Calculating the elctron density distribution during a Monte Carlo simulation
Hello, Le Loupe
Yes. Monte Carlo method can be used to calculate electron density.
Kindly let me know if that answers your question.
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Only based on that s/he may decide how to research the question.
Here are few question which would help to see if I can help:
1) Tell us what you know.
Your question deals with QM - a complex subject. Do you want
answer on level of an interested laymen, college student, PhD,..?
2) What is your goal?
Is this to settle a bet, just curious, do you want to calculate
something? If so what are your resources? A calculator, PC ?
3) How much time you want to give this?
Is it a project, do you want a textbook, an on-line tutorial, latest review
article from the Review of Modern physics, a monograph..?
4) Do you have a particular system on mind?
Density in an isolated atom, or a molecule, - if so which one?
Or do you want to know what is it good for, does it work,
comparison to other methods?
5) Is a reference enough, are you looking for an essay,
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1. I am a post doc, using Qunatum Monte Carlo simulations.
2. How do you get the single electron densities from the probabilities
during the simulation.
Let's make an example:
We have two electrons, and a configuration during the walk is given by
Xi(1),Xi(2) and we simulate i=1...m walks.
The probability for the acceptance of this configuration is given by pi(1,2).
What is p(X1)?
My guess it would be
p(X(1))=1/m * sum_i=1..m pi(X(1),Xi(2))
Is that correct?
Well, yes.
That is much better question.
How would this rate as an answer?
I would say yes.
However, it is a good practice to get some references
to confirm everything, so let's look if other people are
doing it this way:
Here is a paper which shows contours of the electron density
http://www.cr.org/publications/MSM2001/pdf/356.pdf
but they do not give formula used.
Here is paragraph from a thesis which confirms your guess:
In this URL
http://owen.sj.ca.us/rkowen/rkowen/qmc/pages/toc.html
you click on
5.2.8. 8.3 - Lithium One-Electron Densities
to get slide 82 with formula - same as yours, nicely written.
You may want to check
http://plato.phy.ohiou.edu/~drabold/nato/node12.html
for computational/convergence considerations.
Ideally, you are using some universal code, such as CASINO,
which all such mundane formulas already programed in, such as
http://www.tcm.phy.cam.ac.uk/~jrt32/QMCgroup/qmc.html
but you probably do.
SEARCH TERMS
QMC electron-density -functional
(-functional is there to exclude DF papers)
good luck
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