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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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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26 votes
3 answers
10k views

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 ...
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49 votes
5 answers
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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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24 votes
4 answers
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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 ...
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41 votes
3 answers
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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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20 votes
1 answer
877 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 ...
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10 votes
2 answers
2k views

What exactly is an orbital?

What exactly is an orbital? Atomic or molecular. Is it the function that describes the behaviour of the electron? Is it the Schroedinger's equation solution, e.g., for Hydrogen atom? Is it the ...
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23 votes
3 answers
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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 ...
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28 votes
3 answers
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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....
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27 votes
2 answers
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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 ...
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8 votes
1 answer
999 views

How does the radial distribution function of Vanadium differ from that of Calcium and how does this affect the ionic electron configurations?

When Vanadium is ionised it loses the 4s electron first, meaning that it's 3+ ion has a different electron configuration to Calcium despite it being isoelectronic. Can it be explained in terms of ...
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28 votes
2 answers
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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{...
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23 votes
2 answers
12k views

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, ...
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20 votes
3 answers
5k views

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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12 votes
2 answers
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How do Electrons Cross Nodes in Orbitals?

I was wondering in orbitals that have nodes such as the p orbital, how does the electron move from one lobe to the other? I know that people say it is because of the wave/particle nature of electrons ...
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36 votes
2 answers
272k views

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.
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21 votes
5 answers
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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 ...
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  • 487
23 votes
2 answers
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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 ...
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6 votes
1 answer
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Physical reason for why delocalisation leads to stability?

Why does delocalization of electrons generally make compounds more stable (e.g. in carboxylate anions, where the lone pair on the negatively charged oxygen is delocalised into the C=O π* orbital)? Is ...
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9 votes
1 answer
7k views

Energetic Placement of Atomic Orbitals in the HCl Molecular Orbital Diagram

How are the 3p orbitals of chlorine lower in energy than the 1s orbital of hydrogen?
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9 votes
1 answer
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Why is no dynamical correlation recovered in the CASSCF method?

Configuration interaction is the only certain way to get a calculation to converge toward the exact solution of the many-body Schrödinger equation (within the approximations used for the framework of ...
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14 votes
2 answers
767 views

After a unitary transformation, is Koopmans' theorem still valid?

Koopmans' theorem says that the energy of the HOMO of the Hartree-Fock orbitals is equal to the first ionization energy of whatever system is being studied. This is only approximate because it assumes ...
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29 votes
2 answers
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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 ...
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29 votes
2 answers
37k views

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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16 votes
2 answers
23k views

Why are full and half filled orbitals the most stable?

Why are degenerate orbitals (restricted to a single spin) less stable when neither fully filled nor completely empty? Why, in most molecules, are half-filled and fully-filled shells more stable than ...
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14 votes
3 answers
12k views

Most probable point for finding an electron in the 1s orbital of a Hydrogen atom

My professor says that the most probable point for finding an electron in a 1s orbital of a hydrogen atom is at its origin. He explains this by citing the fact that the square of the wave function ...
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26 votes
4 answers
7k views

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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13 votes
1 answer
6k views

The "rules" for LCAOs in Molecular Orbital Theory

In our course on physical chemistry, which involves MOT, we have been taught that in the LCAO approach, the wave function for a molecule … say hydrogen ion ($\ce{H2+}$), can be approximated by a ...
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10 votes
1 answer
2k views

How can two orbitals constructively and destructively interfere simultaneously?

The molecular orbital theory dictates that when two atomic orbitals form molecular orbitals, then two molecular orbitals must form (i.e number of atomic orbitals = number of molecular orbitals). For ...
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8 votes
2 answers
925 views

Trying to understand the statement: 'Resonance is not a flickering between the contributing states. '

So, the famous resonance definition: it is the weighted average of different Lewis structures.... Well, this is purely wrong. Resonance is nothing but quantum 'superposition of the wavefunctions ...
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11 votes
5 answers
4k views

What actually is the Wavefunction?

I am aware that the square of the Wavefunction gives the probability density of finding an electron at a particular point in space. I have also heard that it's a complex number but since it's a ...
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11 votes
3 answers
12k views

What is the difference between ψ, |ψ|², radial probability, and radial distribution of electrons?

I am very confused regarding these four terms- ψ,|ψ|², radial probability and radial distribution I know that ψ is called the wave function but is it the same as radial probability? I also know ...
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18 votes
1 answer
677 views

Analytical solution of the Schrödinger Equation for AB^+ systems

According to Wikipedia, there are not many problems for which the Schrödinger equation can be solved analytically. [1] The $\ce{H2+}$ ion is probably the most complex molecule that can be treated this ...
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7 votes
4 answers
987 views

On Heisenberg's uncertainty principle

Why can't we find the exact position and velocity of a particle? And why is it that if the uncertainty in position is very, very large then the velocity can be determined, and vice versa? Please ...
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5 votes
3 answers
2k views

How are nuclei stable?

We all know that the density of the nucleus is very high. Nuclei are made up of protons and neutrons, and while protons have the same charge, they are closely packed in a nucleus. How does the ...
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20 votes
1 answer
4k 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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33 votes
1 answer
55k views

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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  • 1,668
21 votes
2 answers
3k views

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 (...
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  • 339
15 votes
2 answers
377 views

What constraints are imposed on a wavefunction by the symmetry of the system?

As a follow-up to my answer here, I'd like to ask what exactly does it mean for a wavefunction to "respect the symmetry" of the system. The original context is: immediately after ionisation of $\ce{...
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16 votes
3 answers
2k views

Are there any full worked examples of DFT calculations?

I just started learning DFT and now I am totally confused. Assuming I want to use B3LYP: \begin{align} v_s\left(\textbf{r}\right) &= v_\text{ext}\left(\textbf{r}\right) + \int d^3r\frac{n\left( \...
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  • 2,111
19 votes
3 answers
2k views

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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13 votes
6 answers
8k views

What is a "hydrogen-like" or "hydrogenic" atom?

I'm studying some chemistry on my own in anticipation for the new school year and in my book, I came across the Rydberg equation for the first time. I worked through some examples and everything was ...
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8 votes
3 answers
3k views

How is Negative Temperature Hotter than Infinite Temperature?

Recently I have read articles stating that negative Kelvin has been achieved. I was a bit speculative at first as I though how can you get cold than 0 Kelvin, but after doing some research it makes ...
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  • 7,046
8 votes
2 answers
2k views

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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  • 1,197
6 votes
1 answer
1k views

How much energy does it cost to have electron configurations that are not in accordance with Hund's rules?

What is a ballpark figure for the difference in energy for an atom that follows Hund's rule vs one that has two electrons with opposite spins? I'd be interested to know carbon and nitrogen. Is there ...
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  • 3,760
6 votes
1 answer
2k views

What is the exact definition of the radial distribution function?

I have been very confused by the radial distribution function which is often used in chemistry to predict the probability of finding an electron at a distance from the nucleus. From Atkins' Physical ...
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  • 5,239
13 votes
1 answer
981 views

Why is it possible to image LUMO if these orbitals are, by definition, unoccupied?

LUMO stands for lowest unoccupied molecular orbital. If it's unoccupied, how is it possible to image it? See for example in this paper ("Pentacene imaged with STM and NC-AFM").
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  • 4,119
6 votes
2 answers
442 views

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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2 votes
2 answers
7k views

Predicting bond-strength of metal carbonyls

The metal carbonyls (and similar organometallic compounds) involve a combination of sigma bond, a pi bond and backbonding. The bond strengths under consideration are the metal-carbon bond and the ...
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  • 6,364
8 votes
1 answer
2k views

Quantum Chemistry: Small imaginary frequencies

I am running a freq calculation on a geometry optimized structure using the ORCA quantum chemistry program. The output of the freq. calculation contains small neg. frequencies. Normally, these are ...
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