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In comparison with its restricted variant, an unrestricted Hartree- Fock wave function lowers the ground-state energy because of the inclusion of static correlation through the use of different orbitals for different spins, but at the same time it raises the energy by including higher-energy spin states. The variational principle guarantees that UHF predicts a lower energy than that predicted by RHF because of its greater flexibility, i.e, the first effect must be dominant. On the other hand, UMP leads to a higher energy than RMP because of the mixing in of higher-energy spin states
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In comparison with its restricted variant, an unrestricted Hartree- Fock wave function lowers the ground-state energy because of the inclusion of static correlation through the use of different orbitals for different spins, but at the same time it raises the energy by including higher-energy spin states. The variational principle guarantees that UHF predicts a lower energy than that predicted by RHF because of its greater flexibility, i.e., the first effect must be dominant. On the other hand, UMP leads to a higher energy than RMP because of the mixing in of higher-energy spin states.
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An increase in spin contamination in the Kohn-Sham determinant with increasing exact-exchange admixture has also been reported in calculations on EPR hyperfine coupling constants and electronic g-tensors for transition metal complexes. See, for example: Remenyi, C, Kaupp, M. J. Am. Chem. Soc. 2005, 127, 11399, and references therein
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An increase in spin contamination in the Kohn-Sham determinant with increasing exact-exchange admixture has also been reported in calculations on EPR hyperfine coupling constants and electronic g-tensors for transition metal complexes. See, for example: Remenyi, C.; Kaupp, M. J. Am. Chem. Soc. 2005, 127, 11399, and references therein.
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Modified versions of the original double-hybrid DFT procedures have recently been proposed, (a) Tarnopolsky, A.; Karton, A.; Sertchook. R.; Vuzman, D.; Martin, J. M. L. J. Phys. Chem. A 2008, 112, 3.
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Modified versions of the original double-hybrid DFT procedures have recently been proposed, (a) Tarnopolsky, A.; Karton, A.; Sertchook. R.; Vuzman, D.; Martin, J. M. L. J. Phys. Chem. A 2008, 112, 3.
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(b) Karton, A.; Tarnopolsky, A.; Lamere, J.-F.; Schatz, G. C.; Martin, J. M. L. J. Phys. Chem. A [Online early access], DOI: 10.1021/jp801805p. Published Online: Aug 20, 2008. B2T-PLYP is a version of B2-PLYP, modified for use in thermochemical calculations, while B2K- PLYP and MPW2K-PLYP are versions of B2-PLYP and MPW2-PLYP modified for kinetics calculations.
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UMP2 values are listed in Table S1 of the Supporting Information.
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UMP2 values are listed in Table S1 of the Supporting Information.
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