The matrix elements needed in a CI‐SD, CEPA, MP2, or MP3 calculation with linear r12‐dependent terms for closed‐shell states are derived, both exactly and in a consistent approximate way. The standard approximation B guarantees that in the atomic case the error due to truncation of the basis at some angular momentum quantum number L goes as ∼L−7, at variance with L−3 in conventional calculations (without r12 terms). Another standard approximation A has errors ∼L−5, but is simpler and—for moderate basis sets—somewhat better balanced. The explicit expressions for Mo/ller–Plesset perturbation theory of second and third order with linear r12 terms (MP2‐R12 and MP3‐R12, respectively) are explicitly given in the two standard approximations.
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© 1991 American Institute of Physics.
1991
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