von Neumann Entropies Analysis in Hilbert Space for the Dissociation Processes of Homonuclear and Heteronuclear Diatomic Molecules
Nelson Flores–Gallegos1 and Rodolfo O. Esquivel2
Departamento de Química, Universidad Autónoma Metropolitana–Iztapalapa Rafael Atlixco No. 186, Col. Vicentina, C.P. 09340, México D.F. 1nelsonfloresgallegos@yahoo.com.mx, 2 esquivel@xanum.uam.mx
Recibido el 2 de octubre del 2007
Aceptado el 15 de enero del 2008
Abstract
Quantum Information Theory is a new field with potential implications for the conceptual foundations of Quantum Mechanics through density matrices. In particular, information entropies in Hilbert space representation are highly advantageous in contrast with the ones in phase space representation since they can be easily calculated for large systems. In this work, novel von Neumann conditional, mutual, and joint entropies are employed to analyze the dissociation process of small molecules, Cl2 and HCl, by using the spectral decomposition of the first reduced density matrix in natural atomic orbital–based representation which allows us to assure rotational invariance, N– and v–representability in the Atoms–in–Molecules (AIM) scheme. Quantum information entropies permit to analyze the dissociation process through quantum mechanics concepts such as electron correlation and entanglement, showing interesting critical points which are not present in the energy profile, such as charge depletion and accumulation, along with bond breaking regions.
Key words: Quantum Information Theory, entanglement, diatomic molecules, Ab initio calculations.
Resumen
La Teoría de Información Cuántica es un nueva área de investigación con implicaciones potenciales para el desarrollo conceptual de los fundamentos de la Mecánica Cuántica mediante las matrices de densidad. En particular, las entropías de información en la representación del espacio de Hilbert ofrecen amplias ventajas en comparación con las que se definen en la representación del espacio real debido a que pueden ser fácilmente aplicadas en grandes sistemas. En este estudio, se emplean nuevas entropías de von Neumann de tipo condicional, mutuas y conjuntas para analizar el proceso de disociación de moléculas pequeñas, Cl2 y HCl, usando la descomposición espectral de la matriz densidad reducida de primer orden en una representación natural atómica que permite asegurar su invariancia rotacional, y su N– y v–representabilidad en un esquema AIM. Las entropías informacionales cuánticas permiten analizar el proceso de disociación mediante conceptos mecánico–cuánticos tales como correlación electrónica y entrelazado, mostrando puntos críticos de interés que no se encuentran en el perfil energético, tales como remoción y acumulación de carga, así como puntos de formación y ruptura de enlace.
Palabras clave: Teoría de información cuántica, entrelazado, moléculas diatómicas, cálculos ab initio.
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]]>Acknowledgments
We wish to thank PROMEP–SEP–México for financial support and to the Laboratorio de Supercómputo y Visualización for allocation of supercomputing time. We also wish to thank Edmundo Carrera and José Luis Gázquez for fruitful discussions. We also wish to thank suggestions of one of the referees which helped to enrich the paper.
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