The zero-point energy in the molecular hydrogen crystal

We propose a modified Einstein approximation to describe zero-point energy vibrations in a quantum crystal. Our aim was to develop a computationally cheap tool suitable for lattice structure optimisation. As in the classical Einstein model the representative atom vibrates in an effective potential due to the surrounding atoms of the crystal; the atoms however are not strictly placed at the positions corresponding to the crystal potential energy minima but their positions are described by the quantum mechanical density distributions. The effective potential computed that way is suitable for the application in solid para-hydrogen in contrast to the normal (unmodified) Einstein approximation. We compute the cohesive energy of the para-hydrogen crystal and perform lattice structure optimisation. The hexagonal closed packed is more stable than the fcc closed packed lattice and the lattice constants obtained are in very good agreement with the experimental values.     

The role of the electrostatic interaction in shifting the vibrational frequencies for two adsorbed molecules

We use a simple model to compute the shift of the vibrational frequencies of two adsorbed molecules as a function of inter-molecular distance, and various molecular and metal parameters. We assume that the atoms posses static and dynamic charges and the molecule has an electronic polarizability. The chemical bonds are described by Morse potentials. The electrostatic interactions are computed by a density functional method. We conclude that the use of vibrating point dipoles and of the image theorem in such calculations is an oversimplification.     

锐钛矿型TiO2(101)面本征点缺陷的理论研究

采用平面波超软赝势方法计算了锐钛矿型TiO₂(101)面存在本征空位和间隙点缺陷的几何结构以及缺陷形成能.首先分析了点缺陷对表面结构的影响,发现不同类型缺陷导致缺陷周围原子有不同的位移趋势：O空位的产生导致空位周围的Ti原子向空位外移动,Ti₁和Ti₂空位的产生均使O₁自发地与周围的O原子团聚,O_i原子易被周围的氧原子吸附而成键,而Ti_i2缺陷几乎 关键词： 第一性原理 2')" href="#">TiO₂ 点缺陷 表面结构     

Explanation of atomic displacement around lattice vacancies in diamond based on electron delocalization

The relationship between unpaired electron delocalization and nearest-neighbor atomic relaxations in the vacancies of diamond has been determined in order to understand the microscopic reason behind the neighboring atomic relaxation. The Density Functional Theory (DFT) cluster method is applied to calculate the single-electron wavefunction of the vacancy in different charge states. Depending on the charge and spin state of the vacancies, at outward relaxations, 84-90% of the unpaired electron densities are localized on the first neighboring atoms. The calculated spin localizations on the first neighboring atoms in the ground state of the negatively charged vacancy and in the spin quintet excited state of the neutral vacancy are in good agreement with Electron Paramagnetic Resonance (EPR) measurements. The calculated spin localization of the positively charged vacancy contrasts with the tentative assignment of the NIRIM-3 EPR signal to this center in (p-type) semiconductor diamond. The sign of the lattice relaxation in the diamond vacancy is explained based on the effect of electron delocalization on nearest-neighbor ion-ion screening, and also its effect on the bond length of neighboring atoms.     

Vibrations of copper atoms in Pr2CuO4

The method of isotopic contrast in combination with inelastic neutron scattering has been used to investigate the vibrational spectrum of the copper atoms in Pr₂CuO₄. It is shown that the energy positions of the features of the vibrational spectrum of copper in Pr₂CuO₄ and CuO (which also has a planar oxygen coordination of copper) coincide. We conclude that the dynamical behavior of the copper atoms is formed mainly by their interaction with the nearest-neighbor oxygen atoms. Fiz. Tverd. Tela (St. Petersburg) 41, 1149–1153 (July 1999)     

Calculation of Vacancy Induced Properties in FCC Metals Using an Alternative Lattice Dynamical Model

Combining the conventional Kanzaki's lattice statics method with an alternative lattice dynamical model called decoupling transformation, a new approach is proposed to calculate the vacancy induced properties in FCC metals. This approach has the advantage over the traditional least-square fit approach in the way that all the model parameters are linearly independent and so it can avoid the problem of non-uniqueness in dynamical model parameters when interactions with more distant atoms are taken into account by fitting to the experimental phonon frequencies only. Numerical results on the lattice dynamical properties such as phonon dispersion curves and interatomic interaction force constants and the vacancy induced properties such as the atomic displacements, lattice relaxation energy, divacancy interaction energy and relaxation volume are obtained specifically for two similar FCC metals, to wit, Cu and Ni and are compared with previous calculations. It is concluded that the interatomic interactions up to the fourth nearest neighbours are already good enough for describing both the lattice vibrational and vacancy induced properties for both metals.     

Semiempirical calculation of the peroxide bridge in glassy silicon dioxide

The characteristics of a peroxide bridge are studied by the quantum-mechanical semiempirical method MPNDO/3 in the model of a molecular cluster. The geometry of the cluster was optimized for different distances between silicon atoms. The coordinates of the two oxygen atoms forming the peroxide bridge were employed as the optimization parameters. The minimum total energy of the cluster was sought. The scheme of single-electron levels was found. The effect of the peroxide bridge on the electronic structure of v-SiO₂ reduces to splitting of shallow levels from the edges of allowed bands, corresponding to strongly localized states. The energy of formation of a cluster in the presence of a peroxide bridge is close to the energy of formation of a cluster without defects.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 35–38, April, 1987.The authors thank Professor V. L. Bonch-Bruevich and the participants of his seminar at Moscow State University for their interest in this work and for useful discussions.     

Lattice dynamics of corundum crystals with vacancies in various charge states

The lattice dynamics of an α-Al₂O₃ crystal with vacancies in various charge states is simulated using the recursive method in the shell model. The frequencies of resonant vibrations induced by defects in various directions are calculated. Characteristic features in vibrational spectra of anion-nonstoichiometric α-Al₂O₃ crystals, mostly associated with changes in the effective interaction between vacancies and the nearest neighbor atoms, are analyzed and explained.     

Molecular cluster perturbation theory. I. Formalism

We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wave functions in a coupled-cluster framework. This new MCPT(2) framework uses coupled-cluster perturbation theory and an expansion in terms of molecular dimer interactions to obtain molecular wave functions that are infinite order in both the electronic fluctuation operator and all possible dimer (and products of dimers) interactions. The MCPT(2) framework has been implemented in the new SIA/Aces4 parallel architecture, making use of the advanced dynamic memory control and fine-grained parallelism to perform very large explicit molecular cluster calculations. To illustrate the power of this method, we have computed energy shifts, lattice site dipole moments, and harmonic vibrational frequencies via explicit calculation of the bulk system for the polar and non-polar polymorphs of solid hydrogen fluoride. The explicit lattice size (without using any periodic boundary conditions) was expanded up to 1000 HF molecules, with 32,000 basis functions and 10,000 electrons. Our obtained HF lattice site dipole moments and harmonic vibrational frequencies agree well with the existing literature.     

SrTiO3薄膜氧缺陷的第一性原理研究

在广义梯度近似(GGA)下,利用超软赝势对真空条件下SrTiO3超晶胞的体系能量、原子间电子云重叠布局数和电子态密度等进行了自恰计算.结果显示,对有氧缺陷的超晶胞优化后,晶格参数的几何平均值增大了2.711%,这表明在高温条件下外延生长STO薄膜时,产生了氧缺陷,并且氧空位易处于薄膜表层;另外,表层氧缺陷使表层Ti原子明显的发生偏心位移,两个Ti原子的核间距由0.3905 nm增大至0.4234 nm,b轴上的氧原子则向中心靠近了0.0108 nm、并沿c轴方向上突了0.0027 nm,使STO晶体产生自发极化,氧缺陷还使STO的电子态密度的能隙增宽了1.75 eV,达到2.48 eV,从而使STO晶体由顺电相转向铁电相.     

Lattice statics calculations for a vacancy in magnesium

Using the Green function method of lattice statics, the lattice distortion in the neighborhood of a vacancy in magnesium has been calculated in three different axially-symmetric (AS) host lattice models and also in a model derived from an empirical interatomic pair potential. The variations in the lattice distortion and the relaxation energy of the vacancy are studied as the size of the defect space is allowed to vary from two to four surrounding neighbors. The perfect static lattice Green functions are computed up to 19 neighbors in the 4 models and the values obtained are shown to be not very sensitive to the model chosen. The lattice relaxation is found to be negligible in all models except in a four-neighbor AS model. The relaxation energies in these four models are computed to be 0.0027 eV, 0.034 eV, 0.28 eV and 0.0069 eV respectively. Results for the monovacancy formation energy, the elastic dipole tensor and the volume change of the crystal due to the vacancy are also presented.     

TiO2表面氧空位对NO分子吸附的作用

采用程序升温热脱附(TPD)实验方法测定了NO在TiO2表面吸附后的脱附谱，利用分子轨道理论研究了TiO2吸附NO的原子簇模型及吸附前后的原子簇能级变化．结果表明，NO在TiO2表面吸附后可在两个峰值温度450和980K脱附出N2．TiO2表面经预覆氧处理后，N2的脱附量降低．吸附时NO中的O能够占据TiO2表面氧空位并与N脱离，而N原子则相互结合成为N2脱附．分子轨道理论计算证明在TiO2(110)表面能够存在氧空位并具备吸附NO的结构条件．     

Photoelectron holography analysis of W(1 1 0)(1×1)–O surface

By applying photoelectron holography analysis to a W(1 1 0)(1×1)–O surface, the real space image was reconstructed around the oxygen atoms. The peak positions showed that the oxygen atoms lie within the top layer, which does not contradict the results of the R-factor X-ray photoelectron diffraction analysis of Daimon et al. [Surf. Sci. 408 (1998) 260]. The holographic analysis of the calculated photoelectron diffraction pattern indicated that holographic reconstruction reveals atomic positions up to the third nearest-neighbor scatterers. Our study suggests the possibility that the distance among the adsorbate oxygen atoms is slightly larger than the lattice constant of the substrate.     

The first principle studies of the structural and vibrational properties of solid β-HMX under compression

The structural, vibrational and electronic properties of β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX) crystal under high pressure up to 40 GPa have been studied using density functional theory (DFT). The pressure dependences on the cell volume, lattice constants, and molecular geometry of solid β-HMX are presented and discussed. It is found that the N–N bonds are significantly reduced under compression, which may be of importance for initial decomposition. Based on the optimized crystal structures, the vibrational frequencies for the internal and lattice modes of the β-HMX crystal at ambient and high pressures are computed, and the pressure-induced frequency shifts of these modes are discussed.     

Internally consistent verification of mean-field models for aggregation using large-scale molecular dynamics

The underlying atomistic mechanisms that govern vacancy aggregation in crystalline silicon are probed using a parametrically consistent, two-scale approach. The essential ingredient in this framework is a direct, quantitative comparison between the predictions of atomistic and continuum simulations for the transient size distribution of vacancy clusters. The former is carried out with parallel molecular dynamics simulation of a silicon system containing 215?000 atoms and 1000 vacancies. The continuum model is based on a sequence of coupled Master equations and is parametrized based on the same empirical potential used to perform the atomistic aggregation simulation. An excellent representation of the cluster size distribution can be obtained with consistent parameters only if the relevant physical mechanisms are captured correctly. The inclusion of vacancy cluster diffusion and a model to capture the dynamic nature of cluster morphology at high temperature are necessary to reproduce the results of the large-scale atomistic simulation. Finally, the continuum model is used to investigate cluster evolution for longer times, which are relevant for process simulation of defect-optimized silicon substrates for microelectronic device fabrication.     

The multiple hydrogen location near a α-Fe vacancy

The interaction between 10 hydrogen atoms and a α-Fe structure having a vacancy (V) has been studied using a cluster model and a semi-empirical theoretical method. The energy of the system was calculated by the atom superposition and electron delocalization molecular orbital method. The electronic structure was studied using the concept of density of states and crystal orbital overlap population curves.For the study of a sequential absorption, the hydrogen atoms were positioned in their energy minima configurations, near to the tetrahedral sites neighboring the vacancy, except the last H atom that was located far from the vacancy. The energy difference for H agglomeration was also computed. The vacancy-H_n complexes become less stable than VH species for more than three hydrogen's.The changes in the electronic structure of Fe atoms near the vacancy were also analyzed. The interactions mainly involve Fe 3d and 4s atomic orbitals. The contribution of Fe p orbitals is much less important. The Fe-Fe bond weakened as new Fe-H and H-H pairs were formed. The effect of H atoms is limited to its first Fe neighbors. The detrimental effect of H atoms on the Fe-Fe bonds can be related to the mechanism for embrittlement in α-Fe.     

Numerical Studies on a Static Vacancy on a 2D spin-1/2 Heisenberg Antiferrornagnet Using a Projector Method

We study the problem of a static vacancy on a spin-1/2 Heisenberg antiferromagnetic square lattice of size 4 × 4 exactly by a projector method. We find that the nearest-neighbor spin correlations. deviate from that of the pure model at the neighborhood of the vacancy, and tend to it vibratively as the Manhattan distance from the vacancy increases.     

Lattice dynamics and inelastic neutron scattering experiments on andalusite,Al2SiO5

We report coherent inelastic neutron scattering measurements of the phonon dispersion relations and lattice dynamics shell model calculations of several microscopic and macroscopic properties of andalusite, Al₂SiO₅. Andalusite has an orthorhombic structure with 32 atoms/unit cell. The inelastic neutron scattering measurements (up to energy transfers of 45 meV) were carried out using the triple axis spectrometer at Dhruva reactor, India using a single crystal of andalusite and the phonon dispersion relations along the [100] direction have been measured. The shell model calculations have been used to compute the crystal structure, elastic constants, phonon frequencies, dispersion relations, density of states and the specific heat. The calculated results are in good agreement with available experimental data. The computed one-phonon neutron scattering structure factors based on the shell model have been very useful in the planning and analysis of the inelastic neutron scattering experiments.     

Theoretical strength of 2D hexagonal crystals: application to bubble raft indentation

By means of lattice and molecular dynamics we study the theoretical strength of homogeneously strained, defect-free 2D crystals whose atoms interact via pair potentials with short- and longer-ranged interactions, respectively. We calculate the instability surface, i.e. the boundary in the 3D homogeneous strain space (ε _xx ,?ε _yy ,?ε _xy ), at which the first vanishing of the frequency of a vibrational mode occurs, taking into account all 2(N???1)?+?3 modes of a 2D periodic system of N atoms. We also compute the strain energies of the crystal on the instability surface, thus defining the most dangerous direction(s) of strain where the critical energy density is small. A theory is developed to incorporate the effect of loading device–sample interactions in the lattice instability criterion. The results are applied to the model problem of bubble raft indentation. We analyse the distribution of the unstable phonon modes in the first Brillouin zone as a function of the loading parameter, and discuss the post-critical behaviour of the lattice in the presence of strain gradients as in nano-indentation experiments.