TITLE SIC2H4 TRIPLET SCF and PUMP2 CALCULATION NOPRINT OCCVECTORS SYMMETRY CNV 2 END BASIS DZP ATOMS SI 14 0.0 0.0 -0.6615482 C1 6 2.8885198 0.0 -2.2904091 H1 1 4.7218001 0.0 -1.3803020 H2 1 2.9203532 0.0 -4.3435272 END MULTIPLICITY 3 UHF PUMP2 ENERGY START FINISHThis example is taken from a study of the Si + C2H4 surface - see J. Am. Chem. Soc. 112, 1499 (1990). This paper also contains references describing the origin of the PUMP2 method.
After the SCF output one finds the following,
AFTER PROJECTION 0 PROJECTED UHF ENERGY (PUHF) -366.876041926 PROJECTED SECOND ORDER ENERGY -0.4050884096501 TOTAL ENERGY (PUMP2) AFTER PROJECTION -367.2811303357 S-SQUARED AFTER PROJECTION 2.25464967077 AFTER PROJECTION 1 PROJECTED UHF ENERGY (PUHF) -366.8861435227 PROJECTED SECOND ORDER ENERGY -0.404562841094 TOTAL ENERGY (PUMP2) AFTER PROJECTION -367.2907063638 S-SQUARED AFTER PROJECTION 1.994429682714 AFTER PROJECTION 2 PROJECTED UHF ENERGY (PUHF) -366.8856775658 PROJECTED SECOND ORDER ENERGY -0.4047783871538 TOTAL ENERGY (PUMP2) AFTER PROJECTION -367.290455953 S-SQUARED AFTER PROJECTION 2.000038496833The data under 'Projection 0' are the original UHF and UHF-MP2 results. It can be seen that the value of S2 is significantly in error. The projection operator is then applied twice, both to the SCF energy and to the MP2 energy. After the second projection the value of S2 is much better. The results after the first projection are best ignored. In most cases the total energies (and more particularly, energy differencies) are better after projection than the original UHF-MP2 energies. There are other spin-projection schemes in the literature. It should be noted that the PUMP2 scheme is not the same as the PMP2 scheme due to Schlegel - the PUMP2 scheme is more rigorous.