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Fractional spin in reduced density-matrix functional theory.

N Helbig¹, G Theodorakopoulos, N N Lathiotakis

¹Nano-Bio Spectroscopy Group and ETSF Scientific Development Centre, Departamento Física de Materiales, Universidad del País Vasco, San Sebastián, Spain. nehelbig@gmail.com

The Journal of Chemical Physics

|August 10, 2011

Summary

Investigating fractional spin systems reveals that errors in molecular dissociation correlate with atomic energy variations. Some one-body reduced density matrix (1RDM) functionals exhibit size inconsistency, causing further inaccuracies.

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Area of Science:

Quantum Chemistry
Computational Physics
Materials Science

Background:

Fractional spin systems are crucial for understanding electronic behavior in various chemical and physical contexts.
The one-body reduced density matrix (1RDM) is a fundamental quantity in quantum mechanics for describing electronic structure.
Density functional theory (DFT) approximations often face challenges with systems exhibiting fractional spin components.

Purpose of the Study:

To analyze the performance of various 1RDM functionals for systems with fractional z-component of total spin.
To identify and quantify errors in molecular dissociation and size consistency for these systems.
To compare energy calculations using ensemble versus direct minimization approaches for fractional spin systems.

Main Methods:

Defining fractional spin systems as ensembles of integer spin states.
Evaluating functionals of the 1RDM.
Analyzing atomic total energies as functions of fractional spin.
Investigating size consistency of 1RDM functionals.
Comparing direct ensemble energy evaluation with direct fractional spin energy minimization.

Main Results:

Errors in diatomic molecule dissociation are linked to deviations from constant atomic energies with fractional spin.
Several 1RDM functionals display size inconsistency, introducing additional errors.
Differences arise between direct ensemble energy evaluation and direct fractional spin energy minimization.

Conclusions:

The behavior of 1RDM functionals in fractional spin systems is critical for accurate quantum chemical calculations.
Size inconsistency in 1RDM functionals is a significant source of error, particularly in dissociation processes.
Careful consideration of calculation methodology (ensemble vs. minimization) is necessary for fractional spin systems.