Spin waves electrons

Continuous-Wave Electron Spin Resonance ed L Kevan and M Bowman (New York Wiley) oh 7, pp 285-363... 

Lebedev Y S 1990 High-frequency continuous-wave electron spin resonance Modern Pulsed and... 

Earle K, Budll D and Freed J 1996 Millimeter wave electron spin resonance using quasloptical techniques Advances in Magnetic and Optical Resonance vol 19, ed W Warren (San Diego ... 

Allgeler J, DIsselhorst A, Weber R, Wenckebach W and Schmidt J 1990 High-frequency pulsed electron spin resonance Modern Pulsed and Continuous-Wave Electron Spin Resonance ed L Kevan and M K Bowman (New York Wley) ch 6, pp 267-83... 

A UHF wave function may also be a necessary description when the effects of spin polarization are required. As discussed in Differences Between INDO and UNDO, a Restricted Hartree-Fock description will not properly describe a situation such as the methyl radical. The unpaired electron in this molecule occupies a p-orbital with a node in the plane of the molecule. When an RHF description is used (all the s orbitals have paired electrons), then no spin density exists anywhere in the s system. With a UHF description, however, the spin-up electron in the p-orbital interacts differently with spin-up and spin-down electrons in the s system and the s-orbitals become spatially separate for spin-up and spin-down electrons with resultant spin density in the s system. 

The spin part pl can be derived by labelling the electrons 1 and 2 and remembering that, in general, each can have an a or /i spin wave function giving four possible combinations a(l)P(2), P(l)a(2), a(l)a(2) and P(l)P(2). Because the first two are neither symmetric nor antisymmetric to the exchange of electrons, which is equivalent to the exchange of the labels 1 and 2, they must be replaced by linear combinations giving... 

Equation (7.23) expresses the total electronic wave function as the product of the orbital and spin parts. Since J/g must be antisymmetric to electron exchange the Ig and Ag orbital wave functions of oxygen combine only with the antisymmetric (singlet) spin wave function which is the same as that in Equation (7.24) for helium. Similarly, the Ig orbital wave function combines only with the three symmetric (triplet) spin wave functions which are the same as those in Equation (7.25) for helium. 

In order to include the spin of the two electrons in the wave function, it is assumed that the spin and spatial parts of the wave function can be separated so that the total wave function is the product of a spin and a spatial wave function F — iAspace sp n Since our Hamiltonian for the H2 molecule does not contain any spin-dependent terms, this is a good approximation (NB—the complete Hamiltonian does contain spin-dependent terms, but for hydrogen they are rather small and do not appreciably affect the energetics of chemical bonding). For a two-electron system it turns out that there are four possible spin wave functions they are ... 

To aid our understanding of absorption and emission processes, Eq. (2.1) can be expanded in terms of electronic, vibronic (vibrational components of an electronic transition), and spin wave functions ... 

If any one of these integrals (expectation value equations) is zero, the transition is said to be forbidden. For the electronic and spin wave functions, it is not necessary to evaluate the integral but only to note that an odd function integrated from minus infinity to infinity is zero, while an even function integrated within these limits results in a nonzero value. For example (Figure 2.1),... 

Kevan, L. and M. K. Bowman (1990). Modem Pulsed and Continuous-Wave Electron Spin Resonance. New York Wiley. 

Modern Pulsed and Continueous-Wave Electron Spin Resonance, ed. L. Kevan and M.K. Bowman, John Wiley, New York, 1990. 

Gray, H. B. and Malmstrom, B. G. (1989). Biochemistry 28, 7449 Grupp, A. and Mehring, M. (1990). In Modern Pulsed and Continuous Wave Electron Spin Resonance, p. 195. Wiley, New York... 

The permutational symmetry of the rotational wave function is determined by the rotational angular momentum J, which is the resultant of the electronic spin S, electronic orbital L, and nuclear orbital N angular momenta. We will now examine the permutational symmetry of the rotational wave functions. Two important remarks should first be made. The first refers to the J 0 rotational... 

In order for to embody the Pauli exclusion principle, it must be an antisymmetrized wave function. Antisymmetrization requires that exchange of any two electrons between orbitals or exchange of the spins between electrons in the same orbital causes 4/ to change sign. 

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