Idempotent density matrices for correlated systems from x-ray-diffraction structure factors

Abstract

X-ray structure-factor data can be used to obtain an electron-density matrix corresponding to a wave function that is a single determinant of orbitals. Equations are derived which treat this problem for the case of electronic open shells. The equations are solved for model numerical problems of lithium and berylium atoms. For these cases the structure-factor data are obtained from essentially exact wave functions.

Quantum Crystallography: Current Developments and Future Perspectives

“…Obviously,n oN-electron wavefunction has yet been recovered this way,b ut significant advances can be (and have been) made, including the possibility of tackling the problem from ap hase-space perspective.I ni ts simplest expression, the one-electron reduced density matrix (1-RDM), which was strongly promoted by Weyrich and Massa and co-workers during the 1980s and1 990s, [118][119][120][121] can be seen as the most direct object to connect positiona nd momentum space properties [122] and thereby offers an efficient means to combine XRD, QCBEDa nd PNDd ata with experimental resultsp rovided by inelastic scattering techniques, such as polarized or non-polarized X-ray Compton, (g,eg)s cattering or positrona nnihilation. Obviously,n oN-electron wavefunction has yet been recovered this way,b ut significant advances can be (and have been) made, including the possibility of tackling the problem from ap hase-space perspective.I ni ts simplest expression, the one-electron reduced density matrix (1-RDM), which was strongly promoted by Weyrich and Massa and co-workers during the 1980s and1 990s, [118][119][120][121] can be seen as the most direct object to connect positiona nd momentum space properties [122] and thereby offers an efficient means to combine XRD, QCBEDa nd PNDd ata with experimental resultsp rovided by inelastic scattering techniques, such as polarized or non-polarized X-ray Compton, (g,eg)s cattering or positrona nnihilation.…”

Atomic density radial functions from molecular densities

“…There are several possible routes to an exact representation ofq A . One can, for example, fit the density matrix of a given basis set using the method developed by Frishberg and Massa [25]. Alternatively, one can adopt procedures that use either LiebÕs variational construction [26], or LevyÕs constrained search formulas [27] for the Hohenberg-Kohn functional [28], and then derive the external potential and one-electron functions associated with the stockholder atom [29].…”

Fuzzy Electron‐Density Fragments as Building Blocks in Crystal‐Engineering Design

“…The fact that quantum-chemical representations of molecular electron densities may provide substantial help in the actual evaluation and analysis of X-ray diffraction experiments has received a new confirmation by the introduction of quantum crystallography [1,2], itself a combination of crystallographic and quantum-chemical approaches. The developments leading to quantum crystallography include the early approaches of fitting N-representable density matrices, alternatively, fitting actual molecular wavefunctions to experimentally determined X-ray diffraction data [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. One of the goals of quantum crystallography is finding efficient ways to utilise crystallographic diffraction data for the determination of molecular density matrices or molecular wavefunctions.…”