Hybrid Gaussian-B-spline basis for the electronic continuum: Photoionization of atomic hydrogen

As a first step towards meeting the recent demand for new computational tools capable of reproducing molecular-ionization continua in a wide energy range, we introduce a hybrid Gaussian-B-spline basis (GABS) that combines short-range Gaussian functions, compatible with standard quantum-chemistry computational codes, with B splines, a basis appropriate to represent electronic continua. We illustrate the performance of the GABS hybrid basis for the hydrogen atom by solving both the time-independent and the time-dependent Schrödinger equation for a few representative cases. The results are in excellent agreement with those obtained with a purely B-spline basis, with analytical results, when available, and with recent above-threshold ionization spectra from the literature. In the latter case, we report fully differential photoelectron distributions which offer further insight into the process of above-threshold ionization at different wavelengthsWork supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 290853, European COST Action No. CM1204 XLIC, and MICINN Project No. FIS2010-1512

Calculation of the Infrared Intensity of Crystalline Systems. A Comparison of Three Strategies Based on Berry Phase, Wannier Function, and Coupled-Perturbed Kohn–Sham Methods

Three alternative strategies for the calculation of the IR intensity of crystalline systems, as determined by Born charges, have been implemented in the Crystal code, using a Gaussian type basis set. One uses the Berry phase (BP) algorithm to compute the dipole moment; another does so, instead, through well localized crystalline orbitals (Wannier functions, WF); and the third is based on a coupled perturbed Hartree–Fock or Kohn–Sham procedure (CP). In WF and BP, the derivative of the dipole moment with respect to the atomic coordinates is evaluated numerically, whereas in CP it is analytical. In the three cases, very different numerical schemes are utilized, so that the equivalence of the obtained IR intensities is not ensured a priori but instead is the result of the high numerical accuracy of the many computational steps involved. The main aspects of the three schemes are briefly recalled, and the dependence of the results on the computational parameters (number of k points in reciprocal space, tolerances for the truncation of the Coulomb and exchange series, and so on) is documented. It is shown that in standard computational conditions the three schemes produce IR intensities that differ by less than 1%; this difference can be reduced by an order of magnitude by acting on the parameters that control the accuracy of the calculation. A large unit cell system (80 atoms per cell) is used to document the relative cost of the three schemes. Within the current implementation the BP strategy, despite its seminumerical nature, is the most efficient choice. That is because it is the oldest implementation, and it is based on the simplest of the three algorithms. Thus, parallelism and other schemes for improving efficiency have, so far, been implemented to a lesser degree in the other two cases

Development of Tools for the Study of Heavy-Element Containing Periodic Systems in the CRYSTAL Code and their Application

This thesis investigates the development of first-principles methods for the study of heavy-element containing periodic systems, as well as their application, in particular to crystalline lanthanide oxides. The Generalized Kohn-Sham Density Functional Theory (GKS-DFT, i.e. in which density functional approximations are built directly from KS orbitals, using so-called hybrid functionals) was shown to provide a particularly effective means to correct for self-interaction errors that plague more conventional local or semi-local formulations in a scalar-relativistic (SR) context. As such, the SR GKS-DFT scheme allowed for a detailed characterization of the electronic structure of the lanthanide sesquioxide series, and enabled (for the first time) to rationalize all known electronic and structural pressure-induced phase transitions in the prototypical strongly-correlated and mixed-valence material EuO. But the hybrid functional approach proved even more useful when developing instead fully relativistic theories and algorithms, which include not only SR effect, but also spin-dependent relativistic effects, such as spin-orbit coupling (SOC). Coincidentally, this thesis reports the first implementation for a self-consistent treatment of SOC in periodic systems with a fraction of exact non-local Fock exchange in a two- component spinor basis (2c-SCF). The numerous advantages of using such a formulation, as opposed to the more approximate treatments of previously existing implementations, are discussed. These advantages originate from the ability of the Fock exchange operator to locally rotate the magnetization of the system with respect to a starting guess configuration (local magnetic torque). In addition, the non-local Fock exchange operator permits to include in the two-electron potential the contribution of the spinors that are mapped to certain spin-blocks of the single-particle density matrix. This allows for a proper treatment of the orbital relaxation of current densities, and their coupling with the other density variables. As a result, it is shown that the lack of Fock exchange (or even its more approximate treatment in a one-component basis, as with previous implementations) from more conventional formulations of the KS-DFT means that the calculation would not allow to access the full range of time-reversal symmetry broken states. This is because, it is shown that in the absence of Fock exchange, the band structure is constrained by a sum rule, linking the one-electron energy levels at opposite points in the first Brillouin zone (kj and −kj)

Photoionization using the xchem approach: Total and partial cross sections of Ne and resonance parameters above the 2s22p5 threshold

The XCHEM approach interfaces well established quantum chemistry packages with scattering numerical methods in order to describe single-ionization processes in atoms and molecules. This should allow one to describe electron correlation in the continuum at the same level of accuracy as quantum chemistry methods do for bound states. Here we have applied this method to study multichannel photoionization of Ne in the vicinity of the autoionizing states lying between the 2s22p5 and 2s2p6 ionization thresholds. The calculated total photoionization cross sections are in very good agreement with the absolute measurement of Samson et al. [J. Electron Spectrosc. Relat. Phenom. 123, 265 (2002)], and with independent benchmark calculations performed at the same level of theory. From these cross sections, we have extracted resonance positions, total autoionization widths, Fano profile parameters, and correlation parameters for the lowest three autoionizing states. The values of these parameters are in good agreement with those reported in earlier theoretical and experimental work. We have also evaluated β asymmetry parameter and partial photoionization cross sections and, from the latter, partial autoionization widths and Starace parameters for the same resonances, not yet available in the literature. Resonant features in the calculated β parameter are in good agreement with the experimental observations. We have found that the three lowest resonances preferentially decay into the 2p-1ϵd continuum rather than into the 2p-1ϵs one [Phys. Rev. A 89, 043415 (2014)], in agreement with previous expectations, and that in the vicinity of the resonances the partial 2p-1ϵs cross section can be larger than the 2p-1ϵd one, in contrast with the accepted idea that the latter should amply dominate in the whole energy range. These results show the potential of the XCHEM approach to describe highly correlated process in the ionization continuum of many-electron systems, in particular molecules, for which the XCHEM code has been specifically designedWe acknowledge computer time from the CCC-UAM and Marenostrum Supercomputer Centers, and financial support from the European Research Council under the European Union’s Seventh Framework Programme (No. FP7/2007-2013)/ERC Grant Agreement No. 290853 XCHEM, the MINECO Projects No. FIS2013-42002-R and No. FIS2016-77889-R, and the European COST Action XLIC CM1204 and STSM CM1204-26542. L.A. acknowledges support from the TAMOP NSF Grant No. 1607588, as well as UCF fundings. E.L. and T.K. acknowledge support from the Swedish Research Council, Grant No. 2016-0378