Slater diagram

For nonequivalent p configurations in which the two electrons are in different shells (e.g., the (2p) (3p) excited state of carbon), states exist for all combinations of the allowed L and S values generated in Eqs. 2.76. Slater diagram tabulations of the allowed (M, Ms) combinations are then superfluous the nonequivalent configuration gives rise to S, S, P, P, D, and term symbols. Slater... 

The energy level scheme for a p atom can now be described for the case of small spin-orbit coupling (Fig. 2.9), where Russell-Saunders coupling applies. In the absence of electron-electron interactions, all of the configurations counted in the Slater diagram would have the same energy, because the one-electron p orbitals with m, = 0, 1 are degenerate. When the electron-electron interactions are turned on, the states with term symbols have different... 

Figure 12 Generation of an antiferromagnetic insulator in the Slater approach, (a) The description of the insulator in terms of occupation of spin up and spin down bands and (b) how the up and down spins on adjacent atoms change as the on-site repulsion is gradually increased. When the on-site repulsion is infinite two electrons are not located on the same atom. Compare this diagram with the bottom left-hand picture of Figure 11.

Figure 1.15 Energy band diagram for a sodium lattice. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc. After J. C. Slater, Phys. Rev., 45, 794 (1934).

Density functional theory, 21, 31, 245-246 B3LYP functional, 246 Hartree-Fock-Slater exchange, 246 Kohn-Sham equations, 245 local density approximation, 246 nonlocal corrections, 246 Density matrix, 232 Determinantal wave function, 23 Dewar benzene, 290 from acetylene + cyclobutadiene, 290 interaction diagram, 297 rearrangement to benzene, 290, 296-297 DFT, see Density functional theory... 

Figure 14 Phase diagram for NaN03-KN03-H20, system at 50°C. (Adapted from FF Purdon, VW Slater. Aqueous Solutions and the Phase Diagram. London Edward Arnold, 1946, p 32.)...

Only part of this phase diagram is shown because the full diagram is quite complicated. See FF Purdo, VW Slater. Aqueous Solution and the Phase Diagram. London Arnold, 1946, p 18. 

One of the most important concepts of quantum chemistry is the Slater determinant. Most quantum chemical treatments are made just over Slater determinants. Nevertheless, in many problems the formulation over Slater determinants is not very convenient and the derivation of final expressions is very complicated. The advantage of second quantization lies in the fact that this technique permits us to arrive at the same expressions in a considerably simpler way. In second quantization a Slater determinant is represented by a product of creation and annihilation operators. As will be shown below, the Hamiltonian can also be expressed by creation and annihilation operators and thus the eigenvalue problem is reduced to the manipulation of creation and annihilation operators. This manipulation can be done diagrammatically (according to certain rules which will be specified later) and from the diagrams formed one can write down the final mathematical expression. In the traditional way a Slater determinant I ) is specified by one-electron functions as follows ... 

These forms, used by Slater and Koslcr (1954), will be used extensively in this text. For each n when / = 1, there are three p orbitals oriented along the three Cartesian axes. Diagrams such as those shown in Fig. 1-4 illustrate the three angular forms. 

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