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The unimolecular decomposition rates of energy selected methylnitrite and deuterated methylnitrite ions J. Chem. Phys. 78, 3767 (1983) At low energies, methylnitrite ions dissociate via two channels giving rise to CH 3 0 + NO+ or to [CH30+] + NO fragments. Peculiar characteristics have been detected in the dissociation of energy-selected parent ions, viz., remarkably low rate constants, one of which is found to remain insensitive to an increase of the internal energy, and large isotope effect. These peculiarities are accounted for by a statistical, nonadiabatic model. Ab initio calculations, confirmed by multipolar expansions reveal that the potential energy curves which correlate to these two dissociation asymptotes cross. The crossing takes place at a large value along the reaction coordinate R, indicating a long-range interaction. Production of the CH 3 0 + NO+ fragments results from a simple bond cleavage taking place on a single diabatic surface. On the other hand, production of [CH 3 0 +] + NO fragments is brought about by a transition from one diabatic surface to the other. It leads to deformed methoxy ions which immediately rearrange to the much more stable H 2 COH+ structure. The nonadiabatic rate constant has been calculated by a statistical method. The contribution of each channel is weighted by a transmission coefficient which is equal to the nonadiabatic transition probability. Implementation of this statistical treatment requires partitioning the set of degrees of freedom as follows: {R, y, d, v}. It is necessary to withdraw the isomerization mode y from the statistical treatment, because the equilibrium positions along this coordinate are very different in each electronic state. Physically, this means that the reaction involves tunneling from one surface to the other along the displaced degree offreedomy. The large isotope effect has a double origin: part of it (a factor of -9) results from tunneling alongy; the remainder (an additional factor of 3) comes from the usual RRKM-like effect on the densities of states. The degrees d constitute a set of four low-energy bending modes which form a sink for the internal energy. The nonadiabatic transition probability is determined by the off-diagonal matrix element V 12 (R c )' Effective potential energy curves have been calculated by extending the Quack and Troe method to nonadiabatic reactions. It turns out that the excitation of the set d leads to a decrease of V I2 (R c ) and hence to a decrease of the nonadiabatic transmission coefficient. This accounts for the weak dependence of the rate constants kCH,o+ and kCD,o+ vs the energy (at least above a certain energy threshold).

An approximate solution to the problem of constructing a pair of diabatic states exists only if certain requirements are fulfilled, for example, when the nonadiabatic coupling results from an interaction between two electronic configurations which are doubly excited with respect to one another. It is then possible to build up a model in which the series expansion of the elements of the Hamiltonian matrix is truncated after the first nonzero term. This leads to several conclusions concerning the nonadiabatic transition probability which differentiate conical intersections from avoided crossings. For the latter, the nonadiabatic coupling matrix elements (which are Lorentzians with an area equal to π/2) reach their maximum at the nuclear geometry for which ΔE (the energy gap between adiabatic surfaces) is a minimum. The loci along which the angle θ of the orthogonal transformation which relates adiabatic and diabatic wave functions keeps a constant value are a set of parallel straight lines which coincides with the loci along which ΔE remains constant. This reference direction in the configuration space corresponds to nuclear trajectories which are unable to bring about a nonadiabatic transition. In the case of avoided crossings, there exists only one nuclear degree of freedom which gives rise to surface hopping. Conical intersections, on the other hand, have two such active degrees of freedom. This creates a qualitative difference between the two cases which makes conical intersections more efficient as funnels than avoided crossings. A two-dimensional extension of the Landau–Zener formula is derived for avoided crossings. It contains a factor of anisotropy. It is possible, at least in favorable cases, to extract approximate diabatic quantities from ab initio calculations and to compare them with the predictions of these models. This has been done for two 2A1 electronic states of the CH+2 ion. The results are found to agree with the predictions of the model, at least in a restricted range of internuclear distances.