Advanced density functional theory methods for materials science

In this work we chiefly deal with two broad classes of problems in computational materials science, determining the doping mechanism in a semiconductor and developing an extreme condition equation of state. While solving certain aspects of these questions is well-trodden ground, both require extending the reach of existing methods to fully answer them. Here we choose to build upon the framework of density functional theory (DFT) which provides an efficient means to investigate a system from a quantum mechanics description.

Zinc Phosphide (Zn₃P₂) could be the basis for cheap and highly efficient solar cells. Its use in this regard is limited by the difficulty in n-type doping the material. In an effort to understand the mechanism behind this, the energetics and electronic structure of intrinsic point defects in zinc phosphide are studied using generalized Kohn-Sham theory and utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. Novel 'perturbation extrapolation' is utilized to extend the use of the computationally expensive HSE functional to this large-scale defect system. According to calculations, the formation energy of charged phosphorus interstitial defects are very low in n-type Zn₃P₂ and act as 'electron sinks', nullifying the desired doping and lowering the fermi-level back towards the p-type regime. Going forward, this insight provides clues to fabricating useful zinc phosphide based devices. In addition, the methodology developed for this work can be applied to further doping studies in other systems.

Accurate determination of high pressure and temperature equations of state is fundamental in a variety of fields. However, it is often very difficult to cover a wide range of temperatures and pressures in an laboratory setting. Here we develop methods to determine a multi-phase equation of state for Ta through computation. The typical means of investigating thermodynamic properties is via ’classical’ molecular dynamics where the atomic motion is calculated from Newtonian mechanics with the electronic effects abstracted away into an interatomic potential function. For our purposes, a ’first principles’ approach such as DFT is useful as a classical potential is typically valid for only a portion of the phase diagram (i.e. whatever part it has been fit to). Furthermore, for extremes of temperature and pressure quantum effects become critical to accurately capture an equation of state and are very hard to capture in even complex model potentials. This requires extending the inherently zero temperature DFT to predict the finite temperature response of the system. Statistical modelling and thermodynamic integration is used to extend our results over all phases, as well as phase-coexistence regions which are at the limits of typical DFT validity. We deliver the most comprehensive and accurate equation of state that has been done for Ta. This work also lends insights that can be applied to further equation of state work in many other materials.

Adsorption of carbon dioxide and nitrogen on single-layer aluminum nitride nanostructures studied by density functional theory

The adsorption of carbon dioxide and nitrogen molecules on aluminum nitride (AlN) nanostructures has been explored using first-principle computational methods. Optimized configurations corresponding to physisorption and, subsequentially, chemisorption of CO2 are identified, in contrast to N2, for which only a physisorption structure is found. Transition-state searches imply a low energy barrier between the physisorption and chemisorption states for CO2 such that the latter is accessible and thermodynamically favored at room temperature. The effective binding energy of the optimized chemisorption structure is apparently larger than those for other CO2 adsorptive materials, suggesting the potential for application of aluminum nitride nanostructures for carbon dioxide capture and storage.

Lattice density-functional theory on graphene

A density-functional approach on the hexagonal graphene lattice is developed using an exact numerical solution to the Hubbard model as the reference system. Both nearest-neighbour and up to third nearest-neighbour hoppings are considered and exchange-correlation potentials within the local density approximation are parameterized for both variants. The method is used to calculate the ground-state energy and density of graphene flakes and infinite graphene sheet. The results are found to agree with exact diagonalization for small systems, also if local impurities are present. In addition, correct ground-state spin is found in the case of large triangular and bowtie flakes out of the scope of exact diagonalization methods.

Energy Hyperspace for Stacking Interaction in AU/AU Dinucleotide Step: Dispersion-Corrected Density Functional Theory Study

Double helical structures of DNA and RNA are mostly determined by base pair stacking interactions, which give them the base sequence-directed features, such as small roll values for the purine-pyrimidine steps. Earlier attempts to characterize stacking interactions were mostly restricted to calculations on fiber diffraction geometries or optimized structure using ab initio calculations lacking variation in geometry to comment on rather unusual large roll values observed in AU/AU base pair step in crystal structures of RNA double helices. We have generated stacking energy hyperspace by modeling geometries with variations along the important degrees of freedom, roll, and slide, which were chosen via statistical analysis as maximally sequence dependent. Corresponding energy contours were constructed by several quantum chemical methods including dispersion corrections. This analysis established the most suitable methods for stacked base pair systems despite the limitation imparted by number of atom in a base pair step to employ very high level of theory. All the methods predict negative roll value and near-zero slide to be most favorable for the purine-pyrimidine steps, in agreement with Calladine's steric clash based rule. Successive base pairs in RNA are always linked by sugar-phosphate backbone with C3-endo sugars and this demands C1-C1 distance of about 5.4 angstrom along the chains. Consideration of an energy penalty term for deviation of C1-C1 distance from the mean value, to the recent DFT-D functionals, specifically B97X-D appears to predict reliable energy contour for AU/AU step. Such distance-based penalty improves energy contours for the other purine-pyrimidine sequences also. (c) 2013 Wiley Periodicals, Inc. Biopolymers 101: 107-120, 2014.

Density functional theory embedding for correlated wavefunctions

Methods that exploit the intrinsic locality of molecular interactions show significant promise in making tractable the electronic structure calculation of large-scale systems. In particular, embedded density functional theory (e-DFT) offers a formally exact approach to electronic structure calculations in which the interactions between subsystems are evaluated in terms of their electronic density. In the following dissertation, methodological advances of embedded density functional theory are described, numerically tested, and applied to real chemical systems.

First, we describe an e-DFT protocol in which the non-additive kinetic energy component of the embedding potential is treated exactly. Then, we present a general implementation of the exact calculation of the non-additive kinetic potential (NAKP) and apply it to molecular systems. We demonstrate that the implementation using the exact NAKP is in excellent agreement with reference Kohn-Sham calculations, whereas the approximate functionals lead to qualitative failures in the calculated energies and equilibrium structures.

Next, we introduce density-embedding techniques to enable the accurate and stable calculation of correlated wavefunction (CW) in complex environments. Embedding potentials calculated using e-DFT introduce the effect of the environment on a subsystem for CW calculations (WFT-in-DFT). We demonstrate that WFT-in-DFT calculations are in good agreement with CW calculations performed on the full complex.

We significantly improve the numerics of the algorithm by enforcing orthogonality between subsystems by introduction of a projection operator. Utilizing the projection-based embedding scheme, we rigorously analyze the sources of error in quantum embedding calculations in which an active subsystem is treated using CWs, and the remainder using density functional theory. We show that the embedding potential felt by the electrons in the active subsystem makes only a small contribution to the error of the method, whereas the error in the nonadditive exchange-correlation energy dominates. We develop an algorithm which corrects this term and demonstrate the accuracy of this corrected embedding scheme.

A variational framework for spectral discretization of the density matrix in Kohn Sham density functional theory

Kohn-Sham density functional theory (KSDFT) is currently the main work-horse of quantum mechanical calculations in physics, chemistry, and materials science. From a mechanical engineering perspective, we are interested in studying the role of defects in the mechanical properties in materials. In real materials, defects are typically found at very small concentrations e.g., vacancies occur at parts per million, dislocation density in metals ranges from $10^{10} m^{-2}$ to $10^{15} m^{-2}$, and grain sizes vary from nanometers to micrometers in polycrystalline materials, etc. In order to model materials at realistic defect concentrations using DFT, we would need to work with system sizes beyond millions of atoms. Due to the cubic-scaling computational cost with respect to the number of atoms in conventional DFT implementations, such system sizes are unreachable. Since the early 1990s, there has been a huge interest in developing DFT implementations that have linear-scaling computational cost. A promising approach to achieving linear-scaling cost is to approximate the density matrix in KSDFT. The focus of this thesis is to provide a firm mathematical framework to study the convergence of these approximations. We reformulate the Kohn-Sham density functional theory as a nested variational problem in the density matrix, the electrostatic potential, and a field dual to the electron density. The corresponding functional is linear in the density matrix and thus amenable to spectral representation. Based on this reformulation, we introduce a new approximation scheme, called spectral binning, which does not require smoothing of the occupancy function and thus applies at arbitrarily low temperatures. We proof convergence of the approximate solutions with respect to spectral binning and with respect to an additional spatial discretization of the domain. For a standard one-dimensional benchmark problem, we present numerical experiments for which spectral binning exhibits excellent convergence characteristics and outperforms other linear-scaling methods.

Electronic structures of 4d transition metal monoxides by density functional theory

Bond distances, dissociation energies, ionization potentials and electron affinities of 4d transition metal monoxides from YO to CdO and their positive and negative ions were studied by use of density functional methods B3LYP, BLYP, B3PW91, BPW91, B3P86, BP86, SVWN, MPW1PW91 and PBE1PBE. It was found that calculated properties are highly dependent on the functionals employed, especially for dissociation energy. For most neutral species, pure density functionals BLYP, BPW91 and BP86 have good performance in predicting dissociation energy than hybrid density functionals B3LYP, B3PW91 and B3P86. In addition, BLYP gives the largest bond distance compared with other density functional methods, while SVWN gives shortest bond distance, largest dissociation energy and electron affinity. For the ground state, the spin multiplicity of the charged species can be obtained by +/- 1 of their corresponding neutral species.

Electronic structures of 5d transition metal monoxides by density functional theory

Bond distances, vibrational frequencies, electron affinities, ionization potentials, and dissociation energies of the diatomic 5d transition metal (except La) monoxides and their positively and negatively charged ions were studied by use of density functional methods B3LYP, BLYP, B3PW91, BPW91, B3P86, BP86, MPW1PW91, PBE1PBE, and SVWN. Our calculation shows that for each individual species, the calculated properties are quite sensitive to the method used. Compared with hybrid density functional method B3PW91 (B3P86), pure density functional method BPW91 (BP86) gives longer bond distance (lower vibrational frequency) from HfO to PtO for neutral species, HfO+ to IrO+ for cationic species, and HfO- to AuO- for anionic species. While for B3LYP and BLYP, the trend was observed for cationic species from HfO+ to IrO+ and anionic species from HfO- to AuO- (except TaO-), but not for neutrals. Pure density function methods BLYP, BPW91, and BP86 give larger dissociation energy compared with hybrid density functional methods B3LYP, B3PW91, and B3P86. SVWN in most cases gives the smallest bond distance, while BLYP gives the largest value. MPW1PW91 and PBE1PBE show the same performance in predicting the spectroscopic constants.

Electronic structures of MCO (M = Nb, Ta, Rh, Ir, Pd, Pt) molecules by density functional theory

Equilibrium geometries, vibrational frequencies, and dissociation energies of the transition metal carbonyls MCO (M = Nb, Ta, Rh, Ir, Pd, Pt) were studied by use of diverse density functional methods B3LYP, BLYP, B3P86, B3PW91, BHLYP, BP86, and PBE1PBE. It was found that the ground electronic state is (6)Sigma(+) for NbCO and TaCO, (2)Sigma(+) for RhCO,(2)Delta for IrCO, and (1)Sigma(+) for PdCO and PtCO, in agreement with previous theoretical studies. The calculated properties are highly dependent on the functionals employed, in particular for the dissociation energy. For most of the molecules, the predicted bond distance is in agreement with experiments and previous theoretical results. BHLYP is the worst method in reproducing the experimental results compared with the other density functional methods for the title molecules.

Electronic structures of hafnium dimer and trimer by density functional theory

Equilibrium geometries, vibrational frequencies and dissociation energies of hafnium dimer and trimer were studied by density functional methods B3LYP, BLYP, B3PW91, BHLYP, BP86, B3P86, mPW1PW91 and PBE1PBE. The results indicate that singlet is the ground state both for hafnium dimer and for trimer. For hafnium dimer, the calculated bond distance is less sensitive to the methods used. Except at BHLYP level, the calculated vibrational frequency is comparable to the experimental value. For hafnium trimer, equilateral triangle with D-3h symmetry is slightly favored compared with isosceles triangle with C-2v, symmetry except at BHLYP level. This conclusion is in agreement with experiment in which the ground state of Hf-3 is fluxional and low-spin or closed shell is preferred.

Electron affinities and ionization potentials of 4d and 5d transition metal atoms by CCSD(T), MP2 and density functional theory

The electron affinities and ionization potentials of 4d and 5d transition metal atoms were studied by CCSD(T), MP2 and density functional methods. The calculated results indicate that density functional method B3LYP has the best overall performance in predicting both electron affinity and ionization potential. SVWN gives largest IP and EA for 4d and 5d atoms. For the two basis sets used in this study, LANL2DZ and SDD, the performance of B3LYP/SDD combination is better than B3LYP/LANL2DZ, in particular for electron affinity calculation.

An Energy Descriptor To Quantify Methane Selectivity in Fischer-Tropsch Synthesis:A Density Functional Theory Study

Selectivity is a fundamental issue in heterogeneous catalysis. In this study, the CH(4) selectivity in Fischer-Tropsch synthesis is chosen to be investigated: CH4 selectivity on Rh, Co, Ru, Fe, and Re surfaces is computed by first-principles methods. In conjunction with kinetic analyses, we are able to derive the effective barrier difference between methane formation and chain growth (Delta E(eff)) to quantify the CH(4) selectivity. By using this energy descriptor, the ranking of methane selectivity predicted from density functional theory (DFT) calculations is consistent with experimental work. Moreover, a linear correlation between Delta E(eff) and the chemisorption energy of C + 4H (Delta H) is found. This fundamental finding possesses the following significance: (i) it shows that the selectivity, which appears to have kinetic characteristics, is largely determined by thermodynamic properties; and (ii) it suggests that an increase of the binding strength of C + 4H will suppress methane selectivity.

Freezing of 4He and its liquid-solid interface from density functional theory

We show that, at high densities, fully variational solutions of solidlike types can be obtained from a density functional formalism originally designed for liquid 4He . Motivated by this finding, we propose an extension of the method that accurately describes the solid phase and the freezing transition of liquid 4He at zero temperature. The density profile of the interface between liquid and the (0001) surface of the 4He crystal is also investigated, and its surface energy evaluated. The interfacial tension is found to be in semiquantitative agreement with experiments and with other microscopic calculations. This opens the possibility to use unbiased density functional (DF) methods to study highly nonhomogeneous systems, like 4He interacting with strongly attractive impurities and/or substrates, or the nucleation of the solid phase in the metastable liquid.

Electronic and magnetic structure of LaMnO3 from hybrid periodic density-functional theory

The electronic and magnetic structures of the LaMnO3 compound have been studied by means of periodic calculations within the framework of spin polarized hybrid density-functional theory. In order to quantify the role of approximations to electronic exchange and correlation three different hybrid functionals have been used which mix nonlocal Fock and local Dirac-Slater exchange. Periodic Hartree-Fock results are also reported for comparative purposes. The A-antiferromagnetic ground state is properly predicted by all methods including Hartree-Fock exchange. In general, the different hybrid methods provide a rather accurate description of the band gap and of the two magnetic coupling constants, strongly suggesting that the corresponding description of the electronic structure is also accurate. An important conclusion emerging from this study is that the nature of the occupied states near the Fermi level is intermediate between the Hartree-Fock and local density approximation descriptions with a comparable participation of both Mn and O states.

Exploring chromium (VI) dioxodihalides chemistry: is density functional theory the most suitable tool?

A comparative systematic study of the CrO2F2 compound has been performed using different conventional ab initio methodologies and density functional procedures. Two points have been analyzed: first, the accuracy of results yielded by each method under study, and second, the computational cost required to reach such results. Weighing up both aspects, density functional theory has been found to be more appropriate than the Hartree-Fock (HF) and the analyzed post-HF methods. Hence, the structural characterization and spectroscopic elucidation of the full CrO2X2 series (X=F,Cl,Br,I) has been done at this level of theory. Emphasis has been given to the unknown CrO2I2 species, and specially to the UV/visible spectra of all four compounds. Furthermore, a topological analysis in terms of charge density distributions has revealed why the valence shell electron pair repulsion model fails in predicting the molecular shape of such CrO2X2 complexes