D_{2} | E | C_{2} (z) | C_{2} (y) | C_{2} (x) | rotations |
functions |
functions |
---|---|---|---|---|---|---|---|
A | +1 | +1 | +1 | +1 | - | x^{2}, y^{2}, z^{2} | xyz |
B_{1} | +1 | +1 | -1 | -1 | z, R_{z} | xy | z^{3}, y^{2}z, x^{2}z |
B_{2} | +1 | -1 | +1 | -1 | y, R_{y} | xz | yz^{2}, x^{2}y, y^{3} |
B_{3} | +1 | -1 | -1 | +1 | x, R_{x} | yz | xz^{2}, xy^{2}, x^{3} |
Number of symmetry elements | h = 4 |
Number of irreducible representations | n = 4 |
Abelian group | yes |
Number of subgroups | 3 |
Number of distinct subgroups | 1 |
Subgroup
(Number of different orientations) |
C_{2} (3) |
---|---|
Optical Isomerism (Chirality) | yes |
Polar | no |
Biphenyl | Twistane |
---|
dipole (p) | B_{1}+B_{2}+B_{3} |
---|---|
quadrupole (d) | 2A+B_{1}+B_{2}+B_{3} |
octopole (f) | A+2B_{1}+2B_{2}+2B_{3} |
hexadecapole (g) | 3A+2B_{1}+2B_{2}+2B_{3} |
32-pole (h) | 2A+3B_{1}+3B_{2}+3B_{3} |
64-pole (i) | 4A+3B_{1}+3B_{2}+3B_{3} |
128-pole (j) | 3A+4B_{1}+4B_{2}+4B_{3} |
256-pole(k) | 5A+4B_{1}+4B_{2}+4B_{3} |
512-pole (l) | 4A+5B_{1}+5B_{2}+5B_{3} |