Electron density spin-averaged

Table 5.3 Contributions of -orbitals to the total electron density at the iron nucleus (in a.u. ) as a function of oxidation state and configuration. Calculations were done with the spin-averaged Hartree-Fock method and a large uncontracted Gaussian basis set. (17 1 Ip 5d If)... 

These results, as most related results of density functional theory, have direct connections to the fundamental statement of the Hohenberg-Kohntheorem the nondegenerate ground state electron density p(r) of a molecule of n electrons in a local spin-independent external potential V, expressed in a spin-averaged form as... 

The first set of equations govern the Cj amplitudes and are called the CI- secular equations. The second set determine the LCAO-MO coefficients of the spin-orbitals (f>j and are called the Fock equations. The Fock operator F is given in terms of the one- and two-electron operators in H itself as well as the so-called one- and two-electron density matrices yij and Tyj i which are defined below. These density matrices reflect the averaged occupancies of the various spin orbitals in the CSFs of VP. The resultant expression for F is ... 

Exercise. Give the explicit 2x2 density matrix for a beam of electrons with spin up. Also for a beam with spins in the x-direction. Also for a mixture of both. Find the average of the y-component in this mixed ensemble. 

Here N(sQ is the electron density of states on the Fermi surface for one direction of spin, is the effective volume of phonon generation, is the point contact form factor, averaged over the Fermi surface. It should be noted that point contacts of sizes d > l, d l can work also in diffusive or thermal current regimes [5] and are used for the study of EPI, phase transitions, superconductivity and other interesting physical phenomena. 

We performed adiabatic connection calculations for the inhomogeneous spin-unpolarized electron gas with average electron density n0 = 3/(4wr ) corresponding to rs = 2. In the QMC simulations we model this system by a finite... 

The measured differential cross-sections depend on the rotationally and vibrationally averaged values of

. Allan et al. have discussed the interpretation of (e, 2e) experiments in terms of spin-coupled orbitals and have presented momentum-space electron density maps for individual orbitals for LiH, NH and the 7t electrons in CH2CHX(X = F,C1). The nonorthogonality of the spatial orbitals allows them to assume properties very different from those of MO theory this leads to striking differences in momentum space. 

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