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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1answer
260 views

Amine Inversion and Paramagnetism

In amine inversion, there is a planar $sp^2$ intermediate. The electron pair transferred from the blue lobe to the red one during the inversion. It is natural to assume, for a layman like me, that ...
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What's the configuration of chromium(III) in aqueous medium according to crystal field theory?

It has $\mathrm{3d^3}$ configuration, but how will we decide if they enter $\mathrm{t_{2g}}$ or $\mathrm{e_g}$ orbitals since we don't know which complex will form?
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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 ...
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Rationale for assigning antibonding MOs

How do people decide if a molecular orbital (MO) is bonding or antibonding? From Wikipedia article on antibonding MO: [...] if the antibonding interactions outnumber the bonding interactions, the ...
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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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What is the hybridization of terminal fluorine atoms in molecules like boron trifluoride?

What is the hybridisation of $\ce{F}$ in $\ce{BF3}$ or $\ce{CH3F}$ or $\ce{PF5}$ or $\ce{SF6}$? My book states that the p orbitals of fluorine overlaps, but I feel that sp3 hybridisation occurs in $\...
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Electrons in orbitals with nodes [duplicate]

Node is a region in atomic orbital where there is no possibility of finding electrons. That is no electron can be found there (region of $\psi^2 = 0$) Take example of say $\mathrm{2s}$ orbital: as ...
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1answer
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Acid-base chemistry - determining stability [closed]

I am learning about acid-base reactions and how to identify whether an acid is strong or not by looking at the conjugate base. The more stable a conjugate base the stronger the acid. However, two of ...
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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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Why energy of all d orbitals is same?

This question first popped up in my head when I learnt that $d_{z^2}$ orbital is used in $sp^3d$ hybridization and $d_{x^2-y^2}$ and $d_{z^2}$ orbitals are used in $sp^3d^2$ hybridization. If all ...
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Proof of Brillouin's theorem using the diagonality of the Fock matrix

I'm working my way through Szabo and Ostlund's Modern Quantum Chemistry. I am having trouble understanding the proof and significance of Brillouin's theorem. According to the book: Now, by ...
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How to find if the unpaired electron is placed in hybrid orbital or pure orbital in odd electron species?

Odd electron species contain an unpaired electron which can either be placed in hybrid orbital or in pure orbital. Example: In the case of $\ce{.CF3}$ radical, the unpaired electron is placed in $\...
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Finding number of orbitals in nickel whose |m| = 1 [closed]

I am new to quantum mechanics, and I need to find out total number of orbitals in nickel , which have $ \vert m \vert = 1 $ and at least one electron is present. m = magnetic quantum number I need ...
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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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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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How do we know the number of s and p orbitals in a shell?

How do we know how many s & p orbitals will be in a shell? There is one 2s orbital and three 2p orbitals in shell #2. There is one 3s orbital, three 3p orbitals and five 3d orbitals in shell #3....
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Energy of electrons in the same subshell

So I have this quote from wikia (it's similar to my lecture pdf file) but I don't fully understand the statement Although it is commonly stated that all the electrons in a shell have the same ...
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Why rotate orbitals in a CASSCF calculation?

I'm trying to get the rate constant for the reaction of propene to give propenyl (radical) and H. Using Molpro, I calculated the energy for the optimized geometry of the reactant using CASSCF. It is ...
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How are the π bonds arranged in Osmium Tetroxide?

The structure of $\ce{OsO4}$ has puzzled me greatly for a while. I know that it has a tetrahedral geometry. I am quite piqued at the thought of how the $π$ bonds were arranged in the molecule. My ...
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1answer
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Why do lone pairs of electrons have a higher repulsive force? [duplicate]

I was just wondering why lone pairs of electrons are more repulsive than bonded pairs of electrons. I have read that lone pairs have orbitals which are shorter and more round, compared to bonded ...
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The eigenvector matrix C

I was wondering what the difference between $c_n$ and $c_{jn}$ is? In the context of molecular orbital construction, for example, if $c_{jn}$ is the coefficient of the basis functions $\phi_j$ (...
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1answer
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Why is there no electron swapping after excitation?

If we have 2 electrons in the 1st energy level named X & Y, and one electron in the 2nd energy level named Z. If the electron X was excited and transferred to the higher energy level, why didn't ...
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Does restriction on spin in orbits exist?

For a valence electron in Antimony (Sb) with the electron configuration: $Kr(5s)^2(4d)^{10}(5p)^3$ The 3 valence electrons have the quantum numbers $n=5,l=1,m=1$, resulting in the following ...
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Lone pairs in MO theory?

I have learned that non-bonding MOs are lone pairs. However when considering the MO diagram for the $O_2$ molecule, I do not see any non bonding orbitals yet there are two lone pairs on each oxygen ...
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In an octahedral complex, what happens to the electrons donated by the ligand?

I am trying to understand how complexes are coloured. After some reading, I found out this was due to the d-d splitting induced by the coordinate bonds of ligands to the central metal ion. The ...
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1answer
773 views

What is the basis for naming the p-orbitals with reference to the Cartesian coordinate system as x, y, and z?

There are 3 p-orbitals per subshell, which are $p_x$, $p_y$ and $p_z$. As well as there are 5 d-orbitals, which are $d_{xy}$, $d_{yz}$, $d_{zx}$, $d_{x^2-y^2}$, and $d_{z^2}$. My Question: What is ...
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Shape of a wavefunction

I am trying to plotting the angular parts of a wavefunction ($Y_{(m,l)}(\theta, \phi)$) with Wolfram Mathematica. this is the table of spherical harmonics. I think the shape of these function should ...
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1answer
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Why is 2s more stable than 2p, if 2p experiences greater effective nuclear charge?

I'm referring specifically to this graph, which appeared in a chemistry lecture but which the lecturer could not explain. We know that 2s is lower energy than 2p. But surely those electrons in 2p ...
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Why are complex basis functions not used in electronic structure calculations?

I've noticed while reading about Hartree-Fock in Modern Quantum Chemistry (Szabo and Ostlund) that most basis sets use only real basis functions. What I'm wondering is why aren't complex basis ...
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1answer
145 views

if the shared electrons in covalent bond revolves around their nucleus, how they hold the two molecules together? [duplicate]

Covalent bonds are formed by sharing electrons. The pictures depicting this bond make it seem like that the shared electrons stay in a fixed/limited place. What happens in reality? If they rotate ...
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Which overlap is stronger, and why?

I was just wondering which overlap is stronger, 2s-3p or 3s-2p? I believe this can probably be explained by involving some sort of mathematics (?) which I haven't used yet. Edit: Note that 2s-3p ...
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Observability of Orbitals and Orbital Energies

This question comes from some thoughts I had after reading this question. First of all, is an orbital an observable? I know the answer to this question is no because there is no "single-orbital ...
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Electron cloud distribution

Can a please explain me what is electron cloud distribution in simple words? Electron cloud is the area around which electrons are most probably found. What is meant by electron cloud distribution?
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Canonical MOs vs. Localized MOs: Do both represent reality in the same way?

In my understanding localized molecular orbitals (LMOs) are equivalent to "standard" molecular orbitals, often called canonical orbitals (CMOs—by the way, why are they called canonical?). We can ...
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1answer
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How many d-electrons are in the outer shell of metals like Cadmium (this is counting the 4d electrons)?

First I know similar questions have been asked about counting d-electrons. However, my question is about the electrons in the 4d orbital. For example if I have CdS. The cadmium has a charge of +2. ...
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Nomenclature of This State?

I've read this in a book It says the state having three parallel spin is called triplet state . But as far as I know it is determined by "2S+1", from this it comes out to be 4 . Then how it is "...
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Why is the letter J omitted in the spdf… sequence?

Under spherical symmetry, the irreducible representations corresponding to $L = 0, 1, 2, \cdots$ are assigned the letters $\mathrm{S}, \mathrm{P}, \mathrm{D}, \mathrm{F}, \cdots$ after which the ...
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Is orbital hybridisation real?

Is the concept of orbital hybridisation an accurate description of a physical process that actually occurs in bonding atoms, or is it, like VSEPR, a heuristic tool to reason about the characteristics ...
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Degeneracy of second excited state of H-?

This is a question presented in a IIT-JEE 2015 paper I exam. It says, . Not considering the electronic spin, the degeneracy of the second excited state (n = 3) of H atom is 9, while the degeneracy ...
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Is this what an orbital means?

In this picture, there is a $1s$ and a $2s$ orbital. Are the orbitals only the dark gray circles ? Or are the light gray circles (which are surrounding the dark gray ones on both sides) also included ...
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Why is the probability of finding an electron in an orbital not 100 %?

Here is what I know and please correct me if I am wrong: An orbit can have 2 electrons only but electrons do not exist in defined orbits. An orbital is like a hollow sphere where the 2 electrons are ...
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Significance of phase of atomic orbitals

I am learning about orbitals and bonding and antibonding MOs. So far, I know that when you combine s orbitals, you form both bonding and antibonding MOs- bonding when the wavefunctions are added in ...
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The intuition behind carbon's covalent bonds

As an introduction to hybridization, my textbook discusses that "The formation of covalent bonds often starts with the excitation of the atoms." Taking carbon as an example, the author says: Carbon ...
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How do orbitals fill, what is the difference between them, and why is this stable?

I know about the Aufbau principle and the order in which electrons fill orbitals, but how is it that atoms are more stable when they have a full valence shell? It seems that any shell can be comprised ...
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Why do rare earth metal oxides vary in color so much?

I only know a little about what causes different color, but I know it has to do with the electron orbitals and how they reflect or absorb/emit incoming light. The rare earth metals are in the ...
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1answer
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Theoretically, Which d orbital participates in sp3d and sp3d2?

This question is regarding the old way (inaccurate) $\ce{PCl5}$ and $\ce{SF6}$ are taught in elementary chemistry. In the crystal field splitting diagram for triagonal bypyramidal geometry, $\mathrm{...
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1answer
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Molecular orbital diagram for nitrogen monoxide, the nitrosyl cation and the nitrosyl anion

As I understand it, all of them should have same order of energy of molecular orbitals as a model for $\ce{NO}$ should withstand ionization and adding an electron. JD Lee Pg 109 shows the same ...
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Energy levels in an atom

I have been thinking about energy levels of an atom. When we study line spectra of hydrogen atom we say that when electrons jumps back from a higher shell to a lower shell it emits photons of certain ...
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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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2answers
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Would nodal planes of participating Atomic orbitals be nodal planes of molecular orbital?

As I take sigma 2p antibonding molecular orbital as an example Would it have 3 or 1 nodal planes. The two supposed nodal planes pass through the centres of the two atoms and are same as in the ...

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