纳米晶体线的晶格动力学格林函数及晶格振动

通过求解差分方程,推导了纳米晶体线的晶格动力学格林函数,分析了其晶格振动,并推导了声子数表象中的原子位移及晶格振动哈密顿公式.研究结果表明,纳米晶体线的晶格振动能带分裂为一系列的子带,格波只能沿纳米晶体线的纵向传播,沿纳米晶体线的横截面只存在驻波.     

Counterion vibrations in the DNA low-frequency spectra

The vibrations of univalent metal cations with respect to phosphate groups of the DNA backbone are described using the four-mass model approach (S.N. Volkov, S.N. Kosevich, J. Biomol. Struct. Dyn. 8, 1069 (1991)) extended in this paper. The force constant of the counterion-phosphate interaction is determined by considering the DNA with counterions as a lattice of ion crystal. For such ion-phosphate lattice the Madelung constant and the dielectric constant are estimated. The obtained value of the Madelung constant is lower than for the NaCl crystal, and its value is about 1.3. The dielectric constant is within 2.3-2.7 depending on the counterion type and form of the double helix. The calculations of the low-frequency spectra show that for the DNA with metal cations Na⁺ , K⁺ , Rb⁺ and Cs⁺ the frequency of ion-phosphate vibrations decreases from 174 to 96cm^-1 as the counterion mass increases. The obtained frequencies agree well with the vibrational spectra of polynucleotides in a dry state which prove our suggestion about the existence of the ion-phosphate lattice around the DNA double helix. The amplitudes of conformational vibrations for DNA in B -form are calculated as well. The results demonstrate that light counterions ( Na⁺ do not disturb the internal dynamics of the DNA. However, heavy counterions ( Cs⁺ have effect on the internal vibrations of the DNA structural elements.     

Interaction of translational and rotational modes of a molecular impurity in two-dimensional atomic crystals

The interaction between the translational and rotational degrees of freedom of a diatomic homonu-clear molecule that executes a motion at the site of a two-dimensional close-packed atomic matrix located on a close-packed atomic substrate (a molecular substitutional impurity in the crystal field of the two-dimensional lattice of a solidified rare gas) is investigated theoretically. The relationships describing the effective dynamic properties of an impurity rotator in the presence of translational excitations of its center of inertia are derived in the framework of consistent procedures on the basis of the Lagrangian (the functional-integral method) and Hamiltonian (the canonical-transformation method) formalisms. The inclusion of the translational-rotational interaction leads to a radical change in the inertial properties of the molecule. This manifests itself in a change in the form of the operator for the rotational kinetic energy as compared to the corresponding expression for a free rotator. The inertia tensor components for the molecule become functions of molecular orientation, and the molecule, in terms of rotational motion, transforms into a “parametric rotator” whose effective kinetic energy is represented as a generalized quadratic form of the angular momentum (or the angular velocity) components with a symmetry corresponding to the symmetry of the external crystal field. The translational-rotational interaction also results in the renormalization of the parameters of the crystal potential without a change in its initial form.     

The non-linear interaction of a powerful light beam with crystal lattice vibrations

The interaction of a powerful light beam with a one dimensional crystal lattice consisting of anisotropic and axially symmetric molecules is discussed. Translational and rotational vibrations are taken into account.     

Factor group theoretical analysis of fundamental vibrations of the H2AsO 4? anion in (C6H9N2)H2AsO4 single crystal

Fundamental (lattice, rotational, and intermolecular) vibrations of the H₂AsO₄⁻ anion in (C₆H₉N₂)H₂AsO₄ crystal are calculated using the correlation theorem based on the group theory. The correlation between anionic site of symmetry C _s and the factor group D _2h of the crystal yields 12 modes for both lattice and rotational vibrations. The infrared and Raman spectra of these modes do not coincide. Addition of two hydrogen atoms to AsO₄⁻ ion yields two As-OH bonds in the H₂AsO₄⁻ anion. As a result, the molecular symmetry is reduced from T _d to C _2υ . The free H₂AsO₄⁻ anion having C _2υ symmetry gives in total 15 fundamental normal vibrations. Under the crystal field splitting effects, the number of intermolecular vibrations for the anion in infrared and Raman spectra is calculated to be 56 active vibrations. The calculated fundamental vibrationsmanifest themselves as the main features in an experimental infrared spectrum.     

Polarons in quantum chains with XY exchange and Dzyaloshinsky-Moriya interaction

Excitations of the polaron types are investigated in the spin-1/2 quantum chain with XY exchange and Dzyaloshinsky-Moriya interaction, both coupled to acoustic vibrations of the substrate lattice. The study is carried out via Jordan-Wigner transformation with the help of which the spin chain is mapped onto a chain of spinless fermions. From the resulting effective fermion-lattice Hamiltonian, the discrete equations of motion are derived. These equations are solved in the continuum limit for self-trapped states near the bottom of the fermion spectrum interacting with long-wavelength acoustic lattice modes. The associate polaron solution, which has a pulse shape, is shown to propagate bound to the induced lattice kink distortion by translation along the chain at a constant velocity v. The pair can also experience an additional acceleration ϑ₀ when the free fermion charge is excited above its groundstate. The polaron binding energy is strongly reduced, depending quadratically on the ratio D/J of the Dzyaloshinsky-Moriya interaction strength D to the isotropic XY exchange interaction J. It is also found that polaron parameters depend only on the XY spin-lattice coupling but not on the Dzyaloshinsky-Moriya contribution.     

蒽分子晶体的喇曼散射

在室温和液氮温度下,用氩离子激光器的5145Å激光激发,测量了蒽单品的喇曼散射谱,其喇曼活性主模振动的实验值和理论值符合的较好。计算了旋转振动的均方振幅,并对低波数振动喇曼谱的温度效应进行了讨论。     

用不变本征算符法求晶面吸附原子的振动模

晶体表面的扩散和缺陷对晶体振动模式的影响是表面物理学研究的一个重要和基本的课题.晶格振动的频率对应于系统的能带.由于晶格中原子的振动不是孤立的,并且晶格具有周期性,所以在晶体中形成格波.格波代表晶体中所有原子都参与的频率相同的振动,又常称为一种振动模.本文讨论在表面吸附位势系数β_0与晶体内部原子的周期位势系数β不同的情况下,晶体表面吸附一个质量为m_0(与晶格原子质量m不同)的原子以后晶格的振动模.采用不变本征算符方法,严格地导出此振动模为ω=((2β(1-coshα))/(hm))~(1/2),其中α=ln[-(mβ_0+m_0(-2β+β_0)+(β_0)~(1/2)((-4mm_0β+(m+m_0)~2β_0))~(1/2)/2m_0β].此结果表明,ω不但取决于吸附位势与吸附原子的质量,也与晶格原子的质量与内位势有关.     

Effective Hamiltonian for degenerate vibrational states in symmetric top molecules

A mixed matrix-operator form of the effective rotational Hamiltonian has been discussed for the degenerate vibrational states of symmetric top molecules. In this scheme, a rotational contact transformation can be applied to the effective Hamiltonian such that the operators of the “2, +2,” “2, −2,” and “2, −1” l-type interactions as well as the operators of the Δk = ±3 and ±4 interactions are eliminated from the first-order terms of the expansion of the rotational Hamiltonian in terms of the small parameter λ. The results have been used to discuss the correlation between various interaction parameters in the effective rotational Hamiltonian for the doubly degenerate fundamental vibrational levels of semirigid symmetric top molecules. For example, for C_3v or D₃ molecules, the parameter of the “2, −1” interaction is correlated with other parameters and cannot be determined separately by fitting the experimental data (unless there are certain accidental resonances between vibrational-rotational levels).     

Multiphonon relaxation of optical excitations in CsCdBr<Subscript>3</Subscript>:Pr<Superscript>3+</Superscript> and LiYF<Subscript>4</Subscript>:Nd<Superscript>3+</Superscript> crystals

The technique of calculation of the n-phonon transition rates between electronic sublevels of impurity rare earth ions in dielectric crystals is developed in the case when n>2. The n-phonon transition probabilities are calculated according to the 1st and 2nd orders of perturbation theory. The Hamiltonian of the electron-phonon interaction is constructed in the framework of the exchange charge model and developed as series in relative displacements of the rare earth ion and ligands. The contribution of the lattice anharmonicity on the probabilities of n-phonon transitions is taken into account. On the basis of the developed technique, the nonradiative relaxation rates of ⁴ G _7/2 multiplet of Nd³⁺ ions in LiYF₄:Nd³⁺crystal and ³P₁ multiplet of Pr³⁺ ions in CsCdBr₃:Pr³⁺ crystal were computed. The results of our calculations show that the 2nd order terms in the expressions for the probabilities studied here are comparable with, and in some cases prevail over the 1st order terms. An account of lattice anharmonicity in case of LiYF₄:Nd³⁺ crystal substantially modifies the corresponding multiphonon relaxation rates. The calculated nonradiative relaxation rates for both crystals agree well with the experimental data.     

The Sextic Centrifugal Distortion Terms for an Open-Shell Complex Consisting of a Diatomic Molecule in a (2S+1)Sigma Electronic State and a Closed-Shell Partner

An effective Hamiltonian for calculating rotational energy levels of an open-shell diatomic molecule, in a (2S+1)Sigma electronic state, weakly bonded to a closed-shell partner was presented (W. M. Fawzy, J. Mol. Spectrosc. 191, 68-80 (1998)). The Hamiltonian was given as H = H(ev) + H(rot) + H(sr) + H(ss) + H(cd) + H(srcd) + H(sscd), where all the quartic centrifugal distortion correction terms were included in the Hamiltonian term H(cd) but the sextic centrifugal distortion terms were ignored. This Hamiltonian is useful in cases where the complex has a well-defined equilibrium geometry and if the barrier to large-amplitude motion is large compared to the rotational constant of both the closed-shell molecule and its paramagnetic partner; if the barrier to large-amplitude motion is small compared to the rotational constant of one or both of the fragments, then a different treatment is required. In this paper, we introduce the new Hamiltonian terms H(sex(A))(cd) and H(sex(S))(cd), which represent the sextic centrifugal distortion correction terms for an asymmetric rotor. We also introduce all the nonvanishing matrix elements of each of the H(sex(A))(cd) and H(sex(S))(cd) operators. These operators and their matrix elements are required for calculating the rotational energy levels of relatively high J values in the described type of weakly bonded open-shell complexes. The terms H(sex(A))(cd) and H(sex(S))(cd) and their matrix elements are also valid for any stable asymmetric rotor in a nondegenerate electronic state. A brief discussion of the new Hamiltonian terms and their matrix elements is given. Copyright 2000 Academic Press.     

Temperature dependence of the spin-lattice relaxation time in local triplet-excited states of a doped C60 fullerene crystal

The temperature dependence of the spin-lattice relaxation time of triplet-excited impurity centers of a C₆₀ fullerene crystal is investigated within the framework of the spin-phonon coupling mechanism which arises as a result of the admixture of rotational to translational motions of the molecules due to acoustic lattice vibrations. General expressions are obtained for the transition probabilities for the direct single-phonon and Raman two-phonon processes. The method of atom-atom potentials is used to carry out a concrete calculation of the spin-lattice relaxation time for an isotopic impurity in a C₆₀ crystal. Fiz. Tverd. Tela (St. Petersburg) 39, 1699–1702 (September 1997)     

MOLECULAR MORPHOLOGY AND CRYSTALLIZATION IN THE QUANTUM LIMIT

The effects of phonons on crystallization and crystal morphology are investigated. It is shown that the commensuration of the lattice vibrations with the lattice will favor certain crystal morphologies. Vibrational effects can also be important for the molecular structure of chain molecules. In this case, the contribution from quantum mode forces to denaturation is estimated by using a simple phenomenological model describing the molecule as a continuum. The frequencies of the vibrational modes depend on the molecular dimensionality; hence, the zero-point energies for the folded and the denatured protein are estimated to differ by several electron volts. For a biomolecule, such energy is significant and may contribute to cold denaturing as seen for proteins. This is consistent with the empirical observation that cold denaturation is exothermic and hot denaturation endothermic.     

Surface-induced ordering in thin uniaxial liquid crystal films

The interface localization transition in thin uniaxial liquid crystal films with competing surface fields has been studied using Metropolis Monte Carlo simulations. The model is constructed from a lattice of continuously orientable interacting spins, and the Hamiltonian contains both bilinear and biquadratic contributions. The biquadratic contribution to the Hamiltonian is familiar from the Lebwohl-Lasher model, and accounts for the particle anisotropy in a liquid crystal. The head-tail asymmetry of the molecules in a uniaxial liquid crystal is taken into account through a bilinear contribution familiar from the classical ferromagnetic Heisenberg model with exchange anisotropy Lambda. The critical temperature T(c), characterizing the interface localization transition within the uniaxial liquid crystal film, depends strongly on the relative magnitudes of the bilinear and biquadratic interactions between the spins. For systems dominated by the biquadratic interaction, T(c) is found to be close to the bulk critical temperature of the system. But as the biquadratic interaction strength is reduced, T(c) departs markedly from the bulk critical temperature of the system.     

Microwave spectrum of the hydrogen sulfide molecule H232S in the ground state

Frequencies, line strengths, and intensities of microwave electric dipole rotational transitions of H₂³²S in the ground state have been calculated. The calculation was based on representation of the effective rotational Hamiltonian operator in the form of a Pade operator. As initial information, all known microwave data on frequencies of rotational transitions of H₂³²S in the ground state were used. Some of these data were obtained in the present paper.     

One-Dimensional Hamiltonian for Columnar Liquid Crystals

A one-dimensional Hamiltonian is derived upon microscopic considerations to model the columnar phases of a liquid crystal made of molecules of discrete rotational symmetry. The study deals with the ground state of this Hamiltonian, only the orientational degrees of freedom being taken into account. The intracolumnar interaction is described by the natural cantedness of an isolated column, while interaction parameters H and G characterize the amplitude of the local crystal field at a site originating from the other surrounding columns. The phase diagrams of the orientational ordering along the column are numerically investigated and a previous analytical approach is briefly recalled. A new perturbation development is proposed. This allows us to analyse a multiphase point and to explain the appearance of an infinity of phases in the vicinity of this point. The anisotropy of the columnar lattice is then investigated with the use of the same perturbation development, and some of the properties of a complex phase diagram are examined numerically as well as analytically.     

Floating Wigner molecules and possible phase transitions in quantum dots

A floating Wigner crystal differs from the standard one by a spatial averaging over positions of the Wigner-crystal lattice. It has the same internal structure as the fixed crystal, but contrary to it, takes into account rotational and/or translational symmetry of the underlying jellium background. We study properties of a floating Wigner molecule in few-electron spin-polarized quantum dots, and show that the floating solid has the lower energy than the standard Wigner crystal with fixed lattice points. We also argue that internal rotational symmetry of individual dots can be broken in arrays of quantum dots, due to degenerate ground states and inter-dot Coulomb coupling. Received 12 September 2001 / Received in final form 24 April 2002 Published online 9 July 2002     

Anomalous light absorption in molecular crystals

The method of successive approximations is used to obtain a solution for an infinite chain of nonlinear coupled equations for the Fourier transform of the retarded two-time Green’s function in a system in which the electron vibrational interactions of the lattice photons and of the intramolecular photons are included in the terms of the Hamiltonian that are diagonal in the electron operators. A unique subsequence, which provides a finite contribution to the integral intensity of the absorption spectrum, is extracted from the infinite series and summed. The resulting formulas are used to classify the excited states of a crystal and interpret the cases of anomalous light absorption, when the absorption intensity becomes inversely proportional to the Franck-Condon overlap integral. Zh. éksp. Teor. Fiz. 112, 1021–1040 (September 1997)