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Augmented exact value

Fig. 10.14. Conveigence of Ihe M0ller-Plesset pertuibation theoiy (deviation from the exact value, given in a.u.1 for the HF molecule as a function of the basis set used (cc-pVDZ and augmented cc-pVDZ) and assumed bond length. Re denotes the HF equilibrium distance (following T. Helgaker, P. Jpigensen, and J. Olsen, Molecular Electmnic-Structme Theory Wiley, Chichester, 2000, p. 780, Fig. 14.6). Courtesy of the authors. Fig. 10.14. Conveigence of Ihe M0ller-Plesset pertuibation theoiy (deviation from the exact value, given in a.u.1 for the HF molecule as a function of the basis set used (cc-pVDZ and augmented cc-pVDZ) and assumed bond length. Re denotes the HF equilibrium distance (following T. Helgaker, P. Jpigensen, and J. Olsen, Molecular Electmnic-Structme Theory Wiley, Chichester, 2000, p. 780, Fig. 14.6). Courtesy of the authors.
Unlike HE molecular orbitals, the natural orbitals are not restricted to a low-level approximation, hut are rigorously defined for any theoretical level, up to and including the exact P. As eigenfunctions of a physical (Hermitian) operator, the NOs automatically form a complete orthonormal set, able to describe every nuance of the exact P and associated density distribution, whereas the occupied MOs are seriously mcomplete without augmentation by virtual MOs. Furthermore, the occupancies , of NOs are not restricted to integer values (as are those of MOs), but can vary continuously within the limits imposed by tbe Pauli exclusion principle, namely, for closed-shell spatial orbitals. [Pg.12]


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See also in sourсe #XX -- [ Pg.432 ]




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