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 ...
- 71.1k
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 ...
- 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 ...
- 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 ...
- 4,799
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 ...
- 28.3k
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, ...
- 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 ...
- 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_\...
- 18.9k
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 ...
- 3,050
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 ...
- 84.2k
18
votes
Accepted
How to convert from spin orbitals to spatial orbitals in the Hartree-Fock approximation?
Technical Note: This page makes heavy use of MathJax, give it time to load.
$
%some shortcuts
\newcommand{\op}[1]{\mathbf{#1}}
\newcommand{\ve}[1]{\mathbf{#1}}
\newcommand{\id}[1]{\mathrm{#1}}
\...
- 43.8k
18
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 ...
- 67.3k
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 ...
- 31k
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 ...
- 71.1k
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 ...
- 71.1k
17
votes
Simple Explanation of orbitals
Well, the first step is to stop thinking electrons as being very small balls that orbit around the nucleus in a circular path. This is known as the Bohr model. Despite this model being an excellent ...
- 7,342
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 ...
- 18.9k
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 ...
- 2,396
16
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. ...
- 817
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 ...
- 6,851
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 ...
- 43.8k
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 ...
- 11.6k
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 ...
- 17.3k
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 ...
- 39.1k
13
votes
Simple Explanation of orbitals
Why don't you try with analogies: at least, as a vary basic introduction, I very much appreciate the attempt done here by Goh et al.
An orbital is defined as a region in space in which there
is ...
- 1,738
13
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 ...
- 40.2k
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 ...
- 1,261
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 $\ce{I2}$, ...
- 67.3k
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 ...
- 71.1k
13
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 ...
- 20.8k
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