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| physics_chemistry:point_groups:d3d:orientation_111 [2024/12/14 14:16] – Maurits W. Haverkort | physics_chemistry:point_groups:d3d:orientation_111 [2024/12/14 14:34] (current) – Maurits W. Haverkort |
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| $$A_{k,m} = \begin{cases} | $$A_{k,m} = \begin{cases} |
| \frac{1}{5} (\text{Ea1g}+2 (\text{Eeg$\pi $}+\text{Eeg$\sigma $})) & k=0\land m=0 \\ | \frac{1}{5} (\text{Ea1g}+2 (\text{Eeg}\pi +\text{Eeg}\sigma )) & k=0\land m=0 \\ |
| \frac{1}{6} i \left(\sqrt{6} \text{Ea1g}-\sqrt{6} \text{Eeg$\pi $}-4 \sqrt{3} \text{Meg}\right) & k=2\land m=-2 \\ | \frac{1}{6} i \left(\sqrt{6} \text{Ea1g}-\sqrt{6} \text{Eeg}\pi -4 \sqrt{3} \text{Meg}\right) & k=2\land m=-2 \\ |
| \left(\frac{1}{6}+\frac{i}{6}\right) \left(\sqrt{6} \text{Ea1g}-\sqrt{6} \text{Eeg$\pi $}-4 \sqrt{3} \text{Meg}\right) & k=2\land m=-1 \\ | \left(\frac{1}{6}+\frac{i}{6}\right) \left(\sqrt{6} \text{Ea1g}-\sqrt{6} \text{Eeg}\pi -4 \sqrt{3} \text{Meg}\right) & k=2\land m=-1 \\ |
| \left(\frac{1}{6}-\frac{i}{6}\right) \left(-\sqrt{6} \text{Ea1g}+\sqrt{6} \text{Eeg$\pi $}+4 \sqrt{3} \text{Meg}\right) & k=2\land m=1 \\ | \left(\frac{1}{6}-\frac{i}{6}\right) \left(-\sqrt{6} \text{Ea1g}+\sqrt{6} \text{Eeg}\pi +4 \sqrt{3} \text{Meg}\right) & k=2\land m=1 \\ |
| \frac{1}{6} i \left(-\sqrt{6} \text{Ea1g}+\sqrt{6} \text{Eeg$\pi $}+4 \sqrt{3} \text{Meg}\right) & k=2\land m=2 \\ | \frac{1}{6} i \left(-\sqrt{6} \text{Ea1g}+\sqrt{6} \text{Eeg}\pi +4 \sqrt{3} \text{Meg}\right) & k=2\land m=2 \\ |
| -\frac{1}{2} \sqrt{\frac{7}{10}} (\text{Ea1g}+2 \text{Eeg$\pi $}-3 \text{Eeg$\sigma $}) & k=4\land (m=-4\lor m=4) \\ | -\frac{1}{2} \sqrt{\frac{7}{10}} (\text{Ea1g}+2 \text{Eeg}\pi -3 \text{Eeg}\sigma ) & k=4\land (m=-4\lor m=4) \\ |
| \left(-\frac{1}{4}+\frac{i}{4}\right) \sqrt{\frac{7}{5}} \left(2 \text{Ea1g}-2 \text{Eeg$\pi $}+3 \sqrt{2} \text{Meg}\right) & k=4\land m=-3 \\ | \left(-\frac{1}{4}+\frac{i}{4}\right) \sqrt{\frac{7}{5}} \left(2 \text{Ea1g}-2 \text{Eeg}\pi +3 \sqrt{2} \text{Meg}\right) & k=4\land m=-3 \\ |
| \frac{i \left(2 \text{Ea1g}-2 \text{Eeg$\pi $}+3 \sqrt{2} \text{Meg}\right)}{\sqrt{10}} & k=4\land m=-2 \\ | \frac{i \left(2 \text{Ea1g}-2 \text{Eeg}\pi +3 \sqrt{2} \text{Meg}\right)}{\sqrt{10}} & k=4\land m=-2 \\ |
| -\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(2 \text{Ea1g}-2 \text{Eeg$\pi $}+3 \sqrt{2} \text{Meg}\right)}{\sqrt{5}} & k=4\land m=-1 \\ | -\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(2 \text{Ea1g}-2 \text{Eeg}\pi +3 \sqrt{2} \text{Meg}\right)}{\sqrt{5}} & k=4\land m=-1 \\ |
| -\frac{7}{10} (\text{Ea1g}+2 \text{Eeg$\pi $}-3 \text{Eeg$\sigma $}) & k=4\land m=0 \\ | -\frac{7}{10} (\text{Ea1g}+2 \text{Eeg}\pi -3 \text{Eeg}\sigma ) & k=4\land m=0 \\ |
| \frac{\left(\frac{1}{4}-\frac{i}{4}\right) \left(2 \text{Ea1g}-2 \text{Eeg$\pi $}+3 \sqrt{2} \text{Meg}\right)}{\sqrt{5}} & k=4\land m=1 \\ | \frac{\left(\frac{1}{4}-\frac{i}{4}\right) \left(2 \text{Ea1g}-2 \text{Eeg}\pi +3 \sqrt{2} \text{Meg}\right)}{\sqrt{5}} & k=4\land m=1 \\ |
| -\frac{i \left(2 \text{Ea1g}-2 \text{Eeg$\pi $}+3 \sqrt{2} \text{Meg}\right)}{\sqrt{10}} & k=4\land m=2 \\ | -\frac{i \left(2 \text{Ea1g}-2 \text{Eeg}\pi +3 \sqrt{2} \text{Meg}\right)}{\sqrt{10}} & k=4\land m=2 \\ |
| \left(\frac{1}{4}+\frac{i}{4}\right) \sqrt{\frac{7}{5}} \left(2 \text{Ea1g}-2 \text{Eeg$\pi $}+3 \sqrt{2} \text{Meg}\right) & k=4\land m=3 | \left(\frac{1}{4}+\frac{i}{4}\right) \sqrt{\frac{7}{5}} \left(2 \text{Ea1g}-2 \text{Eeg}\pi +3 \sqrt{2} \text{Meg}\right) & k=4\land m=3 |
| \end{cases}$$ | \end{cases}$$ |
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