Bending Force Constants Research Articles

Lattice dynamics of tetragonal Nd2BaZnO5

AbstractA short‐range force constant model (SRFCM) has been applied to investigate the Raman and the infrared wavenumbers in Nd2BaZnO5 in its tetragonal phase of space group I4/mcm. Calculations of zone‐center phonons are made with five stretching and five bending force constants. All the Raman and infrared values are then assigned to their corresponding modes. Two Raman modes are reassigned on the basis of group theoretical calculations. The calculated Raman wavenumbers exhibit good agreement with the observed values. Copyright © 2007 John Wiley & Sons, Ltd.

Evaluation of the effective mechanical properties of single walled carbon nanotubes using a spring based finite element approach

Abstract The development of a finite element formulation that is appropriate for the computation of Young’s and Shear modulus of single walled carbon nanotubes (SWCNTs) is the purpose of this paper. The method utilizes the atomistic microstructure of the nanotubes. According to the three-dimensional atomic nanostructure of SWCNTs, nodes are defined at the atom locations. Appropriate spring-type elements interconnect these nodes to simulate properly interatomic interactions. This approach is implemented via the use of three-dimensional spring-like elements each node of which obeys to three translations and three rotations. In this way, molecular mechanics theory can be applied directly while the atomic bonds are modeled by using exclusively physical variables such as bond stretching, bond angle bending and torsional rotation resistance force constants. With the proposed method, the Young’s and shear modulus of numerous SWCNTs were determined. The effect of the nanotube radius and thickness on the mechanical behavior of SWCNTs was tested and demonstrated. The numerical results show good agreement with other corresponding values which are available in the literature.

Lattice dynamics of tetragonal R2BaCuO5 (R = La, Nd) oxides in the P4/mbm structure

AbstractA short‐range force constant model (SRFCM) has been applied to investigate the Raman and the infrared wavenumbers in R2BaCuO5 (R = La, Nd) in their tetragonal phase of space group P4/mbm. Calculations of zone‐center phonons are made with six stretching and five bending force constants. All the Raman and infrared values are then assigned to their corresponding modes. The force constants were evaluated by fitting ten Raman and eight infrared modes. The calculated Raman and infrared modes show good agreement with the observed values. Copyright © 2007 John Wiley & Sons, Ltd.

A lattice dynamical investigation of the Raman and the infrared frequencies of the cubic Y 2Ru 2O 7 pyrochlore

A short-range force constant model has been applied for the first time to investigate the Raman and the infrared frequencies in Y 2Ru 2O 7 pyrochlore in its cubic phase of space group Fd3m. The calculations of zone center phonons have been made with four stretching and three bending force constants. The calculated values of Raman and infrared frequencies are in good agreement with the observed ones.

Lattice dynamic investigation of the Raman and infrared wavenumbers of orthorhombic R2BaNiO5 (R = Y, Gd) oxides in Immm structure

AbstractA short‐range force constant model has been applied to investigate the Raman and the infrared wavenumbers in R2BaNiO5 (R = Y, Gd) in their orthorhombic phase of space group Immm. Calculations of zone‐center phonons are made with seven stretching and four bending force constants. The force constants are evaluated by fitting nine Raman and two infrared modes. Two Raman modes are reassigned on the basis of group theoretical calculations. The calculated Raman and infrared modes show good agreement with the observed values. The infrared values are assigned for the first time in these oxides. Copyright © 2006 John Wiley & Sons, Ltd.

Phonons at the zone center for α-NaAlH 4

A short-range force constant model has been applied for the first time to investigate the phonons in α-NaAlH 4 having body centered tetragonal Scheelite structure .The normal symmetry coordinates for the Scheelite structure were computed to investigate the phonons at the zone center. The phonons for α-NaAlH 4 have been calculated involving five stretching and two bending force constants .The calculated Raman frequencies exhibit good agreement with the available measured values. The infrared frequencies have been assigned proper modes for the first time.

Zone center frequencies of the orthorhombic NdMnO 3 perovskite

A short range force constant model has been applied for the first time to investigate the phonons in NdMnO 3 perovskite in the orthorhombic phase. The calculations with nine stretching and eight bending force constants provide good agreement for the observed Raman frequencies. The infrared frequencies have been assigned for the first time.

Parametrization of an anharmonic Kirkwood–Keating potential for AlxGa1−xAs alloys

We introduce a simple semiempirical anharmonic Kirkwood-Keating potential to model A(x)B(1-x)C-type semiconductors. The potential consists of the Morse strain energy and Coulomb interaction terms. The optical constants of pure components, AB and BC, were employed to fit the potential parameters such as bond-stretching and -bending force constants, dimensionless anharmonicity parameter, and charges. We applied the potential to finite temperature molecular-dynamics simulations on Al(x)Ga(1-x)As for which there is no lattice mismatch. The results were compared with experimental data and those of harmonic Kirkwood-Keating model and of equation-of-motion molecular-dynamics technique. Since the Morse strain potential effectively describes finite temperature damping, we have been able to numerically reproduce experimentally obtained optical properties such as dielectric functions and reflectance. This potential model can be readily generalized for strained alloys.

Lattice dynamic investigation of the Raman and infrared wavenumbers of orthorhombic R2BaCuO5 (R = Y, Ho, Gd) oxides

A short-range force constant model was applied for the first time to investigate the Raman and infrared wavenumbers in R2BaCuO5 (R = Y, Ho, Gd) oxides in their orthorhombic phase of space group Pnma. Calculations of zone center phonons were made with 17 stretching and four bending force constants. The force constants were evaluated using the electronegativities and the atomic distances. The calculated values of Raman wavenumbers are in reasonable agreement with the available observed values. The infrared wavenumbers were assigned for the first time. Copyright © 2004 John Wiley & Sons, Ltd.

Zone center phonons of the orthorhombic trifluorides MF 3 (M=Dy, Lu)

A short range force constant model has been applied for the first time to investigate the phonons in trifluorides MF 3 (M=Dy, Lu) in their orthorhombic phase. The calculations with 14 stretching and bending force constants provide good agreement for the observed Raman frequencies. The infrared frequencies have been assigned for the first time.

QM/MM determination of kinetic isotope effects for COMT-catalyzed methyl transfer does not support compression hypothesis.

Secondary alpha-D3 kinetic isotope effects calculated by the hybrid AM1/TIP3P/CHARMM method for the reaction of S-adenosylmethionine with catecholate anion in aqueous solution and catalyzed by rat liver catechol O-methyltransferase at 298 K are 0.94 and 0.85, respectively, in good accord with experiment. The large inverse effect for the enzymatic reaction is not due to compression but arises from significant increases in the stretching and bending force constants involving the isotopically substituted atoms of the transferring methyl group as between the reactant complex and the transition structure, larger than for the reaction in water.

Normal coordinate analysis of the orthorhombic trifluorides MF 3 (M=Gd, Tb, Er, Yb)

A short-range force constant model has been applied for the first time to investigate the phonons in trifluorides MF 3 (M=Gd,Tb,Er,Yb) in their orthorhombic phase. The normal symmetry coordinates for the orthorhombic trifluorides have been computed. The calculations with 14 stretching and bending force constants provide good agreement for the observed Raman frequencies. The infrared frequencies have been assigned.

Lattice dynamical study of optical modes inTl2Mn2O7andIn2Mn2O7pyrochlores

The Raman and IR spectra and force field have been investigated for ${A}_{2}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ $(A=\mathrm{T}\mathrm{l},\mathrm{I}\mathrm{n})$ by means of a short-range force constant model which includes four stretching and four bending force constants. Unusual spectral and force field changes are observed and analyzed. The stretching force constant Mn-O and $A\ensuremath{-}{\mathrm{O}}^{\ensuremath{'}}$ are found to be relatively higher than those of other pyrochlore oxides of the ${A}_{2}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ family, while the remaining force constant values are significantly smaller, especially for ${\mathrm{Tl}}_{2}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}.$ This trend may be due to strong hybridization of the Tl $(6s)$ orbital with O $(2p)$ and Mn $(3d).$ The assignment of all the modes has been proposed and potential energy distribution is also reported. The evaluated frequencies are close to the available observed infrared and Raman frequencies, giving further support to the present assignments.

Zone center wavenumbers of tetragonal AGa2X4 (A = Cd, Zn; X = S, Se)

AbstractA short‐range force constant model (SRFCM) was applied to investigate the phonons in AGa2X4 (A = Cd, Zn; X = S, Se) defect chalcopyrite compounds in the tetragonal phase. The calculation with six stretching and one bending force constants in the SRFCM agrees well with the observed Raman and infrared wavenumbers. In CdGa2X4, the nearest Ga—X interatomic force constants of its bonds were found to be stronger than the nearest Cd—X interatomic force constants, whereas in ZnGa2X4, the nearest Zn—X interatomic force constants of its bonds were found to be weaker than the nearest Zn—X interatomic force constants. The variation of interatomic force constants is discussed. The dominant force constants have nearly the same ratio when Se replaces S. Copyright © 2003 John Wiley & Sons, Ltd.

An analytical expression for E g and A g modes of pyrochlores

A general analytical expression has been derived for E g and A 1g modes in terms of stretching and bending force constant for cubic pyrochlore structure compounds. The expression has been applied to different pyrochlore oxides accounting six stretching and four bending force constants. The calculation of E g and A 1g mode has been carried out by using the earlier reported values of force constants for titanates, hafnates and stannates. The analytical expression can be applied to any pyrochlore structure compounds for evaluating and assigning E g and A 1g mode if the interatomic force constants are already known.

Success and failure of polarized-ion models: Bending and atomization energy of groups 2 and 12 dihalides

Polarized-ion models—with and without dipole reaction fields and charge-quadrupole interaction—are evaluated in calculating atomization energies, bond angles, and bending force constants of groups 2 and 12 dihalides. A study of the sensitivity to changes in the input parameters reveals a strong dependence on dipole polarizabilities. The charge–quadrupole bending terms of a multipole expansion are important for quasi-linear molecules, where the preceding terms in the expansion tend to cancel each other. They normally stabilize the linear geometry, but enhance bent structures, if a certain criterion for the ratio of quadrupole polarizabilities of metal and halide ions is fulfilled. The models explain the bent alkaline earth halides, but fail spectacularly for the group 12 halides—HgBr2 and HgI2 are even calculated as unstable relative to the constituent atoms. The unexpected weakness of ionic bonds is related to the large increase of the ionization energies by relativistic effects and the lanthanide contraction.

Scaled quantum mechanical computations of vibrational spectra of organoelement molecules, containing the atoms P, S, and Cl

Density functional theory has been used for the calculation of vibrational force fields of organoelement molecules. Optimal scaling factors for various stretching and bending force constants are derived from a training set of 12 molecules, containing H, C, N, O, P, S, and Cl atoms, and used to scale force constants for further 14 molecules. These 13 scaling factors, applied to B3LYP force fields, allow compute the 310 frequencies of 26 molecules with the total standard deviation of about 11 cm −1 for 6-31G* and 6-31+G* basis sets, the latter set being preferable for computations of Raman spectra.

Vibrational spectra and force field calculation of A2Mn2O7 (A = Y, Dy, Er, Yb) pyrochlores

AbstractRaman and infrared spectra were recorded for A2Mn2O7 (A = Y, Dy, Er, Yb) pyrochlores. For the first time, lattice dynamic analysis of cubic manganate pyrochlores was carried out using a short‐range force model with four stretching and four bending force constants at the zone center. The assignment of all their modes is proposed. The calculated force constants are discussed and compared for the different pyrochlores. The evaluated wavenumbers are close to the available observed infrared and Raman wavenumbers, giving further support to the present assignments. Copyright © 2003 John Wiley & Sons, Ltd.

A lattice dynamical investigation of Raman and infrared wavenumbers at the zone center of the orthorhombic NdNiO 3 perovskite

A short-range force constant model has been applied for the first time to investigate the phonons in NdNiO 3 perovskite in the orthorhombic phase. The calculations with the ten stretching and ten bending force constants provide a good agreement for the observed Raman and infrared wavenumbers. The infrared wavenumbers have been calculated for the first time. All Raman and infrared wavenumbers are assigned to their specific mode of vibrations.

Sequence-Dependent Dynamics of Duplex DNA: The Applicability of a Dinucleotide Model

The short-time (submicrosecond) bending dynamics of duplex DNA were measured to determine the effect of sequence on dynamics. All measurements were obtained from a single site on duplex DNA, using a single, site-specific modified base containing a rigidly tethered, electron paramagnetic resonance active spin probe. The observed dynamics are interpreted in terms of single-step sequence-dependent bending force constants, determined from the mean squared amplitude of bending relative to the end-to-end vector using the modified weakly bending rod model. The bending dynamics at a single site are a function of the sequence of the nucleotides constituting the duplex DNA. We developed and examined several dinucleotide-based models for flexibility. The models indicate that the dominant feature of the dynamics is best explained in terms of purine- and pyrimidine-type steps, although distinction is made among all 10 unique steps: It was found that purine-purine steps (which are the same as pyrimidine-pyrimidine steps) were near average in flexibility, but the pyrimidine-purine steps (5′ to 3′) were nearly twice as flexible, whereas purine-pyrimidine steps were more than half as flexible as average DNA. Therefore, the range of stepwise flexibility is approximately fourfold and is characterized by both the type of base pair step (pyrimidine/purine combination) and the identity of the bases within the pair (G, A, T, or C). All of the four models considered here underscore the complexity of the dependence of dynamics on DNA sequence with certain sequences not satisfactorily explainable in terms of any dinucleotide model. These findings provide a quantitative basis for interpreting the dynamics and kinetics of DNA-sequence-dependent biological processes, including protein recognition and chromatin packaging.