Lattice Dimerization Research Articles

Coulomb correlations in one-dimensional conductors with incommensurate band fillings and the semiconductor-metal transition in polyacetylene

The one-dimensional Hubbard and Hubbard-Peierls models are studied for various regimes of band filling. A variational ansatz for the ground state is worked out for small values (on the scale of the bandwidth) of the on-site Coulomb interaction. It is shown that this term enhances the lattice dimerization in the half-filled band case, but suppresses the lattice distortion in the incommensurate case. The semiconductor-metal transition in doped polyacetylene is tentatively attributed to this effect. Parameter values extracted from properties of the undoped material yield a critical dopant concentration of about 3%.

Coulomb correlations and optical gap in polyacetylene

A model including both electron-phonon coupling (as in the SSH Hamiltonian) and electron-electron interactions (on-site term U, nearest-neighbor term V) is treated within the variational scheme of Gutzwiller. It is shown that for weak electron-phonon coupling the primary effect is a bond-order wave induced by electronic correlation, whereas the lattice dimerization is a secondary effect. Correspondingly the optical gap is mainly due to electronic correlation.

Lattice distortions and short-range magnetic order in classical magnetoelastic Heisenberg chains.

Lattice distortions of a two-dimensional array of one-dimensional classical Heisenberg spin chains with magnetoelastic coupling are studied in the limit of strong interchain elastic interactions. Exact integration over the spin degrees of freedom leads to a temperature-dependent free-energy functional of the elastic variables only. The equilibrium lattice structure is obtained from the ground state of this free-energy functional and the phase diagram indicates the presence of a tricritical point. The necessity of performing the calculations at constant pressure is stressed and it is shown that a dimerized phase could be reached by applying pressure to certain magnetic materials, provided that there exist positive second-neighbor elastic interactions. The consequences of lattice distortions on the short-range magnetic order are studied by calculating the wave-number-dependent magnetic susceptibility. It is found that the dominant short-range magnetic order is of period four in the dimerized lattice phase.

Soliton Formation at the Neutral-to-Ionic Phase Transition in the Mixed-Stack Charge-Transfer Crystal Tetrathiafulvalene -p- Chloranil

Intrinsic paramagnetic defects have been detected by ESR measurements in tetrathiafulvalene -$p$- chloranil single crystals, associated with the neutral-to-ionic phase transition at ${T}_{c}=84$ K. Two kinds of paramagnetic species are identified with delocalized spins propagating on either donor or acceptor sites. Total spin density and electric conductivity were found to increase discontinuously as temperature is lowered across ${T}_{c}$. These features are attributed to the formation of mobile solitonlike (and antisolitonlike) paramagnetic defects induced in the dimerized lattice at the phase transition.

Coulomb effects on 13C-NMR and polarons in (CH) x and a bound state of solitons

Using the PPP Hamiltonian model of (CH) x , we study the effects of the Coulomb interaction on the 13C-NMR of doped (CH) x and the electronic and lattice structures of polarons. The broad asymmetric 13C-NMR signal is explained by the Coulomb-induced charge density modulation around charged solitons. Polarons accompany the Coulomb-induced charge and spin density modulations which have a dip at the centre and different spreadings, the former being wider. The lattice dimerization in polarons is not only relaxed but also reversed in a central region. A polaron accompanies four midgap levels. With a suitably screened Coulomb interaction, we can get polaron and soliton levels in good agreement with the data of electrochemical doping voltage spectroscopy. The positively and negatively charged solitons make a breather-like bound state, which may explain the self-pinning of photogenerated solitons.

Theory of Electronic Structures and Lattice Distortions in Polyacetylene and Itinerant Peierls Systems. II: Coulomb Interaction Dependences of the HF Ground State, Lattice Dimerization and 1Bu Excited State in Regular Trans-Polyacetylene

We study the Coulomb interaction dependences of the HF ground state, lattice dimerization and I Bu excited state in regular trans-poly acetylene using the PPP hamiltonian model developed in a previous paper. The nature of the HF ground state is determined by the relative magnitudes of the on site and nearest neighbour parts and the screening of the longer range part of the effective Coulomb potential. The Coulomb interaction with relatively large nearest neighbour part and not too strongly screened longer range part induces lattice dimerization. The driving force of the Coulomb induced dimerization is the nearest neighbour exchange interaction. The lattice dimerization in polyacetylene is due to the Coulomb mechanism. The SSH model is implicitly taking into account the nearest neighbour exchange interac­ tion. The Franck-Condon band gap is mostly determined by the nearest neighbour exchange interaction. The IBu excited state is excitonic. The exciton binding energy is estimated for the effective Coulomb potential with the screened long range part. It is not large owing to very small effective mass of electron and hole. To explain the observed I Bu excitation energy, the short range part of the effective Coulomb potential must be screened by about half compared to the one in small conjugate molecules. The condition for splitting of the exciton into a zwitter­ ionic pair of charged solitons is discussed.

Statistical Mechanics of Biomembrane Phase Transition. III–Basic Concept of Cell Membrane Phase Transition–

Statistical mechanical study on the biomembrane phase transition is extended to the cell membrane, which consists of various kinds of lipids and embraces substantial amount of proteins. The modified dimer model used in our previous study is adopted. The activation energies for excited dimers are taken to be distributed “randomly” on the dimer lattice. The proteins are represented by hard blocks which inhibit any excited dimer to invade the lattice sites occupied by the proteins. This model of statistical mechanics exhibits a well-defined phase transition. The free energy, specific heat, etc., have essential singularities at the transition point.

Statistical Mechanics of Biomembrane Phase Transition. II. The First Order Transition with Pseudo-Critical Properties

The modified dimer model representing the cooperative nature of the conformation changes of the hydrocarbon chains is analyzed on the basis of the transfer matrix formalism established rigorously in the previous paper. The free energy is evaluated in the limit of infinite dimer lattices by means of the trial function of the free fermion type. The power series expansion of the free energy with respect to ρ, the disorder parameter, has been calculated up to the ρ 4 term without resorting to any further approximation. The modified dimer model is extended so as to include the dilation of the dimer lattice. This extended model with certain parameter values exhibits the first order phase transition. Finiteness of the hydrocarbon chains is also taken into consideration in our formalism. The finiteness may bring the transition point to the vicinity of the spinodal. In consequence, the pseudo-critical phenomena appear in a very narrow temperature region around the transition point. The quasi-critical behavior obse...

Theory of Electronic Structures and Lattice Distortions in Polyacetylene and Itinerant Peierls Systems. I: UHF Transfer Matrix Method Adapted to the Long Range Coulomb Interaction and UHF States in Regular Bond Alternated Lattice

We develop in this series a theory of itinerant Peierls systems that mainly aims to study polyacetylene. In order to investigate roles of the long range Coulomb interaction in electronic structures and lattice distortions in a Peierls system, we develop a transfer matrix technique adapted to the. unrestricted Hartree·Fock (UHF) approximation. The method makes it pos­ sible to calculate UHF states and equilibrium lattice geometries in a lattice with any aperiodic structure due to the presence of solitons. Applying the method, we obtain the UHF states in the case of regular lattice that may become the HF ground state. There are at least eight such UHF states which are distinguished by the long range orders in the spin and charge densities and the bond orders. The nearest neighbour exchange interaction is responsible to produce such plentiful UHF states. We calculate the bond alternation potential and the band gap in trans polyacetylene using paramet­ rizations of the Hamiltonian and the elastic potential that are able to well reproduce spectra and equilibrium geometries of small conjugated hydrocarbons. The bond alternation potential is very sensitive to the strength of the nearest neighbour Coulomb interaction. The Coulomb potential with fast damping prevents the bond alternation. The band gap is much larger than the energy 2 eV of the lowest absorption band as long as the Coulomb interaction in poly­ acetylene is similar to that in small conjugated hydrocarbons, suggesting the excitonic nature of the absorption band. We make also an illustrative calculation for an itinerant spin Peierls system with an antiferromagnetic spin order as well as a lattice dimerization.

Arrangement of tubulin subunits and microtubule-associated proteins in the central-pair microtubule apparatus of squid (Loligo pealei) sperm flagella.

This study provides a comprehensive, high-resolution structural analysis of the central-pair microtubule apparatus of sperm flagella. It describes the arrangement of several microtubule-associated "sheath" components and suggests, contrary to previous thinking, that microtubules are structurally asymmetric. The two microtubules of the central pair are different in several respects: the C2 tubule bears a single row of 18-nm-long sheath projections with an axial periodicity of 16 nm, whereas the C1 tubule possesses rows of 9-nm globular sheath components with an axial repeat of 32 nm. The lumen of the C2 tubule always appears completely filled with electron-dense material; that of the C1 tubule is frequently hollow. The C2 tubule also possesses a series of beaded chains arranged around the microtubule; the beaded chains are composed of globular subunits 7.5-10 nm in diameter and appear to function in the pairing of the C1 and C2 tubules. These findings indicate: that the beaded chains are not helical, but assume the form of lock washers arranged with a 16-nm axial periodicity on the microtubule; and that the lattice of tubulin dimers in the C2 tubule is not helically symmetric, but that there are seams between certain pairs of protofilaments. Proposed lattice models predict that, because of these seams, central pair and perhaps all singlet microtubules may contain a ribbon of 2-5 protofilaments that are resistant to solubilization; these models are supported by the results of the accompanying paper (R. W. Linck, and G. L. Langevin. 1981. J. Cell Biol. 89: 323-337.

Arrangement of subunits in microtubules with 14 profilaments.

The structure of 14-protofilament microtubules reassembled from dogfish shark brain tubulin was analyzed by high resolution electron microscopy and optical diffraction. The simultaneous imaging of the protofilaments from near and far sides of these tubules produces a moiré pattern with a period of approximately 96 nm. Optical diffraction patterns show that the 5-nm spots that arise from the protofilaments for the two sides of the tubule are not coincident but lie off the equator by a distance of 1/192 nm-1. These data provide evidence that in reassembled microtubules containing 14 protofilaments, the protofilaments are tilted 1.5 degrees with respect to the long axis of the tubule, giving a left-handed superhelix with a pitch of 2.7 micron. The hypothesis is that the tilt of the protofilaments occurs to accommodate the 14th protofilament. It is determined that when the 14th protofilament is incorporated, the 3-start helix is maintained, but the pitch angle changes from 10.5 degrees to 11.2 degrees, the angle between protofilaments measured from the center of the microtubule changes by 2 degrees, and the dimer lattice is discontinuous. These observations show that the tubulin molecule is sufficiently flexible to accomodate slight distortions at the lateral bonding sites and that the lateral bonding regions of the alpha and beta monomers are sufficiently similar to allow either alpha-alpha and beta-beta subunit pairing or alpha-beta subunit pairing.

Pressure dependence of the spin-peierls transition

We derive the pressure dependence of the transition temperature of the spin-Peierls transition within both mean-field theory and the extended theory of Cross and Fisher. The salient differences between the results of these cases are delineated. The anharmonicity of the dimerized lattice mode plays a crucial role in the deduced behavior, especially in the Cross-Fisher case. Using data for TTF-CuBDT, values for lattice force constants and related observables are calculated and are found to be internally consistent.

Phase Transition of SnCl2(H2O)x(D2O)2−x as Studied by High Resolution Heat Capacity Measurement

Abstract The previously published heat capacity data on Sncl2(H2O)x(D2O)2−x (x=2.00, 1.97, 1.75, 1.50, 0.96, 0.50, 0.25, 0.03) were analyzed to derive anomalous contribution due to the phase transitions that occur between 218 and 235 K depending on the isotopic composition. The phase transition is of the first-order for x=2.00, 1.97, and 1.75. The entropy discontinuities at the transitions are (0.149±0.005), (0.152±0.005), and (0.133±0.010) J K−1 mol−1, respectively, out of the total transition entropies of 3.98, 3.90, and 3.89 J K−1 mol−1. The first-order transition does not occur for the other crystals for which the heat capacity anomaly is rounded. Apparent critical exponent α of the heat capacity was calculated for all of the crystals. They are in the range from 0.43 to 0.80 and have the same value below and above the transition temperature for each of the crystals in agreement with the spatial two dimensionality of the crystal structure. No evidence was found for crossing-over to the three dimensional ordering. Change of the transitional behavior with the isotopic composition was discussed in analogy with the liquid-vapor critical phenomenon. An argument based on the crystallographic symmetry of the actual crystal and the corresponding dimer lattice was advanced for this interpretation of the unusual isotope effect.

On low temperature fluorescence of perylene crystals

At low temperatures, the broad excimer fluorescence band of α-perylene crystals is replaced by a weakly structured emission at higher energy. This emission originates from a new crystal state (Y-state) which is populated independently of the high temperature excimer (E-state). Due to the temperature dependence of its first order decay rate and due to the thermally activated formation of the E-state, the Y-emission grows rapidly at temperatures below 90 K. The Y-emission differs from the fluorescence of the monomeric β-perylene at 5.5 K by its Stokes shift of 1300 cm −1, the lack of vibronic structure, the long first order decay time of 40 ns and the absence of bimolecular annihilation indicating a localized state. The Y-state is attributed to a less relaxed pair state formed upon contraction of the dimeric crystal lattice.

The dimer interaction and lattice energy of ethylene and pyrazine in the multipole expansion; a comparison with atom-atom potentials

The long-range interactions between ethylene (C2H4) and between pyrazine (C4N2H4) molecules have been calculated in the multipole expansion from LCAO-SCF wave functions on the monomers. In first-order perturbation theory, the R -5 and R -7 dependent terms have been considered. The second-order energy has been calculated in a new (non-empirical) application of Unsöld's approximation up to R -10 terms inclusive. The electrostatic interactions appear to be relatively large for the dimers. Their contributions to the lattice energies of the crystals and, similarly, the contributions of the so-called dispersion cross terms are much less important, however, because these anisotropic interactions cancel to a large extent. The quadratic dispersion terms, which behave more isotropically, yield the major part of the lattice energy. The induction energy is very small. Difficulties appear in the calculations of the lattice energies because of the non-convergence of the multipole expansion. A comparison is made between the multipole expansion results and results obtained with the aid of empirical non-bonded atom-atom potentials. For the dispersion interactions the agreement is satisfactory; the results for the electrostatic energy disagree.

Theory of the spin-peierls transition for one-dimensional classical and quantum chains

A spin-lattice coupling induced lattice dimerization (spin-Peierls transition) in exactly soluble linear magnetic models is investigated. The transition can be of first or second order for classical spin model but of second order only for quantum X-Y model.

On the Dimer Solution of Planar Ising Models

Derivations of the partition function of the Ising model on a general planar lattice L, which proceed via an associated dimer problem and use Pfaffians, are simplified by constructing a lattice LΔ (the ``terminal lattice'' derived from an ``expanded lattice'' of L) for which (A) the allowed dimer configurations are in one-one correspondence with allowed Ising polygon configurations on L, and which (B) is planar if L is planar so that Kasteleyn's theorem may be used directly to construct the appropriate Pfaffian. This is in contrast to previous use of nonplanar associated dimer lattices for which the correspondence is not one-one, so that is has been necessary to prove a somewhat obscure ``cancellation theorem.''

Statistical Mechanics of Dimers on a Plane Lattice. II. Dimer Correlations and Monomers

In part I of this paper, exact expressions were obtained for the partition function and thermodynamic properties of an $m\ifmmode\times\else\texttimes\fi{}n$ plane square lattice filled with $\frac{1}{2}\mathrm{mn}$ rigid dimers each occupying two adjacent lattice sites. In this part the correlation properties of the model are studied with the aid of a general perturbation theory for Pfaffians. Closed formulas are derived for the changes in the probability of a dimer occupying a given bond that are induced by the proximity of an edge or a corner of the lattic (singlet correlations) and, in the center of the lattice by the fixed position of another dimer (pair correlations). We show how to calculate the number of configurations of a dimer lattice containing a pair of monomers (or holes) a fixed distance apart. The explicit result when the separation vector is ($p$, 0) or ($p$, 1) involves a Toeplitz determinant $|{a}_{i\ensuremath{-}j+1}|$ ($i, j=1, 2, \ensuremath{\cdots}p$) defined by $\ensuremath{\Sigma}\stackrel{\ensuremath{\infty}}{n=\ensuremath{-}\ensuremath{\infty}}{a}_{n}{e}^{\mathrm{in}\ensuremath{\theta}}=\mathrm{sgn}{cos\ensuremath{\theta}}\mathrm{exp}[\ensuremath{-}iinvcot(\ensuremath{\tau}cos\ensuremath{\theta})],$ where $\ensuremath{\tau}=\frac{x}{y}$ and $x$ and $y$ are the activities of $x$ and $y$ dimers. A similar result holds along the diagonals ($p, p\ifmmode\pm\else\textpm\fi{}1$). The relative number of configurations decays to zero with radial separation $r$ as $\frac{B}{{r}^{\frac{1}{2}}}$.