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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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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metal ion complex with carbon dioxide [closed]

Using ORCA and Avogadro, I stimulated the possible MO orbitals of carbon dioxide complex with lithium ion (Lithium chloride) and cesium ion (cesium chloride) each at a time. i expected that Due to ...
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Diagrams for the wave functions [closed]

I came across a question in one of the papers of JEE Advanced, which i didn't understand. The question is as follows: $P$ is the probability of finding the $\mathrm{1s}$ electron of hydrogen atom in ...
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2answers
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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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63 views

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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Evaluation of an element of a basis function and its derivative using some chemistry package [migrated]

Given some element and one of the basic functions of one of the Gaussian basis sets, I'd like to be able to recover the maximum value any of the basis functions can take, as well as their maximum ...
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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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Analytic Hessians for meta-GGA functionals [migrated]

In many of the free/open-source QM programs like GAMESS, ORCA, NWChem, the calculation of analytic hessians is not possible when a meta-GGA density functional is used, like M06-2X. My first question ...
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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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1answer
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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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1answer
45 views

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
29 views

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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106 views

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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2answers
92 views

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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2answers
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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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1answer
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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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1answer
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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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2answers
114 views

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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Exchange energy

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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1answer
53 views

Computational chemistry software to generate files of cartesian coordinates and zmatrix of molecules

Is there any software that I can provide bond lengths, bond angles and torsion dihedrals of a molecule and generate an output file in the format of cartesian coordinates or zmatrix? Example: I would ...
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1answer
284 views

Szabo and Ostlund's calculation of repulsion integral on page 172 via A.41

Returning to Szabo & Ostlund after a hiatus I tried to recreate his STO-3G calculation for HeH+ which begins on p. 168. It all went fine except for the two-electron, two-center integrals. I ...
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2answers
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Azimuthal Quantum Number and Magnetic Quantum Number

I know that azimuthal quantum numbers and magnetic quantum numbers are used to find the no. of and the orientation of subshells respectively, but why do they have to be called so? I reckon that ...
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1answer
36 views

How do orbitals overlap in difluorosilane? [closed]

In $\ce{SiH2F2}$ four orbitals of silicon $(\mathrm{3s},$ $\mathrm{3p}_x,$ $\mathrm{3p}_y,$ $\mathrm{3p}_z)$ overlap with two hydrogen $(\mathrm{1s})$ and two fluorine $(\mathrm{2p}).$ I want to know ...
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Electron tunneling between orbitals

Electrons can move through potential barriers by tunneling. Atomic/molecular orbitals are separated by energy differences. Therefore I was wondering if an electron can tunnel from one orbital to ...
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spatial degeneracy in the states of atoms and molecules

I would like to know if the exact ground state of a closed-shell atom or molecule can have a spatial degeneracy. If we ignore relativistics effects, the Hamiltonian of the system $H$ commutes with the ...
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1answer
49 views

How to control the optimization step size in Gaussian?

I would like to perform a geometry optimization for a weakly bound methane dimer structure with Gaussian 16. During this process, the Newton-Raphson step should be controlled such that its length ...
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19 views

Approximate Hamiltonian in variational method (Example of Helium atom)

As one know, the exact Helium Hamiltonian \begin{equation} \hat H = \left( -\frac{\hbar}{2m_e}\Delta_1 - \frac{Ze^2}{r_1} \right) + \left( -\frac{\hbar}{2m_e}\Delta_2 ...
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1answer
69 views

Is the given statement regarding Radial Probability Distribution Function correct or not?

Radial Distribution Function $(4πr^2R^2(r))$ gives the probability of the electron being present at a distance $r$ from the nucleus. Answer: The given statement is correct. My Query: According to me, ...
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1answer
60 views

How to find a symmetry group of a system if all the symmetry transformations do not obey closure and don't form a group?

For instance, consider a system with $p_x$ and $p_z$ orbitals at the vertices of a square (on xy-plane). A square by itself would have $D_4$ symmetry. However, because of the $p_x$ orbital; the $90^\...
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1answer
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How would you know if the light emitted is of one wavelength or if it is a mixture of two or more wavelengths? [closed]

I am just learning some chemistry after a long time without studying it and I have thought about something. Some copper compounds emit green light when heated to flame. So, I would like to know if it ...
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46 views

Energy levels for single electron atom [duplicate]

Is it because for single electron atom, energies of all the orbitals with the same n are the same (degeneracy). For example, hydrogen atom energy levels, the electrons are degenerate and also, single ...
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How can an atom have 2 outer shells?

For example, my textbooks says how many electrons in the outer shell in Nickel? and it says the answer is the electrons in both the d shell and s shell. Doesn't shell equal= n quantum number? And n=4 ...

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