hydration to give one of three possible C 1 structures, the B3LYP/6-31G*,
B3LYP/6-31+G*, and MP2/6-31G* converge to the oxodihydroxo form, and with
the exception of C 1 #1, this also happens at the HF/6-31G* and B3LYP/6-311+G*
levels. The forms that actually exist are 15–45 kJ/mol less stable than the corresponding oxodihydroxoborate dihydrate. Addition of the second water molecule
only gives stable structures at HF/6-31+G* and HF/6-311+G* levels, reverting to
the oxodihydroxoborate at the other levels. When both can exist, the oxodihydroxoborate is 45–50 kJ/mol more stable. Hydrating the boric acid part of the
complex stabilizes the corresponding anion form.
3.10 Transition State Connecting Tetrahydroxoborate
and Oxodihydroxoborate-Water Complex
The transition states connecting hydrated tetrahydroxoborate and the hydrated
oxodihydroxoborate anions are shown in Fig. 16. The transition state essentially
looks like a C s boric acid interacting with a hydroxyl anion. It is stabilized
somewhat by the interaction between the empty p-orbital of the boron and
the hydroxyl non-bonding electron pairs, and also hydrogen bonding between the
hydroxyl oxygen and the syn-hydrogens of boric acid, which tilt towards the
hydroxyl. The electronic barrier (from tetrahydroxoborate) is between 84 and
114 kJ/mol, depending on level. The transition state could conceivably connect to
either the van der Waals complex between boric acid and hydroxide, or to either the
C 1 #1 or #3 forms of the monohydrated oxodihydroxoborate anion.
A water molecule can stabilize the transition state in one of two ways. It can
stabilize the boric acid portion of the transition state (C 1 #1, #3, and #5) in one of
the three possible sites (as a hydrogen bond donor-acceptor and two donor-donor
types, respectively). Alternatively, it can stabilize the hydroxyl portion of the
molecule (C 1 #2 and #4) where the free boric acid hydrogen is pointing either
toward or away from the water molecule, respectively. The stabilization of the
hydroxide lowers the energy more. When compared with the unhydrated transition
state, addition of the water to the boric acid part of the molecule actually increases
the barrier by between 10 and 25 kJ/mol, whereas stabilization of the hydroxide
part of the molecule lowers the barrier by between 5 and 15 kJ/mol.
Waton and coworkers used the temperature-jump method to study the equilibrium between boric acid and borate [77]. The kinetics did not fit a simple equilibrium, but was analyzed by postulating an intermediate which they called [B
(OH) 3 ,OH
−
]. Our analysis of their published rate constants (k 23 ) at 4 and 20 °C
suggests an activation barrier of 42 kJ/mol, giving an enthalpy of activation of
39 kJ/mol. We hypothesize that this intermediate is actually [BO(OH) 2 ]
−
⋅ H 2 O.
Our calculated electronic barriers are much too high (101–117 kJ/mol), but these
are lowered upon addition of an extra one (90–103 kJ/mol) or two (69–86 kJ/mol)
water molecules. This leads one to think that additional water molecules might
An Ab Initio Study of Boric Acid, Borate …
171
B3LYP/6-31+G*, and MP2/6-31G* converge to the oxodihydroxo form, and with
the exception of C 1 #1, this also happens at the HF/6-31G* and B3LYP/6-311+G*
levels. The forms that actually exist are 15–45 kJ/mol less stable than the corresponding oxodihydroxoborate dihydrate. Addition of the second water molecule
only gives stable structures at HF/6-31+G* and HF/6-311+G* levels, reverting to
the oxodihydroxoborate at the other levels. When both can exist, the oxodihydroxoborate is 45–50 kJ/mol more stable. Hydrating the boric acid part of the
complex stabilizes the corresponding anion form.
3.10 Transition State Connecting Tetrahydroxoborate
and Oxodihydroxoborate-Water Complex
The transition states connecting hydrated tetrahydroxoborate and the hydrated
oxodihydroxoborate anions are shown in Fig. 16. The transition state essentially
looks like a C s boric acid interacting with a hydroxyl anion. It is stabilized
somewhat by the interaction between the empty p-orbital of the boron and
the hydroxyl non-bonding electron pairs, and also hydrogen bonding between the
hydroxyl oxygen and the syn-hydrogens of boric acid, which tilt towards the
hydroxyl. The electronic barrier (from tetrahydroxoborate) is between 84 and
114 kJ/mol, depending on level. The transition state could conceivably connect to
either the van der Waals complex between boric acid and hydroxide, or to either the
C 1 #1 or #3 forms of the monohydrated oxodihydroxoborate anion.
A water molecule can stabilize the transition state in one of two ways. It can
stabilize the boric acid portion of the transition state (C 1 #1, #3, and #5) in one of
the three possible sites (as a hydrogen bond donor-acceptor and two donor-donor
types, respectively). Alternatively, it can stabilize the hydroxyl portion of the
molecule (C 1 #2 and #4) where the free boric acid hydrogen is pointing either
toward or away from the water molecule, respectively. The stabilization of the
hydroxide lowers the energy more. When compared with the unhydrated transition
state, addition of the water to the boric acid part of the molecule actually increases
the barrier by between 10 and 25 kJ/mol, whereas stabilization of the hydroxide
part of the molecule lowers the barrier by between 5 and 15 kJ/mol.
Waton and coworkers used the temperature-jump method to study the equilibrium between boric acid and borate [77]. The kinetics did not fit a simple equilibrium, but was analyzed by postulating an intermediate which they called [B
(OH) 3 ,OH
−
]. Our analysis of their published rate constants (k 23 ) at 4 and 20 °C
suggests an activation barrier of 42 kJ/mol, giving an enthalpy of activation of
39 kJ/mol. We hypothesize that this intermediate is actually [BO(OH) 2 ]
−
⋅ H 2 O.
Our calculated electronic barriers are much too high (101–117 kJ/mol), but these
are lowered upon addition of an extra one (90–103 kJ/mol) or two (69–86 kJ/mol)
water molecules. This leads one to think that additional water molecules might
An Ab Initio Study of Boric Acid, Borate …
171