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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How does s subshell not have a node in the center despite the nucleus being there?

In most images of 1s subshell I see that there's no node shown at the center, and even the formula n-l-1 gives 0 as the answer. But, isn't the nucleus ...
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Why is there a drastic drop in the energy of d orbital after Ca? [duplicate]

Here, in this picture, Catherine Drennan from MIT explains the logic behind electronic configuration of ions atoms. She gives this image Here, the enrgy of 3d drops drastically after Ca. why does ...
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Why do sp³ orbitals have tetrahedral symmetry when they are linear combinations of orbitals with octahedral symmetry?

I'm trying to understand how orbitals hybridize. What I understand—or at least think I understand—is the following: The "standard" $\mathrm{s}, \mathrm{p}, \mathrm{d}, …$ orbitals are ...
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What is the status of unpaired electrons in Fe3+

Fe has 6 electrons in d-orbital. 1 paired and 4 unpaired. When Fe2+ is formed, 2 electrons from 4s are lost. But when we need Fe3+, is it the paired electron that will be ionized or unpaired. I mean ...
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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 $\frac12$-...
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How to compute the electronic energy reported by Gaussian from the AlphaOrbitalEnergies?

I followed the instructions on Wolfram Language & System Documentation Center — FCHK (.fchk) to analyze the *.fchk file. I ran an energy calculation with ...
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4 votes
1 answer
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How do computational programs decide how many virtual orbitals to compute?

How do computational programs decide how many virtual orbitals to compute? For example, a Gaussian job of benzene at the TD-DFT B3LYP/3-21G level of theory calculates from 42 electrons a total of 66 ...
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3 votes
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2p wave function radial distribution

The following graph shows the values of the wave function $\psi_{210} $ (i.e. the $2\mathrm{p}_z$ orbital) versus the radius (divided by $a_{0}$). I don't understand it, however, since the $2\mathrm{...
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Size of Orbitals, Making Intuitive Sense of Quantum Model, Nomenclature of Subshells in the Quantum Model

Alright, so I am doing the Quantum Mechanical (or what some people call the Wave Mechanical model) of an atom. There's this part where we have different zones of the probablity of finding electrons, ...
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Crystal Field Splitting Energy - Tetrachlorocuprate and Tetrachlorocobaltate

I'm a high schooler from India and it's my first time on this stack exchange. I was wondering why the crystal field splitting energy of tetrachlorocuprate differs so much from tetrachlorocobaltate. ...
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How are the energies of, e.g. the 4p orbitals of the first transition series, determined?

Take a first row transition metal, say manganese. The 4s and 3d orbitals are occupied in Mn; each orbital's energy can can be definitely determined by ionising that orbital, obtaining the resulting Mn+...
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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 ...
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How are names for atomic orbitals with high $l$ generated?

I'm looking at Table of Real Spherical Harmonics and trying to understand how the names for the real orbitals are generated. Note that I'm a physicist. In chemistry parlance, I'm trying to come up ...
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Does a node require Change in sign of wave function

In a quantum Chemistry course we were asked to find the number of nodes of the wave function $$\Psi=\frac{\sin^2 x}{x^2} : -3\pi \le x \le 3\pi$$ Clearly this has a removable discontinuity in x=0 so ...
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Where do electrons jump to when they jump to next shell in emission spectrum? Why are there no emission lines for jumps btwn orbitals, same shell?

In the emission spectrum, do electrons that jump up to the next shell go to any orbital in that shell? Or if the electron is originally in say the p orbital, does it jump to the next p orbital in the ...
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Notation for orbital coefficient matrix in RHF vs UHF

My question stems from Table 1 of this paper: "Generalized Hartree–Fock Description of Molecular Dissociation, by Carlos A. Jiménez-Hoyos, Thomas M. Henderson, and Gustavo E. Scuseria" https:...
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2 answers
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Why are higher-energy orbitals larger in size/radius?

I know the different atomic orbitals of atoms are derived from the wave function in the Schroedinger equation. Because I'm not a mathematician, though, I can't decipher the Schroedinger equation and ...
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How do the orbitals distort when adding more protons?

How do the orbitals distort as you move along the series of chemical elements with greater protons. I cant imagine, the first 1s orbital remains a similar shape at Kr 36 protons as compared to He 2. ...
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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 &...
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Why is the momentum operator imaginary?

I'm a beginner in quantum mechanics, and I'm pretty much confused with the momentum of electron in hydrogen atom. The wave function of the electron in 1s orbital of hydrogen atom is $\Psi_{1s} = \frac{...
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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 ...
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Lennard-Jones Potential repulsion by nucleus nucleus or Pauli repulsion?

I read different things, some textbooks say that the repulsive part of the lennard jones potential is due to the repulsion of the nuclei when they are too close, others say it is due to the pauli ...
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3 votes
2 answers
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When people say "The energy of an orbital depends on its ℓ value due to screening effect" , what is screening what?

My book says: Both the attractive and repulsive interactions depend upon the shell and shape of the orbital in which the electron is present. For example electrons present in spherical shaped, s ...
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Can two noble gases attract each other?

If two hydrogen atoms are far apart, they have no effect on one another. But as they are bought closer together, they begin to excerpt an effect. The two nuclei, having the same positive charge, repel ...
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Determination of energies in MO diagrams

How do we determine the relative placements of molecular orbitals in their diagrams? I understand that we can use point groups to find symmetry-allowed interactions between orbitals that we write on ...
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What are the wavefunctions for interacting electrons inside an atom?

The electron cloud for the single electron orbital $1s^1$ is radially symmetric in 3 dimensions. This is perhaps because of the probability distribution function (p.d.f.) $|\psi|^2 = ce^{-\frac{2r}{...
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Can the electronic configurations give any information about the actual structure of the atom?

The zeroth order wavefunction for an He atom in the ground state is $\psi^0_\text{He}=\psi_{1s}(1)\psi_{1s}(2)$ and hence the electronic configuration $1s^2$. But then we start making purterbations, ...
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5 votes
1 answer
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Could a positron be made to stably orbit an atom? [closed]

Suppose you have a single atom of neon, argon or some other noble gas of your choice. While the entire atom is electrically neutral a nearby positron would probably be more strongly attracted to the ...
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3 votes
3 answers
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Where are orbitals located in an atom? [closed]

I am having trouble understanding what are the orbitals. Till now what I have understood, I have depicted in this diagram. Is the diagram correct?? If not, what should be the corrections?
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Does the 1s orbital have two different phases? [duplicate]

How can the 1s orbital (in H atom for example) interfere both constructively and destructively (to give rise to bonding and antibonding molecular orbitals) with another 1s orbital, if the 1s orbital ...
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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 (...
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Why is maximum number of covalent bonds 3? [duplicate]

In my textbook it is mentioned that maximum 3 covalent bonds can be formed within 2 atoms, which makes sense as 1 p orbital from each can be used for sigma bond and the remaining 2 can form pi bonds. ...
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2 votes
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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. ...
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Molecular orbitals in an ionic diatomic compound

The wavefunction of a heteronuclear diatomic molecule, after the orbital approximation and the Born-Oppenheimer approximation, is $$\psi = c_A \chi_A \pm c_B \chi_B $$ where $\chi$ are the starting AO ...
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3 votes
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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 ...
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1 vote
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Can electrons change principal quantum number upon excitation?

I wanted to know when can excitation of electron take place i.e excitation of electron only takes place between subshells having same principal quantum number or is it seen by difference in energy ...
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2 answers
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Electronic Configuration and Octave Rule [closed]

According to Octave rule, a shell cannot hold more than 8 electrons But according to atomic orbitals, The maximum number of electrons in the shell with principal quantum number ...
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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 $p\pi-d\pi$...
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2 votes
1 answer
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Comparing strengths of σ-bonds formed by $\mathrm d_{z^2}$ and $\mathrm p_z$ orbitals

According to my professor $\mathrm d_{z^2}–\mathrm d_{z^2}$ σ-bond is stronger than $\mathrm p_z–\mathrm p_z$ σ-bond as the extent of overlapping is greater in $\mathrm d_{z^2}–\mathrm d_{z^2}$ ...
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1 answer
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Order of Shielding Effect for orbitals

From what I know Shielding effect is the ability of inner electrons to repel outer electrons and reduce the Nuclear charge felt by the outer electrons and this is caused by electron-electron repulsion....
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1 answer
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Which electron should be considered the last one?

Today I came across a problem which asked some quantum number informations regarding the last electron of Zinc. Now as far as I have studied 4s subshell is filled in preference to 3d subshell bcos of ...
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1 vote
1 answer
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How can 2 molecular orbitals form simultaneously? [duplicate]

I understand (for example in the case of H2) that two s orbitals produce through constructive interference a bonding orbital and that the out of phase combination of two s orbitals leads to ...
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1 vote
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Selection of p-orbital(s) when considering sp or sp2 hybridisation

I am considering $z$-axis as the internuclear axis in all cases. When we consider overlap of s and p orbital to form a $\sigma$-bond, the chosen orbital must be p$_z$ orbital for a proper overlap. ...
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2 answers
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Exchange energy of d6 configuration

In NCERT Chemistry book, it is given as: Exchange energy is responsible for the stabilization of energy state. Exchange energy is approximately proportional to the total number of possible pairs of ...
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1 vote
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Probability of finding electron in each orbital

This may include some quantum physics. Are there anyways to describe the wave function of Hydrogen's orbital (or that of a Hydrogen-like atom) in terms of the wave function of each orbital? You can ...
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2 votes
1 answer
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Effect of d-orbital electron shielding on atomic radius

In a standard book it is given: "Atomic radius of Gallium is less than that of Aluminium. This can be understood from the variation in the inner core of the electronic configuration. The ...
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2 votes
1 answer
293 views

Why doesn't the graph of radial part of wavefunction of 2p orbital change its sign? [closed]

Below I have given the graphs of radial part of the wave functions of $\mathrm{2s}$ and $\mathrm{2p}$ orbitals respectively. The graph of the $\mathrm{2s}$ orbital makes sense. It has a radial node ...
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1 vote
1 answer
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Why d and s orbitals overlap even when there is considerable difference in their energies?

In my grade 11 chemistry NCERT textbook, its written that hybridization happens when orbitals of almost same energy overlaps. But S orbital and D orbital have significant difference in their energies. ...
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1 vote
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molecular orbital theory and crystal field theory confusions

I am a high school student and I am very confused in Molecular orbital theory, it says that when two orbitals overlaps in the same phase, they form antibonding orbitals and when they overlap in ...
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-1 votes
1 answer
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What does the wave function of an electron look like? [closed]

In quantum mechanics, in the 'particle in a box' topic, I studied that by solving the Schrödinger equation, we can actually find out what the wave function of the particle in a box looks like. ...
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