31
votes
What is the physical basis for Hund's first rule?
Disclaimer
My following answer is the "traditional" explanation of Hund's first rule, which is based on a smaller value of $V_\mathrm{ee}$ (electron-electron repulsions) in the triplet state arising ...
- 70.1k
22
votes
Accepted
What is the physical basis for Hund's first rule?
The lowest energy state has parallel spins to maximize the exchange energy.
As you say, there's a Coulomb repulsion between two electrons to put them in the same orbital.
There's also a quantum ...
- 27.5k
22
votes
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Do Electrons Really 'Spin'?
It depends on what you mean by "spin".
If you mean "have intrinsic internal angular momentum, independent of its trajectory through space", then yes, electrons spin, and that's what the quantum ...
- 4,826
18
votes
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How to convert from spin orbitals to spatial orbitals in the Hartree-Fock approximation?
Technical Note: This page makes heavy use of MathJax, give it time to load.
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\newcommand{\op}[1]{\mathbf{#1}}
\newcommand{\ve}[1]{\mathbf{#1}}
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- 43.5k
12
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Do Electrons Really 'Spin'?
Despite the success of the Schrödinger Equation in predicting energy levels of the hydrogen atom, experimental observations suggest that it doesn't tell the whole story of electron behavior in atoms.
...
- 18.4k
12
votes
What is the physical basis for Hund's first rule?
Some understanding can be gained by looking at the symmetry of the orbital parts of the wavefunctions involved.
The total wavefunction for electrons must be anti-symmetric with respect to exchanging ...
- 28.6k
12
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Why do spin isomers of hydrogen (ortho and para hydrogen) change their nuclear spin with temperature variance?
The effect is due to the symmetry properties of the rotational energy levels and those of the nuclear spin. The change with temperature is, as usual, traced back to the Boltzmann distribution.
In ...
- 28.6k
11
votes
Can an organic molecule have a triplet ground state?
As Martin has mentioned, carbenes are a good starting point if you are looking for organic compounds with a triplet ground state.
In these carbenes, the HOMO is not twofold degenerate, as your ...
- 70.1k
11
votes
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Name for a spin state with a multiplicity of 13
I have seen multiplicity 13 referred to as simply a 13-let. This #-let nomenclature is sometimes used for high multiplicities (e.g. higher than 10).
- 1,332
11
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Difference between spin-orbit coupling and the Russell-Saunders Effect?
I'm not aware of the Russell–Saunders effect, but the Russell–Saunders coupling scheme is definitely a thing. As you noted, the Wikipedia page on "spin-orbit interaction" doesn't talk about ...
- 70.1k
11
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Can an electron be excited to a spin state with s ≠ 1/2?
The major mistake is considering a nucleus like if it were an elementary particle.
Compare a nucleus spin configuration to spin electronic configuration of atoms. In both cases, there are multiple ...
- 35.8k
10
votes
What does an electron's spin of 0.5 and minus 0.5 signify?
It is very tempting (and often also very useful!) to picture electron spin as an angular momentum vector, similar to a spinning top. Using this analogy, there are two properties (or numbers) of this ...
- 2,376
9
votes
Can an organic molecule have a triplet ground state?
There are various examples of molecules in triplet ground state. The smallest (organic) is possibly methylene, $\ce{:\!CH2}$.
Carbenes in general may adopt triplet state as their ground states.
...
- 43.5k
9
votes
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Atoms or molecules with spin 1 in the ground state?
Atoms
Atomic carbon with its $\mathrm{1s^2 2s^2 2p^2}$ configuration has a triplet ground state ($S = 1$), precisely because of Hund's first rule.
However, in the context of the Stern–Gerlach ...
- 70.1k
8
votes
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Are nuclear spin isomers "allotropes"?
Some peer review journal articles and an India high school textbook and various study guides do refer to the spin isomers as allotropes.
There are physical differences such as different heat ...
- 39.8k
8
votes
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Carbon-13 NMR for chloroform
You assumed that coupling to the three chlorides would yield some type of quartet. This is correct in principle. However, chlorine is one of the many quadrupole nuclei that are basically unobservable ...
- 66.4k
8
votes
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Mechanism for interconversion of spin isomers of hydrogen
The first question is:
What is the mechanism by which spin isomers of hydrogen switch between the ortho and para forms?
There is some explanation in ChemPhysChem 2006, 7 (3), 551–554 (non-paywall ...
- 39.8k
8
votes
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Are electrons in a helium atom diametrically opposite?
Throughout your question it is clear that you are considering electrons as particles. This is not entirely incorrect; for example, the cathode ray tube is best explained by electrons being considered ...
- 66.4k
7
votes
Atoms or molecules with spin 1 in the ground state?
Triplet oxygen has two unpaired electrons with the same spin, and a total spin value of 1.
In fact, by Hund's rule, the triplet states are preferred over the singlet states which have two electrons ...
- 17.2k
7
votes
What accounts for the high spin state of the complex Tris(acetylacetonato)iron(III)?
I will go into the theoretical details first and come to the practical answer for your exact case later; separated from the theory by a horizontal rule.
Approaching the complex theoretically, our ...
- 66.4k
7
votes
2 electrons with the same spin in the same orbital
It is impossible. Having two electrons with the same spin in the same orbital is a violation of the Pauli exclusion principle.
- 241
7
votes
Electron has volume or not?
If volume is understood classically, i.e. as the quantity of three-dimensional space enclosed by a closed surface, then quantum systems in general do not have a certain volume. One could, in principle,...
- 18.8k
7
votes
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NMR - coupling of chemically equivalent protons
The "n+1" rule refers to a situation where you have a proton of type A with $n$ protons of type B next to it. Proton A's signal will be split $n+1$ times by the B's. However, none of the B's will ...
- 17.2k
7
votes
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Grasping the concept of Electronic Spin, Effective Spin and Fictitious Spin
Here's what I believe they're trying to say.
First, note that the discussion is mostly limited to high spin complexes (3 unpaired electrons out of the 7 d electrons), so the figure you reproduced is ...
- 10k
7
votes
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Why are most organic molecules diamagnetic, when most of them have non-paired nucleus spins?
As requested, this is my answer:
The question is essentially about why nuclear contributions to magnetic behavior is generally neglected.
It is true that both nuclei and the electrons can carry ...
- 5,323
6
votes
Is the reasoning of spin contamination correct?
Commuting operators indeed admit a set of simultaneous eigenfunctions, and since the non-relativistic electronic Hamiltonian commutes with total spin operators $\hat{S}_{z}$ and $\hat{S}^{2}$, the ...
- 18.8k
6
votes
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Why is a spin change favourable in intersystem crossing?
There are two things going on here. You have conflated with "forbidden" with unfavorable. In many systems, the first excited triplet is lower in energy than the first excited singlet. Hence, the order ...
- 3,022
5
votes
Are nuclear spin isomers "allotropes"?
Apart from the sources that DavePhD listed, there is also the 1932 Nobel Prize in Physics, awarded to Werner Heisenberg:
"for the creation of quantum mechanics, the application of which has, ...
- 70.1k
5
votes
Why only one peak is observed in NMR spectrum of H2?
For starters, it is incorrect to think of the ground state being substantially more populated in NMR spectroscopy. Because the energy difference between aligned and misaligned nuclear spins in the ...
- 66.4k
5
votes
A question on spin of an electron
No, electrons (and other leptons) are fermions and therefore must have half-integer spin. It is possible to couple the spin of several electrons together to obtain an integer total electron spin. ...
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