Density-matrix spectra for integrable models

The spectra which occur in numerical density-matrix renormalization group (DMRG) calculations for quantum chains can be obtained analytically for integrable models via corner transfer matrices. This is shown in detail for the transverse Ising chain and the uniaxial XXZ Heisenberg model and explains in particular their exponential character in these cases.     

Density-matrix formalism with three-body ground-state correlations

A density-matrix formalism which includes the effects of three-body ground-state correlations is applied to the standard Lipkin model. The reason to consider the complicated three-body correlations is that the truncation scheme of reduced density matrices up to the two-body level does not give satisfactory results to the standard Lipkin model. It is shown that the inclusion of the three-body correlations drastically improves the properties of the ground states and excited states. It is pointed out that lack of mean-field effects in the standard Lipkin model enhances the relative importance of the three-body ground-state correlations. Formal aspects of the density-matrix formalism such as a relation to the variational principle and the stability condition of the ground state are also discussed. It is pointed out that the three-body ground-state correlations are necessary to satisfy the stability condition.     

Internal coordinates for molecular dynamics and minimization in structure determination and refinement

We present a software module which allows one to efficiently perform molecular dynamics and local minimization calculations in internal coordinates when incorporated into a molecular dynamics package. We have implemented a reference interface to the NIH version of the X-PLOR structure refinement package and we show that the module provides superior torsion-angle dynamics functionality relative to the native X-PLOR implementation. The module has been designed in a portable fashion so that interfacing it with other packages should be relatively easy. Other features of the module include the ability to define rather general internal coordinates, an accurate integration algorithm which can automatically adjust the integration step size, and a modular design, which facilitates extending and enhancing the module.     

Polaron stability in molecular crystals

A semi-empirical Peierls–Holstein model is applied to studies of the stability of polarons in two-dimensional molecular crystal systems. Calculations for a broad range of intra- and inter-molecular parameters within this model were performed in order to obtain detailed knowledge concerning the stability of the polaron solution with respect to a rigid lattice band solution. For realistic values of the parameters the polaron solution is stable with a polaron energy in the range 50–100 meV. A metastable polaron solution is also identified. The polarons that result from our model are highly localized and it is questionable if adiabatic polaron transport can occur in the system.     

Electrostatic interactions in molecular crystals

Lattice dynamics calculations for nitrogen and carbon dioxide have been carried out for empirical intermolecular potentials which incorporate accurate representations of the molecular charge distributions. In the case of nitrogen, the higher order moments are found to make large negative contributions to the harmonic librational frequencies. The differences between nitrogen and carbon dioxide and the implications for other crystals are discussed.     

Self-energy in conducting molecular crystals

I have calculated the self-energy, i.e. the effect of the electron-phonon interaction on the electronic energy levels, to second order of perturbation theory for conducting 1-d molecular crystals. The resulting level shifts should have important effects above ～100K on the density of states and properties dependent on it. Evaluating the shifts for tetrathiafulvalene tetracyanoquinodimethane, (TTF) (TCNQ), with the known phonon frequencies and coupling constants, I can explain the “anomalous” temperature variation of the magnetic susceptibility.     

一维分子晶体中的极化子

本文从量子化的Holstein模型出发,运用相干态展开法和能量极小原理,通过实施连续近似得到了一维分子晶体模型处于基态的极化子满足的非线性薛定谔方程及其定态孤子解、基态能量、晶格位移,其结果与Holstein T[1].从半经典理论所得的结果完全一致,因此相干态展开方法在处理与极化子有关的其他物理问题中是一种非常有效的方法.     

Habit of long-chain molecular crystals

The quantitative analysis of the temperature dependence of the heat capacity of molecular crystals with chains of different lengths was performed using the theory of diffuse first-order phase transitions. The same chemical structure of the “core” of molecular crystals of {CH₃(CH₂)_nCH₃} normal paraffins, {COH(CH₂)_nCOH} diols, {CH₃(CH₂)_nCOH} normal alcohols, and {CH₃(CH₂)_nCOOH} saturated carboxylic and {COOH(CH₂)_nCOOH} dicarboxylic acids enabled the comparative analysis of phase transition parameters.     

Site representation for charge transfer excitations in molecular crystals

A phenomenological site hamiltonian is constructed for molecular crystals whose lowest electronic excitations involve an electron transfer, as in many donor-acceptor and free-radical crystals. When only the lowest chargetransfer states are retained, a fermion representation of the site hamiltonian is obtained which leads to a typical many-body problem. The model reduces in special cases to the Hubbard and the Pariser-Parr-Pople models. However, instead of a one-electron, frozen core model, the site representation includes core rearrangements and polarization.     

Density-matrix approach for the electroluminescence of molecules in a scanning tunneling microscope

The electroluminescence (EL) of molecules confined inside a nanocavity in the scanning tunneling microscope possesses many intriguing but unexplained features. We present here a general theoretical approach based on the density-matrix formalism to describe the EL from molecules near a metal surface induced by both electron tunneling and localized surface plasmon excitations simultaneously. It reveals the underlying physical mechanism for the external bias dependent EL. The important role played by the localized surface plasmon on the EL is highlighted. Calculations for porphyrin derivatives have reproduced corresponding experimental spectra and nicely explained the observed unusual large variation of emission spectral profiles. This general theoretical approach can find many applications in the design of molecular electronic and photonic devices.     

Superradiance from crystals of molecular nanomagnets

We show that crystals of molecular nanomagnets can exhibit giant magnetic relaxation due to the Dicke superradiance of electromagnetic waves. Rigorous theory is presented that combines superradiance with the Landau-Zener effect.     

Singlet triplet-triplet-triexcitons in organic molecular crystals

A theory on the formation of triexcitons consisting of one singlet exciton and two triplet excitons is developed by considering exciton-exciton dynamical interactions. The conditions for the existence of the singlet-triplet-triplet-triexciton bound states are established and discussed.     

Quadrupole relaxation enhancement--application to molecular crystals

A general theory of field dependent spin-lattice relaxation for nuclei of the spin quantum number 1/2 (1H, 19F, 13C) caused by dipole-dipole interactions with neighboring quadrupolar nuclei (nuclei possessing a quadrupolar moment) is presented. The theory is valid for arbitrary motional conditions and should be treated as a quadrupolar counterpart of the paramagnetic relaxation enhancement theory. When the energy level splitting of the dipolar spin (I=1/2) matches one of the transition frequencies of the quadrupolar nuclei one can observe a local enhancement of the dipolar spin relaxation (referred to as "quadrupolar peaks"). To see such effects the dynamics modulating the spin interactions has to be relatively slow. This brings the system beyond the validity range of perturbation approaches and requires the stochastic Liouville equation to be applied. The presented theory describes the quadrupolar relaxation enhancement (QRE) for an arbitrary spin quantum number of the quadrupolar nuclei and includes the asymmetry of the quadrupolar coupling. It has been applied to interpret the shape of magnetization curves (amplitude of 1H magnetization versus magnetic field) for the molecular crystal [C3N2H5]6[Bi4Br18] ([C3N2H5]-imidazolium). The magnetization curves show several dips (local minima) attributed to 1H-14N quadrupolar relaxation enhancement effects. In addition, as a limiting case a perturbation approach to QRE has been presented and its validity conditions have been discussed.