A simple truth hidden in plain sight: All molecules are entangled according to chemical common sense

TL;DR

This paper introduces a physically motivated equation linking molecular electron count to chemical common sense, revealing that all molecules are entangled through their electron numbers, which underpins fundamental principles of molecular quantum mechanics.

Contribution

It proposes a new physical principle connecting electron entanglement in molecules with chemical intuition, including a novel state function based on chemical potential.

Findings

All molecules are entangled in their electron numbers.

The energy is piecewise linear with respect to electron number.

A new state function based on chemical potential is defined.

Abstract

A physically motivated equation that determines the number of electrons of a molecule is proposed based on chemical common sense. It shows that all molecules are entangled in the number of electrons and results in the fundamental assumption of molecular energy convexity that underpins molecular quantum mechanics. The proposed physical principle includes the molecular size consistency principle as a special case. Application of wavefunction theory to the principle shows that an individual molecule with a noninteger number of electrons is locally physical albeit locally unreal. The energy of a molecule is piecewise linear with respect to its continuous number of electrons. The continuity of the number of electrons allows the definition of an electronic chemical potential of a single molecule. A state function equivalent to the energy of a molecule can be defined using the chemical potential as a variable. The aforementioned physical principle can alternatively be expressed as a simple additivity with the new state function. The latter also shows that the quantum entanglement in the number of electrons can be viewed as all molecules sharing the same chemical potential.