Partition function zeros for the two-dimensional Ising model

The distribution of complex temperature zeros of the partition function of the two-dimensional Ising model in the absence of a magnetic field is investigated. For anisotropic square and triangular lattices the distribution function is two-dimensional and satisfies a partial differential equation derived from a generalized scaling theory. Corresponding results for the isotropic square, triangular and honeycomb lattices are also presented.     

Theory of infra-red and optical spectra of antiferromagnets

The contributions of magnons to the optical properties of antiferromagnets having the rutile structure are discussed. The properties considered are electric-dipole active two-magnon absorption in the infra-red, and magnon sidebands on sharp-line exciton transitions in the visible. The discussion is based on a thorough treatment of the properties of excitons and magnons in the antiferromagnetically ordered state. The site-group and space-group symmetries of the magnetic excitations are derived and the selection rules for electric and magnetic dipole transitions are determined. The occurrence of magnetic Davydov splittings of the excitons is investigated, and their symmetry properties throughout the Brillouin zone are derived. The functional dependences of exciton energy on wave vector are calculated. Applications of the theory are made to experimental results on excitons and magnons in MnF₂, FeF₂ and CoF₂.

The possible mechanisms for two-magnon and magnon-sideband absorption are discussed, and the influence of crystal symmetry on these mechanisms is described. The two-magnon state responsible for electric-dipole absorption is identified and selection rules for electric-dipole activity are presented. A spin Hamiltonian for the two-magnon process is set up and used to derive expressions for absorption coefficients for electric vector parallel and perpendicular to the crystal c-axis. Comparison with experiment for MnF₂ yields numerical values for the parameters of the basic coupling mechanism. The exciton-magnon states which give rise to magnon-sideband absorption are explicitly constructed and electric-dipole selection rules are derived for all possible types of sideband. Spin Hamiltonians for the various magnonsideband absorption processes are presented and used to derive expressions for sideband shapes. The results are applied to the experimental spectra for MnF₂ and FeF₂ and the sideband shapes in MnF₂ are calculated numerically. The sideband shapes observable in emission spectra are also briefly discussed.     

Relation between the Superconducting Transition Temperature and the Axial Ratio in R Ni 2 B 2 C ( R =Y,Ho, Er,Tm, Lu) Under High Pressure

The effect of pressure on the lattice parameters of R Ni 2 B 2 C ( R = Y, Ho, Er, Tm, Lu) has been measured in order to investigate the relation of T C to axial ratio c/a in the tetragonal lattice or the cohesive properties of these materials. The large anisotropies are observed in the lattice compression curves especially for R =Ho and Tm; the c -axis is more compressible than the a -axis. On the other hand, the anisotropy in the lattice compression is found to be relatively small for R =Y and Lu. The close relation between T C and c/a is pointed out particularly for R =Ho.     

Symmetry analysis of the interplay between local moment anisotropies and propagation vectors in the borocarbides

Representational analysis is used to examine the interplay between Fermi surface nesting and local moment effects in the formation of the magnetically ordered states of the rare-earth nickel borocarbides, RNi₂B₂C. We derive compatibility tables for the propagation wavevector k, the local moment anisotropy and the ordered moment direction μ _k for materials with this tetragonal crystal structure. The magnetic structures observed in the rare-earth nickel borocarbides are discussed in this context.     

Interpersonal success factors for strategy implementation: a case study using group model building

Strategy implementation has been identified as an area of system dynamics literature requiring greater attention. Most strategies fail to be implemented successfully, and processes for effectively implementing strategy are yet to be fully explained and explored. The reported interpersonal success factors for strategy implementation are reported outcomes for group model building, suggesting potential applicability. A case study using validated survey methods yielded promising results, and suggests that further study is needed. This application of group model building may be a manifestation of the IKEA affect, where individuals value more highly solutions that they have partially assembled, and competency motivation, where individuals have positive affect to the successful completion of a complex task.     

Synthesis and crystal structures of two novel 3,4,5- trimethoxyphenyl derivatives from (Z)-1-[(2′,3′-dinitro-4′-methoxy)-phenyl]-2-[(3″,4″,5″-trimethoxy)-phenyl] ethene

The title compounds, (Z)-1-[(2′,4′-dimethoxy-3′-nitro)-phenyl]-2-[(3″,4″,5″-trimethoxy)-phenyl]ethene, C₁₉H₂₁O₇N (I), and 2-amino-4-methyl-6-(3,4,5-trimethoxy-phenyl)-pyrimidine, C₁₄H₁₇O₃N₃ (II), were obtained unexpectedly from a reaction involving (Z)-1-[(2′,3′-dinitro-4′-methoxy)-phenyl]-2-[(3″,4″,5″-trimethoxy)-phenyl]ethene (IV). The molecular structures of these compounds were obtained by single-crystal X-ray diffraction. Crystallization of I occurs in the centrosymmetric monoclinic space group P2₁/c (No. 14) with a=7.7311(5), b=19.9239(13), c=11.5725(8); and β=92.193(3) and Z=4. Crystallization of II occurs in the centrosymmetric monoclinic space group C2/c (No. 15) with a=21.296(2), b=6.8963(7), c=20.001(2); and β=114.121(6) and Z=8. Details of the synthesis and the structural characterization of the title compounds are presented and discussed.     

Asymptotic enumeration of dense 0-1 matrices with specified line sums

Let s=(s₁,s₂,…,sm) and t=(t₁,t₂,…,tn) be vectors of non-negative integers with . Let B(s,t) be the number of m×n matrices over {0,1} with jth row sum equal to sj for 1?j?m and kth column sum equal to tk for 1?k?n. Equivalently, B(s,t) is the number of bipartite graphs with m vertices in one part with degrees given by s, and n vertices in the other part with degrees given by t. Most research on the asymptotics of B(s,t) has focused on the sparse case, where the best result is that of Greenhill, McKay and Wang (2006). In the case of dense matrices, the only precise result is for the case of equal row sums and equal column sums (Canfield and McKay, 2005). This paper extends the analytic methods used by the latter paper to the case where the row and column sums can vary within certain limits. Interestingly, the result can be expressed by the same formula which holds in the sparse case.     

Natural linear-scaled coupled-cluster theory with local transferable triple excitations: applications to peptides

The natural linear-scaled coupled-cluster (NLSCC) method ( Flocke, N.; Bartlett, R. J. J. Chem. Phys. 2004, 121, 10935 ) is extended to include approximate triple excitations via a coupled-cluster with single, double, and triple excitation method (CCSDT-3). The triples contribution can potentially be embedded in a larger singles and doubles region. NLSCC exploits the extensivity of the CC wave function to represent it in terms of transferable natural localized molecular orbitals (NLMOs) or functional groups thereof that are obtained from small quantum mechanical (QM) regions. Both occupied and virtual NLMOs are local because they derive from the single-particle density matrix. Noncanonical triples amplitudes are avoided by applying the unitary localization matrix to the canonical CC wave function for a QM region. A generalized NLMO code interfaced to the ACES II quantum chemistry software package provides NLMOs for the relevant number of atoms in a given functional group. Applications include linear polyglycine and the pentapeptide met-enkephalin, which was chosen as a more realistic three-dimensional system with nontrivial side chains. The results show that the triples contributions are quite large for aromatic bonds suggesting an interesting active space method for triples in which different bonds require different excitation levels. The NLSCC approach recovers a very large percentage (>99%) of the CCSD or CCSDT-3 correlation energy.     

A coupled cluster study of the electronic spectroscopy and photochemistry of Cr(CO)6

The transition energies to the low-lying singlet and triplet excited states of Cr(CO)(6) are computed by equation-of-motion coupled cluster singles and doubles (EOM-CCSD) and similarity transformed equation-of-motion coupled cluster singles and doubles (STEOM-CCSD) methods with all-electrons basis sets. Both experimental and optimized geometries are used for the calculations. Calculations with various basis sets, among them one of the largest calculations performed at the EOM-CCSD level, based on atomic natural orbitals with 627 functions, were used to evaluate the basis set influence on computed transition energies. The presence of a shoulder at 3.9 eV in the experimental absorption spectrum, assigned to the (1)A(1g)-->(1)T(2u) transition, which was not reproduced by recent density functional theory (DFT) or multi-state complete active space perturbation theory (MS-CASPT2) is supported by the present STEOM-CCSD calculations with a theoretical value of 3.92 eV. In addition to this weak (1)A(1g)--> a (1)T(2u) absorption, we observe two strong absorptions corresponding to (1)A(1g)--> a (1)T(1u) at 4.37 eV (vs. an experimental value of 4.46 eV) and (1)A(1g)--> b (1)T(1u) at 5.20 eV (vs. an experimental value of 5.53 eV). Both are characterized as metal-to-ligand charge-transfer (MLCT) allowed transitions. The first metal-centered (MC) absorption at 4.37 eV in our best calculation is degenerate with the lowest MLCT absorbing state. The one-dimensional potential energy curves associated to the low-lying singlet MLCT and MC states as a function of the chromium axial carbonyl bond distance q(a) = [Cr-CO(axial)] show that an avoided crossing exists between the a (1)T(1g) (MC) and a (1)T(1u) (MLCT) states near 1.92 A, which is very close to the equilibrium Cr-CO distance. Moreover, the MC state seems to be dissociative for the CO loss. These two important features could explain the ultra-fast dissociation of CO (100 fs) observed in recent low intensity laser probed gas phase experiments.