GENERAL COMMENTS - SILICATES (crystals)

Most oxides and non- or partially-polymerized silicates consist of arrays of oxygen atoms which are in at least approximately closest-packed arrangement, and the O-O distances are such as to indicate that O-O interaction should be significant.  Thus the Urey-Bradley model should be appropriate and results are generally in agreement with this.

A number of calculations on silicates (including quartz) and oxides have been done by Iishi and colleagues, using one form or another of the Urey-Bradly/Shimanouchi potential function.  These have not been reproduced exactly in all cases, for reasons which are not clear.  Among the examples the closest match is for quartz (QTZUB).  Even in this case the torsion (tau) forces used by Iishi and Yamaguchi were not defined, so there is some guesswork involved.  For diopside (DIOPTI) and forsterite (FORSTI) the calculated frequencies are similar, but there is enough difference to indicate some systematic difference in method.  The Iishi calculations in these cases used "central forces" to represent repulsions between oxygen atoms in different silicate tetrahedra, rather than complete U-B forces for the larger polyhedra.  It would seem that these "central forces" are not exactly the same as the normal O-O "bonds" used in the VIBRATZ calculation.  In FORSTI and DIOPTI, Iishi and colleagues used a wide range of O-O repulsion force constants, finely subdivided on the basis of O-O distance.  Although there is a good theoretical basis for this, and the values in some cases could be specified independently and fixed during the calculation, the fits with observed frequencies are not really significantly better than when only a few O-O values or even a single one is used (see DIOPXX and FORSTXX).

The quartz examples illustrate some of the different models which have been used for silicates.  QTZE reproduces a calculation by Etchepare et al using strictly valence forces.  Again, they did not define the torsion forces used, so there is a slight uncertainty.  QTZV is a simplified valence model which drastically reduces the number of force constants while at the same time giving better agreement; in fact this is the best model in terms of fit with observed.  The simplified Urey-Bradley model which uses O-O "bonds" only has the smallest number of force constants (5) and does not give a significantly worse fit than some of the others, for example the Iishi and Yamaguchi model (QTZUB) which uses 8 force constants.  Although many investigators have insisted that torsion forces are necessary in quartz, the data do not support this; fits are not significantly improved by addition of torsion, and there are apparently no modes which depend strongly on torsion.  Also, Si-O-Si bending does not usually improve fits. On the other hand, an Si-Si "repulsion" as used by Iishi usually improves fits for quartz as well as most other polymerized silicates.  See Lazarev (Vibrational Spectra and Structure of Silicates, 1972) on the difficulty of identifying Si-O-Si bending and torsion forces, even in siloxane molecules.

The internal stretching modes of the silicate tetrahedra are usually easy to identify and assign.  Internal stretching modes of less-strongly bonded tetrahedra such as aluminates are more difficult.  Other modes may be difficult or impossible to assign because a given mode may have significant contributions of several kinds, for example O-T-O bending and M-O stretching and bending. 

The different models used for silicates, for example full valence, complete Urey-Bradley and partial or approximate Urey-Bradley are really very similar and there is no reason to say that any one of them is "correct"  or even superior.  The fit with observed frequencies in even the best cases is far from perfect, although it is possible that this situation may improve as better measurements become available.

GENERAL COMMENTS - CARBONYL COMPLEXES.

These files illustrate the use of 3-atom angle bending forces in two perpendicular directions.  Since the M-C-O configuration is apparently always linear, VIBRATZ must define bending in two directions which are mutually perpendicular, but which are arbitrarily oriented in terms of rotation around the axis of the group.  Others have used different methods for these compounds, for example in the case of Ni(CO)4, three different bending coordinates per M-C-O group, each being oriented toward one of the neighboring groups.  This gives a total of 12 M-C-O coordinates, compared to 8 as used by VIBRATZ.  This has the advantage of allowing meaningful interactions among the bending coordinates, whereas this is not possible in VIBRATZ.  However, although some investigators have used such interactions, they do not really seem to be significant.


SPECIFIC FILES

ACETHH, ACETDD, ACETHD.  Acetylene, C2H2.  This is a valence model, illustrating linear point groups, angle/angle automatic interaction with non-zero sharing code, and manual bond-bond interaction. Note that only standard in-plane bending is required for the angle forces, since only one plane is computed for the degenerate bending modes.  

ALLENEUB.  Allene, C3H4.  This is a Urey-Bradley model. Note that the central and outer carbon atoms have to be given different type numbers since they have different coordination numbers.  The torsion angles must use the outer carbon atoms, bypassing the central one.   The central (180 degree) C-C-C angle only bends in the E species, and the single angle coordinate is sufficient.

BENZUB, BENZUB1.  Benzene, C6H6.  This reproduces (almost) a U-B calculation by Scherer and Overend (Spec. Acta. 17, 719, 1961) of the in-plane vibrations.  Illustrates manual interactions - their "rho" interaction is done with three sets of manual interactions.  The small discrepancies with their results might be due in part to the opposite C-C repulsion, which is approximated with a standard bond.  This force is omitted in BENZUB1, and further refinement of the force constants gives essentially as good a result.

C2CL6UB.  Substituted ethane, C2Cl6.  This reproduces (exactly) a calculation by Shimanouchi, and also illustrates tau angles to fit the A1u vibration.  There are 9 possible tau's, but only the 3 with tau = 180 are used.  See also ETHANE.

CCL4UB, CCLBRUB.  Subsituted methanes, CCl4 and CCl2Br2.  These reproduce calculations by Shimanouchi.  Compare with next.

CCL4XX, CBR4XX, CCLBRXX. Subsituted methanes, CCl4, CBr4 and CCl2Br2.  These illustrate the simplified U-B model in which the ligand-ligand repulsions are simply entered as standard bonds.  In this case an angle/angle interaction is also added.  The force constants for CCL2Br2 were transferred from CCl4 and CBr4 with no further refinement.  Complete valence models for substituted methanes have also been reproduced.

CHAIN.  Single silicate chain, SiO3.  This illustrates the use of space-group symmetry for a linear (one-dimensional) polymer.  A very simple valence force field is used.  Tau forces have been added to eliminate some zero frequencies, but there are no modes in real chain silicates which can be identified as torsion.

CO3A, CO3P, CO3UB.  Carbonate radical, CO3--.  CO3A uses out-of-plane 3-atom bending to account for the A2" vibration, while CO3P uses a single psi angle (note that the "only one per central atom" box in the psi dialog must be checked, to prevent three identical psi angles from being located).  CO3UB reproduces a calculation by Janz & Mikawa (J. Mol. Sp. 1, 92, 1960).

COCO3UB.  Bidentate carbonate complex, CoCo3.  This reproduces a calculation by Fujita etal. (J. Ch. Phys. 36, 339, 1962).  There are two symmetrically distinct oxygen atoms, and since one is the central atom of a U-B "polyhedron" (2-coordinated) and the other is not, they must be given two different type numbers.

DIOPTI.  Diopside, CaMgSi2O6.  This attempts to reproduce a calculation by Tomisaka & Iishi (Mineral. J. Japan., 10, 84, 1980).  See the general discussion of silicates and also DIOPXX.  This calculation uses the Shimanouchi approximation of U-B forces within the silicate tetrahedra, but apparently only "central forces" for repulsions among ligands of the Mg and Ca (6- and 8- coordinated) polyhedra.  Results are similar, but certainly not the same - their "central forces" are perhaps not exactly the same as standard bonds, or some other information is missing (e.g. a value for kappa is not given).

DIOPXX.  Diopside, CaMgSi2O6.  This uses the simplified U-B approximation in which all repulsive forces (including those in silicate tetrahedra) are approximated as standard bonds.  This uses only 10 force constants as opposed to 18 total, 8 adjustable(not counting kappa) for DIOPTI.  Note that both calculations use an Si-Si force.

ETHANEUB.  Ethane, C2H6.  This duplicates an early calculation by Shimanouchi.

ETHYLUB, ETHYLUBD.  Ethylene, C2H4, C2D4.  This duplicates a calculation by Scherer & Overend (J. Ch. Phys. 33, 1681)on in-plane vibrations, with added tau and psi forces to do out-of-plane vibrations as well.  It is necessary to use manual interactions to duplicate the specific angle/angle interactions they used.

FE(CO)5UB.  Bypyramidal Fe(CO)5.  This attempts to duplicate a calculation by Murata and Kawai, but the results are not very close.  This illustrates the two-coordinate option (two bending coordinates at right angles) for 180-degree angles.  This uses a first-order approximation whereas Murata and Kawai apparently used a second-order approximation, as indicated by their use of kappa.  They did not specify how they handled the 180-degree Fe-C-O angles.  See also Ni(CO)4UB.

FORMICUB, FORMICUBD.  Formic acid, HCOOH, DCOOD.  This duplicates calculations on in-plane vibrations by Nakamoto & Kishida, J. Ch. Phys., 41, 1554, 1964, which used idealized angles.  The two distinct oxygen atoms must be given different type numbers because they have different U-B coordinations. The out-of-plane vibrations in A" have been modeled with a psi angle and an out-of-plane 3-atom angle rather than tau, but the agreement is not good for DCOOD.

FORSTI.  Forsterite, MgSiO4 (crystal). This is an attempt to duplicate the U-B calculation by Iishi (Am. Mineral., 63, 1198, 1978).  As for diopside, the results are similar, but not close to being identical, for unknown reasons.  This assumes that O-O interactions are "central forces", not part of U-B polyhedra except for SiO4 tetrahedra, as in diopside.

FORSTXX.  Forsterite, MgSiO4 (crystal). This uses the simplified U-B approximation in which all repulsive forces (including those in silicate tetrahedra) are approximated as standard bonds.  This gives a fit which is about as good as reported by Iishi with only 8 force constants.

H4SIO4C.  Siloxane, Si(OH)4.  This is an example of a calculation using Cartesian forces, in this case from a molecular orbital calculation on a hypothetical molecule.  This uses the file Fch4sio4.car.  In the Control Window, click on Cartesian Forces to see the options and the file input.

METHANOL.  CH3OH.  This is an attempt to reproduce the calculation by Zerbi etal (J. Chem. Phys. 38, 122, 1962), which is not successful, although other calculations by this group have been reproduced fairly well.  Their assigned frequency (observed) for V1 of CH3OH in the Margottin-Maclou assignment is grossly inconsistent with that for CD3OD and with their given O-H force constant. 

NI(CO)4UB.  Nickel carbonyl, Ni(CO)4. This reproduces very closely a calculation by Murata & Kawai (J. Ch. Phys, 26, 1355).  This uses the 2-coordinate option (bending forces at right angles) for the Ni-C-O angles - the coordinates used by Murata & Kawai were not specified, but were apparently the same.

POLYTHUB.  Polythene (polyethylene) n(CH2).  This reproduces a calculation by Shimanouchi and illustrates calculation of an organic polymer in a space group.

QTZE. Quartz, SiO2. This reproduces a valence-force calculation by Etchepare et al. 

QTZHV. High quartz, SiO2.  This uses the same valence model as qtzv (with different refined values).

QTZUB.  Quartz, SiO2. This reproduces a U-B calculation by Iishi & Yamaguchi, Am Mineral. 60:907, 1975.  See general comments on silicates.

QTZV. Quartz, SiO2.  This uses a simpler valence-force than the previous (6 vs. 9 force constants) yet gives a better fit - in fact the best fit of all models tried for quartz.  Note that no torsion is used.

QTZXX. Quartz, SiO2.  This uses the approximation to U-B forces in which repulsive forces are entered as standard bonds (O-O in this case).

SF6UB.  Sulfur hexafluoride, SF6.  This reproduces a calculation by Kim et al. (J. Mol. Spect. 26, 46, 1968).  The fit is better if the U-B f' is set to -0.1f.

SF6XX. Sulfur hexafluoride, SF6.  This uses the simple X-X "bond" approximation to U-B, attaining a better fit than SF6UB with one fewer force constants (although setting f' to -0.1f in SF6UB improves the fit while reducing the number of force constants). 

SHEET.  Silicate sheet, Si2O5.  This illustrates use of space-group symmetry for a 2-dimensional polymer.  Two of the Lattice translation boxes in the Title/Axes dialog are checked. 

