The Cyclic Cluster Model (CCM) is a real-space approach to quantum-chemical calculations on periodic systems. Rather than working in reciprocal space with Bloch functions and k-point sampling, the CCM constructs a finite but periodically embedded cluster, the Wigner-Seitz supercell, and applies Born-von-Kármán boundary conditions directly in real space. This allows the full machinery of molecular quantum chemistry, including Hartree-Fock theory, to be applied to crystalline systems without the need for k-space integration.
The AICCM (Ab Initio Cyclic Cluster Model) extends this framework to the ab initio HF level for one- and two-dimensional periodic systems. The key technical contribution is a revised weighting scheme for three- and four-center electron repulsion integrals, which ensures that the periodic boundary conditions are correctly enforced for all multi-center interactions within the cluster. Validation against full periodic CRYSTAL09 calculations for one-dimensional hydrogen chains confirms that the AICCM reproduces the periodic HF limit accurately.
The code is not publicly available. The implementation reached HF level for 1D and 2D periodic systems but was never extended to full 3D periodicity. The codebase dates from doctoral research at the Mulliken Center for Theoretical Chemistry, University of Bonn (2009-2013) and is not in a state suitable for public release. The ideas and methodology, however, inform the ongoing development at vibe-qc.com.