Born-Oppenheimer approximation breakdown

How important the breakdown of the Born-Oppenheimer approximation is in limiting our ability to carry out ab initio simulations of chemical reactivity at metal surfaces is the central topic of this review. Stated more provocatively, do we have the correct theoretical picture of heterogeneous catalysis. This review will restrict itself to a consideration of experiments that have begun to shed light on this important question. The reader is directed to other recent review articles, where aspects of this field of research not mentioned in this article are more fully addressed.10-16... 

Perhaps the first evidence for the breakdown of the Born-Oppenheimer approximation for adsorbates at metal surfaces arose from the study of infrared reflection-absorption line-widths of adsorbates on metals, a topic that has been reviewed by Hoffmann.17 In the simplest case, one considers the mechanism of vibrational relaxation operative for a diatomic molecule that has absorbed an infrared photon exciting it to its first vibrationally-excited state. Although the interpretation of spectral line-broadening experiments is always fraught with problems associated with distinguishing... 

In the light of the accumulated evidence, it appears quite likely that the scattering of nitric oxide from metals does induce electronic transitions which represents a fundamental breakdown of the Born-Oppenheimer approximation. Clearly this falls in the category of electronically nonadi-abatic phenomena that we set out to understand. But there is a broader question. Is the Born-Oppenheimer breakdown significant within a broader chemical context ... 

Hence, according to the symmetry selection rule, n —> n transitions are allowed but n —> ti transitions are forbidden. However, in practice the n —> it transition is weakly allowed due to coupling of vibrational and electronic motions in the molecule (vibronic coupling). Vibronic coupling is a result of the breakdown of the Born-Oppenheimer approximation. 

Understand that intermolecular radiationless transitions of excited states are caused by a breakdown of the Born-Oppenheimer approximation. 

The electronic contributions to the g factors arise in second-order perturbation theory from the perturbation of the electronic motion by the vibrational or rotational motion of the nuclei [19,26]. This non-adiabatic coupling of nuclear and electronic motion, which exemplifies a breakdown of the Born-Oppenheimer approximation, leads to a mixing of the electronic ground state with excited electronic states of appropriate symmetry. The electronic contribution to the vibrational g factor of a diatomic molecule is then given as a sum-over-excited-states expression... 

All of the calculations have been performed at the experimental equilibrium distance R = 1.128 A, in order to enable a proper comparison with the EOM-CCSD reference. In so far as there are neither largely interacting excited states nor special reasons for expecting a breakdown of the Born Oppenheimer approximation, great changes in the MAE are not expected if one takes the (SC) SDCI ground state equilibrium value for Re which is Re = 1.140 A (very close to the CCSD value, as expected Cfr. table 1). We have performed a separate calculation of the whole set of VEE with the aug-cc-pVDZ basis set at the Rg distance, in any case. The results have not been included in table II for the sake of clarity, but the total MAE values where 2.34 eV for the MR-SDCI and 0.17 eV for (SC)2mR-SDCI. 

Breakdown of the Born-Oppenheimer Approximation. The B-O approximation is based on the independence of the motions of nuclei and electrons. This is generally a reasonable assumption, except at the crossing point of two electronic states where a minor nuclear displacement is linked to the transition between two electronic states (Figure 3.31). 

In most cases these differ significantly from the theoretical value of 6.514 an explanation is not given in the original papers, but the differences may reflect subtle vibrational averaging effects or breakdown of the Born-Oppenheimer approximation. 

The results given in table 10.3 constitute a good data set with which to test theoretical relationships [86, 87] relating to breakdown of the Born-Oppenheimer approximation. As we have described elsewhere, the vibration-rotation term values may be expressed as power series using the Dunham parameters T ... 

A large number of elementary molecular collision processes proceeding via (or in) excited electronic states are known at present. A prominent feature of all these is that as a rule they can not be interpreted (even at a very low kinetic energy of nuclei) in terms of the motion of a representative point over a multidimensional potential-energy surface. The breakdown of the Born-Oppenheimer approximation, which manifests itself in the so-called nonadiabatic coupling of electronic and nuclear motion, induces transitions between electronic states that remain still well defined at infinitely large intermolecular distances. 

There are two reasons why so much is unknown. First, at high densities three (and even four) body forces are important. This is particularly so when chemically reactive atoms are present. Then, even for two-body forces, the strongly repulsive regime is not well understood and, in addition, close in, as one approaches the united atom limit, there is considerable promotion of molecular orbitals. This is a universal mechanism for electronic excitation which means a breakdown of the Born-Oppenheimer approximation for close collisions. 

The breakdown of the Born-Oppenheimer approximation, due to avoided crossings or conical intersections between two electronic states, and the consideration of nonadiabatic couplings and nonadiabaticity will be now outlined, and the analytic expressions for the fs signals involving nonadiabatic... 

In such cases it has been assumed that = w, Y. = B, etc., although in the highest approximations these identities are not precisely correct. Some of the values of in the table have been corrected for breakdown of the Born-Oppenheimer approximation, which can affect the last decimal place. Because of differences in the method of data analysis and limitations in the model, care should be taken in comparing values for different molecules to a precision beyond 0.001 A. 

Bunker, P.R., Moss, R.E. Breakdown of Born-Oppenheimer approximation—effective vibration-rotation Hamiltonian for a diatomic molecule. Mol. Phys. 1977,33,417-24 ... 

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