Low-symmetry Systems Research Articles

On the electronic structure of N,N′-ethylenebis(acetylacetonatiminato)Co(II), Co(II)acacen

A single crystal ligand ENDOR study on N,N′-ethylenebis(acetylacetonatiminato)Co(II), Co(acacen), is reported. The hyperfine tensors of the two nitrogens, of four carbon-13 and of five protons as well as the nitrogen quadrupole tensors have been evaluated. A DOUBLE ENDOR experiment was carried out in order to determine the signs of the carbon-13 hyperfine couplings. The problems of asymmetric contributions to the hyperfine tensors, which are especially important for low symmetry systems with low-lying excited states, are discussed. The ligand hyperfine tensors can be understood assuming π-spin density on the ligand system and hence support the |2 A, yz⟩ groundstate for Co(acacen). They furthermore provide detailed knowledge on the electronic structure of the complex via the spin density distribution. The structural information derived from the proton ENDOR results is in good agreement with the X-ray data.

On the use of localised molecular orbitals in some triatomic radicals

The population localisation method of Verwoerd is extended to an ab initio framework and is applied to molecular systems of low symmetry for which there is evidence of delocalisation and which contain a large number of non-bonded electrons. Three isoelectronic radicals are chosen, HCN −, HCO and HBO −, which, for example, have large experimental proton isotropic hyperfine coupling contants of 13.75 mT, 12.6 mT and 9.42 mT respectively, suggesting that the unpaired electron is extensively delocalised in each radical. The purpose of this paper is to investigate whether this delocalisation can be usefully discussed within the concept of localised orbitals. The rephrasing of the population localisation method into one solving an eigenvalue problem eliminates numerical difficulties encountered elsewhere, but produces a procedure which is non-uniform in nature. Some of the difficulties inherent in the procedure are illustrated, but careful application of the method produces highly localised, and similar, orbitals for all three radicals even though the delocalisation of the spin density in each, inferred from ESR, is very different. Some advantages of the method are discussed.

Ab initioHartree-Fock calculations of crystalline systems using full-symmetry analysis of basis-set expansions

A technique is presented for carrying out ab initio Hartree-Fock calculations on systems of infinite three-dimensional periodicity. The method represents an adaptation of standard molecular basis-set expansion techniques and fully utilizes translational and point-group symmetry to simplify the calculations. It is shown that the expression for total energy may be written as a sum of pairwise interactions between neutral charge units consisting of a nucleus and a localized compensating electronic charge. The resulting sums are rapidly convergent. The technique is illustrated with sample calculations on face-centered-cubic lattices of hydrogen, lithium, and sodium. Generalization to systems of lower symmetry is discussed.

THE GENERAL TYPES OF MULTIPLE SOLUTION IN PATTERSON METHOD FOR LOW SYMMETRY SYSTEMS

In solving the crystal structures containing heavy atoms by patterson method, if the heavy atoms have a pseudo-symmetry which is higher than that of the whole structure, this will result in multi-solution positions of light atoms (two, four or eight possible positions). Expressed in reciprocal space, this problem is equivalent tc that some of the component signs of the diffraction structure amplitudes are undetermined. Seventy four space groups of low symmetry systems (trielinic, mono-clinic and orthorhombic systems) have been analysed. For an asymmetric unit involving only one heavy atom, with the possible positions of the heavy atom and the pseudo-symmetry given, the multi-solution types of light atoms and the distribution rule for components of diffraction struture amplitudes are obtained. In addition, a possible way for resolving these problems by direct method is proposed.

A.C. electrical conductivity of pure and doped potassium perchlorate

A.C. electrical conductivity of potassium perchlorate (KP) has been measured in the temperature range 25–325°C at frequencies ranging from 50–500 Hz using an automated technique. The results are interpreted in terms of a novel mechanism involving Schottky defects in the anion sublattice and Frenkel defects in the cation sublattice. The conductivity behavior of KP is compared with literature data on similar low-symmetry systems containing polyatomic ions.

Spin-lattice relaxation of some less common weakly quadrupolar nuclei

Nuclear magnetic spin-lattice relaxation times have been measured for the weakly quadrupolar nuclei 6Li, 9Be, and 133Cs in some simple inorganic and organometallic compounds in isotropic liquid phase. In an attempt to separate the various mechanistic contributions to the total relaxation rate, temperature-dependent T 1 and NOE experiments were performed. For aqueous solutions of the lithium ion extraordinarily long relaxation times were found (up to 1000 sec), with negligible quadrupolar relaxation and with the bulk of the relaxation rate arising from dipolar interactions involving hydrate protons. In systems of lower symmetry, quadrupolar and 6Li 1H dipolar relaxations account for up to 50% of the relaxation rate and the observed relaxation times are typically of the order of tens of seconds. In the hydrated beryllium ion 9Be relaxation is predominantly quadrupolar and dipolar at low temperatures, while spin-rotation prevails at elevated temperatures. In systems of lower beryllium valence electron symmetry the quadrupolar mechanism dominates. In spite of relaxation times of up to 30 sec, 133Cs relaxation in the solvated ionic state appears to be entirely quadrupole dominated.

G-shift measurements for Yb3+in Tm3Al5O12

g shifts arising from interactions with singlet groundstate host lattice Tm3+ ions have been measured by EPR for Yb3+ at orthorhombic sites in cubic Tm3Al5O12. The g values in absence of any Yb-Tm interactions (gCF) have been deduced by two methods. The first involves measurement of the Yb hyperfine parameters (both by EPR and by Mossbauer techniques) which are related to the gCF using the fact that J remains a good quantum number. The second method involves measurement of the g values as a function of host lattice susceptibility chi , the extrapolation to zero chi giving the gCF. Complete agreement between the two sets of gCF values was not obtained. The results show that in fact extrapolation of the g values as a function of the bulk isotropic susceptibility can lead to erroneous results when the local symmetry is lower than cubic. Obtaining the g shifts from the hyperfine values could be a generally useful method in low symmetry systems.

Vibrational spectra of crystalline dimethylglyoxime, HONCCH 3CH 3CNOH

Infrared and Raman spectra of crystalline powders of dimethylglyoxime- d 0 and - d 2 have been investigated. Polarized i.r. spectra of a single crystal specimen were recorded and used in the vibrational assignment. Small band shifts with the rotation of the polarizer were observed in accord with a previous hypothesis on occurrence of intermode mixing in systems of low symmetry.

Strahlungsinduzierte und ionenaustauschbedingte Kristalldefekte in Zirkoniumphosphaten

Abstract For the low-symmetry system of the ion-exchanger zirconium phosphate the influence of irradiation and ion-exchange on the crystal disorder has been investigated by means of photographic x-ray diffraction methods. The weakening and the shifting of Bragg reflections and the broadening of maxima of diffuse scattering allow the estimation of the concentration and the strength of defects induced in this system.

Low-symmetry features of the ESR spectra of KY(MoO4)2-KEr⋅(MoO4)2 crystals

We have studied the ESR spectrum of crystals of the low-symmetry system KY(MoO4)2-KEr(MoO4)2 at low temperatures and frequencies of 10, 30, and 60 GHz. The resonance absorption band in the spectrum has a triplet structure whose origin is due to the existence in KEr(MoO4)2 of one-dimensional chains of Er3+ ions interacting via strong dipole-dipole coupling along the crystallographic c axis. We discuss the features of the ESR spectrum of KEr(Mo04)2 caused by the presence in the energy spectrum of the Er3+ ion of an excited state lying close to the ground state, as well as by components of the local crystal field whose symmetry is lower than orthorhombic. We make a comparison with the ESR spectra of the other previously studied molybdates, KDy(MoO4)2 and KYb(MoO4)2. We reach a conclusion regarding the significant role of the individual characteristics of rare-earth ions in determining the ESR spectra of low-symmetry concentrated magnetic crystals.

Some consequences of molecular symmetry in the theory of photoelectron angular distributions

The molecular photoelectron angular distribution is treated by regarding the ionization process as a coherent superposition of component transitions, each having specific molecular symmetry transformation properties. The symmetry-related properties of the resulting contributions and the selection rules that govern their occurrence in some specific ionization models are examined, and a generally applicable rule is obtained requiring interferences between ionization components with appropriate molecular symmetry transformation properties to vanish identically. Application of molecular symmetry methods to the angular momentum transfer formulation leads to the development of methods for generating angular-momentum-transfer selection rules. These methods are applied to direct ionization in an orbital approximation for 40 symmetries and for the general case of an n-fold rotational symmetry, and meaningful restrictions on the allowed values of the angular momentum transfer are shown to apply even to some low symmetry systems.

Decoupled networks: An approach to low symmetry vibrational problems

By considering the condition for lowest order decoupling of the vibrations of local atomic configurations of continuous bonded covalent systems, we arrive at an approximation which we call a decoupled network (DCN). The DCN them serves as a basis for a method of relating vibrational and configurational data in low symmetry systems. This method applied to amorphous, crystalline and molten As 2S 3 yields significant insight into the relationship between the features of the vibrational spectra and the local order.

Behavior of the In-Plane g Tensor in Low-Symmetry d1 and d9 Systems with Application to Copper and Vanadyl Chelates

A general expression is developed for the orientations and magnitudes of the principal in-plane g values of low-symmetry d1 and d9 complexes considered as highly perturbed axial systems. The low-symmetry components of the ligand field cause participation of | 3z2 − r2〉 in the ground state and reorientation of the | xz〉, | yz〉 orbital set. The way in which these effects show up in the in-plane g ellipse is investigated for a number of possible bonding situations. A critical evaluation is made of the information which can be (and that which cannot be) obtained from the in-plane g values, and the observed g parameters from electron paramagnetic resonance of several copper and vanadyl chelates of Schiff's bases and ketoenolates are discussed in terms of the theory.