Single electron spin states

The chemical potential p of the electron assembly, otherwise known as the Fermi energy, is found by differentiation with respect to a L, the actual number of electrons distributed among the sites. Here, because of our somewhat imusual specification of site occupancies, one encounters a common factor of 2 throughout, that may be absorbed in the definition for p (recall that the bonds with two termini actually refer to single electron spin states), so that... 

As a remark, it should be noted that a single electron ground state from a filled band (which would be the case of americium within a band description because the 5 f band is spin-orbit splitted into a filled 5/2 sub-band and an empty 7/2 sub-band) is equivalent to a localized state and thus a spin-polarized band description leads to the same conclusion as a simple Mott description. 

Powder samples of Y Cs2 exhibited localized-electron behavior both at temperatures above 200 K and temperatures below 90 K, but with different Curie—Weiss curves (Allen, 1998). The Curie—Weiss curve at low temperature corresponded to 0.29(4) electrons per fullerene similar to that of La Cs2/ with a small Curie constant of 2.7(8) K, and to 1.0(1) electrons at high temperature, with an extremely large Curie constant of 280(30) K. This single electron spin clearly agrees with the single impaired electron which is expected, and as observed in solution ESR experiments (see Section 6.1). The high-temperature susceptibility is weakly temperature dependent, and if it arises from a metal then the density of state (DOS) is 10(1) states per molecule per electonvolt at 294 K. 

Table 2 Electronic spin states (Zeeman g factors) S (geffective) and changes in the advances in oxidation states of the spinach WOC induced by single turnover flashes in room temperature magnetic susceptibility (Ay) upon PSll complexes. Syn. denotes Synechocystis 6803 ...

The Fermi contact shift describes the influence of the unpaired electron spin on nnclear chemical shifts as a resnlt of throngh-bond hyperfine conpling. The contact shift is caused by the presence of unpaired electron spin density at the observed nnclens. Thns, spin density must be transferred to an s orbital of the nnclens of interest, which is typically achieved through spin polarization. In the case of a single, isolated spin state for a molecule in solution, contact shift can be described by... 

The situation is quite different with S-T -type CIDNP because nuclear spins are flipped in that case. Owing to the coupling of nuclear spin motion and electron spin motion, not only the electron spin state oscillates in such a system but also the nuclear spin state. Since, however, one-half of the pairs or biradicals cannot participate in this because their nuclear spin state does not allow an electron-nuclear flip-flop transition, the oscillation is not symmetrical. Its turning points are zero nuclear spin polarization and 100% nuclear spin polarization of one sign only. In contrast, the distribution of nuclear spin polarizations between singlet and triplet members of the ensemble is symmetrical. As an example, consider an ensemble of biradicals, where each biradical contains a single proton. Let the ensemble be created in the state T >, and without initial nuclear spin polarization. Half of the pairs, namely those that have nuclear spin /J>, cannot undergo flip-flop transitions. The others oscillate between T a> and S/3>. When all of those happen to be in S/ >, every nuclear spin of the triplet biradicals and every... 

To satisfy the Pauli principle the antisymmetric wavefunction must be combined with one of the three symmetric spin states, given by equations (7.26)-(7.28). This particular excited state can therefore exist in three different forms. These have slightly different energies because of the small magnetic interactions which occur between the spin and orbital motions of the electrons, and this causes any spectral lines involving this state to be split into three. For this reason it is known as a triplet state. The symmetric wavefunction, yr, combines with the single antisymmetric spin state, and it is said to form a singlet state. ... 

We propose a nuclear spin quantum computer based on magnetic resonance force microscopy (MRFM). It is shown that a MRFM single-electron spin measurement provides three essential requirements for quantum computation in solids (a) preparation of the ground-state, (b) one- and two-qubit quantum logic gates, and (c) a measurement of the final state. — G.P. Berman, G.D. Doolen, RC. Hammel, V.L Tsifrinovich [Rhys. Rev. B 61 (2000) 14694]... 

In the work of Xiao et al. the resonance of a single electronic spin is observed directly in a field-effect transistor (FET). After creating a paramagnetic trap, they observe the source/drain current in the FET, as a function of the ESR frequency. Under a magnetic field, the Fermi level of the channel electrons is adjusted to lye between the two electronic states of the paramagnetic trap. The idea is that, if only the lower spin state is occupied, then no electron can jump from the channel to the trap. But if only the upper spin... 

In order to create an exciton wavefunction we remove a single electron from state — Rft) (the subscript h standing for hole ) and put it in state — R ) (the subscript p standing for particle ). This is the expected excitation, from an occupied valence to an unoccupied conduction state, by the absorption of a photon as discussed earlier in this chapter. When this is done, the total momentum and total spin of the many-body wavefunction must be preserved, because there are no terms in the interaction hamiltonian to change these values (we are assuming as before that the wave-vector of the incident radiation is negligible compared with the wave-vectors of electrons). 

So far, I have ignored the existenee of spin. Spin is an internal angular momentum that some partieles have and others do not. Eleetron spin is a two-valued quantity vve denote the spin variable for a single eleetron s, and the spin states are written o (s) and 3(s), or just a and p for short when the meaning is obvious. The notation I am going to use is that afsj) means eleetron 1 in spin state a. With an eye to the discussion above about indistinguishability, we consider the following four combinations of spin states for two electrons ... 

A more general way to treat systems having an odd number of electrons, and certain electronically excited states of other systems, is to let the individual HF orbitals become singly occupied, as in Figure 6.3. In standard HF theory, we constrain the wavefunction so that every HF orbital is doubly occupied. The idea of unrestricted Hartree-Fock (UHF) theory is to allow the a and yS electrons to have different spatial wavefunctions. In the LCAO variant of UHF theory, we seek LCAO coefficients for the a spin and yS spin orbitals separately. These are determined from coupled matrix eigenvalue problems that are very similar to the closed-shell case. 

Electron spin resonance (or electron paramagnetic resonance) is now a well-established analytical technique, which also offers a unique probe into the details of molecular structure. The energy levels involved are very close together and reflect essentially the properties of a single electronic state split by a small perturbation. 

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