3 Results and Discussion
In our previous work, the structure, energy, and vibrational spectra of orthoboric
acid, metaboric acid, and tetrahydroxoborate was thoroughly discussed. We now
focus on the polyborate ions. First we discuss those observed in the crystal structure
of alkali metal borates, followed by structurally related ions. The more
highly-charged ions might be observed in low-water, high ionic-strength environments. We also discuss other possibilities.
3.1 Triborate Species
3.1.1 [B 3 O 3 (OH) 4 ]
−
The structure of the crystallographically-observed triborate ion, [B 3 O 3 (OH) 4 ]
− , is
given in Fig. 1. The ion, present in the sodium borate mineral ameghinite, could be
formed by the addition of hydroxide ion to metaboric acid. Firstly, four different
C 2v structures were optimized. None of these was an energy minimum. All possess
an imaginary A 2 mode, suggesting desymmetrization to C 2 . Structures 3 and 4
possess also an imaginary B 2 mode, and for some MP2 levels, an imaginary B 1
mode, suggesting desymmetrization to C s . Most of the C 2 forms are minima at
some levels. None of the three C s forms are minima, desymmetrizing instead to C 1
#5–7, respectively. C 2 #1 was not a minimum at HF/6-31+G* and MP2/6-31+G*,
coalescing into C 1 #6. C 2 #2 was only a minimum ay B3LYP/6-31G* and MP2/
6-31G*, morphing into C 2 #4 at HF/6-31+G* and HF/6-311+G* levels, or
desymmetrizing to C 1 #7 at the other levels. C 2 #3 was not a minimum at MP2/6-31
+G*, becoming C 1 #4. C 2 #4 was not stable at the MP2 levels, becoming C 1 #2
instead. The order of stability was C 1 #6 (0.0 kJ/mol) < C 2 #3 (−0.4 to 1.4 kJ/mol)
< C 1 #5 (2.8–3.6 kJ/mol) < C 2 #1 (4.7–9.8 kJ/mol) < C 1 #7 (12–14 kJ/mol) < C 2
#4 (11–23 kJ/mol) < C 2 #2 (17–24 kJ/mol).
3.1.2 [B 3 O 3 (OH) 5 ]
2−
The structure of the triborate ion [B 3 O 3 (OH) 5 ]
2− is given in Fig. 1. Neither of the
two C s forms is stable and both desymmetrize to the corresponding C 1 forms. Of
these, structure #2 is 2.1–3.4 kJ/mol more stable than structure #1.
3.1.3 [B 3 O 3 (OH) 6 ]
3−
The structure of the triborate ion [B 3 O 3 (OH) 6 ]
3− is given in Fig. 1. First, two D 3h
structures were tried. Neither were minima, and the number of imaginary
120
C. C. Pye
In our previous work, the structure, energy, and vibrational spectra of orthoboric
acid, metaboric acid, and tetrahydroxoborate was thoroughly discussed. We now
focus on the polyborate ions. First we discuss those observed in the crystal structure
of alkali metal borates, followed by structurally related ions. The more
highly-charged ions might be observed in low-water, high ionic-strength environments. We also discuss other possibilities.
3.1 Triborate Species
3.1.1 [B 3 O 3 (OH) 4 ]
−
The structure of the crystallographically-observed triborate ion, [B 3 O 3 (OH) 4 ]
− , is
given in Fig. 1. The ion, present in the sodium borate mineral ameghinite, could be
formed by the addition of hydroxide ion to metaboric acid. Firstly, four different
C 2v structures were optimized. None of these was an energy minimum. All possess
an imaginary A 2 mode, suggesting desymmetrization to C 2 . Structures 3 and 4
possess also an imaginary B 2 mode, and for some MP2 levels, an imaginary B 1
mode, suggesting desymmetrization to C s . Most of the C 2 forms are minima at
some levels. None of the three C s forms are minima, desymmetrizing instead to C 1
#5–7, respectively. C 2 #1 was not a minimum at HF/6-31+G* and MP2/6-31+G*,
coalescing into C 1 #6. C 2 #2 was only a minimum ay B3LYP/6-31G* and MP2/
6-31G*, morphing into C 2 #4 at HF/6-31+G* and HF/6-311+G* levels, or
desymmetrizing to C 1 #7 at the other levels. C 2 #3 was not a minimum at MP2/6-31
+G*, becoming C 1 #4. C 2 #4 was not stable at the MP2 levels, becoming C 1 #2
instead. The order of stability was C 1 #6 (0.0 kJ/mol) < C 2 #3 (−0.4 to 1.4 kJ/mol)
< C 1 #5 (2.8–3.6 kJ/mol) < C 2 #1 (4.7–9.8 kJ/mol) < C 1 #7 (12–14 kJ/mol) < C 2
#4 (11–23 kJ/mol) < C 2 #2 (17–24 kJ/mol).
3.1.2 [B 3 O 3 (OH) 5 ]
2−
The structure of the triborate ion [B 3 O 3 (OH) 5 ]
2− is given in Fig. 1. Neither of the
two C s forms is stable and both desymmetrize to the corresponding C 1 forms. Of
these, structure #2 is 2.1–3.4 kJ/mol more stable than structure #1.
3.1.3 [B 3 O 3 (OH) 6 ]
3−
The structure of the triborate ion [B 3 O 3 (OH) 6 ]
3− is given in Fig. 1. First, two D 3h
structures were tried. Neither were minima, and the number of imaginary
120
C. C. Pye