Born-Oppenheimer diagonal correction

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. 

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

Handy, N.C., Yamaguchi, Y, Schaefer 111, H.F. The diagonal correction to the Born-Oppenheimer approximation—its effect on the singlet-triplet splitting of CH2 and other molecular effects, J. Chem. Phys. 1986, 84,4481. ... 

As noted in Chapter 2 of this volume, the Born-Oppenheimer diagonal correction produces a mass dependent modification of a mass independent Born-Oppenheimer potential energy surface. This medication can be inferred from experimental measurements of rovibrational levels of a series of isotopomers and can be computed directly, using the methods of this chapter. The state of LiH is considered here. It has been the... 

The Born-Oppenheimer diagonal correction is given in Eq. (2a). In that equation, the gradients refer to space fixed frame (SFF) coordinates. For diatomic molecules, considerable savings result from a transformation to body fixed frame (BFF) coordinates. This transformation is accomplished in two steps. The SFF coordinates are transformed to center of mass fixed frame (CMFF) coordinates and then the CMFF coordinates are transformed to BFF coordinates. The details of the transformation are beyond the scope of this review. Here we sketch the ideas involved. A detailed treatment, based on the pioneering work of Kronig, can be found in Ref. 7. In particular, first the rigorously removable center of mass of the nuclei and... 

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