Simulation cell and primitive cell

General discussion of the Cambridge quantum Monte Carlo code CASINO; how to install and setup; how to use it; what it does; applications.
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Jhalak
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Simulation cell and primitive cell

Post by Jhalak »

What is the difference between simulation cell and primitive cell? How do we count the number of up-spin and down-spin electrons in our simulation cell?
Neil Drummond
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Re: Simulation cell and primitive cell

Post by Neil Drummond »

Dear Jhalak,

Suppose we are interested in studying the bulk properties of a crystalline solid. We could in principle do this by looking at an enormous piece of the material surrounded by vacuum, but with current QMC technology we are limited to hundreds of atoms in our simulations. For this sort of system size, surface effects would dominate, and we would not be able to describe bulk properties.

Fortunately we can eliminate surfaces by studying a finite piece of crystal subject to periodic boundary conditions. This finite piece of crystal subject to periodic boundary conditions is our simulation cell.

The primitive cell of the crystal is the smallest possible unit cell. Thus our simulation cell must consist of an integer number of primitive cells.

Best wishes,

Neil.
Neil Drummond
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Re: Simulation cell and primitive cell

Post by Neil Drummond »

P.S. The number of electrons in the simulation cell is simply given by the number of electrons in the primitive cell times the number of primitive cells in the simulation cell.
Jhalak
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Re: Simulation cell and primitive cell

Post by Jhalak »

Dear Neil,
Thank you for the kind response, and I think more elaboration will be better for me. Suppose we are simulating a material, which forms a simple cubic unit cell. I want to make a simulation cell consisting two unit cells towards each coordinate axes, altogether 8 unit cells per simulation cell. Now while specifying the number of spin up and down electrons, should I count all the electrons present in the simulation cell, that means 27*A (A= no. of electrons in the element present in each lattice point, 27= no. of lattice points in my simulation cell), or I can count those present in single unit cell?

Moreover, should I optimize the whole simulation cell using Gaussian (I use Gaussian 03 to generate the trial wave functions), or the trial wave functions generated for the individual particles will work, while preparing gwfn.data file?

Thank you.
Jhalak
Neil Drummond
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Re: Simulation cell and primitive cell

Post by Neil Drummond »

Dear Jhalak,

If you have eight unit cells in your simulation cell (2x2x2 primitive cells) and your primitive cell contains n electrons then the number of electrons in your simulation cell is N=8n. The number of primitive lattice points in the simulation cell must be eight.

If you are relaxing the geometry using DFT then you can just work with a single primitive cell. Moreover, when generating the trial wave function for QMC you can again just work in a single primitive unit cell and use multiple Bloch k points. For your 2x2x2 simulation cell, you would want to use a 2x2x2 k-point grid.

Best wishes,

Neil.
Sharma_Omprakash
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Joined: Fri Feb 27, 2015 11:20 am

Re: Simulation cell and primitive cell

Post by Sharma_Omprakash »

Neil Drummond wrote:Dear Jhalak,

If you have eight unit cells in your simulation cell (2x2x2 primitive cells) and your primitive cell contains n electrons then the number of electrons in your simulation cell is N=8n. The number of primitive lattice points in the simulation cell must be eight.

If you are relaxing the geometry using DFT then you can just work with a single primitive cell. Moreover, when generating the trial wave function for QMC you can again just work in a single primitive unit cell and use multiple Bloch k points. For your 2x2x2 simulation cell, you would want to use a 2x2x2 k-point grid.

Best wishes,

Neil.
Dear Sir,
I want to know how to count the number of up and down electron for simulation cell of NxNxN ? e.g. In GaAs, Ga have 3 electron ( 2-up and 1-dn) and As have 5 electron (4-up and 1-dn). So in 1x1x1 Sim. cell neu=6 and ned=2 (total 8 electrons). For 2x2x2 Sim.cell neu and ned should be 8x6=48 and 8x2=16 but example of CASINO INPUT file contains equal neu and ned i.e. neu=32 and ned=32 instead of 48 and 16 respectively. Please explain this.
Thank you
Rajesh
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