Born-Oppenheimer corrections

In perturbation theory language, one can say that the adiabatic Born-Oppenheimer states are a good zero-order approximation for describing nuclear motion if the non-Born-Oppenheimer corrections are small. This is... 

MVDl = one-electron mass-velocity plus Darwin D2 = two-electron Darwin DBOC = diagonal Born-Oppenheimer correction. Please see text for details, rii and are the stretching, 112 is the bending quantum number. 

Gauss, J., Tajti, A., KaUay, M., Stanton, J.F., Szalay, P.G. Analytic calculation of the diagonal Born-Oppenheimer correction within configuration-interaction and coupled-cluster theory, J. Chem. Phys. 2006,125,144111. 

For the majority of systems the Born-Oppenheimer approximation introduces only very small errors. The diagonal Born-Oppenheimer correction (DBOC) can be evaluated relatively easy, as it is just the second derivative of the electronic wave function with respect to the nuclear coordinates, and is therefore closely related to the nuclear gradient and second derivative of the energy (Section 10.8). 

The ionization potentials and electron affinities of the atoms H, C, N, O and F have been computed by means of coupled-cluster methods using doubly augmented correlation-consistent one-electron basis sets in conjunction with explicitly correlated Slater-type geminals. Excitations up to the level of connected quintuples have been accounted for, and all orbitals in the core and valence shells have been correlated. Relativistic effects (spin-orbit as well as scalar) and diagonal Born-Oppenheimer corrections have been included. 

The mass-velocity and Darwin terms (denoted as MVD ) were computed at the ae-CCSD(T) level of theory [145] with the d-aug-cc-pwCV5Z basis set. The spin-orbit corrections ( SO ) were obtained from the experimentally observed spin-orbit splitting [159]. The diagonal Born-Oppenheimer correction was was crudely estimated from the total... 

The ionization potentials and electron affinities of the H, C, N, O and F atoms have been computed by means of state-of-the-art electronic structure methods. The conventional coupled-cluster calculations were performed up to the connected pentuple excitation level. For the purpose of the basis set truncation correction the implementation of the CCSD(F12) model in Turbomole was applied. Final results were supplemented with relativistic and diagonal Born-Oppenheimer corrections. Estimated values of the IPs and EAs are in good agreement with the experimental values and the deviations do not exceed 0.7 meV, in the cases of H, C and N atoms and the IP of O atom. The results obtained for fluorine differ by ca. 1 and 5 meV from the experiment, respectively for the IP and EA. The EA of oxygen is plagued with discrepancy that amounts to ca. 4 meV. 

Diagonal Born-Oppenheimer correction calculated at the ae-CCSD(T)/d-aug-cc-pwCV5Z level. 

Fig. 2. Contributions to diagonai Born-Oppenheimer correction due to mass polarization (MP), angular momentum (L ) and internal motion(K ) as a function of...

Diagonal Born-Oppenheimer correction (DBOC) for RHF, ROHF, UHF, and Cl wave functions. 

As the reactants and products are all closed-shell molecules, there are no first-order spin-orbit corrections - the only first-order relativistic corrections are the mass-velocity and Darwin corrections (15.8.5), which are similar in magnitude to the anharmonic corrections but of opposite sign. The non-Born-Oppenheimer corrections may be assumed to be small for the reactions considered here. 

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