Quantum Expectation Identities for the Three-State Model of a Molecular Domain

The electronic distribution of a molecular domain is examined in this study. A theoretical formulation of quantum molecular properties is presented using the Quantum Expectation Identity theorem (QEI), with a focus on the three-state model of the density matrix for the quantum state of a molecular domain as an open system. The report examines the relationship between ab initio statistical fluctuation-correlation theorems for quantum observables and their derivatives. We focus on three main quantities of a domain: the electronic population, its chemical potential, and its maximum capacity for accepting or donating charge with the neighbors. The analytical expressions for the quantities are presented and discussed in detail. At the end, we explore the concept of quantum purity and its proper application in the molecular domain.