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physics_chemistry:point_groups [2022/10/31 15:48] – Maurits W. Haverkortphysics_chemistry:point_groups [2022/11/02 15:04] – Maurits W. Haverkort
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 ===== A flow diagram to determine the point group ===== ===== A flow diagram to determine the point group =====
 +
 +<diagram>
 +| | | | | | | | | AAA | | | | | | |AAA=A point in space
 +| | | | | | | | | |!| | | | | | | |
 +| | | |,|-|-|-|-| BBB |-|-|-|-|.| | | |BBB=Linear ($C_{\infty}$)?
 +| | | YES | | | | | | | | | | NON | | |NON{border-color:#fff}=No|YES{border-color:#fff}=Yes
 +| | | |!| | | | | | | | | | | |!| | | |
 +| |,| CCC |.| | | |,|-|-|-|-| DDD |-|-|-|-|-|.| |CCC=Inversion ($i$)?|DDD=Two or more $C_n$ \\ with $n>2$?
 +| YES | | NON | | YES | | | | | | | | | | | NON |NON{border-color:#fff}=No|YES{border-color:#fff}=Yes
 +| |!| | | |!| | | |!| | | | | | | | | | | | |!| |
 +| Dih | | Civ |,| CCC |.| | | | | |,|-|-|-| GGG |-|-|-|.| |Dih=$D_{\infty h}$|Civ=$C_{\infty v}$|CCC=Inversion ($i$)?|GGG=$C_n$?
 +| | | | | | | YES | | NON | | | | YES | | | | | | | | NON |NON{border-color:#fff}=No|YES{border-color:#fff}=Yes
 +| | | | | | | |!| | | |!| | | | | |!| | | | | | | | | |!| |
 +| | | | | |,| EEE |.| Tds |,|-|-| FFF |-|-|.| | | |,| HHH |.| |EEE=$C_5$?|Tds=$T_{d}$|FFF=$n \, C_2 \, \perp \, C_n$?|HHH=$\sigma_h$?
 +| | | | | YES | | NON | | YES | | | | | | NON | | YES | | NON |NON{border-color:#fff}=No|YES{border-color:#fff}=Yes
 +| | | | | |!| | | |!| | | |!| | | | | | | |!| | | |!| | | |!| |
 +| | | | | Ihs | | Ohs |,| HHH |.| | | |,| HHH |.| Css |,| CCC |.| |Ihs=$I_h$|Ohs=$O_h$|HHH=$\sigma_h$?|Css=$C_s$|CCC=Inversion ($i$)?
 +| | | | | | | | | | | YES | | NON | | YES | | NON | | YES | | NON |NON{border-color:#fff}=No|YES{border-color:#fff}=Yes
 +| | | | | | | | | | | |!| | | |!| | | |!| | | |!| | | |!| | | |!| |
 +| | | | | | | | | | | Dnh |,| III |.| Cnh |,| CCC |.| Cis | | C1s |Dnh=$D_{nh}$|III=$n\, \sigma_v$?|Cnh=$C_{nh}$|CCC=$n \, \sigma_v$?|Cis=$C_{i}$|C1s=$C_1$
 +| | | | | | | | | | | | | YES | | NON | | YES | | NON |NON{border-color:#fff}=No|YES{border-color:#fff}=Yes
 +| | | | | | | | | | | | | |!| | | |!| | | |!| | | |!| |
 +| | | | | | | | | | | | | Dnd | | Dns | | Cnv |,| JJJ |.|Dnd=$D_{nd}$|Dns=$D_n$|Cnv=$C_{nv}$|JJJ=$S_{2n}$?
 +| | | | | | | | | | | | | | | | | | | | | | | YES | | NON |NON{border-color:#fff}=No|YES{border-color:#fff}=Yes
 +| | | | | | | | | | | | | | | | | | | | | | | |!| | | |!| |
 +| | | | | | | | | | | | | | | | | | | | | | | S2n | | Cns |S2n=$S_{2n}$|Cns=$C_{n}$
 +</diagram>
  
 <flow> <flow>

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