desymmetrization to C i #1. The C 2h #3 structure was stable at all levels! The C 2h #2
structure (B3LYP/6-311+G*) breaks apart into two boric acid molecules. The C 2v
#1 structure has an A 2 imaginary mode at all levels leading to C 2 #1. The D 2 #1
structure (MP2/6-311+G*) has an imaginary B 3 and B 2 mode, leading to C 2 #2 and
C 2 #3. The C 2v #2 structure has an A 2 and B 1 imaginary mode at all levels leading to
C 2 #4 and C s #9. The D 2 #2 structure has an imaginary B 3 and B 2 modes at all
levels, leading to C 2 #5 and C 2 #6. The C 2h #4 structure (HF/6-311+G*) is
unstable, possessing both a B g and A u mode, suggesting desymmetrization to C i #2
and C 2 #7.
The C i #1 structure is stable at all levels except HF/6-31G* and HF/6-311+G*,
where it dissociated. The C 2 #1 structure is only stable at HF/6-31+G*. It dissociates at HF/6-31G*, HF/6-311+G*, and B3LYP/6-311+G*. At the other levels, it
ascends in symmetry via C 1 #1 to the new C s #10 structure, which exists at all
levels. The C 2 #2 structure ascends in symmetry to C 2h #1. The C 2 #3 structure
coalesces to C 2 #1. The C 2 #4 structure ascends in symmetry to the new C 2v #3. The
unstable C s #9 structure only exists at MP2/6-31G*, ascending in symmetry to C 2v
#3 otherwise. It desymmetrizes to the stable C 1 #2 at MP2/6-31G*. The C 2 #5
structure is stable at all levels, but the C 2 #6 structure ascends in symmetry to C 2v
#3. The C i #2 and C 2 #7 ascend in symmetry to C 2h #3 and C 2v #3, respectively.
To summarize these results, there are at least four stable structures at all levels.
Their energy ordering is as follows: C 2v #3 (0.0 kJ/mol) < C 2h #3 (5.7–9.8 kJ/mol)
< C s #10 (8.1–13.1 kJ/mol) < C 2 #5 (16.4–21.6 kJ/mol). The endothermic
gas-phase dimerization energy of boric acid lies in the range 35.8–103.8 kJ/mol.
3.4.4 [B 2 (OH) 5 ]
+
Another structure of interest is the cationic [B 2 (OH) 5 ]
+ (Fig. 6). Initially we tried
four structures of C 2v symmetry. None of these was a minimum except for C 2v #4 at
all levels except MP2/6-311+G*. All non-minima had imaginary A 2 modes, and in
some cases, B 1 modes. Deymmetrization along the A 2 modes led to the stable C 2
#1–#4 structures. Deymmetrization along the B 1 modes led to the unstable C s #7–
#9 structures. In addition, there are six other C s structures obtainable by flipping the
hydrogen atoms. The C s #1 and #3 structures are unstable at all levels. The C s #2
structure is only stable at HF/6-31G*, HF/6-31+G*, and B3LYP/6-31+G*. The C s
#4, #5, and #6 structures are stable at all levels except MP2/6-311+G*. These C s
structures desymmetrize into the corresponding C 1 #1–#9 structures. The C 1 #1–#6
structures are stable, but the C 1 #7–#9 structures convert to other structures already
obtained. Of these structures, C s #4 is the most stable, followed by C 2v #4 (8.0–
10.2 kJ/mol). The structure (with hydroxide) is thermodynamically unstable relative to two boric acid molecules (880–1020 kJ/mol).
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C. C. Pye
structure (B3LYP/6-311+G*) breaks apart into two boric acid molecules. The C 2v
#1 structure has an A 2 imaginary mode at all levels leading to C 2 #1. The D 2 #1
structure (MP2/6-311+G*) has an imaginary B 3 and B 2 mode, leading to C 2 #2 and
C 2 #3. The C 2v #2 structure has an A 2 and B 1 imaginary mode at all levels leading to
C 2 #4 and C s #9. The D 2 #2 structure has an imaginary B 3 and B 2 modes at all
levels, leading to C 2 #5 and C 2 #6. The C 2h #4 structure (HF/6-311+G*) is
unstable, possessing both a B g and A u mode, suggesting desymmetrization to C i #2
and C 2 #7.
The C i #1 structure is stable at all levels except HF/6-31G* and HF/6-311+G*,
where it dissociated. The C 2 #1 structure is only stable at HF/6-31+G*. It dissociates at HF/6-31G*, HF/6-311+G*, and B3LYP/6-311+G*. At the other levels, it
ascends in symmetry via C 1 #1 to the new C s #10 structure, which exists at all
levels. The C 2 #2 structure ascends in symmetry to C 2h #1. The C 2 #3 structure
coalesces to C 2 #1. The C 2 #4 structure ascends in symmetry to the new C 2v #3. The
unstable C s #9 structure only exists at MP2/6-31G*, ascending in symmetry to C 2v
#3 otherwise. It desymmetrizes to the stable C 1 #2 at MP2/6-31G*. The C 2 #5
structure is stable at all levels, but the C 2 #6 structure ascends in symmetry to C 2v
#3. The C i #2 and C 2 #7 ascend in symmetry to C 2h #3 and C 2v #3, respectively.
To summarize these results, there are at least four stable structures at all levels.
Their energy ordering is as follows: C 2v #3 (0.0 kJ/mol) < C 2h #3 (5.7–9.8 kJ/mol)
< C s #10 (8.1–13.1 kJ/mol) < C 2 #5 (16.4–21.6 kJ/mol). The endothermic
gas-phase dimerization energy of boric acid lies in the range 35.8–103.8 kJ/mol.
3.4.4 [B 2 (OH) 5 ]
+
Another structure of interest is the cationic [B 2 (OH) 5 ]
+ (Fig. 6). Initially we tried
four structures of C 2v symmetry. None of these was a minimum except for C 2v #4 at
all levels except MP2/6-311+G*. All non-minima had imaginary A 2 modes, and in
some cases, B 1 modes. Deymmetrization along the A 2 modes led to the stable C 2
#1–#4 structures. Deymmetrization along the B 1 modes led to the unstable C s #7–
#9 structures. In addition, there are six other C s structures obtainable by flipping the
hydrogen atoms. The C s #1 and #3 structures are unstable at all levels. The C s #2
structure is only stable at HF/6-31G*, HF/6-31+G*, and B3LYP/6-31+G*. The C s
#4, #5, and #6 structures are stable at all levels except MP2/6-311+G*. These C s
structures desymmetrize into the corresponding C 1 #1–#9 structures. The C 1 #1–#6
structures are stable, but the C 1 #7–#9 structures convert to other structures already
obtained. Of these structures, C s #4 is the most stable, followed by C 2v #4 (8.0–
10.2 kJ/mol). The structure (with hydroxide) is thermodynamically unstable relative to two boric acid molecules (880–1020 kJ/mol).
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