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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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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Localized molecular orbitals - Mulliken charge of particular atoms

As I'm sure you all know, running a Hartree-Fock calculation gives an optimized orbital coefficient matrix C, where the columns give the molecular orbitals. Aka for M basis functions: , C will be a ...
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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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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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Do orbitals overlap during formation of an ionic bond?

During the formation of NaCl, do orbitals of Na and Cl overlap? If not then how electrons just come out of it's orbital in Na and go to other empty orbitals of Cl without orbital overlapping?
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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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2answers
81 views

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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72 views

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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75 views

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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1answer
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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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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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1answer
52 views

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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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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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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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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1answer
105 views

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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1answer
93 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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1answer
58 views

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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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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1answer
127 views

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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Application of statement: extent of overlapping is always less than 50% because of electronic repulsion [closed]

Question from the online class: Can two s-orbitals overlap as shown? Dotted circles in diagram depict maximum probability region of s-orbitals in ideal situation when atoms A and B are not bonded. ...
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1answer
54 views

Radial node in p or d-orbital

While studying atomic orbitals and nodes, the only illustration of a radial node that I could find is in an s-orbital (like here). How do the radial nodes look like in p or d-orbitals? (I don't know ...
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Relation between the number of hybridised orbitals and the number of sigma bonds

March's Advanced Organic Chemistry (8th Ed.), has in its first chapter several tantalizing statements of the following variety; Boron has only three valence electrons available to form bonds, hence ...
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1answer
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Can chlorine show negative mesomeric effect due to presence of d orbital? [closed]

I was wondering in this problem that if chlorine will show positive mesomeric effect as it is at para-position and strength of inductive effect decreases with distance from carbon atom and chlorine ...
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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 ...
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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 ...
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S(p)-C(p) vs. O(p)-C(p) overlap

In Grossman, The Art of Writing Reasonable Organic Reaction Mechanisms, he provides the following explanation. The question asks to explain why the difference in pKa values between PhSH and EtSH is ...
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Basics of wave-mechanical model of atom

Why is it that for the $\mathrm{d}$ subshell we have $\ \ \mathrm{d}_{xy}, \ \ \mathrm{d}_{yz}, \ \ \mathrm{d}_{xz}, \ \ \mathrm{d}_{x^{2}-y^{2}},$ and $\mathrm{d}_{z^{2}}$ orbitals only? Why aren't ...
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1answer
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Excitation of electron in Niels Bohr's atomic model

Professor taught us that an electron gains or looses only those energies which are equal to difference in two energy levels. That is $E_1 + \Delta E = E_2$ or $E_1 + \Delta E = E_3.$ What if we give, ...
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1answer
23 views

When is the n+l rule followed when working with energy of different orbitals?

While going through my book, I came across a problem which gave some options about the order of energy of 3s, 3p and 3d orbitals of hydrogen atom. The correct answer was given as: 3s, 3p and 3d ...
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Why does dilithium have a longer bond length than dihydrogen?

I've tried MO theory however they both have a bond order of 1. Which means we can not relate the bond order to the bond length. My thinking - I think that the h2 bond length is shorter due to only ...
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1answer
71 views

Why is it that nitrogen hybridizes in ammonia, yet in F2, fluorine does not [closed]

It seems rather arbitrary to me that we have decided that nitrogen sp3 hybridizes in ammonia to stay consistent with VSEPR, yet that fluorine uses its 2p orbital to bond with another fluorine in F2 (I....
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Quantum numbers associated with electron

I wanted to get your opinion on something. I was given the electron 5p^3 and was told to find the quantum numbers associated with it. I got: n=5 l=1 Ml=1 Ms= +1/2 However, my teacher has told me that ...
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Interpreting data on molecular orbitals in GaussView 6.0 [duplicate]

Introduction I have been trying to use computational software to gain more insight into how molecular orbitals are formed, as well as their shapes and sizes in accordance with Molecular Orbital Theory....
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1answer
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Oribital comparison [closed]

When comparing the orbitals 2s and 2p only in the z axis, do they have the same energy levels and size? I am not so sure just because I know they both have a quantum number of 2. Thank you in advance!
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Confusion regarding orbital, electron and Quantum no’s [closed]

Now , In some textbook I have read that orbital is nothing but the shape of electron . s,p,d orbitals etc. So , after knowing shape of an orbital . I got to know that inside the orbital is an electron ...
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What are "Secondary Orbital Interactions" in Organic Chemistry? [closed]

We used these to analyze the stability of molecules in an Organic Chemistry Course. My teacher analyses the stability of compounds on 3 levels: Atom level by studying the hybridization of the main ...
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2answers
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do electrons in different orbitasl in a same subshell have same energy

In valence bond theory, I suppose that electrons in say, 2px and 2py have the same energy because of the same structure of orbitals. But what about 3dxy and 3dz^2? Do they also have the same energy? I ...
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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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2answers
101 views

Why electrons do not distribute evenly among the atoms in a molecule? [closed]

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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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
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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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1answer
44 views

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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2answers
160 views

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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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
176 views

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
105 views

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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53 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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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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