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Understanding the “incomprehensible” world of materials is the biggest challenge to the materials science community. To access the properties of the materials and to utilize them for positive changes in the world are of great interest. Often scientists use approximate theories to get legitimate answers to the problems. Density functional theory (DFT) has emerged as one of the successful and powerful predictive methods in this regard. The accuracy of DFT relies on the approximate form of the exchange-correlation (EXC) functional. The most complicated form of this functional can be as accurate as more complicated and computationally robust method like Quantum Monte Carlo (QMC), Random Phase Approximation (RPA). Two newest meta-GGAs, SCAN and SCAN+rVV10 are among those functionals. Instantaneous charge fluctuation between any two objects gives rise to the van der Waals (vdW) interactions (often termed as dispersion interactions). It is a purely correlation effect of the interacting electrons and thus non-local in nature. Despite its small magnitude it plays a very important role in many systems such as weakly bound rare-gas dimers, molecular crystals, and molecule-surface interaction. The traditional semi-local functionals can not describe the non-local of vdW interactions; only short- and intermediate-range of the vdW are accounted for in these functionals. In this thesis we investigate the effect of the weak vdW interactions in surface properties, rare-gas dimers and how it can be captured seamlessly within the semi-local density functional approximation. We have used summed-up vdW series within the spherical-shell approximation to develop a new vdW correction to the meta-GGA-MS2 functional. This method has been utilized to calculate binding energy and equilibrium binding distance of different homo- and hetero- dimers and we found that this method systematically improves the MGGA-MS2 results with a very good agreement with the experimental data. The binding energy curves are plotted using this MGGA-MS2, MGGA-MS2-vdW and two other popular vdW-corrected functionals PBE-D2, vdW-DF2. From these plots it is clear that our summed-up vdW series captures the long-range part of the binding energy curve via C6, C8, and, C10 coefficients. The clean metallic surface properties such as surface energy, work functions are important and often play a crucial role in many catalytic reactions. The weak dispersion interactions present between the surfaces has significant effect on these properties. We used LDA, PBE, PBSEsol, SCAN and SCAN+rVV10 to compute the clean metallic surface properties. The SCAN+rVV10 seamlessly captures different ranges of the vdW interactions at the surface and predicts very accurate values of surface energy (σ), and work function (Φ) and interlayer relaxations (δ%). Our conclusion is adding non-local vdW correction to a good semilocal density functional such as SCAN is necessary in order to predict the weak attractive vdW forces at the metallic surface. The SCAN+rVV10 has also been employed to study the hydrogen evolution reaction (HER) on 1T-MoS2. We have chosen as a descriptor differential Gibbs free energy (ΔGH to understand the underlying mechanism of this catalytic reaction. Density functional theory calculations agree with the experimental findings. In the case of layered materials like 1TMoS2, vdW interactions play an important role in hydrogen binding, that SCAN+rVV10 calculation was able to describe precisely. We have also used SCAN and SCAN+rVV10 functionals to understand bonding of CO on (111) metal surfaces, where many approximations to DFT fail to predict correct adsorption site and adsorption energy. In this case SCAN and SCAN+rVV10 do not show systematic improvements compared to LDA or PBE, rather, both SCAN and SCAN+rVV10 overbind CO more compared to PBE but less compared to the LDA. This overbinding of CO is associated with the incorrect charge transfer from metal to molecule and presumably comes from the density-driven self-interaction error of the functionals. In this thesis we assessed different semi-local functionals to inivestigate molecule surface systems of π-conjugated molecules (thiophene, pyridine) adsorbed on Cu(111), Cu(110), Cu(100) surfaces. We find the binding mechanism of these molecules on the metallic surface is mediated by short and intermediate range vdW interactions. Calculated values of binding energies and adsorbed geometries imply that this kind of adsorption falls in the weak chemisorption regime. Structural phase transitions due to applied pressure are very important in materials science. However, pressure induced structural phase transition in early lanthanide elements such as Ce are considered as abnormal first order phase transition. The Ce α-to-γ isostructural phase transition is one of them. The volume collapse and change of magnetic properties associated with this transition are mediated by the localized f -electron. Semi-local density functionals like LDA, GGA delocalize this f -electron due to the inherent self-interaction error (SIE) of these functionals. We have tested the SCAN functional for this particular problem, and, it was found that the spin-orbit coupling calculations with SCAN not only predicts the correct magnetic ordering of the two phases, but also gives a correct minima for the high-pressure α-Ce phase and a shoulder for the low-pressure γ-Ce phase. / Physics

Water is of essential importance for life on earth, yet the physics concerning its various anomalous properties has not been fully illuminated. This thesis is dedicated to the understanding of liquid water from aspects of microscopic structures, dynamics, electronic structures, X-ray absorption spectra, and proton transfer mechanism. This thesis use the computational simulation techniques including density functional theory (DFT), ab initio molecular dynamics (AIMD), and theoretical models for X-ray absorption spectra (XAS) to investigate the dynamics and electronic structures of liquid water system. The topics investigated in this thesis include a comprehensive evaluation on the simulation of liquid water using the newly developed SCAN meta-GGA functional, a systematic modeling of the liquid-water XAS using advanced ab initio approaches, and an explanation for a long-puzzling question that why hydronium diffuses faster than hydroxide in liquid water. Overall, significant contributions have been made to the understanding of liquid water and ionic solutions in the microscopic level through the aid of ab initio computational modeling. / Physics