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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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What is d-orbital collapse?

When I was perusing the works of Schwarz on atomic structure, I came across the unfamiliar term of d-orbital collapse. He describes it as a variation in energetic sequence from group 1 to 3 elements ...
C. WJ's user avatar
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Inter electronic repulsion in s and d orbitals

This was written in a lecture slide: Two electrons present in the same d-orbital repel each other more strongly than do two electrons in the same s-orbital. Why is there a difference in the amount ...
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Free Web-Based Orbital Solver to look into the Walsh orbitals of a perturbed cyclopropane

There exists a free online orbital calculator. When I draw cyclopropane it plots three molecular orbitals, but unfortunately it doesn't use the Walsh orbitals. Are there any free online tools which ...
laminin's user avatar
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Why is octaoxygen diamagnetic?

I tried considering that according to LCAO-MO theory $\ce{O2}$ is paramagnetic, which is confirmed by experimental evidence. Since octaoxygen has the crystal structure in figure, I thought there is a ...
Colard's user avatar
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Are there bonds which share single electron?

Are there bonds which share single electron? During chemical bonding, I asked our teacher why there are only 2 electrons shared in a bond. He said that because it's that one orbital can accommodate ...
Iceberry's user avatar
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How to evaluate the expectation value of the Hamiltonian for a three electron Slater determinant?

I'm having trouble with a few concepts dealing with slater determinants and many electron systems. In particular, when dealing with 3 electron systems, I know that $$ \psi_0 = \frac{1}{\sqrt{6}} \det ...
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How does the Jahn-Teller distortion result in both elongation and compression?

Recently, I have been reading up on the Jahn-Teller effect and I have read articles and posts on it, such as What is the mathematical basis behind the Jahn-Teller effect?. However, many of these ...
Tan Yong Boon's user avatar
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Orbital Interaction for electrophile and nucleophile

Clearly, the above diagrams depict the interaction between empty orbital of electrophile with filled orbital of nucleophile. We may assume that the HOMO of nucleophile being more electronegative will ...
Solid - NMR's user avatar
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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 $\...
SmarthBansal's user avatar
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Relative orbital energies of Mn and Ni

In this MO diagram, why are the atomic Mn $3d$ orbitals higher in energy than the Ni $3d$ orbitals?
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Why can't lone pairs remain in unhybridised orbitals?

I have seen that lone pairs are almost invariably counted for determining the hybridisation of an atom. My question is why can't they remain in unhybridised orbitals.
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The sign of the lobes in an atomic orbital

In atomic orbital diagram of an atomic orbital, the lobes are represented as either positive or negative. It is said that the wave function is 'positive' where the lobe is depicted positive and '...
Nothing's user avatar
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Nature of π-bonds in permanganate ion

I was doing a question which asked about the nature of $\pi$ bonds between the $\ce{Mn}$ and $\ce{O}$ atoms in $\ce{MnO4-}$. According to the answer all the three $\pi$ bonds were formed by $p\pi-d\pi$...
Rhydberg's user avatar
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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 ...
amilton moreira's user avatar
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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 ...
newbie105's user avatar
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Why is Cr+ unstable?

We know that half-filled and fully filled orbitals are highly stable. In ground state $\ce{Cr}$ has a $\ce{3d^5\! 4s^1}$ configuration. Therefore, the elctronic configuration of $\ce{Cr+}$ should have ...
S R Maiti's user avatar
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Why the tendency of ClO3 to form dimer is high?

I read that tendency of $\ce{ClO2}$ to form dimer is less and that of $\ce{ClO3}$ to form dimer is more. I can understand the reason for the former because the unpaired electron is more delocalized ...
Arishta's user avatar
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Howcome orbitals become 'core-like' when electrons are removed?

It seems to me that f-orbitals for lanthanide metals are treated as 'core-like' when a certain number of electrons have been removed. Or, as Radiochemistry puts it, The 4f binding energy is so ...
Linear Christmas's user avatar
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Energy of d(x²-y²) and d(xy) orbitals the same with respect to trigonal symmetry?

In the orbital splitting diagrams of trigonal planar and trigonal bipyramidal complexes the d$_{x² - y²}$ and d$_{xy}$ orbitals have the same energy. I have always assumed that this is because they ...
Dion Silverman's user avatar
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Hund's Rule for Determining Term Symbol Energy Order

In order to determine the energy order based on J-value for term symbols we employ Hund's rule: In a less than $\frac12$-filled subshell Lowest J-value is Lowest energy In a more than $\frac12$-...
Allod's user avatar
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How to find the appropriate isovalue with given probability to plot atomic orbitals

As far as I know, a plot of orbitals is drawn by taking region with 90% probability for an electron to be found. Meanwhile, the program which can plots orbitals, such as VMD, gets isovalue (...
Jinseo Kim's user avatar
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Hydrogen atom orbital projections resemble to some Chladni figures! Mathematical reasoning?

Chladni figures are formed by sprinkling salt on a vertically vibrating membrane, f.e. . Some of them are purported to be projections of hydrogen atom orbitals f.e. 1s, 2s, 2p, 3d, e.t.c., f.e. One ...
Curious One's user avatar
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Generating hybrid atomic orbitals for Boron

My professor was showing us how to form hybrid atomic orbitals for Boron by taking a linear combination of rotated 2p orbitals and 2s orbitals (of Boron). This was done in a particular manner such ...
LamGyro's user avatar
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What is the type of orbital depicted in this diagram?

The following image is from this answer for the question Why is one lobe of an sp3 hybridized orbital smaller than its other half?: I understood everything from that answer, but couldn't identify ...
Vishnu's user avatar
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Oxidative Addition - Really concerted?

I guess you are all familiar with the oxidative addition or reductive elimination reaction in organometallic chemistry. If you read further into the topic you may find different pathways like via ...
Justanotherchemist's user avatar
3 votes
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337 views

Implementing the projected atomic orbital (PAO) localization in Gaussian

I am currently attempting to learn how to setup the active space for performing CASSCF calculations. The textbook I am using as a reference is: Roos, Björn O. "Multiconfigurational quantum ...
Max's user avatar
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3 votes
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Reducible representations - choice of new basis

I was looking at this tutorial about reductions of representations. At first, the basis consists of four orbitals $(s_N, s_1, s_2, s_3)$ and the representations look like this and we want to reduce ...
Eenoku's user avatar
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118 views

If a single electron fills a degenerate energy level, does it fill all degenerate orbitals at once?

For example, if a single electron fills the 2p orbitals. Since all orbitals are degenerate, there is no reason why there would be any preference for px, py, pz. Is the electron hence in a ...
Stikke's user avatar
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Request for a graph of the combined probability density of the three p-orbitals

This started when i was wondering why p-orbitals have an unsymmetrical shape (which isn't clear to me yet). But then i came across Halliday/Resnick/Walker's Fundamentals of Physics. In it, they have ...
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Quantum Numbers

Why are the Lanthaide (atomic #'s 57-71) elements in period 6, but in terms of electron configuration, are assigned the principal quantum number of 4? Why are certain subshells assigned quantum ...
Paul Kelley's user avatar
3 votes
1 answer
466 views

Orbital overlap and bond strength

In Peter Sykes' A Guidebook to Mechanism in Organic Chemistry, it says that sp3 orbitals have greater relative overlap compared to sp bonds. We know that the $\ce{C-H}$ bond is shorter in ethyne ...
gauri agrawal's user avatar
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Is the $2p$ RPD defined along the z-axis?

In MIT $5.111$ class (lecture $6$), we are to compare the most probable radius of a $2s$ orbital and a $2p$ orbital. The graph used by the professor represents the RPD versus $r$: My question is: in ...
niobium's user avatar
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Nonplanar polarization in allenes and aromatic compounds

I recently came across this elaborate article on electrophilic aromatic subsitution. In the third chapter "General mechanistic considerations in electrophilic aromatic substitution" the ...
jona173's user avatar
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0 answers
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Do any molecules contain a phi bond?

In chemistry, phi bonds (φ bonds) are covalent chemical bonds, where six lobes of one involved atomic orbital overlap six lobes of the other involved atomic orbital. I researched this question a lot; ...
Nitrogen-8's user avatar
2 votes
1 answer
67 views

Where are the electrons located when two atomic orbitals overlap? (VBT)

According to the valence bond theory(VBT), a covalent bond is formed by the overlapping of atomic orbitals containing electrons of opposite spin which pair together. However what is the physical ...
Nothing's user avatar
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0 answers
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Do d-orbital electrons shield each other or not?

"The shielding of one 4f electron by another is less than that of one d electron by another, and as the nuclear charge increases along the series, there is fairly regular decrease in the size of ...
Avish Bhatia's user avatar
2 votes
1 answer
203 views

How do the orbitals in atoms synchronize their phases during the formation of a bond?

Suppose I have two hydrogen atoms, each with one electron in their 1s orbital. Then we can represent the wave functions of these two as say $|\Psi\rangle_1$ and $|\Psi\rangle_2$ for each of the two ...
Hadi Khan's user avatar
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2 votes
0 answers
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What will the correct value of spin quantum number for last electron of Na+ ion?

Electronic configuration of $Na^+$ ion is $1s^2,2s^2,2p^6,3s^0$. I have noticed usually , we take spin quantum number as +1/2 first & then -1/2. So , like for the above Q:It is for first 3e=+1/2 &...
Goku777's user avatar
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0 answers
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Exploiting 8-fold symmetry of ERI tensor for building Coulomb and Exchange matrices

I'm trying to write a restricted Hartree Fock code in Fortran that reads in a file of zeroth-iteration 1 and 2 electron integrals (FCIDUMP format) and uses them to do the SCF procedure from an initial ...
Rob's user avatar
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2 votes
0 answers
79 views

Is there a way to experimentally verify the shapes of atomic orbitals?

The shapes of the orbitals as we know, is the interpretation of the Schrödinger equation that calculates the probability distributions of where to find the electrons with a significant probability. ...
CCCC's user avatar
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2 votes
0 answers
409 views

Names of the f suborbitals. (Reference Request)

Today, I have been browsing the internet to know the names of the "f" orbitals. But I have varying answers on the web. Different sources seem to be stating different names. Like here, and ...
Habib's user avatar
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0 answers
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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}{...
DJA's user avatar
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2 votes
0 answers
26 views

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 ...
Mike Serfas's user avatar
2 votes
0 answers
68 views

Ionic radius for tetrahedral metal–ligand complexes

The ionic radii for metal–ligand complexes that are in an octahedral coordination are easy to find. I understand that when the $\mathrm{e_g}$ orbital is filled, the ionic radius increases because the ...
bobsburger's user avatar
2 votes
0 answers
45 views

Focusing on HOMO when discussing thermal electrocyclic reactions

When taking into consideration the outcome of a thermal electrocyclic reaction, why do we focus specifically on the HOMO of the conjugated polyene? Why does it seemingly have the highest contribution ...
TheRelentlessNucleophile's user avatar
2 votes
0 answers
394 views

What exactly are the graphs of orbitals?

In my QM class we are finding the wave functions of the hydrogen atom. In spherical coordinates, these wave functions are functions of 3 variables: $r,$ $\theta,$ and $\phi.$ My professor stated that "...
LamGyro's user avatar
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2 votes
0 answers
115 views

Is Tkatchenko's MBD-NL method self-consistent?

I have a question regarding Tkatchenko's [1] new nonlocal many-body dispersion method (MBD-NL). Does anyone know if it's a self-consistent method? I read this paper many times but I'm still not sure. ...
Chruuz Roman's user avatar
2 votes
0 answers
127 views

Direction of electron density in p orbitals

$\mathrm{s}$ orbitals are spherically symmetric while $\mathrm{p}$ orbitals are not. For Boron, the electronic configuration is $\mathrm{1s^2 2s^2 2p^1}$. In which p orbital does the most energetic ...
Apoorv Potnis's user avatar
2 votes
0 answers
173 views

Bent's rule: electronegativity and s character

I'm very much confused about Bent's rule. What I perceive from it is that more electronegative element occupies a position which has less s character. What I can infer from here is that s character ...
Rachit Agrawal's user avatar
2 votes
0 answers
136 views

How do computational chemistry programs determine the irreducible representation of a molecular orbital?

I was coding a simple RHF code to test my understanding of computational chemistry when I stumbled upon this question. How exactly do computer programs like Gaussian, GAMESS-US etc. know which ...
ANZGC FlyingFalcon's user avatar