Relationship between bond stretching frequencies and internal bonding for [16O4]- and [18O4]phosphates in aqueous solution

Hua Deng, Jianghua Wang, Robert Callender, W. J. Ray

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

A normal-mode analysis is used to show that the fundamental stretching frequency, defined as v2 = (vs2 + nava2)/(na + 1) where vs and va are the symmetric and asymmetric modes, respectively, and na the degeneracy of the asymmetric modes, depends almost entirely on the force constant and reduced mass of a P-..O (or P-OH) bond in phosphoric acid or its anions to a good approximation. On the other hand, vs or va, separately, depend not only on these parameters but also on molecular geometry. Thus, P-..O (or P-OH) bond order is more closely related to the fundamental frequency than to the symmetric or asymmetric stretching frequencies. Similar conclusions apply to V-..O (or V-OH) bonds in vanadate molecules. The frequencies for the four different P-..O bonds and three different P-OH bonds in [18O4] phosphoric acid and its three anions were measured by Raman and FT-IR spectroscopy. The measured values, plus those for [16O4] phosphates, were correlated with P-..O valence bond order, by using a modification of the Hardcastle-Wachs procedure (Hardcastle, F. D.; Wachs, I. J. Phys. Chem. 1991, 95, 5031). The bond order/stretching frequency correlations thus produced are expected to hold accurately over a wide range, for both [16O] and [18O] phosphates. Thus, P-..O bond order and bond length in phosphates can be determined from vibrational spectra by using the derived bond order/stretching frequency correlation and the bond length/bond order correlation of Brown and Wu (Acta Crystallogr. 1976, B32, 1957). The accuracy is very high. The error in these relationships is estimated to be within ±0.04 vu and ±0.004 Å for bond orders and bond lengths, respectively, as judged by examining the affects of neglecting small terms in normal-mode analysis and by comparisons of derived bond lengths of P-..O bonds from frequency data to the results from small-molecule crystallographic data.

Original languageEnglish (US)
Pages (from-to)3617-3623
Number of pages7
JournalJournal of Physical Chemistry B
Volume102
Issue number18
StatePublished - Apr 30 1998

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Bond length
Stretching
phosphates
Phosphates
aqueous solutions
Phosphoric acid
Anions
Negative ions
phosphoric acid
Molecules
Vanadates
Vibrational spectra
Infrared spectroscopy
anions
vanadates
Geometry
vibrational spectra
molecules
valence
geometry

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry

Cite this

Relationship between bond stretching frequencies and internal bonding for [16O4]- and [18O4]phosphates in aqueous solution. / Deng, Hua; Wang, Jianghua; Callender, Robert; Ray, W. J.

In: Journal of Physical Chemistry B, Vol. 102, No. 18, 30.04.1998, p. 3617-3623.

Research output: Contribution to journalArticle

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title = "Relationship between bond stretching frequencies and internal bonding for [16O4]- and [18O4]phosphates in aqueous solution",
abstract = "A normal-mode analysis is used to show that the fundamental stretching frequency, defined as v2 = (vs2 + nava2)/(na + 1) where vs and va are the symmetric and asymmetric modes, respectively, and na the degeneracy of the asymmetric modes, depends almost entirely on the force constant and reduced mass of a P-..O (or P-OH) bond in phosphoric acid or its anions to a good approximation. On the other hand, vs or va, separately, depend not only on these parameters but also on molecular geometry. Thus, P-..O (or P-OH) bond order is more closely related to the fundamental frequency than to the symmetric or asymmetric stretching frequencies. Similar conclusions apply to V-..O (or V-OH) bonds in vanadate molecules. The frequencies for the four different P-..O bonds and three different P-OH bonds in [18O4] phosphoric acid and its three anions were measured by Raman and FT-IR spectroscopy. The measured values, plus those for [16O4] phosphates, were correlated with P-..O valence bond order, by using a modification of the Hardcastle-Wachs procedure (Hardcastle, F. D.; Wachs, I. J. Phys. Chem. 1991, 95, 5031). The bond order/stretching frequency correlations thus produced are expected to hold accurately over a wide range, for both [16O] and [18O] phosphates. Thus, P-..O bond order and bond length in phosphates can be determined from vibrational spectra by using the derived bond order/stretching frequency correlation and the bond length/bond order correlation of Brown and Wu (Acta Crystallogr. 1976, B32, 1957). The accuracy is very high. The error in these relationships is estimated to be within ±0.04 vu and ±0.004 {\AA} for bond orders and bond lengths, respectively, as judged by examining the affects of neglecting small terms in normal-mode analysis and by comparisons of derived bond lengths of P-..O bonds from frequency data to the results from small-molecule crystallographic data.",
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