40 votes

What are angular and radial nodes?

The accepted answer has nice pictures, but has a couple of small factual inaccuracies in the last paragraph. In particular, it is not necessary for an angular node to be a plane (even though it ...
orthocresol's user avatar
  • 70.9k
32 votes

When are two orbitals orthogonal?

Unfortunately, the sense in which orbitals are orthogonal is more or less impossible to define rigorously without recourse to functions of some kind. So, I'll give an explanation a shot using some ...
hBy2Py's user avatar
  • 17.3k
27 votes
Accepted

Why is the letter J omitted in the spdf... sequence?

Omitting j when alphabetically enumerating things has a long tradition. First of all, the alphabet did not always exist in the form we know it today. Quoting Wikipedia: After [...] the 1st century ...
mhchem's user avatar
  • 3,316
27 votes

Why do n AOs only form n MOs?

If you have $n$ functions (e.g. AOs) you can make a maximum of $n$ new linearly independent functions (e.g. MOs). If you try to make $n+1$ MOs, then any one of them can be expressed as a linear ...
Jan Jensen's user avatar
  • 4,809
24 votes
Accepted

Shape of the P1/2 Orbital

As orthocresol mentioned, this is all about relativity, so let's talk about it. I am hardly an expert myself, but I'll try to give an answer to the best of my limited knowledge. For an interesting and ...
Nicolau Saker Neto's user avatar
24 votes
Accepted

Canonical MOs vs. Localized MOs: Do both represent reality in the same way?

NOTE: In the below, I'm implicitly discussing a ground-state, closed-shell wavefunction, where all occupied orbitals are doubly occupied. The discussion would be similar for open-shell wavefunctions, ...
hBy2Py's user avatar
  • 17.3k
23 votes

Why is the letter J omitted in the spdf... sequence?

For the azimuthal quantum number (l) of an atom, there is no "j" because some languages do not distinguish between the letters "i" and "j". L is the total orbital quantum number in spectroscopic ...
MaxW's user avatar
  • 22.3k
21 votes
Accepted

Degeneracy of second excited state of H-?

I think it is important to understand that for hydrogen atom (or any other one-electron system) all orbitals from the same shell have same energy. For instance, $E_\mathrm{2s} = E_\mathrm{2p}$, $E_\...
Wildcat's user avatar
  • 19k
20 votes
Accepted

Are the canonical orbitals of Hartree-Fock also the natural orbitals?

There is a bit of a terminology problem in the field that makes things very confusing and I will try to clarify some of this here. Part of the problem arises from the fact that sometimes only one kind ...
levineds's user avatar
  • 3,070
19 votes
Accepted

When are two orbitals orthogonal?

One atomic (or molecular) orbital is said to be orthogonal to another atomic (or molecular) orbital if there is no interaction between the electrons in one orbital with the electrons (wavefunction) in ...
ron's user avatar
  • 84.6k
19 votes
Accepted

What is Drago's rule? Does it really exist?

Going through what you posted, I think ‘Drago’s rule’ (which I never encountered, either at school or at university) gives good predictions but uses a largely terrible set of arguments. For any atomic ...
Jan's user avatar
  • 67.8k
18 votes
Accepted

Shape of a wavefunction

You are plotting different functions. The figures have no reason to be more than vaguely reminiscent of each other. Now, those nice puffy things above are the isosurfaces of $\psi$ function. This is ...
Ivan Neretin's user avatar
  • 31.1k
18 votes
Accepted

Can the idea of entropy be extended to orbitals?

No. The reason why a gas particle in a large volume has a large entropy is not because it has a lot of space to move around per se. A better explanation is that for a given energy, there are many ...
orthocresol's user avatar
  • 70.9k
18 votes
Accepted

Is the notion of orbitals different in theoretical chemistry?

Unfortunately, it only gets more complicated the deeper you dig. There is some explanation here: What exactly is an orbital?, but you should bear in mind that electronic structure theory is something ...
orthocresol's user avatar
  • 70.9k
17 votes

Exchange energy of d6 configuration

As @orthocresol points out, the key is that you need to compare the exchange energy before vs after the ionization process. Anything that is unchanged by ionization cannot affect ionization energy. ...
agaitaarino's user avatar
16 votes
Accepted

Why a higher s character increases a carbon atom's electronegativity?

Electronegativity is the power of an atom to attract bonding pairs of electrons to itself. It clearly depends on the nuclear charge: the larger it is, the more strongly the nucleus attracts electrons ...
Wildcat's user avatar
  • 19k
16 votes

Why do electrons jump back after absorbing energy and moving to a higher energy level?

This is a very fundamental question and for really understanding the "why" some advanced physics is involved. I will describe the process rather superficially. As you might know, the level ...
Paul's user avatar
  • 2,396
15 votes
Accepted

Is it correct to talk about an empty orbital?

"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 properties of vacant orbitals are those ...
TAR86's user avatar
  • 6,881
14 votes
Accepted

Orbitals SPDF. Why they named like that?

From the abstract of Structure of the Line Spectra of the Elements as published in the 1890 Journal of the Chemical Society. There are three kinds of series — principal, sharp (well-defined), and ...
DavePhD's user avatar
  • 40.5k
14 votes
Accepted

What is the hybridization of terminal fluorine atoms in molecules like boron trifluoride?

TL;DR: As a rule of thumb, terminal (heavy) atoms are almost always best described as having sp hybrid orbitals (at the most). For more on this, I refer you to my answer on What is the hybridization ...
Martin - マーチン's user avatar
14 votes
Accepted

Predicting sigma bond overlap strengths of s-s, p-p, s-p, sp-sp etc

I think the issue might be what orbitals are being referred to. Both books could be correct if they are referring to different $\mathrm{p-p}$ overlap. For example, suppose two atoms are bonding along ...
Tyberius's user avatar
  • 11.7k
14 votes
Accepted

Are all degenerate d-orbitals identical?

Yes, they are identical. One thing that we don't really teach well with orbitals is thinking about the symmetry of the orbital with respect to the name of the orbital. $p_{x}$ has the same symmetry as ...
Zhe's user avatar
  • 17.4k
14 votes
Accepted

Why is the $\mathrm d_{z^2}$ orbital so different from the rest?

The Wikipedia is helpful in explaining why radial variations should arise in the density of non-s orbitals: The non radial-symmetry properties of non-s orbitals are necessary to localize a particle ...
Buck Thorn's user avatar
  • 21.5k
14 votes
Accepted

Why does the same electron transition release photons of different frequencies for some elements?

I am glad that you updated the question because it highlights a very common misconception. First of all the JavaLab Flame Test is completely wrong for both copper, calcium and many more salts ...
AChem's user avatar
  • 39.8k
13 votes

Why do n AOs only form n MOs?

You're correct in saying that p-orbitals are identical, and it follows that the following configurations are the same: You must only consider their relative alignments (i.e. their symmetry). To ...
obackhouse's user avatar
  • 1,271
13 votes

How is the structure of triiodide ion (I3-) possible?

First things first: the bonding orbitals of $\ce{I3-}$ do not contain any significant d-orbital contributions. In fact, the $\ce{I-I}$ bond lengths are significantly longer than in $\ce{I2}$, ...
Jan's user avatar
  • 67.8k
13 votes
Accepted

What is the exact definition of the radial distribution function?

The atomic orbitals (wavefunctions) $\psi(r,\theta,\phi)$ are comprised of a radial component $R_{n,l}(r)$, as well as an angular component $Y_{l,m}(\theta,\phi)$. These are obtained by separately ...
orthocresol's user avatar
  • 70.9k
13 votes
Accepted

How does an electrons's wave function change when it moves between energy levels?

You need to go back to the very start. Here, you're kind of asking: I have a solution $\psi_0$, how do I get the next solution $\psi_1$? The answer is to look at how $\psi_0$ was obtained, and it ...
orthocresol's user avatar
  • 70.9k
12 votes
Accepted

Natural Bond Orbital analysis: Significance of stabilization energy determined by 2nd order perturbation

TL;DR: Lewis $\to$ Non-Lewis $\mathbf{E(2)}$ values have no direct physical significance, are intrinsically un-measurable, and serve only to quantify the extent to which the "real" wavefunction for a ...
hBy2Py's user avatar
  • 17.3k
12 votes
Accepted

Precise definition of atomic orbital

In school I was taught that an atomic orbital is the 3-dimensional region in which the electron is located with a probability of 90%. This is not correct. An atomic orbital is a solution to ...
Zhe's user avatar
  • 17.4k

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