318
T. Ishimoto and M. Tachikawa
Table 17.2 The optimized geometrical parameters of the unit structure of H 2 SQ in its antiferroelectric phase. Bond distances and angles are shown in angstroms and degrees, respectively
Calculation
Experiment
Dimer
Tetramer
Neutron
C(1)–O(1)
1.276
1.276
1.289(1)
C(2)–O(2)
1.273
1.277
1.287(1)
C(3)–O(3)
1.273
1.244
1.227(1)
C(4)–O(4)
1.239
1.248
1.230(1)
C(1)–C(2)
1.431
1.425
1.414(1)
C(1)–O(4)
1.464
1.454
1.464(1)
C(2)–C(3)
1.432
1.444
1.461(1)
C(3)–C(4)
1.462
1.471
1.500(1)
O(1)–H(1)
–
1.025
1.030(1)
O(2)–H(2)
1.008
1.030
1.037(1)
O(1)· · ·O(3)
–
2 .473
2.553(1)
O(2)· · ·O(4)
2.543
2.474
2.554(1)
H(1)· · ·O(3)
–
1 .448
1.524(2)
H(2)· · ·O(4)
1.535
1.441
1.517(2)
C(4)–C(1)–C(2)
91.0
9 0 .7
9 1 .66(4)
C(4)–C(1)–O(1)
138.7
138.7
136.14(4)
C(2)–C(1)–O(1)
130.3
130.6
132.21(5)
C(1)–C(2)–C(3)
89.9
9 1 .1
9 1 .72(4)
C(1)–C(2)–O(2)
139.7
139.3
136.85(5)
C(3)–C(2)–O(2)
130.0
129.6
131.43(5)
C(2)–C(3)–C(4)
91.0
8 9 .2
8 8 .40(3)
C(2)–C(3)–O(3)
138.9
137.7
136.59(5)
C(4)–C(3)–O(3)
130.0
133.1
135.01(5)
C(3)–C(4)–C(1)
87.8
8 8 .9
8 8 .23(3)
C(3)–C(4)–O(4)
138.7
137.3
136.48(5)
C(1)–C(4)–O(4)
133.6
133.8
135.30(5)
C(1)–O(1)–H(1)
–
127.4
112.70(7)
C(2)–O(2)–H(2)
126.6
126.7
113.61(7)
C(3)–C(3)· · ·H(1)
–
129.6
118.15(5)
C(4)–O(4)· · ·H(2)
141.3
130.6
116.24(5)
experimental tendency. Not only was the difference of the two hydrogen bond structures along the a and c axis directions reproduced, but also the unit structure of
C 4 O
2−
4 . Applying the adequate cluster model as tetramer, it can be found that both
local structures represented hydrogen bond structures and generally the systems including unit structures are reproducible.
T. Ishimoto and M. Tachikawa
Table 17.2 The optimized geometrical parameters of the unit structure of H 2 SQ in its antiferroelectric phase. Bond distances and angles are shown in angstroms and degrees, respectively
Calculation
Experiment
Dimer
Tetramer
Neutron
C(1)–O(1)
1.276
1.276
1.289(1)
C(2)–O(2)
1.273
1.277
1.287(1)
C(3)–O(3)
1.273
1.244
1.227(1)
C(4)–O(4)
1.239
1.248
1.230(1)
C(1)–C(2)
1.431
1.425
1.414(1)
C(1)–O(4)
1.464
1.454
1.464(1)
C(2)–C(3)
1.432
1.444
1.461(1)
C(3)–C(4)
1.462
1.471
1.500(1)
O(1)–H(1)
–
1.025
1.030(1)
O(2)–H(2)
1.008
1.030
1.037(1)
O(1)· · ·O(3)
–
2 .473
2.553(1)
O(2)· · ·O(4)
2.543
2.474
2.554(1)
H(1)· · ·O(3)
–
1 .448
1.524(2)
H(2)· · ·O(4)
1.535
1.441
1.517(2)
C(4)–C(1)–C(2)
91.0
9 0 .7
9 1 .66(4)
C(4)–C(1)–O(1)
138.7
138.7
136.14(4)
C(2)–C(1)–O(1)
130.3
130.6
132.21(5)
C(1)–C(2)–C(3)
89.9
9 1 .1
9 1 .72(4)
C(1)–C(2)–O(2)
139.7
139.3
136.85(5)
C(3)–C(2)–O(2)
130.0
129.6
131.43(5)
C(2)–C(3)–C(4)
91.0
8 9 .2
8 8 .40(3)
C(2)–C(3)–O(3)
138.9
137.7
136.59(5)
C(4)–C(3)–O(3)
130.0
133.1
135.01(5)
C(3)–C(4)–C(1)
87.8
8 8 .9
8 8 .23(3)
C(3)–C(4)–O(4)
138.7
137.3
136.48(5)
C(1)–C(4)–O(4)
133.6
133.8
135.30(5)
C(1)–O(1)–H(1)
–
127.4
112.70(7)
C(2)–O(2)–H(2)
126.6
126.7
113.61(7)
C(3)–C(3)· · ·H(1)
–
129.6
118.15(5)
C(4)–O(4)· · ·H(2)
141.3
130.6
116.24(5)
experimental tendency. Not only was the difference of the two hydrogen bond structures along the a and c axis directions reproduced, but also the unit structure of
C 4 O
2−
4 . Applying the adequate cluster model as tetramer, it can be found that both
local structures represented hydrogen bond structures and generally the systems including unit structures are reproducible.