Urgent! Questions on repeating "Properties of an isolated benzene molecule"

[hzkvictory]

   I am repeating the example shown in "Properties of an isolated benzene molecule" and I have some questions.

   When using the multipole boundary condition, is the periodic superscell (in which there are periodic images of the benzene molecule) approach used or just a single isolated box (in which there is only one benzene molecule) is used?         
   In this specific example of a charged benzene, the size of the box is not explilcitly given. I would like to know very much the size of the box containing the charged benzene. Can I find the size of the box in the output file?
   I would also like to know, if I calculate a different charged molecule, how can I know the size of the box that is actually used.

   I found a paper about the multipole expansion solution to solve the Poisson's equation
(http://journals.aps.org/prb/abstract/10.1103/PhysRevB.46.4495). I would like to ask you if the method described in this paper is relevant to the multipole method used in ATK.

Thank you for your prompt reply.

[kstokbro]

The multipole boundary conditions is implemented using a real space multigrid poisson solver. In this case there is no periodic boundary conditions, we are simulating a truly isolated molecule. This is a standard approach in molecular quantum chemistry softwares, but maybe a less know methodology in the solid state community.

The potential at the boundary is determined by calculating the monopole, dipole and quadrupole moments of the charge distribution inside the box, and using these moments to extrapolate the value of the electro-static potential at the boundary of the box. Thus, the asymptotic values are determined using the charge multipoles, and we only need to describe the potential inside the box, using the asymptotic values as boundary conditions.

Currently, the main approximation is that we use a first order stensil for the multigrid solver, we are working on also implementing higher order stensils.

The reference you give is not relevant.

To get the box size, I recommend that you calculate the ElectrostaticDifferencePotential, and get the box using
potential = ElectrostaticDifferencePotential(molecule_configuration)
a, b, c = potential.unitCell()
print a, b, c

[hzkvictory]

Dear kstokbro,
    Thank you very much for your reply. Yeah, you are right. I eye on solid, and is not familiar with chemistry
community. 
    I calculated the a,b,c of the isolated box following your instruction. I am very interested in the detailed theory about solving the Poisson's equation under multipole boundary condition. And I would like to  know if this is the relevant paper: http://onlinelibrary.wiley.com/doi/10.1002/jcc.540160707/references
    And if you can tell me a reference, that would be highly appreciated.

[kstokbro]

The reference seems to be a more complex theory, but maybe they also describe the simple theory, will see if I can get the paper. Will see if I can find a paper reference, however, the theory is rather simple and will not find its way in a research paper but more a basic computational chemistry book.