.
ECCC3 Paper 32
THE DISSOCIATION MECHANISM.
In order to understand the origin of a dissociation barrier,
very often, analyses rely on correlation diagrams and the origin of
barriers is usually explained in terms of
avoided crossings.
There is no doubt that correlation diagrams may prove valuable but
to rely on them exclusively will probably result in
missing important physical features.
As shown by Evleth and coworkers
[Evleth 81] ,
in a related situation,
correlation diagrams tend to be too schematic and are
loosing more and more significance with better basis sets.
It seems more revealing to continue our analysis of
the machinery with the help of MO graphics.
The H3O+
cation is thermodynamically stable (cf table 4)
, and therefore the cationic
core is very strongly bound.
With the D95**/R4 basis set, the
cation electronic formation energy is 0.281 Hartree
(7.64 eV ; 176.32 Kcal/Mole ).
Table 4. Electronic energies (D95**/R4 basis set)
| Species |
Energy (Hartree) |
| H3O. |
-76.506 |
| H3O+ |
-76.330 |
| H2O |
-76.049 |
| H. |
-0.500 |
In agreement with
previous
ab initio computations, we find also
that H3O. is thermodynamically
unstable (cf table 4) and that the dissociation products are
H2O and H..
With the D95**/R4 basis set,
the electronic dissociation energy is 0.043 Hartree
(1.17 eV ; 26.98 Kcal/mole ).
At the local minimum geometry, the Rydberg electron resides in a region
of space which is
as extended as in a 3s atomic orbital.
As it is revealed by a series of ab initio
computations along the
dissociation pathway (cf. table 5), performed
with a proton displacement step of 0.20 �, the MO contracts and fells on
the outgoing proton to become a 1s atomic atomic orbital inside an
hydrogen atom. This represents a dramatic spatial
contraction, somesort of a
nonradiative transition from a 3s to a 1s AO,
which would correspond to a jump by 2 principal
quantum numbers !.
Table 5. Dissociation pathway (D95**/R4 basis set).
| O--H Stretch (�) |
Energy(A.U) |
IP (eV) |
Spin Density on H in H2O |
Spin Density on H. |
| 1.05 |
-76.504 |
4.89 |
+ |
+ |
| 1.10 |
-76.502 |
5.17 |
+ |
+ |
| 1.15 |
-76.499 |
5.44 |
+ |
+ |
| 1.20 |
-76.498 |
5.71 |
+ |
+ |
| 1.25 |
-76.501 |
6.31 |
+ |
+ |
| 1.30 |
-76.503 |
6.80 |
- |
+ |
| 1.35 |
-76.507 |
7.29 |
- |
+ |
At the transition state geometry,
the magnitude of the collapse of the outer molecular orbital on the
dissociating proton
can be visualized in figures 5 and 6.
Figure 5.
Figure 6.
In table 6, we list the energies and
the geometries of the
Cs transition state obtained with the
VD/R6 and DH/R8 basis sets.
The transition state geometry features, along the dissociation
pathway, an O-H. stretch around 1.2 �.
The electronic dissociation barrier is quite small around 0.2 eV,
in agreement with previous ab initio computations. (cf Table 7)
Table 6. Energy and geometry at the transition state.
| Basis set | Energy( Hartree) |
Stretches ( �) |
Bends (degree) |
Electronic dissociation barrier ( kcal/mole ) |
| VD/R6 |
-76.512,586 |
1.172 ; 0.959 ; 0.959
|
107.216�; 107.216�; 108.087� |
4.229 |
| DH/R8 |
-76.499,920 |
1.173 ; 0.961 ; 0.961
|
107.907�; 107.907�; 108.359� |
4.294 |
So we can see that the so-called "Rydberg" 4A1
orbital is in fact strongly
dissociative, and has almost prevailed over the bonding
contributions of the inner MOs.
The H3O. radical has retained little
of the cohesion of its parent cation H3O+ (cf table 4).
In order to assess more realistically dissociation barriers, one
must take into account the zero-point energies (ZPE) at the local minimun and
at the transition state.
A normal mode vibrational analysis at the local minimun geometry and
at the transition state geometry are reported respectively in table 7 and 8.
Table 7. Vibrational analysis at the local minimum
| Basis set | Isotopomer |
Frequencies (cm-1) |
ZPE (kcal/mole) |
| VD/R6 |
H3O.
|
998 ; 1614 ; 1614 ; 3054 ; 3054 ; 3375
|
19.583
|
| VD/R6 |
D3O.
|
745 ; 1168 ; 1168 ; 2242 ; 2242 ; 2411
|
14.263
|
| VD/R6 |
D318O.
|
735 ; 1162 ; 1162 ; 2224 ; 2224; 2406
|
14.173
|
| DH/R8 |
H3O.
|
967 ; 1614 ; 1614 ; 3090 ; 3090 ; 3387
|
19.676
|
| DH/R8 |
D3O.
|
729 ; 1168 ; 1168 ; 2270 ; 2270 ; 2420
|
14.334
|
| DH/R8 |
D318O.
|
719 ; 1163 ; 1163 ; 2251 ; 2251 ; 2414
|
14.243
|
At the transition state, the hessian matrix has been projected so that
the real normal modes are orthogonal to the gradient
[Miller 80] .
Table 8 Vibrational analysis at the transition point.
| Basis set | Isotopomer |
Frequencies (cm-1) |
ZPE (kcal/mole) |
| VD/R6 |
H3O.
|
806 ; 1091 ; 1699 ; 3742 ; 3848
|
15.990
|
| VD/R6 |
D3O.
|
605 ; 787 ; 1238 ; 2690 ; 2827
|
11.646
|
| VD/R6 |
D318O.
|
598 ; 784 ; 1230 ; 2680 ; 2804
|
11.573
|
| DH/R8 |
H3O.
|
781 ; 1094 ; 1694 ; 3759 ; 3878
|
16.020
|
| DH/R8 |
D3O.
|
587; 789 ; 1235 ; 2702 ; 2850
|
11.670
|
| DH/R8 |
D318O.
|
580; 786 ; 1228 ; 2692 ; 2823
|
11.596
|
Table 9. Dissociation barriers with various isotopomers.
| Basis set | Isotopomer |
Dissociation barrier (kcal/mole) |
| VD/R6 |
H3O.
|
0.638
|
| VD/R6 |
D3O.
|
1.630
|
| VD/R6 |
D318O.
|
1.647
|
| DH/R8 |
H3O.
|
0.636
|
| DH/R8 |
D3O.
|
1.612
|
| DH/R8 |
D318O.
|
1.629
|
| [Talbi 89]
|
H3O.
|
0.40
|
| [Talbi 89]
|
D3O.
|
1.32
|
The barriers calculated by taking into account the zero point
vibration energies (ZPE) are listed in table 9.
Our computed dissociation barriers are positive, which means that
H3O.
and its isotopomers are predicted to be theoretically metastable.
Anyway, for all practical purpose, the computed barriers are so low,
that the radical is predicted to be barely metastable and might
not be experimentally observed.
For H3O.,
our UHF barrier values are consistent with the values obtained by
Talbi and Saxon
[Talbi 89]
at the MCSCF level.
Their electronic dissociation barrier (3.59 kcal/mole),
their ZPE at equilibrium (19.52 kcal/mole )
the transition states geometries ( O--H.=1.168 �
vs 1.174 �) and the ZPE at the transition state are
(14.90 kcal/Mole) are similar.
All numerical UHF hessian computations were achieved
with the GAMESS (Nvib=2) option.
When GAMESS hessian computations are performed
with the default (Nvib=1)option, each nuclear displacement is
achieved only in the positive cartesian direction, which
might result in an incomplete
exploration of the PES. In fact, with the
(Nvib=1) option, the ZPE (10.38
kcal/mole for
H3O. DH/R8 ) was
estimated at a much lower value at the transition point.
It must be stressed that
the harmonic approximation might not be very well verified, both
at the local minimum and at the transition state.
As expected, computed oxygen
isotopic substitution effect on the dissociation
barrier is negligible.
Deuterium substitution does not increase dramatically the
dissociation barrier.
Therefore experimentally observed dramatic isotopic substitution
effects cannot be explained at this level of theory.
It must also be realized that the low momentum,
diffuse Rydberg
electronic cloud is going to be very easily polarizable.
Since
the outer "Rydberg" electron controls
the dissociation process,
when the Rydberg electronic cloud
is polarized and therefore distorted,
a
dissociation process might be further favoured.
