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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How to count the number of principal levels and orbitals of an atom or element?

In the example of lithium element which has an atomic number 3 , if I do its electronic configuration it will be = 1s^2 , 2s^1 , this element has two sublevel 1s and 2s , but how to calculate or count ...
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Intergrating odd and even functions [closed]

$$\int_{-\infty}^{\infty} \left(\frac{1}{6}\gamma_3x^3 + \frac{1}{24}\gamma_4 x^4\right) \mathrm{e}^{-\alpha x^2}\,\mathrm{d}x$$ Does the $x^3$ term make this an odd function, so when integrated it is ...
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What do '+ve' and '-ve' mean, concerning protons and electrons? (e.g., plutonium has 94 protons +ve, 94 electrons -ve) [closed]

From Arvin Ash on YouTube, 'How quantum mechanics and the Schrödinger Equation explain atomic orbitals, 2, 8, 18, 32'. What, exactly, does ve stand for?
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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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What is the number of the orbitals which are completely filled with electrons in an element whose atomic number is 16?

All my knowledge To solve this answer you have to do electronic configuration of an atom whose atomic number is 16 , so the electronic configuration will be = 1s^2, 2s^2 ,2p^6 ,3s^2 ,3p^4 , what I ...
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How Quantum codes calculate the electron density? [closed]

I'm a newbie student in theoretical chemistry, and i just start to learn to basics in this field, and I always encounter a bunch of concepts like Hartree-Fock (HF), Electron Density, DFT. I managed to ...
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55 views

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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Semi-Infinite Potential Square Well: Negative Potential

I am having trouble with a problem involving a Semi-infinite potential square well: I have written down some notes that I added to the post. I have problems understanding the physical situation. See ...
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208 views

How to determine the shape of hybridized atomic orbitals in VB theory?

From diagrams, it's rather obvious how $sp$ orbitals are hybridized - the hybrids are just a composite of the $s$ and the $\pm p_{(x)}$ orbitals. However, $sp^2$ orbitals are not just composites of $s,...
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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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How are London Dispersion Forces generated?

While talking about the gaseous state of matter we came to the topic of London Dispersion Forces caused by the generation of a dipole in one atom which induces a dipole in another. While talking about ...
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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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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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What does Brightness/ intensity of spectral lines depend on?

My book states that it depends upon "The number of photons of same frequency or wavelength ABSORBED or EMITTED" From what I understood, if many hydrogen atoms within the discharge tube EMIT the same ...
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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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292 views

Who came up with the box and arrow diagrams for electron configurations?

In general chemistry texts, the electron configurations are sometimes shown in boxes with up and down arrows to show the concept of paired spins. My impression for years was that Hund used such ...
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Oscillator Strength and Absorption Intensity in TDDFT

When I run a linear-response time-dependent DFT calculation in my favourite electronic structure program, for each excitation I'm given an oscillator strength, $f_i$, and transition dipole moment $$\...
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2answers
535 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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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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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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Can single molecules of C and O2 react in isolation, and if so how will momentum be conserved?

I am trying to figure out how is it possible to reconcile the reality of exothermic reactions, which means that kinetic energy is transferred to (heats) the surrounding matter, with the principle of ...
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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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606 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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Calculate the wavelength of the radiation released when an electron moves from n= 5 to n=2

Calculate the wavelength of the radiation released when an electron in a hydrogen atom moves from $n = 5$ to $n = 2$. How can I find this wavelength?
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195 views

Is the correct zeroth-order wave function $\phi^{(0)}$ an eigenfunction of the perturbation Hamiltonian $H'$?

Consider the perturbation treatment of He $1s2s$ excited state configuration. The quantum mechanical Hamiltonian for the He-atom is: \begin{aligned} \hat{H} = \sum_{i=1}^2 h_i + \frac 1 {r_{1 2}} \\ ...
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Bohr's model of atom

"the most remarkable success of the Bohr's theory is that it provides a satisfactory explanation for the line spectrum of hydrogen." But what is the problem with line spectrum of hydrogen which ...
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537 views

What is Nesbet's theorem?

In a talk by Frank Neese there was a slide with title "Nesbet's theorem" and an equation indicating something like "if your wavefunction has the double excitation amplitudes correct, then you can get ...
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1answer
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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
56 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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Challenges Associated with Earth's field NMR

The ACS recently hosted a virtual conference and there was an interesting talk on NMR experiments using the Earth's magnetic field. What surprised me was the number of molecules studied with Earth's ...
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588 views

Why does the transverse magnetization in Fourier Transform NMR consist of Ix+iIy ($\hat{I}_{\!x}+\mathrm{i}\hat{I}_{\!y}$)?

More specifically, the expression for the average expectation value of the transverse magnetization has the following form: $$M^+(t)=N\gamma \hbar\,\text{Tr}(\hat{\sigma}(t)\hat{F}^+)$$ with $\hat{\...
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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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476 views

Angular momentum of an electron in an atom

The Orbital Angular momentum of an electron in an atom is given by $\hbar \sqrt{l(l+1)}$ and the Spin Angular Momentum is $\hbar \sqrt{s(s+1)}$. So what is the resultant Angular momentum of an ...
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2answers
80 views

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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1answer
257 views

Why don't the MO energies sum up to Hartree-Fock SCF value?

I would like to calculate Hartree-Fock energy of $\ce{H3^+}$ ion from orbital energies. So I performed the following calculation in Gaussian 16: ...
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1answer
80 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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1answer
548 views

Hartree-Fock vs. DFT vs. Hohenberg-Kohn vs. Kohn-Sham

What is the difference between these four approaches? My current understanding is that Hartree-Fock uses only 1 slater-determine (accounting for antisymmetry) but neglects correlation between ...
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64 views

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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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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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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72 views

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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1answer
43 views

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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1answer
76 views

Total orbital angular momentum in a filled p subshell

From "Physical Chemistry", P. Atkins, J. De Paula, 9th edition, page 358 "A closed shell has zero orbital angular momentum because all the individual orbital angular momenta sum to ...
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1answer
48 views

Failure Cases of Adiabatic Approximation

We may exactly write the wavefunction of a molecular system as $$ \phi(r, R, t) = \sum_{k = 0}^{\infty} \chi_k(R, t) \psi_k(r, R) $$ where $r$ is the coordinates of electrons, $R$ is the coordinates ...

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