Application of the group function theory to infinite systems

✍ Scribed by L. N. Kantorovich

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 415 KB
• Volume: 76
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(2000)76:4<511::aid-qua3>3.0.co;2-2

✦ Synopsis

We consider application of the group function theory to an arbitrary infinite system consisting of weakly overlapping structural elements which may be atoms, ions, molecules, bonds, etc. We demonstrate that the arrow diagram (AD) expansion developed previously is ill-defined for such a system resulting in divergences in any physical quantity associated with the entire system such as, for example, the energy and charge density. A "linked-AD" theorem is then formulated and proven, which results in a diagrammatic expansion that scales correctly with the system size. Coulomb systems with long-range interactions between structure elements are also considered and the diagrammatic expansion is rearranged in such a way as to also give the correct (linear) scaling. We give an explicit expression for the total energy up to the third order with respect to overlap. Finally, we discuss the problem of choosing structure elements (SE) in a general insulating system and propose a variational method based on a configuration interaction (CI) type expansion within the Fock subspace associated with every SE.