General discussion
W. Kutzelnigg, The adiabatic approximation I. The physical background of the Born-Handy ansatz, Mol. Phys. 90, 909-916 (1997)
HF-SCF
N.C. Handy, Y. Yamaguchi, and H.F. Schaefer III, The diagonal correction to the Born–Oppenheimer approximation: Its effect on the singlet–triplet splitting of CH2 and other molecular effects, J. Chem. Phys. 84, 4481 (1986)
MP1 and MP2
A. Tajti, P.G. Szalay, and J. Gauss, Perturbative treatment of the electron-correlation contribution to the diagonal Born-Oppenheimer correction, J. Chem. Phys. 127, 014102 (2007)
CCSD
J. Gauss, A. Tajti, M. Kállay, J.F. Stanton, and P.G. Szalay, Analytic calculation of the diagonal Born-Oppenheimer correction within configuration-interaction and coupled-cluster theory, J. Chem. Phys. 125, 144111 (2006)