A generalised methodology using conformal geometric algebra for mathematical chemistry

Abstract

This paper presents a novel and generalised mathematical formulation for mathematical and theoretical chemistry. The formulation presented employs network theoretic methods and standard Conformal Geometric Algebra (Conformal Clifford Algebra) with a unique algebraic extension that introduces special non-integer basis vectors, known as ‘shades’. The methodology developed lays preliminary foundations for both generic and more specialised characterisations and modelling of chemical systems by computing a multi-vector function, termed the ‘hyperfield’ (an algebra-geometric characterisation of a many-agent chemical system). In this paper, the formulation has been applied to inorganic compounds, in the context of their emergent properties (such as boiling and melting points) and intra-molecular characteristics. Case studies have been presented for the calculation of melting point, boiling point, maximum solubility in water and equilibrium bond length of 21 diatomic molecules. This work finds that a network theoretic model of many-agent systems modelled in $${\mathbf{R}}^{\mathrm{4,1}}$$ space, using an algebraic extension of non-integer basis vectors, presents a promising and unifying method for theoretical mathematical chemistry.