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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Rydberg states above the first ionization threshold [closed]

What does "rydberg states above the first ionization threshold" mean?
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How to construct spin free coefficient of 2-hole 1-particle configuration?

It is clear that we can expand a cationic state of a molecule in terms of configuration interaction (up to double excitation). It means: $$|I \rangle = \sum_j c^{(I)}_j a_j|\phi_0 \rangle \ + \ \sum_{...
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Why do molecules showing a pure rotational spectra require a permanent dipole?

I understand that pure rotational spectra only exist for molecules which have a permanent dipole moment. The common explanation is "so that they can interact with the E-field of the incoming ...
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Spin orbital coupling and total angular momentum

The Sodium emission spectrum has 2 bright yellow lines called the Na-D lines. Superficially I understand the cause; there's spin-orbit coupling and the 3p orbital is split into 3p(3/2) and 3p(1/2). ...
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Question on symmetry-adapted, possibly antibonding combinations of core orbitals

In this question, it is said that the core electrons do mix and form delocalised, symmetry-adapted orbitals. The boron trifluoride molecule is often said to have no anti-bonding orbitals filled, with ...
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Do different eigenstates of total angular momentum have necessarily different energies?

Let $H$ be the Hamiltonian of a specific atom and $J$ the total angular momentum. Since $H$ and $J$ commute, they have common eigenstate. So we can label the atomic states by their energy and total ...
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Azimuthal Quantum Number [closed]

In the radial equation of hydrogen atom the differential equation is described by But why is l taken to be integer. I know the principal quantum number n correspond to energy levels so that's why it'...
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Fundamental vibrational modes for QM9 molecules

QM9 dataset contains about $134000$ small organic molecules with following properties computed using DFT approaches: ...
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How does an MRI work? [closed]

This is my interpretation of an MRI: There's an external magnetic field and most of the hydrogen nuclei will align themselves with that field (which is the lower energy state) but some are not aligned ...
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Why does the Most Stable State of an Atom Tend to be One with Full s and p Subshells?

I'm new to posting on stack exchange, although I've read a lot of it before. This question seems like it might end up being marked as a duplicate, but I've looked through a lot of the similar ...
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How is it possible to draw a radial wave function for the 2p orbital?

Below is a picture of the radial component of the wave function distribution for the 1 through 3s orbitals. It makes sense to me that there are points where the wave function is 0, since by definition,...
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How are class II force field cross-terms derived?

In some class II force fields, there are cross-terms that characterize bond-bond, bond-angle interactions and others. Example of equations below: $$\sum_{bond-bond}^{}k_{bb}(b-b_{0})(b^{'}-b^{'}_{0})$$...
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How does a body lose electrons? [closed]

If there is a Na and cl in solid form , There will be atoms inside of them.How do they lose electrons ?.We know solid body has a structure and covering.Just like you can touch is the covering of table ...
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Is there any theory more advanced than MOT?

I am currently going through molecular orbital theory(MOT), I should appreciate it's a very nice theory and it's helping me to fill the gaps of normal hybridization concepts and valance bond theory(...
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Comparison between Molecular Orbital Theory and Valence Bond Theory

I have been reading about introductory Molecular Orbital Theory lately. Till now, I have used Valence Bond Theory to evaluate bonding. I have a few questions about it:- In VBT, we used the idea that ...
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nodes and probability density

The square of the wavefunction gives probability density of finding an electron somewhere in the orbital. The text I'm referring to says that the value of probability density is always higher than ...
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Can we relate approximate Hartree-Fock orbitals to true solutions in the basis-set limit?

Assume that we've "solved" the RHF Hartree-Fock equations in some finite basis, that is, we have arrived at a self-consistent set of coefficients $c_{\mu{}i}$ such that each spatial ...
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Do higher orbitals have more energy or less energy? [duplicate]

I've recently learned that as an orbital gets larger, its energy gets closer to 0. Before this, I learned that when an electron moves down an orbital it releases the energy difference between those ...
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Proof for second-order perturbation term of energy

In perturbation theory, if \begin{align}{\hat {H}} &= {\hat {H}^{(0)}} + λ{\hat {H}^{(1)}} \tag{1}\\ {ψ} &= {ψ^{(0)}} + λ{ψ^{(1)}} +λ^2{ψ^{(2)}} + ... \tag{2}\\ {E} &= {E^{(0)}} + λ{E^{...
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Why can’t every element emit all the colours from the emission spectrum [closed]

If there is an infinite number of levels, this means that every electron can jump from as many variations as possible. Hence, why can’t every element emit every colour? Please don’t use very ...
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Atoms visualisation [closed]

In 7th class I was been taught that in an atom, electrons revolve around shells and the electrons with higher energy level are placed likewise in the shell above of that electron: In 11th class I ...
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Effective core potential and Gaussian basis set

Is using the effective core potential (ECP) and Gaussian basis set simultaneously in ab initio calculation a valid approach? For example, is it correct to use ECP for one of the atoms and, instead of ...
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How can an electron being a wave have such property as spin?

Here's what I know about electrons. Electrons have wave-like properties and the number of wavelengths in the $n^\text{th}$ shell is equal to $n(\lambda).$ Also, I read in my book that they have ...
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Binding energy vs. ionization energy [closed]

I am studying binding energy in the context of photoelectric spectroscopy, and I came across a graph of relative numbers of electrons vs binding energy (in units of megajoules per mole). The element ...
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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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Why does the energy level of a particle in a box decrease with length?

I want to know the intuition of why L is in the denominator of the equation for the energy of a particle in a box. This helps explain why resonance is stabilizing without using molecular orbitals. ...
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Negative s - orbital chatacter

I am learning about how to calculate s-orbital character. While doing so, I came across a formula $$\cos\theta = \frac{s}{s-1}.$$ For cycloproprane, I used $\theta = 60^\circ,$ and got $s = -1.$ How ...
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Potential energy surface in transition state theory

I would like to study the typical reaction from the transition state theory: $$\ce{AB + C <=> ABC^‡ -> A + BC}$$ Assuming $\ce{ABC^‡}$ is a colinear molecule, the potential energy surface of ...
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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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Behavior of ionic salts in solution

The electrons of an isolated sodium chloride bound pair in vacuum reside at a semi-classical level in their ground state, so that the Born-Oppenheimer approximation applies, and the 'molecule' acts ...
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What does an electron's spin of 0.5 and minus 0.5 signify?

While teaching me magnetism, my teacher told me about the spin of an electron. He told me that the spin of .5 means that if we rotate the electron twice counter-clockwise on its axis, we would have ...
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On the spin-adaptation of 2nd order Møller-Plesset perturbation theory

$\newcommand{\Ket}[1]{\left|#1\right>}$ $\newcommand{\Bra}[1]{\left<#1\right|}$ $\newcommand{\BraKet}[2] { {\left<#1} \left|#2 \right>}$ In spin adaptation (common in electronic structure ...
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Why does covalent bonding not break down if observer effect can be applied to atomic electrons? [closed]

The observer effect in quantum mechanics states that when unobserved, quantum particles such as electrons can simultaneously occupy two different states. In an atom of any element, where there are ...
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Normal (Regular) or Inverted Terms?

I have a question on the order of the spin-orbit molecular states. I understand how to find the terms that split from a parent molecular state in a diatomic molecule. But my question is on how to find ...
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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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1answer
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Could observer effect cause electrons in one orbital to be found in another?

The observer effect states that when unobserved, absolutely small particles like electrons can simultaneously be in two different states at the same time. (Tro, N. J. (2015). Principles of Chemistry: ...
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What exactly are electron states?

From Tro's Chemistry: Structure and Properties [1, p. 93]: 2.5 Quantum Mechanics and the Atom As we have seen, the position and velocity of the electron are complementary properties—if we know one ...
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Why do 1s and 2s orbitals intersect? [closed]

So I was going through the Schrödinger wave equation to determine the shapes of orbitals. We know that an orbital is nothing more than a region where probability of finding an electron is maximum. ...
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Software to perform molecular dynamic simulation

I have got aggregate of 4 non-protein compounds I would submit for molecular dynamics simulation. The problem is I can't find software capable to do that. Amber, GROMACS, LAMMPS, all of them require ...
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Cross-conjugation and aromaticity in pyrene

I have read about non-huckel double bonds and clar's rule, but what made me confuse is that huckel's perception gives me the feeling that central bonds in polycyclic aromatic hydrocarbons (ex: pyrene) ...
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How to calculate Hirshfeld charges from Gaussian?

I am new to Gaussian and want to calculate Hirshfeld charges from Gaussian 09 or 16. I found this input file for Methanol: ...
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Why is black-body radiation curve smooth without a sharp cutoff?

Planck's law is able to predict a graph that is consistent with experimental observation: In essence, unlike Rayleigh-Jeans law that assumes equipartition theorem to hold (that each mode of motion ...
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Analysis of post-HF wavefunctions

Hartree-Fock method introduces electron (spin)orbitals and they are commonly used for qualitative rationalization of many molecular properties. However, MOs have meaning only if we ignore electron ...
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Grasping the concept of Electronic Spin, Effective Spin and Fictitious Spin

Trying to learn alone some aspects of quantum mechanics is, sometimes, a struggle. Reading the excellent paper by Piwowarska [1] I was hoping to, finally, understand what is the origin of the so-...
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Difference between spin-orbit coupling and the Russell-Saunders Effect?

The Russell-Saunders effect is the same thing as 'spin-orbit interaction, correct? The reason I am asking is because I was reviewing the Wikipedia page on 'spin-orbit interaction' and it does not ...
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Solving the Schrödinger equation for a rotating triatomic linear molecule

This source is showing that solving the Schrödinger equation for a triatmoic linear molecule yields the same formula for the rotationaI quantum states $BJ(J+1)$ as for dipoles. For dipoles, the total ...
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What is the basic difference between accidental degeneracy and normal degeneracy?

As definition suggests accidental degeneracy is defined by the degeneracy generated by two symmetry protected states. But how is it different from a non accidental degeneracy.
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Quantum mechanics electron probability [closed]

Schrödinger's equation yields us the solutions of 90% probability of presence of electrons in orbitals. Hence, the electrons in theory should be able to exist elsewhere in space as well. In that case, ...
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Explanation of terminology in equation used for energy calculation using Hartree–Fock method

I found in the literature that the energy of the Hartree–Fock method is given by the following equation: $$E_\mathrm{HF} = \int (\Psi^* \hat{H}\Psi)\,\mathrm d\tau$$ The term $\Psi$ is the wave ...
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Why do subshells and orbitals exist? [closed]

I'm just a curious high school student. Sorry if this sounds dumb. How exactly did the concept of atomic subshells and orbitals come about? And why exactly are there n-1 subshells and 2l+1 orbitals? ...

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