Linked Questions

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2answers
460 views

Why is up spin in the px orbital and down spin in the py orbital considered an excited state? [duplicate]

Why is this form of p orbital occupation an excited state? I understand that there should be one up spin and one down spin in one orbital box by Pauli's exclusion rule. But in the p orbitals, it doesn'...
30
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2answers
3k views

What is the exchange interaction?

As the wikipedia article for the exchange interaction so aptly notes, exchange "has no classical analogue." How wonderful. Exchange shows up essentially while enforcing the condition that two ...
14
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5answers
3k views

Why does the two-electron exchange integral in Hartree-Fock theory have positive values?

In Section 2.3.6 of Szabo & Ostlund's Modern Quantum Chemistry, the exchange integral has the form of $$\int \mathrm{d}\mathbf{r}_1\,\mathrm{d}\mathbf{r}_2\, \psi_a^*(\mathbf{r}_1) \psi_b(\...
11
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2answers
18k views

Why are full and half filled orbitals the most stable?

Why are degenerate orbitals (restricted to a single spin) less stable when neither fully filled nor completely empty? Why, in most molecules, are half-filled and fully-filled shells more stable than ...
9
votes
1answer
19k views

How do I find the ground state term symbol for transition metal complexes?

I have a problem where I'm trying to match metal complexes with the proper ground state term symbol. I've tried doing a Google search and looking for a process, but haven't had any luck. I decided ...
10
votes
1answer
8k views

Derivation of the Orgel diagram for octahedral d2 complexes

The Orgel diagram for a typical octahedral $\mathrm{d^2}$ complex is shown below: (source: Kettle, Physical Inorganic Chemistry, p 146) I understand that the right-hand half of the graph shows how ...
11
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2answers
520 views

Hartree-Fock dipole moment

I read this sentence in a paper (J. Phys. Chem. A 2014, 118 (20), 3678–3687. DOI: 10.1021/jp502475e): Calculations using Hartree–Fock theory systematically overestimated dipole moments and ...
-1
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1answer
2k views

Half-Filled Shells and Stability explanation [duplicate]

I am reading a book about Advanced Chemistry, and it is discussing the subject of half-filled orbitals. The book notes that Chromium has an electron structure of $1s^2 2s^2 2p^63s^23p^63d^54s^1$ ...
4
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1answer
199 views

Spin interaction term for a two-particle system of fermions with a potential that contains spin-spin interaction

Consider a two-particle system consisting of two identical fermions in a potential $$V(\vec{r})\vec{\sigma_{1}}\cdot\vec{\sigma_{2}}$$ where $V(\vec{r})$ is the spatial part of the potential and the ...
4
votes
1answer
242 views

Volume of orbitals

As I was learning about atomic structure, the lecturer made a seemingly dubious claim: The volume of a p orbital is one-third that of the s orbital. Thus, inter-electronic repulsions are ...
-3
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1answer
534 views

Identical particles: Why is triplet oxygen more stable than singlet oxygen?

Quoting from Eisberg Resnick Quantum Physics: If we consider space variables of two electrons (identical particles) to have almost the same values, then their wavefunctions are 'almost' identical ...
4
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0answers
264 views

Relative energies of singlet and triplet states in Jablonski diagrams

In a Jablonski diagram, we have singlet and triplet excited states where spin is conserved or changed, respectively. My book says any singlet excited state is found to have higher energy than the ...