Title : From the Bansal nonlinear wave function to chemical bonding: A stratified B-Chem framework for atomic structure, molecular geometry, and symmetry
Abstract:
Quantum chemistry provides established mathematical descriptions of atomic structure, electronic configurations, chemical bonding, molecular geometry, and symmetry. However, these descriptions employ different mathematical representations depending on the physical system and observable properties under investigation. The development of a coordinated computational framework connecting these representations remains an important theoretical objective. In this presentation, I introduce the proposed Bansal Chemistry (B-Chem) framework, beginning with the Bansal nonlinear wave-function formulation and extending toward atomic structure, chemical bonding, and molecular organization. The framework employs stratified algebraic layers, hypercomplex mathematical representations, nonlinear formulations, and geometrically admissible projections to organize the relationships between underlying chemical-state descriptions and observable physical quantities. Particular attention is given to the representation of electrons, atomic configurations, molecular orbitals, bond formation, bond classification, geometric constraints, and molecular symmetry.
The proposed approach accommodates covalent, ionic, coordinate, and delocalized bonding through distinguishable mathematical and geometrical descriptions. Illustrative applications involving atomic systems, hydrogen, molecular bonding, and water demonstrate the intended progression from elementary chemical structure toward increasingly complex molecular organization. The objective is not to introduce new chemical elements, interactions, or fundamental laws, but to investigate whether the B-Chem architecture provides a coherent and computationally interpretable representation of established chemical phenomena. The presentation concludes by identifying mathematical consistency requirements, observable constraints, and opportunities for comparison with established quantum-chemical and molecular-structure models.
