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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Probability density and radial distribution function of finding the most probable distance of electron in 2p orbital in hydrogen atom

Referring to the answer by DSVA (Most probable point for finding an electron in the 1s orbital of a Hydrogen atom) There's a maximum of finding the electron at a certain distance away from the core (...
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How can I drive Heisenberg's uncertainty principle from the wave function [closed]

I want to find Heisenberg's uncertainty principle from the wave function.
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Violation of pauli's exclusion principle? ( During formation of neutron star or black holes) [closed]

Sorry it's a bit long so i was watching Action labs video on how neutron stars are formed and in that he says " if there's enough mass, then the mass will keep on collapsing in on itself in the ...
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Proof for equation of radial probability distribution curve

So my textbook says the equation for this is $$P(r) = 4\pi r^2\Psi^2 $$ It also gives the volume of the shell formula $$\mathrm{d}V = \frac 43 \pi(r+\mathrm{d}r)^3 - \frac 43 \pi r^3$$ which I ...
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How do I show that a transition is electric dipole allowed with group theory/symmetry?

This is actually a follow up of this question The follow-up is not because of the electric instead of magnetic dipole (this is trivial). It is because I'm interested in extra info. Suppose I have a ...
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-2 votes
2 answers
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If two atoms join, do they lose their original spectral lines? [closed]

Each element and even isotope of element has its own set of unique spectral absorption lines. What happens to these lines after two or more atoms join together into molecule? Are all of the lines that ...
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Which quantum numbers does the orbital angular momentum depend on? [closed]

I learned from a question that I recently solved that the orbital angular momentum depends on both the azimuthal and magnetic quantum numbers. I did not expect this because the formula for the orbital ...
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1 answer
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Estimating the energy required for dissociation from visible absorption spectra

I have been having trouble solving the following problem. The question calls for an estimation of the energy (in kj/mol) required to dissociate ClO in its excited state when it is excited from the v = ...
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Interpair vs. intrapair nondynamic correlations

What is the difference between interpair and intrapair nondynamic correlations? What would an example of each “look” like in the context of the $\ce{H4}$ system [1]? Reference Ramos-Cordoba, E.; ...
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Modelling barrier-less reactions

I am currently exploring a few dissociative reactions whose PES is barrierless (no first order saddle point). I have found a few approaches in literature like flexible nudged elastic band theory, ...
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Is Lennard-Jones potential "abused"?

Bond Formation For example, when describing the potential energy curve of hydrogen molecule, the Lennard-Jones potential is employed and the energy minimum corresponds to the bond length of the ...
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ORCA finished by error termination in SCF gradient [migrated]

I try to optimize and compute frequencies for the system built up from C, O, H, and Co atoms in the following functionals: B2PLYP, B2PLYP-D3, B3LYP, B3LYP-D3, BLYP, BLYP-D3, DSD-PBEP86, PBE, PBE-D3, ...
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How to calculate <ab|ab> integrals to carry out Schwarz pre-screening of molecular integrals

During writing my own two-electron integration library I faced an issue of dealing with integrals that have very small values beyond the C/C++ double data type. ...
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If you are doing an ONIOM calculation in Gaussian, how do you add both custom MM parameters and a custom basis set using GEN and Amber=SoftFirst?

I am trying to calculate a biological system using AMBER forcefields as my low-layer in ONIOM3. I also want to use a non-native basis set (aug-pc-1 for opt+freq, aug-pc-2 for SPE) that requires custom ...
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Calculating zero-point energy for the Varshini potential

As per my understanding, for a harmonic oscillator, we can find the zero-point energy by the relation below: $$ E_0 = \left(0 + \frac{1}{2}\right)\hbar \omega$$ The equation for the potential in ...
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How do the spin-matrices change in systems without spherical symmetry?

The (non-relativistic) spin matrices of a free electron, with $z$ as the quantization axis, read: $$ \boldsymbol{S}_{x}=\frac{\hbar}{2}\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right],...
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Why do sp³ orbitals have tetrahedral symmetry when they are linear combinations of orbitals with octahedral symmetry?

I'm trying to understand how orbitals hybridize. What I understand—or at least think I understand—is the following: The "standard" $\mathrm{s}, \mathrm{p}, \mathrm{d}, …$ orbitals are ...
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How to obtain excited state energies from configuration interaction? (Helium example)

A theory of CI method For going beyond the Hartree–Fock (one determinant) approximation one introduce configuration interaction (CI). Interaction means the mixing (interaction) of different electronic ...
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Hund's Rule for Determining Term Symbol Energy Order

In order to determine the energy order based on J-value for term symbols we employ Hund's rule: In a less than $\frac12$-filled subshell Lowest J-value is Lowest energy In a more than $\frac12$-...
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Electronic vibrational rotational transition of electrons -- for a transition from $\Sigma$ to $\Pi$ how are P and R branches possible?

Suppose we have a diatomic molecule in a $^1\Sigma$ state, and it transitions to an excited $^1\Pi$ state. Note that the total spin of the electrons remains unchanged ($\Delta S=0$) as we can assume ...
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Why are Slater-type orbitals used for atomic calculations instead of hydrogen-like orbitals?

Originally, Hartree–Fock atomic calculations were done by using numerical methods to solve the Hartree–Fock equations, and the resulting orbitals were given as tables of the radial functions for ...
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How to compute the electronic energy reported by Gaussian from the AlphaOrbitalEnergies?

I followed the instructions on Wolfram Language & System Documentation Center — FCHK (.fchk) to analyze the *.fchk file. I ran an energy calculation with ...
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Shielding vs electron-electron repulsion

Example of shielding: (source) The last electron in the 6s subshell of $\ce {Cs}$ is shielded from the nucleus by the inner electrons. Example of electron-electron repulsion: The electron affinity of ...
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6-31G basis set of Silicon and the p-orbitals

Following is the 6-31G basis set of silicon. The numbers in the bracket denotes power raised to 10, e.g. $1.231(+3)=1.231 * 10^3$ Now silicon is $1s^22s^22p_x^22p_y^22p_z^23s^23p_x^13p_y^1$. Now I am ...
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4 votes
2 answers
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Spontaneous reaction between chlorine and a hypothetical atom

Suppose, my hypothetical element is $\ce X$, whose first ionization energy is $\pu{200kJ/mol}$. An atom of this element will react with an atom of chlorine (assume that I've already dissociated a ...
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2 votes
1 answer
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My book's claim about the shielding effect of s,p,d and f electrons

It's a relatively unknown Bangladeshi book. It's called "Chemistry-First Paper (Class XI-XII)" by Professor Haradhan Nag According to my book, "Electrons of s and p orbitals produce ...
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1 vote
1 answer
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Gaussian type orbitals and p-type orbital

The Gaussian orbital for $p_x$ is defined as: $$\psi_{p_x}=C(x-x_A)e^{-(\vec r - \vec R_A)^2}$$ Where $C$ is a constant. Now if we multiply two such orbitals with two different centers, then $$C_1(x-...
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1 vote
1 answer
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Why do DFT calculations output molecular orbitals?

My understanding is that DFT finds the electron density which minimizes some energy functional. How does it make the connection from this optimized density to molecular orbitals?
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A question regarding hydrogen emission and absorption spectrum

I have read in many articles as well as my textbook that when an electric discharge is passed through a sample of hydrogen gas it excites the electrons and glows emitting light.When this light is ...
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What is the physical significance of the damping function in calculation of vdW interaction energy?

In order to take care for the singularity (also removing the double counting of exchange-correlation) obtained with this expression, $$E_\mathrm{vdW} = \frac{C^6}{R^6}$$ many type of damping functions ...
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3 votes
1 answer
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2p wave function radial distribution

The following graph shows the values of the wave function $\psi_{210} $ (i.e. the $2\mathrm{p}_z$ orbital) versus the radius (divided by $a_{0}$). I don't understand it, however, since the $2\mathrm{...
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7 votes
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Variational (Rayleigh-Ritz) method and multielectron wavefunction

I am studying Rayleigh-Ritz method and I have some problem to understand what the final wavefunction looks like. Suppose that we have a system with $N$ electrons, atom or molecule. We are interested ...
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A question regarding excitation of electrons in atomic orbital [closed]

In Bohr's model of an atom, the formula used to find the energy between the 2 orbits and wavelength of emitted photon was valid only for single electron species like hydrogen.In the case of a multi-...
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3 votes
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State-of-the-art results on molecular vibronic energy calculation

Could someone kindly point me to the latest records in scale, accuracy, or timescale for molecular vibronic energy calculation? I tried to start with Google Scholar: https://scholar.google.com/scholar?...
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1 answer
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Comparison between Atomic Spectrum of Hydrogen and Alkali Metals

I posted a question on Chemistry Stack Exchange a while back. It was related to the naming of atomic orbitals. One of the answers to it mentioned a research experiment. The link to the question is ...
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Is the shortness of boron trifluoride's bonds better understood and explained now than it was "way back" in the 20th century?

Wikipedia's Boron trifluoride; Structure and bonding says: In the boron trihalides, BX3, the length of the B–X bonds (1.30 Å) is shorter than would be expected for single bonds,7 and this shortness ...
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Size of Orbitals, Making Intuitive Sense of Quantum Model, Nomenclature of Subshells in the Quantum Model

Alright, so I am doing the Quantum Mechanical (or what some people call the Wave Mechanical model) of an atom. There's this part where we have different zones of the probablity of finding electrons, ...
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Analytical Prediction of Molecular Interactions [duplicate]

Is it possible to predict the molecular interaction between any two molecules analytically or through some simulation mechanism based upon analytical theory? I see a rather big gap between, say ...
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9 votes
2 answers
573 views

How to find the orbital a given wavefunction represents?

We were given the following question in chemistry class (under the topic “Atomic Structure”): Which orbital does the following wavefunction represent? $$φ(r) = \frac{1}{81(6π)^{1/2}}\left(\frac{Z}{a}\...
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Schrodinger operator with matrix potential and Green's function

Clearly Schrodinger operators with matrix potentials appear very naturally in molecular dynamics/quantum chemistry, particularly when considering a crude adiabatic basis or diabatic basis for an ...
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Book reccomendations for Pertubation Theory? [duplicate]

I'm sorry if this is an inappropriate place to ask this, but I'm still trying to get the hang of this site. So my book is Thomas Engel and Philip Reid Physical Chemistry $3^{rd}$ ed. I'm on the ...
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How to find the wave equation in a 1D box with a 2 different V(x) values

So this is for a simple infinite well $1$D box. The bounds are defined as $V(x)=0$, for $0<x<\frac{L}{2}$, and $V(x)=V_0$ for $\frac{L}{2}<x<L$ with everywhere in the box having a ...
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2 votes
2 answers
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Why is the momentum of the wave function in a 1-D particle-in-a-box = 0?

Is this implying that a particle in the box for 1-dimension has no momentum? Or is the momentum average out to $0$ on throughout the region $0\leq x\leq a$? For reference, I was told the state was $n =...
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1 answer
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Filling 3d and 4s orbitals

So the 3d orbital comes after the 4s orbital on the periodic table because it has a higher energy level, but then why are the electrons removed from the 4s orbital before the 3d orbital? For the 3d ...
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7 votes
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How does the MO-LCAO theory explain the direction of valence bonds?

As all the bells sound, the common explanation of geometry of a molecule (consider the water molecule) is due to overlaping electron density. The valence bond theory of the water molecule describes ...
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Does a node require Change in sign of wave function

In a quantum Chemistry course we were asked to find the number of nodes of the wave function $$\Psi=\frac{\sin^2 x}{x^2} : -3\pi \le x \le 3\pi$$ Clearly this has a removable discontinuity in x=0 so ...
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1 vote
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Computing full Electron-Nuclear Interaction Integrals using Obara-Saika Scheme?

Following my previous question Here, I had been trying to implement One and Two electron integrals in the code. I am currently stuck at the implementation of the OS Scheme, where I read the references ...
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7 votes
1 answer
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Can Electron Repulsion Integrals be negative?

I am trying to write a HF code that can calculate the orbital energies for a given molecule at RHF level. I got upto calculating electron repulsion integrals (ERI) and kinetic energy (KE) integrals, ...
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1 vote
1 answer
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Tight-binding model in the presence of a metal atom

Consider a molecule such as a porphyrin ring. For many purposes, a simple tight-binding model in which only pi-electrons are included provide a very good description of the electronic levels, shape of ...
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Notation for orbital coefficient matrix in RHF vs UHF

My question stems from Table 1 of this paper: "Generalized Hartree–Fock Description of Molecular Dissociation, by Carlos A. Jiménez-Hoyos, Thomas M. Henderson, and Gustavo E. Scuseria" https:...
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