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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18
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2answers
2k views

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 ...
6
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0answers
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+500

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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1answer
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+400

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
20 views

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 ...
6
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0answers
62 views

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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12 views

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.
0
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1answer
48 views

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
40 views

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 ...
3
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2answers
101 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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Electronic Configuration of Lanthanum [duplicate]

Lanthanum has electronic configuration [Xe] 4f0 5d1 6s2. Why is the 4f sub-shell not filled even though we know that 4f is filled before 5d subshell? I know that for some elements energy level of 4f&...
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0answers
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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
44 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 ...
8
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1answer
273 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 ...
0
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1answer
35 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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2answers
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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 ...
1
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0answers
24 views

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 ...
1
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1answer
45 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 ...
0
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0answers
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 ...
1
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1answer
67 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, ...
1
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1answer
57 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^\...
12
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1answer
1k views

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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0answers
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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1answer
69 views

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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0answers
49 views

How to plot the wave function after a Hartree-Fock calculation?

I have written a code in Mathematica and have obtained the final energy of the hydrogen molecule. I have used Gaussian basis functions for this calculation. Now I need to plot the ground state wave ...
0
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0answers
23 views

What is the link between the classical and quantum definition of the symmetry number?

From what I understand, the symmetry number for a molecule can be defined in 2 ways: 1. The quantum mechanical symmetry number corrects for overcounting the number of possible rotational states of a ...
0
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1answer
53 views

Expression of the potential in the hydrogen atom while solving radial part of the wave function

I was reading about the derivation of wavefunction of Hydrogen atom from Atkins book. After the separation of variables and writing the wave function, $\psi_{(r,\theta,\phi)}=R_{(r)}Y_{(\theta,\phi)}$...
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0answers
30 views

Deriving the absorption coefficient from state transitions

This source states that the absorption coefficient $\gamma$ is proportional to the difference in particle number density $\Delta n$ per unit volume between the initial and the final rotational state ...
2
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1answer
104 views

Why does de Broglie wavelength lambda = c / frequency?

For a chemistry problem, I want the velocity of the de Broglie wave to agree with one of these values: A) $c^2/v$ B) $h\nu/mc$ C) $mc^2/h$ D) $v\lambda$ We know that $$\lambda = \frac{h} {mv}$$ But ...
5
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1answer
84 views

Casimir effect and van der Waals forces

The Casimir effect makes two close metal plates in a vacuum attract. I was pondering and figured out that two close molecules should experience the same effect, as they are close and between molecules ...
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0answers
29 views

Uncertainity principle of a particle on a ring in $m=0$ state

When a particle is on a ring, we know that the commutator $[L_z,x]=i\hbar y$ and $[L_z,y]=-i\hbar x$. So we can't measure $L_z$ and $x$ & $L_z$ and $y$ simultaneously with infinite accuracy. When $...
0
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1answer
36 views

What is the reason that ice melts with increasing pressure at constant temperature (revelation)?

I've seen many explanations regarding this topic where they explain it in the sense of the anomalous expansion of water, but I actually want an answer where I can understand the different forces at ...
0
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0answers
63 views

What are the rules for constructing Kohn-Sham orbitals?

I just recently began to study quantum chemistry and need some clarification for the construction of Kohn-Sham orbitals. Consider a system of several atoms. Let there be $N$ electrons in this system. ...
2
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2answers
54 views

Do commuting operators always share the same eigenfunctions?

Do commuting operators always share the same eigenfunctions? Could you kindly explain to me if this is true or false and examples for this, as I am a little confused.
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3answers
69 views

$\psi$ Represents amplitude of electron wave and $\psi^2$ represents electron density in a given space. How?

The $\psi$ represents amplitude of electron wave. So it's dimension should be $\left[L\right] $. But $\psi^2$ represents density of electrons in a given space. So it's dimension should be $\left[ML^{-...
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1answer
47 views

Which of the following would be an example of something that is quantized? [closed]

How do we defind quantized there, why it is climbing a flight of stairs? Thank you!
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1answer
50 views

Two electron integrals between 1s STO

I am trying to understand SCF cycle by trying to code up solved example from Quantum Chemistry by Levine (page 443, 5th edition). The problem is shown below: One electron integrals are straight ...
0
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0answers
30 views

Obtaining energy and wave function for excited states

Suppose I have done a HF calculation and obtain the energy and wave function of ground state. If I want to produce the spectrum of the specie (say Hydrogen molecule), should I use CI (configuration ...
0
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1answer
53 views

Do quantum particles have mass? [closed]

Quantum particles are never objects but are always waves. But do they have mass or can they carry mass?
2
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0answers
49 views

The true shape of p orbitals

I'm trying to model $\mathrm{p}$ orbitals using a 3D program. What confuses me is that there are 2 shapes of $\mathrm{p}$ orbitals. I'm not sure which one is the accurate model. And what is the ...
2
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0answers
42 views

How is the ΔL = ±1 selection rule derived?

I understand there are selection rules in spectroscopy and quantum mechanics which governs whether a transition happens or not. For example, in atomic spectroscopy, the total orbital angular momentum ...
3
votes
1answer
48 views

Associated occupation numbers of frozen natural orbitals (FNOs) from MP2 method

The paper Frozen Virtual Natural Orbitals for Coupled-Cluster Linear-Response Theory gives the following (simplified) description of frozen natural orbitals (FNOs). In the MP2 method, the unrelaxed ...
-1
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1answer
48 views

Can carbon have electrons in a 5d orbital? [closed]

(a) Sketch the radial probability distribution for a 5d orbital in a carbon atom. You should label the axes, but do not need to include numbers. Use arrows to indicate the radial nodes. (b) Label the ...
5
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0answers
54 views

On the localized screening of cerium (when compared to iron)

I was reading the paper 'A linear response approach to the calculation of the effective interaction parameters in the LDA+U method' by Cococcioni - (Paper here) . Quoting from the first paragraph on ...
5
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2answers
105 views

High-temperature DFT

Why is it so difficult to perform DFT calculations that consider temperature? I have seen that time-dependent DFT is needed to model systems at high temperature. Why is this the case? What about ...
2
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1answer
40 views

What is the meaning of the J value in term symbols [closed]

I understand how to work out the J values of term symbols. e.g. a d1 configuration gives J values of 5/2 and 3/2. resulting in 2D 3/2 However I dont understand the meaning of it, and why it arises.
4
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0answers
35 views

Is there a mistake in diagramatic representation of RS perturbation theory described in Szabo and Ostlund textbook?

I'm trying to understand rules of the diagrammatic representation of the many body perturbation theory that described in Szabo and Ostlund "Modern Quantum Chemistry" textbook. One of the ...
2
votes
1answer
134 views

The particle in a two-dimensional box model and graphene

I have been having trouble with understanding and solving the following problem. For two-dimensional conjugated systems, we may use the particle in a two-dimensional box model. In this case the total ...
2
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0answers
50 views

What is the precise meaning of “in-phase” (and “out-of-phase”) in this context?

I am currently studying the textbook Infrared and Raman Spectroscopy, 2nd edition, by Peter Larkin. In a section entitled Symmetry: Infrared and Raman Active Vibrations, the author says the following: ...
2
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0answers
41 views

Determining symmetry correction by looking at rotational quantum states

I'm trying to understand the relationship between symmetry correction and rotational quantum states, particularly in the case of dipoles with identical atoms. For an angular momentum quantum number $...

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