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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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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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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Periodic table -No of Elements in a period [closed]

if the nth period were to end with the filling of the last sub shell of the nth shell then find the no of elements in 4 rd period
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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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Two questions about rotation of a single atom

1. Some sources state that physical rotation of monoatomic molecules or rotation about the internuclear axis of a linear polyatomic molecule are non-physical (because of symmetry) and are therefore ...
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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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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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How many electron clouds are in an atomic orbital? [duplicate]

If an atomic orbital consisted of 2 electrons (its maximum capacity), how many electron clouds would there be? I think its 2 electron clouds, one for each electron but I'd love some confirmation.
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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 ...
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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 ...
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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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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 ...
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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 ...
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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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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 $...
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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 ...
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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. ...
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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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$\psi$ 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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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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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 ...
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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 ...
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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?
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
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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.
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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 ...
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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 ...
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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: ...
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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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1answer
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How to find the number of valence electrons with the help pf quantum numbers? [closed]

I'm bit confused on how to find the number of valence electrons. For example, Boron ($\ce{B) has the electronic configuration as: $\mathrm{1s^2 2s^2 2p^1}$. So what would be its number of valence ...
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Symmetry Adapted molecular orbitals of Formaldehyde

I am currently trying to find the Symmetry Adapted linear Combinations (SALCs) of Formaldehyde $\ce{H2C=O}$, and use the 1s orbitals on the hydrogen atoms, and 2s, 2px, 2py and 2pz orbitals on the ...
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Why is atomic orbital one electron wave function? Why distance from centre is proportional to angular wave function?

Consider the following statements: An atomic orbital is one electron wave function $\psi(r,\theta,\varphi)$ obtained from the solution to the Schrödinger equation. There two electrons in an atomic ...
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Quantization of particle on a sphere

While studying particle on a sphere, I read that boundary condition on $\theta$ and $\phi$ results in quantization. I understand boundary condition for $\phi$ part which varies from 0 to 2$\pi$. As $\...
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What is the relationship between entropy and heat capacity?

The molar heat capacity of hydrogen gas and deuterium gas are nearly the same, 28.8 J/K mol and 29.2 J/K mol respectively, but the absolute entropy of deuterium (145.0 J/K mol) is significantly larger ...
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Wave function of a perturbed system

In perturbation theory, wave function of a perturbed system can be expressed in a power series of some $\lambda$ as $\psi^{(0)} + \lambda\psi^{(1)}+\lambda^2\psi^{(2)}......$. Then we express ...
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How do you optimize an organo-metalic compound containing cerium in in Gaussian?

I am trying to perform optimisation of the molecule attached. I need to get partial charges and frequencies. The issue is that it doesn't converge with following input: ...
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Would the 1st excited state of Li2 be vibrationally excited?

I'm quite torn about an interesting past paper question that's come up during my revision, shown below. On the one hand, you're promoting an electron in a bonding orbital. In general, since this ...
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How do you calculate the norm of a function describing a molecular orbital?

I'm a bit confused by a past paper question I came across for one of my courses, shown below. The wavefunctions corresponding to the lowest, $\psi_{1}$, and second-lowest, $\psi_{2}$, energy ...
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Wave function of a harmonic oscillator

In a question it is given that consider $H-X$ chemical bond and find $H-X$ bond distance for which there is zero probability density of finding the proton. It is easy to solve we have just to ...
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1answer
71 views

Ground state term symbol for Cerium (Ce)

I need to calculate the term symbol of the ground state configuration of Cerium. The electron configuration is: $[Xe] 4f^1 5d^1 6s^2$ Since the d and f electrons are in different subshelles, they are ...
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I'd like to model some compounds with DFTB, but some elements don't have parameter files in the official site. Is there a workaround?

I was reading a bit about this technique, Density Functional based Tight binding (DFTB). It's claimed it can provide a speed improvement of several fold when compared to plain DFT, still giving ...
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Oscillation of particle in harmonic oscillator

In harmonic oscillator, as vibration quantum number increases then does the distance of oscillation of particle from the mean position where there is minimum potential energy increases? If yes, then ...
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Finding vibrational frequencies and heat capacity from bond enthalpies?

So I have heat of formation data for H2, HD, and D2, and I'm being asked to find the difference in vibrational frequency and zero point energies between H-H and H-D. I know that i need to use the ...
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156 views

Does an orbital have its own energy, separate from the electron? Can I picture them as a entity independent from the hosted particle? [closed]

Does an orbital have its own energy, separate from the electron? If so, is it possible for an electron to have a different energy than the orbital it occupies?

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