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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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Heisenberg uncertainty principle and lifetime of the excited state

A key relation in optical spectroscopy also used to derive natural bandwidth is: $\Delta E \Delta t=ℏ$ $\Delta E$ is the energy uncertainty of a state, $\Delta t$ should be the uncertainty of the ...
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Why doesn't the particle in a ring model have a potential energy term?

I was thinking of the "particle on a ring" problem as a subdivision of a bigger problem, i.e. the hydrogen atom. While in the hydrogen atom problem, the Hamiltonian contains a potential energy term, ...
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1answer
75 views

Finding the color of crystal violet theoretically

I am trying to find the color of an organic molecule, crystal violet, theoretically. I suspect that the color is due to the large conjugated system. My question is, how would I go about finding the ...
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What would be the best way to study Quantum Chemistry? [on hold]

Title. I have a relatively sound mathematical foundation (linear algebra, differential equations, multi variable calculus etc.), so I’d like to ask what the “best” way to study Quantum Chemistry would ...
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How to evaluate the expectation value of the Hamiltonian for a three electron Slater determinant?

I'm having trouble with a few concepts dealing with slater determinants and many electron systems. In particular, when dealing with 3 electron systems, I know that $$ \psi_0 = \frac{1}{\sqrt{6}} \det ...
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1answer
42 views

Radial pair distribution function (VMD). How to define it for a water NaCl system with multiple Na and Cl?

I'm struggling to understand a paper in which someone has presented radial distribution functions (RDFs) for a system that contains multiple Na, Cl, and water atoms/molecules. I don't know exactly ...
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35 views

How does one plot molecular orbitals (probability electron density plot) for complex nonlinear molecules?

For molecules such as $\ce{H2}$, we can put the molecule along one of the Cartesian axes, with probability density along the other orthonormal axis and plot it. We can do the same for planar molecules ...
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Stablility of ground state Bohr Orbit [duplicate]

Bohr's theory of the hydrogen atom predicts that the energy of the electron in the $n$th energy level is given by $$E_n = -R_H \left(\frac 1{n^2} \right),$$ where $R_H = 2.18 \times 10^{-18} \ J$. ...
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1answer
40 views

How does increasing temperature reduce the efficiency of solar cells?

I've seen several answers and trying to confirm. 1) Does temperature increase the ground state energy of electrons once they reach the positively doped semiconductor, thus reducing the voltage ...
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0answers
19 views

Why do identical protons not couple with each other in 1H NMR? [duplicate]

So basically I'm wondering why the different protons in ...let's say trans-stilbene do not couple with each other. I'm aware of the fact that they are chemically and magnetically equivalent. They ...
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1answer
36 views

Quantitative MO theory- how is the overlap integral and the weighting coefficients of the molecular orbital actually evaluated?

Title. In my inorganic chemistry course, we learn about SALCs and qualitative MO treatment, with only a fleeting reference to the S integral and actual molecular wave functions (only hydrogen, $\ce{H2}...
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1answer
33 views

Molecular Orbital Mixing to get the Molecular Orbitals of a large molecule

I am trying to get the molecular orbital for arbitrarily placed nuclear centres (identical). In other words , I am trying to solve the following one electron hamiltonian. $$h=-\dfrac{1}{2}\nabla^{2}-\...
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1answer
35 views

Chemical bonding based on hybridisation model

A snippet from a textbook: Therefore, the hybridization model predicts that an $\mathrm{sp}$-hybridized carbon atom is more electronegative than an $\mathrm{sp}^3$-hybridized carbon atom. Evidence ...
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1answer
147 views

Dominant contribution of v = 0 → v = 1 transition in vibrational spectroscopy

Recently I had studied vibrational spectroscopy using the quantum harmonic oscillator model. After stating the gross selection rule [that vibrational oscillation demands a change in dipole moment for ...
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0answers
28 views

Quantum numbers and orbitals

Are values of n, l and m pertain to any specific orbitals, especially talking about the magnetic quantum number? I mean, if we're talking about l=2 that are the d orbitals, so does m=-1 mean dz2 or m=...
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1answer
68 views

How are octet-rule models supported by thermodynamics and quantum theory? [closed]

I understand that the four quantum numbers dictate how many electrons can "fit in a shell," but I don't understand how gaining a full octet is particularly energetically favorable. The example of ...
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1answer
33 views

Quantum Chemistry [closed]

How to find the degeneracy of a given state in quantum mechanics? What is the formula?
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1answer
70 views

Conformer generation for radicals

Is there an automatic way to generate conformers for radical like systems (spin multiplicity is doublet)? My system for the study is a substituted fullerene with a missing H atom from the functional ...
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1answer
75 views

Overlap matrix (H2 molecule, STO-3G) [on hold]

I'd want to implement SCF method using Modern Quantum Chemistry (Szabo). But when I want to calculate overlap matrix for H2 (STO-3G basis) my results aren't equal to true overlap matrix that there's ...
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1answer
54 views

Angular momentum of an electron in an atom

The Orbital Angular momentum of an electron in an atom is given by $\hbar \sqrt{l(l+1)}$ and the Spin Angular Momentum is $\hbar \sqrt{s(s+1)}$. So what is the resultant Angular momentum of an ...
2
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1answer
33 views

Correlation energy in quantum chemistry

In density functional theory (DFT) there is classic Coulomb energy and non-classic correlation energy. But what is difference between them? In books these energies are explained very similarly. Both ...
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How to derive a state symmetry in D2h point group from its wavefunction?

Let's have an atomic carbon with the following electron configuration: $$ 1s^2 2s^2 2p^2 $$ One of it's levels is ${}^1S_0$, which is corresponding with the following state: $$ \begin{align} \left| ...
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1answer
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Potential energy curve for dissociation of cation of carbon dioxide

Can anyone suggest me some literature where I can find the potential energy curve or the electronic states for singly ionized $\ce{CO2}$ ($\ce{CO2+}$) dissociating into singly charged oxygen ($\ce{O+}$...
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1answer
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How to specify atomic carbon terms in the coupled and uncoupled representation?

So, we know, that the atomic carbon in the electronic configuration $1s^22s^22p^2$ has the following terms $${}^1S, {}^1D, {}^3P$$ My question is - how can I correctly specify these terms in the ...
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1answer
28 views

Difference between adiabatic and nonadiabatic tunneling for molecule

What is the difference between adiabatic and nonadiabatic tunneling for a molecule in a laser-field? Does nonadiabatic tunneling necessarily relate to the Conical intersection or curve-crossing?
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1answer
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Roothaan matrix equation equation orbital coefficients

To go from the Hartree_Fock $f\psi{_i}=\epsilon\psi{_i}$ to the Roothaan equation $FC=SC\epsilon$. equation we expand the orbitals as $\psi{_i}=\sum C_{\mu i}\phi_i$ But for Helium atom we ...
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1answer
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What happens if the electron in the lowest energy level of an atom loses its energy?

What happens if the electron in the lowest energy level of an atom loses its energy? Excited states spontaneously give of energy and transition to a lower energy state. Why can't an electron in the ...
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0answers
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Generating density matrix of a wavefunction from common quantum chemistry software

I am looking for density matrixes for a couple of closed shell and open-shell systems, and I wonder if there is a trivial way to make e.g. Gaussian just generate an output for me. I may be wrong but ...
5
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1answer
53 views

Why do people add H(core)+F in Hartree-Fock?

I'm trying to implement my own HF code, and it seem usual that, after building the Fock matrix $F$, they add that to the pre-existing $H_{core}$, from the two-point interactions, when computing final ...
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0answers
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Putting high symmetry points labels to a band structure plot

So far I've got this plot using Quantum Espresso. I want to put gamma, X, L, etc labels to the k-path. Quantum Espresso's ouput states the following: ...
3
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1answer
138 views

What is the exact definition of the radial distribution function?

I have been very confused by the radial distribution function which is often used in chemistry to predict the probability of finding an electron at a distance from the nucleus. From Atkins' Physical ...
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0answers
39 views

Photoelectric effect — Expected observations for waves

I understand why treating light as particle-like photon packets leads to the observed results. I seek to understand why one would expect different results if light were treated as a wave (and thus ...
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1answer
77 views

Raman spectra in Gaussian [closed]

I want to simulate Raman spectra of benzene in Gaussian 09. Calculated spectra for a single ring Benzene ($\ce{C6H6}$) in Gaussian differs about $\pu{40 cm^{-1}}$ for each peak, compared with ...
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How is occupation number of lowest unoccupied natural orbital defined?

I have run some calculations to analyse the occupation of natural orbitals. Since it is needed to run in triplet state, I get two orbitals with occupation number 1. Now, which orbital occupation ...
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0answers
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Calculate molecular orbitals of high-lying or Rydberg states in GAMESS (US)

I am trying to calculate the high-lying or Rydberg orbitals (i.e. unoccupied orbitals with their energies just below the ionization energy) of a nitrogen molecule. I use GAMESS(US) with the following ...
2
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1answer
26 views

Calculate the transition dipole moments between the 1s inner shell and the high-lying states of a molecule

I am trying to calculate the transition dipole moments between the 1s inner shell and the high-lying states of N2, namely, $<\psi_{1s}|{\bf r}|\psi_{high-lying}>$. For this, I installed ...
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Can LCAO be seen as superposition?

In wave physics, when waves interact, the principle of superposition applies. It states that the displacement of the resultant wave is made up of the sum of the individual displacements of the ...
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1answer
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How can f-f transitions happen?

The question might seem quite easy to answer but still I am unable to find any useful information. I am aware of laporte- or symmetry-forbidden transitions and for f-f also spin-forbidden transitions ...
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1answer
48 views

How to write a cube file?

This is a technical question. I have a real-space representation of a potential in a grid of points, however I have the grid in the format: x y z w v meaning: the coordinates of each point, the ...
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1answer
51 views

Can the oxidation of hydrogen peroxide be reversed? [closed]

Hydrogen peroxide is said to be unstable, for it undergoes auto-oxidation on standing/heating: $$\ce{2H_2O_2 -> 2H_2O + O_2}$$ where $\Delta S=\pu{70.5 J {mol}^{-1}K^{-1}}$ and $\Delta H^{\Theta} ...
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Why has na 1S0 term Ag symmetry?

This question is a continuation of Molpro - Connection between atomic term symbols and system symmetry. In the Feodoran's answer I found it somehow confusing, that ${}^1S_0$ term should be totally ...
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Relationship between the 2nd theorem of Hohenberg and Kohn and the Variational Principle

In Density Functional Theory, the 2nd theorem of Hohenberg and Kohn states: The electron density of the system that minimises the ground-state energy is the exact electron density of the system. ...
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Vanishing integral rule for two-electron integrals

I understand the vanishing integral rule for a one-electron integral to be: $$\langle i | \hat{O} | j \rangle = 0 \hspace{1cm} \mathrm{if} \hspace{0.2cm} \Gamma_O \neq \Gamma_i \otimes \Gamma_j$$ ...
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1answer
78 views

Molpro - Connection between atomic term symbols and system symmetry

Let's say I have a carbon atom with the electron configuration $1s^22s^22p^2$. We know, that using atomic term symbols we can describe the following states: $${}^3P_0, {}^3P_1, {}^3P_2, {}^1D_2, {}^...
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1answer
68 views

Getting the pressure of a system by series expansion

An average number, $N$, of bosons of spin $S = 0$ is conned to a two-dimensional domain with surface $A$. The gas is ultrarelativistic with a single particle energy $\epsilon = cp$, where $c$ is the ...
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2answers
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What is the sense of electronic configuration of an atom if an electron can be in any superposition of energy eigenfunctions?

I recently started learning abou the quantum mechanical explanation of hydrogen atom. In the derivation of the wave functions of hydrogen atom we find its energy eigenfunctions. But according to the ...
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2answers
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Connection of term symbols with specific microstates for atomic carbon

I'm currently studying atomic term symbols. I wanted to try it on a simple atomic carbon with the electron configuration $1s^22s^22p^2$. I know, that only open-shell electrons are involved in the ...
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1answer
38 views

Can Hartree-Fock mix more orbitals than there are electrons?

I'm trying to understand Hartree-Fock well enough to write my own implementation. A point that I seem to be coming to that I'm not sure is correct: the method only produces one-electron orbitals that ...
5
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1answer
41 views

What determines the coefficients in the wavefunction of a hybrid orbital?

I was studying the hybridization of carbon atoms and I came to figure out that the $sp$ hybridization wavefunction is given as $$|sp_{+}\rangle =\frac{1}{\sqrt{2}}\left(\psi_{2s}+\psi_{2p_x}\right)$$ ...
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1answer
51 views

Molecular orbitals symmetry - states notation

I'm reading some papers and I'm repeatedly seeing the following notation of system states: Could you, please, explain to me the meaning of it? E.g. the state $B^2 \Sigma_u^+$ - I'm aware, that $\...