Force Constant Refinement Research Articles

Spectral Studies and Normal Coordinate Analysis of Some Symmetric 1,5-Diaryl-3-cyanoformazans

The 1,5-diaryl-3-cyanoformazans were prepared and subjected to IR, MS,1H NMR, and13C NMR spectral analysis. The results indicate the presence of a strong intramolecular hydrogen bond in the formazan molecule. Moreover, the two phenyl rings are equivalent and the CN and NH stretching vibrational modes are slightly affected with electron-withdrawing substituents and interact with the neighboring CC stretching mode. Thesyn, s-cisformazan form was supported by calculating the frequencies, normal coordinate analysis, force constant refinement, and group theory treatment. High quality of fitting between the experimental and calculated frequencies with all formazans has been achieved.

ASYM20: A Program for Force Constant and Normal Coordinate Calculations, with a Critical Review of the Theory Involved

The theory of harmonic force constant refinement calculations is reviewed, and a general-purpose program for force constant and normal coordinate calculations is described. The program, called ASYM20. is available through Quantum Chemistry Program Exchange. It will work on molecules of any symmetry containing up to 20 atoms and will produce results on a series of isotopomers as desired. The vibrational secular equations are solved in either nonredundant valence internal coordinates or symmetry coordinates. As well as calculating the (harmonic) vibrational wavenumbers and normal coordinates, the program will calculate centrifugal distortion constants, Coriolis zeta constants, harmonic contributions to the α′s. root-mean-square amplitudes of vibration, and other quantities related to gas electron-diffraction studies and thermodynamic properties. The program will work in either a predict mode, in which it calculates results from an input force field, or in a refine mode, in which it refines an input force field by least squares to fit observed data on the quantities mentioned above. Predicate values of the force constants may be included in the data set for a least-squares refinement. The program is written in FORTRAN for use on a PC or a mainframe computer. Operation is mainly controlled by steering indices in the input data file, but some interactive control is also implemented.

ν 6 and ν 8 infrared bands and force field of disilane

The infrared absorption spectrum of the ν 6 and ν 8 bands of disilane (Si 2H 6) was recorded at medium resolution (0.1-0.05 cm −1). A rotation analysis of the P( J) and R( J) structure of ν 6 was carried out, yielding the band origin and information on the B constant of the ground and v 6 = 1 states of the molecule, and on the D J centrifugal distortion constant. About 400 transitions of the ν 8 band were assigned and analysed, giving information on the band origin and the rotational constants of the v 8 = 1 state. Using the new and previous information on the vibrational spectrum of Si 2H 6 and Si 2D 6, a force constant refinement was performed. Several force field models were tried and a discussion of the results is presented.

Determination of eigenvectors in DNA polymer spectroscopy by isotopic substitution

AbstractA simple relationship between frequency shifts to be expected in molecular vibrational spectra upon isotopic substitution and component values of eigenvectors is displayed. Application of this expression to the problem of force constant refinement is discussed in terms of a refinement algorithm developed some years ago to overcome particular problems associated with large molecular systems. Calculations of expected isotopic shifts have been calculated and are tabulated here for experimental reference.

IR-Dichroism of metal dithiocarbamate single crystals by attenuated total reflectance spectroscopy

Reliable assignments of most of the bands of vibrational molecular spectra suffer from ambiguous interaction of atomic displacements. Various experimental methods must be used to ascertain the assignment. By means of dichroic measurements of vibrational bands additional information can be obtained to reach this goal. Thus FT-IR ATR spectra of single crystals of Cd(DEDTC)2 were recorded. If the molecular site with respect to the crystallographic cell is taken into account, the symmetry of certain vibrational modes can be determined. For aC 2h factor group of the monoclinic cell it is possible to distinguish betweenA u andB u symmetry species by the different dichroic ratios of the vibrational bands. This method supports vibrational assignment being verified by force constant refinement calculations. As a result a correlation between molecular site, symmetry and dichroic ratios of vibrational modes of single crystals is presented.

Force constant refinement in cartesian coordinates

The recently increasing interest in physically reliable force fields leads to a revisiting of applied computational methods. The combination of ab initio calculations and experimental information or the application of parametric methods is discussed extensively (ref. 1,2). Force constant refinement in cartesian coordinates offers several advantages in comparison with the much more familiar methods using internal (symmetry) coordinates: The formalism for solving the vibrational eigenvalue problem and the iterative matching of calculated to observed eigenvalues is very clear, the received eigenvectors seem to be physically meaningful and well suited for intensity calculations using quantum chemical methods. To examine the capability of the proposed method calculations have been carried out on Trimethylphosphineoxide-compounds. Metal-bis-diethyldithiocarbamate — complexes and Thiophene.

Lattice Vibrations of V2O5. Calculation of Normal Vibrations in a Urey‐Bradley Force Field

AbstractA normal coordinate analysis of the vibration spectrum of crystalline V2O5 is carried out in the assumption of a Urey‐Bradley force field. The calculated frequencies are adjusted to 29 experimental infrared and Raman frequencies by an automatic force constant refinement program. Analysis of the potential energy distribution and the atomic displacements allows the classification of the modes into nine types of oxygen vibrations and three types of chain modes. A discussion is given of effective charges and infrared intensities. An assignment of the infrared spectrum of polycrystalline V2O5 is added.

Infrared and Raman spectra and normal coordinate analysis of boranediamine

Vibration transition frequencies obtained from moderate-resolution Fourier transform infrared (FT IR) spectra and low-resolution Raman spectra are reported for /sup 11/BH(NH/sub 2/)/sub 2/, /sup 10/BH(NH/sub 2/)/sub 2/, /sup 11/BH(ND/sub 2/)/sub 2/, and /sup 10/BH(ND/sub 2/)/sub 2/. A force-constant refinement calculation using the observed frequencies allows the normal coordinates for the planar modes of boranediamine (BDA) to be determined in terms of 17 independent force constants. One of the two symmetry types of the out-of-plane normal coordinates is determined in terms of four independent force constants. The accuracy of the force field is tested by its ability to reproduce transition frequencies of /sup 11/BD(ND/sub 2/)/sub 2/ and to reproduce observed centrifugal distortion constants of /sup 11/BH(NH/sub 2/)/sub 2/ and observed inertial defects of eight isotopically substituted species of boranediamine. The results are most consistent with a planar structure for the molecule. The B-N stretch force constant is found to be 6.0 mdyn/angstrom and the N-H stretch force constant is 6.8 mdyn/angstrom. These results are consistent with a partial double bond for B-N.

Normal coordinate treatment and force constant refinement in cartesian coordinates

The classical method of solving the problem of vibrational eigenvalues, the Wilson GF-matrix method, sometimes leads to problems with redundant coordinates. Most of these problems disappear when a more recent method devised by Gwinn is applied for the computation of eigenvalues and normal coordinates, based on cartesian displacement coordinates. Gwinn's method is combined here with the least-squares method for force constant refinement. Assignment of the calculated to the observed frequencies during the refinement procedure is preserved utilizing the orthogonality of the eigenvectors. New internal coordinates describing in-plane bending and ring puckering are introduced and transformation to cartesian displacement coordinates is performed. The method of damped least squares is applicable if required. The FORTRAN IV program used also takes account of isotopic data and the calculation of intermolecular force fields. The results of refinements for water, heavy water and formaldehyde show good agreement with the data from programs based on symmetry coordinates. Finally the algorithm has been tested by calculations on benzene.

Absolute Raman intensities of CHCl3 and CDCl3 and force field for chloroform

AbstractThe absolute Raman intensities of the fundamental bands of vapour HCCl3Jand DCCl3 have been measured with an experimental accuracy of ten per cent. The vibrational potential function for chloroform has been calculated by a standard least squares forceconstant refinement including data on anharmonicity corrected values of the 12C/13C displacements and also the absolute intensities measured in this work. The results are compared with those of Previous works and the influence of the intensity data upon the refinement is discussed.

Normal coordinate analysis of cis‐1,4‐polybutadiene

AbstractThe fundamental vibrational frequencies of an isolated chain of cis‐1,4‐polybutadiene have been calculated. Infrared and polarized Raman data are used in the force constant refinement routine. The assignments of the vibrational frequencies are discussed in terms of the potential energy distribution.

Force-constant computations : III. Force-constant ranges for perchloryl fluoride and some improvements in the fletcher-powell method of refinement

The frequency data from one isotopic species of perchloryl fluoride are used to compute approximate values of some of the force-constants. The uncertainty in these values which arises from the absence of sufficient frequency data is made to manifest itself in the form of ranges, e.g. 9.5 ± 0.1 N cm −1 for Cl-O stretching and 3.5 ± 0.5 N cm −1 for Cl-F stretching. The ranges are derived by systematic variation of the arbitrarily chosen off-diagonal symmetry force-constants, and are delimited by the extremal force-constant sets F‡. The relationships between the F‡ matrices, multiple frequency assignments, and a criterion for “ complete mixing ” of vibrations is discussed. The Fletcher-Powell method of force-constant refinement is improved by a new initiation procedure and its performance is shown to be optional. Failure diagnostics for the Fletcher-Powell method are also presented.

Vibrational analysis of poly(vinylidene fluoride)

AbstractA vibrational analysis has been carried out for the two crystalline forms of poly(vinylidene fluoride) (PVF2). The Raman spectrum of the planar form of PVF2 is also reported. The band assignments are made on the basis of the spectral properties including the infrared dichroism and Raman intensities. A force field is derived based on a force constant refinement procedure utilizing the frequency data for both crystal forms.

Normal coordinates for the planar vibrations of urea using 15N and 18O frequency shift data

A force constant refinement calculation to the observed planar vibration frequencies of OC(NH 2 ) 2 and OC(ND 2 ) 2 and simultaneously to the observed frequency shift data of 18 OC(NH 2 ) 2 and OC( 15 NH 2 ) 2 has enabled the normal coordinates for the planar vibrations of urea to be determined with some degree of precision in terms of twenty-one independent force constants. The accuracy of the determined force field is tested by its ability to reproduce the observed 15 N frequency shifts of OC( 14 NH 2 )( 15 NH 2 ), the lower symmetry of which causes the A 1 and B 1 species vibrations of the symmetric molecule to combine into one symmetry species containing all thirteen vibrations. The observed 15 N frequency shift on the weak absorption at 1066 cm −1 , coupled with the calculations of this paper, confirm that this band arises from the B 1 species NH 2 rocking mode, as originally assigned by Waldron and by Stewart, but reassigned by Yamaguchi et al . The corresponding absorption in urea- D 4 is observed at 850 cm −1 , in excellent agreement with the product rule.

Programme for normal co-ordinate calculations; vibrational analysis of diborane and halides M2X6(M = Al, Ga, or ln)

An outline is given of an Algol computer programme for normal co-ordinate analysis. Some improvements in the force-constant refinement process are reported. The spectra of diborane, and of six halides of the formula M2X6(M = Al, Ga, or ln), have been analysed. In each case the force field is built up from the SVFF by adding interaction terms one by one, only those that are determined by the data being accepted. Force fields for all of the M2X6 molecules can be constructed by choosing 10 or more force constants from a set of 13; the force field for diborane differs considerably from these. A B–B force constant of 2·511 mdynes/A was found for diborane. In contrast, calculations for the M2X6 molecules became unstable when an M–M force constant was included, contrary to a previous report. An error in our previous calculations on auric chloride is corrected.

Normal coordinates for the planar vibrations of benzene

Force constants and normal coordinates have been recalculated for all of the in-plane vibrations of benzene, making use of the recently observed data on one of the Coriolis constants in the E 2 g species from the work of Callomon et al. The extent to which the force field is uniquely determined by the data is reviewed for each symmetry species in turn, and the results of a force constant refinement calculation are reported in which a modified valency force field was used based on the hybrid orbital model. The results show considerable differences from Whiffen's normal coordinates for benzene, but somewhat smaller differences from Scherer's recent calculations.

The calculation of force constants and normal co-ordinates—VII Normal co-ordinates in the E species of allene

Force constant and normal co-ordinate calculations are reported for the E species vibrations of the allene molecule. Data on the fundamental vibration frequencies of allene- h 4, allene- d 4 and allene-1.1- d 2 and on the five experimentally determined Coriolis zeta constants of C 3H 4 and C 3D 4, were used in a force constant refinement procedure. Allowing for product and sum rules this gives 21 independent data which were used to refine to the most general harmonic force field (10 parameters) with one constraint (in the absence of any constraints the refinement was not satisfactory). The results have been used to calculate the complete ζ z Coriolis interaction matrix for the allene-1.1- d 2 molecule, and hence to calculate the expected rotational structure of the perpendicular bending vibrations of this molecule; the good agreement obtained with the observed spectra is a check on our results.

Accurate force constants from heavy isotopic substitution—I. 12CF 4 and 13CF 4

In P art A, a brief outline is given of the 2 principal ways of determining force constants, the method of force constant refinement and the method of force constant display, with particular reference to the assessment of error in the frequency data employed. If D ennison's R ule is assumed to be valid, small isotopic frequency shifts may be almost unaffected by ignorance of the anharmonicity, and in cases where such shifts arise from substitution at an atom in a bridge position, such shifts may be as useful or even more useful than data on Coriolis coefficients in defining the force field. This directly contradicts an earlier conclusion by D uncan and M ills[1]. However isotopic shifts resulting from substitution at a terminal atom, as in deuteration, are likely to be so influenced by uncertainty in anharmonicity as to be virtually useless for the purpose. In the utilization of small isotopic shifts both the force constant refinement and force constant display methods require to be modified so as to calculate the shifts Δν on each mode, these being then compared with the experimental values of the shifts. In P art B, the method of small isotope shifts is applied to CF 4, for which purpose data on ν 3 and ν 4 of 12CF 4 and 13CF 4 are reported. Due to a slight Fermi resonance between ν 3 and 2ν 4 the shift Δν 3 carries an uncertainty of about ±1 cm −1 and this renders it virtually useless for defining the force field. However a shift of 2·5 ± 0·1 cm −1 on ν 4, is far more effective in fixing the force constants than either of the measured Coriolis coefficients. The values obtained after correcting for Fermi resonance and anharmonicity are as follows: ω 3 1311·9 cm −1, ω 4 631·3 cm −1, F 33 6·489, F 34 −0·827, Δω 3 39·4 cm −1, Δω 4 2·5 cm −1, F 44 1·010, mdyn/Å With this force field the intensity data of S churin [18] yield the following values of the bond polar properties: (1) (2) ∂μ/∂ r ±6·38 ±4·62 μ ±0·25 ±1·77

The calculation of force constants and normal coordinates—VI. Force constants of the silyl group

Normal coordinate calculations have been carried out for a number of molecules of three-fold symmetry containing the silyl group. All available data on frequencies and Coriolis interaction constants for all isotopic species (where possible) were used in force constant refinement calculations. Since these data were not sufficient to fix the general harmonic force field (GFF), the silyl group force field was constrained according to the model which has been successfully applied to the methyl group in previous papers in this series. In general, the refinements were made independently for each molecule, and the results show a pleasing degree of uniformity for the silyl group when the nature of the fourth atom attached to the Si atom is taken into account. On the basis of the transferability of force constants in almost identical molecules, some assignments for silyl acetylene and methyl silyl acetylene are questioned, and alternative assignments proposed.

The calculation of force constants and normal co-ordinates—III: Constrained force fields for the methyl halides

A method is discussed for imposing any desired constraint on the force field obtained in a force constant refinement calculation. The application of this method to force constant refinement calculations for the methyl halide molecules is reported. All available data on the vibration frequencies, Coriolis interaction constants and centrifugal stretching constants of CH 3X and CD 3X molecules were used in the refinements, but despite this apparent abundance of data it was found that constraints were necessary in order to obtain a unique solution to the force field. The results of unconstrained calculations, and of three different constrained calculations, are reported in this paper. The constrained models reported are a Urey—Bradley force field, a modified valence force field, and a constraint based on orbital-following bond-hybridization arguments developed in the following paper. The results are discussed, and compared with previous results for these molecules. The third of the above models is found to reproduce the observed data better than either of the first two, and additional reasons are given for preferring this solution to the force field for the methyl halide molecules.