Force Constant Calculations Research Articles

First-Principle Studies of Phonons III-N Compound Semiconductors in Wurtzite Structure

 Abstract—The phonon dispersion relations and density of states of the nitrides BN, AlN, GaN and InN in the wurtzite structure are investigated by using separately the local density approximation (LDA) and the generalized gradient approxi- mation (GGA) within the framework of density functional theory. The results show that the highest optical phonon frequency at the Brillouin zone center decreases, but the phonon band gap increases, with increasing the cation/anion mass ratio. The frequencies calculated with GGA are lower than those with LDA. The GGA is more suitable for AlN and GaN, but the LDA for BN and InN. dynamical properties of the GaN, AlN, BN and InN by the first-principle calculation based on the density functional theory. The exchange-correlation potentials in the local density approximation (LDA) (12) and the generalized gradient approximation (GGA) (13) are separately used in the calculations. The optimum plane-wave energy cut-off has been tested carefully by keeping the total energy error less than 0.001 Hartree, and is determined as 45 Ryd for all these compounds. A 3  3  3 Monkhorst-Pack mesh and ten special k point have been used to perform the Brillouin zone (BZ) integration. The self-consistent convergence of the total energy is taken to be 10 -6 eV/atom, in order to obtain accurately the phonon dispersion curves. Moreover, a 444 q mesh is employed for the force constant calculation in the first BZ by interpolation. The whole calculation is carried out by using the Quantum ESPRESSO code (14), and the calculated results of the phonon frequencies and densities of states (DOS) are shown in Fig. 1 to Fig. 4. III. RESULTS AND DISCUSSION To obtain the equilibrium lattice constant a, c and the internal geometrical constant u, we fit the energy versus volume curves to the Murnaghan equation of state. Table I lists the calculated values of the structural parameters in this work. It is seen that our results are in good agreement with the previous theoretical and experimental values.

Frequencies and polarization vectors of phonons: Results from force constants which are fitted to experimental data or calculatedab initio

The properties of phonons may be calculated from the dynamical matrix which is determined by force constants. Often the force constants are obtained by fitting them to experimental phonon frequencies, e.g., for wave vectors $\mathbf{q}$ on high-symmetry directions of the Brillouin zone. It is well known that these force constants do not necessarily lead to correct frequencies for wave vectors for nonsymmetrical $\mathbf{q}$ and to correct polarization vectors. In the present paper this is demonstrated by comparing for fcc Ni, fcc Al, and bcc Fe the frequencies and polarization vectors calculated from fitted force constants with the results from ab initio calculated force constants. However, for most regions of the Brillouin zone the differences between the results obtained from the two sets of force constants are not large.

Structure impact on the thermal and electronic properties of bismuth telluride by ab-initio and molecular dynamics calculations

We use molecular dynamics and ab-initio methods to predict the thermal and electronic properties of new materials with high figures of merit. The simulated systems are bulk bismuth tellurides with antisite and vacancy defects. Optimizations of the materials under investigation are performed by the SIESTA code for subsequent calculations of force constants, electronic properties, and Seebeck coefficients. The prediction of the thermal conductivity is made by Non-Equilibrium Molecular Dynamics (NEMD) using the LAMMPS code. The thermal conductivity of bulk bismuth telluride with different stoichiometry and with a number of substitution defects is calculated. We have found that the thermal conductivity can be decreased by 60% by introducing vacancy defects. The calculated thermal conductivities for the different structures are compared with the available experimental and theoretical results.

Pseudo-Jahn–Teller origin of icosahedral instability in boron buckyball, B80

A study of Ih to Th pseudo-Jahn–Teller (PJT) distortion in B80 is presented. Reduced matrix elements for vibronic coupling and resulting force constants were calculated in Ih to elucidate the origin of B80 symmetry breaking. Important orbital excitations involved are between inner orbitals 9hg, 5hg, and 6gu and virtual orbitals 8t2u and 8gg. Low-lying occupied orbitals interact more strongly than frontier molecular orbitals due to their density distribution on the capping atoms. The large energy gaps, associated with these excitations, attenuate the PJT effect. The force constant calculations for B80 point to a weak PJT energy stabilization of 304cm−1 at B3LYP/6-31G(d).

Solvent effect on the vibrational spectra of Carvedilol

Carvedilol (CRV) is an important medicament for heart arrhythmia. The aim of this work was the interpretation of its vibrational spectra with consideration on the solvent effect. Infrared and Raman spectra were recorded in solid state as well in solution. The experimental spectra were evaluated using DFT quantum chemical calculations computing the optimized structure, atomic net charges, vibrational frequencies and force constants. The same calculations were done for the molecule in DMSO and aqueous solutions applying the PCM method. The calculated force constants were scaled to the experimentally observed solid state frequencies. The characters of the vibrational modes were determined by their potential energy distributions. Solvent effects on the molecular properties were interpreted. Based on these results vibrational spectra were simulated.

B112 LD-BTEフォノン計算手法の開発(OS-6:マイクロ・ナノ熱工学(1))

In this study we try to build a framework for phonon calculation. There are several steps to obtain thermal properties of nanostructure material: first step is force constants (FCs) calculation, after that we can calculate phonon properties with those FCs (LD calculation), and finally phonon dynamics can be simulated with the Boltzmann transport equation (BTE) for phonons. We introduce a LD and BTE calculation scheme in the LJ FCC crystal.

AB INITIOSTUDY OF SPECTROSCOPIC CONSTANTS AND ANHARMONIC FORCE FIELD OFAsH2RADICAL

The equilibrium structure, spectroscopic constants and anharmonic force field of AsH2have been investigated at B3LYP, B3PW91 and MP2 methods employing the basis sets of cc-pVNZ and aug-cc-pVNZ (N ∈ { T , Q }), respectively. The computed geometries, rotational constants, part of vibrational frequencies, quartic and sextic centrifugal distortion constants are compared with the available experimental data or theoretical results. The other vibrational frequencies, equilibrium rotational constants, anharmonic constants, vibration–rotation interaction constants, cubic and quartic force constants of AsH2are also predicted for the first time. Furthermore, the calculated results show that the DFT method is superior to MP2 at the calculations of geometries, spectroscopic constants and force constants. The B3PW91/aug-cc-pVQZ results are more reliable. Our predictions can provide useful data for the experimental studies of the corresponding spectroscopic constants of AsH2.

Hyperconjugation in β,β′‐silyl substituted vinyl cations – indications from IR spectroscopy

AbstractAlkyl substituted vinyl cations 1a–c have been synthesized in the form of their [B(C6F5)4]− salts and have been characterized by NMR and IR spectroscopy. The IR absorption bands detected for the νas(CC+) vibrations in vinyl cations are of great diagnostic value, due to their high intensity and relative isolated position in the IR spectra ($\tilde {\nu }$ = 1930–2020 cm−1). DFT calculations of the harmonic force constants at the B3LYP/cc‐pvtz level of theory allowed for an unequivocal assignment of the band after scaling of the theoretical values to account for the anharmonicity of the experimental vibrational potential. A study on the energy of the νas(CC+) of alkyl (1) and aryl substituted vinyl cations (2) revealed a systematic trend, which indicates a decreasing stabilization of the vinyl cations by β‐SiC hyperconjugation when the electron donating ability of the substituent R2 next to the positively charged carbon atom is increased. Copyright © 2010 John Wiley & Sons, Ltd.

The theory of the canonical force field revisited

In a previous Letter, Kuczera’s theory of the canonical force field was generalized to the case of redundant curvilinear internal coordinates related by non-linear constraints. A central issue in this theory is the projection from the space of internal coordinates onto the pure vibrational manifold. In this Letter we present a new mathematical treatment of the projection that solves some problems of inconsistency that have arisen when applying the theory to molecules with a central atom. In addition to solving these problems, this treatment greatly simplifies the attainment of the projection and, consequently, the calculation of canonical force constants.

Modelling of hot carrier solar cell absorbers

Hot Carrier cells aim to tackle the carrier thermalisation loss after absorption of above band gap photons by separating and collecting carriers before they thermalise. Such slowing of carrier cooling may be achieved by modulation of the phonon decay mechanisms in nanostructures. 3D force constant modelling of quantum dot nanostructures indicates that complete mini-gaps in the phonon dispersion can be achieved across reciprocal space for very small (1 nm) close packed quantum dots with a large mass difference between quantum dot (QD) and matrix. This work uses force constants from the literature for bulk materials. A 3D model using the more accurate ab-initio calculation of force constants indicates that only very small mini-gaps in reciprocal space exist for larger quantum dots with a small mass difference, although thus far the model has not been able to simulate these small, high mass difference, closely packed QD systems. For such small QD systems it is indicated that if correctly engineered the mini-gaps could prevent the major Klemens’-type decay mechanism of a longitudinal/transverse optical (LTO) phonon decaying to two longitudinal acoustic (LA) phonons of half the energy and equal and opposite momenta. As this is the primary decay mechanism of non-equilibrium ‘hot’ phonons emitted by hot electrons, its prevention can create a ‘hot phonon bottleneck’ which will re-heat the electron gas and thus slow the rate of carrier cooling.

Scaled Quantum FT‐IR and FT‐Raman Spectral Analysis of 1‐Methoxynaphthalene

The structural and vibrational property of 1‐methoxynaphthalene has been studied. The fundamental vibrational frequencies and intensity of vibrational bands were evaluated using B3LYP/6‐31G (d, p) basis set and was scaled using various scale factors, which yielded a good agreement between observed and calculated frequencies. The vibrational spectra were interpreted with the aid of normal coordinate analysis. The results of the calculations were applied to simulated spectra of the title compound, which shows excellent agreement with observed spectra. The calculated force constants in vibrational internal coordinates are in closely coincides with the experimentally observed force constants.

Tautomerism, normal coordinate analysis, vibrational assignments, calculated IR, Raman and NMR spectra of adenine

The Raman (3700–100 cm −1), infrared (4000–200 cm −1), mass spectrum and 1H NMR temperature-dependent study of adenine have been recorded. Quantum chemical calculations were carried out for N(9)H- amino, N(7)H- amino, N(9)H- imino and N(7)H- imino adenine tautomers using RHF, B3LYP and MP2 with full electron correlation up to 6-311++G(d,p) basis set. The computational results reveal the non-planar N(9)H- amino conformer of adenine to be the most stable structure of adenine. The planar (C s) form of N(9)H- amino adenine is found to represent a transition state, lying 8 cm −1 above the non-planar conformer and with one imaginary frequency. Comparison between theoretical and experimental 1H NMR spectra favors the assignment of the signals to N9(H) and N7(H)- amino tautomers over the corresponding imino tautomers. On the other hand, the recorded IR, Raman and 13C NMR spectra were fully consistent with N9(H)- amino adenine tautomer, therefore it is the only tautomer in both the gas and solid phases and in solution. Moreover, the results of NH 2 potential surface scans utilizing B3LYP and MP2 = full methods at 6-31G(d) basis also support the non-planarity of N(9)H- amino adenine. The mass spectral measurements indicate the presence of 3% adenine dimmer which indicates weak inter-molecular hydrogen bonding interactions in adenine. Additionally, intramolecular hydrogen bonding is also predicted between N 1 and H 15 atoms. The theoretical infrared and Raman spectra have been successfully simulated by means of both DFT and MP2 calculations, allowing the interpretation of the complex bands observed. Aided by normal coordinate analysis, potential energy distributions and the calculated force constants, a revised and accurate vibrational assignment for all fundamentals has been provided for the non-planar N(9)H-adenine tautomer. The results are reported herein and compared with similar molecules whenever appropriate.

Vibrations in cylindrical shells with transverse elastic isotropy: Application to III–V nitride nanotubes

The vibrational modes of cylindrical shells with transverse elastic isotropy and arbitrary thickness are calculated in the framework of the elasticity theory and a comparison with the isotropic approach is presented. Cylindrical shells are a good model for nanotubes and here an application for nanotubes of transversely isotropic elastic materials is given. We have obtained the expression for the frequency of the radial breathing mode and it is shown that calculated frequencies coming from that expression compare fairly well with those obtained from different ab initio, force constant model calculations and experimental results. Further, the dispersion relations depend on all the elastic coefficients and therefore they are quite different for nanotubes with hexagonal or wurtzite structure. This demonstrates the need to go beyond the isotropic model to investigate the vibrational spectrum of transversely isotropic elastic material nanotubes and nanowires.

Ab initio calculation of cubic force constants in formamide monomer, formamide dimer, formic acid dimer and their D, D2 and D4 derivatives. An estimation of fermi resonance and intra-intermolecular coupling

We report preliminary results of the ab initio calculations in the 4-31G basis set of cubic force constants in normal modes for the HCONH2 and DCONH2 monomers, and a series of cyclic dimers (HCONH2)2, (HCOND2)2, (HCOOH)2, and (HCOOD)2. These include diagonal cubic constants and nondiagonal constants, describing Fermi resonances between X—H(D) stretching modes and overtones of other vibrations, and couplings between intra- and intermolecular modes. Results allow us to interpret experimental Fermi resonance observed in the infrared spectrum of the HCONH2 monomer. Diagonal anharmonicities improve an agreement between experimental and calculated frequencies for the dimers. The calculation shows that the coupling between the X—H(D) and X …. Y stretching vibrations is substantially stronger in the formic acid dimers than in the formamide dimers.

An efficient algorithm for the density-functional theory treatment of dispersion interactions

The quasi-self-consistent-field dispersion-corrected density-functional theory formalism (QSCF-DC-DFT) is developed and presented as an efficient and reliable scheme for the DFT treatment of van der Waals dispersion complexes, including full geometry optimizations and frequency calculations with analytical energy derivatives in a routine way. For this purpose, the long-range-corrected Perdew-Burke-Ernzerhof exchange functional and the one-parameter progressive correlation functional of Hirao and co-workers are combined with the Andersson-Langreth-Lundqvist (ALL) long-range correlation functional. The time-consuming self-consistent incorporation of the ALL term in the DFT iterations needed for the calculation of forces and force constants is avoided by an a posteriori evaluation of the ALL term and its gradient based on an effective partitioning of the coordinate space into global and intramonomer coordinates. QSCF-DC-DFT is substantially faster than SCF-DC-DFT would be. QSCF-DC-DFT is used to explore the potential energy surface (PES) of the benzene dimer. The results for the binding energies and intermolecular distances agree well with coupled-cluster calculations at the complete basis-set limit. We identify 16 stationary points on the PES, which underlines the usefulness of analytical energy gradients for the investigation of the PES. Furthermore, the inclusion of analytically calculated zero point energies reveals that large-amplitude vibrations connect the eight most stable benzene dimer forms and make it difficult to identify a dominating complex form. The tilted T structure and the parallel-displaced sandwich form have the same D(0) value of 2.40 kcal/mol, which agrees perfectly with the experimental value of 2.40+/-0.40 kcal/mol.

Scaled Quantum Chemical Force Fields for 1,1-Difluorocyclopropane and the Influence of Vibrational Anharmonicity

Potential functions and harmonic (omega(i)) and anharmonic (nu(i)) fundamental frequencies have been calculated for 1,1-difluorocyclopropane (DFCP) and its d4 and d2 isotopomers using the program Gaussian 03. B3LYP and MP2 models were employed, each with the bases 6-311++G** and cc-pVTZ. Anharmonicity corrections Delta(i) = omega(i) - nu(i) are listed and shown to be different for symmetric and antisymmetric CH stretching modes in situations where Fermi resonance appears to be absent. The same effect is missing in C2H4, for which similar calculations were made. The quadratic force fields for DFCP have been scaled in symmetry coordinate space with 15 scale factors both to observed frequencies nu(obsd)and also to omega (obsd), where omega(obsd) = nu(obsd) + Delta. With nu(obsd) especially, different scale factors are needed for the symmetric and antisymmetric CH stretching force constants due to their differing anharmonicities. The source of the latter in the quartic and cubic force field is explored. MP2 calculations of valence interaction force constants involving the stretching of bonds on a common carbon atom are preferred to those from a B3LYP model. In either model, scaling to omega(obsd) rather than to nu(obsd) does not remove the necessity of varying scale factors for differing types of motion in the same group. Theoretical values of the five quartic centrifugal distortion constants are listed for the normal species and compared with new experimental data. The predictions are sufficiently good to be useful in fitting pure rotational transitions. A weakness is identified in the current Gaussian 03 code for the calculation of vibration-rotation quantities, and limitations are noted in the manner in which Fermi resonance is handled.

Strain-induced Raman-mode shift in single-wall carbon nanotubes: Calculation of force constants from molecular-dynamics simulations

The force-constant calculation based on molecular-dynamics simulations is carried out to investigate the effect of axial strain on the Raman modes of $(n,n)$ and $(n,0)$ single-wall carbon nanotubes. It is found that the frequencies of both radial breathing mode (RBM) and tangential modes (TMs) upshift in compression but downshift in tension. Especially, a sharp reduction in the RBM occurs when the tubes buckle under compression. More interestingly, the critical strain of RBM is inversely proportional to the tube diameter and also depends on the tube chirality. Moreover, three TMs present two different kinds of slopes with axial strain, which can be assigned to the experimentally measured ${G}^{+}$ and ${G}^{\ensuremath{-}}$ peaks. TMs change trends with strain satisfactorily agree with the experimental results. Under compression, the results are valuable to understand the effect of axial strain on tubes under nonhydrostatic pressure.

Radiation Torque and Force on Optically Trapped Linear Nanostructures

We study the optical trapping of highly elongated linear nanostructures in the focal region of a high-numerical aperture lens (optical tweezers). The radiation torque and trapping force on these nanostructures that are modeled as chains of identical spherical scatterers are calculated by means of multipole field expansions in the framework of the transition matrix approach. We investigate both orientational and trapping stability and calculate force constants and trap parameters in order to clarify the role of the linear geometry in the optical trapping mechanism. Furthermore, we calculate optical trapping of nanowires of different materials and compare our theoretical findings with available experimental results.

Strain relaxation in small adsorbate islands: O on W(110)

The stress-induced lattice changes in a $p(1\ifmmode\times\else\texttimes\fi{}2)$ ordered oxygen layer on W(110) are measured by low-energy electron diffraction. We have observed that small oxygen islands show mismatch with the underlying lattice. Our results indicate that along $[1\overline{1}0]$, the average mismatch inversely scales with the island size as $1/L$ for all oxygen coverages up to 0.5 ML, while along [001], it is significant only for the smallest oxygen islands and scales as a higher power of the inverse island size. The behavior along $[1\overline{1}0]$ is described by a one-dimensional finite-size Frenkel--Kontorova model. By using this model, together with the calculated force constants, we make a quantitative estimate of the change in surface stress upon oxygen adsorption. The result is consistent with our ab initio calculations, which give a relative compressive stress of $\ensuremath{-}4.72\text{ }\text{N}/\text{m}$ along $[1\overline{1}0]$ and a minute relative tensile stress of 0.15 N/m along [001]. The scaling along [001] is qualitatively explained as an effect induced by the lattice relaxation in the $[1\overline{1}0]$ direction.

Intrinsic lattice thermal conductivity of semiconductors from first principles

We present an ab initio theoretical approach to accurately describe phonon thermal transport in semiconductors and insulators free of adjustable parameters. This technique combines a Boltzmann formalism with density functional calculations of harmonic and anharmonic interatomic force constants. Without any fitting parameters, we obtain excellent agreement (<5% difference at room temperature) between the calculated and measured intrinsic lattice thermal conductivities of silicon and germanium. As such, this method may provide predictive theoretical guidance to experimental thermal transport studies of bulk and nanomaterials as well as facilitating the design of new materials.