New answers tagged quantum-chemistry
6
You're describing simple Hückel theory. This is usually applied to $\pi$-conjugated systems to understand the stabilization in conjugated and aromatic molecules.
There are a variety of Python packages, for example:
Felix Plasser wrote one for his blog and the current location is at his homepage
Randle Taylor has a SHMO package on GitHub, including a GUI ...
0
When we talk about exchanging electron $i$ with electron $j$, we are actually changing the wavefunction according to
$$\Psi(..., x_i, ..., x_j, ...) \to \Psi(..., x_j, ..., x_i, ...).$$
The operation is taken by the parity operator $P$. Applying it twice would
return the wavefunction to its original form. So the following eigenvalue equation is satisfied
$...
0
Electrons don't have a well-defined orbital radius even in a hydrogen atom
An electron "orbiting" in a hydrogen atom does not have a well-defined position or even just a well-defined radius just because it has a well-defined energy.
The orbital is more like a 3D probability density function covering a cloudy space of a defined shape (spherical in the case ...
5
In terms of how they got the relation for the diagonal elements, I believe it is relatively straightforward. Given a list of atomic energies (energy of atom relative to separated nucleus and electrons), one can try to fit these values to a function of nuclear charge. If you plot a few values, it suggests trying an exponential fit (I don't know why all the ...
6
The answer to this question rests on the fact that Hartree-Fock is a variational method.
A variational method is one where you supply a guess wavefunction ($|\Psi\rangle$) with some parameter(s) ($\alpha$) and then use those parameter(s) to minimize the energy. Doing this, you are guaranteed that your resulting energy is an upper bound to the exact ground ...
-1
When one "arbitrarily" insists that the box is of a certain length, that is where any method fails. The molecular geometry provides the boundary conditions on the standing waves for the electrons, so people fix things by adding an extra length (fudge factor) to account for the discrepancy in the model. So, the Kekule structure(s) (Lewis structure(s)) ...
6
Yes, you're exactly right - multiple papers in chemistry ML drop the units.
There are even comparisons (usually by statistics, ML or comp. sci. researchers) where models are compared by "averaging" errors down a column like that. Of course that's meaningless, since you can't average electron volts or Hartree (energies), Debye (dipole moments), and volume (...
4
You (probably) cannot apply Koopmans' theorem. (Please also note that it is named after Tjalling Charles Koopmans, the s at the end is part of the name.)
Open shell systems are usually hard to describe and unrestricted density functional approximations might not even describe the system correct qualitatively. The problem usually comes down to the ...
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