63 votes
Accepted

What is Bent's rule?

That's a good, concise statement of Bent's rule. Of course we could have just as correctly said that p character tends to concentrate in orbitals directed at electronegative elements. We'll use this ...
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  • 81.6k
45 votes
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Difference between shells, subshells and orbitals

Here's a graphic I use to explain the difference in my general chemistry courses: All electrons that have the same value for $n$ (the principle quantum number) are in the same shell Within a shell (...
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  • 10k
39 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 ...
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39 votes

Why are covalent bonds directional?

The meaning of covalent bonds being directional is that atoms bonded covalently prefer specific orientations in space relative to one another. As a result, molecules in which atoms are bonded ...
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  • 18.4k
35 votes
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How do I visualize an atom?

I have searched and searched, oh how I have searched. Do you know what I always tell my mom when she asks me to find something in the Internet she was not able to find herself? I ask her: "Are you ...
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  • 18.4k
30 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 ...
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  • 16.8k
28 votes

When is it true that more nodes equals higher energy?

General case There is indeed a mathematical theorem that deals with the number of nodes an eigenfunction corresponding to a certain eigenvalue can possess. It was laid down by Courant$^{[1, 2]}$ and ...
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  • 17.2k
28 votes

What are the magnetic quantum numbers for the three real p orbitals?

The answer is... it is not so simple. Some quantum mechanics follow, but the TL;DR version is that while $m_l=0$ corresponds to $p_z$, the orbitals for $m_l=+1$ and $m_l=-1$ lie in the $xy$-plane, but ...
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  • 41.3k
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 ...
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  • 4,759
26 votes
Accepted

Why is one lobe of an sp3 hybridized orbital smaller than its other half?

When combined at a given atomic center, any two atomic orbitals add in a vectorial manner. For example, consider the orbital $\phi$ defined by $\ce{p_{x}}$ and $\ce{p_{y}}$ atomic orbitals as \begin{...
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  • 17.2k
26 votes
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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 ...
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  • 3,298
24 votes
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What would follow in the series sigma, pi and delta bonds?

tl;dr The next in the series is called φ bond. There is even a tiny Wikipedia article about it. Nicolau pointed me to the Wikipedia article, that had at the time a tiny section about the φ ...
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24 votes
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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, ...
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22 votes
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How can I find the symmetry labels of atomic orbitals in a molecule?

First, you have to know the geometry of your compound. The complex $\ce{[PtCl4]^2-}$, for example, is square planar. The next step is to determine the point group of the compound from this geometry by ...
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  • 17.2k
22 votes

Physical intuition behind negative values for wave function?

The wavefunction of a particle actually has no physical interpretation to it until an operator is applied to it such as the Hamiltonian operator, or if you square it which gives its probability of ...
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  • 7,036
22 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 ...
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22 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 ...
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  • 21.4k
21 votes

Evidence of orbitals?

Let me approach this another way than the others: orbitals are NOT physical objects! They do not exist in physical sense, they are theoretical constructs, chemical concepts that help understand / ...
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  • 5,230
20 votes

Reason for the stronger acidic property of phenol than alcohol

In fact I find a more simple reasoning with resonance structure. When phenol loses the $\ce{H+}$ the phenolate ion is stabilized due to the resonance effect, as shown below: The energy of the ...
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  • 8,819
20 votes
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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_\...
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  • 18.4k
19 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 ...
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  • 2,962
18 votes

Reason for the stronger acidic property of phenol than alcohol

The effect is indeed amazing, if you compare the $\mathrm{p}K_\mathrm{a}$ of tert-butanol (17.0) with that of phenol (9.95). Deprotonation is facilitated when the reaction goes downhill (energywise). ...
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18 votes
Accepted

Why do atoms "want" to have a full outer shell?

You are attaching too much importance to Lewis structures. The 8-electron rule and Lewis structures which are derived from it are only rough guidelines for working out the electronic structure of a ...
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  • 17.2k
18 votes
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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}} \...
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18 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 ...
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  • 81.6k
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 ...
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  • 29.6k
18 votes
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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 ...
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  • 65.5k
17 votes
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What is the usage of orbitals more complex than f orbitals?

Surprisingly, I learned that there are also usages for orbitals g,h,i and even j. Actually, the letter "j" is not used, so it is s, p, d, f, g, h, i, k, l, etc. The higher angular momentum ...
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  • 38.8k
17 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 ...
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  • 63.6k
17 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 ...
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