Force Constant Calculations Research Articles

Linearized force constants method for lattice dynamics in mixed semiconductors

A simple and accurate method of calculating phonon spectra in mixed semiconductors alloys, on the basis of preliminarily (from first principles) relaxed atomic structure, is proposed and tested for (Zn,Be)Se and (Ga,In)As solid solutions. The method uses an observation that the interatomic force constants, calculated ab initio for a number of microscopic configurations in the systems cited, show a clear linear variation of the main (diagonal) values of the interatomic force constants with the corresponding bond length. We formulate simple rules about how to recover the individual 3×3 subblocks of the force constants matrix in their local (bonds-related) coordinate systems and how to transform them into a global (crystal cell-related) coordinate system. Test calculations done for 64-atom supercells representing different concentrations of (Zn,Be)Se and (Ga,In)As show that the phonon frequencies and compositions of eigenvectors are faithfully reproduced in a linearized force constants calculation, as compared to true ab initio calculations.

Influence of methoxy- and nitro-substitutions in the aromatic ring on proton donation ability in hydrogen bond and on the amino group parameters of free and H-bonded molecules of 2-aminopyrimidine

Amino- and imino- forms of pyrimidine are widely presented as part of antibiotics, corrective medications for heart failures and metabolic stimulators. Hydrogen bonding is one of the fundamental interactions between biologically active molecules. This type of interactions provides flexibility, speed and variety of the biochemical processes. Proton donation properties of aminopyrimidines significantly depend on the position, number and kind of the substituent in its aromatic ring. In present work we studied the influence of the methoxy- and nitro-substitutions in the phenyl radical of pyridine and pyrimidine cycles on the proton donation ability of the amino group in hydrogen bonds as well as on its geometrical, force, electro-optical and thermodynamical characteristics in free and H-bonded (1:1 and 1:2, with various proton acceptors) molecules of primary aromatic amines. Acetonitrile, dioxane, tetrahydrofourane, dimethylformamide, dimethylsulfoxide and hexamethylphosphoramide (whose proton accepting properties vary within a wide range) were used as proton acceptors in our research. In the region of the amino group stretching and deformation vibrations the IR spectra of free and H-bonded (1:1) molecules of 2-amino-4,6-dimethoxy- and 2-amino-5-nitropyrimidine were studied in complexes with proton acceptors in CCl 4 within the temperature range 288–328 K. The spectra of 1:2 complexes were studied in undiluted aprotic solvents. The following spectral characteristics of absorption bands in amino group stretching vibrations were determined: M (0) (zero spectral moment, integrated intensity B); M (1) (first spectral moment, band “centre of gravity”); effective half width, related to the second central moment (Δ ν 1/2) eff = 2( M (2)) 1/2, frequencies of the deformation vibrations δ(HNH) of free and H-bonded molecules. It was shown that changes of the absorption band spectral characteristics of the amino group stretching and deformation vibrations in the analyzed temperature interval are actually linear. Linear regression parameters Y = aT + b (where Y = M (0), M (1), 2( M (2)) 1/2) of free and H-bonded (1:1, with proton acceptors) molecules of 2-aminopyrimidines were determined. Vibrational and electro-optic tasks were solved for free and H-bonded molecules. Valence angles γ(HNH), force constants K(NH), electrooptic parameters ∂ μ/∂ q NH and ∂ μ / ∂ q NH ′ were determined. Comparative analysis of the influence of methoxy- and nitro-substitution on the amino group spectral characteristics of aniline, 2-aminopyridine and 2-aminopyrimidine in CCl 4 was performed. It was shown that effect of hetero substitution and external substituents in the aromatic ring on spectral characteristics is not additive. Linear correlations were established between spectral, geometrical, force and electro-optical characteristics of the amino group in free and H-bonded (1:1 and 1:2) molecules of substituted 2-aminopyrimidines. Some of these correlations are universal, while most of them are sensitive to the kind, position and number of the substituents in the aromatic ring. During association of 2-aminopyrimidines with dioxane and tetrahydrofourane (1:1 complexes) the charge transfer through the hydrogen bond reveals quite considerable influence on complex formation. The temperature dependence of monomer–complex (1:1) equilibrium constants was studied and following thermodynamical characteristics were determined (using Vant-Hoff equation): enthalpy −Δ H 1 and entropy Δ S 1. Enthalpy −Δ H 2 of 1:2 complexes was determined using the empirical “Intensity rule”. It was shown that H-bond strength in 1:1 complexes is higher than in 1:2 complexes. This is also confirmed by the independent calculations of force constants K(NH) in complexes of different composition. The qualitative agreement was stated between experimental results and quantum-mechanical calculations (DFT-B3LYP/6-31G(d,p)) of the amino group spectral characteristics, valence angles γ(HNH) and force constants K(NH). The tendency in changes of values mentioned above is correctly reflected by quantum-mechanical calculations, depending on kind, position and number of substituents in pyrimidine cycle, so the results of these calculations can be used in research of free molecules and systems with hydrogen bonds.

Phonon dispersion of graphite by inelastic x-ray scattering

We present the full in-plane phonon dispersion of graphite obtained from inelastic x-ray scattering, including the optical and acoustic branches, as well as the midfrequency range between the $K$ and $M$ points in the Brillouin zone, where the experimental data have been unavailable so far. The existence of a Kohn anomaly at the $K$ point is further supported. We fit a fifth-nearest neighbor force-constant model to the experimental data, making improved force-constant calculations of the phonon dispersion in both graphite and carbon nanotubes available.

Lagrangian approach to molecular vibrational Raman intensities using time-dependent hybrid density functional theory

The authors propose a new route to vibrational Raman intensities based on analytical derivatives of a fully variational polarizability Lagrangian. The Lagrangian is constructed to recover the negative frequency-dependent polarizability of time-dependent Hartree-Fock or adiabatic (hybrid) density functional theory at its stationary point. By virtue of the variational principle, first-order polarizability derivatives can be computed without using derivative molecular orbital coefficients. As a result, the intensities of all Raman-active modes within the double harmonic approximation are obtained at approximately the same cost as the frequency-dependent polarizability itself. This corresponds to a reduction of the scaling of computational expense by one power of the system size compared to a force constant calculation and to previous implementations. Since the Raman intensity calculation is independent of the harmonic force constant calculation more, computationally demanding density functionals or basis sets may be used to compute the polarizability gradient without much affecting the total time required to compute a Raman spectrum. As illustrated for fullerene C60, the present approach considerably extends the domain of molecular vibrational Raman calculations at the (hybrid) density functional level. The accuracy of absolute and relative Raman intensities of benzene obtained using the PBE0 hybrid functional is assessed by comparison with experiment.

Locating the active sites of enzymes using mechanical properties

We have applied the calculation of mechanical properties to a dataset of almost 100 enzymes to determine the extent to which catalytic residues have distinct properties. Specifically, we have calculated force constants describing the ease of moving any given amino acid residue with respect to the other residues in the protein. The results show that catalytic residues are invariably associated with high force constants. Choosing an appropriate cutoff enables the detection of roughly 80% of catalytic residues with only 25% of false positives. It is shown that neither multidomain structures, nor the presence or absence of bound ligands hinder successful detections. It is however noted that active sites near the protein surface are more difficult to detect and that non-catalytic, but structurally key residues may also exhibit high force constants.

Theoretical study of the molecular structure and normal coordinate analysis of hydrogen cyanide addition compound with boron trifluoride, HCN–BF 3

An extensive HF, MP2, B3LYP and CCSD study of the molecular structure and normal vibrations have been performed for the HCN–BF 3 molecule. Calculations with a wide range of basis sets were classified into two groups based on the optimized N–B bond distance. The results for Group A are compared with the experimental structure of the solid phase molecules. The N–B lengths of Group A are approximately linear related to the N–B–F valence angles and also to the N–B stretching frequencies. HF/DZV calculation was used to represent the solid phase model. The N–B lengths of Group B are close to those of the gas phase molecule and both N–B–F angles and N–B sensitive frequencies have roughly the same values. Differences in the chemical bond between gaseous and solid phase HCN–BF 3 are discussed based on the calculated force constants, vibrational frequencies and potential energy distributions. Vibration mode analysis indicates that the ν 4 mode in the 600–700 cm −1 region can be assigned to the BF 3 symmetric deformation, which shifts upon 10B/ 11B isotopic substitution. The ν 5 mode which is insensitive to isotope substitution and changes band position with the N–B distance is assigned to the N–B bond stretching vibration.

Vibrational spectroscopy of resveratrol

In this article the authors deal with the experimental and theoretical interpretation of the vibrational spectra of trans-resveratrol (3,5,4′-trihydroxy- trans-stilbene) of diverse beneficial biological activity. Infrared and Raman spectra of the compound were recorded; density functional calculations were carried out resulting in the optimized geometry and several properties of the molecule. Based on the calculated force constants, a normal coordinate analysis yielded the character of the vibrational modes and the assignment of the measured spectral bands.

DFT calculations and vibrational (FT-IR, FT-Raman) spectra on an uracilyl-pyridinium salt

In the present article we have studied the structural and vibrational properties of the N-protonated derivative of a cross-conjugated heterocyclic mesomeric betaine formed by an uracilyl and a dimethylamino substituted pyridinium group. Fourier transform infrared and Raman spectra were recorded from solid samples. Quantum chemistry density functional theory calculations were performed at the B3PW91/6-31G ∗∗ level. Geometrical parameters, charge distribution and natural bond orders were calculated for the ground-state minimum energy structure. The optimized geometry was found twisted with respect to the two aromatic planes. The pyridinium ring presents a quinoid structure, while the uracilyl ring only presents a localized double-bond, which is far from the carbonyl groups. The molecule is strongly polar along the longest molecular axis, being largely originated by the charge separation between the heterocycles. A force field and normal coordinate calculation was performed in order to correctly assign the measured infrared and Raman bands. Assignments suggest the existence of centro-symmetrical structures in solid state bonded by the C O and N–H groups of the uracilyl ring. The calculated force constants in vibrational internal coordinates are in agreement with the structural parameters.

Tight-binding calculations of the elastic constants and phonons of hcp Zr: Complications due to anisotropic stress and long-range forces

We have calculated the phonons and elastic constants of zirconium in the hexagonal-close-packed (hcp) crystal structure using the Naval Research Laboratory (NRL) empirical tight-binding (TB) approach; the tight-binding parameters are obtained by fitting to ab initio density-functional theory--generalized gradient approximation energy bands and total energies for many different structures and volumes. We address difficulties involved with the fitting procedure and give results for elastic constants, force constants, quasiharmonic phonons, and specific heat. Because the predicted TB lattice constants at the zero-temperature energy minimum are slightly different from those experimentally observed at room temperature, our TB model has an anisotropic stress at the experimental lattice constants. We correct for these stresses in our calculations of the elastic constants and sound speeds. Such techniques are also useful for calculating such properties for arbitrary $c∕a$. Our phonon calculations were done by the direct-force method in real space using calculated force constants; these fall off quite slowly with distance, which causes problems with the calculated phonon spectrum due to the slow convergence with increasing supercell size. This long-range behavior could play a large role in determining the unusually anharmonic and anomalous physical properties of Zr. We show that similar, although less severe, problems should arise for other metals. These considerations suggest that the direct-force method for calculating phonons may be problematic for many metals.

Assignment of the First Photoelectron Band of CH3CHBr(X2A) Using Ab-initio and Density Functional Theory (DFT) Computational Calculations

HeI photoelectron spectra have been recorded for the reaction of atomic fluorine with ethyl bromide at different reaction times. A structured band associated with a short-lived primary reaction product has been recorded at a mixing distance of 12 mm above the photon beam. The adiabatic and vertical ionization energies of this band was measured as 7.78 ± 0.01 and 8.05 ± 0.01 eV, respectively . The average vibrational separation of 700 ± 30 cm−1 was observed in this band. Vertical ionization energies were computed in this work for CH3CHBr(X2A) and CH2CH2Br(X2A) via ΔSCF, ΔMP2 (full) and Δ(B3LYP) levels of theory using different basis sets. Mulliken population analysis and force constant calculations have also been carried out for CH3CHBr(X2A) and CH2CH2Br(X2A) and their singlet cationic states. Comparison between the experimental vertical ionization energies and the corresponding values computed for CH3CHBr (X2A) and CH2CH2Br(X2A) at different levels of theory led to the assignment of the observed first photoelectron band to the ionization of CH3CHBr(X2A). The observed vibrational structure was assigned to the excitation of C–Br stretching mode in CH3CHBr+ (X1A).

Raman and infrared spectroscopic and theoretical studies of dinuclear rhenium and osmium complexes, M 2(O 2CCH 3) 4X 2 (M = Re, Os; X = Cl, Br)

Infrared, far-infrared and Raman spectra of Re 2(O 2CCH 3) 4X 2 (X = Cl, Br) and Re 2(O 2CCD 3) 4Cl 2 have been recorded. Assignments of the vibrational spectra of Os 2(O 2CCH 3) 4Cl 2 and its deuterated derivative have been completed together with the Re complexes on the basis of normal-coordinate analysis. Force constant calculation was made for the acetate ion as well as for a four-atomic unit (with the CH 3 and CD 3 groups considered as point masses) using optimized masses of 16.7, 17.8, 20.5 and 21.6 for 12CH 3, 13CH 3, 12CD 3 and 13CD 3 groups, respectively. The force constants of the acetate ion have been adopted to the starting force field of the M 2(O 2CCH 3) 4X 2 type complexes. The metal–halide (0.889, 0.997 and 1.286 N cm −1) and metal–metal stretching (3.32, 3.34 and 3.57 N cm −1) force constants were obtained for Re 2(O 2CCH 3) 4Cl 2Re 2(O 2CCH 3) 4Br 2 and Os 2(O 2CCH 3) 4Cl 2 complexes, respectively. It was shown that the so-called diatomic approximation in most cases overestimates the M–M stretching force constants by 30–40%. Much better correlation has been obtained to fit these force constants, which produced values very close to those obtained by full normal-coordinate calculations. The Re–Re stretching force constants showed a reasonable correlation with the Re–Re bond distances for 18 rhenium complexes.

Computational note on the quantum chemistry calculated force constants of the CF 3SeX (X=H, D, Cl, Br) molecules

Computational note on the quantum chemistry calculated force constants of the CF 3SeX (X=H, D, Cl, Br) molecules

FTIR and ab Initio Study of the 1/1 Complex between Water and Carbon Dioxide in Solid Nitrogen

Infrared spectra of the 1/1 complex between water and carbon dioxide isolated in a nitrogen matrix are reported. Isotopic substitution of water (HOD, D2O) suggests the existence of two very weak complexes with a nearly T-shaped structure where the C atom is bonded to the water oxygen: one of C2v symmetry and another one of Cs symmetry, in which a slight distortion results in a very weak interaction between one hydrogen atom of water and one oxygen atom of carbon dioxide. This result is supported by force constant calculations, consistent with a double, symmetrical, and unsymmetrical force field, and ab initio calculations. At the MP2/aug-cc-PVTZ level corrected from basis set superposition error the C2v structure is a saddle point with an imaginary frequency for H2O rocking, in contrast to a Cs structure, which would have nonequivalent hydrogen atoms. Nevertheless, the energies of both structures, with a stabilization energy of 1.97 kcal mol-1, differ by less than 0.01 kcal mol-1 from each other. A comparison of calculated and observed frequency shifts allows us to suggest the presence in the matrix of both C2v and Cs complexes.

An infrared study of carbon-oxygen bonding in magnesite to 60 GPa

Infrared spectra of magnesite, MgCO 3 , have been measured in the diamond anvil cell from 0 to 60 GPa at 300 K. Mode shifts were determined for the in-plane bend, the asymmetric-stretch, and the out-of-plane bend of the carbonate group, as well as a magnesium ion translational mode. The in-plane bend shows a small positive shift and ultimately merges with the out-of-plane bend, exhibiting an accidental degeneracy by 60 GPa. The asymmetric stretch exhibits highly nonlinear behavior, shifting monotonically to pressures of ~30 GPa, at which point its shift markedly decreases to ~50 GPa. At 50 GPa, it again shifts strongly with pressure. We calculate force constants for the carbonate group under pressure from our data, and correlate these with the C-O bond length. Our data are consistent with a slight lengthening (~0.01 A) of the C-O bond between 30 and 50 GPa to a maximum bond distance of ~1.27 A. Although our finding of bond lengthening is in general agreement with previously published Rietveld refinements of X-ray diffraction data for magnesite under pressure, our data indicate that the lengthening is likely substantially smaller than previously proposed. The expansion of the C-O bond in magnesite can be produced by rotations of the MgO 6 octahedra, and such non-ionic crystal-chemical effects may be a key contributor to the remarkable stability of R 3 c -structured carbonates to very high pressures.

Experimental and quantum chemical study on the vibrational spectroscopy of N-methylphenothiazines: Part 1

In this work the authors deal with the vibrational spectroscopy of three derivatives of phenothiazine: the 10-methyl- 10H-phenothiazine, the 10 methyl- 10H-phenothiazine-3-carbaldehyde and the 10-methyl- 10H-phenothiazine-3-yl-methanol. The authors investigated the vibrational spectroscopic behaviour of the phenothiazine skeleton and dealt with the aldehyde and the alcohol substituent effect on the vibrational spectroscopic and structural properties of these skeleton. The infrared and Raman spectra of the compounds have been recorded in condensed state. The Gaussian 98 program package was applied with the ab initio HF method since in this case beside the infrared also the Raman spectoroscopic properties appear in the output file. On the basis of the calculated force constants and geometric parameters, normal coordinate analysis was applied for the interpretation of the experimental vibrational spectra. Problems arose with the choice of the internal coordinates of the molecules. Full interpretations of the vibrational fundamentals of the compounds are presented. The relative mean deviations between the measured and calculated frequencies were below 1%.

Infrared and Raman spectroscopic and theoretical studies of nonaaqua complexes of trivalent rare earth metal ions

Infrared (IR), far-infrared (far-IR) and Raman spectra have been recorded of the hydrated lanthanide(III) trifluoromethanesulfonates, [Ln(OH 2) 9](CF 3SO 3) 3, (Ln = La, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu), and also for the deuterated [La(OD 2) 9](CF 3SO 3) 3 compound. This has enabled complete assignments of all seven metal–oxygen stretching modes for the first time. Force constant calculations have been performed for an LnO 9 3+ moiety, with a tricapped trigonal prismatic oxygen atom arrangement in D 3h point group symmetry. The lanthanide contraction in reflected in continuously increasing trends for the averaged Ln O stretching frequencies and force constants with increasing inverse of ionic radii. The stretching force constants increased from 0.81 to 1.16 Ncm −1 for the LnO 6 prism in the series from La to Lu, while those for the capping LnO 3 bonds increased from 0.49 to 0.65 Ncm −1. The Ln O stretching force constants showed a smooth correlation with the Ln O bond distances to the prism oxygen atoms, while the correlation to the Ln O capping oxygen atoms has a different shape, reflecting the increased ligand–ligand repulsion with decreasing lanthanide ion size.

Calculation of Vibrational Spectra of Linear Tetrapyrroles. 3. Hydrogen-Bonded Hexamethylpyrromethene Dimers

The structure and vibrational spectra of hexamethylpyrromethene (HMPM) have been investigated by X-ray crystallography, IR and Raman spectroscopies, and density functional theory calculations. HMPM crystallizes in the form of dimers, which are held together by bifurcated N-H(...N)(2) hydrogen bonds, involving one intramolecular and one intermolecular N-H...N interaction. The monomers are essentially planar, and the mean planes of the monomers lie approximately perpendicular to one another, so that the four N atoms in the dimer form a distorted tetrahedron. The structure of the HMPM dimer is well-reproduced by B3LYP/6-31G calculations. A comparison of the calculated geometry of the dimer with that of the monomer reveals only small changes in the N-H...N entity and the methine bridge angles upon dimerization. These are a result of weakening of the intramolecular N-H...N hydrogen bond and the formation of a more linear N-H...N intermolecular hydrogen bond. Using an empirical relation between the shift of the N-H stretching frequency of pyrrole and the enthalpy of adduct formation with bases [Nozari, M. S.; Drago, R. S. J. Am. Chem. Soc. 1970, 92, 7086-7090], estimates of the strength of the intra- and intermolecular hydrogen bonds are obtained. IR and Raman spectroscopies of HMPM and its isotopomers deuterated at the pyrrolic nitrogen atom and at the methine bridge reveal that the molecule is monomeric in nonpolar organic solvents but dimeric in a solid Ar matrix and in KBr pellets. The matrix IR spectra show a splitting of vibrational modes for the dimer, particularly those involving the N-H coordinates. Due to intrinsic deficiencies of the B3LYP/6-31G approximation, a satisfactory reproduction of these modes of the monomeric and dimeric HMPM requires specific adjustments of the NH scaling factors for the calculated force constants and, in the case of the NH out-of-plane modes of HMPM dimers, also of intra- and intermolecular coupling constants. This parametrization does not significantly affect the other calculated modes, which in general reveal a very good agreement with the experimental data.

Probing Protein Mechanics: Residue-Level Properties and Their Use in Defining Domains

It is becoming clear that, in addition to structural properties, the mechanical properties of proteins can play an important role in their biological activity. It nevertheless remains difficult to probe these properties experimentally. Whereas single-molecule experiments give access to overall mechanical behavior, notably the impact of end-to-end stretching, it is currently impossible to directly obtain data on more local properties. We propose a theoretical method for probing the mechanical properties of protein structures at the single-amino acid level. This approach can be applied to both all-atom and simplified protein representations. The probing leads to force constants for local deformations and to deformation vectors indicating the paths of least mechanical resistance. It also reveals the mechanical coupling that exists between residues. Results obtained for a variety of proteins show that the calculated force constants vary over a wide range. An analysis of the induced deformations provides information that is distinct from that obtained with measures of atomic fluctuations and is more easily linked to residue-level properties than normal mode analyses or dynamic trajectories. It is also shown that the mechanical information obtained by residue-level probing opens a new route for defining so-called dynamical domains within protein structures.

Experimental and theoretical studies of the vibrational spectra of cis-1-bromo-2-fluoroethene

The gas-phase infrared spectrum of cis-1-bromo-2-fluoroethene has been studied at low resolution in the range 200–6500 cm −1, leading to a complete assignment of the fundamentals, except the lowest vibrational mode ν 9 predicted at 167 cm −1. The remaining vibrational structure has been mainly interpreted in terms of first overtone or two quanta combination bands. Isotopic 79/81Br shift has been observed only in the ν 8 fundamental. The equilibrium structure and the quadratic force field have been investigated theoretically at CCSD(T) level of theory employing Dunning’s correlation consistent triple-zeta basis set. Cubic and semidiagonal quartic force field have been calculated using second-order Møller–Plesset perturbation theory and Ahlrich’ split valence (SV) contracted basis set. After a minor scaled quantum mechanical (SQM) adjustment of the quadratic force constants, the vibrational analysis, based on the second-order perturbation theory, has been carried out with the calculated force constants.

Cluster approach in first-principle calculations for ferroelectrics

It is shown that, proceeding from the first principles, it is possible to separate the contributions from short-and long-range interactions to the lattice dynamics and dielectric properties of crystalline dielectrics. The cluster calculations of local force constants and potentials for the matrix and impurity atoms in ferroelectrics with the perovskite structure were made by the Hartree-Fock MOLCAO-SCF method. The parameters of the Devonshire-Slater-Barrett single-ion model are calculated for barium titanate and potassium niobate. The influence of the quantum statistics on the Curie temperature in these ferroelectrics and the isotope effect in barium titanate are also considered.