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Quantum Statistical Mechanics of Electronically Open Molecules: Reduced Density Operators.

Jacob Pedersen^1,2, Bendik Støa Sannes², Ida-Marie Høyvik²

¹Department of Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark.

Journal of Chemical Theory and Computation

|October 1, 2025

Summary

We developed a new reduced density operator for open quantum systems, accounting for electron sharing between molecules and their environment. This method resolves ambiguities in quantum mechanics and generalizes the grand canonical ensemble for accurate electronic structure calculations.

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Area of Science:

Quantum Chemistry
Theoretical Chemistry
Statistical Mechanics

Background:

Standard quantum statistical mechanics often neglects electron exchange between molecules and their environment.
Existing formulations face ambiguities in defining partial trace operations for composite fermionic systems.
Accurate modeling of open quantum systems requires accounting for environmental interactions.

Purpose of the Study:

To present a reduced density operator for electronically open molecules.
To resolve the fermionic partial trace ambiguity in composite systems.
To generalize the grand canonical density operator for open quantum systems.

Main Methods:

Explicitly averaged over environmental degrees of freedom using a composite Hamiltonian.
Included particle-number non-conserving interactions for electron sharing.
Defined an unambiguous partial trace in composite fermionic Fock space using a common orthonormal orbital basis.

Main Results:

Developed a novel reduced density operator that generalizes the grand canonical density operator.
Introduced a generalized chemical potential allowing for fractional electron transfer.
Framework explicitly considers environmental electron occupancy across various theoretical treatments.

Conclusions:

The new reduced density operator accurately describes electronically open molecules by including environmental interactions.
The methodology provides a hierarchical approach to improve approximations and is compatible with diverse environmental models.
This work offers a more comprehensive framework for quantum statistical mechanics of open systems.