Questions tagged [orbitals]

An orbital is a mathematical function describing an exact or approximated one-electron wavefunction in either an atom ( for atomic orbitals) or in a molecule (molecular orbitals).

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Do we understand chemistry from particle physics?

My chemistry knowledge is of a high-school level. In high-school, the properties of atoms were mostly presented as empirical phenomena. We learned some physical principles such as the idea that ...
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What causes bands to shift in energy or become narrow?

This is the density of states for pure palladium in bulk : This is the density of states of palladium hydride : clearly the d bands are shifting and becoming narrow. The narrowing of bands is said ...
Ajaykrishnan R's user avatar
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Atomic Sub-shell question

Which orbital of sub-shells $s$, $p$, $d$ and $f$ have Magnetic Orbital Quantum Number $m_l=0$. Like in p sub-shell, which orbital from $p_x, p_y, p_z$ will have $m_l$ as Zero? Also, how to determine ...
Samvid Sharma's user avatar
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Is there a momentum representation of the atomic stationary states?

In standard quantum mechanics, the atomic orbitals are represented by the following wave functions (where $u = 2 \mathrm{Z} r / n a$): $$\tag{1} \psi_{n l m}(r, \theta, \varphi) = \phi_{n l}(r) \, Y_{...
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Uncertainties $\Delta r$ and $\Delta p_r$ for the hydrogenoid stationary states

I'm interested in the general formulas that give the exact uncertainties $\Delta r$ and $\Delta p_r$ (the radial momentum) for all stationary states $|n,l, m \rangle$ (or $\psi_{nlm}(r, \theta, \...
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Evaluation of $\langle nlm|\frac{1}{r^2}|nlm\rangle$ [closed]

I am trying to prove that $$⟨nlm|\frac{1}{𝑟^2}|nlm⟩=\frac{1}{𝑛^3*𝑎^2*(l+\frac{1}{2})}$$ (where $𝑎$ is the Bohr radius) for the $|𝑛𝑙𝑚⟩$ state of hydrogen. I know how to do this using Hellmann–...
Keith Duong's user avatar
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How to calculate total angular momentum $L$ of partially filled $p$-orbitals?

Why has $^1D$ configuration lower energy than $^1S$ ? Hund's second rule says that for two configurations with the same multiplicity, the configuration with the highest total orbital angular momentum $...
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Measurement of electrons positions in an orbital, thought experiment

An orbital can hold upto 2 electrons. Let's take 1s orbital of helium. Now, we use probability density to depict where we can find the electrons in the orbital if we make measurements. Since two ...
LuffyYadav's user avatar
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4 answers
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Is Bohr's model one-dimensional?

Purdue university in its article on Bohr's Model explains: At first glance, the Bohr model looks like a two-dimensional model of the atom because it restricts the motion of the electron to a circular ...
Govind Prajapat's user avatar
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Why aren‘t other metals colored?

From an online lecture, I heard that $d$ orbitals cause metals to have a peak in their reflectivity curve at some wavelength. This is generally the case for most metals. However, the peak lies mostly ...
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How was Rutherford's model of an atom wrong?

They mention that Rutherford's model of an atom was wrong as in a circular orbit the electron would accelerate and hence radiate energy along with electric and magnetic fields. But why does the ...
Unknxwn's user avatar
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Electric fields created by electrons

If I want to calculate the electric field inside the $1s$ cloud of an atom. Do I have to consider the protons only or the electrons too? If I take the electric field created by protons only then won't ...
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Is there an Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotential of $\rm Eu$ atom?

I'm currently finding an Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotential of $\rm Eu$ atom which has a localized $f$-orbital. But no matter how much I search in online, I can't find that. ...
Y. S. Lym's user avatar
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Total angular momentum $j$ and the total magnetic quantum number $M$

I'm not sure if I am overcomplicating things with this question, but I have a question where we have a beryllium atom where its outermost electron is excited to the 3p orbital state. I have each ...
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Isotopes and electron transitions

Do neutrons in the nucleus (isotopes) affect the frequency of electron transitions through valence shells?
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Bohr‘s rule $2n^2$ and Schroedingers equation [closed]

Bohr's model of electron orbitals is outdated. To what extent has Bohr's rule of atomic structure with $2n^2$ electrons per shell been redescribed? Is the Schroedinger equation based on Bohr's rule ...
HolgerFiedler's user avatar
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Is there a misinterpretation of NIST data, in this conclusion about the order of 4s and 3d, in neutral scandium, contradicting HF calculations?

Is there a misinterpretation of NIST data, in this conclusion about the order of 4s and 3d, that contradicts Hartree Fock calculations? I understand that it is a clear conclusion based on Hartree Fock ...
barlop's user avatar
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Varying mass of electron in an atom

Let's take a heavy atom (since velocity of electron is high in it) and project it with relativistic velocity. So the electron revolving around the nucleus in partial particle - wave character can have ...
Le nerd's user avatar
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Solar-system model of atom [closed]

Smart people, like us, poo-poo people who think of the atom as a mini solar-system with electrons orbiting the nucleus, like planets. We talk about smeared out probability waves etc. But, given wave-...
john's user avatar
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What does the energy of the electron in the energy level of an atom really mean?

I am confused about the meaning of the energy of the electron in the energy level of the atom. How does an electron have a higher energy in a higher energy level and at the same time, it can be ...
Rahal's user avatar
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What is the difference bewteen atomic orbitals and wannier functions?

They both use the "s, px , py, pz, dxy...." formalism Both of them are in real space. Wannier is orthogonal but atomic orbitals are not... But what's the fundamental difference between them?
雾岛董香's user avatar
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Why are lithium and beryllium such good conductors but not chlorine?

Why are lithium and beryllium so conductive? The $2s$ band has a much different energy range from the $2p$ band, so I guess the only explanation is that $N$ states are empty. But if that was the case, ...
Root Groves's user avatar
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Confusion with Hund's rule

Hund's first rule states: The term with the largest possible value of $S$ for a given configuration has the lowest energy. But, in practice, in order the find the ground state, we fill up the ...
Solidification's user avatar
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Moments of hydrogen orbitals/Transition dipole moments

I'm interested in calculating transition dipole elements for atomic transitions. This means I would like to calculate things like $$ r_{nlm,q}^{n'l'm'} = \langle\psi_{nlm}|r_q|\psi_{n'l'm'}\rangle $$ ...
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Could an electron wavefunction wrap multiple times around its orbit?

In the Bohr model a whole number of electron de Broglie waves with $\lambda=h/mv$ fit around an orbit with radius $r$ so that we have: $$2\pi r=n\lambda.$$ But could the electron waves wrap around the ...
John Eastmond's user avatar
3 votes
1 answer
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Molecular orbital notation

I'm reading about papers about atom-ion interaction. There are some states as showned above. The notations of the states look like molecular orbital since $\Sigma$ and $\Pi$ is usually used in orbital ...
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How to calculate the $d$ orbital energy from Atomic Spectra Database?

I am struggling to understand how to calculate the $d$ orbital energy of the Fe atom. I tried to search the $\text{Fe I}$ in the Atomic Spectra Database, so I thought I could use the energy difference ...
Jack's user avatar
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How to find the standard atomic orbital energy data?

I found a website that provides the $d$ orbital energy of atoms. The data were found using Photoelectron Spectroscopy, which measures the energy needed to ionize electrons from atoms in the gas phase. ...
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Why are electron orbitals shaped how they are?

I'm new to quantum physics, but as far as I've understood, electron orbitals are defined as the region where an electron has a 90% probability to be. Unless I'm wrong, every point has some probability ...
Atharv Rao's user avatar
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5 answers
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Bohr model of the atom

According the classical physics, the electron should radiate energy and fall to the nucleus in a short period of time. However, this was not the case. Hence, Bohr proposed his theory, suggesting that ...
Quin Gardiner Bax's user avatar
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Understanding Dirac's argument for the indistinguishability of electrons

In his paper 'On the theory of quantum mechanics' (1926), Dirac makes the following argument for why electrons should be considered indistinguishable: Consider now a system that contains two or more ...
APK92's user avatar
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$p$-like or $s$-like bands

What do people mean by $p$-like or $s$-like band structures? I know that d- or f-type electrons are typically more localized, while p and s-type electrons are typically more delocalized, but how would ...
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Do attosecond lasers allow us to further constrain the location of electrons within the established probability clouds, via time?

It has only been within the last few years that I learned the atomic model I grew up with (the Bohr model) was wrong, and that I should instead be thinking about electron orbitals as a cloud of ...
Curious Layman's user avatar
2 votes
1 answer
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Tight binding on a square lattice with three orbitals symmetries

I came across a tricky problem while studying tight binding within the second quantization frame: Consider a square lattice with one atom per unit cell, where each atom has three active hydrogen atom ...
Chris Ze Third's user avatar
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Books on Hyperfine Splitting (Theoretical Physics)

Do you have any good recommendations on books (theoretical physics) about hyperfine splitting?
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Why is there an exponential in the radial component of the hydrogen electron orbital wavefunction?

The solution for the Schrödinger equation for an electron in a (spherically symmetric) potential well shaped like $V=1/r$ is described by a wave function of the form $\Psi_{nlm}(r, \theta, \phi) = R_{...
acdr's user avatar
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What happens to left-over energy in atomic excitations?

The question relates to quantization of energy. As we know, to make an electron jump to a higher energy level, a discrete amount of energy must be given to it. If the energy provided is less than the ...
washikiballa's user avatar
2 votes
2 answers
214 views

Why using real wave functions instead of complex ones?

I have already seen similar questions asked in the site (like this or this), but I don't feel that my question has been fully addressed. I understand that orbitals $np_x$ and $np_y$ are linear ...
efrenump's user avatar
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Franck-Condon principle

I am having trouble understanding the Franck-Condon principle for radiative transitions and would be very thankful for any help. Why do we have multiple different wave functions for the exact same ...
velo's user avatar
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1 vote
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What is the interpretation of these hydrogen probability density diagrams?

In the diagram above, what is the interpretation of all of the individual renders? Does the hydrogen atom continuously change between these states? For example, will $(n, l, m_l)$ become $(2, 0, 0)$ ...
JBatswani's user avatar
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Signal in hopping term in diatomic chain using the tight binding method

I am currently studying the tight binding method, and while solving solving a problem I came across something I don't understand. There are two atoms A and B, A has only type s orbitals and B has only ...
Ana Branco's user avatar
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Which is higher enegy/outermost, $s$ or $d$ orbitals of transition metals?

The outermost electron shell of Au is 6s but the highest energy orbitals electrons occupy is 5d. Likewise, the outermost shell of Co is 4s while the highest energy orbit is 3d. Are these correct? I've ...
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Double nomenclature of molecular orbitals

I'm studying molecules from Brandsen-Joachain's book: "Physics of atoms and molecules". In chapter 9 he talks about molecular orbitals, and then he specifically talks about them for ...
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Would there be any way to avoid gravitational waves emission in some orbital configurations?

In principle every object orbiting another (e.g. a planet revolving around a star) would emit gravitational waves, relaxing the orbit over time. ​ However, this would not happen if the orbits had a ...
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Physical meaning of Russell–Saunders and $jj$ coupling

In the case of Russell–Saunders coupling (LS coupling), the total $L$ and total $S$ are coupled to a total $J$. In the case of $jj$ coupling, first, all the individual $j = l + s$ values are formed, ...
QuantumQuasar's user avatar
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For hydrogen atom wave function, why eigenstate of Hamiltonian isn't only spherical harmonics if $H$ commutes with square of angular momentum? [closed]

I was reading quantum mechanics and I read about CSCO. So, commuting operators should share common eigen states, does that mean same eigen states? because in hydrogen atom wave function, Hamiltonian ...
Shuvajit Dutta's user avatar
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Why does electrons only acquire certain energy levels around an atom? [duplicate]

According to Bohr's hypothesis electrons can exist only at certain special distance from the nucleus only on certain particular orbits which is determined by Planck's constant, how does reach to this ...
Bhavya Singh's user avatar
8 votes
2 answers
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How "wide" are absorption and emission lines?

There are various absorption lines that correspond to the difference in energy levels between electron orbits. E.g. the https://en.wikipedia.org/wiki/Lyman-alpha_line correpsonding to the difference ...
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QM - States with same orbital angular momentum quantum number but different magnetic quantum number are equiprobable

I'm studying the hydrogen atom. My professor says that in a spherically symmetric problem, the choice of the $z$-axis is arbitrary and so, given a fixed value of the orbital angular momentum quantum ...
Tom Avery's user avatar
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Can we use hybridised orbitals in Tight-Binding Method for calculation energy dispersion?

I am working on a model of a Fe square planar complex with nitrogen and oxygen given below is a monomer of that polymer. While constructing the hamiltonian matrix of this monomer I'm confused as to if ...
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