Redundant coordinates in harmonic force-field calculations

Redundancy relations between vibrational coordinates may be linear (as for rectilinear coordinates used in deriving a G matrix), or non-linear (as for curvilinear coordinates used in formulating model force fields). It is shown that geometrically defined internal coordinates are necessarily curvilinear. Hence it is shown that linear force constants can occur in model force field calculations involving redundant coordinates, in disagreement with the recent proposal of Gussoni and Zerbi.

General derivative relations for anharmonic force fields

The brace notation, introduced by Allen and Csaszar (1993, J. chem. Phys., 98, 2983), provides a simple and compact way to deal with derivatives of arbitrary non-tensorial quantities. One of its main advantages is that it builds the permutational symmetry of the derivatives directly into the formalism. The brace notation is applied to formulate the general nth-order Cartesian derivatives of internal coordinates, and to provide closed forms for general, nth-order transformation equations of anharmonic force fields, expressed as Taylor series, from internal to Cartesian or normal coordinate spaces.

The anharmonic force field of HCN and HCP

The quadratic, cubic, and quartic force field of HCN has been calculated by a least squares refinement to fit the most recent observed data on the vibration-rotation constants of HCN, DCN and H13CN. All of the observed parameters are fitted within their standard errors of observation. The corresponding parameters for other isotopic species are calculated. For HCP and DCP the more limited data available have been fitted to an anharmonic force field using constraints based on comparison with HCN. Using this force field the zero-point rotational constants B0 have been corrected to obtain the equilibrium constants Be, and hence the equilibrium structure has been determined to be re(CH) = 1•0692(7)A, and re(CP) = 1•5398(2)A.

The calculation of force constants and normal coordinates 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 CH3X and CD3X 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.

Vibration-rotation spectra and the harmonic force field of HOCl

Vibration-rotation spectra of HOCl have been measured at a resolution of 0.05 cm−1 to determine vibration rotation constants, and 35–37 Cl isotope shifts in the vibration frequencies. The spectrum of DOCl has also been recorded, and a preliminary analysis for the band origins has been made. The vibrational frequency data and centrifugal distortion constants have been used to determine the harmonic force field in a least-squares refinement; the force field obtained also gives a good fit to data on the vibrational contributions to the inertial defect. The equilibrium rotational constants of HOCl have been obtained, and an equilibrium structure has been estimated.

An anharmonic force field for SO3

An anharmonic force field for SO3 based on the valence force model has been investigated. The results of extending the model to include some further estimated cubic interaction potential constants have also been investigated. The phenomenological parameters calculated from both model force fields agree with those few values which have been experimentally determined. A calculation of the inertia defect has been made, and thus the value of C0 has been determined. The equilibrium structure has been determined to be: re = 1.4184 ± 0.0010 Å.

Nitrous acid: vibrational frequency shifts due to 15N substitution, and the harmonic force field

Vibration rotation spectra of HO15 NO and DO15 NO have been measured at a resolution of 0•04 cm-1 to determine the isotopic shifts in the vibrational band origins. These have been used together with recently determined data on the vibrational band origins, Coriolis constants, and centrifugal distorition constants, to determine the harmonic force field of both cis and trans nitrous acid in least squares refinement calculations. The results are discussed in relation to recent ab initio calculations, the inertia defects, and the torsional potential function.

The harmonic force field and rz structure of HNCO

The presently available microwave, millimeter wave, and far-infrared data of five isotopic species of isocyanic acid, namely, HNCO, H15NCO, HN13CO, HNC18O, and DNCO, have been used to obtain improved values of the ground-state rotational constants, the five quartic distortion constants, and some higher-order distortion constants in the Ir S reduced Hamiltonian of Watson. The appropriate planarity relation among the quartic centrifugal distortion constants has been imposed in the fitting procedure. The general harmonic force field of isocyanic acid has been determined using all existing data, and assuming a trans bent equilibrium geometry of the molecule with an NCO angle of 170°. Finally an rz structure has been obtained using the Az, Bz, and Cz rotational constants of five isotopic species. The bending of the NCO chain is found to be 8° in the trans configuration.

The infrared spectrum, equilibrium structure and harmonic and anharmonic force field of thioborine, HBS

Infrared spectra of the two stretching fundamentals of both HBS and DBS have been observed, using a continuous flow system through a multiple reflection long path cell at a pressure around 1 Torr and a Nicolet Fourier Transform spectrometer with a resolution of about 0•1 cm-1. The v3 BS stretching fundamental of DBS, near 1140 cm-1, is observed in strong Fermi resonance with the overtone of the bend 2v2. The bending fundamental v2 has not been observed and must be a very weak band. The analysis of the results in conjunction with earlier work gives the equilibrium structure (re(BH) = 1•1698(12) , re(BS) = 1•5978(3) ) and the harmonic and anharmonic force field.

Intensities in the v7, v8 and v9 bands of CH2NH, and the harmonic force field of methyleneimine

A high resolution Fourier transform infrared spectrum of methyleneimine, HN=CH2, has been obtained in the gas phase in the region 700 to 1300 cm−1. The rovibrational line intensities of the three lowest fundamentals ν7 (A′), ν8 (A″), and ν9 (A″) have been simulated including all Coriolis interactions between the three bands, and by fitting the observed spectrum the relative signs and magnitudes of the vibrational transition moments have been determined. All of the available spectroscopic data have been used to determine the harmonic force field of methyleneimine.

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.

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-h4, allene-d4 and allene-1.1-d2 and on the five experimentally determined Coriolis zeta constants of C3H4 and C3D4, 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 ζz Coriolis interaction matrix for the allene-1.1-d2 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.

The general harmonic force field of methyl fluoride

The complete general harmonic force field of methyl flouride was recalculated using the most recent literature frequency, Coriolis ζ, and centrifugal distortion data for 12CH3F, 13CH3F, 12CD3F, 12CHD2F and 12CH2DF. The anharmonic corrections applied to the observed frequency data and the adopted molecular geometry are considered to be more realistic than those used hitherto. There is excellent overall agreement between the fitted force constants and the highest quality ab initio force field currently available.