Browsing by Subject "Density functional theory"

Developing accurate and efficient theoretical approaches to describe the electronic structure has been a long-standing task in quantum chemistry. The main workhouse in quantum chemistry, density functional theory (DFT), has been widely used because of the good accuracy and the affordable computational cost. However, the applicability of commonly used density functional approximations (DFAs) is limited by intrinsic problems such as the delocalization error. Green's function theory that recently has gained increasing attention is shown to outperform the Kohn-Sham DFT approach on many aspects but is also computationally demanding. In this work, DFT and Green's function theory are connected to develop accurate and robust approaches for describing both ground state and excited state properties. For ground state calculations, the renormalized singles (RS) Green's function that captures all singles contributions from the KS Green's function is applied in the GW and the T-matrix approximation to predict accurate quasiparticle (QP) energies. GRSWRS and GRSTRS are shown to outperform over commonly used G0W0 and G0T0 for predicting ionization potentials (IPs) and core-level binding energies (CLBEs). The RS with correlation (RSc) Green's function that also includes higher order contributions in GW is shown to provide further improvements over GRSWRS. The concept of RS has also been used in the multireference DFT approach, which describes strongly correlated systems. We also provide an analytical approach to calculate QP energies of DFAs that can be expressed as a functional of the non-interacting Green's function. For excited state calculations, we combine localized orbital scaling correction (LOSC) with Bethe-Salpeter equation (BSE) to calculate excitation energies of molecular systems. QP energies from LOSC that systematically eliminates the delocalization error are used in BSE, which bypasses the expensive GW calculations. BSE/LOSC is shown to predict accurate excitation energies of valence, charge transfer and Rydberg excitations. We also combine the RS Green's function with BSE. BSE/GRSWRS is shown to provide a comparable accuracy to the computationally expensive BSE/evGW. We show that combining the merit of DFT and Green's function theory leads to accurate and efficient theoretical approaches for describing both the ground state and the excited state.

Quantum chemistry methods nowadays reach its maturity with various robust ground state correlation methods. However, many problems related to response do not have satisfactory solutions. Chemical reactivity indexes are some static response to external fields and number of particle change. These chemical reactivity indexes have important chemical significance, while not all of them had analytical expressions for direct evaluations. By solving coupled perturbed self-consistent field equations, analytical expressions were obtained and verified numerically. In the particle-particle (pp) channel, the response to the pairing field can describe N±2 excitations, i.e. double ionization potentials and double electron affinities. The linear response time-dependent density-functional theory (DFT) with pairing fields is the response theory in the density-functional theory (DFT) framework to describe $N\pm 2$ excitations. Both adiabatic and dynamic kernels can be included in this response theory. The correlation energy based on this response, the correlation energy of the particle-particle random phase approximation (pp-RPA), can also be proved equivalent to the ladder approximation of the well-established coupled-cluster doubles. These connections between the response theory, ab initio methods, and Green's function theory would be beneficial for further development. Based on RPA and pp-RPA, the theory of second RPA and the second pp-RPA with restrictions can be used to capture single and double excitations efficiently. We also present a novel methods, variational fractional spin DFT, to calculate singlet-triplet energy gaps for diradicals, which are usually calculated through spin-flip response theories.

Perovskites are a category of semiconductors with outstanding optoelectronic properties. Especially in the last decades, three-dimensionally connected (“3D”) hybrid perovskites gained an important position as an innovative solar-cell material by including organic cations. Related molecularly engineered materials, for example, atomic-scale two-dimensionally connected (“2D”) layered crystals and nano-scale structures offer a wide range of compositional, structural, and electronic tunability. Based on quantum chemistry simulations (specifically, density functional theory), this dissertation aims to contribute to the understanding of the relationship between the components and structure of hybrid perovskites and their electronic properties, related to alloying, energy level alignment in quantum wells, impact of chiral organic constituents on the atomic structure of 2D perovskites and resulting spin character of the electronic levels, and on the structure of related perovskite nanostructures.First, to investigate the tunability of 2D hybrid perovskites, 1) the author simulated the Sn/Pb alloying at the central metal site and explained the corresponding “bowing effect” on the bandgap values with different contribution preferences towards the conduction bands versus valence bands from different elements; 2) taking the conjugation length in different oligothiophene cations and the inorganic layer thickness as two independent factors, the author confirmed a gradual change of quantum well types. Second, to gain an in-depth understanding of the spin properties of the energy bands (specifically, the spin-selectivity) in hybrid perovskites, 1) the author analyzed the frontier bands of the 2D hybrid perovskite S-1-(1-naphthyl)ethylammonium lead bromide and revealed a giant spin-splitting originated from the inorganic moiety; 2) the author (together with experimental collaborators) identified a difference in the inter-octahedron Pb-X-Pb (X stands for the halides) distortion angles as the crucial geometric descriptor for spin-splitting in 2D hybrid perovskites by a correlation analysis of 22 experimental and relaxed structures with various chiral or achiral organic cations; 3) for perovskite nano-crystals with chiral surface ligands, simulations by the author helped to attribute the chirality transfer between organic cations and inorganic substrate to the geometric distortions driven by hydrogen bonds. Third, the author investigated 2D hybrid perovskites containing oligoacene organic cations, validated the theoretical method for geometry evaluation and predicted the expected quantum well type, crystal symmetry, and detailed expected spin-splitting properties that determine the potential for spin-selective transport and optoelectronics Finally, driven by the computational needs of large-scale hybrid perovskites DFT simulations, the application of an innovative hardware, tensor processing units (designed by Google), to quantum chemistry calculations (specifically, to solve for the density matrix) was explored. The author removed the code bottleneck to facilitate the largest “end-to-end” O(N^3) DFT simulations ever reported and benchmarked the accuracy and performance of this new hardware with test cases from biomolecular systems to solid-state and nano-scale materials.

The development of the technology depends heavily on the development of materials. However, how to select the best materials for a specific purpose — i.e. materials selection, is a tricky problem in academia, industry, and our daily lives. Recently, because of the rapid development of computers, ab initio theoretical calculations can be used to aid in materials selection. However, since many approximations in the theoretical calculations exist, choosing appropriate approximations to obtain accurate and predictable materials properties is still difficult. This is the main focus of this thesis. More specifically, we will focus on the materials selection for photovoltaics, which plays a significant role in the energy field today. While modern commercial thin-film PV cells, e.g., based on metal chalcogenide zinc-blende-type materials (Cu(In,Ga)(S,Se)2 (CIGSSe), CdTe) suffer from problems like relying on elements that are either toxic or rare in the earth’s crust, a recent alternative candidate based on kesterite Cu2ZnSn(S,Se)4 (CZTS) peaked at relatively low efficiencies (12.6%) due to the limited open circuit voltage (Voc) caused by the prevalent anti-site structure disorder (e.g. Cu on Zn, Zn on Cu). A possible path forward to reduce this antisite disorder is to pursue materials in which the Cu/Zn combination is replaced by elements that are chemically less similar but that retain the same valence. Recently, Cu2 BaSnS4 ́x Sex (CBTSSe) materials with a trigonal structure (space group P31 ) and composed of only earth abundant metals have been proposed and demonstrated as emerging PV absorbers to address the above issues of CZTSSe. Results obtained as part of this thesis elucidated the band structure and electronic properties of the CBTSSe alloys. A recent device prepared from the Cu2BaSnS4 ́xSex (x « 3) has now been demonstrated with power conversion efficiency (PCE) exceeding 5%. Starting from this early prototype, many avenues remain to optimize the materials, including the underlying chemical positions, the electronic, optical and defect properties of specific compounds. In this thesis, we expand on the CBTSSe paradigm by exploring 16 related compounds, denoted I2-II-IV-VI4 (I=Cu,Ag; II=Sr,Ba; IV=Ge,Sn; VI=S,Se), and some of their alloys for their possible utility as thin-film PV absorbers.

A main methodological result of this thesis concerns the appropriate approximations we can use to obtain accurate and predictable structure, electronic, optical and defect properties for photovoltaic materials. Specifically, structure optimization using computationally expensive hybrid density functional theory is more appropriate than the normally used (semi)local functional (PBE, LDA) and can lead to reasonable and predictable structure and electronic properties. Furthermore, a detailed approach to obtain accurate carrier effective masses is pursued. For the optical properties, the effect of different broadening functions on the onset of absorption coefficients is discussed, and the correct onset behavior can be obtained using Gaussian broadening. At last, a validation of the infinite-size limit of charged defect formation energies calculated by supercell approach is given based on a benchmark study for the gallium vacancy (within charge state q = 0, -1, -2, -3) in GaAs. In general, the bare supercell approach, a supercell approach developed earlier by Freysoldt and coworkers, and a cluster approach can lead to the same infinite-size limit for the charged defect formation energies. Then, based on the appropriate approximations mentioned above, a study of materials properties is described in the I2-II-IV-VI4 (I=Cu,Ag; II=Sr,Ba; IV=Ge,Sn; VI=S,Se) 16 compound systems based on the theoretical structure, electronic and optical properties. Four compounds (Cu2BaSnS4, Cu2BaSnSe4, Cu2BaGeSe4, Cu2SrSnSe4) are identified as potential PV candidates based on their appropriate electronic, and optical properties. Then, two further re- finements are pursued for the Cu2BaSnS4 and Cu2BaGeSe4 compounds. The specific alloys Cu2BaGe1 ́xSnxSe4 (x « 3/4) and Cu2BaSnS4 ́xSex (x « 3) prove to be the best candidates for photovoltaics absorbers among the alloys of these two compounds.

The computational success of density functional theory relies on the construction of suitable approximations to the exchange-correlation energy functional. Use of functional approximations depending explicitly upon the density alone appear unable to address all aspects of many-body interactions, such as the fundamental constraint that the ground state energy is a piecewise linear function of the total number of electrons, and the ability to model nonlocal effects. Functionals depending explicitly upon occupied and unoccupied Kohn–Sham orbitals are considered necessary to address these and other issues. This dissertation considers certain issues relevant to the successful implementation of explicitly orbital-dependent functionals through the optimized effective potential (OEP) approach, as well as extending the potential functional formalism that provides the formal basis for the OEP approach to systems in the presence of noncollinear magnetic fields.

The self-consistent implementation of orbital-dependent energy functionals is correctly done through the optimized effective potential approach—minimization of the ground state energy with respect to the Kohn–Sham potential that generates the set of orbitals employed in the energy evaluation. The focus on the potential can be problematic in finite basis set approaches as determining the exchange-correlation potential in this manner is an inverse problem which, depending upon the combination of orbital and potential basis sets employed, is often ill-posed. The ill-posed nature manifests itself as nonphysical exchange-correlation potentials and total energies. We address the problem of determining meaningful exchange-correlation potentials for arbitrary combinations of orbital and potential basis sets through an L-curve regularization approach based on biasing towards smooth potentials in the energy minimization. This approach generates physically reasonable potentials for any combination of basis sets as shown by comparisons with grid-based OEP calculations on atoms, and through direct comparison with DFT calculations employing functionals not depending on orbitals for which OEP can also be performed. This work ensures that the OEP methodology can be considered a viable many-body computational methodology.

A separate issue of our OEP implementation is that it can suffer from a lack of size-extensivity—the total energy of a system of infinitely separated monomers may not scale linearly with the total number of monomers depending upon how we construct the Kohn–Sham potential. Typically, a fixed reference potential is employed to aid in the convergence of a finite basis set expansion of the Kohn–Sham potential. This reference potential can be utilized to ensure other desirable properties of the resulting potential. In particular, it can enforce the correct asymptotic behavior. The Fermi–Amaldi potential is often used for this purpose but suffers from size-nonextensivity owing to the explicit dependence of the potential on the total number of electrons. This error is examined and shown to be rather small and rapidly approaches a limiting linear behavior. A size-extensive reference potential with the correct asymptotic behavior is suggested and examined.

We also consider a formal aspect of the potential-based approach that provides the underlying justification of the OEP methodology. The potential functional formalism of Yang, Ayers, and Wu is extended to include systems in the presence of noncollinear magnetic fields. In doing so, a solution to the nonuniqueness issue associated with mapping between potentials and wave functions in such systems is provided, and a computational implementation of the OEP in noncollinear systems is suggested.

Finally, as an example of an issue for which orbital-dependent functionals seem necessary to obtain a correct description, we consider the ground state structures of C_{4N + 2} rings which are believed to exhibit a geometric transition from angle-alternation (N ≤ 2) to bond-alternation (N > 2). So far, no published DFT approach has been able to reproduce this behavior owing to the tendency of common density functional approximations to bias towards delocalized electron densities. Calculations are presented with the rCAM-B3LYP exchange-correlation functional that correctly predict the structural evolution of this system. This is rationalized in terms of the recently proposed delocalization error for which rCAM-B3LYP explicitly attempts to address.

Density functional theory is a formally exact theory to describe ground state properties due to the existence of the exact functional. In practice, the usefulness of density functional theory relies on the accuracy of density functional approximations. After decades of effort of functional developments, the present-day state-of-the-art density functional approximations have achieved reasonably good accuracy for small systems. However, the error grows with system size. One of the dominant errors intrinsic in the mainstream density functional approximations is the delocalization error, which arises because of the violation of Perdew-Parr-Levy-Balduz (PPLB) linearity condition. The PPLB condition governs the formulation of the density functional theory for fractional-charge systems, for which the ground state energy for the exact functional, as a function of the fractional electron number, should yield a series of line-segments across the integer points. In this dissertation, by imposing the PPLB condition in a local, size-consistent way, we develop the local scaling correction (LSC) and its updated version, the localized orbital scaling correction (LOSC), which largely improve upon the mainstream density functional approximations across system sizes. With the LOSC, we open a door towards a systematic elimination of delocalization error. Besides the ground state functional development, we also develop a gentlest ascent dynamics approach for accessing the excited states via time-independent ground state density functionals. This is also useful for exploring Kohn-Sham energy landscapes of approximate density functionals. I will also review the PPLB formulation of density functional theory for fractionally charged systems, and show that it is equivalent to the formulation normally used for fractional system calculations under certain assumptions. Furthermore, I will examine the behavior of the fractional system energy as a function of the fractional number of electrons for different mainstream functionals, and relate it to their errors for integer systems.

Density functional theory has proven to be an invaluable tool for modeling matter and chemistry . This can be seen from the fact that density functional theory papers are far and away the most cited theory from the physical sciences. While density functional theory excels at predicting total energies and equilibrium geometries, standard approximate functionals can be inadequate for determining some properties such as dissociation energies, reaction barriers, and band gaps. These deficiencies can be traced to delocalization error in density functional approximations. In finite systems, delocalization error can be attributed to the incorrect treatment of fractional electron charge whereby the total energy deviates from the correct behavior of linear interpolation between integer points. For bulk systems the delocalized nature of the orbitals results in a linear total energy at fractional charges, but the slope is incorrect due to delocalization error. Multiple methods have been proposed to fix this deficiency and produce the correct linearity condition such asthe Fermi-Löwdin orbital self-interaction correction, Koopmans-compliant functionals, the screened range-separated hybrid functional, the generalized transition state method, and the localized orbital scaling correction. All of these methods rely on spatially localized orbitals for their corrections, highlighting the importance of localized orbitals in modern density functional theory. The traditional method of obtaining localized orbitals minimizes the spatial variance, but here we explore an alternative approach that minimizes the combination of spatial and energetic variance. Minimizing the energetic variance allows for the occupied and unoccupied spaces to be considered together, a feature that is not prescribed in other localization schemes. The localization in energy results in localized orbitals that are more correlated with certain energy ranges, thereby making them more chemically relevant for the states that are associated with frontier energies. We show how these localized functions can be used in the localized orbital scaling correction to remedy many of the density functional approximation shortcomings related to delocalization error.