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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How long would it take for a tank of same-spin hydrogen atoms to become a tank of H₂?

In the question Is there an energy cost associated with flipping the spin of an electron?, it is shown that it is very unlikely for two hydrogen atoms to bond if their electrons have the same spin. ...
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Calculating the Molecular Orbitals of a Molecular State [closed]

I am performing ab initio calculations on a heteronuclear diatomic compound using the MRCI method on the MOLPRO quantum chemistry package. I obtained the molecular states of the compound but I was ...
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Why does the Heisenberg uncertainty principle work in an atom? [closed]

Where is my logic wrong? An electron can only assume quantized energies in an atom. If an electron is localized in space in a hydrogen atom, its radius is known. If its radius is known, its ...
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What is mass-independent isotope separation/fractionation?

How can any separation/fractionation of isotopes be mass-independent, if the only difference between two isotopes is mass? The only clue(s) on Wikipedia mention molecular symmetry, 'forbidden' spin-...
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Is the correlation energy of a system always negative?

The correlation energy of a system is defined as the difference between the exactly energy and the energy in the Hartree-Fock method: $E_\mathrm{cor} = E - E_\mathrm{HF}$. In the case of an atom or a ...
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Is there any publicly available software that can do deterministic CCSDTQP other than MRCC?

MRCC can do arbitrary order coupled cluster but much of the code is computer-generated (not hand-coded by a human) so it can be slow. There are some stochastic codes for high-order coupled cluster, ...
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On diagonal terms in the Coulomb matrix

I have seen many machine learning algorithms for prediction of quantum chemistry properties that use Coulomb matrix as their input. Coulomb matrix is defined as, $$\boldsymbol{M}_{i j}^{\mathrm{...
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Properties that probe electron kinetic energy

This post is inspired by a question regarding the meaning of off-diagonal elements of the KE matrix (in some AO basis). One answer suggests that a diagonalized KE matrix might not be very useful. I ...
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Accuracy of Quantum Chemistry ML models

I am trying to compare the performance of few Quantum Chemistry property prediction ML models. I was looking at the following table from DOI: 10.1039/c7sc02664a The problem is that it does not ...
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Global reactivity parameters from open shell DFT calculations using Koopman's theorem

Koopmans' theorem is a useful approach to calculate the global reactivity parameters from the HOMO-LUMO energies. My question is, does it apply to the open-shell systems where we get two sets of ...
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Using a the particle in a box - one dimension, to calculate the zero point energy of an hydrogen atom

I have been tasked with using the one dimensional particle in a box model to calculate the zero point energy of an hydrogen atom with different sizes. Using the formula $E_1=h^2/(8mL^2)$ for a box ...
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Psi4 gradient calculation with complete basis set? [closed]

I'm trying to set up a gradient calculation for psi4. In my input.dat file, I have tried the following keywords: set basis cc-pVTZ gradient('CCSD(T)') which is ...
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Why are the OV and VO blocks of the CIS 1RDM zero?

I know the reduced density matrix has the form: $$ \gamma(\alpha,\beta) = \langle\Psi_N|c^{\dagger}_{\alpha} c_{\beta}|\Psi_n \rangle $$ but when $\Psi_N$ is the configuration interaction singles (CIS)...
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The fifth shell of an atom [closed]

According to the $2n^2$ rule, the fifth shell should accommodate 50 electrons. However, my chemistry book says that the $2n^2$ rule does not apply to the fifth shell. Could you explain why this ...
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Electron Spin, and the Stern-Gerlach Experiment

I think I understand the basics of the electron spin. However, I'm trying to figure out how to tell if, when shooting a beam of atoms (the Stern-Gerlach experiment), how to tell if an element will ...
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Why is the iron inter-system crossing non-negligible at high temperatures?

Inter-system crossing (ISC) is a radiationless process involving forbidden transitions between singlet and triplet state. These are more common with heavy atom molecules, so I understand that ISC is ...
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IRC analogue of conical intersections and minimum energy crossing points?

In my project, there are some spin forbidden organometallic reactions that involves both the triplet minima and singlet transition state (TS). Using the penalty method in qchem as well the method of ...
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The concept of normal coordinates of a molecule

Sometime ago I had posted the What is the origin of "normal" in normal coordinates and normal modes? in math & sci history problems. Nobody was sure for the reason for using the word normal there -...
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How to extract force constants for normal modes from ORCA?

I am following the computational method described in Scientific Reports.[1] Where the authors analyze the contribution of each excited state normal-modes to the shift of the transition energy. For ...
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Software that determines whether a molecule can exist and draw it from a formula?

I have run calculations that predict atomic configurations. As a simple example, in a system that contains H and O, I might get a list like: ...
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Which DFT functional is best for predicting macroscopic properties of molecular liquids?

Which DFT functional (KS-DFT, to be more specific) performs best at predicting macroscopic properties (density, surface tension, boiling point, relative permittivity etc.) of molecular liquids (...
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Are there any datasets containing molecules with more than 38 heavy atoms?

I have been testing a machine learning approach for molecular energy prediction. The current dataset that I have is QM9, which is consist of molecules with up to 9 heavy atoms. I was wondering if ...
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How to formulate the 1 dimensional time-dependent Schrodinger’s equation from a given function?

Assuming $f(t) =e^{−iωt}$, formulate the 1 dimensional time-dependent Schrodinger’s equation. I started solving the problem as \begin{align} E &= hf, \tag1\label{eq:1}\\ E &= ħw, \tag2\...
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Molecular dynamics (Mac OSX user): what software can I use to plot RDFs for NPT simulations? VMD only works for NVT (constant volume)

I would be very grateful if someone could recommend a way to plot RDFs for NPT ensemble molecular dynamics simulation results. I use CP2K to run NVT simulations and usually use VMD to process ...
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Why does the d orbital size decreases on addition of electrons?

In Concise Inorganic Chemistry by JD Lee (4th edition; adapted by Sudarshan Guha), on page 80 under section 3.7 "The Extent of d-orbital Participation in Molecular Bonding" it is given: A second ...
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What is the biggest known difference between rₑ and r₀?

What is the biggest known difference between $r_e$ and $r_0$? Where $r_0$ is the average bond length of the lowest vibrational state, and $r_e$ is the location where the potential is lowest. For a ...
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Who came up with the box and arrow diagrams for electron configurations?

In general chemistry texts, the electron configurations are sometimes shown in boxes with up and down arrows to show the concept of paired spins. My impression for years was that Hund used such ...
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Potential energy of electron in excited hydrogen atom

The angular momentum of electron in an excited H atom is $\frac{h}{\pi}$. The potential energy (PE) of electron is? Let $\frac{h}{\pi}=\frac{nh}{2\pi}$, therefore $n=2$. So, $$E=\frac{-13.6}{4}=\pu{-...
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Term symbols for nitrogen: determining J

I'm trying to figure out what terms are possible for nitrogen with the electron configuration $\ce{[He] 2s^2 2p^3}$. There is an old question on StackExchange and the corresponding answer was a great ...
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Potential energy of electron density at the nucleus

Consider the hydrogen atom for simplicity. The electronic density at the nucleus is not null. The attractive potential between a small volume of electronic density $\mathrm dV$ (at position $\vec r$)...
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What is meant when people say a molecule has high multi-reference character?

I have read some other posts explaining what multi-reference and multi-configuration are with regards to the wave-function (such as What exactly is meant by 'multi-configurational' and 'multireference'...
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Applying the constant number of electrons in DFT density optimisation

(Previous related question: Finding mathematically the ground state density in DFT) I am studying the density optimisation procedure (in particular for Orbital-Free DFT) this thesis. The derivative ...
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Cauchy-Schwarz integral screening different inequalites

Eq. (9.12.23) in [1] states that: $$\sum_{abcd}c_{ab}c_{cd}g_{abcd}>0\tag{MEST 9.12.23}\label{91223}$$ with $c_{ab}=c_ac_b$ for $c_a$ being some distribution coefficients and $g_{abcd}$ being the ...
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Finding mathematically the ground state density in DFT

To find the ground state density in DFT, you set the following Lagrangian: $$L = E[\rho(\vec r)] - \mu\left(\int \rho(\vec r) \mathrm{d}\vec r - N\right)$$ While minimising with respect to the ...
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1answer
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Probability density “AT” the nucleus?

Just had a conceptual question from radial wave functions. I wanted to know if probability density AT the nucleus is maximum, or zero. From the attached images, it is clear that the function is at ...
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What will happen if electron as a wave undergo destructive interference while travelling in its Orbit?

Today I came across a justification of Bohr's angular momentum quantization using the De- Broglie's hypothesis. The justification said that since the electrons are having wave nature also then while ...
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What gives rise to the color of sapphires?

Here is what I know: Sapphires are composed primarily of $\ce{Al2O3}$ (in pure form colorless) as well as Fe and Ti (trace impurities responsible for the color). I know that the proportion and ...
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1answer
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How to calculate molecular emission spectra?

Is there free software that can calculate the fluorescence emission spectra of organic molecules? Let's say, for example, rubrene There is a bunch of quantum free quantum chemistry software: https://...
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725 views

Radial Probability Distribution Curve versus ψ² versus r curve for 1s orbitals

My question is basic, but I have already referred to a couple of books. This is an excerpt from Linus Pauling's book: the most probable distance of the electron from the nucleus, which is the ...
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Additional example determining Marcus parameters searched

Background / theory: The electron transfer in organic materials was formalized by the Marcus theory, introducing $|H_{ab}|$ to describe the how molecules (or more generally: sites) are coupled with ...
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Why does the SCF not converge in a structure optimization with GAMESS of the thiourea molecule at the PM6 level of theory?

I'm using GAMESS to run a geometry optimization on a thiourea molecule, using PM6. However, the output file keeps displaying the error message, "NO FORCE FIELD, SCF DOES NOT CONVERGE." Is there an ...
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Wave-particle duality [closed]

Can I get an answer stating some analogies on how electrons behave like a wave, and what does it even mean for an electron to behave like a wave? Also, if going around the nucleus, is electron a real ...
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The influence of diffuse functions on electron density calculations

I am not a quantum chemist, but I am (starting to be) a user of electronic structure software. In the picture (screenshot) is the electron density of the same molecule. On the left I calculated the ...
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How can I obtain the wave function of the dihydrogen system, by hand using Self Consistent Field DFT calculations? [duplicate]

After doing some energy calculations for the $\ce{H2}$ system in Gaussian, using ωB97X-D/STO-3G level of theory, and generating a .wfn file, I wanted to understand better how the computer does ...
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How to account for solvation of a molecule explicitly in quantum calculation?

I'm looking for a way to account for hydrogen bonds formed with my molecule in aqueous solution explicitly in DFT calculation. I'll do it in order to compare stability of two structures in water. As ...
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Developing Computational Chemistry Software

I want to learn to develop novel methods in computational chemistry (e.g. Grimme's empirical dispersion, DFTB, new DFT functionals, etc.) What is the ideal way to learn this by oneself? I have read ...
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Electronic States of the (unstable) tetrahedral CrCl4

I was probing for first order Jahn-Teller instability in the coordination complex CrCl4 (2 electrons in E set). Taking the direct product yields the states A1 + A2 + E, so I took the symmetric and ...
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What is meaning of LAV2P basis set?

I am working on energy optimization of molecular structure using DFT with Schrödinger software and I found that job is running on LAV2P basis set. I want to know what is the meaning of this basis set ...
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2answers
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What does Brightness/ intensity of spectral lines depend on?

My book states that it depends upon "The number of photons of same frequency or wavelength ABSORBED or EMITTED" From what I understood, if many hydrogen atoms within the discharge tube EMIT the same ...
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Prove that idempotency is a necessary and sufficient condition for a densiy matrix to be N-representable

As I understand, a necessary and sufficient condition for a density matrix $P$ to be represented by a wavefunction $|\Psi\rangle$ is that it is idempotent, i.e. $P^2=P$. It is easy to see that if $P=|\...

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