548 research outputs found
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)
Hidden Relaxation Term in Approximate Treatments of Responses to Electric and Magnetic Fields
Recently a generalization of the ``\textit{modern theory of orbital
magnetization}'' to include non-local Hamiltonians (e.g. hybrid functionals of
the generalized Kohn-Sham theory) was provided for magnetic response
properties. Results indicated inequivalence between sampling of direct and
reciprocal spaces for those calculations far from the complete basis set limit.
We show that this can be explained by a hidden ``relaxation'' contribution to
the reciprocal-space derivatives. The missing relaxation term is shown to
(generally) affect the results of calculations of not only magnetic, but also
electric response properties, within the context of the ``\textit{modern theory
of polarization}''. Necessary conditions are provided to permit avoiding the
calculation of the hidden relaxation term
First-Principles Calculation of the Optical Rotatory Power of Periodic Systems: Modern Theory with Modern Functionals
An analysis of orbital magnetization in band insulators is provided. It is
shown that a previously proposed electronic orbital angular-momentum operator
generalizes the ``modern theory of orbital magnetization'' to include non-local
Hamiltonians. Expressions for magnetic transition dipole moments needed for the
calculation of optical rotation (OR) and other properties are developed. A
variety of issues that arise in this context are critically analyzed. These
issues include periodicity of the operators, previously proposed band
dispersion terms as well as, if and where needed, evaluation of reciprocal
space derivatives of orbital coefficients. Our treatment is used to determine
the optical rotatory power of band insulators employing a formulation that
accounts for electric dipole - electric quadrupole (DQ), as well as electric
dipole-magnetic dipole, contributions. An implementation in the public
\textsc{Crystal} program is validated against a model finite system and applied
to the -quartz mineral through linear-response time-dependent density
functional theory with a hybrid functional. The latter calculations confirmed
the importance of DQ terms. Agreement against experiment was only possible with
i) use of a high quality basis set, ii) inclusion of a fraction of non-local
Fock exchange, and iii) account of orbital-relaxation terms in the calculation
of response functions
Perturbation Theory Treatment of Spin-Orbit Coupling. III: Coupled Perturbed Method for Solids
Giant Magnetic Moments of Nitrogen Stabilized Mn Clusters and Their Relevance to Ferromagnetism in Mn Doped GaN
Using first principles calculations based on density functional theory, we
show that the stability and magnetic properties of small Mn clusters can be
fundamentally altered by the presence of nitrogen. Not only are their binding
energies substantially enhanced, but also the coupling between the magnetic
moments at Mn sites remains ferromagnetic irrespective of their size or shape.
In addition, these nitrogen stabilized Mn clusters carry giant magnetic moments
ranging from 4 Bohr magnetons in MnN to 22 Bohr magnetons in Mn_5N. It is
suggested that the giant magnetic moments of Mn_xN clusters may play a key role
in the ferromagnetism of Mn doped GaN which exhibit a wide range (10K - 940K)
of Curie temperatures
Structural Relaxation of Materials with Spin-Orbit Coupling: Analytical Forces in Spin-Current DFT
Analytical gradients of the total energy are provided for local density and
generalized-gradient hybrid approximations to generalized Kohn-Sham
spin-current density functional theory (SCDFT). It is shown that gradients may
be determined analytically, in a two-component framework, including spin-orbit
coupling (SOC), with high accuracy. We demonstrate that renormalization of the
electron-electron potential by SOC-induced spin-currents can account for
considerable modification of crystal structures. In the case of Iodine-based
molecular crystals, the effect may amount to more than half of the total
modification of the structure by SOC. Such effects necessitate an SCDFT, rather
than DFT, formulation, in which exchange-correlation functionals are endowed
with an explicit dependence on spin-current densities. An implementation is
presented in the \textsc{Crystal} program
Efficient Calculation of Derivatives of Integrals in a Basis of Non-Separable Gaussians Through Exploitation of Sparsity
A computational procedure is developed for the efficient calculation of
derivatives of integrals over non-separable Gaussian-type basis functions, used
for the evaluation of gradients of the total energy in quantum-mechanical
simulations. The approach, based on symbolic computation with computer algebra
systems and automated generation of optimized subroutines, takes full advantage
of sparsity and is here applied to first energy derivatives with respect to
nuclear displacements and lattice parameters of molecules and materials. The
implementation in the \textsc{Crystal} code is presented and the considerably
improved computational efficiency over the previous implementation is
illustrated. To this purpose, three different tasks involving the use of
analytical forces are considered: i) geometry optimization; ii) harmonic
frequency calculation; iii) elastic tensor calculation. Three test case
materials are selected as representatives of different classes: i) a metallic
2D model of the Cu (111) surface; ii) a wide-gap semiconductor ZnO crystal,
with a wurtzite-type structure; and iii) a porous metal-organic crystal, namely
the ZIF-8 Zinc-imidazolate framework. Finally, it is argued that the present
symbolic approach is particularly amenable to generalizations, and its
potential application to other derivatives is sketched
Generalized Kohn-Sham Approach for the Electronic Band Structure of Spin-Orbit Coupled Materials
Spin-current density functional theory (SCDFT) is a formally exact framework
designed to handle the treatment of interacting many-electron systems including
spin-orbit coupling at the level of the Pauli equation. In practice, robust and
accurate calculations of the electronic structure of these systems call for
functional approximations that depend not only on the densities, but also on
spin-orbitals. Here we show that the call can be answered by resorting to an
extension of the Kohn-Sham formalism, which admits the use of non-local
effective potentials, yet it is firmly rooted in SCDFT. The power of the
extended formalism is demonstrated by calculating the spin-orbit-induced
band-splittings of inversion-asymmetric MoSe monolayer and
inversion-symmetric bulk -MoTe. We show that quantitative agreement
with experimental data is obtainable via global hybrid approximations by
setting the fraction of Fock exchange at the same level which yields accurate
values of the band gap. Key to these results is the ability of the method to
self-consistently account for the spin currents induced by the spin-orbit
interaction. The widely used method of refining spin-density functional theory
by a second-variational treatment of spin-orbit coupling is unable to match our
SCDFT results.Comment: 12 pages, 3 figure
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