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Topic: Linear Combinations of Atomic Orbitals  (Read 1286 times)

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Offline jgr

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Linear Combinations of Atomic Orbitals
« on: December 11, 2023, 03:27:43 AM »
Hi,

Just wondering for sp3 hybridised orbitals, why there are only 4 linear combinations (see file attached)? I don't understand why there can't be 2^3=8?

Thanks!
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Offline Corribus

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Re: Linear Combinations of Atomic Orbitals
« Reply #1 on: December 11, 2023, 12:22:29 PM »
Because some options are equivalent in terms of energy. For instance, if you have two atomic orbitals, A and B, and A and B are indistinguishable, the A(+)B(-) combination is equivalent to A(-)B(+).
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Offline Corribus

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Re: Linear Combinations of Atomic Orbitals
« Reply #2 on: December 12, 2023, 11:25:44 AM »
Sorry, I realized "equivalent in terms of energy" was a bad choice of words. I should have said "mathematically indistinguishable". You can see this by considering the symmetry of the various (duplicate) combinations.
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What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman
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