# Questions tagged [orbitals]

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### What determines a bonding/antibonding molecular orbital?

Citing from this site: Bonding molecular orbitals are formed by in-phase combinations of atomic wave functions, and electrons in these orbitals stabilize a molecule. Antibonding molecular orbitals ...
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### Why are atoms stable? [closed]

I will ask my question in a way that's all handwaving and no math, and I will welcome handwaving answers. I'm interested in visualizing the concepts. A long time ago we had an idea about the atom as a ...
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### Physics history — the Ultraviolet Catastrophe [duplicate]

I will ask my question in a way that's all handwaving and no math, and I will welcome handwaving answers. I'm interested in visualizing the concepts. We had an idea about the atom as a massive nucleus ...
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### About the calculation of the Spin-orbit correction for the Hydrogen atom

I'm using first order perturbation theory to calculate the energy corrections due to the fine structure of the Hydrogen atom. I'm having some doubts about the calculation of the spin-orbit term. Some ...
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### How do I find expectation value of $1/r$?

I know that the expectation value of $x$ is $\left\langle \psi \middle| x \middle| \psi \right\rangle=\int_{-\infty}^{+\infty} \psi(x)^2x \,dx$. But what if I need to calculate $\frac{1}{r}$? Do I ...
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### What is the difference between angular momentum of electron by Bohr and orbital angular momentum?

Orbital angular momentum of an electron is $\hbar \sqrt{\ell(\ell+1)}$ where $\ell$ is angular quantum number. Angular momentum of an electron by Bohr is given by $mvr$ or $\frac{nh}{2\pi}$ (where $v$ ...
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### Are angles ($\theta$ and $\phi$) in spherical coordinates treated as operators in quantum mechanics?

Position is specifically considered as an operator in quantum mechanics. I want to know if $\theta$ and $\phi$ are explicitly considered as operators in quantum mechanics for solutions to 3D ...
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### Can multiple electrons transition simultaneously?

In my atomic lecture notes we prove (at least for electric dipole transitions), that only one electron can 'jump' at once. The proof is as follows. The matrix element (assuming distinguishable ...
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### Why does the antibonding orbital has higher energy (than the bonding orbital) if the Coulomb repulsion is lesser?

Depending on its strength, the attractive double dirac delta potential shown below can support two bound states. They are called the bonding and the antibonding orbitals as shown in the figure below ...
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### How can real $d$ orbitals be computed from complex orbitals?

I recently completed MIT's 8.04 quantum mechanics course on edX and have been writing python code to compute hydrogen-like electron orbitals, basically just for fun. My program computes the ...
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### When is the principal quantum number $n$ a good quantum number?

Since I don't know an associated operator to the principal quantum number $n$, I don't know when it is a good quantum number. By 'good quantum number' I mean a quantum number that is conserved over ...
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### Why does exchange occur between electrons having same spin in “degenerate orbitals”?

I am a high schooler and I read in my chemistry book that half filled degenerate orbitals are stable because electrons with the same spin in those degenerate orbitals exchange their positions and this ...
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### Can protons have orbital if they gain more energy? [closed]

I read that because a proton is much more massive than electron but an electron has slightly more energy so it doesn't fall into the nucleus and orbital is due to the constructive interference of ...
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### How to “restrict to a subgroup” to explain representation structure?

I am reading from Quantum Theory, Groups and Representations - Woit. In Chapter 21, on page 237 in discussion of the energy eigenstates of the Coulomb potential, the following figure is presented: ...
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### What actually makes a Bohr's radius stable?

I was told that Bohr introduced the concept of Stationary orbits in which electrons were stable in my school but I never got the reason behind this stability. So can someone explain why is Bohr's ...
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### How charge is explained, in context of bonding?

In ionic compounds, like NaCl, Cl gains negative charge due to addition of electrons. In covalent compounds, like Cl2, sharing of electrons occurs. Here too, Cl atom has got an extra electron in its ...
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### How to calculate the sphere of influence of a planet?

I'm making an orbit simulator, and to make it simpler, I'm only simulating one celestial object(planet, moon, sun) acting on each object(sattelite). So that the sattelites and rockets can switch ...
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### Why do relativistic effects that cause contraction of the $s$ and $p$ orbitals impact the $s$ and $o$ orbitals further away from the nucleus?

I was reading quite a well-known paper titled 'Relativistic Effects in Structural Chemistry' by PEKKA PYYKKO. In the paper, he describes how the electrons occupying $s$ and $p$ orbitals move at ...
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### Fermi Energy and single particle state

I have a question about Fermi energy and the single particle state. I have it a bit hard, on how to formulate my question, for the below text, because I don't fully understand the concepts so well. ...
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### Do actually sharing of electrons make bond?

My book says, "When we bring two atoms close, respective repulsion and attraction happens between the two's electrons and protons. Experimentally it is found that the attraction force is greater ...
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### Are all atoms spherically symmetric? If so, why are atoms with half-filled/filled sub-shells often quoted as 'especially' spherically symmetric?

In my atomic physics notes they say In general, filled sub-shells are spherically symmetric and set up, to a good approximation, a central field. However sources such as here say that, even for the ...
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### Is it better to think of electron shells as depending on the value of $n$, or depending on the energy difference between sub-shells?

Often electron shells are defined as 'states with the same principal quantum number $n$' which would suggest that $3s$, $3p$, $3d$ sub-shells are all in the same shell. Conversely, it is also often ...
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### What significance can we assign to 'breathing' of $s$-shell orbitals?

In my atomic lecture notes it says We can visualise an $l=0$ $s$-state as a spherical cloud expanding and contracting - breathing, as the the electron moves in space. Similarly in the video enter ...
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### Does Hartree-Fock method always converge to global energy minimum?

I'm not asking about whether the Hartree-Fock method will always converge, but, if it does, it seems like Wikipedia is saying that it will always converge to the global minimum energy of the TISE. ...
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### What is the ratio of energies of Hydrogen in its first excited state and second excited state?

Since Energy of an electron in a particular orbit is given by $E= -13.6/n^2$ eV So, I equated the energies in $n=2$ and $n=3$ which are the 1st and 2nd excited states respectively. The answer was 9/4. ...
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### Planetary model of the atom

Wherever I look about the early planetary model of the atom, it says the electron must lose energy while revolving around the nucleus. And therefore fall into the nucleus. Thus, the atom is unstable. ...
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### First-order perturbative correction of the ground state energy of the Helium atom in spherical coordinates [closed]

I want to calculate the first order perturbative corrected ground state energy $E^{(1)} = \langle H'\rangle$ with the perturbing Hamilton $H' = \frac{e^2}{|\vec r_1 - \vec r_2 |}$ using the spatial ...
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### Orbital Angular Momnetum Explained as simply as possible

TL;DR Why is $\ell$ defined as the shape of an orbital? And what relation does angular momentum of the electron have with the shape of the orbital? Why is the $z$-component the magnetism (why does ...
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### What exactly is the “energy” of an orbital?

In chemistry, I have come across the term " energy of orbital" several times but I am unable to understand it from a physics point of view. 1) is the energy of an orbital the electric ...
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### What do atomic orbitals represent in quantum mechanics?

I am learning the basics of quantum mechanics and am familiar with the Schrödinger equation and its solution, but I was confused about what the familiar atomic orbital shapes represent? Do they ...
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### Why does perturbation theory work for helium atoms?

I saw the following argument for calculating the energy levels of a helium atom. First, ignore the Coulomb interaction term between two electrons. For this simplified model, we have the same solutions ...
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### How do we know that the probability of finding an electron on some specific pattern is high and on other patters are not?

I have watched a video about the positions of electrons inside of an atom and on some specific patterns probability of finding an electron is high for example in- s,n,d why?
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### Why $d,f$ electrons are more localized than $s,p$ electrons？

I’m reading Assa Auerbach’s Interacting electrons and quantum magnetism. In 1.3, it says In contrast, transition metals and mixed valence rare earth compounds contribute $d$ and $f$ electrons to the ...
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### Why ferroelectricity requires empty $d$-orbitals?

I understand that ferroelectricity needs off-centre cations, but why it requires the cation to be empty or fully filled d-orbits? Ref: Multiferroicity in atomic van der Waals heterostructures Nature ...
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### How should we think about excited electron states?

Consider an atom of your choice. I wanted to have a way of organizing all of its electron excited states into some kind of mathematical structure, that was a sufficiently generic framework that the ...
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### Do the 'fine transitions' of electrons in a molecule or atom involve jumps between sublevels within a 'level', e.g. from $s$ to $d$?

Hyperfine transitions, like the (astronomically) famous 21cm line, involve just spin flips, right? And the electron jumps we first learn about in school, that release visible or near-visible photons, ...
### Ionisation energy of hydrogen: Why are kinetic and potential energy connected by $2 T = -V$ in the derivation? [duplicate]
The following is a translation from the German Wikipedia: The ionisation energy or binding energy B is the sum of potential energy V and kinetic energy T of the electron. $B = V+T$. Since the ...