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 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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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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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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954 views

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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554 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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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
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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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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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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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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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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271 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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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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557 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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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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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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73 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
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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
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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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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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Direction of spins in the singlet vs. triplet state

Suppose we consider the first excited state of the helium atom. We know that the first excited state of helium can exist as a triplet or singlet. The possible functions related to the spin of the two ...
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Role of 'p' Orbitals in Graphite Carbons

In the graphite arrangement of carbons, if we model them according to hybridization theory, the carbons in graphite are sp2 hybridized. This would mean that one s and two p orbitals hybridize, making ...
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358 views

Mechanistic Explanation of Circular Dichroism

I'm wondering if someone can give me a physically motivated reason for why chiral molecules interact with left and right circularly polarized light (LCP) (RCP) differently. Particularly, a quantum ...
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1answer
59 views

Fluorescence quenching by palladium(II) vs. platinum(II) complexes

Why do we observe much stronger (in most cases complete) fluorescence quenching by $\ce{Pd^2+}$ than $\ce{Pt^2+}?$ I work with complexes of both metals and there is no real 100% explanation I can find ...
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Radial Probability Distribution Curve versus ψ² versus r curve for 1s orbitals [duplicate]

My question is basic, but I have already referred to a couple of books. This is an excerpt from Linus Pauling's book: the most probable distance of the electron from the nucleus, which is the ...
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60 views

Would there be 6p½ -> π* backbonding in oganesson tetracyanide?

It is known that oganesson, although a group 18 element, is more likely to behave like a group (1)4 element; i.e. with 4 valence electrons outside a flerovium core. This contributes to the fact that ...
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Why is five electrons in d orbital more stable than seven electrons / eight electrons?

The half filled and full filled configuration is considered to be most the stable among the other configurations. But d7 or d8 configuration has a greater exchange energy mathematically. So why isn't ...
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2answers
359 views

Identifying radial probability distribution curve given $n$ and $l$ value

The correct radial probability distribution curve for the hydrogen atomic orbital with principal quantum number,$ n = 3$ and azimuthal quantum number, $l = 1$ is: ($4πr^2ψ^2 $= radial probability ...
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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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Rotating orbitals and parameters for a many-body calculation

I am confused with some results I am getting. Given a molecule (In particular, I was toying with triangulenes, some benzenoids and things like that, but this is not very important), I perform first a ...
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Comparing geometries and substrates calculated with DFT for different pathways

As DFT calculation is an excellent tool for confirming and understanding experimental results, I got deep into this field as organic chemist. I successfully isolated interesting transition states (TS) ...
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1answer
65 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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58 views

Question regarding conflicting results of checking the electron-preciseness of isoelectronic species via NBO and EHM calculations

It is well known that the tert-butyl cation's empty 2p orbital on the central carbon is stabilised by hyperconjugation from neighboring C-H bonds. This would mean that the central 2p "lone pair&...
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1answer
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Is the lone electron pair of an amide nitrogen part of the π system when building a Hückel matrix?

Is the lone electron pair of the nitrogen atom part of the conjugated π system in the α,β-unsaturated amide pictured below? Is there a general rule for choosing when to include a nitrogen atom in a ...
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883 views

Why is Coupled Cluster not variational?

It has been noted in several sources (e.g. J. Romero et al. Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz. arXiv:1701.02691 [quant-ph]) that one of the ...
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How to transform 'Cartesian gradient' taken from the formatted checkpoint file into the input orientation?

I would like to extract the energy gradient at a particular geometry with many digits from the formatted checkpoint file. However, Gaussian prints the gradient components related to the standard ...
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1answer
2k views

Born–Oppenheimer adiabaticity

The Born–Oppenheimer aproximation is said to be adiabatic. What does "adiabatic" mean? What would be a non-adiabatic approximation to the Schrödinger equation?
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Why don't carbon nanotubes behave like quantum dots?

If carbon nanotubes (CNTs) have the size required to have an bound electron energy state, why don't CNTs behave like quantum dots, such as having optical tunability, amongst other properties?
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1answer
100 views

Quantum chemistry Python package to solve the Coupled-Perturbed Hartree–Fock equations

Two of the most well-known Python quantum chemistry pakcages, PySCF and Psi4, can solve the Hartree–Fock equations. However, I am interested in finding analytic derivatives of the electron integrals: $...
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1answer
211 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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167 views

Calculating the zero-point energy for the C2N2 molecule

I shall calculate the zero-point energy for the $\ce{C2N2}$ molecule in the $^{1}\Sigma_{g}^{+}$ electron ground state with the following vibrational wavenumbers (symmetries in parentheses) which were ...
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1answer
132 views

Solution of the Roothaan Equations of H2 by Symmetry Arguments

FWIW my background is in physics and maths, but I am just starting a chemistry PhD (the last time I took a chemistry class was high school). I have only some background in representation theory, and ...
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2answers
182 views

Significance of the ground state energy in quantum chemistry?

In quantum mechanics, quantum chemistry, and condensed matter physics courses, it seems like finding the ground state energy of a Hamiltonian is incredibly important. I can understand why having the ...
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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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132 views

Hund's rule for comparing term symbol energies in excited state

This question was asked in an exam: The lowest energy electronic state for excited state carbon atom is, a. $^1D_2$ b. $^3D_1$ c. $^3D_3$ d. $^3D_2$ Although we have been taught Hund's rule for ...

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