Molecular Modeling Under Open Boundary Conditions

The patent divides the continuous infinite lead into discrete atomic layers or segments that can be systematically treated. By segmenting the lead into manageable units (atomic layers with specific indices), the method enables numerical treatment of otherwise infinite systems while maintaining accuracy in representing open boundary conditions.

The patent employs a nested structure where atomic layers are organized hierarchically with increasing distance from the device region. Each layer n encompasses all atoms at distance n, creating nested shells that systematically approximate the infinite lead. This nesting allows progressive refinement of the model by including more layers while maintaining computational feasibility.

The patent applies different levels of detail and treatment to different regions of the lead. The device region receives full quantum mechanical treatment, while the lead regions are treated with progressively coarser approximations as distance increases. This local differentiation allows accurate representation of open boundaries where it matters most while reducing computational load in distant regions.

The patent implements a truncated version of the infinite lead by including a finite number of atomic layers (e.g., N layers in each direction). This partial action provides sufficient accuracy for most practical applications while dramatically reducing computational requirements compared to attempting to model the complete infinite system.