X-ray constrained unrestricted Hartree–Fock and Douglas–Kroll–Hess wavefunctions

Abstract

The extension of the X-ray constrained (XC) wavefunction approach to open-shell systems using the unrestricted Hartree-Fock formalism is reported. The XC method is also extended to include relativistic effects using the scalar second-order Douglas-Kroll-Hess approach. The relativistic effects on the charge and spin density on two model compounds containing the copper and iron atom are reported. The size of the relativistic effects is investigated in real and reciprocal space; in addition, picture-change effects are investigated and discussed for the isolated Cu atom. It is found that the relativistic terms lead to changes in the densities that are much smaller than those from the X-ray constraint. Nevertheless, the use of the relativistic corrections in the ab initio model always leads to an improvement in the agreement statistics. An interesting result of the unrestricted XC technique is the possibility of obtaining experimentally derived spin densities from X-ray data.

Unconstrained and X-ray constrained extremely localized molecular orbitals: analysis of the reconstructed electron density

“…As already observed Hudá k et al, 2010;Genoni, 2013a), the energies of constrained wavefunctions are always higher, in keeping with what is expected in a variational procedure when a constraint is added without introducing a new variational parameter. .…”

“…However, as already observed by Jayatilaka and co-workers Whitten et al, 2006;Jayatilaka et al, 2009;Hudá k et al, 2010), the convergence towards the desired agreement is not always fast and straightforward. In order to avoid large values of producing only minimal improvements in the 2 statistics and large unphysical changes of the energy, the following termination criteria have recently been proposed (Genoni, 2013b):…”

“…Since then, many researchers have drawn inspiration from Clinton's original ideas (Clinton & Massa, 1972;Clinton et al, 1973;Frishberg & Massa, 1981;Massa et al, 1985;Tanaka, 1988;Howard et al, 1994;Hibbs et al, 2005;CassamChenaï, 1995;Snyder & Stevens, 1999;Gillet et al, 2001;Gillet, 2007). Within this framework, the most promising method is the X-ray constrained (initially called 'experimental') wavefunction approach developed by Jayatilaka and co-workers (Jayatilaka, 1998;Bytheway, Grimwood, Figgis et al, 2002;Grimwood et al, 2003;Hudá k et al, 2010). This method provides a single Slater determinant which, other than minimizing the corresponding energy, reproduces a set of experimentally collected X-ray structure-factor amplitudes within a predefined precision.…”

Quantum Crystallography: Current Developments and Future Perspectives

“…[16] Furthermore, the modeling of atomicd isplacements initially led to additional problems in case of two-center electron density functions. [27] Nowadays, Jayatilaka's X-ray constrained wavefunction (XCW) fittinga pproach [28][29][30][31][32] and its later developments [33][34][35][36][37][38][39][40] are the most popular modernv ersions of theo riginal quantum crystallographic methods based on X-ray diffraction. [19] The radial decay of the pseudo-atomsa nd the core and valence scattering factors in multipole modelsa re directly calculated from wavefunctions and hence the analytical shape of the refined electron density is significantly influenced by quantum chemistry.I ti si mportant to mention that, to ag ood approximation, the set of multipolar orbitals may be relatedt oa tomic hybridization states [20] and even to some individual orbital occupancies, for example that of d-orbitals in transition metals, [21] and more recently that of f-orbitals in lanthanides.…”

“…[24] The first discussion about the perspective of obtaining wavefunctions from X-ray scattering (here:C ompton scattering) goes back to 1964 and the first Sagamore conference, [25,26] whereas the first quantum crystallographic method according to the original definition [24] and based on X-ray diffraction was proposed by Clinton and Massa in 1972. [27] Nowadays, Jayatilaka's X-ray constrained wavefunction (XCW) fittinga pproach [28][29][30][31][32] and its later developments [33][34][35][36][37][38][39][40] are the most popular modernv ersions of theo riginal quantum crystallographic methods based on X-ray diffraction. They practically aim at determining wavefunctions that minimize the energy, while reproducing, within the limit of experimental errors, X-ray structure factor amplitudes collected experimentally.A sa na lternative, joint refinement methods for the complete reconstruction of N-representable one-electron density matrices exploit both X-ray diffraction and inelastic Compton scattering data.…”