Calculating the elctron density distribution during a Monte Carlo simulation

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Request for Question Clarification by hedgie-ga on 31 May 2003 04:21 PDT

Hello, Le Loupe

       Yes. Monte Carlo method can be used to calculate electron density.

        Kindly let me know  if that answers your question.

      There is an art and skill of searching and answering and
       there is also art of asking, art of formulating the question so
       that researcher can estimate where you are and what you
       are after. 
  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,
 website or a book?

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Clarification of Question by leloupe-ga on 02 Jun 2003 13:17 PDT

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

hedgie