Quantum chemical “Aufbau” principles: how to estimate the shape of highly flexible (bio-)polymers? A recursively extendable “chemion picture” of Euler-Hückel-type

TL;DR

This paper introduces a new quantum chemical method to model the shape of flexible polymers by breaking down their torsion angles into simpler one-dimensional curves.

Contribution

The novel 'chemion picture' recursively constructs Hamiltonians for flexible polymers using Euler-Hückel-type principles.

Findings

The method uses monofocal hydrides as anchor units to build chemionic Hamiltonians.

Standard quantum methods like RHF and FCI are applied to solve Schrödinger equations for alkanes and related oligomers.

The approach provides a non-empirical foundation for modeling polymer conformations.

Abstract

An outline is given of how to split the n-dimensional space of torsion angles occurring in flexible (bio-)polymers (like alkanes, nucleic acids, or proteins, for instance) into n one-dimensional potential curves. Forthcoming applications will focus on the “protein folding problem,” beginning with polyglycine.

In accordance with Euler’s topology rules, molecules are considered to be composed of “vertices” (atoms, ligands, bonding sites, functional groups, and bigger fragments). Following Hückel, each vertex is represented by only one basis function. Starting from the “monofocal” hydrids \documentclass[12pt]{minimal}
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\begin{document}$$\text {SH}_{2}$$\end{document}SH2, ClH as anchor units, “chemionic” Hamiltonians (of individual “chemion ensembles” and proportional nuclear charges) are constructed recursively, together with an appropriate basis set for the first five (normal) alkanes and some related oligomers like primary alcohols, alkyl amines, and alkyl chlorides.

Standard methods (“Restricted Hartree-Fock RHF” and “Full Configuration Interaction FCI”) are used to solve the various stationary Schrödinger equations. Two software packages are indispensable: “SMILES” for integral evaluations over Slater-type orbitals (STO), and “Numerical Recipes” for matrix diagonalizations and inversions. While managing with only two-center repulsion integrals, “implicit multi-center integrations” lead us to the non-empirical fundament of Hoffmann’s “Extended-Hückel Theory.”