The C 1 #2 form is higher in energy than the nearly isoenergetic C s #2 and C 1 #3
forms. At MP2/6-311+G*, C s #2 converts to C 1 #4. From the high-energy anhydrous C 2v #2 form, the unstable C 2v #2 and C s #3 forms arise. The lower-energy C s
#3 form converts to C 1 #5. The C 2v #2 form could convert to a C 2 form (unstable)
or one of two C s forms. In all of these, the water molecule moves (C s ) or would
move (C 2 ) to a structure close to C 1 #5. In all cases, conformers possessing a
hydrogen bond to the oxo group are the most stable within each grouping based on
the naked anion.
For the dihydrate, we can construct several structures based on the three
anhydrous forms. From C 2v #1, the C 2 #1, C s #1, and C 1 #1 forms may be constructed. The C 2 #1 form is unstable at HF/6-311+G* and MP2/6-311+G*, giving
C 1 #2a and C 1 #2 forms, respectively. From C s #1, the stable C 1 #3–6 forms can be
constructed. From C 2v #2, the C 2v #1 form can be constructed (only stable at HF/
6-31+G*), as well as C s #2 (stable at MP2/6-311+G*). The C 2v #1 form converts to
the stable C 2 #2 form (C 1 #8 at MP2/6-311+G*), whereas most attempts to obtain
C s #2 result in migration of the double acceptor water molecule towards the double
donor water molecule.
For the trihydrate, two structures exist for each of the three anhydrous forms.
Both a C 2 and a C s #1 exist for the C 2v #1 anhydrous form, although at B3LYP/
6-31G* and the MP2 levels, the C 2 structure desymmetrizes to C 1 #1. Both C 1 #2
and C 1 #3 can exist for the C s #1 anhydrous form. The C 2v form could exist for the
C 2v #2 anhydrous form, but it has imaginary frequencies. Nearly all attempts to
desymmetrize (C s #2,3) result in the double acceptor water molecule moving
toward the other double donor water molecules, and at the only level where such a
structure exists (C s #3, MP2/6-31+G*), an imaginary frequency would desymmetrize by moving the double acceptor water molecule towards the double donor
water molecules.
In the presence of additional water molecules, the BOH twisting vibrations can
increase to 600–800 cm
−1 (if hydrogen bonded), the in-plane BO 3 deformations
increase to 480–600 cm
−1 , the out-of-plane BO 3 deformation is hardly affected, the
B-O(H) and B-O symmetric stretching frequency increases slightly, and the coupled
antisymmetric B-OH stretch and BOH deformations all increase in frequency to
about 1100–1300 cm
−1 (Fig. 14). For water molecules that are hydrogen-bonded to
the lone oxygen of this strong base, the OH frequency is lowered to around
3000 cm
−1 .
3.9 Boric Acid-Hydroxide Complex and Its Hydrates,
B(OH) 3 ⋅ OH
−
⋅ nH 2 O
The boric acid-boric acid complex was investigated next (Fig. 15). All attempts to
locate the complex between hydroxide and the C 3h form of boric acid resulted in
deprotonation to form the oxodihydroxoborate anion-water complex. The C s
An Ab Initio Study of Boric Acid, Borate …
169
forms. At MP2/6-311+G*, C s #2 converts to C 1 #4. From the high-energy anhydrous C 2v #2 form, the unstable C 2v #2 and C s #3 forms arise. The lower-energy C s
#3 form converts to C 1 #5. The C 2v #2 form could convert to a C 2 form (unstable)
or one of two C s forms. In all of these, the water molecule moves (C s ) or would
move (C 2 ) to a structure close to C 1 #5. In all cases, conformers possessing a
hydrogen bond to the oxo group are the most stable within each grouping based on
the naked anion.
For the dihydrate, we can construct several structures based on the three
anhydrous forms. From C 2v #1, the C 2 #1, C s #1, and C 1 #1 forms may be constructed. The C 2 #1 form is unstable at HF/6-311+G* and MP2/6-311+G*, giving
C 1 #2a and C 1 #2 forms, respectively. From C s #1, the stable C 1 #3–6 forms can be
constructed. From C 2v #2, the C 2v #1 form can be constructed (only stable at HF/
6-31+G*), as well as C s #2 (stable at MP2/6-311+G*). The C 2v #1 form converts to
the stable C 2 #2 form (C 1 #8 at MP2/6-311+G*), whereas most attempts to obtain
C s #2 result in migration of the double acceptor water molecule towards the double
donor water molecule.
For the trihydrate, two structures exist for each of the three anhydrous forms.
Both a C 2 and a C s #1 exist for the C 2v #1 anhydrous form, although at B3LYP/
6-31G* and the MP2 levels, the C 2 structure desymmetrizes to C 1 #1. Both C 1 #2
and C 1 #3 can exist for the C s #1 anhydrous form. The C 2v form could exist for the
C 2v #2 anhydrous form, but it has imaginary frequencies. Nearly all attempts to
desymmetrize (C s #2,3) result in the double acceptor water molecule moving
toward the other double donor water molecules, and at the only level where such a
structure exists (C s #3, MP2/6-31+G*), an imaginary frequency would desymmetrize by moving the double acceptor water molecule towards the double donor
water molecules.
In the presence of additional water molecules, the BOH twisting vibrations can
increase to 600–800 cm
−1 (if hydrogen bonded), the in-plane BO 3 deformations
increase to 480–600 cm
−1 , the out-of-plane BO 3 deformation is hardly affected, the
B-O(H) and B-O symmetric stretching frequency increases slightly, and the coupled
antisymmetric B-OH stretch and BOH deformations all increase in frequency to
about 1100–1300 cm
−1 (Fig. 14). For water molecules that are hydrogen-bonded to
the lone oxygen of this strong base, the OH frequency is lowered to around
3000 cm
−1 .
3.9 Boric Acid-Hydroxide Complex and Its Hydrates,
B(OH) 3 ⋅ OH
−
⋅ nH 2 O
The boric acid-boric acid complex was investigated next (Fig. 15). All attempts to
locate the complex between hydroxide and the C 3h form of boric acid resulted in
deprotonation to form the oxodihydroxoborate anion-water complex. The C s
An Ab Initio Study of Boric Acid, Borate …
169