By van Vleck

When j = 0, these formulae give — 1 = 9Nh /S2Tr e jj, K which is in exact agreement with the result obtained for the dielectric constant by Van Vleck, Epstein and Pauling. ... 

The spin-Hamiltonian concept, as proposed by Van Vleck [79], was introduced to EPR spectroscopy by Pryce [50, 74] and others [75, 80, 81]. H. H. Wickmann was the first to simulate paramagnetic Mossbauer spectra [82, 83], and E. Miinck and P. Debmnner published the first computer routine for magnetically split Mossbauer spectra [84] which then became the basis of other simulation packages [85]. Concise introductions to the related modem EPR techniques can be found in the book by Schweiger and Jeschke [86]. Magnetic susceptibility is covered in textbooks on molecular magnetism [87-89]. An introduction to MCD spectroscopy is provided by [90-92]. Various aspects of the analysis of applied-field Mossbauer spectra of paramagnetic systems have been covered by a number of articles and reviews in the past [93-100]. 

For Sm3+ and Eu3+ the /T values (given in emu kelvin per mole) obtained by including the Van Vleck contribution are reported in brackets. The experimental values refer to the Ln2(S04)3 8H20 series, obtained as an average of the different measurements reported by Van Vleck [9]. 

As already observed for some isotropic polynuclear clusters [30 - 32], slow relaxation of the magnetization in an external magnetic field can occur because of the inefficient transfer of energy to the environment, for example, the helium bath, and consequent reabsorption of the emitted phonon by the spin system. The phenomenon, also known as phonon bottleneck (PB), was first introduced by Van Vleck [33]. It is characteristic of low temperatures, where relaxation is dominated by the direct process between closely spaced levels, and results from the low density of phonons with such a long wavelength to match the small energy separation... 

Basis of analysis beyond Dunham s theory, by van Vleck and others 4. Basis of application of Dunham s and van Vleck s theory to analysis 262... 

BASIS OF ANALYSIS BEYOND DUNHAM S THEORY, BY VAN VLECK AND OTHERS... 

That effective hamiltonian according to formula 29, with neglect of W"(R), appears to be the most comprehensive and practical currently available for spectral reduction when one seeks to take into account all three principal extramechanical terms, namely radial functions for rotational and vibrational g factors and adiabatic corrections. The form of this effective hamiltonian differs slightly from that used by van Vleck [9], who failed to recognise a connection between the electronic contribution to the rotational g factor and rotational nonadiabatic terms [150,56]. There exists nevertheless a clear evolution from the advance in van Vleck s [9] elaboration of Dunham s [5] innovative derivation of vibration-rotational energies into the present effective hamiltonian in formula 29 through the work of Herman [60,66]. The notation g for two radial functions pertaining to extra-mechanical effects in formula 29 alludes to that connection between... 

The general formula giving the paramagnetic susceptibihty for free ions has been established by Van Vleck ... 

Whereas Si and s2 are true one-electron spin operators, Ky is the exchange integral of electrons and in one-electron states i and j (independent particle picture of Hartree-Fock theory assumed). It should be stressed here that in the original work by Van Vleck (80) in 1932 the integral was denoted as Jy but as it is an exchange integral we write it as Ky in order to be in accordance with the notation in quantum chemistry, where Jy denotes a Coulomb integral. 

The second high-frequency term involves a sum over all discrete states and an integration over the continuum states the difficulties involved have been outlined before. Little is known about the continuum states, but what few calculations there are for simple systems92 suggest that they may be at least as important as the discrete states. For this reason early calculations were done in the closure approximation, notably by Van Vleck in the 1930 s. The difficulties of calculating xHF have been reviewed by Weltner.93 Experimentally xHF may be obtained from rotational magnetic moments. For linear molecules these can be obtained from molecular-beam experiments, which also measure the anisotropy x Xi- directly. The anisotropies may also be derived from crystal data, the Cotton-Mouton effect and, recently, Zeeman microwave studies principally by Flygare et al.9i... 

The term was first used by Van Vleck who explained it thus, referring to carbon in CH4 ...the spins of the four electrons belonging to sp3 were assumed paired with those of the four atoms attached by the carbon. Such a condition of the carbon atom we may conveniently call its valence state. He then showed a calculation which led to the conclusion that The valence state of C has about 7 or 8 more volts of intra-atomic energy than the normal state. This is the energy required to make the C atom acquire a chemically active condition... [1]. Mulliken defines it saying [it is] a certain hypothetical state of interaction of the electrons of an atomic electron configuration and A valence state is an atom state chosen so as to have as nearly as possible the same condition of interaction of the atom s electrons with one another as when the atom is part of a molecule. [2]. 

One must agree that the precise recipe implied by Van Vleck s and Sherman s language is daunting. The use of characters of the irreducible representations in dealing with spin state-antisymmetrization problems does not appear to lead to any very useful results. Prom today s perspective, however, it is known that some irreducible representation matrix elements (not just the characters) are fairly simple, and when applications are written for large computers, the systematization provided by the group methods is useful. 

The Yamanouchi-Kotani basis in the 77-electron --adapted spin space is closely related to the standard Young tableaux used in characterizing irreps of the symmetric group [50] and is conveniently represented by Van Vleck s branching diagram [18, 42]. To a basis function QfM we assign an array... 

Although the theory of these related phenomena is fairly well established, very few calculations of the constants involved have been reported. Presumably this is because they involve the calculation of off-diagonal matrix elements. A detailed account of the theory of /l-doubling in 2II states of diatomics has been given by Van Vleck,123 Mulliken and Christy,124 and Hinkley, Hall, Walker, and Richards.125 A brief synopsis is presented here. 

The most important source of line broadening in microwave studies of bulk gas samples is collisional or pressure broadening, the theory of which was first developed by Van Vleck and Weisskopf [77], They developed the line shape function... 

We can then make an even more drastic approximation and represent the molecular orbitals in these configurations by pure 2p atomic orbitals on the O atom. This approximation was called pure precession by Van Vleck [41] in this approximation the electrons in these outermost orbitals are in a spherically symmetric environment and they have a well defined value of the orbital angular momentum quantum number / (unity for a p orbital). In the pure precession approximation, we can derive very simple expressions for the g-factors [66], The values for OH predicted on the basis of this very simple model are given in table 9.4. The fact that they agree reasonably well with the experimental numbers suggests that the theoretical model is essentially correct. 

Let us now consider whether neglecting the atomic polarization P is justified. A simple classical treatment of atomic polarization of a gas molecule has been given by Van Vleck, Coop and Sutton, and Smyth. It is based on the approximation that the vibrations of the molecule are harmonic. Van Vleck argues that the result of this classical treatment is (to the same level of approximation) valid also under quantum mechanics. 

Many attempts were made to carry out reliable quantum mechanical calculations of dissociation energies, particularly in the early 1930 s, with the depressing results summed up by Van Vleck... 

The discussion of the electronic states of atoms and molecules and the correlation rules is too large a subject to be treated adequately in this book. Herzberg2i7 gives a full treatment, Gaydon lists the rules and gives examples of their application, and an account from the theoretical point of view is given by Van Vleck and Sherman 33. 

---