometimes indicating a weakly bound mole-
cule, is formed, then the energy rises toward the transition state. The complex is
indeed weakly bound: its energy of"39 kJ mol"^1 compared to separated Cl"þ
CH 3 Cl is only that of a moderately strong hydrogen bond [ 37 ], while a typical
covalent bond has an energy of about 400 kJ mol"^1. The simplest, albeit perhaps
incomplete, picture of the complex is that the chloride ion is electrostatically
attracted to the partial positive charge on the carbon of chloromethane, and nicely
consonant with this, in an electron density slice the contour lines show a sharp
contrast between the short covalent C–Cl bond (1.856, cf. 1.803 A ̊in CH 3 Cl) and the
long (3.200 A ̊) “complex” bond (this author’s observations). It thus seems to be an
ion-dipole complex. The transition state and the complex were calculated without
constraints. The negative activation energy is not paradoxical, as the proximate
reactant for its formation is the complex, making the barrier from this"2.1"
("39.0) kJ mol"^1 ¼36.9 kJ mol"^1.
These results are in accord with the long-accepted mechanism for the SN 2
reaction in the gas phase: experiments using ion cyclotron resonance were inter-
preted in the way shown for the calculations of Fig. 2: “It is not possible to explain
the observed rates on the basis of a single-well potential” [ 38 ]; the profile in Fig. 2 is
called adouble-well potential. Quantitative information comes from benchmark
calculations by Bento et al., who even checked for relativistic effects, which were
found to be negligible [ 39 ]. CCSD(T)/aug-cc-PVQZ (Sections 5.4.3 and 5.3.3)
gave relative energies of"44 andþ10.5 kJ mol"^1 , compared to"39 and"2.1 kJ
mol"^1 at out modest computational level. That the transition state lies slightly
8.1 Solvation 529