Youngs modulus for buckyball

[David1986]

Can I calculate the Youngs modulus for a bucky ball? If yes, what changes should I do?

Thanks

[Petr Khomyakov]

Young's modulus is a mechanical property of solid materials, see https://en.wikipedia.org/wiki/Young's_modulus. What exactly do you want to calculate for a buckyball, which is a molecule, not a solid?

[David1986]

I convert  the bucky ball to a bulk configuration. I consider the bucky ball as a pressurized capsule. But i want to know that what changes should I do in script?
Thanks 

[Julian Schneider]

It is still a tricky case because enclosing it in a bulk configuration does not make it a bulk system, for which you can calculate a well-defined stress tensor.

One possibility is that you optimize the buckyball, calculate the stress, then strain the cell in one direction, calculate the stress again and then get the Young's modulus as
(stress_strained - stress_unstrained)/strain

Note that the stress is normalized to the volume of the cell, which is arbitrary, so  you have to correct the stress for the actual volume of the buckyball.
How you define that volume depends very much on what you want to do with the Young's modulus.
One could think of using the volume of a sphere with the same diameter as the buckyball, but you really need to think carefully yourself, whether this fits your application.
I have attached an example script which assumes the volume of a solid sphere.

Please remember again, that there is no real straightforward definition for the Young's modulus in your system, and we can only give you one possible auxiliary way to estimate a quantity, which could be used as a Young's modulus, but you should carefully review whether this makes sense in your application!

[Anders Blom]

Julian, maybe this is what you did, but I suppose one could apply an external pressure and then optimize the structure, and compute the local stress on all atoms, and average that? It wouldn't give a Young's modulus, but might tell us something about the response of the buckyball to external pressure?

[Julian Schneider]

Anders, as far as I see it, you cannot really do an optimization under external stress/pressure here, because this quantity is not well-defined for a molecule in a vacuum-padded cell, since the stress is normalized to the volume of the cell, which is arbitrary in a vacuum padded cell (unless you consider a crystal of may interacting buckyballs).

The only reasonable picture, I could think of, is that when you consider the buckyball as a kind of spherical macroscopic solid, which can be strained by clamping the two ends. Then you are right, one could approximate the stress as the sum of all local stresses, normalized by the volume of the  sphere (that is actually equivalent to what I did in the script).
But that assumption may already be a far-fetched approximation for such a microscopic molecule.

[zh]

C60 can form  a solid,
e.g., see
Nature 347, 354 - 358 (27 September 1990); doi:10.1038/347354a0
Solid C60: a new form of carbon
http://www.nature.com/nature/journal/v347/n6291/abs/347354a0.html

For the simulation of an finite system under constant pressure, the ill-defined is the volume, just as mentioned by Julian Schneider.   In literature, there are several different approaches proposed for the estimation of volume of an finite system. They include
1) the  sum of individual atomic volumes
Sun, D. Y.; Gong, X. G. J. Phys.: Condens. Matter 2002, 14, L487-L494.   
2)  the method based on the  quantum  volume  enclosed  by  a  charge  isosurface
Cococcioni, M.; Mauri, F.; Ceder, G.; Marzari, N. Phys. Rev. Lett. 2005, 94, 145501-1—145501-4.
3) the method by finding the  minimal  polyhedron  enclosing  the  finite  system.
Calvo, F.; Doye, J. P. K. Phys. Rev. B 2004, 69, 125414-1— 125414-6.   
4) the method based on the  average  inter-particle  distance
 Landau, A. I. J. Chem. Phys. 2002, 117, 8607-8612.

Just for the question of "Youngs modulus for a bucky ball?",
Is there any experimental data for the measurement of Young's modulus of a bulky ball molecule?