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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83
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7answers
121k 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 ...
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 ...
22
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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 ...
42
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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 ...
39
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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? ...
10
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2answers
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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 ...
22
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3answers
2k views

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 ...
25
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3answers
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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....
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 ...
8
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1answer
906 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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2answers
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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 ...
5
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3answers
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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 ...
36
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2answers
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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.
22
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5answers
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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 ...
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{...
27
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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 ...
20
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1answer
495 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 ...
21
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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 ...
14
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2answers
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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 ...
9
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1answer
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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?
14
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2answers
659 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 ...
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, ...
8
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1answer
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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 ...
26
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2answers
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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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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. $$\...
26
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4answers
6k 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 ...
12
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3answers
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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 ...
9
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2answers
768 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 ...
10
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5answers
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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 ...
3
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1answer
687 views

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 ...
7
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4answers
970 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 ...
18
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1answer
611 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 ...
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 (...
15
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2answers
327 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{...
32
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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, ...
16
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3answers
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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( \...
18
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3answers
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 $\...
8
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3answers
2k 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 ...
6
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1answer
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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 ...
11
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3answers
10k 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 ...
6
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2answers
11k views

Calculate the wavelength of the radiation released when an electron moves from n= 5 to n=2

Calculate the wavelength of the radiation released when an electron in a hydrogen atom moves from $n = 5$ to $n = 2$. How can I find this wavelength?
33
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1answer
3k views

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 ...
21
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1answer
31k views

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 ...
18
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1answer
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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 ...
15
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1answer
1k views

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?
9
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1answer
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How to choose proper active space in method such as CASPT2 and CASSCF?

I am confused about other research paper which use CASPT2 method. I am not clear about how to choose active space. What can I refer to? (tutorial reviews, papers, or any other things)
23
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1answer
323 views

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 ...
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2answers
2k views

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 ...
16
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1answer
2k views

Explaining the Relative Energies of Various Vibrational Modes

Specifically, I'm wondering why it is that the asymmetric stretch in most (although there are exceptions to this I believe) molecules is higher in energy than the symmetric stretch. Similarly, I ...
11
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2answers
4k views

The energy gap between a pi-conjugated system with (2 bonding and 1 anti-bonding orbital) and (1 bonding and 2 anti-bonding) orbitals

I asked a question previously about "why" it is the case the expanding the size of pi-conjugated systems decreases the required energy to excite an electron from a HOMO to a LUMO band: Why does the ...