Valence Force Field Research Articles

Breathinglike phonon modes of multiwalled carbon nanotubes

The breathinglike phonon modes of multiwalled carbon nanotubes are studied within a valence force field model for nanotubes with two and three layers of armchair type and within a continuum model for nanotubes with a large number of layers. A bond-polarizability model is used to calculate the nonresonant Raman intensity of the breathinglike modes. It is obtained that among all breathinglike modes of a given multiwalled tube, the in-phase one has a maximal intensity. The predicted intensity of the breathinglike modes is compared to available low-frequency experimental Raman data. Special attention is given to the comparison with Raman data on double-walled carbon nanotubes.

Calculations on the size effects of Raman intensities of silicon quantum dots

Raman intensities of Si quantum dots (QD's) with up to 11489 atoms (about 7.6 nm in diameter) for different scattering configurations are calculated. First, phonon modes in these QD's, including all vibration frequencies and vibration amplitudes, are calculated directly from the lattice-dynamic matrix by using a microscopic valence force field model combined with the group theory. Then the Raman intensities of these quantum dots are calculated by using a bond-polarizability approximation. The size effects of the Raman intensity in these QD's are discussed in detail based on these calculations. The calculations are compared with the available experimental observations. We are expecting that our calculations can further stimulate more experimental measurements.

Vibrational analysis of substituted phenols: Part I. Vibrational spectra, normal coordinate analysis and transferability of force constants of some formyl-, methoxy-, formylmethoxy-, methyl- and halogeno-phenols

The Raman (including FT-Raman) and Fourier transform infrared (FTIR) spectra of 1,3-dihydroxybenzene, 1,4-dihydroxybenzene, 2-hydroxybenzaldehyde, 2-hydroxy-3-methoxybenzaldehyde, 4-hydroxy-3-methoxybenzaldehyde, 1,2-dihydroxy-3-methoxybenzene, 2,5-dihydroxytoluene, 2,6-dihydroxytoluene, pentachlorophenol and pentabromophenol were measured. Raman polarisation measurements were made wherever possible. A normal coordinate treatment was carried out for both the in-plane and out-of-plane vibrations of these molecules using a 123-parameter-modified valence force field. An overlay least-squares technique was employed to refine the force constants using 347 frequencies of 10 molecules. The reliability of these force constants was tested by making a zero-order calculation for 10 related molecules. Unambiguous vibrational assignments of all the fundamentals were made using the potential energy distributions and eigenvectors.

Strain relaxation and interfacial stability in III–V semiconductor strained-layer heteroepitaxy: atomistic and continuum modeling and comparisons with experiments

A systematic study is presented of interfacial stability and strain relaxation through misfit dislocation formation in III–V semiconductor layer-by-layer heteroepitaxy. A multiscale modeling strategy is developed that links continuum elasticity theory with atomistic structural relaxation and Monte Carlo simulations using a valence force field description of interatomic interactions. Results are presented for the energetics of the transition from a coherent to a semicoherent film/substrate interface consisting of a misfit dislocation network, the semicoherent interface structures, the associated strain fields, and the film surface morphological characteristics for InAs epitaxy on GaAs(1 1 1)A. The capability of continuum elasticity theory to provide a satisfactory description of the atomistic simulation results is discussed. In addition, using thin compliant substrates and grading the composition of the deposited film are demonstrated to have beneficial effects on film strain relaxation. Furthermore, the dynamics of strain relaxation is analyzed based on a phenomenological mean-field theoretical framework. Our theoretical results are in very good agreement with our experimental measurements on InAs/GaAs(1 1 1)A samples for films grown by molecular beam epitaxy on thick and thin GaAs buffer layers.

Physical characteristics, vibrational spectroscopy and normal-coordinate analysis of 2-aminophenol and 2-phenylenediamine complexes

Hg(II) and Cd(II) complexes with 2-aminophenol ( Amph) and 2-phenylenediamine ( Phda) as ligands were prepared and characterized by elemental analysis, electrical conductivity, thermogravimetric analysis (DTA/TG), X-rays, FT-IR and FT-Raman spectra. The complexes formed can be formulated as [M(L) 2· nH 2O]· mH 2O. The electrical conductivity of 0.001 M DMSO solutions revealed the non-electrolytic behavior of the Amph complexes while Phda complexes behave as a 1:2 electrolyte. DTA analysis reveals the presence of two types of water coordinating as aligned and as water of crystallization. Δ E a of the stepwise decomposition was evaluated. X-ray powder diffraction studies on the ligands and their complexes are described. The fundamental frequencies of these complexes have been assigned on the basis of normal coordinate calculations, carried out using a generalized valence force field (GVFF). The proposed assignments are discussed in relation to the group frequencies in structurally related molecules and in terms of the computed potential-energy distributions among the symmetry coordinates.

Raman spectroscopic studies on matrix-isolated phosphorus molecules P4 and P2

The Raman spectra of P4 and P2 molecules have been studied in nitrogen, argon, krypton, and xenon matrices at 15 K. The vibrational frequencies of the P4 molecule are up to 14 cm−1 higher than the experimental gas phase data. This apparent blue-shift is not caused by matrix effects but rather due to an underestimation of the fundamentals in the gas phase as a course of the elevated temperatures. The observed frequencies confirm a recent theoretical prediction on the basis of high-level calculations. From the observed frequencies of the P4 molecule a general valence force field was calculated.

Vibrational Analysis of Ferrocyanide Complex Ion Based on Density Functional Force Field

Vibrational properties of ferrocyanide complex ion, <TEX>$[Fe(CN)_6]^{4-}$</TEX> , have been studied based on the force constants obtained from the density functional calculations at B3LYP/<TEX>$6-31G^{\ast\ast}$</TEX> level by means of the normal mode analysis using new bond angle and linear angle internal coordinates recently developed. Vibrations of ferrocyanide were manipulated by twenty-three symmetry force constants. The angled bending deformations of C-Fe-C, the linear bending deformations of Fe-C<TEX>${\equiv}$</TEX>N and the stretching vibrations of Fe-C have been quantitatively assigned to the calculated frequencies. The force constants in the internal coordinates employed in the modified Urey-Bradley type potential were evaluated on the density functional force field applied, and better interaction force constants in the internal coordinates have been proposed. The valence force constants in the general quadratic valence force field were also given. The stretch-stretch interaction and stretch-bending interaction constants are not sensitive to the geometrical displacement in the valence force field.

Formation and stacked layer of quantum dots

Three-dimensional formation occurring at the initial stage of the heteroepitaxial growth of a lattice-mismatched system is reviewed. It is experimentally proved that the formation of InAs islands on the GaAs substrate is due to the Stranski–Krastanov (S–K) growth mode. This formation has been proposed to realize a mesoscopic island structure which can be utilized as a quantum dot (QD). They are naturally formed with the S–K growth mode. They have been called naturally- or self-formed QDs. The strain energy of the QD is calculated with the valence-force field model, and then the possible formation of dislocation-free QDs is described. The experimental results of InAs/GaAs and InP/GaP QDs are presented. In the stacked layer of InAs/GaAs QDs, the GaAs spacer thickness for the vertical ordering of QDs is investigated. The ordering, dependent on the spacer thickness, is found by the transmission electron microscope images of cross-sectional stacked layers. The QD can be neither stacked nor vertically ordered when the thickness is greater than 2 h where h denotes the QD height. The QDs are crushed when the spacer is thinner than h. The vertically ordered QDs are stacked when the GaAs spacer thickness is between h and 2 h.

Phonons in single wall carbon nanotube bundles

We review recent and original results on the vibrational properties of single wall carbon nanotubes (SWNT). We especially focus on calculations and experiments performed on nanotube bundles. So far, the main technique for probing the dynamics has been Raman spectroscopy. Here, we discuss: (i) the relation between frequency of the A 1 g radial breathing mode and nanotube diameter, (ii) the origin of resonance and the consequences on the profile and intensity of the Raman lines, and (iii) the assignment and resonant behaviour of the Raman lines between 700 and 1000 cm −1. Recently, inelastic neutron scattering techniques (INS) were shown to be effective tools to probe the vibrational density of states of SWNT. We review the INS results and focus on the study of low frequency excitations, especially libration-twist modes and acoustic modes. Both Raman and INS results are analysed in the light of calculations performed in a valence force field model taking into account van der Waals intertubes interactions in the bundles.

Electronic structure of Ge/Si self-assembled quantum dots with different shapes

Pyramid and hut shapes of self-assembled Ge quantum dots over a range of the lateral size of less than 500 Å and dome structures beyond the lateral size of 1000 Å are typically observed. We have investigated the electronic properties of approximate models of the pyramid and hut structures by taking the profiles of strain components into account. To obtain the elastic strain distribution, a valence force field model is used. The electronic confined state energies for electrons and holes are then obtained by diagonalizing the resultant Hamiltonian matrix of the Schrödinger equation based on strain-modified potential. Theoretical results are compared with the transition energies observed by photoluminescence spectroscopy.

Electron and hole localization in coupled InP/InGaP self-assembled quantum dots

The electronic structure of vertically coupled (stacked) cylindrical InP/InGaP self-assembled quantum dots is calculated by the multiband effective mass theory. The nonuniform strain distribution is obtained through the valence force field method. The energy levels of stacks of three vertically coupled quantum dots are followed as they evolve from the ground state of the single quantum dot and split into triplets with decreasing dot distance. The holes are found to couple via the light hole states in the spacers between the dots. We found a reversal of the total angular momentum of the ground state of the hole from 3/2ℏ to 1/2ℏ with decreasing thickness of the spacer. The theoretical results are compared with recent photoluminescence measurements.

Syntheses and Structures of Donor-Acceptor Complexes of Selenium Dioxide with Pyridine and Trimethylamine

Donor-acceptor (DA) complexes of pyridine (py)·SeO2 and trimethylamine (TMA)·SeO2 were prepared by direct reactions of solid selenium dioxide with the amines. Both are white solids decomposing slowly at room temperature. The former complex decomposes into its components, while the latter one undergoes a redox reaction. The single-crystal structure determination of py·SeO2 has revealed that the chain-like structure of (SeO2)n is destroyed during the formation of the DA bond and the py·SeO2 molecule is bound to the nearest neighbouring molecule through two weak Se···O interactions. More labile TMA·SeO2 complex could not be prepared as single crystals. Analogous molecular structure of both complexes was proved by their Raman spectra. A modified general valence force field was used for the interpretation of Raman spectra of TMA·SeO2 and TMA·SO2.

Electronic structure of the valence band in cylindrical strained InP/InGaP quantum dots in an external magnetic field

The multiband effective-mass model of cylindrical self-assembled quantum dots in a magnetic field normal to the layer of the quantum dots is presented. The strain distribution is computed by the valence force field method. The strain-dependent multiband Hamiltonian is modified into an axially symmetric form, which commutes with the total angular momentum F z = fℏ, where f denotes the total magnetic quantum number. The heavy hole and the light hole parts in the mixed hole state are resolved. It is found that the heavy hole component dominates in the ground states for both f= 1 2 and f= 3 2 . The electronic structure exhibits numerous anticrossings between the hole levels. The Zeeman splitting between the +| f| and −| f| states is also computed.

Microscopic interface phonon modes in structures of GaAs quantum dots embedded in AlAs shells

By means of a microscopic valence force field model, a series of novel microscopic interface phonon modes are identified in shell quantum dots (SQDs) composed of a GaAs quantum dot of nanoscale embedded in an AlAs shell of a few atomic layers in thickness. In SQDs with such thin shells, the basic principle of the continuum dielectric model and the macroscopic dielectric function are not valid any more. The frequencies of these microscopic interface modes lie inside the gap between the bulk GaAs band and the bulk AlAs band, contrary to the macroscopic interface phonon modes. The average vibrational energies and amplitudes of each atomic shell show peaks at the interface between GaAs and AlAs. These peaks decay fast as their penetrating depths from the interface increase.

Valence force field analysis on nitrogen in silicon

Nitrogen doping attracts attention because it reduces void defects drastically. But the mechanism has not been clarified yet. Various configurations of nitrogen have been proposed by using the first principles calculation but there is no description how the stress plays a role in determining these nitrogen configurations. We reveal normal vibration modes corresponding to well-known infrared absorption peaks at 766 and 963 cm −1 of nitrogen split interstitial (N–N) and derive force constants for bond stretching and bond bending. Local strain energy near nitrogen is calculated for the optimized structures of N–N, nitrogen–vacancy complex, substitutional N and interstitial N. As a result, it is found that in structures of N–N and N 2–V 2 with filled electron orbitals, strain energy plays an important role in the determination of the stable structure.

Studies of the effects of hydrogen bonding on monolayer structures of C 18H 37X (X=OH, SH) on HOPG

Based on Scanning tunneling microscopy (STM) observations of 1-C 18H 37X (X=OH, SH) adsorbed on HOPG, the hydrogen bonded complexes were studied using density functional theory (DFT) and molecular mechanics (MM). At B3LYP/6-31g and B3LYP/6-311g** levels, molecular dimers connected by hydrogen bond were obtained. The models of 1-C 18H 37X monolayer were optimized by consistent valence force field (CVFF), whose structures and interaction energies agree well with DFT calculations. It is noticed that due to the stronger hydrogen bond interactions between C 18H 37OH molecules, C 18H 37OH adsorbed on HOPG shows only one kind of molecular arrangement, while C 18H 37SH exhibits two kinds of packing induced by alkyl–alkyl and adsorbate–substrate interactions.

Chemical bonding, elasticity, and valence force field models: A case study forα−Pt2Siand PtSi

We have carried out a detailed study of the chemical bonding for two room-temperature stable platinum silicide phases, tetragonal alpha-Pt_2Si and orthorhombic PtSi. An analysis of the valence electronic charge density reveals surprising evidence of covalent three-center bonds in both silicide phases, as well as two-dimensional metallic sheets in alpha-Pt_2Si. These elements of the bonding are further analyzed by constructing valence force field models using the results from recent first principles calculations of the six (nine) independent, non-zero elastic constants of alpha-Pt_2Si (PtSi). The resulting volume-, radial-, and angular-dependent force constants provide insight into the relative strength of various bonding elements as well as the trends observed in the elastic constants themselves. The valence force field analysis yields quantitative information about the nature of the chemical bonding which is not easily discernable from the more qualitative charge density plots. More generally, this study demonstrates that the detailed variations in the elastic constants of a material contain useful information about the chemical bonds which can be extracted using valence force field models. Inversely, these models also allow identification of specific elements of the chemical bonding with particular trends in the elastic constants, both within a given material and among a class of related materials.

Derivation of class II force fields. VIII. Derivation of a general quantum mechanical force field for organic compounds

A class II valence force field covering a broad range of organic molecules has been derived employing ab initio quantum mechanical "observables." The procedure includes selecting representative molecules and molecular structures, and systematically sampling their energy surfaces as described by energies and energy first and second derivatives with respect to molecular deformations. In this article the procedure for fitting the force field parameters to these energies and energy derivatives is briefly reviewed. The application of the methodology to the derivation of a class II quantum mechanical force field (QMFF) for 32 organic functional groups is then described. A training set of 400 molecules spanning the 32 functional groups was used to parameterize the force field. The molecular families comprising the functional groups and, within each family, the torsional angles used to sample different conformers, are described. The number of stationary points (equilibria and transition states) for these molecules is given for each functional group. This set contains 1324 stationary structures, with 718 minimum energy structures and 606 transition states. The quality of the fit to the quantum data is gauged based on the deviations between the ab initio and force field energies and energy derivatives. The accuracy with which the QMFF reproduces the ab initio molecular bond lengths, bond angles, torsional angles, vibrational frequencies, and conformational energies is then given for each functional group. Consistently good accuracy is found for these computed properties for the various types of molecules. This demonstrates that the methodology is broadly applicable for the derivation of force field parameters across widely differing types of molecular structures. Copyright 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1782-1800, 2001

Statistical aspects of electronic and structural properties in partially ordered semiconductor alloys

We have investigated the statistical effects of spontaneous ordering on the electronic and structural properties of a semiconductor alloy as a function of order parameter using an empirical pseudopotential method in conjunction with a valence force field method in a supercell approach. The theoretical modeling yields valuable information on the statistical fluctuation of electronic properties, which includes the individual band edge as well as the band gap, for understanding the effects of ordering on various optical and transport measurements. The results on the average bond lengths and the statistical distributions of different types of bonds provide a guideline for the measurability of the effects of ordering in a partially ordered alloy in terms of the order parameter.

Theoretical predictions of unstable two-phase regions in wurtzite group-III-nitride-based ternary and quaternary material systems using modified valence force field model

Group-III (B, Al, Ga, and In)-nitride quaternary alloys and group-III (Al, Ga, and In)-nitride-based mixed anion (As, P, and Sb) quaternary alloys are useful for blue and green light emitting devices and high-temperature, high-power, and high-frequency electronic devices. It is known that these alloys are very difficult to grow in certain compositional regions. The thermodynamical stability of these alloys is studied with respect to an unstable two-phase region in the phase field. The unstable two-phase region is predicted based on a strictly regular solution model. The interaction parameter used in our model is obtained analytically using the valence force field (VFF) model modified for wurtzite structures. The calculated interaction parameters, which are required to predict the unstable two-phase region, agree well with experimental results for related alloy systems. The modified VFF model can also be used to predict the microscopic crystal structure, such as first neighbor anion–cation bond lengths. In order to verify our calculations, we compare the calculated and experimental results for the first neighbor anion–cation bond lengths in the InGaN system. The calculated results agree well with the experimental results. From our calculation results, the unstable two-phase regions for four A1−x−yBxCyD type group-III-nitride quaternary alloys and nine A1−xBxC1−yDy type group-III-nitride mixed anion quaternary alloys are calculated. The predicted unstable two-phase regions agree well with experimentally observed regions of phase separation in ternary alloys, which suggests our model calculations can provide useful guidance in ternary and quaternary systems where there is no experimental data.