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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81
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7answers
118k views

Why is the 2s orbital lower in energy than the 2p orbital when the electrons in 2s are usually farther from the nucleus?

My chemistry book explains that even though electrons in the $\mathrm{2p}$ orbital are closer to the nucleus on average, electrons from the $\mathrm{2s}$ orbital spend a very short time very close to ...
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5answers
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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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3answers
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What is the inert pair effect?

I was reading about the p-block elements and found that the inert pair effect is mentioned everywhere in this topic. However, the book does not explain it very well. So, what is the inert pair effect? ...
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Can hot food ever emit x-rays or gamma rays?

I was just wondering, if heating food up is the result of increasing the energy of bends and stretches in the bonds of the molecules, is it ever possible for tiny amounts of x-rays and gamma rays be ...
35
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Difference between shells, subshells and orbitals

What are the definitions of these three things and how are they related? I've tried looking online but there is no concrete answer online for this question.
33
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3answers
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Pauli exclusion principle and resonance

I've always been a bit uncomfortable with the concept of more than two electrons in a single orbital-like region(probability-wise) which occurs in resonance. This seems to disobey Pauli's exclusion ...
33
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1answer
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Is there an energy cost associated with flipping the spin of an electron?

THE STORY: A common example used to illustrate the limitations of restricted Hartree-Fock (RHF) theory is the H$_2$ dissociation energy ($D_e$) curves. RHF enforces electrons to be paired into spin ...
31
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1answer
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Acidity of substituted phenols

Phenol has a $\mathrm pK_\mathrm a$ approximately equal to $9.9$. When one studies the acidity of chlorophenols, one notices the following: First of all, chlorophenols are more acidic than phenol, ...
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What is the exchange interaction?

As the wikipedia article for the exchange interaction so aptly notes, exchange "has no classical analogue." How wonderful. Exchange shows up essentially while enforcing the condition that two ...
30
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1answer
504 views

Imaginary Bonding Interactions

Usually in chemistry, we deal with bonding interactions. That is, if I have the diatomic A-A molecule or A-B molecule, there's a favorable interaction (i.e., a bond) and a prototypical MO diagram like ...
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3answers
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Do electrons have some volume, area or shape?

I am in 8th grade now and when I was in 6th grade, my science book had diagrams of the electronic configuration of atoms. The electrons were round like spherical balls. Is it true that the electrons ...
28
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3answers
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Why are covalent bonds directional?

It is said that covalent bonds are directional, while ionic bonds are not. Why? Is it because of the orientation/directional properties of the overlapping orbitals?
28
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1answer
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Suggest methods and basis sets for a variety of systems

Please help me with any/all of the cases below. In the following cases, the named method and basis set are not suitable for the chemical systems. Why aren't they? Could you suggest a suitable method/...
27
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4answers
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How do Quantum Software Packages Work?

If one wants to calculate a moderate size Alkane (with say 10-15 Carbons , assuming 100 electrons , with Restricted Hartree Fock based methods) we can simply say that electron-electron part will be $...
26
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2answers
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What do the quantum numbers actually signify?

I know how to calculate them and such stuff, but I wanted to know what they actually signify. I have a vague idea that they have something to do with an electron's position in an atom but what do all ...
26
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4answers
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Why don't equivalent hydrogens cause splitting in NMR?

When doing NMR spectroscopy, it is an observed fact that equivalent hydrogens do not split one another. Why don't equivalent hydrogens split each other's signals? For example, why is the NMR spectrum ...
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Why do atoms “want” to have a full outer shell?

Okay, so I know that this is about filling the orbitals of the atom, and I understand that. What I don't understand is why? For example, an Oxygen atom has 8 protons and 8 electrons spinning around it....
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Why are noble gases stable

I was recently asked the question "Why are noble gases stable? with the expectation of providing an answer beyond the general explanation of "they have full valence layers" and I couldn't think of one....
25
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2answers
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Sp5 hybridization in cyclopropane?

I have never before heard/read about something as a $sp^5$ hybridization. Today, Henry Rzepa's blog post made me aware of the existance of such a bonding system. That made me search a little bit and I ...
24
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2answers
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How to find the second order perturbation to wave function?

Today, I'm looking for how to find the 2nd perturbation to the base in Rayleigh Schrödinger Perturbation Theory (RSPT). SETUP Starting from the 2nd order perturbation in Dirac's notation: \begin{...
24
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1answer
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Canonical MOs vs. Localized MOs: Do both represent reality in the same way?

In my understanding localized molecular orbitals (LMOs) are equivalent to "standard" molecular orbitals, often called canonical orbitals (CMOs—by the way, why are they called canonical?). We can ...
23
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3answers
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What is the physical basis for Hund's first rule?

According to Hund's first rule, a set of degenerate orbitals are singly occupied first, before the second slot in any of the orbitals are populated. This is quite intuitive because electron-electron ...
23
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2answers
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Why is chemical accuracy defined as 1 kcal/mol?

"Chemical accuracy" in computational chemistry, is commonly understood to be $1~\mathrm{kcal\over mol}$, or about $4~\mathrm{kJ\over mol}$. Spectroscopic accuracy is $1~\mathrm{kJ\over mol}$, and that ...
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3answers
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Symmetry lost in orbitals?

I've always thought that orbitals lead to a loss of symmetry, and have never been able to give myself a satisfactory answer to this. I'll explain via an example: Let's take an $\ce{N^3+}$ atom. It's ...
23
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1answer
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How dependent are computed charges using the quantum theory of atoms in molecules on the used level of theory?

The quantum theory of atoms in molecules is based on the topology of the electron density. This mathematical analysis allows to find critical points and hence has a unambiguous way of separating a ...
22
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Physical intuition behind negative values for wave function?

So a positive and a positive wave function create a bonding orbital where the probability of finding an electron is summed while a positive and a negative create an anti-bonding orbital with a lower ...
22
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2answers
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Why do n AOs only form n MOs? [duplicate]

The textbooks I have read introduce LCAO by considering the H2 molecule. In this example, there are only two possible combinations of the two 1s orbitals (in phase and out of phase). When there are ...
22
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3answers
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What is charge shift bonding?

Can someone explain to me charge shift bonding? I recognize that it is proposed as another domain of bonding - one different from ionic and covalent bonding. I am also told that $\ce{C-F}$ exhibits ...
22
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1answer
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What is behind of the attraction between a burned matchstick with a magnet?

I do not know how to understand the reasons of why a burned matchstick is attracted by a magnet (most probably) of Neodymium. Here are some screenshots of a video in which this natural phenomenon is ...
22
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2answers
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Is Hydrogen Bonding a Type of Dipole Dipole Interaction?

I understand that dipole dipole forces is due to the attraction of the different partials charges of atoms in different molecules due to their different electro-negativities. For hydrogen bonding, ...
22
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1answer
881 views

DFT Code for Atoms : Sources

Some time ago I implemented the restricted and unrestricted Hartree-Fock methods. I had a lot of fun and I learned a lot. It goes without saying that Szabo and Ostlund's book "Modern Quantum Chemistry"...
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2answers
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Derivation of the Heisenberg uncertainty principle

The Heisenberg uncertainty principle states that $$\Delta x \Delta p \geq \frac{\hbar}{2}$$ where $\Delta x$ is the uncertainty in the position, $\Delta p$ is the uncertainty in linear momentum, and ...
21
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2answers
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How to calculate wavenumbers of normal modes from the eigenvalues of the Cartesian force constant matrix?

I would like to get the wavenumbers (Frequencies -- in Gaussian) from the eigenvalues of the force constant matrix (...
21
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1answer
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What's the difference between PBE and B3LYP methods?

I can't find an answer to that question. I was told that in B3LYP, more variables implemented in the method are empirical, but I can't find anywhere if it's true, and I'm sure it's not the only ...
21
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2answers
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Why is a singlet state called singlet and a triplet state called triplet?

I kind of get the idea of singlet and triplet states. But why are they called singlet and triplet (what is the single and what is the triple in these cases)? I feel that I am missing something ...
21
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3answers
800 views

Non-integer hybridization

I've known that hybridization in distorted geometries is not exactly $sp^3$ or $sp^2$ or whatever. For example, $\ce{PH3}$ has nearly pure $p$ orbitals in the $\ce{P-H}$ bond, and the lone pair is in ...
21
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1answer
472 views

Is the Springborg 6D phase space model used in modern molecular orbital modeling?

In a series of papers in the early 1980s, Michael Springborg explored an interpretation of the Wigner phase space function as an electron density in a six-dimensional $(q,p)$ phase space. He applied ...
20
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4answers
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Why does the energy gap for π - π* transitions shrink with the size of the pi-conjugated system?

Quoting from this site: As conjugated pi systems become larger, the energy gap for a π - π* transition becomes increasingly narrow, and the wavelength of light absorbed correspondingly becomes ...
20
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3answers
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Why is manganese(II) coloured although the transition should be spin-forbidden?

In every basic coordination chemistry class, at some early point the crystal field theory and LFSE will be taught, explaining that there will be an energy difference between d-orbitals (typically ...
20
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1answer
508 views

Is it possible to compute the colour of *any* molecule?

Above are some spectral emission lines for hydrogen, helium and neon. Using the Schroedinger equation, it's possible to derive the colours that hydrogen will emit when light is fired at it. A little ...
20
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1answer
455 views

What is occuring on the quantum level when a molecule rotates plane polarized light?

What is occuring on the quantum level when a molecule rotates plane polarized light? Also, why do enantiomers then rotate light in opposite directions? I would think that the electromagnetic waves ...
20
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1answer
242 views

Similarities and Differences between Resonance and MCSCF treatments

Recently, there has been a question by Voldemort concerning different resonance structures of $\ce{NCO-}$, requesting an explanation why one resonance structure would be more preferred than another. ...
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2answers
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Is it correct to talk about an empty orbital?

Professor A. J. Kirby mentions: The properties of an orbital are those of an electron contained in it. It is normal practice, illogical though it may sound, to talk of 'vacant orbitals'.The ...
19
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3answers
538 views

Do modern dispersion-corrected DFT methods give more accurate molecular geometries?

I was discussing with a colleague the use of modern dispersion-corrected density functionals. I take it almost as a given that the methods generally produce "better" (for some definition) geometries, ...
19
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3answers
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What is a virtual state?

In talking about Raman spectroscopy, one finds the Stokes line is simply the difference between the energy of an incoming photon and an emitted photon. This energy corresponds to a vibrational ...
19
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2answers
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Jahn-Teller Distortions in Square Planar Complexes?

A Jahn-Teller distortion is predicted whenever a non-linear symmetric molecule has degenerate orbitals and has unequal electron occupation in those degenerate orbitals. Of course, this most often is ...
18
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3answers
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When are two orbitals orthogonal?

When are two orbitals considered to be orthogonal? It will be helpful if you can provide an example molecule (or molecular orbitals in a molecule) since I can't really think of a scenario where ...
18
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3answers
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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. $$\...
18
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2answers
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Why is black-body radiation curve smooth without a sharp cutoff?

Planck's law is able to predict a graph that is consistent with experimental observation: In essence, unlike Rayleigh-Jeans law that assumes equipartition theorem to hold (that each mode of motion ...
18
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3answers
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Computing two-electron integrals with an STO-3G basis set

I am trying to implement a restricted Hartree-Fock calculation using an STO-3G basis set, for fun. I managed to perform this calculation where only $\mathrm{1s}$ orbitals are present ($\ce{H2}$ and $\...

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