Direct Dynamics Simulations Using Hessian-Based Predictor-Corrector Integration Algorithms

In previous research [J. Chem. Phys.111, 3800 (1999)] a Hessian-based integration algorithm was derived for performing direct dynamics simulations. In the work presented here, improvements to this algorithm are described. The algorithm has a predictor step based on a local second-order Taylor expansion of the potential in Cartesian coordinates, within a trust radius, and a fifth-order correction to this predicted trajectory. The current algorithm determines the predicted trajectory in Cartesian coordinates, instead of the instantaneous normal mode coordinates used previously, to ensure angular momentumconservation. For the previous algorithm the corrected step was evaluated in rotated Cartesian coordinates. Since the local potential expanded in Cartesian coordinates is not invariant to rotation, the constants of motion are not necessarily conserved during the corrector step. An approximate correction to this shortcoming was made by projecting translation and rotation out of the rotated coordinates. For the current algorithm unrotated Cartesian coordinates are used for the corrected step to assure the constants of motion are conserved. An algorithm is proposed for updating the trust radius to enhance the accuracy and efficiency of the numerical integration. This modified Hessian-based integration algorithm, with its new components, has been implemented into the VENUS/NWChem software package and compared with the velocity-Verlet algorithm for the H2CO→H2+CO, O3+C3H6, and F−+CH3OOH chemical reactions

Elementary excitations, exchange interaction and spin-Peierls transition in CuGeO3_3

The microscopic description of the spin-Peierls transition in pure and doped CuGeO_3 is developed taking into account realistic details of crystal structure. It it shown that the presence of side-groups (here Ge) strongly influences superexchange along Cu-O-Cu path, making it antiferromagnetic. Nearest-neighbour and next-nearest neighbour exchange constants $J_{nn}$ and $J_{nnn}$ are calculated. Si doping effectively segments the CuO_2-chains leading to $J_{nn}(Si)\simeq0$ or even slightly ferromagnetic. Strong sensitivity of the exchange constants to Cu-O-Cu and (Cu-O-Cu)-Ge angles may be responsible for the spin-Peierls transition itself (``bond-bending mechanism'' of the transition). The nature of excitations in the isolated and coupled spin-Peierls chains is studied and it is shown that topological excitations (solitons) play crucial role. Such solitons appear in particular in doped systems (Cu_{1-x}Zn_xGeO_3, CuGe_{1-x}Si_xO_3) which can explain the $T_{SP}(x)$ phase diagram.Comment: 7 pages, revtex, 7 Postscript figure

Temperature Dependence of Spin and Bond Ordering in a Spin-Peierls System

We investigate thermodynamic properties of a one-dimensional S=1/2 antiferromagnetic Heisenberg model coupled to a lattice distortion by a quantum Monte Carlo method. In particular we study how spin and lattice dimerize as a function of the temperature, which gives a fundamental process of the spin-Peierls transition in higher dimensions. The degree of freedom of the lattice is taken into account adiabatically and the thermal distribution of the lattice distortion is obtained by the thermal bath algorithm. We find that the dimerization develops as the temperature decreases and it converges to the value of the dimerization of the ground state at T=0. Furthermore we find that the coupling constants of spins fluctuate quite largly at high temperature and there thermodynamic properties deviate from those of the uniform chain. Doping of non-magnetic impurities causes cut of the chain into short chains with open boundary. We investigate thermodynamic properties of open chains taking relaxation of the lattice into consideration. We find that strong bonds locate at the edges and a defect of the bond alternation appears in the chain with odd number of sites, which causes enhancement of the staggered magnetic order. We find a spreaded staggered structure which indicates that the defect moves diffusively in the chain even at very low temperature.Comment: 7 pages, 17 figures; added comments on section 2 and 3, corrected typo

Mean-field theory of the spin-Peierls systems: Application to CuGeO3

A mean-field theory of the spin Peierls systems based on the two dimensional dimerized Heisenberg model is proposed by introducing an alternating bond order parameter. Improvements with respect to previous mean-field results are found in the one-dimensional limit for the ground state and the gap energies. In two dimensions, the analysis of the competition between antiferromagnetic long range order and the spin-Peierls ordering is given as a function of the coupling constants. We show that the lowest energy gap to be observed does not have a singlet-triplet character in agreement with the low temperature thermodynamic properties of CuGeO3.Comment: 3 Revtex pages. Submitted to Rapid Comm. Figures available upon reques

Cinco libros, dos prólogos y cuatrocientos sesenta y cinco capítulos para Tirant lo Blanch

Abordo en este artículo las características de la división textual de la versión anónima de la novela de Joanot Martorell que imprimió Diego de Gumiel en 1511, con el objetivo, a mi juicio, de ofrecer a sus lectores una obra que se amoldara al patrón de los libros de caballerías que tanto éxito empezaban a gozar ya a fines de la primera década del siglo XV

Isomerization dynamics of a buckled nanobeam

We analyze the dynamics of a model of a nanobeam under compression. The model is a two mode truncation of the Euler-Bernoulli beam equation subject to compressive stress. We consider parameter regimes where the first mode is unstable and the second mode can be either stable or unstable, and the remaining modes (neglected) are always stable. Material parameters used correspond to silicon. The two mode model Hamiltonian is the sum of a (diagonal) kinetic energy term and a potential energy term. The form of the potential energy function suggests an analogy with isomerisation reactions in chemistry. We therefore study the dynamics of the buckled beam using the conceptual framework established for the theory of isomerisation reactions. When the second mode is stable the potential energy surface has an index one saddle and when the second mode is unstable the potential energy surface has an index two saddle and two index one saddles. Symmetry of the system allows us to construct a phase space dividing surface between the two "isomers" (buckled states). The energy range is sufficiently wide that we can treat the effects of the index one and index two saddles in a unified fashion. We have computed reactive fluxes, mean gap times and reactant phase space volumes for three stress values at several different energies. In all cases the phase space volume swept out by isomerizing trajectories is considerably less than the reactant density of states, proving that the dynamics is highly nonergodic. The associated gap time distributions consist of one or more `pulses' of trajectories. Computation of the reactive flux correlation function shows no sign of a plateau region; rather, the flux exhibits oscillatory decay, indicating that, for the 2-mode model in the physical regime considered, a rate constant for isomerization does not exist.Comment: 42 pages, 6 figure

Temperature-dependent spin gap and singlet ground state in BaCuSi2O6

Bulk magnetic measurements and inelastic neutron scattering were used to investigate the spin-singlet ground state and magnetic gap excitations in BaCuSi2O6, a quasi-2-dimensional antiferromagnet with a bilayer structure. The results are well described by a model based on weakly interacting antiferromagnetic dimers. A strongly temperature-dependent dispersion in the gap modes was found. We suggest that the observed excitations are analogous to magneto-excitons in light rare-earth compounds, but are an intrinsic property of a simple Heisenberg Hamiltonian for the S=1/2 magnetic bilayer.Comment: 10 pages, 4 figures, REVTeX and PS for text, PS for figures direct download: http://papillon.phy.bnl.gov/preprints/bacusio.htm

Molecular astronomy of cool stars and sub-stellar objects

The optical and infrared spectra of a wide variety of `cool' astronomical objects including the Sun, sunspots, K-, M- and S-type stars, carbon stars, brown dwarfs and extrasolar planets are reviewed. The review provides the necessary astronomical background for chemical physicists to understand and appreciate the unique molecular environments found in astronomy. The calculation of molecular opacities needed to simulate the observed spectral energy distributions is discussed