Questions tagged [orbitals]

An orbital is a one-electron wavefunction, usually derived by solving the Schrodinger equation. This tag applies to questions about all forms of orbitals; additionally, questions about the construction and properties of molecular orbitals should be tagged with [molecular-orbital-theory].

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Physical interpreation of coulomb and exchange integral

When trying to solve the Schrodinger equation for the electronic hamiltonian: $$H_{el} = \sum_{i=1}^{N} \bigg( - \frac{1}{2}\nabla_i^2 - \sum_A \frac{Z}{r_{i_A}} \bigg) + \sum_{i>j=1}^{N}\frac{1}{...
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Why electrons do not distribute evenly among the atoms in a molecule?

I was wondering why the state where electrons are evenly (or the closest to being evenly) distributed among the atoms in a molecule is not the lowest energy state? For example, in a water molecule it ...
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Evidence of orbitals?

How do we know that there are different types of orbitals? For example, what evidence is there for the existence of $\mathrm{p}$ orbitals instead of there being multiple $\mathrm{s}$ orbitals (for ...
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How do we explain NMR shielding in filled valence shells?

It is universally recognized that NMR measures the shielding of nuclei from magnetic fields by electrons. The electrons move, producing an eddy current that produces an opposing magnetic field. It is ...
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1answer
184 views

What does it actually mean by stability of an atom

There are several rules related to stability of an atom, like octet rule, half filled or fully filled d orbital etc. But none of them (at my best knowledge) does not explain why an atom is stable when ...
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1answer
241 views

Why does the d orbital size decreases on addition of electrons?

In Concise Inorganic Chemistry by JD Lee (4th edition; adapted by Sudarshan Guha), on page 80 under section 3.7 "The Extent of d-orbital Participation in Molecular Bonding" it is given: A second ...
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3answers
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Correlation between Coulomb's law and VSEPR theory

I've always been told in chemistry lessons that lone pairs repel more due to a greater charge density than bonding pairs. And that makes sense when steric effects are involved when bond orbitals ...
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1answer
42 views

Could observer effect cause electrons in one orbital to be found in another?

The observer effect states [1] that when unobserved, absolutely small particles like electrons can simultaneously be in two different states at the same time. If we look at an atom of any element, ...
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How can I determine whether sp-mixing occurs for heteronuclear diatomics?

I'm trying to draw out the molecular orbital diagram of nitrogen monoxide (NO) but I do not know whether sp-mixing occurs. This is important in order to determine the arrangement of molecular orbitals....
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1answer
51 views

Stability of an atom in absence of EM field

According to Bohr model of atom, electrons move up an energy level in presence of EM field and emit a photon moving down the level. In complete absence of any external EM field, shouldn't the electron ...
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2answers
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Why is the radial distribution at the nucleus 0 but not the radial wave function?

The modulus squared of the radial wave function gives the probability of finding an electron in an infinitesimal volume dv. On the other hand, the radial distribution gives the probability of finding ...
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1answer
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Radial wave-functions and spherical harmonics of p-orbitals in a certain hypothesis

I know that the s-orbitals of H atom are spherically symmetrical. But the p,d or f orbitals aren't. So, the H-atom needn't necessarily be spherically symmetrical, as the wave-function would be a ...
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1answer
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Are electron orbital orientations filled in any particular order? [duplicate]

This question is about the magnetic quantum numbers and their corresponding orbital orientations, e.g., px, dyz, etc. Are the electrons in any given subshell distributed across the orbitals in any ...
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1answer
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Why are s orbitals more “penetrating” than p orbitals?

In polyelectronic atoms, the reduction in the net central force due to electron-electron repulsion is accounted for through an effective nuclear charge that depends on a “shielding effect” of inner ...
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1answer
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Number of orbitals Lithium

I have a very rudimentary question on orbitals (I have basic chemistry knowledge, using for a comp chem project) Lithium, to my understanding, has three electrons allocated to the 1s and 2s orbitals. ...
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1answer
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Is the pz orbital wave function three- or four-dimensional?

The wave function of the $2\mathrm{p}_z$ orbital is $$Ψ = \frac{1}{4\sqrt{2π}}\left(\frac Z a\right)^{5/2} r \mathrm e^{-Zr/a}\cos θ.$$ I'm confused if this function will be a three-dimensional ...
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Distance of subshells from nucleus [closed]

Which subshell is more closer to the nucleus.4f or 6s? 6s gets filled first so does it have to be more closer to the nucleus?
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35 views

The covalent bond in HCl and the Lewis model

Can the formation of the covalent bond in HCl be explained through the hybridization model? We know for sure that it can be explained by the theory of molecular orbitals. In this way, it would be ...
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What is the relationship between polarisation of ion and their bond strength/enthalpy?

Starting with things I Know: Size and charge of ions affect the bond strength and the lattice energy of ionic compounds Decrease in ionic radius(size) increases the bond strength and increases the ...
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How are natural orbitals derived from the electron density matrix?

I have a $4\times4$ electron density matrix in 6-31G for $\ce{H2}$ using psi4 and I am wondering how to get the natural orbitals of the system. I have diagonalised the density matrix $\mathbf{M}$ into ...
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2answers
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Does an electron's spin change when being excited?

My preconception is that when you fill an empty orbital by exciting an electron (with a photon), the empty orbital should be filled by an electron with the same spin. However, I've seen examples of ...
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1answer
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Are the canonical orbitals of Hartree-Fock also the natural orbitals?

My question stems from the comments on my answer to After a unitary transformation, is Koopmans' theorem still valid?. There was some confusion relating to differing terminology referring to different,...
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2answers
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Which d orbitals can form sigma, pi, delta bonds?

If two $\mathrm d_{xy}$ orbitals approach each other on $x=y,$ $z=0$, would a σ bond be formed? I would think so. Can $\mathrm d_{z^2}$ form π bond with another $\mathrm d_{z^2}?$ (As all others can ...
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Why do electrons jump back after absorbing energy and moving to a higher energy level?

Electrons in a shell absorb energy and move to higher energy levels, but they release their energy and jump back to the shell they originally were in. Why do they jump back? Why can they not keep ...
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1answer
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What would follow in the series sigma, pi and delta bonds?

I realise, that this question is a stretch, but I was wondering, how would a bonding orbital be called if it was formed from two $f_{x(x^2−3y^2)}$ or $f_{y(3x^2−y^2)}$ orbitals. Have there been any ...
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1answer
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What does orbital mean, exactly? [duplicate]

My teacher told me that orbital is the probability distribution data of the electron around nucleus which is amplitude data in a way. An example of how my teacher actually told what it means involves ...
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Does electron mass decrease when it changes its orbit?

I have studied this in my chapter atomic structure that when an electron changes its orbit from lower energy to higher energy state , it does not state in my book that it moves there but that it ...
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2answers
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Predicting sigma bond overlap strengths of s-s, p-p, s-p, sp-sp etc

How can we qualitatively predict $\sigma-$bond strengths of overlap between: $\ce{s-s}$ $\ce{s-p}$ $\ce{p-p}$ $\ce{sp-s}$ $\ce{sp-p}$ $\ce{sp-sp}$ etc.? My school-book says $\ce{s-s}$ overlap bond ...
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Why are there only a few types of sigma overlaps?

While studying σ-bonds, I saw that only s–s, s–p and p–p orbital overlaps are being taught. But are there more such cases possible? Because apart from s and p, there are also d and f orbitals.
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1answer
78 views

What does Pauli’s exclusion principle mean in atomic or fundamental way? [closed]

It means is that no electron can have same n , l and $m_l$ but can have two different spin quantum number. I want to know why is this rule valid?Means there must be some other things happening also ...
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1answer
143 views

Is the quantum number $L$ a combination of the azimuthal and magnetic quantum numbers $(\ell, m_\ell)$?

Somehow, I am getting confused about this... In the $J=L+S$ equation about total angular momentum, which of the four quantum numbers used to describe the electrons and their states is included in the $...
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2answers
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Half sigma bonds

$\ce{N2+}$ has $2$ $\pi$-bonds and a half sigma bond. First of all, how can a "half" sigma bond exist? Usually when we encounter non integral bond orders, it is mostly because of resonance ...
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244 views

Atomic Orbitals

I read in a textbook that after an electron jumps to a higher energy level when supplied with high temperatures or current, they again fall back to their respective energy level by losing energy and ...
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1answer
103 views

Why is HBr colorless while Br2 isn't?

Bromine ($\ce{Br2}$) has a dark reddish color. If it reacts with something like benzene, this results in the formation of Bromobenzene and $\ce{HBr}$: $$\ce{Br2 + C6H6 ->[{Cat.}]C6H5Br + HBr}$$ It ...
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What is the definition of energy-independent basis?

I am reading this article by Zatsarinny and Fischer [1]. At some point they span a wave function $\Psi_{E}$ in terms of energy independent basis $$\Psi_{E}=\sum_{k} A_{E k} \Psi_{k}$$ For example, The ...
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1answer
54 views

Electron configuration of non-hybridized carbon

I'm currently learning about orbital hybridization in carbon. I see that carbon has an electron configuration of 1s2 2s2 2p2. However, there are actually three p-orbitals in the second shell, namely ...
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1answer
135 views

Can we observe the shapes of MOs? [duplicate]

Condensed question formulation: Is there an experimental method to directly visualise the 3D form of a MO wave function, or at least the electron density associated with it? Full statement: ...
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Help determining normalisation constant in SALC of methane

We have been told that a symmetry adapted combination of four hydrogen orbitals is used to create localised hydrogen orbitals for methane. These orthonormal combinations are denoted ψa1, ψt’2, ψt’’2 ...
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539 views

Sulfur can violate the octet rule because it has an “empty D orbital” is there any other information the periodic table isnt telling us?

In sulfur or any atom with an expanded octet on the 3rd row, where does the idea that they have an empty D orbital come from ?
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Can we relate approximate Hartree-Fock orbitals to true solutions in the basis-set limit?

Assume that we've "solved" the RHF Hartree-Fock equations in some finite basis, that is, we have arrived at a self-consistent set of coefficients $c_{\mu{}i}$ such that each spatial ...
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1answer
45 views

stability of a negative charge in halogens and that of orbitals

when we talk about stability of halogen anions we say, $\ce{I-} \gt \ce{Br-} \gt \ce{Cl-} \gt \ce{F-}$, and the reason is that "the negative charge (the electrons) have more space to move about ...
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2answers
361 views

What about the aromaticity of cyclopropenylidene?

Here's a compound which we have to tell whether it's aromatic or not. Drawing pi-orbital for the 3-membered ring, I think there are only 2 pi electrons delocalised all over the ring. The orbital ...
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1answer
58 views

Does the octet rule only apply to the second and third shell or does it apply further?

In my textbook, examples for the octet rule are only given for up to the third shell. What about the fourth and fifth shell? I still get confused over the fact that the $n=3$ shell has 18 electrons ...
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What are angular and radial nodes?

Nodes are the points in space around a nucleus where the probability of finding an electron is zero. However, I heard that there are two kinds of nodes, radial nodes and angular nodes. What are they ...
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1answer
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Alternative explanation of ethene's pi bond [closed]

This tutorial about ethene's bonds has the following paragraph that I hope someone can paraphrase in a better way: The pi bond dominates the chemistry of ethene. It is very vulnerable to attack - a ...
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What type of bonding is there among d-block metals?

Metallic bond strength in $\mathrm{d}$-block elements increases up to the middle and then decreases. Why does pairing decrease the strength of metallic bond? What does pairing have to do with metallic ...
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Misconception in valence bond theory

Since the overlap increases with directional properties of orbital, $$\ce{p - p > s - s > s - p}$$ However it is also observed that the bond strength of $$\ce{H-F > H-H > F-F}$$ $$\ce{\{s ...
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276 views

How is it possible to draw a radial wave function for the 2p orbital?

Below is a picture of the radial component of the wave function distribution for the 1 through 3s orbitals. It makes sense to me that there are points where the wave function is 0, since by definition,...
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1answer
420 views

Can the idea of entropy be extended to orbitals?

The forward reaction for: $\ce{HF<->H^+ +F^-}$ is entropically favourable; but energetically unfavorable: as there is too much electron density for $\ce{F^-}$ ion to cope up. That's a reason why ...
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1answer
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What did I do wrong in my orbital notation for this Os (Osmium) question?

I was given a question where I had to write the orbital notation of Osmium (Os) and I got it wrong. The question: 6s2 --> ↑↓ 4f --> ↑↓↑↓↑↓↑↓↑↓↑↓↑↓ 5d6 --> ↑↓↑↓↑↑ The arrows above are my ...

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