Transferability Of Force Constants Research Articles

A study on the properties and transferability of force fields in redundant and independent coordinates

The theory of canonical and regular force fields has been used to develop a new approach to study the transferability of force constants in terms of redundant rectilinear internal coordinates. It has been found that the force field of a group of atoms is transferable when it is expressed in canonical form, and that the force field in terms of symmetry-independent coordinates is transferable when these coordinates are orthogonal to the redundancy conditions. As an illustrative example, the approach has been applied to obtain transferable harmonic force constants for the CH 3 group in methane and chloromethane molecules.

Phonon spectra of PdxFe1−x alloys with transferable force constants

The transferable force constant model of van de Walle et al (2002 Rev. Mod. Phys. 74 11) hasbeen combined with the itinerant coherent potential approximation to calculatethe complete phonon spectra and elastic constants in the magnetic type-II alloyPdxFe1−x across the concentration range. The calculated dispersion curves and elastic constants agreevery well with the experiments. We discuss the results in the light of the behavior ofinter-atomic force constants between various pairs of chemical species. The resultsdemonstrate that the combination of the transferable force constant model and the ICPAmethod for configuration averaging serve as an efficient and reliable first-principles-basedtool to compute the phonon spectra for disordered alloys at any arbitrary concentration.

Using bond-length-dependent transferable force constants to predict vibrational entropies in Au-Cu, Au-Pd, and Cu-Pd alloys

A model is tested to rapidly evaluate the vibrational properties of alloys with site disorder. It is shown that length-dependent transferable force constants exist, and can be used to accurately predict the vibrational entropy of substitutionally ordered and disordered structures in Au-Cu, Au-Pd, and Cu-Pd. For each relevant force constant, a length- dependent function is determined and fitted to force constants obtained from first-principles pseudopotential calculations. We show that these transferable force constants can accurately predict vibrational entropies of L1$_{2}$-ordered and disordered phases in Cu$_{3}$Au, Au$_{3}$Pd, Pd$_{3}$Au, Cu$_{3}$Pd, and Pd$_{3}$Au. In addition, we calculate the vibrational entropy difference between L1$_{2}$-ordered and disordered phases of Au$_{3}$Cu and Cu$_{3}$Pt.

Vibrational analysis of substituted phenols: Part II. Transferability of valence force constants

A zero-order normal coordinate analysis was made for the in-plane and out-of-plane vibrations of 2,6-dimethylphenol, 2,3-dimethylphenol, 3,5-dimethylphenol, 2,6-dichloro-4-nitrophenol, 2,4-dichloro-6-nitrophenol, 3-chloro-4-hydroxy-5-methoxybenzaldehyde, 3-bromo-4-hydroxy-5-methoxybenzaldehyde and 3-iodo-4-hydroxy-5-methoxybenzaldehyde and for the in-plane vibrations of 2-amino-4-nitrophenol by transferring the force constants obtained beforehand. The transferability of the force constants was demonstrated by the good agreement between the observed and calculated frequencies. On the basis of calculated potential energy distributions and eigenvectors, several assignments suggested by earlier workers have been revised.

Force constants for substitutional alloys

Recently, the importance of the vibrational aspects of alloy phase stability has attracted much interest. There is much controversy over the extent to which the vibrational free energy affects order-disorder temperatures and other phase equilibria. Here, we examine the feasibility of defining transferable force constants for an alloy in much the same spirit as tight-binding Slater-Koster parameters can be defined for substitutional alloys. In particular, the predictive ability of such alloy specific, but configuration independent, force constants for the elastic, relaxation, and vibrational properties is examined.

Valence States in Molecules. 3. Transferable Vibrational Force Constants from Homonuclear Data

A recently introduced valence-state potential energy function (von Szentpaly, L. Chem. Phys. Lett. 1995, 245, 209.) and its dissociation energy (DVS) serve to establish an arithmetic combining rule for scaled force constant increments, λ = kRe/DVS. λ is transferable from homo- to heteronuclear molecules at an accuracy of 1.6% average absolute error in harmonic vibrational wavenumbers, ṽe, of 42 diatomic molecules covering a force constant range of factor 30. The parallel to combining rules for repulsive potentials in solid-state and atomic physics is shown, and the reasons for the failure of previous attempts to obtain transferable force constant increments are examined.

Calculation of Force Constants for Structures with Tetrahedral Symmetry

This paper develops an analytical method for calculating the transferable force constants in symmetrically complete coordinates directly from the nontransferable force constants in independent coordinates allowing a direct treatment of the redundancy problem. In calculating the force constants for structures with tetrahedral symmetry, the interdependence of the tetrahedral angles must be considered to be a constraint on the potential energy function. The methane molecule is chosen as the simplest example of a tetrahedron. The potential energy of methane is a function of six equally weighted tetrahedral angles constrained such that the sum of the changes in angle over all six angles is zero. The calculations with independent coordinates are done with two different parameterizations, first with five tetrahedral angles, and second with three tetrahedral angles and two dihedral angles. These are the two most useful and common parameterizations used in molecular orbital calculations. The methane tetrahedron is modeled with seven force constants; this paper demonstrates that only five independent variables Kr, Krr, (KrA-KrV), (Kθ-KV) and (Kθ-KA) are needed. This agrees with the fact that the entire vibrational spectrum of methane can be calculated from only five force constants. Sample Gaussian 90 calculations are done with Slater type orbital 3-21G* basis sets and compared with neutron dispersion data for diamond, silicon, germanium, and tin. This method can be extended to other constrained systems such as rings.

Vibrational analysis of substituted benzonitriles. III. Transferability of force constants—the case of some halogeno-, methoxy- and nitro-benzonitriles

A zero-order normal coordinate analysis of both the in-plane and out-of-plane vibrations was made for 2-chloro, 6-fluorobenzonitrile, s-trichlorobenzonitrile, p- and m-methoxybenzonitriles and m-nitrobenzonitrile, transferring the force constants from our earlier work. The observed and calculated frequencies agree with an average error of 16.8 cm −1, demonstrating the transferability of the force constants obtained previously. On the basis of calculated potential energy distributions and eigenvectors, several assignments suggested by earlier workers have been revised.

Vibrational analysis of substituted benzonitriles. IV. Transferability of force constants—the case of some aminobenzonitriles

A zero-order normal coordinate analysis was made for the in-plane vibrations of p-, m- and o-aminobenzonitrile and 2-chloro, 5-aminobenzonitrile by transferring the force constants from our earlier work. The observed and calculated frequencies agree with an average error of 19.3 cm −1. Unambiguous vibrational assignments of in-plane fundamentals of the four molecules have been made, and several assignments suggested by earlier workers have been revised.

Vibrational analysis of substituted benzonitriles. II. Transferability of force constants—the case of dicyanobenzenes

A zero-order normal coordinate analysis was made for p-, m- and o-dicyanobenzenes and their deuterated isomers by transferring the force constants from Part I. The observed and calculated frequencies agree with an average error of 18.7 cm −1, demonstrating the transferability of the force field obtained in Part I. On the basis of the calculated potential energy distributions and eigen vectors, several assignments suggested by earlier workers have been revised.

Vibrational analysis of substituted anilines, anisoles and anisidines: Part II. Transferability of valence force constants

A zero-order normal coordinate analysis was made for the in-plane vibrations of 2, 6-dinitroaniline, 3, 5-dichloro- p-anisidine, 3, 5-dibromo- p-anisidine and 2, 6-dibromo-4-nitroanisole by transferring the force constants obtained beforehand. The transferability of the force constants was demonstrated by the good agreement between the observed and calculated frequencies. On the basis of the calculated potential energy distributions and eigenvectors, several assignments suggested by earlier workers have been revised.

Normal coordinate analysis of 1,4-diethynylbenzene

Normal coordinate analysis has been carried out for the 1,4-diethynyl benzene molecule on the basis of experimental frequencies from the natural compound and its deuterated derivatives. A canonic force field has been set up by transferring force constants from related molecules. This force field has been refined to the experimental frequencies. A reassignment of the vibrational spectrum of 1,4-diethynyl benzene has been carried out.

An in-plane force field for some benzene derivatives having unsaturated substituents

A simplified in-plane overlay valence force field has been developed for some benzene derivatives that have unsaturated substituents. The molecules used in the optimization of the force constants are benzene, styrene, benzaldehyde, ethynylbenzene and m- and p-diethynylbenzene. The force field comprises 57 force constants, out of which 33 have been transferred from our other overlay calculations and 24 are optimized on about 600 experimental frequencies, giving an rms frequency deviation of 10.5 cm −1 which includes the CH stretching vibrations. Some revisions in the assignments have been made. For comparison a fully independent overlay force field has been optimized for some methyl substituted benzenes using the same approximations in the force field. The transferability of force constants and limitations of the transferability are discussed.

An out-of-plane force field for some benzene derivatives having unsaturated substituents

A simplified out-of-plane valence force field has been developed for some benzene derivatives that have unsaturated substituents. The molecules treated in this study are benzene, styrene, benzaldehyde, ethynylbenzene and m- and p-diethynylbenzenes. In the force field we have used two different approximations. The first one includes 27 independent force constants, 12 of which are directly transferred from analogous molecules and 15 optimized on 242 experimental frequencies, giving an rms frequency deviation of 6.69 cm−1. The second and somewhat simpler one deals with 12 transferred and 12 optimized force constants giving an rms deviation of 6.95 cm−1. For comparison a force field for some methyl substituted benzenes has also been derived using the same approximations. The transferability of force constants is discussed in the light of the results achieved. On the basis of the calculations certain revisions in previous assignments have been made.

Vibrational Spectra, Assignments, and Valence Force Field for S-nitrosocysteine and Isotopic Analogs

S-nitrosocysteine and the isotopically-substituted S15NO and N- d3 analogs have been prepared. FT-IR spectra have been obtained on the normal molecule and the 15N isotopomer. Spectra of the N- d3 analog were obtained with a dispersive instrument. The fundamental frequencies of the three isotopomers were calculated by using force constants previously obtained through overlay calculations on amino acids and from a normal coordinate analysis of methyl thionitrite. The average computational error between the observed and calculated frequencies using the transferred force constants was 11 cm−1. This difference was decreased to 7 cm−1 by slightly modifying some of the force constant values by a least-squares refinement. Vibrational assignments are made for all three isotopic analogs by utilizing the potential energy distribution. Out of a total of 96 fundamentals occurring above 300 cm−1, 65 may be classified as group vibrations by the potential energy criterion.

ChemInform Abstract: THE CONFORMATION AND VIBRATIONAL SPECTRA OF TRANS‐1,4‐DICYANOCYCLOHEXANE

Abstract The IR spectra of trans -1,4-dicyanocyclohexane as a melt, as a solute in various solvents, as KI and polyethylene pellets and as amorphous and annealed crystalline solids at 90 K have been recorded in the region 4000-50 cm −1 . Additional spectra at high pressures (1–50 kbar) have been recorded and the dichroic ratios of oriented polycrystalline films are obtained above 200 cm −1 . Raman spectra of the compound as a melt, as an amorphous and crystalline solid at 90 K and dissolved in acetone, chloroform and benzene have also been recorded. The compound exists as an equilibrium mixture of ee and aa conformers in solution, in the melt and in the amorphous solid at 90 K, but as one conformer only, apparently the ee form, in the crystalline state. Unlike the corresponding dihalocyclohexanes, trans -1,4-dicyanocyclohexane cannot be converted to an “ aa crystal” either by exposure to high pressure or by annealing to a metastable crystal. The fundamental frequencies of both conformers have been interpreted in terms of C 2h molecular symmetry and the assignments supported with a force constant calculation by the overlay technique transferring force constants from various related molecules.

The conformation and vibrational spectra of trans-1,4-dicyanocyclohexane

The IR spectra of trans-1,4-dicyanocyclohexane as a melt, as a solute in various solvents, as KI and polyethylene pellets and as amorphous and annealed crystalline solids at 90 K have been recorded in the region 4000-50 cm−1. Additional spectra at high pressures (1–50 kbar) have been recorded and the dichroic ratios of oriented polycrystalline films are obtained above 200 cm−1. Raman spectra of the compound as a melt, as an amorphous and crystalline solid at 90 K and dissolved in acetone, chloroform and benzene have also been recorded.The compound exists as an equilibrium mixture of ee and aa conformers in solution, in the melt and in the amorphous solid at 90 K, but as one conformer only, apparently the ee form, in the crystalline state. Unlike the corresponding dihalocyclohexanes, trans-1,4-dicyanocyclohexane cannot be converted to an “aa crystal” either by exposure to high pressure or by annealing to a metastable crystal.The fundamental frequencies of both conformers have been interpreted in terms of C2h molecular symmetry and the assignments supported with a force constant calculation by the overlay technique transferring force constants from various related molecules.

Properties and application of the reduced isotopic product rule for molecular vibration frequencies

The well-known approximate separation of low molecular vibrational frequencies from high frequencies has in the past been combined with the Redlich-Teller isotopic product rule to split the latter into separate rules for the high and for the low frequencies ( reduced isotopic product rules). A number of variants and properties of these rules are discussed, along with some modifications applicable when redundant coordinates are involved. A discussion is given of the use of nonbonded distances instead of the related bond angles, and the employment of computer programs which calculate normal frequencies from postulated force constants. A comparison is made of the relative advantages of using these reduced product rules for testing assignments of observed vibration frequencies as opposed to the use of frequencies or frequency product ratios calculated from transferred force constants. Finally benzene, ethylene, methyl isocyanide, and cyclohexane are worked out as examples and some suggestions made of possible remaining uncertainties in the assigned fundamental frequencies.

Analysis of vibrational spectra of phenylphosphine, diphenylphosphine and their chloro derivatives. Overlay technique calculation of their force field in the reduced model approximation

A normal coordinate analysis using the "reduced model" of benzene ring was carried out with (C6H5)nPX3-n (n = 1, 2; X = H, Cl) compounds. 46 wavenumbers of vibrational transitions of the phenyl- and phosphine group were determined by means of the overlay technique. The transferability of force constants used in this calculation is discussed and an improved assignment of vibrations in the phenyl and phosphine group, based on PED calculations is presented.

The vibrational spectra of cis, cis-, trans, trans- and cis, trans-1,4-dichloro-1,3-butadiene

The i.r. spectra of cis, cis, trans, trans and cis, trans-1,4-dichloro-1,3-butadiene were recorded in cyclohexane solution in the region 600-40 cm −1. Raman spectra, including polarization measurements of the neat liquids were obtained. Some previously unobserved fundamentals, particularly in the low frequency region, were assigned, and a few revisions in the earlier interpretations were made. Force fields containing 21 parameters for the cis, cis and the trans, trans compounds were constructed by transferring force constants from cis- and trans-1-chloro-1,3-butadiene. By mixing the force constants from these monochlorobutadienes a 29 parameter force field was derived for the cis, trans compound. The calculated r.m.s. amplitudes of vibration and perpendicular amplitude correction coefficients are presented.