Questions tagged [orbitals]

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How are hybrid orbitals more energetically favorable than their components?

In the orbital hybridization theory, the $s$ and the $p$ orbitals are said to combine to form hybrid orbitals which are degenerate in energy. How does the linear combination of the $s$ and $p$ ...
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92 views

How come the xenon $6s$ state is metastable?

I'm having some trouble puzzling out some aspects of the electronic excitation spectrum of xenon, and I'd appreciate some help with it. This classic paper ─ the first one to pioneer the use of laser-...
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1answer
149 views

In chemical compounds, where does the “magic” come from in atomic “magic numbers”?

It is well known that atoms with a full electron shell are more stable, it is one of the first facts taught in a middle school Chemistry course: "An element whose atoms have no electrons outside ...
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54 views

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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37 views

What does $LS$ coupling and $jj$ coupling signify?

When we consider $1s2p$ electrons in $LS$ coupling we get one singlet and one triplet but in $jj$ coupling, we get $2$ doublets. I know the mathematical (quantum number) work behind it. But what I don'...
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29 views

Do the electron pair in an orbital, have a net orbital magnetic moment?

It has been made clear to me that 2 electrons in an orbital have opposite spins, and hence their spin magnetic moment nullify each other. But does the same happen with the Orbital magnetic dipole ...
2
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1answer
55 views

Can an electron transit within the same $n$-level?

Under selection rules for multi-electron atoms in LS coupling, its generally written that there is no restriction on the total quantum number $n$. Does it mean that an electron transit within the same ...
2
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2answers
61 views

Number of nodes in Hartree-Fock solution

The Hartree-Fock equation for atoms is of the form $\left[\frac{d}{dr^2}+f(r)-\epsilon\right]P(r)=g(r) \tag1$ Usually algorithms to solve this equation assumes that the number of nodes of $P(r)$, ...
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42 views

Question on Kleinman-Bylander pseudopotentials

When Kleinman-Bylander pseudopotentials are used the Hamiltonian operator is given by $$\hat{H} = -\frac{1}{2}\nabla^2+V_{\textrm{local}}+\delta \hat{V}_{\textrm{NL}}$$ where $$\hat{V}_{\textrm{NL}} = ...
2
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36 views

What exactly does it mean for an element to experimentally violate the Madelung ordering rule?

The Madelung ordering rule says that as you increase the atomic number of a neutral atom, the electron orbitals fill up in order of increasing value of $n+l$, and in increasing order of $n$ within a ...
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43 views

What are the prerequisites for a free electron and an atom/ion to recombine?

I'm mostly interested about recombination not in plasma (e.g., recombination of beta particles with atoms that they pass by), although the rules are probably the same. Say, there's a free electron ...
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48 views

A question about almost stationary orbits

For an orbit around the earth with period equal to a sidereal day with eccentricity $e=0$ and inclination $i=0$, the path on earth would be a single point on the equator. I have done some simulations ...
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1answer
250 views

Physical Intuition for thermodynamic limit of the average occupancy, $\langle N\rangle$, of an orbital

Say your allowed occupancies for an orbital are $0, 1, 2$, and the values of energy associated with these occupancies are $0, \epsilon, 2 \epsilon$. Give an expression for the ensemble average ...
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124 views

Gravitational aberration and unstable orbits

From this link http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html it says that Putting a "light travel delay" (technically called "retardation") into newtonian gravity would make ...
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1answer
85 views

The Existence of the $^1D$ term and the non-existence of the $^3D$ term?

Yesterday I asked this question concerning the existence of terms. This question is on the same topic. I have been looking at some tables (in Yang and Hamilton (2010), pg 199) at the terms that exist ...
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57 views

Is it possible to reach orbit without turning the rocket?

A comment to this question sparked my interest. If we start a rocket from the surface at the equator, it has some angular momentum with regard to Earth. This angular momentum is definitely much too ...
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256 views

Hund's rules on wikipedia

I'm trying to understand the examples on Hund's rules on Wikipedia, but I have a problem. Wikipedia says that for Silicon the possible combinations of quantum numbers are $1D$, $3P$ and $1S$ (first ...
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59 views

A question on energy levels of molecular orbitals

Here is a phenomenon from MO theory for diatomic homonuclear molecules that I could not understand. If $Z \le 7$ then $\sigma_{2pz}$'s energy is higher than $\pi_{2px}$'s energy. I did not get ...
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1answer
56 views

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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1answer
39 views

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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35 views

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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23 views

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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36 views

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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25 views

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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24 views

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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33 views

How to couple the $^3p_2$ with $d_{5/2}$?

The first two electrons' LS term is $^3p_2$,how can this term coupling with another electron $d_{5/2}$?(this electron in another shell) for $^3p_2$,$L_{12}=1$,$S_{12}=1$,and only the orientation of $...
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61 views

Do different eigenstates of total angular momentum have necessarily different energies?

Let $H$ be the Hamiltonian of a specific atom (not hydrogen) and $J$ the total angular momentum. Since $H$ and $J$ commute, they have common eigenstate. So we can label the atomic states by their ...
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1answer
39 views

How to determine possible term symbols in case there are more than 2 electrons

I'm doing some exercises on $LS$ coupling during my self-study of atomic physics. I understand how to construct a table of possible microstates. I also understand how to map term symbols to those ...
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62 views

Double zeta polarised, triple zeta double polarized. What is the definition?

I understand that a single zeta basis contains the hydrogen stationary states $\psi_{nlm_l}$ for a particular selection of quantum numbers $(n,l,m_l)$. You can decide the quantum numbers that will be ...
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36 views

Visualization of a system of two electron orbitals

There are many clear and beautiful 3D pictures of different orbitals of a single electron: sphere-symmetric s orbitals, p-, d- and so on. But what is about systems of many electron? In this case ...
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1answer
129 views

Expansion of the Bohr-Sommerfeld Model to any atomic/molecular system

I know that the Bohr model of the atom was modified by Sommerfeld to include elliptical orbits, and that the resulting Bohr-Sommerfeld theory has long been put aside in favor of quantum mechanics. ...
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41 views

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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49 views

Naive question on the development of quantum numbers

In my freshman Chem 101 course, we are going over the development of the atomic model upto the basic modern quantum model. I learned that the azimuthal and magnetic quantum numbers were introduced to ...
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27 views

Determining the binding energy in the L-shell in copper

Im having trouble grasping the following problem: Calculate the binding energy in the L-shell for copper, if the binding energy for the K-shell is $ \ 1,439*10^{-15} J\ $. I know that you find the ...
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52 views

Has man ever observed the spectrum of a single hydrogen atom?

Were there this kind of experiment done before? The spectrum we observed is radiated by huge number of hydrogen atoms in the gas, not by single hydrogen atom. I know it's very hard to test a single ...
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23 views

Crystal Field Theory (CFT) in $s$-$p$ orbitals system

Crystal Field Theory (CFT) is a model that describes the breaking of degeneracies of electron orbital states, usually d or f orbitals (Source: wiki). My doubts: Is it possible to have CFT effect in ...
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35 views

How to calculate orbital densities/shapes of atoms in 3D?

When we read about orbitals, I'm sure we are all used to seeing illustrations of them by drawing some contour "along" the probability density function so that the electron's position is equiprobable ...
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72 views

How can I calculate the hyperfine structure of a $p$-orbital?

I have a little problem with the calculation of the hyperfine structure of the 3p orbital in the hydrogen atom. The Hamiltonian is: Were represents the magnetic moment of the proton and the ...
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62 views

In the pilot-wave theory, is the quantum potential moving electrons randomly inside atoms?

As we know, in the pilot-wave theory (Bohmian mechanics), particles are guided on certain trajectories by the wavefunction. Here (In Bohmian mechanics, do electrons move inside an atom?) I asked about ...
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100 views

When will Hund's rules fail?

I heard someone mentioned that Hund's rules do not always work. Looking at atomic spectrum: (https://qudev.phys.ethz.ch/phys4/PHYS4_lecture10v1_2page.pdf page 10 Hg spectrum) How could singlet (with ...
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1answer
144 views

A dreidel on a spinning table

In the spirit of the holidays. Let's assume that a dreidel is spinning counter-clockwise at frequency $f$ on a table. From external point of view, what will I see if I rotate the table clockwise at ...
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156 views

How to use Hund's third rule for excited electronic configurations?

Hund third rule states: For a given term, in an atom with outermost subshell half-filled or less, the level with the lowest value of the total angular momentum quantum number ${\displaystyle J\...
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37 views

Orbitals and configurations with degenerated energy

When we have to choose, given $n$, $\ell$, where to put an electron, when there are several $m$ orbitals, with the same energy, is there a concrete quantum mechanic rule or some superselection rule to ...
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25 views

Spin in 3d orbitals of 2 irons

Which technique/method/theory must I use in order to calculate/see what happens at the spin of 3d orbitals when two atoms of Iron come close?
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864 views

Electron Levels of Atomic Nitrogen Vs. Molecular Nitrogen

So I have a question about the the affect of the electron energy levels of Nitrogen when it becomes diatomic. In Figure 1 below you see the electron energy levels of atomic Nitrogen, and it shows that ...
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60 views

How does the filling of the 2p orbitals occur?

When electrons enter the 2p orbitals, electrons of the same spin occupy the 2p orbitals first and then electrons of the opposite spin fill up the orbitals. Why is that? My professor told me that there ...
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33 views

Surface potential and symmetry breaking

I am studying surface states currently and am a little confused about something. If I consider p-orbits on a surface state that is the top layer of an HCP structure -- I understand the hopping terms ...
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1k views

How do the Fermi level, HOMO and LUMO change with doping?

I am a bit confused about solid state physics of organic materials because as I know the workfunction changes with the doping of a material but the Fermi level is constant with doping. So depend on ...
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1answer
28 views

Hybridisation of orbitals

When we talk about the electronic configuration of boron , sulphur , nitrogen. What I got to learn new was about their hybridisation. For example , boron has electronic configuration as $1s^2 2s^2 2p^...
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17 views

What are the possible orbital occupation for a triplet state?

I am trying to run some Hartree fock calculation for interaction between an atom and a molecule. The molecule is in its triplet state and i have to indicate the orbitals that these unpaired electrons ...