Matrices and Density Functionals

It is a fundamental postulate of quantum mechanics that the wave function contains all possible information about a system in a pure state at zero temperature, whereas at nonzero temperature, or in a general mixed state, this information is contained in the density matrix of quantum statistical mechanics. Normally, this is much more information that one can handle for a system with W = 100 particles the many-body wave function is an extremely complicated function of 300 spatial and 100 spin variables that would be impossible 

For a general quantum system at temperature T, the density operator in a canonic ensemble is defined as 

The coordinate-space matrix element of this operator for an N-particle system is 

Similarly, the single-particle density matrix is defined as 

The structure of reduced density matrices is quite simple all coordinates that y does not depend upon are set equal in and 4, and integrated over. 

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R. Erdahl, in Density Matrices and Density Functionals Proeeedings of the A. J. Coleman Symposium, Kingston, Ontario, 1985, edited by R. Erdahl and V. Smith (Reidel, Dordrecht, 1987), p. 51, and references therein. 

Quantum Systems in Chemistry and Physics is a broad area of science in which scientists of different extractions and aims jointly place special emphasis on quantum theory. Several topics were presented in the sessions of the symposia, namely 1 Density matrices and density functionals 2 Electron correlation effects (many-body methods and configuration interactions) 3 Relativistic formulations 4 Valence theory (chemical bonds and bond breaking) 5 Nuclear motion (vibronic effects and flexible molecules) 6 Response theory (properties and spectra atoms and molecules in strong electric and magnetic fields) 7 Condensed matter (crystals, clusters, surfaces and interfaces) 8 Reactive collisions and chemical reactions, and 9 Computational chemistry and physics. 

Yang W (1986) Phys Rev A34 4575 Borman S (19 ) Chem Eng News 68 22 Hohenberg PC, Kohn W (1964) Phys Rev 136B 864 Hohenberg PC, Kohn W, Sham LJ (1990) Adv Quantum Chem 21 7 Lowdin P-O (1987) In Erdahl R, Smith VH (eds) Density matrices and density functionals, Reidel D, Dordrecht, p 21... 

Hunter G (1985) In Erdahl R, Smith VH (eds) Density matrices and density functionals. Reidel, Dordrecht, p 583... 

Density Matrices and Density Functionals, the A. John Coleman Symposium, Kingston, August 25-29, 1985. Sponsored by National Sciences and Engineering Research Council of Canada Queen s University. Coorganizers R. M. Erdahl and V. H. Smith, Jr. Proceedings R. M. Erdahl and V. H. Smith, Jr., editors. Density Matrices and Density Functionals, Reidel (1987), 600 pp. 

M. Levy, Correlation energy functionals of one-matrices and Hartree-Fock densities, in Density Matrices and Density Functionals (R. Erdahl and V. H.. Smith, Jr., ed.), Reidel, Dordrecht, The Netherlands, 1987, p. 479. 

Density matrices and density functionals (Chair R. Pauncz)... 

Lowdin, who contributed in no small measure to the development of formal many-electron theory through his seminal work on electron correlation, reduced density matrices, perturbation theory, etc. many times expressed his concerns about the theoretical aspects of density functional approaches. This short review of the interconnected features of formal many-electron theory in terms of propagators, reduced pure state density matrices, and density functionals is dedicated to the memory of Per-Olov Lowdin. 

Density matrices and density functionals have important roles in both the interpretation and the calculation of atomic and molecular structures and properties. The fundamental importance of electronic correlation in many-body systems makes this topic a central area ofresearch in quantum chemistry and molecular physics. Relativistic effects are being increasingly recognized as an essential ingredient ofstudies on many-body systems, not only from a formal viewpoint but also for practical applications to molecules and materials involving heavy atoms. Valence theory deserves special attention since it... 

M. Levy, in Density Matrices and Density Functionals, edited by R. Eradahl... 

R. Erdahl and V. H. Smith, eds. Density Matrices and Density Functionals, (Reidel, Dordrecht, 1987). 

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