33
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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 ...
- 17.4k
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 ...
- 4,819
24
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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, ...
- 17.4k
24
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Cyclobutadiene - Jahn–Teller effect or not?
Very interesting question, and it kept me up despite daylight saving time cheating me of one hour of sleep last night... A good reference is Albright, Burdett and Whangbo, Orbital Interactions in ...
- 71.6k
22
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How do atomic orbitals interfere both constructively AND destructively to give two molecular orbitals?
What does MO formation entail?
A very common misconception is that the formation of MOs involve addition, or subtraction, of two physical objects. And the confusion arises because, how can the same ...
- 71.6k
19
votes
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Why is the bond order of CO+ 3.5?
For a long time it was taught in school and universities that the HOMO of carbon monoxide is anti-bonding. Without more context it was also often taught that the bond order in CO is three, since there ...
- 44.3k
19
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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 ...
- 85.1k
18
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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 ...
- 71.6k
17
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After a unitary transformation, is Koopmans' theorem still valid?
Disclaimer: I like Tyberius' answer, but I'd like to go a little further.
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\newcommand{\ll}{\left\langle}\newcommand{\rr}{\right\rangle}
\newcommand{\lb}{\left|}\newcommand{\rb}{\right|}
\newcommand{...
- 44.3k
17
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Molecular orbital diagram for BF3
I think you are most of the way to the answer, but I will start the process from scratch for the sake of a full explanation for future readers.
First, we determine the symmetry group of $\ce{BF3}$, ...
- 11.8k
17
votes
Does a neutral dimercury molecule exist?
There has been recent research on mercury dimers in its ground state. Bond energies, transition energies, band spectrum and other spectroscopic parameters has been calculated. Here are the abstracts ...
- 26.3k
16
votes
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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 ...
- 19.1k
15
votes
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Mechanism for the Cleavage of Diborane?
Is it known how this cleavage occurs?
The mechanism proposed for the cleavage reaction involves an initial attack by the donor on one boron atom in diborane, leading to cleavage of one $\ce{B-H-B}$ ...
- 4,174
15
votes
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Using group theory to make molecular orbital diagrams
Group theory really just formalises the process that you're going through when you construct molecular orbital diagrams by inspection (though as the molecules get bigger it gets significantly harder ...
- 17.2k
15
votes
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Explanation for bond lengths in trans-hexatriene
If you derive the π-type molecular orbitals of hexatriene, the three lower-energy MOs which are filled would look something like this (image from p 33 of Fleming's Molecular Orbitals and Organic ...
- 71.6k
15
votes
How do atomic orbitals interfere both constructively AND destructively to give two molecular orbitals?
Unfortunately, in quantum mechanics there is rarely an explanation "in simple terms." Quantum mechanics is a mathematical construct that so far seems to predict the results of all ...
- 10.3k
13
votes
Why is the inversion barrier larger in PH3 than it is in NH3?
Disclaimer: This answer neglects quantum tunnelling effects, which are significant in such compounds. The gist of it is that because nitrogen is smaller and lighter than phosphorus, the rate of ...
- 71.6k
13
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Pi molecular orbitals of polyenes
These pi-type MOs are most commonly derived using Hückel MO theory. I've never been a fan of Wikipedia's technical articles, so for further reading I'd suggest using the QMUL resources online, which ...
- 71.6k
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 ...
- 1,271
13
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Molecular orbital diagram and irreducible representations for dinitrogen
Because this is a diatomic molecule, there are no group orbitals. Put another way, the group orbitals are the molecular orbitals. Knowing the nitrogen atomic orbitals (AOs) and their irreducible ...
- 7,499
13
votes
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Pauli exclusion principle
Wikipedia has the correct definition:
A more rigorous statement is that with respect to exchange of two identical particles the total wave function is antisymmetric for fermions, and symmetric for ...
- 41.2k
13
votes
What theory accurately explains metallic bonding in beryllium?
The usual MOT explanation for why the group IIA elements are metals is that the band caused by the overlap of the np orbitals is sufficiently wide to overlap that due to the ns orbitals (the one you ...
- 3,154
13
votes
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Why does color of substances not disappear after some time?
If you are seriously interested in understanding why things are colored, there is a book called The Physics and Chemistry of Color: The Fifteen Causes of Color, by Kurt Nassau. It should be available ...
- 41.6k
12
votes
Structure of NO2 compound?
According to Electronic Structure of NO2 Studied by Photoelectron and Vacuum-uv Spectroscopy and
Gaussian Orbital Calculations J. Chem. Phys. 53, 705 (1970) :
The highest molecular orbital $4a_1$ is ...
- 40.8k
12
votes
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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 ...
- 17.5k
12
votes
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What is the dipole moment direction in the nitrosonium ion?
In non-neutral species the dipole moment in calculations is dependent on the choice of the co-ordinate system. For this reason the origin is chosen to be the centre of mass. With $r=107.8~\pu{pm}$ on ...
- 44.3k
12
votes
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"NBO diagrams" versus MO diagrams
A molecular orbital diagram is a schematic representation of how we interpret bonding in certain species. It is as much an accurate representation for a specific bonding situation as a Lewis structure ...
- 44.3k
11
votes
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Molecular orbital diagram of a complex including an oxido ligand
Although chemists and chemistry students alike often indiscriminatorily use the $\mathrm{t_{2g}}$ and $\mathrm{e_g}$ descriptors for the d-orbitals of a d-block metal in coordination complexes, those ...
- 68.4k
11
votes
After a unitary transformation, is Koopmans' theorem still valid?
I'm basing my attempt at an answer off of Modern Quantum Chemistry by Szabo and Ostlund, p.119-122.
The general development of Hartree-Fock is done via functional variation of the ground state energy $...
- 11.8k
11
votes
Accepted
Has it been observed that the dihydrogen molecule dissociates into ions?
Surely1. At the end of the day, it is just the matter of supplying enough energy: the homolysis requires approximately 4.5 eV per hydrogen molecule, while for heterolysis more than 17 eV per molecule ...
- 19.1k
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