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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.


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