Questions tagged [quantum-chemistry]

Quantum chemistry is a subfield of quantum mechanics. Like its parent field, quantum chemistry focuses on understanding physical phenomena occuring at the atomic scale. Quantum chemistry however is more focused on providing useful descriptions of electronic structure to aid in understanding chemical problems (e.g. reactions, spectra, dynamics, ...).

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HCl added to water

Suppose we throw $\ce{ΗCl}$ inside a container full of $\ce{H2O}$. This reaction takes place. $\ce{HCl + H2O -> Cl- + H3O+}$ for each molecule of $\ce{HCl}$ added to water Now both $\ce{Cl-}$ and $\...
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Problem related to 5p orbital wave function describing them? [closed]

This question appear in our first year UG chemistry course. According to me first and last option are the correct. (According to material which were taught to us 2pz orbital can be completely ...
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For Calcium and Potassium, as 4s is then lower energy than 3d,(and lower means or normally means nearer), would 4s thus be nearer the nucleus than 3d? [closed]

For Calcium and Potassium, as 4s is then lower energy than 3d, (and lower normally means nearer), would 4s thus be nearer the nucleus than 3d? For example. I read in the accepted answer to Why does ...
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How do you draw the pi MO diagram for the acetate ion CH3COO-

How do you draw the pi MO diagram for the acetate ion CH3COO- ? I get stuck with the number of electrons on the 2p orbital of Oxygen atom. My teacher said 1 oxygen has 1e, the other has 2e. But ...
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Is there an error at page 138, 4.4 of Introduction of Computational Chemistry 3rd Edition?

Firstly, I found the RHF expansion of $\Phi_2$ and $\Phi_3$ is not symmetric at equation (4.29). Then I expand $\Phi_2$ by myself, the results showed it's $ \Phi_2 = (\chi_A\chi_A-\chi_B\chi_B)(\alpha\...
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How is Perchloric Acid (HClO4) a stable molecule? [closed]

I understand that chlorine only needs 1 electron to fill the 3p orbitals and make it stable, but how can it have 7 bonds to oxygen and still not fill the 3d orbitals? Does it have 2 lone pairs that I ...
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Equation describing electrons in a atom/ion [closed]

When not only 1 electron exist in the atom/ion the electrons of the atom/ion interact with each other and with the nucleus. Do we solve this equations: or this equation? x is the position of a ...
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Can two hydrogen atoms with parallel electron spins form a covalent bond?

Is it possible for two hydrogen atoms with parallel electron spins (i.e. a pair of spin-up electrons, or a pair of spin-down electrons) to form a covalent bond? I've seen some say there is no sigma ...
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1answer
128 views

Can the environment of a molecule affect its HOMO LUMO gap?

For example, if a particular molecule is inside a particular protein, can its absorption maxima change with respect to the isolated molecule? Also, within the same protein, can the molecule's HOMO-...
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Electronic states of VO vanadium oxide in $C_{2v}$ point group

The electron configuration of $V^{2+}$: ... 3$d^{3}$ with 3 d electrons in 3 d orbitals. In $C_{\infty v}$, $d_{xz}$ and $d_{yz}$ have $\Pi$ IRREP; $d_{z}^{2}$ has $\Sigma^{+}$ IRREP; $d_{x^{2}-y^{2}}$...
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Electron coordinates in QM programs

I find it somewhat unusual that one does not need to define electron coordinates in an electronic structure calculation. Taking Hartree Fock for example, the Fock operator includes the one-electron ...
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How do we write spin multiplicity for Mn(2+), Mn(7+)?

Mn has atomic number = 25 Since it is an exception to electronic configuration , unlike having = $\mathrm{3d^7}$ , it has electronic configuration = $\mathrm{3d^5,4s^2}$. Formula for spin multiplicity ...
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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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How can we find the normalised wave function for this particle?

A particle moving on the x-axis has a probability of $1/5$ for being in the interval $(-d-a,-d+a)$ and $4/5$ for being in the interval $(d-a,d+a)$, where $d \gg a$. The normalised wave function for ...
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Physical origin of induction and dispersion energies

I am reading this book on non-covalent interactions. Chapter 1 states that there are 3 types of non-covalent interactions: Electrostatic interactions, which are just the coulomb interactions between ...
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Matrix elements evaluation in Hartree-Fock method

In Roothaan's matrix formulation of the Hartree-Fock method, we eventually must evaluate the elements in the Fock matrix in the form: $$F_{\mu\nu} = \langle \mu | {-\frac{1}{2}}\nabla^2 | \nu \rangle ...
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Average distance of 1s electron from nucleus in He⁺ ion

What would be the average value of $r$, i.e. $\langle r\rangle$, in the $\mathrm{1s}$ orbital of $\ce{He+}?$ $$ \text{a}.~\frac{3}{2}a_0 \qquad \text{b}.~\frac{3}{4}a_0 \qquad \text{c}.~3a_0 \qquad ...
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What molecules other than N$_2$ have wrong orbital ordering when calculated using Hartree-Fock?

N$_2$ is a canonical example of this aspect of the failure of HF method, for instance, see table 4.9 in "Modern Quantum Chemistry" by Szabo and Ostlund. Here it is shown that in HF, the HOMO ...
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106 views

Evidence that electrons don't exist between orbitals? [closed]

I don't understand the logical jump that was made early on in the atomic age, to conclude that electrons jump in and out of existence when moving between orbitals? Similarly, why do electrons need to ...
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Number of electrons in a 2D box for degenerate energy levels

As we know that the energy of a 2-D box depends on two quantum numbers say $n$ and $m$ so $$ {E \propto n^2 +m^2} $$ Now if we say that $n=1$ and $m=1$ so only one energy level is there and 2 ...
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1answer
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How do fullerenes withstand external pressure from collapsing the molecule?

As Fullerene's have an empty shell inside their structure how they withstand the pressure from the outside? As a sidetone, are there any methods for calculating the force that the "vacuum" ...
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Is configuration interaction able to produce degenerate ground states?

I am new to multi-determinant theories. What motivates me in asking this question is the following observation: Consider the Dyson orbital of a $\ce{CO2}$ molecule whose axis is parallel to the $z$ ...
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1answer
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What does it mean for an electron to be in a bonding/antibonding orbital?

My confusion arises from the fact that bonding and antibonding orbitals are created simultaneously. I have read this answer that clarifies about the existence of the molecular orbitals itself. But now ...
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Why can two wavefunctions can be interchanged in integrals involving hermitian operators?

In many textbooks, it is said that because operators in QM are hermitian, we can write: $$\int \psi^*\hat{A}\phi\,\mathrm d\tau = \int\phi^*\hat{A}\psi\,\mathrm d\tau$$ An operator $\hat{A}$ is called ...
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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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1answer
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How can Spin-Orbit-Coupling allow interactions between states with different multiplicities?

I can understand how spin-orbit coupling generates the hyperfine structures that we see in textbooks but maybe my view that the L + S momenta interacting to generate a third J momentum is too ...
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1answer
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The MOs computed with HF method by programs like Gaussian are symmetry adapted orbitals?

I know that some molecules have symmetry elements, and that we can associate operators to them. These operaors commute with the molecular electronic hamiltonian $H$, so the wavefunction can be chosen ...
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How does the electronic structure Hamiltonian scales with basis sets and the number electrons?

Given a chemical system with $N$ electrons and a basis set $S = \{\phi_i\}$ with $K$ basis functions. If one to discretize the Hamiltonian with this basis sets, what is the dimension? The electronic ...
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How can I formally justify the description of an electronic excitation that includes only the relevant orbitals?

I am writing a small program to animate electronic transitions. To do this, I am animating a Rabi cycle for a single electron as it moves from an occupied into a virtual orbital. The on-resonance ...
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542 views

Why does calcium emit circularly polarized light?

One page 31 of Quantum Metrology, Imaging, and Communication by Simon, Jaeger and Sergienko, the authors state that: ... calcium has two electrons in its outermost, partially filled shell; these ...
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Charge polarisation in acetamide molecule due to different lithium salts (varying anions)

I am trying to understand how will acetamide molecules behave in the presence of lithium salts with different anions (nitrate, bromide and perchlorate). Among the three, it is evident that bromide is ...
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In Kohn Sham DFT, what do we know theoretically about the exchange correlation energy?

As I understand Kohn Sham theory, it is proposed that the ground state energy for a molecule can be derived from the ground state of a fictitious set of non-interacting electrons moving in a ...
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1answer
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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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1answer
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Question on theoretical existence (or lack thereof) of spherical symmetry of flerovium and/or oganesson

It is known that flerovium, with a [core]7s²7p² configuration, is predicted to be noble-gas-like; this is due to the "7p²" part of flerovium actually being (7p(1/2))², i.e. mathematically ...
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What does valence electron mean (in the context of spdf orbitals)?

For a little bit of context, my background is in physics and my understanding of chemistry doesn't go past, say, middle school level. Recently, I decided to self-study chemistry and picked up "...
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How can I understand if my system has degenerate electronic configuration?

How can I understand if my system has degenerate electronic configuration? I'm running some post-HF methods and in the meanwhile try to understand which is the most accurate method for my system. ...
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Relationship between MO energies in Hartree-Fock theory and the core Hamiltonian

I am looking at Hartree-Fock (HF) theory as presented in Frank Jensen's book "Introduction to Computational Chemistry", Second edition. The total energy $E$ of the system can be expressed as ...
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What exactly is a photon gas?

I came upon this question in a JEE Advanced mock test online: The number of photons of wavelength $\lambda$ required to achieve pressure $P$ in an empty cubical box of edge length $l$ is given by $\...
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1answer
614 views

What would happen if electrons were spin-1?

We were speaking about this in class, but I can't understand it quite well. What would happen if (hypothetically of course) the allowed $m_s$ values were $-1$, $0$ and $1$? What impact does this have ...
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1answer
60 views

Orbital angular momentum of an electron in s-orbital

I'm a beginner in quantum mechanics, and I'm pretty much confused with the orbital angular momentum of electron in s-orbital of hydrogen atom. I've read that average angular momentum of an electron in ...
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1answer
38 views

Quantifying location and volume of "lone pairs" for VSEPR

Of course molecular shape and the VSEPR model come up frequently. As discussed previously in a valence bond picture like VSEPR, the lone pair electrons are closer to the atom than bonding pairs, and &...
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1answer
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Spin contamination and expansion of unrestrict determinants

I was studying with the book "Modern Quantum Chemistry" of Sazbo and Oustland. In the chapter 2, they talk about unrestrict (UR) determiants. It's explaneid that UR determinants are not ...
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1answer
84 views

In the LCAO method for $H_2^+$, why do we only add or subtract orbitals but never alter one of the phases of the orbitals?

TLDR: Atkins' physical chemistry contains the quote "In general, from N atomic orbitals we can build N molecular orbitals". In the case of $H^+_2$, we use a combination of N=2 orbitals to ...
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Apparent inversion of oxidation state of sulfate ion using minimal basis set

It is well known that the sulfate ion has essentially no 3d-2p bonding; hence I used the minimal basis set(STO-3G) for the NBO calculation I did via Gaussian, just to check it. However, I got a ...
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2answers
56 views

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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Relation of partial charge with wavefunction

Suppose we have an one electron system. The probability $P$ that electron's position is in some interval $x + dx$ is given by: $$P = \int_x^{x+dx}|Ψ(x)|^2 dx$$ So if we measure $N$ times the electron'...
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80 views

Meaning of $^2[\,1/2]$ terms in atomic spectroscopy

I was trying to analyze some atomic emission spectroscopy data and I encountered unfamiliar notation of the terms for me. Commonly, the electronic states of the atoms can be described by quantum ...
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Spectroscopic constants weye and weze

I am using Morse potential to calculate the spectroscopic constants of a diatomic molecule. So far I was able to calculate $R_e$, $\omega_e$, $\omega_ex_e$, $B_e$ but wasn't able to calculate $\...
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1answer
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Obtaining orbitals from a many-body wave function

I have seen how sometimes people talk of orbitals obtained from a CAS or DMRG calculation. I haven't found any explanation of how this is possible. Given the many body wave function (obtained from ...

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