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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What is meant by “non-relativistic”?

I am reading a document on cosmology and particle physics (this s the first time I look into something like this). It frequently states the word "non-relativistic" but I do not understand ...
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How can 2 molecular orbitals form simultaneously? [duplicate]

I understand (for example in the case of H2) that two s orbitals produce through constructive interference a bonding orbital and that the out of phase combination of two s orbitals leads to ...
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Question regarding conflicting results of checking the electron-preciseness of isoelectronic species via NBO and EHM calculations

It is well known that the tert-butyl cation's empty 2p orbital on the central carbon is stabilised by hyperconjugation from neighboring C-H bonds. This would mean that the central 2p "lone pair&...
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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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Is the lone electron pair of an amide nitrogen part of the π system when building a Hückel matrix?

Is the lone electron pair of the nitrogen atom part of the conjugated π system in the α,β-unsaturated amide pictured below? Is there a general rule for choosing when to include a nitrogen atom in a ...
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785 views

Why is Coupled Cluster not variational?

It has been noted in several sources (e.g. J. Romero et al. Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz. arXiv:1701.02691 [quant-ph]) that one of the ...
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How to transform 'Cartesian gradient' taken from the formatted checkpoint file into the input orientation?

I would like to extract the energy gradient at a particular geometry with many digits from the formatted checkpoint file. However, Gaussian prints the gradient components related to the standard ...
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Born–Oppenheimer adiabaticity

The Born–Oppenheimer aproximation is said to be adiabatic. What does "adiabatic" mean? What would be a non-adiabatic approximation to the Schrödinger equation?
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Why don't carbon nanotubes behave like quantum dots?

If carbon nanotubes (CNTs) have the size required to have an bound electron energy state, why don't CNTs behave like quantum dots, such as having optical tunability, amongst other properties?
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Why don't the MO energies sum up to Hartree-Fock SCF value?

I would like to calculate Hartree-Fock energy of $\ce{H3^+}$ ion from orbital energies. So I performed the following calculation in Gaussian 16: ...
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Quantum chemistry Python package to solve the Coupled-Perturbed Hartree–Fock equations

Two of the most well-known Python quantum chemistry pakcages, PySCF and Psi4, can solve the Hartree–Fock equations. However, I am interested in finding analytic derivatives of the electron integrals: $...
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Why doesn't the graph of radial part of wavefunction of 2p orbital change its sign? [closed]

Below I have given the graphs of radial part of the wave functions of $\mathrm{2s}$ and $\mathrm{2p}$ orbitals respectively. The graph of the $\mathrm{2s}$ orbital makes sense. It has a radial node ...
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Calculating the zero-point energy for the C2N2 molecule

I shall calculate the zero-point energy for the $\ce{C2N2}$ molecule in the $^{1}\Sigma_{g}^{+}$ electron ground state with the following vibrational wavenumbers (symmetries in parentheses) which were ...
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Solution of the Roothaan Equations of H2 by Symmetry Arguments

FWIW my background is in physics and maths, but I am just starting a chemistry PhD (the last time I took a chemistry class was high school). I have only some background in representation theory, and ...
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Significance of the ground state energy in quantum chemistry?

In quantum mechanics, quantum chemistry, and condensed matter physics courses, it seems like finding the ground state energy of a Hamiltonian is incredibly important. I can understand why having the ...
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Probability of finding electron in each orbital

This may include some quantum physics. Are there anyways to describe the wave function of Hydrogen's orbital (or that of a Hydrogen-like atom) in terms of the wave function of each orbital? You can ...
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Hund's rule for comparing term symbol energies in excited state

This question was asked in an exam: The lowest energy electronic state for excited state carbon atom is, a. $^1D_2$ b. $^3D_1$ c. $^3D_3$ d. $^3D_2$ Although we have been taught Hund's rule for ...
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Can actinides form diamagnetic coordination complexes?

I am not sure how accurate I can predict the magnetic properties of actinide diamagnetic complexes, due to the fact that they share the F-block electron as Lanthanides, which are already tricky, ...
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1answer
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Is the effective nuclear charge only defined for valence electrons?

I've just been taught about the effective nuclear charge and screening effect in school. I'd like to ask and confirm if the effective nuclear charge is only defined for valence electrons. If not then ...
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How can antibonding orbitals be more antibonding than bonding orbitals are bonding?

In molecular orbital theory, the fact that a bonding and antibonding molecular orbital pair have different energies is accompanied by the fact that the energy by which the bonding is lowered is less ...
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First ionization energy and electron gain enthalpy of dihydrogen / stability comparison of dihydrogen ions [duplicate]

Subset of: How can antibonding orbitals be more antibonding than bonding orbitals are bonding? Stability of $\ce{H2^{-}}<\ce{H2^{+}}<\ce{H2}$ Stability of $\ce{N2^{-}}<\ce{N2^{+}}<\ce{N2}...
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Limitations of Quantum Chemistry [closed]

I have a physics background and I am interested in the applications of quantum mechanics in predicting chemical reactions, and I’m wondering where should I start? I am particularly interested in the ...
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How are London Dispersion Forces generated?

While talking about the gaseous state of matter we came to the topic of London Dispersion Forces caused by the generation of a dipole in one atom which induces a dipole in another. While talking about ...
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How to find the number of valence electrons with the help of 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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How are Quantum Dot molecules formed and what properties do they hold apart differently from singular quantum dots? [closed]

I am trying to understand the science and phenomena behind the function and operation of quantum dot molecules, but the only articles I run into talk about the synthesis of them. Could this be ...
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1answer
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What does the wave function of an electron look like? [closed]

In quantum mechanics, in the 'particle in a box' topic, I studied that by solving the Schrödinger equation, we can actually find out what the wave function of the particle in a box looks like. ...
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388 views

What are the molecular orbitals of the hypothetical linear H₃⁺ molecule?

What would be the wave function of the lowest energy molecular orbital of a hypothetical linear $\ce{H3+}$ molecule? According to the LCAO method, I feel the lowest energy MO will be $\mathrm{1s(A) + ...
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153 views

Is the correct zeroth-order wave function $\phi^{(0)}$ an eigenfunction of the perturbation Hamiltonian $H'$?

Consider the perturbation treatment of He $1s2s$ excited state configuration. The quantum mechanical Hamiltonian for the He-atom is: \begin{aligned} \hat{H} = \sum_{i=1}^2 h_i + \frac 1 {r_{1 2}} \\ ...
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Slater Matrix of Methane Molecule

I am going through Hartree-Fock calculations in detail, but the textbooks I am referring all considered homonuclear molecules as examples. So I am trying to come up with my own the Slater determinant ...
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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 would one separate a mixture of isotopes (different nuclear spins) at temperatures near 0 Kelvin?

Suppose we have two isotopes of the same element. For example, isotope A could have a nuclear spin I = 0, isotope B could have nuclear spin I = 3/2. Let us say we have a compound where this element is ...
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Ignoring spin, consider an electron in a hydrogen 2p orbital, what is its orbital magnetic moment?

I know that a magnetic dipole moment is given by $$\mu=\frac {-e}{2m}I$$ and that the z component of angular momentum is $$m_j\hbar.$$ However, I have also seen that angular momentum $I$ is given by $$...
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Szabo/Ostlund exercise on spin orbital orthonormality

I have a question about exercise 2.1 in Szabo and Ostlund's Modern Quantum Chemistry, which concerns the inner product between different spin orbitals: $\require{begingroup}\begingroup\newcommand{\br}{...
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What is the point of introducing virtual orbitals in Hartree-Fock calculations?

Let us for simplicity discuss RHF formalism. For $2n$-electron system we have $n$ Hartree-Fock equations written for $n$ spatial orbitals $\{ \phi_{k} \}_{k=1}^{n}$ $$ \newcommand{\mat}[1]{\boldsymbol{...
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1answer
404 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 ...
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f-electrons in chemistry of heavy transition metals

In one lecture at a recent MCR-X conference I was puzzled by a side-note "f-hole is critical to describe DoS of $\ce{IrO2}$ correctly." The context was DFT periodic plane-wave calculations ...
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Using symmetry and group theory arguments to explain iron(II) in a tetrahedral crystal field

I am trying to figure out how to explain $1s \rightarrow 3d$ spectroscopic transitions for $\ce{Fe^{2+}}$ in $T_\mathrm{d}$ symmetry. These transitions make up the pre-edge region in K edge X-ray ...
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1answer
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Bond lengths: 1-D particle-in-a-box for 1,3-butadiene

When estimating the length for a one-dimensional particle-in-a-box model for a hydrocarbon (such as 1,3-butadiene), do we include the bond lengths between the (terminal) carbon and hydrogen atoms at ...
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Model of a particle in a linear box

I'm studying the model of a particle in a linear box when we have a chain of unsaturated carbons. I have a chain with 3 bonds and 4 atoms of carbon. I'm applying the expression $\lambda = \frac{8cmL^2}...
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1answer
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Hartree-Fock vs. DFT vs. Hohenberg-Kohn vs. Kohn-Sham

What is the difference between these four approaches? My current understanding is that Hartree-Fock uses only 1 slater-determine (accounting for antisymmetry) but neglects correlation between ...
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Why are electrons filled in fourth shell before the third shell is filled?

I am a beginner and am learning about atomic structure and I am getting confusions regarding the aufbau principle. It is said that the electrons will be filled first in lowest available energy level. ...
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Oscillator Strength and Absorption Intensity in TDDFT

When I run a linear-response time-dependent DFT calculation in my favourite electronic structure program, for each excitation I'm given an oscillator strength, $f_i$, and transition dipole moment $$\...
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High symmetry points and x-coordinates

Is it possible to work out the x-coordinates related to high symmetry points? The software I'm using doesn't provide me with that, so I was wondering if there is a way to manually figure it out, as I ...
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2answers
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Normalization of a free particle in 1 dimension

I am having difficulty normalizing the wavefunction for a free particle in 1 dimension. I have sent an attachment of my working out. My attempt at the normalisation Free electron: $$-\frac{\hbar^2}{2m}...
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1answer
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Quantum Espresso, phonon band dispersion

I am having a trouble calculating the phonon band dispersion of graphene at $K$-point using Quantum-Espresso, using normconserving+LDA and normconserving+PBE, ecutwfs=60, Ecutrho=400.0, forc_conv_thr=...
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How is kinetic energy accounted for when describing diatomic bonds with a Morse potential?

The Morse potential can be used to describe the potential energy of the a diatomic bond: This curve suggests that the lowest state $v = 0$ is the most stable, since it has the lowest potential energy....
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How to calculate molecular dipole moment from a known wavefunction?

Say I have a molecular wavefunction as a set of molecular orbitals and want to calculate the molecule's dipole moment, but don't know how! I searched a lot but couldn't find any practical example. $$\...
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How to carry out basis set fitting and extrapolation

I am playing around with basis set extrapolations, and i would like to perform some simple tests by doing some parameter fitting and checking the errors. The functional form of the fitted curve is ...

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