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Questions tagged [quantum-chemistry]

Quantum chemistry is a subfield of quantum mechanics. Like its parent field, quantum chemistry focuses on physical phenomena that occur at an atomic scale, usually specifically aiming at chemical reactions.

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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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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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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
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Can the oxidation of hydrogen peroxide be reversed? [on hold]

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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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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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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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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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 ...
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1answer
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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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Are there any selection rules for collisional excitation/relaxation?

There are well-known selection rules for possible optical transitions of an isolated atom (molecule) between different electronic states. But are there any rules, limiting possibilities of collisional ...
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1answer
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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 $\...
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How would vicinal coupling of two 1H with intervening 12c nuclei look with a naive Fermi contact model?

Multiple sources I've found talk about vicinal J-coupling between two hydrogen-1 nuclei with two intervening carbon-13 isotopes as in: 1H-13C-13C-1H Which would be (electron spin of covalent bonds ...
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2answers
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Why are the radial wavefunction and radial distribution function different?

I'm having trouble understanding the following two graphs, which are the radial wavefunction of the hydrogen 1s orbital and the corresponding radial distribution function: Specifically, why is the ...
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STO 3G basis expansion of p orbitals

I am expanding $2p_{x},2p_{y},2p_{z}$ (slater type )orbitals in gaussian STO-3G basis as follows, $$|2p_{x}\rangle=C_{1}x\exp(-\alpha_{1}r^{2})+C_{2}x\exp(-\alpha_{2}r^{2})+C_{3}x\exp(-\alpha_{3}r^{2}...
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Implementing the projected atomic orbital (PAO) localization in Gaussian

I am currently attempting to learn how to setup the active space for performing CASSCF calculations. The textbook I am using as a reference is: Roos, Björn O. "Multiconfigurational quantum ...
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1answer
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Can someone tell the me the data bank which has all the STO-3G basis sets for many electron atoms?

I am trying to express the slater orbitals of Helium atom in terms of 3 gaussian functions (STO-3G basis set). Is there any data bank or reference table in which I can find the exponents and ...
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Significance of this unusual matrix element

Recently, I was solving some questions on Rigid Rotor. I found this question very amusing. Evaluate the integral i) <$Y_{l,m+2}$ | $L_{x}^{2}$ | $Y_{l,m}$ > I evaluated it, found that the value ...
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Chemistry: What's the difference between “binding energy” and “ionization energy”?

In respect to PhotoElectron Spectroscopy (PES), we are analyzing graphs with "binding energy (MegaJoules)" on the x-axis, and with "relative number of electrons" on the y-axis. I have also seen the x-...
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Constructing two body Hamiltonian for Helium atom in hydrogen slater orbitals single particle basis [duplicate]

I am trying to construct a two body states to calculate the matrix elements of electronic Hamiltonian of Helium atom. $$H=-\frac{1}{2}\nabla^{2}_{1}-\frac{1}{2}\nabla^{2}_{2}-\frac{2}{\vec{r}_{1}}-\...
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Is the notion of orbitals different in theoretical chemistry?

I am just an average chemistry student that is currently exposed to theoretical chemistry. And I am seeing very puzzling things, such as 1p, 2f, 3g orbitals. In my attempt to reconcile this, I was ...
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Are any other orthonormalizations schemes besides Lowdin normally used when solving SCF equations?

When solving equations of the form: $$F(C)C = SC\epsilon$$ (e.g. Hartree-Fock-Roothan or Kohn-Sham-Roothan) where $F$ is the fock matrix, $C$ is the coefficient matrix and $S$ the overlap matrix, ...
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1answer
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what is the issue in evaluating two electron integral?

What sort of issue is there in two electron integral in quantum chemistry ? Is it a problem of convergence when we do numerically? Can someone suggest any review article or reference articles which ...
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How to calculate the magnetic exchange coupling in a charged radical complex?

I have a neutral complex with two magnetic centers. For this case it is easy to calculate the exchange coupling as the broken symmetry state is converged properly. But when I am making the complex ...
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1answer
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According to MO theory, do 1s orbitals in dioxygen interfere?

According to MO theory, are the 1s orbitals in $\ce{O2}$ too radially contracted to interfere with each other and thus cannot form bonding and antibonding orbitals, or do they still do that?
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1answer
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Why is the active space for the dinitrogen cation defined this large in my example?

I have a Molpro script which computes $\ce{N2^+}$ potential energies. The significant part is the input for the wave function: ...
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1answer
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Shape of the container and the number of possible energy states

A question came up when studying the formula for calculating the total number of possible energy states of a particle within a container. Why is the number of possible energy states independent of ...
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Slater Determinant in Python package

Is there any library functions which I could use in python to construct slater determinant? Can someone suggest me something to fix this issue ? Is it really possible to determinant with functions as ...
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1answer
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Solving two electron integral numerically

Is there any software package in python or C to evaluate two electron integral repulsion integral in quantum chemistry of atoms. I am trying to solve the helium atom by constructing many body basis....
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1answer
71 views

What exactly is meant by 'multi-configurational' and 'multireference'?

Some topics here have touched on this before (see 1, 2, 3), but I haven't found a clear definition yet. I would like to know what exact property of the wave function these terms refer to. It would ...
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Calculating the number of energy states in a particular momentum direction

Given is a 2D scenario of a particle within a container: The circumference shows all the possible 2D spatial directions for a given momentum value of the particle. One of those momentum directions is ...
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In 1 dimension, the curvature of Ψ = K.E. of wave. Is this the case for 2 dimensions and 3 dimensions also?

In 1 dimension, the curvature of Ψ = K.E. of wave. Is this the case for 2 dimensions and 3 dimensions also? Moreover, is curvature of Ψ = K.E. of wave = 2nd derivative of Ψ?
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How to use Hund third rule for cases like Nb, Ru, Rh, Pt?

How do I use Hund third rule to determine the value of $J$ for ground state for cases like Nb, Ru, Rh, Pt where there is 1 electron in s orbital and then an incomplete p orbital, and besides, S nor L ...
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1answer
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Help understanding the equation for Spin Energy in Zero Field

I’m working with a system that experiences spin frustration and for me this is the first time dealing with such a phenomenon. To grasp the concept, I’ve decided to go to the basics and read the ...
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1answer
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Magnetic couplings using DFT in a spin frustrated system

I’m working with a trimeric copper system that have the classic triangular shape and experiences spin frustration. This is my first time dealing with such system and, so far, from what I’m reading, I ...
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2answers
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Restrictions on transitions in Spectroscopy

Just for the sake of an example, let's assume a transition from one energy state to a higher energy state in atomic absorption spectrum If the energy difference between the ground state and first ...
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1answer
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Eigenvalues of Hessian matrix when the molecule is not at its equilibrium configuration

Given the potential energy surface (PES) of a system, we can calculate the Hessian matrix $H$ of each point $x$ on the PES. $$H_{ij}(x) = \frac{\partial^2 E}{\partial R_i \partial R_j}|_{R = x}$$ ...
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What is the intuition of using “dimer method” for searching transition states?

I learned dimer method for searching transition state in this paper: A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. However, I still ...
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1answer
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What is the difference between carbon in an excited state and with sp³ hybridization?

What is the difference between the carbon in the excited state, $\ce{[(1s)^2] (2s)^1 (2p)^3}$, and $\pu{sp^3}$ hybridization?
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1answer
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Why density functional theory favors a uniform electron density?

Why density functional theory (DFT) favors a uniform electron density when we use it to calculate ground state electronic structure self-consistently? For example, when we use DFT for calculating ...
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Keeping the electronic configuration in the ground state is expensive in Ab-initio MD?

In E. Sandré & A. Pasturel's An Introduction to Ab-Initio Molecular Dynamics Schemes If using small time steps (typically in the order of a few tenth of femto-second), the changes in the ...
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1answer
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Why $\psi(r_e, r_n) = \sum \psi_e^i(r_e|r_n) \chi^i(r_n)$ in Born-Huang expansion?

Given a molecular system, the time-independent Schrodinger Equation (SE) that we want to solve is $$\hat H \psi(r_e, r_n) = E \psi(r_e, r_n)$$ $\hat H$ is hermitian, so the set of solutions $\psi(r_e,...
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1answer
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What exactly is a potential energy surface?

I first learned about potential energy surface (PES) when I was studying Born-Oppenheimer approximation. In the approximation, the PES is essentially electronic PES which is defined as follows: ...
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Calculation of average bond length from force constant and IR absorption?

I need some help beginning a problem set problem (just want hints, I'd like to figure it out myself). The problem gives me the IR absorption for a diatomic, as well as the force constant for the ...
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1answer
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How does the Wave-Mechanical model reconcile with the particle definition of an electron?

While just starting chemistry, I have a little pit of particle physics knowledge. I was introduced with the wave-mechanical model of an atom and was slightly confused, because from particle physics, I ...
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1answer
103 views

Is the Lowdin Orthogonalization used in diagonalizing the atomic orbitals really a basis change?

This is kind of more on the mathematics side of quantum chemistry, but I can't quite figure out why the Lowdin Orthogonalization is called a basis set change. I get how it works from the perspective ...
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1answer
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Structure of atom [closed]

Consider one He+ ion in exited state(n=5).In the answer it is given that no. of spectral lines produced is 4 not 10.can't we use the general equation?