@article {Ferraro:1974-07-01T00:00:00:0003-7028:379,
author = "Ferraro, J. R. and Williams, J. M. and LaBonville, P.",
title = "A Modified Urey-Bradley Force Field for the Normal Coordinate Treatment of Oxonium Ions H_{3}O^{+} and D_{3}O^{+}
",
journal = "Applied Spectroscopy",
volume = "28",
number = "4",
year = "1974-07-01T00:00:00",
abstract = "In a recent spectroscopic study we reported the normal coordinate treatment (NCT) of the oxonium ions, H_{3}O^{+} and D_{3}O^{+}, accomplished for the first time using known distances and O—H—O angles determined by neutron diffraction in solid
H_{3}O^{+}CH_{3}C_{6}H_{4}SO_{3}
^{−2}. Both the general valence force field (GVFF) and the Urey-Bradley force field (UBFF) were used as the potential energy fields in the NCT. The results using the GVFF compared very well with those
from an unmodified UBFF. Realizing the possible limitations of the UBFF, we have determined the effect a modified Urey-Bradley force field (MUBFF) would have on the results. Using the GVFF, it is possible to evaluate all six force constants as has been done for ammonia. However, it was found
that in the case of H_{3}O^{+} and D_{3}O^{+} a very high estimated dispersion resulted. Consequently, regression analysis was used to determine which of the six simple valence force constants were needed to obtain results with reasonable estimated dispersion.
The final general

[Table I & II]

valence force constants chosen were f_{d}, f_{dd}, f_{α} and f_{αα}. The Urey-Bradley force field was consequently modified by adding f_{αα} (borrowed from the GVFF) to the usual
force field consisting of K, H, F. It was then possible to compare both fields term for term by transferring the Urey-Bradley constants to internal coordinate space. Both the force constant and g matrices were symmetrized using symmetry coordinates. Table I records a comparison of the theoretically
calculated frequencies with the experimental values. Two solutions (set 1 and 2) to the secular equation corresponding to inverse assignments for the stretching modes (a_{1} and e) are observed to be equally reasonable. Tables IIA and IIB tabulate the force constants obtained for both
fields. Table III presents the potential energy distribution (PED) matrix. The force constants and the PED, using the MUBFF, are insignificantly different from values obtained when the unmodified UBFF is used. Some improvement is noted in the percent deviation of the theoretically calculated
frequencies from the experimental values when the MUBFF is used. However, the over-all conclusions determined from the unmodified UBFF for H_{3}O + and D_{3}O + are not changed by modifying the UBFF, and we conclude that in this case it may be proper to use an unmodified UBFF.",
pages = "379-380",
url = "http://www.ingentaconnect.com/content/sas/sas/1974/00000028/00000004/art00019",
doi = "doi:10.1366/000370274774332335",
keyword = "Oxonium ions, Modified Urey-Bradley force field, Normal coordinate treatment"
}