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Questions tagged [spin]

Spin is a type of angular momentum which is intrinsic to atomic and sub-atomic particles. Electrons in orbitals can be either spin paired or spin unpaired which influences the magnetic properties of the species containing these orbitals.

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Mulliken Spin Density

I would like to know if a Mulliken population analysis to calculate spin densities is in general a valid choice. I see that it is made use of, for example here1. So up to-date researches apparently ...
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How long would it take for a tank of same-spin hydrogen atoms to become a tank of H₂?

In the question Is there an energy cost associated with flipping the spin of an electron?, it is shown that it is very unlikely for two hydrogen atoms to bond if their electrons have the same spin. ...
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"Alternative" derivation of the spin-only formula

The spin-only formula $$\mu_\mathrm{so} = \mu_\mathrm{B} \sqrt{n(n+2)} = \mu_\mathrm{B}\cdot 2\sqrt{S(S+1)}$$ is usually a good first approximation to calculate the magnetic moment of transition ...
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What is the magnetic moment of potassium hexacyanochromate(II)?

I calculated the magnetic moment of $\ce{K4[Cr(CN)6]}$? in the following way: $\ce{Cr^{+2}}$ has $4$ d electrons. And since $\ce{CN-}$ is a strong field ligand, the electrons will pair up in the $\...
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Why is spin-contamination undesirable?

Why is spin-contamination, introduced by e.g. Unrestricted Hartree Fock, undesirable, and to which problems further on can it lead? The only problem I currently see myself is that spin-contamined ...
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Why does diamagnetic current induce a downfield while the paramagnetic current induces an upfield shift?

I know that aromatic rings exhibit diamagnetic ring currents which causes the protons outside the ring to go downfield in H-NMR. Antiaromatic compounds exhibit paramagnetic ring currents which have ...
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How to calculate the spin of atomic nuclei?

I have recently been learning about nuclear magnetic resonance spectroscopy. It is mentioned that the spin of the $^{1}$H nucleus is $\frac{1}{2}\ $and the spin of the $^{2}$H nucleus is $1$. This ...
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Integrating out spin in 2-electron energy function

I am just starting to learn Quantum Chemistry for my research. I am currently reading Modern Quantum Chemistry by Szabo and I am a little confused by a concept. The two-electron ground state energy is:...
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Ground state term symbol, why is $L = |M_L|$, if L must be a maximum?

I'm trying to understand how to predict ground state term symbol of atoms. After finding the biggest S, why the biggest L will be $L = |M_L|$, where $M_L = \sum m_l$? I know this rule works to ...
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What is the origin of the spin selection rule?

Why is the change in total spin ∆S = 0 during an absorption of a photon, in contrast to the ∆L = ±1, where the photon transfers its angular momentum? I am aware that spin-orbit coupling breaks this, I ...
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Orientation of spin polarization in O2

Oxygen gas in ground state is spin polarized. Is the direction of its spin (significantly) correlated to the orientation of the double bond? I googled "orientation of oxygen magnetic moment" ...
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Fermi Contact Interactions and resultant coupling contants

I am currently learning about spin-spin coupling mechanisms and have become very confused about the mechanisms by which spin-spin coupling happens in NMR. I understand how we can draw diagrams where ...
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Direction of spins in the singlet vs. triplet state

Suppose we consider the first excited state of the helium atom. We know that the first excited state of helium can exist as a triplet or singlet. The possible functions related to the spin of the two ...
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Spin Multiplicities of Ions

The multiplicity is fundamentally defined as $2S + 1$ where $S$ is the total spin. From what I understand, the multiplicity corresponds with the number of unpaired/paired electrons. For example, in ...
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Nomenclature of This State?

I've read this in a book It says the state having three parallel spin is called triplet state . But as far as I know it is determined by "2S+1", from this it comes out to be 4 . Then how it is "...
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Why do protons in same chemical environment do not exhibit spin-spin coupling?

Reading introductory tutorials on proton NMR for the determination of chemical structure, I was told that protons can exhibit spin-spin coupling, thus creating multiplets on an NMR graph. The coupling ...
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Spin-preserving excitations

I'm currently working on quantum chemistry with quantum machine learning and one of the operations considered for the calculation is the excitation (and desexcitation) of an electron from an orbital ...
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Electronic vibrational rotational transition of electrons -- for a transition from $\Sigma$ to $\Pi$ how are P and R branches possible?

Suppose we have a diatomic molecule in a $^1\Sigma$ state, and it transitions to an excited $^1\Pi$ state. Note that the total spin of the electrons remains unchanged ($\Delta S=0$) as we can assume ...
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How can I determine the spin of a molecule?

I was reading statistical mechanics today and came across a line For $\ce{O2}$ and $\ce{N2},$ we get half-spin, and that is why we get $σ = 2$ in their rotational partition equation. I didn't ...
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Why is it important to know the spin of bioinorganic complexes?

During a bioinorganic chemistry course, my teacher gives a lot of importance to spin states of metal ions and how they changes (or not) after the formation of a complex. For example, when hemoglobin'...
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Why ¹H–¹⁴N coupling is not observed in ¹H NMR

Since the nuclear spin value of $\ce{^{14}N}$ is $I = 1$, we should expect a coupling between $\ce{^1H}$ and $\ce{^{14}N}$. Hence, the proton peak in a primary amine $(\ce{-NH2})$ should split in a ...
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Determining absorption spectrum, magnitude of Δo and spin for Iron Oxalate

Iron Oxalate ions form an emerald green solution when dissolved. If the ions in solution appears emerald green to our eyes, what color of visible light is it mostly absorbing? What does that tell you ...
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How fast do electron's quantum spin flip?

In a recent lecture it was taught that carbenes with their electrons in a triplet configuration do not undergo concerted reactions as one of the electrons must first undergo a spin flip; on what ...
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What's the most up to date explanation for the stability of high multiplicity states?

"However, accurate quantum-mechanical calculations (starting in the 1970s)... singly occupied orbitals are less effectively screened or shielded from the nucleus, so that such orbitals contract ...
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Do all p orbitals really have the same energy?

If we solve the time-independent Schrödinger equation for any atom by considering only the electrostatic potential, an electron has the same probability of occupying the $p_{x}$ orbital as it does the ...
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Is the number of particles with opposite spin roughly equal?

I was reading about the Pauli exclusion principle and this question occured to me about the electron. It can be +1/2 or -1/2 spin. And usually atoms outside stars (where it is cool enough to attach ...
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Why are HOMO and LUMO energies invariant under spin-flip?

Atomic theory says singlet and triplet energies for the same orbital differ because of exchange interaction. However, molecular orbital (MO) theory describes the energy between the HOMO (highest ...
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the ratio between high spin state and low spin state when they coexist

I am considering the spin state's effect on the charge carrier's lifetime, I was told that high spin and low spin state could coexist when the crystal field splitting energy and the pairing energy are ...
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T1 spin-lattice relaxation times, deviation from exponential relationship

For longitudinal relaxation, one would think that the magnetic moment obeys this simple relationship $$M_z = M_0\left[1 - 2\exp\left(\frac{-t}{T_1}\right)\right].$$ However there is always a point ...
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Electron Spin, and the Stern-Gerlach Experiment

I think I understand the basics of the electron spin. However, I'm trying to figure out how to tell if, when shooting a beam of atoms (the Stern-Gerlach experiment), how to tell if an element will ...
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Degeneracy of Orbitals

(Sorry, in advance if my question is silly or low quality but I want to ask this to someone.) When an electron enters an orbital, it should technically have an electric Field and also magnetic field(...
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