structure D 2d #2 has an imaginary E mode at both MP2/6-31+G* and MP2/6-311
+G*. These structures could either desymmetrize to C 2 #2/3 (stable), or C s #3/4
(unstable), both of which have slightly puckered ring(s). Desymmetrization of these
C s #3 and #4 structures via C 1 #3/4 results in ascent in symmetry to C 2 #2/3. C 2 #1
is stable at all levels. C 2v #1 has an imaginary B 1 mode at both MP2/6-31+G* and
MP2/6-311+G*, and an imaginary B 2 mode at MP2/6-31+G*. These lead to C s #5
and 6 respectively. C s #5 is stable at MP2/6-311+G*. Both C s structures are
unstable at MP2/6-31+G*, leading to stable C 1 #5 and 6 structures. C s #1 and #2
are unstable at MP2/6-31+G*, converting into C 1 #1 and #2. The energy ordering is
D 2d #1 < C s #1 < C 2 #1 < C 2v #1 < C s #2 < D 2d #2.
C 2v #1
C 2v #2
C 2v #3
C 2v #4
C 2 #1/C 1 #4
C 2 #2
C 2 #3
C s #1
C s #2/C 1 #2
C s #5
C s #6
C s #7
C 1 #1
C 2v #5
C 2v/2 #6/
C s #10
C 2v #7
C 2v #8
C 2 #7
C s #11
C 2h #1
C 2h #2
C 2v #1
C 2v #2
C 2 #4
C s #1
C s #2
C s #3
C 1 #1
Fig. 3 Structure of tetraborate ions, [B 4 O 5 (OH) 4 ]
2− and [B 4 O 9 ]
6–
A Crystallographic Review of Alkali Borate Salts …
125