Point Group D1h

Spherical harmonics and Multipoles
Symmetric Powers of Γxyz


First nonvanshing multipole: Quadrupole


Spherical Harmonics Yl / Multipole Symmetric Power [Γl(xyz)]
l 2l+1 Multipole Symmetry Rank l(xyz)]
s (l=0) 1 Monopole A'1 1 A'1
p (l=1) 3 Dipole A''1⊕A''2 3 A''1⊕A''2
d (l=2) 5 Quadrupole A'1⊕A'2 6 2A'1⊕A'2
f (l=3) 7 Octupole A''1⊕A''2 10 2A''1⊕2A''2
g (l=4) 9 Hexadecapole A'1⊕A'2 15 3A'1⊕2A'2
h (l=5) 11 Dotricontapole A''1⊕A''2 21 3A''1⊕3A''2
i (l=6) 13 Tetrahexacontapole A'1⊕A'2 28 4A'1⊕3A'2
j (l=7) 15 Octacosahectapole A''1⊕A''2 36 4A''1⊕4A''2
k (l=8) 17 256--pole A'1⊕A'2 45 5A'1⊕4A'2
l (l=9) 19 512--pole A''1⊕A''2 55 5A''1⊕5A''2
m (l=10) 21 1.024--pole A'1⊕A'2 66 6A'1⊕5A'2
n (l=11) 23 2.048--pole A''1⊕A''2 78 6A''1⊕6A''2
o (l=12) 25 4.096--pole A'1⊕A'2 91 7A'1⊕6A'2
q (l=13) 27 8.192--pole A''1⊕A''2 105 7A''1⊕7A''2
r (l=14) 29 16.384--pole A'1⊕A'2 120 8A'1⊕7A'2
t (l=15) 31 32.768--pole A''1⊕A''2 136 8A''1⊕8A''2
u (l=16) 33 65.536--pole A'1⊕A'2 153 9A'1⊕8A'2
v (l=17) 35 131.072--pole A''1⊕A''2 171 9A''1⊕9A''2
w (l=18) 37 262.144--pole A'1⊕A'2 190 10A'1⊕9A'2
x (l=19) 39 524.288--pole A''1⊕A''2 210 10A''1⊕10A''2
y (l=20) 41 1.048.576--pole A'1⊕A'2 231 11A'1⊕10A'2
z (l=21) 43 2.097.152--pole A''1⊕A''2 253 11A''1⊕11A''2
(l=22) 45 4.194.304--pole A'1⊕A'2 276 12A'1⊕11A'2
(l=23) 47 8.388.608--pole A''1⊕A''2 300 12A''1⊕12A''2
(l=24) 49 16.777.216--pole A'1⊕A'2 325 13A'1⊕12A'2
(l=25) 51 33.554.432--pole A''1⊕A''2 351 13A''1⊕13A''2
(l=26) 53 67.108.864--pole A'1⊕A'2 378 14A'1⊕13A'2
(l=27) 55 134.217.728--pole A''1⊕A''2 406 14A''1⊕14A''2
(l=28) 57 268.435.456--pole A'1⊕A'2 435 15A'1⊕14A'2
(l=29) 59 536.870.912--pole A''1⊕A''2 465 15A''1⊕15A''2
(l=30) 61 1.073.741.824--pole A'1⊕A'2 496 16A'1⊕15A'2
(l=31) 63 2.147.483.648--pole A''1⊕A''2 528 16A''1⊕16A''2
(l=32) 65 4.294.967.296--pole A'1⊕A'2 561 17A'1⊕16A'2
(l=33) 67 8.589.934.592--pole A''1⊕A''2 595 17A''1⊕17A''2
(l=34) 69 17.179.869.184--pole A'1⊕A'2 630 18A'1⊕17A'2
(l=35) 71 34.359.738.368--pole A''1⊕A''2 666 18A''1⊕18A''2
(l=36) 73 68.719.476.736--pole A'1⊕A'2 703 19A'1⊕18A'2
(l=37) 75 137.438.953.472--pole A''1⊕A''2 741 19A''1⊕19A''2
(l=38) 77 274.877.906.944--pole A'1⊕A'2 780 20A'1⊕19A'2
(l=39) 79 549.755.813.888--pole A''1⊕A''2 820 20A''1⊕20A''2
(l=40) 81 1.099.511.627.776--pole A'1⊕A'2 861 21A'1⊕20A'2
(l=41) 83 2.199.023.255.552--pole A''1⊕A''2 903 21A''1⊕21A''2
(l=42) 85 4.398.046.511.104--pole A'1⊕A'2 946 22A'1⊕21A'2
(l=43) 87 8.796.093.022.208--pole A''1⊕A''2 990 22A''1⊕22A''2
(l=44) 89 17.592.186.044.416--pole A'1⊕A'2 1.035 23A'1⊕22A'2
(l=45) 91 35.184.372.088.832--pole A''1⊕A''2 1.081 23A''1⊕23A''2
(l=46) 93 70.368.744.177.664--pole A'1⊕A'2 1.128 24A'1⊕23A'2
(l=47) 95 140.737.488.355.328--pole A''1⊕A''2 1.176 24A''1⊕24A''2
(l=48) 97 281.474.976.710.656--pole A'1⊕A'2 1.225 25A'1⊕24A'2
(l=49) 99 562.949.953.421.312--pole A''1⊕A''2 1.275 25A''1⊕25A''2
(l=50) 101 1.125.899.906.842.624--pole A'1⊕A'2 1.326 26A'1⊕25A'2
(l=51) 103 2.251.799.813.685.248--pole A''1⊕A''2 1.378 26A''1⊕26A''2
(l=52) 105 4.503.599.627.370.496--pole A'1⊕A'2 1.431 27A'1⊕26A'2
(l=53) 107 9.007.199.254.740.992--pole A''1⊕A''2 1.485 27A''1⊕27A''2
(l=54) 109 18.014.398.509.481.984--pole A'1⊕A'2 1.540 28A'1⊕27A'2
(l=55) 111 36.028.797.018.963.968--pole A''1⊕A''2 1.596 28A''1⊕28A''2
(l=56) 113 72.057.594.037.927.936--pole A'1⊕A'2 1.653 29A'1⊕28A'2
(l=57) 115 144.115.188.075.855.872--pole A''1⊕A''2 1.711 29A''1⊕29A''2
(l=58) 117 288.230.376.151.711.744--pole A'1⊕A'2 1.770 30A'1⊕29A'2
(l=59) 119 576.460.752.303.423.488--pole A''1⊕A''2 1.830 30A''1⊕30A''2
(l=60) 121 1.152.921.504.606.846.976--pole A'1⊕A'2 1.891 31A'1⊕30A'2
(l=61) 123 2.305.843.009.213.693.952--pole A''1⊕A''2 1.953 31A''1⊕31A''2
(l=62) 125 4.611.686.018.427.387.904--pole A'1⊕A'2 2.016 32A'1⊕31A'2
(l=63) 127 ----- A''1⊕A''2 2.080 32A''1⊕32A''2
(l=64) 129 ----- A'1⊕A'2 2.145 33A'1⊕32A'2
(l=65) 131 ----- A''1⊕A''2 2.211 33A''1⊕33A''2
(l=66) 133 ----- A'1⊕A'2 2.278 34A'1⊕33A'2
(l=67) 135 ----- A''1⊕A''2 2.346 34A''1⊕34A''2
(l=68) 137 ----- A'1⊕A'2 2.415 35A'1⊕34A'2
(l=69) 139 ----- A''1⊕A''2 2.485 35A''1⊕35A''2
(l=70) 141 ----- A'1⊕A'2 2.556 36A'1⊕35A'2
(l=71) 143 ----- A''1⊕A''2 2.628 36A''1⊕36A''2
(l=72) 145 ----- A'1⊕A'2 2.701 37A'1⊕36A'2
(l=73) 147 ----- A''1⊕A''2 2.775 37A''1⊕37A''2
(l=74) 149 ----- A'1⊕A'2 2.850 38A'1⊕37A'2
(l=75) 151 ----- A''1⊕A''2 2.926 38A''1⊕38A''2
(l=76) 153 ----- A'1⊕A'2 3.003 39A'1⊕38A'2
(l=77) 155 ----- A''1⊕A''2 3.081 39A''1⊕39A''2
(l=78) 157 ----- A'1⊕A'2 3.160 40A'1⊕39A'2
(l=79) 159 ----- A''1⊕A''2 3.240 40A''1⊕40A''2
(l=80) 161 ----- A'1⊕A'2 3.321 41A'1⊕40A'2
(l=81) 163 ----- A''1⊕A''2 3.403 41A''1⊕41A''2
(l=82) 165 ----- A'1⊕A'2 3.486 42A'1⊕41A'2
(l=83) 167 ----- A''1⊕A''2 3.570 42A''1⊕42A''2
(l=84) 169 ----- A'1⊕A'2 3.655 43A'1⊕42A'2
(l=85) 171 ----- A''1⊕A''2 3.741 43A''1⊕43A''2
(l=86) 173 ----- A'1⊕A'2 3.828 44A'1⊕43A'2
(l=87) 175 ----- A''1⊕A''2 3.916 44A''1⊕44A''2
(l=88) 177 ----- A'1⊕A'2 4.005 45A'1⊕44A'2
(l=89) 179 ----- A''1⊕A''2 4.095 45A''1⊕45A''2
(l=90) 181 ----- A'1⊕A'2 4.186 46A'1⊕45A'2
(l=91) 183 ----- A''1⊕A''2 4.278 46A''1⊕46A''2
(l=92) 185 ----- A'1⊕A'2 4.371 47A'1⊕46A'2
(l=93) 187 ----- A''1⊕A''2 4.465 47A''1⊕47A''2
(l=94) 189 ----- A'1⊕A'2 4.560 48A'1⊕47A'2
(l=95) 191 ----- A''1⊕A''2 4.656 48A''1⊕48A''2
(l=96) 193 ----- A'1⊕A'2 4.753 49A'1⊕48A'2
(l=97) 195 ----- A''1⊕A''2 4.851 49A''1⊕49A''2
(l=98) 197 ----- A'1⊕A'2 4.950 50A'1⊕49A'2
(l=99) 199 ----- A''1⊕A''2 5.050 50A''1⊕50A''2
(l=100) 201 ----- A'1⊕A'2 5.151 51A'1⊕50A'2
(l=101) 203 ----- A''1⊕A''2 5.253 51A''1⊕51A''2
(l=102) 205 ----- A'1⊕A'2 5.356 52A'1⊕51A'2
(l=103) 207 ----- A''1⊕A''2 5.460 52A''1⊕52A''2
(l=104) 209 ----- A'1⊕A'2 5.565 53A'1⊕52A'2
(l=105) 211 ----- A''1⊕A''2 5.671 53A''1⊕53A''2
(l=106) 213 ----- A'1⊕A'2 5.778 54A'1⊕53A'2
(l=107) 215 ----- A''1⊕A''2 5.886 54A''1⊕54A''2
(l=108) 217 ----- A'1⊕A'2 5.995 55A'1⊕54A'2
(l=109) 219 ----- A''1⊕A''2 6.105 55A''1⊕55A''2
(l=110) 221 ----- A'1⊕A'2 6.216 56A'1⊕55A'2
(l=111) 223 ----- A''1⊕A''2 6.328 56A''1⊕56A''2
(l=112) 225 ----- A'1⊕A'2 6.441 57A'1⊕56A'2
(l=113) 227 ----- A''1⊕A''2 6.555 57A''1⊕57A''2
(l=114) 229 ----- A'1⊕A'2 6.670 58A'1⊕57A'2
(l=115) 231 ----- A''1⊕A''2 6.786 58A''1⊕58A''2
(l=116) 233 ----- A'1⊕A'2 6.903 59A'1⊕58A'2
(l=117) 235 ----- A''1⊕A''2 7.021 59A''1⊕59A''2
(l=118) 237 ----- A'1⊕A'2 7.140 60A'1⊕59A'2
(l=119) 239 ----- A''1⊕A''2 7.260 60A''1⊕60A''2
(l=120) 241 ----- A'1⊕A'2 7.381 61A'1⊕60A'2
(l=121) 243 ----- A''1⊕A''2 7.503 61A''1⊕61A''2
(l=122) 245 ----- A'1⊕A'2 7.626 62A'1⊕61A'2
(l=123) 247 ----- A''1⊕A''2 7.750 62A''1⊕62A''2
(l=124) 249 ----- A'1⊕A'2 7.875 63A'1⊕62A'2
(l=125) 251 ----- A''1⊕A''2 8.001 63A''1⊕63A''2
(l=126) 253 ----- A'1⊕A'2 8.128 64A'1⊕63A'2
(l=127) 255 ----- A''1⊕A''2 8.256 64A''1⊕64A''2
(l=128) 257 ----- A'1⊕A'2 8.385 65A'1⊕64A'2
(l=129) 259 ----- A''1⊕A''2 8.515 65A''1⊕65A''2
(l=130) 261 ----- A'1⊕A'2 8.646 66A'1⊕65A'2
(l=131) 263 ----- A''1⊕A''2 8.778 66A''1⊕66A''2
(l=132) 265 ----- A'1⊕A'2 8.911 67A'1⊕66A'2
(l=133) 267 ----- A''1⊕A''2 9.045 67A''1⊕67A''2
(l=134) 269 ----- A'1⊕A'2 9.180 68A'1⊕67A'2
(l=135) 271 ----- A''1⊕A''2 9.316 68A''1⊕68A''2
(l=136) 273 ----- A'1⊕A'2 9.453 69A'1⊕68A'2
(l=137) 275 ----- A''1⊕A''2 9.591 69A''1⊕69A''2
(l=138) 277 ----- A'1⊕A'2 9.730 70A'1⊕69A'2
(l=139) 279 ----- A''1⊕A''2 9.870 70A''1⊕70A''2
(l=140) 281 ----- A'1⊕A'2 10.011 71A'1⊕70A'2
(l=141) 283 ----- A''1⊕A''2 10.153 71A''1⊕71A''2
(l=142) 285 ----- A'1⊕A'2 10.296 72A'1⊕71A'2
(l=143) 287 ----- A''1⊕A''2 10.440 72A''1⊕72A''2
(l=144) 289 ----- A'1⊕A'2 10.585 73A'1⊕72A'2
(l=145) 291 ----- A''1⊕A''2 10.731 73A''1⊕73A''2
(l=146) 293 ----- A'1⊕A'2 10.878 74A'1⊕73A'2
(l=147) 295 ----- A''1⊕A''2 11.026 74A''1⊕74A''2
(l=148) 297 ----- A'1⊕A'2 11.175 75A'1⊕74A'2
(l=149) 299 ----- A''1⊕A''2 11.325 75A''1⊕75A''2
(l=150) 301 ----- A'1⊕A'2 11.476 76A'1⊕75A'2
(l=151) 303 ----- A''1⊕A''2 11.628 76A''1⊕76A''2
(l=152) 305 ----- A'1⊕A'2 11.781 77A'1⊕76A'2
(l=153) 307 ----- A''1⊕A''2 11.935 77A''1⊕77A''2
(l=154) 309 ----- A'1⊕A'2 12.090 78A'1⊕77A'2
(l=155) 311 ----- A''1⊕A''2 12.246 78A''1⊕78A''2
(l=156) 313 ----- A'1⊕A'2 12.403 79A'1⊕78A'2
(l=157) 315 ----- A''1⊕A''2 12.561 79A''1⊕79A''2
(l=158) 317 ----- A'1⊕A'2 12.720 80A'1⊕79A'2
(l=159) 319 ----- A''1⊕A''2 12.880 80A''1⊕80A''2
(l=160) 321 ----- A'1⊕A'2 13.041 81A'1⊕80A'2
(l=161) 323 ----- A''1⊕A''2 13.203 81A''1⊕81A''2
(l=162) 325 ----- A'1⊕A'2 13.366 82A'1⊕81A'2
(l=163) 327 ----- A''1⊕A''2 13.530 82A''1⊕82A''2
(l=164) 329 ----- A'1⊕A'2 13.695 83A'1⊕82A'2
(l=165) 331 ----- A''1⊕A''2 13.861 83A''1⊕83A''2
(l=166) 333 ----- A'1⊕A'2 14.028 84A'1⊕83A'2
(l=167) 335 ----- A''1⊕A''2 14.196 84A''1⊕84A''2
(l=168) 337 ----- A'1⊕A'2 14.365 85A'1⊕84A'2
(l=169) 339 ----- A''1⊕A''2 14.535 85A''1⊕85A''2
(l=170) 341 ----- A'1⊕A'2 14.706 86A'1⊕85A'2
(l=171) 343 ----- A''1⊕A''2 14.878 86A''1⊕86A''2
(l=172) 345 ----- A'1⊕A'2 15.051 87A'1⊕86A'2
(l=173) 347 ----- A''1⊕A''2 15.225 87A''1⊕87A''2
(l=174) 349 ----- A'1⊕A'2 15.400 88A'1⊕87A'2
(l=175) 351 ----- A''1⊕A''2 15.576 88A''1⊕88A''2
(l=176) 353 ----- A'1⊕A'2 15.753 89A'1⊕88A'2
(l=177) 355 ----- A''1⊕A''2 15.931 89A''1⊕89A''2
(l=178) 357 ----- A'1⊕A'2 16.110 90A'1⊕89A'2
(l=179) 359 ----- A''1⊕A''2 16.290 90A''1⊕90A''2
(l=180) 361 ----- A'1⊕A'2 16.471 91A'1⊕90A'2
(l=181) 363 ----- A''1⊕A''2 16.653 91A''1⊕91A''2
(l=182) 365 ----- A'1⊕A'2 16.836 92A'1⊕91A'2
(l=183) 367 ----- A''1⊕A''2 17.020 92A''1⊕92A''2
(l=184) 369 ----- A'1⊕A'2 17.205 93A'1⊕92A'2
(l=185) 371 ----- A''1⊕A''2 17.391 93A''1⊕93A''2
(l=186) 373 ----- A'1⊕A'2 17.578 94A'1⊕93A'2
(l=187) 375 ----- A''1⊕A''2 17.766 94A''1⊕94A''2
(l=188) 377 ----- A'1⊕A'2 17.955 95A'1⊕94A'2
(l=189) 379 ----- A''1⊕A''2 18.145 95A''1⊕95A''2
(l=190) 381 ----- A'1⊕A'2 18.336 96A'1⊕95A'2
(l=191) 383 ----- A''1⊕A''2 18.528 96A''1⊕96A''2
(l=192) 385 ----- A'1⊕A'2 18.721 97A'1⊕96A'2
(l=193) 387 ----- A''1⊕A''2 18.915 97A''1⊕97A''2
(l=194) 389 ----- A'1⊕A'2 19.110 98A'1⊕97A'2
(l=195) 391 ----- A''1⊕A''2 19.306 98A''1⊕98A''2
(l=196) 393 ----- A'1⊕A'2 19.503 99A'1⊕98A'2
(l=197) 395 ----- A''1⊕A''2 19.701 99A''1⊕99A''2
(l=198) 397 ----- A'1⊕A'2 19.900 100A'1⊕99A'2
(l=199) 399 ----- A''1⊕A''2 20.100 100A''1⊕100A''2
(l=200) 401 ----- A'1⊕A'2 20.301 101A'1⊕100A'2
(l=201) 403 ----- A''1⊕A''2 20.503 101A''1⊕101A''2
(l=202) 405 ----- A'1⊕A'2 20.706 102A'1⊕101A'2
(l=203) 407 ----- A''1⊕A''2 20.910 102A''1⊕102A''2
(l=204) 409 ----- A'1⊕A'2 21.115 103A'1⊕102A'2
(l=205) 411 ----- A''1⊕A''2 21.321 103A''1⊕103A''2
(l=206) 413 ----- A'1⊕A'2 21.528 104A'1⊕103A'2
(l=207) 415 ----- A''1⊕A''2 21.736 104A''1⊕104A''2
(l=208) 417 ----- A'1⊕A'2 21.945 105A'1⊕104A'2
(l=209) 419 ----- A''1⊕A''2 22.155 105A''1⊕105A''2
(l=210) 421 ----- A'1⊕A'2 22.366 106A'1⊕105A'2
(l=211) 423 ----- A''1⊕A''2 22.578 106A''1⊕106A''2
(l=212) 425 ----- A'1⊕A'2 22.791 107A'1⊕106A'2
(l=213) 427 ----- A''1⊕A''2 23.005 107A''1⊕107A''2
(l=214) 429 ----- A'1⊕A'2 23.220 108A'1⊕107A'2
(l=215) 431 ----- A''1⊕A''2 23.436 108A''1⊕108A''2
(l=216) 433 ----- A'1⊕A'2 23.653 109A'1⊕108A'2
(l=217) 435 ----- A''1⊕A''2 23.871 109A''1⊕109A''2
(l=218) 437 ----- A'1⊕A'2 24.090 110A'1⊕109A'2
(l=219) 439 ----- A''1⊕A''2 24.310 110A''1⊕110A''2
(l=220) 441 ----- A'1⊕A'2 24.531 111A'1⊕110A'2
(l=221) 443 ----- A''1⊕A''2 24.753 111A''1⊕111A''2
(l=222) 445 ----- A'1⊕A'2 24.976 112A'1⊕111A'2
(l=223) 447 ----- A''1⊕A''2 25.200 112A''1⊕112A''2
(l=224) 449 ----- A'1⊕A'2 25.425 113A'1⊕112A'2
(l=225) 451 ----- A''1⊕A''2 25.651 113A''1⊕113A''2
(l=226) 453 ----- A'1⊕A'2 25.878 114A'1⊕113A'2
(l=227) 455 ----- A''1⊕A''2 26.106 114A''1⊕114A''2
(l=228) 457 ----- A'1⊕A'2 26.335 115A'1⊕114A'2
(l=229) 459 ----- A''1⊕A''2 26.565 115A''1⊕115A''2
(l=230) 461 ----- A'1⊕A'2 26.796 116A'1⊕115A'2
(l=231) 463 ----- A''1⊕A''2 27.028 116A''1⊕116A''2
(l=232) 465 ----- A'1⊕A'2 27.261 117A'1⊕116A'2
(l=233) 467 ----- A''1⊕A''2 27.495 117A''1⊕117A''2
(l=234) 469 ----- A'1⊕A'2 27.730 118A'1⊕117A'2
(l=235) 471 ----- A''1⊕A''2 27.966 118A''1⊕118A''2
(l=236) 473 ----- A'1⊕A'2 28.203 119A'1⊕118A'2
(l=237) 475 ----- A''1⊕A''2 28.441 119A''1⊕119A''2
(l=238) 477 ----- A'1⊕A'2 28.680 120A'1⊕119A'2
(l=239) 479 ----- A''1⊕A''2 28.920 120A''1⊕120A''2
(l=240) 481 ----- A'1⊕A'2 29.161 121A'1⊕120A'2
(l=241) 483 ----- A''1⊕A''2 29.403 121A''1⊕121A''2
(l=242) 485 ----- A'1⊕A'2 29.646 122A'1⊕121A'2
(l=243) 487 ----- A''1⊕A''2 29.890 122A''1⊕122A''2
(l=244) 489 ----- A'1⊕A'2 30.135 123A'1⊕122A'2
(l=245) 491 ----- A''1⊕A''2 30.381 123A''1⊕123A''2
(l=246) 493 ----- A'1⊕A'2 30.628 124A'1⊕123A'2
(l=247) 495 ----- A''1⊕A''2 30.876 124A''1⊕124A''2
(l=248) 497 ----- A'1⊕A'2 31.125 125A'1⊕124A'2
(l=249) 499 ----- A''1⊕A''2 31.375 125A''1⊕125A''2
(l=250) 501 ----- A'1⊕A'2 31.626 126A'1⊕125A'2
(l=251) 503 ----- A''1⊕A''2 31.878 126A''1⊕126A''2
(l=252) 505 ----- A'1⊕A'2 32.131 127A'1⊕126A'2
(l=253) 507 ----- A''1⊕A''2 32.385 127A''1⊕127A''2
(l=254) 509 ----- A'1⊕A'2 32.640 128A'1⊕127A'2
(l=255) 511 ----- A''1⊕A''2 32.896 128A''1⊕128A''2
(l=256) 513 ----- A'1⊕A'2 33.153 129A'1⊕128A'2



Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement