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By Boeckman R.K., Coffen D.L., Overman L.E. (eds.)

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On the positive side, MP theory is size-consistent at any order. 2 ELECTRON CORRELATION: POST-HARTREE –FOCK METHODS 17 where the Tˆi operator generates all of the configurations with i electron excitations. Because Brillouin’s Theorem states that singly-excited configurations do not mix directly with the HF configuration, the Tˆ2 operator T^ 2 ¼ occ X vir X i, j tijab cijab (1:38) a, b is the most important contributor to Tˆ. If we approximate Tˆ ¼ Tˆ2, we have the CCD (coupled-cluster doubles) method, which can be written as the Taylor expansion: !

4. 3 Optical Rotation and Optical Rotatory Dispersion Optical rotation and ORD provide spectral information unique to enantiomers, allowing for the determination of absolute configuration. 74,75 Although HF fails to adequately predict optical rotation, a study of eight related alkenes and ketones at the B3LYP/6-31GÃ level demonstrated excellent agreement between the calculated and experimental optical rotation (reported as [a]D, with units understood throughout this discussion as deg . [dm . 9. An RMS error this large, however, implies that molecules with small rotations might actually be computed with the wrong sign, the key feature needed to discriminate the absolute configuration of enantiomers.

Cisl Srk sl : (1:59) sl=k The Mulliken population is easy to compute and understand. All electrons that occupy an orbital centered on atom k “belong” to that atom. However, Mulliken populations suffer from many problems. If a basis set is not balanced, the population will reflect this imbalance. Orbital populations can be negative or greater than zero. This deficiency can be removed52 by using orthogonal basis functions (the Lo¨wdin orbitals53). But perhaps most serious is that the Mulliken procedure totally neglects the spatial aspect of the atomic orbitals (basis functions).

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Organic Syntheses by Boeckman R.K., Coffen D.L., Overman L.E. (eds.)


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