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Theoretical Details To DBOC CorrectionsCorrections for making the BornOppenheimer approximations in the quantum chemical treatment of atoms and molecules are easily computed using perturbation theory. The lowestorder correction is obtained in firstorder and takes the form
This correction is known as the "diabatic BornOppenheimer correction (DBOC)" and its inclusion leads to the socalled adiabatic approximation with massdependent potentials that are different for the various isotopomers of a molecule. As shown by Handy, Yamaguchi, and Schaefer (J. Chem. Phys. 84, 4481 (1986)), analytic derivative techniques can be used to compute E(DBOC). At the HFSCF level, the DBOC correction can be thus calculated as
With the corresponding AO integrals and the CPHF coefficients , this can be recasted in the following form for RHF
}
with as the RHFSCF density matrix
For UHF, this yields }
with as the UHFSCF density matrix
with the sum running over spatial orbitals instead of spin orbitals. A slightly different, though equivalent expression for the DBOC at the HFSCF level has been given earlier by Handy et al (J. Chem. Phys. 84, 4481 (1986)). A corresponding scheme for correlated calculations of DBOC is currently implemented.
