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The stress effect in an EPR study is first treated rigorously in terms of the piezospectroscopic tensor, taking account of the local symmetry of a defect. It is found that the degree of alignment ($\frac{{n}_{\ensuremath{\perp}}}{{n}_{\ensuremath{\parallel}}}$) provides incisive information on the structure of a defect; in general, a nonplanar vacancy cluster results in $\frac{{n}_{\ensuremath{\perp}}}{{n}_{\ensuremath{\parallel}}}l1.0$ and a {110}-planar vacancy chain gives rise to $\frac{{n}_{\ensuremath{\perp}}}{{n}_{\ensuremath{\parallel}}}g1.0$. We reanalyze the results on the $\mathrm{S}\mathrm{i}\ensuremath{-}P1$ and $\mathrm{S}\mathrm{i}\ensuremath{-}P3$ spectra. Based on the quenched-in alignment under 110g uniaxial stress, we confirm the assignment on the $\mathrm{S}\mathrm{i}\ensuremath{-}P1$ and the $\mathrm{S}\mathrm{i}\ensuremath{-}P3$ spectra to a negative charge state of nonplanar pentavacancy cluster and to the neutral charge state (spin 1) of the {110}-planar tetravacancy chain, respectively. Tentative models of the $\mathrm{S}\mathrm{i}\ensuremath{-}A3$ as a tetravacancy cluster and the $\mathrm{S}\mathrm{i}\ensuremath{-}A4$ spectra as a {110}-planar trivacancy chain are discussed.

The polarized infrared spectrum of nitrogen deuterated l -alanine single crystals is reported. The dichroism of the bands between 3200 and 300 cm−1 is analyzed correlated with local symmetry models for groups of atoms in the molecule. Analysis of the models were found to yield assignments consistent with those previously reported for alanine. Reassignment of the symmetric degenerate deformation modes of the NH3+group axe suggested by the observed dichroism of the deuterated alanine spectrum. Assignments newly resolved polarization behavior of the methyl hydrogen stretching bands are reported. Splitting of the methyl and ammonium group degenerate modes are observed along with factor group splittings of up to ∼ 12 cm−1 in a few of the fundamental bands. The value of considering the CH3 and NH3+ groups as identical dynamical units in the analysis of the skeletal modes of normal alanine is emphasized in the present study.

This paper investigates the relationship between Killing Tensors and separable systems for the geodesic Hamilton-Jacobi equation in Riemannian and Lorentzian manifolds: locally, a separable system consists of the vector and covector associated with a separable coordinate. It is shown that there are only two types of separable system, those associated with local symmetry groups and those which can be obtained by a simple transformation from orthogonal systems. Some sufficient conditions for existence are given and some global problems are enumerated. The results are illustrated with a demonstration that the existence of separable systems in a certain class of {2, 2} space-times is a consequence of the algebraic properties of the Weyl tensor.

The requirement that (either Abelian or non‐Abelian) local symmetry transformations be globally and unitarily implementable kinematical symmetries of relativistic systems implies the emergence of a dynamical group which has been suggested in earlier studies. The group leads to a 4‐velocity operator and to the Newton‐Wigner position operator. Demanding gauge invariance of localization determines a unique interaction structure. Superselection rules for the gauge charges arise.

The polarized emission and absorption spectra of single crystals of europium ultra(penta)phosphate, EuP5O14, were measured and interpreted. Most of the observed transitions were identified and the energy level structure of the 7F multiplet defined. The over‐all site symmetry is found to be extremely low (C1), but in the immediate vicinity of the Eu3+ ion the local symmetry appears to deviate little from C2v. Crystal field calculations were performed for such symmetry and gave a respectable fit to the observed Stark splittings of the 7F multiplet. A simple structural model for the first coordination shell of the Eu3+ ion is proposed, consistent with the spectroscopic behavior and with the signs and relative magnitudes of the calculated crystal field parameters. Finally, the decay times of the 5D0 and 5D1 emitting states of the ion were calculated and found to be consistent with measurement.

Electron Spin Resonance study of Dy in LaSb single crystal indicates appreciable angular variation of the ESR linewidth at X band frequency. The data is interpreted in terms of a random stress model with possible local tetragonal distortions.

It is well known that the study of the fine structure of the IR bands, together with the polarization of the Davidov splitting components and with the analysis of the changes in selection rules, going from vapor and liquid states to the crystal, permit the determination of the local symmetry, factor group symmetry and number of molecules in the unit cell of a molecular crystal. The activity of each multiplet component and its polarization in the IR spectrum of the crystal is determined in fact by affiliation with one or the other factor group symmetry class, and the corresponding transition moments μx, μy and μz, active in the IR absorption, are directed along the characteristic directions of the unit cell axes, determined by its symmetry.

Relative stabilities of 1-bicyclo[2.2.2]octyl (9), 1-benzobicyclo[2.2.2]-octenyl (10), 1-dibenzobicyclo[2.2.2]octadienyl (11), and 1-tribenzobicyclo[2.2.2]octatrienyl(12) radicals were obtained by means of the relative rates of the free radical bromine abstraction from the corresponding bridgehead bromides by a silyl radical. It was found that 9 and 12 were more stable than expected. The observed order of stability 9>10>12>11 can not be explained by the usual concepts alone. The extra stabilization of 9 or 12 (or destabilization of 10 or 11) was interpreted in terms of the local symmetry (or local asymmetry) of these radicals.

Working in the classical tree approximation and for the Abelian case only we indicate the existence of converse routes to the Higgs mechanism. In particular, we show how a carefully formulated compatibility between gauge invariance and massiveness of a vector field leads to spontaneous breakdown of the local symmetry.

A semiempirical MO method was used to calculate potential energy surfaces for ketene dimerization. One supra-supra and two supra-antara pathways were investigated. Six parameters were used to characterize the relative motion of individual groups. Two levels of approximation for the motion were considered. First, synchronous reaction pathways were followed, and a set of single-dimensional potential curves generated. Then, deviations from these synchronous reaction pathways were considered for each parameter and five two-dimensional potential surfaces for each pathway generated. Agreement with the available experimental data is satisfactory. However, we conclude that contrary to the Woodward-Hoffmann rules [1] the supra-supra pathway is allowed and the supra-antara pathways essentially forbidden. In the former case the local symmetry of the orbitals involved in the ring formation is not conserved during the reaction, in the latter case the nuclear repulsion is dominating.

The electron paramagnetic resonance of Gd${\mathrm{P}}_{5}$${\mathrm{O}}_{14}$ and of mixed ${\mathrm{Gd}}_{x}{\mathrm{Eu}}_{1\ensuremath{-}x}$ ultraphosphates has been studied. The Gd ultraphosphate shows a strong anisotropic structure, but the observed linewidths of the order of several-hundred gauss forbid a detailed analysis of the local symmetry of gadolinium. However, mixed samples containing predominantly ${\mathrm{Eu}}^{3+}$ and 5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ at.% of gadolinium show a number of relatively narrow lines (linewidths: 5-10 G). The angular variations of the allowed and forbidden absorption lines have been fitted to the spin Hamiltonian corresponding to ${C}_{S}$ symmetry. Eight different centers have been found, four of them being related to the others by two reflexion planes. A refinement of the crystal structure of europium ultraphosphate Eu${\mathrm{P}}_{5}$${\mathrm{O}}_{14}$ (monoclinic space group $P{2}_{\frac{1}{b}}\ensuremath{-}{C}_{2h}^{5}$) has been carried out by application of the least-squares method of calculation to single-crystal x-ray data ($R=0.040$). The cell parameters are $a=8.744$, $b=12.949$ and $c=8.925$ \AA{}, $\ensuremath{\gamma}=90.46\ifmmode^\circ\else\textdegree\fi{}$, $Z=4$. Crystal-structure studies show that the structure consists of P${\mathrm{O}}_{4}$ tetrahedra sharing tops in zig-zag chains running parallel to the $b$ axis and P${\mathrm{O}}_{4}$ tetrahedra loops connecting the chains. The oxygen atoms around the Eu atom form an eight-coordinate polyhedron. The correlations between the crystallographic structure and the EPR results for rare-earth ultraphosphates are discussed in detail.

The realization of supergauge transformations on fields defined over an 8-dimensional space whose points are labeled by ${x}_{\ensuremath{\mu}}$ and the anticommuting Majorana spinor ${\ensuremath{\theta}}_{\ensuremath{\alpha}}$ is described. The covariant derivative is defined and applied to the problem of decomposing superfields into irreducible (chiral) parts and to the problem of constructing "supersymmetric" Lagrangians. Further, it is shown how to build internal symmetries (both global and local) into these Lagrangians. An example is discussed in which the internal (global) symmetry is spontaneously violated, giving rise to a supermultiplet of Goldstone particles (including fermions). When a local symmetry is broken the Higgs mechanism (for bosons and fermions) is shown to be operative. A possible solution to the problem of defining a conserved fermion number is indicated.

A number of cyclo-silicates and germanates with the benitoite, wadeite or tetra-germanate structure have been investigated by i.r. and Raman spectroscopy, so as to evidence the essential spectroscopic features of the Si 3 O 9 and Ge 3 O 9 rings and to show how these features are modified under the influence of a change of structure, with or without modification of the local symmetry of the ring. One band in the i.r. spectrum and two bands in the Raman spectrum have been found to be highly specific of the ring structure. The two Raman bands are observed in the 600-500 cm −1 region for the silicates, and 550-450 cm −1 region for the germanates; they correspond to bending motions of the ring, involving a predominant displacement of the ring oxygens, and no large displacement of the cations, as evidenced by the small 28 Si- 30 Si isotopic shift. The characteristic i.r. band is observed in the 760-700 cm −1 region for the silicates, and the 550-500 cm −1 region for the germanates, with a large (14 cm −1 ) 28 Si- 30 Si isotopic shift. This important mass effect of the cation is also reflected in the large frequency ratio ν(silicate) ν(germanate). This band is unique as long as the ring has the local C 3 h symmetry, irrespective of the crystal structure (benitoite or wadeite); but it is split into a multiplet for distorted rings. It is thus a sensitive means of detecting the local symmetry of the ring.

The i.r. intensities of the carbonyl stretching vibrations of a series of compounds, X3M—Mn(CO)5(X = Cl, Br and I; M = Si, Ge and Sn) with C4ν, local symmetry around the manganese atom have been measured. The intensities of the A1 mode of the four planar carbonyl groups increase as the halogen atom changes from Cl to I and/or the IVb metal atom changes from Si to Sn, and these increases correlate with the decrease of the metal-metal stretching force constants. This relationship between the i.r. intensities and the metal-metal stretching force constants can be interpreted in terms of the interaction of the IVb metal-manganese σ-orbitals with the π∗ (radial) orbitals of the four planar carbonyl groups.

Electron paramagnetic resonance spectrum of the Cu2+ ion in CsCl is studied at different temperatures. The local symmetry at the Cu2+ site is found to be tetragonal. A model of substitutional Cu2+ ion associated with a first neighbour cation vacancy is proposed to explain the observed spectrum.

In the first portion of this paper a theoretical calculation is presented for the ``free‐ion'' spectrum of Pr3+ (4f2). A least‐squares calculation is made to obtain a set of Slater and spin‐orbit parameters that gives a theoretical spectrum in closest possible agreement with the observed absorption spectrum of Pr3+ (4f2) in ethylsulfate crystals. The disagreement between the calculated and observed spectrum may be explained as due primarily to the neglect of the configuration interaction in the ``free‐ion'' calculation, and to a much smaller extent as due to the effect of the lattice environment surrounding the Pr3+ (4f2) ion.In comparing the spectrum of Pr3+ (4f2) in ethylsulfate crystals with the spectrum of the same ion in other crystals, the shift in energy of the J levels may be explained as due to the difference in chemical bonding in the various crystals. This ``chemical bonding'' shift may be accounted for by a simple change in the Slater and spin‐orbit parameters.Assuming that the local symmetry ...

The infrared and laser Raman spectra of methylcyclopentadienyl nickel nitrosyl have been measured. The spectra have been interpreted and discussed in terms of the spectra of cyclopentadienyl nickel nitrosyl and dimethylferrocene. The “local symmetry” of the NiNO group is also discussed.

The infrared spectra of CH 3 CH 3 , CD 3 CD 3 and CH 3 CD 3 have been measured under medium resolution (∼0.4 cm −1 ). The rotation-vibration bands have been analysed, and the rotational constants B ″ have been obtained from the parallel bands. By using the A ″ values determined by Welsh et al. , the Coriolis constants for the degenerate vibrations have been determined from the analysis of a successive series of Q branches for the perpendicular bands. A normal coordinate analysis has been made and the potential constants on the basis of the local symmetry force field (LSFF) have been obtained from the fundamental frequencies and the Coriolis constants of CH 3 CH 3 and CD 3 CD 3 . These potential constants have been checked by the comparison of the calculated values of CH 3 CD 3 with the observed. The potential constants and the Coriolis constants have been discussed in connection with some related molecules such as CH 3 X and CH 3 CN.

The vibrational spectrum of C 4 H 6 Fe(CO) 3 has been studied. An assignment of the frequencies on the basis of the local symmetry of the Fe(CO) 3 fragment (C 3v ) explains most of the observations, but the FeC and CO stretching modes of E symmetry are both split. Therefore the effective symmetry must be C s The C 4 H 6 vibrations are assigned on the basis of C s symmetry throughout.

Electron spin resonance (ESR) of trivalent gadolinium in reduced barium titanate has been observed at room temperature and 163°C with an X-band spectrometer. According to this temperature rise, the amount of Gd 3+ ions substituting Ti 4+ remarkably increased in BaTiO 3 reduced at 1300°C, while those substituting Ba 2+ decreased. The local symmetry of the crystalline field acting on Gd 3+ at the Ti 4+ site is cubic. Hence the observed spectrum was analyzed using a spin Hamiltonian \begin{aligned} \mathscr{H}{=}g\beta\vec{H}{\cdot}\vec{S}+{b_{4}}^{0}\left[{Y_{4}}^{0}+\frac{\sqrt{70}}{14}({Y_{4}}^{4}+{Y_{4}}^{-4})\right]+{b_{6}}^{0}\left[{Y_{6}}^{0}-\frac{\sqrt{14}}{2}({Y_{6}}^{4}+{Y_{6}}^{-4})\right] \end{aligned} where g , b 4 0 and b 6 0 are 1.992, 26±1 and -4±3 gauss, respectively, at room temperature and 1.992, 25.0±0.5 and -1.9±0.5 gauss at 163°C (above Curie temperature).

The magnetic structure of ${\mathrm{Er}}_{2}$${\mathrm{O}}_{3}$ and ${\mathrm{Yb}}_{2}$${\mathrm{O}}_{3}$ have been determined by analysis of neutron diffraction data on powders and single crystals. Noncollinear antiferromagnetic structures were found, with the moment direction related to the local symmetry axis. For ${\mathrm{Er}}_{2}$${\mathrm{O}}_{3}$, the moment on the ${C}_{2}$ site is $(5.36\ifmmode\pm\else\textpm\fi{}0.08){\ensuremath{\mu}}_{B}$ and at the ${C}_{3i}$ site the moment is $(6.06\ifmmode\pm\else\textpm\fi{}0.23){\ensuremath{\mu}}_{B}$. For ${\mathrm{Yb}}_{2}$${\mathrm{O}}_{3}$, the corresponding moments are $(1.86\ifmmode\pm\else\textpm\fi{}0.06){\ensuremath{\mu}}_{B}$ and $(1.05\ifmmode\pm\else\textpm\fi{}0.06){\ensuremath{\mu}}_{B}$. The N\'eel points are 3.4\ifmmode^\circ\else\textdegree\fi{}K for ${\mathrm{Er}}_{2}$${\mathrm{O}}_{3}$ and 2.3\ifmmode^\circ\else\textdegree\fi{}K for ${\mathrm{Yb}}_{2}$${\mathrm{O}}_{3}$. Calculations of the dipole-dipole energies for the observed structures indicate that the dipole forces are not sufficient to explain the structures. The dependence of the long-range magnetic order on the reduced temperature is the same in both systems. Good agreement with this temperature dependence was obtained by assuming a biquadratic exchange interaction and making a simple molecular-field approximation.

Extensive experiments are performed on trapping of the HCl, DCl, HBr, DBr, and HI molecules in rare‐gas lattices. Concentration, deposition rate, and temperature‐dependent studies yield the monomer spectra of the molecules. The HCl and DCl monomers in Ar, Kr, and Xe show hindered rotational spectra that is interpreted on the basis of 0h site symmetry. HCl in Ne also appears to rotate. HBr and DBr in Ar shows additional splitting which is attributed to either site splitting due to loss of one of the near‐neighbor atoms or site distortion toward D3h symmetry. HBr and DBr in the larger Kr lattice give spectra similar to the HCl spectra. The spectra indicate the predominant local symmetry is 0h and the barriers to rotation in the lattices are given from an interpretation of the spectra. The barriers to rotation are interpreted by extension of an electrostatic model.Calculations of rotational energy levels have been performed for the linear molecule in a lattice site of D3h symmetry. The perturbed rigid‐rotor ...

The infra-red (250–4000 cm −1 ) and Raman spectra (50–3200 cm −1 ) have been obtained for (C 5 H 5 )W(CH 3 )(CO) 3 and the method of local symmetry was used as a basis for a vibrational assignment. The results differ somewhat from previous studies on similar molecules.

The gas phase molecular structure of 2,3-dimethyl-2-butene has been investigated by the electron, diffraction technique. The following structural parameters (ra structure) have been obtained: CC = 1.336±0.004 A; C-C = 1.505±0.002 A; C-H = 1.092±0.003 A; ∠CC-C = 123.4±0.4°; ∠C-C-H = 110.5±0.7°; methyl torsional angle CC-C-H = 31±3°. If local C3v symmetry is assumed then a twist of 13 ±4° of the carbon skeleton is observed. This twist reduces to virtually 0° if no local symmetry is imposed on the methyl group. The twisted structure is in good agreement with that obtained by valence force-field calculations.

The crystal field which surrounds a polyatomic ion in a crystal lattice acts as a perturbation on the vibrational levels and influences them to a large extent. It depends upon the symmetry of the surrounding field whether degenerate vibrational levels may be split and whether infra-red inactive vibrations may become active. The influence of the (face-centred) cubic-crystal field on the vibrations of the borohydride ion, imbedded in the lattice of the alkali-halides, is discussed. The local symmetry group of the BH4− ion is found to be Td in the solid solutions studied.

The infrared absorption spectra of Co III , Cr III and Fe III tris acetylacetonates have been recorded from 55 to 400 cm −1 . The vibrations of the heavy atom skeleton are discussed on the basis of local symmetry, perturbed to give rise to the overall molecular symmetry.

The purely numerical computation of defect induced properties in polymers currently in use is time consuming since symmetry arguments cannot be exploited. Within the framework of Lifshitz's Green Function method, symmetry arguments well known from the treatment of chemical defects may be used for conformational defects, too, to reduce the computational work drastically. With this objective in mind, conformational defects are classified with respect to their local symmetry in a single polyethylene (PE) chain and, for irregular PE skeletons, the defect matrix is set up in terms of appropriate symmetry states. The defect matrix of a gauche position in an otherwise transplanar PE backbone is explicitly given and the projected densities of states of this system are calculated. The applicability of optical selection rules, obtained from local symmetry, to bulk PE is briefly discussed.

The infrared spectrum (1400–70 cm−1) of orthogermanates and of some orthosilicates of tetravalent elements (Zr, Hf, Th, U, Ce) has been investigated. A fairly detailed assignment has been deduced from both group-theoretical considerations, and relationships between the observed frequencies and, either the mass, or the ionic radius of the tetravalent cations. Some correlations between the bending frequencies, the D2d local symmetry of the anion and the ionic radius of the cation are also discussed.

Dimethyl sulfide and dimethyl sulfide-d1 were prepared, and their infrared spectra were measured in the gaseous and liquid states. The Raman spectra were measured in the liquid state. The assignments of their spectra were made. On these assigned frequencies, two sets of modified Urey-Bradley force constants and a set of local symmetry force constants were determined by a least-squares technique. The obtained force constants were then transferred to the treatment of the vibrational frequencies of dimethyl sulfide-d3. The centrifugal distortion constants obtained from the vibrational data were compared with those from the data of the microwave spectra in order to confirm the reasonableness of the obtained force constants.

Infrared (250–4000 cm −1 ) and laser Raman spectra (75–3300 cm −1 ) were obtained on C 5 H 5 V(CO) 4 and CH 3 COC 5 H 4 V(CO) 4 . A vibrational assignment is proposed which is based upon the concept of “local symmetry”. The cyclopentadienyl ring breathing frequency was found to be associated with the strong sharp Raman line at 1117 cm −1 . Force constants calculated for the carbonyl stretching vibrations were comparable to those of similar π-bonded metal carbonyls.

The potential energy surfaces for clusters of some three to sixty atoms under Lennard-Jones forces have been systematically explored using numerical optimization techniques. In searching for minimum-energy configurations three particularly compact non-lattice growth schemes emerge showing tetrahedral, pentagonal (D5 h ) and icosahedral symmetry respectively. All these systems were found to be appreciably more stable than microcrystallites based on the face-centred cubic structure while certain lattice elements were shown to be metastable for small numbers of atoms. Some qualitative conclusions are then drawn concerning the occurrence of saddle-points for delocalized motion and the contribution of these to the generation of configurational entropy in small clusters. A crucial feature of the energy surfaces examined is the breakdown of strict local symmetry in compact clusters of more than two ‘shells’ of atoms and the possibility of delocalized motion of surface atoms around a solid-like core. The...

The theoretical and experimental correlations between the symmetries of the microfields about ions, the degree of splitting of energy levels, and the selection rules for radiation have been so successful for ions in crystals that the extension of this approach to discover the precise point symmetries about ions in solutions appears limited only by instances where the spectra of the solutions are sufficiently discrete. The spectra of crystals containing a rare earth ion in known local symmetry furnish the quantum characters of the energy levels and then the numbers of lines in the respective transitions of the ions in solutions lead to the symmetries of the fields about the dissolved ions.Salts of europium which are regarded as strong electrolytes exhibit sufficiently sharp absorption spectra in solutions at room temperature while their fluorescence spectra become adequately discrete at the temperature of dry ice. The absorption spectrum of europic chloride in water proved to be the same as in a mixture of...

The effects of pressure up to 50 kbar and of compositional changes on the absorption spectra of a number of chromium‐containing silicate, phosphate, and borate glasses were observed. The spectra were analyzed into their component bands, and ligand‐field theory was used to interpret the results to obtain information about the local symmetry, distortion, and local compressibility of the chromium sites. The absorption properties are explained by assuming that, on the average, the trivalent chromium ions are surrounded by six oxygen ions in an octahedral arrangement. The behavior of the spectra indicates that a random distribution of Cr–O distances about an average Cr–O distance exists and that only small disortions from cubic symmetry occur. The variation of the ligand‐field parameters and the compressibilities of the sites depends mainly on the number of oxygen ions per unit volume in the glass, whether the changes are induced by external pressure or by compositional changes. Those glasses with a more open oxygen packing exhibit smaller crystal‐field strengths, larger compressibilities, and larger distortions from octahedral symmetry than do the more densely packed glasses. Also, the compressibilities of the chromium sites are much less than the bulk compressibilities of the glasses.

Electronic transitions at a foreign probe ion in a lattice exhibit vibrational sidebands. They may be used as a new tool to investigate lattice dynamics. To make this too effective the theory of vibronic spectra has been refined. The principal refinement is that of a partial Born-Oppenheimer approximation which establishes a rigid coupling of the electronic wavefunctions of the foreign ion to its own nucleus. The structural form of the one-phonon sideband is given as a projection of the classical Greens' function (imaginary part) onto single multipole-fields in lattice space. Employing a variety of electronic transitions and by careful group-theoretical analysis a complete irreducible sequence of projections can be extracted from the experiments. These functional forms depend sensibly on the eigenvectors of the lattice modes, whence they contain information, which cannot be received from neutron scattering. Moreover, the spectra related to the higher multipoles give insight into the disturbed (local) dynamics, whereas the lower type spectra concern the undisturbed (ideal) one. Systems, where the foreign probe ion has high symmetry, are most suitable for the new method. For systems of low local symmetry approximations are suggested by the low-frequency behaviour of the measured one-phonon band. Because of the high resolution of optical measurements, the information from vibronic spectra is comparable or even superior in detailed richness to neutron scattering data.

Measurements are reported on the magneto-crystalline anisotropy of manganese ferrous ferrites at low temperatures. Results are also given on the anisotropy that can be induced by cooling the samples in a magnetic field down to 4°K. The local symmetry axis of this uniaxial anisotropy is the [100] axis. Time dependent anisotropies at 4°K have been found. These manifest themselves as a rotational hysteresis and as a time dependent torque. These quantities can be described by an extension of the after-effect theory of Neel's. At lower temperatures another contribution to the rotational hysteresis appears, that is independent of time and field, it depends linearly on the concentration of ferrous ions.

The i.r. and Raman spectra of Co(π-C3H5)(CO)3 are reported, and an assignment proposed. The vibrations of the Co(CO)3 portion of the molecule can be assigned assuming a [local symmetry] of C3v, in contrast to the molecule Mn(π-C3H5)(CO)4, where the overall symmetry had to be used.

Infrared spectra in the range 700–250 cmP −1 have been studied for several π-arenechromiumtricarbonyl complexes (arene = benzene, chlorobenzene, methyl benzoate, anisole, mesitylene, aniline, N-dimethylaniline, o - and p -toluidine). Comparison with the ligand spectra enabled the ligand frequencies to be localized and the A 1 and E Cr-C-O bending and Cr-C stretching modes were reassigned on the basis of a C 3V local symmetry for the -Cr(CO) 3 groupings. A normal coordinate treatment has been carried out on C 6 H 6 -Cr(CO) 3 , in a point-ring approximation, using a diagonal symmetry force field.

Infrared and Raman spectra of solutions and solid samples of (π-C 5 H 5 )Re(CO) 3 have been obtained. An assignment of the normal modes in terms of ‘local symmetry’ is offered and compared with the data for (π-C 5 H 5 )Mn(CO) 3 and related compounds. The frequencies and force constants of M-CO bonds and photochemical substitution of CO group to other ligands demonstrate the enhanced strength of Re-CO band in C 5 H 5 Re(CO 2 ) as compared with the Mn-CO band in C 5 H 5 Mn(CO) 3 .

Raman and i.r. spectra of the title compounds are reported and assigned for both solids and solutions. ν(C–H) modes show correlationsplitting, but the remainder of the internal modes of the π-allyl ligands can be discussed in terms of Cs local symmetry. ν(C–C–C) modes of the allyl skeleton are placed ca. 1383 and 1020 cm.–1 in the parent complex.

Hydrodynamics is developed in the critical region of phase transition by noticing that the effect of spontaneous symmetry breaking must fully be taken into account there, where the symmetry breaking appearing locally above the critical temperature T c increases its both coherence length and life time to infinity as temperature T approaches T c . It is predicted that an energy density wave will finally be observed as we approach arbitrarily close to T c from above. In magnets, only the diffusive excitation of local magnetization is expected if the observation takes place during a finite time which is much larger than the life time τ SB of the local symmetry breaking above T c . This situation of observation cannot be realized in the limit T → T c since the life time τ SB diverges in the same limit. On the other hand, if the time needed for the observation is less than the life time τ SB specifically in the critical region, the alternative hydrodynamic excitation to be observed is an energy density wave.

A complete SCF calculation is performed to obtain g-values for both cis and trans isomers of the semidione radical (CHO) 2 − . Results are then generalized to all carbonyl π radicals through the equation 〈g〉=2.0026 + Γ∑ ρ0 ΔE where Δ E is an n → π ∗ excitation energy, ϱ 0 is the Λ spin density on oxygen, and Γ is a function of both total molecular symmetry and local symmetry at the carbonyl group. Theoretical and empirical expressions for Λ are obtained. The general equation can be used to determine spin densities from measured g -values and visible /uv absorption spectra.

1. A forsterite ceramic with copper introduced from solution contains two types of Cu2+. One of these gives a broad nearly isotropic line with geff=2.18, which is due to Cu2+ in a tetragonally deformed octahedron of oxygen ions. The Jahn-Teller effect, which is responsible for this deformation, is averaged by reorientation of the tetragonal axis. The second type is seen only at low temperatures and has a resolved HS; it is due to Cu2+ in an analogous environment, but with the reorientation frozen-in. 2. The relation between the two types of center is the same throughout the volume of the specimen. 3. Cu2+ enters the vitreous phase on firing at 1000 ° C. 4. Ordering of the local symmetry of the environment of the copper occurs as the firing temperature is raised.

The i.r. and Raman spectra of the bimetallic carbonyls ReCo(CO)9 and MnCo(CO)9 have been examined in the CO stretching region, 2200-1800 cm−1. Tentative assignments have been made for the fundamental CO stretching modes and with the additional data from 13CO enrichment, simplified sets of CO force constants calculated. The results show that although the symmetry of the molecules is probably Cs, each half of the molecule maintains its local symmetry, e.g. C4v on the -Re(CO)5 unit, in the spectral analysis.

In Laves phase compounds Zr(Fe 1- x M x ) 2 where M=V, Cr, the crystal structure changes from MgCu 2 type to MgZn 2 type with composition x . MgCu 2 type compounds are ferromagnetic and MgZn 2 type compounds are paramagnetic. The local symmetry of the surroundings of Fe affects the magnetic moment. Magnetization measurement on MgCu 2 type compounds shows that V and Cr atoms act on the magnetic moment of Fe to decrease at the rate of 1.4 µ B and 0.4 µ B . Decrease of the magnetization is interpreted by assuming a discrete magnetic moment distribution of Fe, which are obtained from the configuration of V or Cr atoms in the surroundings of Fe.

Linear splitting of ESR signals of Gd3+ ions introduced into SrMoO4 and CaWO4 lattices were observed under applied electric field. Measured signal shifts can be described quite accurately in terms of a correction which is added to the spin Hamiltonian and at most includes only quadratic terms of spin projection operators. It has been found that the constant Re (R), characteristic of the signal shifts of Gd3+ impurity ions, is somewhat greater for SrMoO4 than for CaWO4. The experimental results can be explained consistently only by assuming that the local symmetry of the neighbourhood of Gd3+ ions in SrMoO4 and CaWO4 is represented by the S4-group. By way of a specific example it is shown that the study of ESR spectra in an externally applied electric field gives a wide opportunity for establishment and more exact definition of a symmetry group of the local neighbourhoods for impurity ions in crystals.

Polarization functions are added in two steps to a split-valence extended gaussian basis set: d-type gaussians on the first row atoms C. N, O and F and p-type gaussians on hydrogen. The same d-exponent of 0.8 is found to be satisfactory for these four atoms and the hydrogen p-exponent of 1.1 is adequate in their hydrides. The energy lowering due to d functions is found to depend on the local symmetry around the heavy atom. For the particular basis used, the energy lowerings due to d functions for various environments around the heavy atom are tabulated. These bases are then applied to a set of molecules containing up to two heavy atoms to obtain their LCAO-MO-SCF energies. The mean absolute deviation between theory and experiment (where available) for heats of hydrogenation of closed shell species with two non-hydrogen atoms is 4 kcal/mole for the basis set with full polarization. Estimates of hydrogenation energy errors at the Hartree-Fock limit, based on available calculations, are given.

Infrared and Raman spectra of solutions of the compounds ArCr(CO)3 (where Ar = C6H6, C6H5F, C6H5CH3, ortho-C6H4(CH3)2 and 1.2.3-C6H3(CH3)3) have been obtained. These confirm that the method of “local symmetry” is of very restricted validity when discussing the C-O stretching vibrations, and also provide unambiguous evidence for the assignment of low-frequency skeletal modes hitherto reported only in solid-phase spectra. For (C6H5CH3) Cr(CO)3, a detailed vibrational assignment is proposed.

In the temperature range 120 to 800 °K and frequency range 1000 to 300 cm−1 a study has been made of the infrared absorption spectra of the impurity anions WO-and MoO-in KI and CsI single crystals. It is shown that W and MOO form neutral complexes W · M2+ and MoO · M2+ in KI lattice with cations M2+ (Ca2+, Sr2+, Ba2+) similar to the complexes SO · M2+, CrO · M2+ and SeO · M2+ observed earlier in the f.c.c. lattices. Here a lowering of the local symmetry to C2v of the impurity tetrahedrons results in the appearance of triplets in their vibration regions v3(A2) and v4(F2). The fine structure in the infrared spectrum of MoO · M2+ + KI was interpreted to be isotopic. A local symmetry of the impurity WO and MoO in CsI lattice was not identified unequivocally from the IR absorption spectra. The latter have doublet and quartet structure in the vibration regions v1(A1) and v3(F2), respectively, and depend on the impurity tetrahedrons and M2+ cation concentration. One, probably, should assume the interstitial formation of impurities into b.c.c. lattice of CsI which results in the existence of complex anion-cation neutral complexes of different kinds. [Russian Text Ignored.]

The infrared spectra of tetraphenylgermane and pentadeuterotetraphenylgermane have been recorded from 4000 to 33 cm−1. The Raman spectra have also been recorded of the samples as solids. The phenyl vibrations have been assigned assuming C2v local symmetry. The spectrum of the completely deuterated molecule is found to be very similar to those observed for the corresponding completely deuterated monophenylgermanes. The proposed assignments are consistent with previous assignments given for other phenyl- and pentadeuterophenylgermanes.