The tetrahedral borate structure is observed in the crystal structure of sodium
1:1:8 and 1:1:4, and lithium 1:1:16 and 1:1:4 (Table 2). Our calculated B-O bond
lengths range from 1.4702–1.4904 Å, with HF < B3LYP < MP2 (Table 9). These
are slightly longer than the experimentally determined (X-ray) bond lengths of
1.463–1.483 Å and compare favorably with previous calculations.
The vibrational spectra (unscaled) of borate, as well as some experimental
vibrational frequencies from the literature, is given in Table 10. Undistorted borate,
of S 4 symmetry, has 21 modes of internal vibration and spans the vibrational
representation
Fig. 6 Variation of vibrational frequencies of B(OH) 3 (3500–4000 cm
−1
) as a function of
hydration and structure
D 2d #1
D 2d #2/S 4 #3
S 4 #1
S 4 #2
Fig. 7 Structure of borate, B(OH) 4
−
An Ab Initio Study of Boric Acid, Borate …
159
1:1:8 and 1:1:4, and lithium 1:1:16 and 1:1:4 (Table 2). Our calculated B-O bond
lengths range from 1.4702–1.4904 Å, with HF < B3LYP < MP2 (Table 9). These
are slightly longer than the experimentally determined (X-ray) bond lengths of
1.463–1.483 Å and compare favorably with previous calculations.
The vibrational spectra (unscaled) of borate, as well as some experimental
vibrational frequencies from the literature, is given in Table 10. Undistorted borate,
of S 4 symmetry, has 21 modes of internal vibration and spans the vibrational
representation
Fig. 6 Variation of vibrational frequencies of B(OH) 3 (3500–4000 cm
−1
) as a function of
hydration and structure
D 2d #1
D 2d #2/S 4 #3
S 4 #1
S 4 #2
Fig. 7 Structure of borate, B(OH) 4
−
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159