Quantum Crystallography: Density MatrixDensity Functional Theory and the XRay Diffraction Experiment
Abstract
Density Matrix Theory is a Quantum Mechanical formalism in which the wavefunction is eliminated and its role taken over by reduced density matrices. The interest of this is that, it allows one, in principle, to calculate any electronic property of a physical system, without having to solve the Schrodinger equation, using only two entities much simpler than an Nbody wavefunction: first and second order reduced density matrices. In practice, though, this very promising possibility faces the tremendous theoretical problem of Nrepresentability, which has been solved for the former, but, until now, voids any hope of theoretically determining the latter. However, it has been shown that single determinant reduced density matrices of any order may be recovered from coherent Xray diffraction data, if one provides a proper Quantum Mechanical description of the Crystallography experiment. A deeper investigation of this method is the purpose of this work, where we, first, further study the calculation of Xray reduced density matrices Nrepresentable by a single Slater determinant. In this context, we independently derive necessary and sufficient conditions for the uniqueness of the method. We then show how to account for electron correlation in this model. For the first time, indeed, we derive highly accurate, yet practical, density matrices approximately Nrepresentable by correlateddeterminant wavefunctions. The interest of such a result lies in the Quantum Mechanical validity of these density matrices, their property of being entirely obtainable from Xray coherent diffraction data, their very high accuracy conferred by this known property of the Nrepresenting wavefunction, as well as their definition as explicit functionals of the density. All of these properties are finally used in both a theoretical and a numerical application: in the former, we show that these density matrices may be used in the context of Density Functional Theory to highly accurately determine the unknown HK functional, associated with the theorem of Hohenberg and Kohn. The latter is provided by the calculation of helium correlation energy, where we test approximating the secondorder density function by the leading term of its McLaurin's series expansion.
 Publication:

Ph.D. Thesis
 Pub Date:
 1990
 Bibcode:
 1990PhDT.......243S
 Keywords:

 QUANTUM MECHANICS;
 Chemistry: Physical; Physics: Molecular; Physics: Atomic