Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms

In this paper we study the problem of uniqueness of solutions to the Hartree and Hartree-Fock equations of atoms. We show, for example, that the Hartree-Fock ground state of a closed shell atom is unique provided the atomic number $Z$ is sufficiently large compared to the number $N$ of electrons. More specifically, a two-electron atom with atomic number $Z\geq 35$ has a unique Hartree-Fock ground state given by two orbitals with opposite spins and identical spatial wave functions. This statement is wrong for some $Z>1$, which exhibits a phase segregation.Comment: 18 page

Existence of a minimizer for the quasi-relativistic Kohn-Sham model

We study the standard and extended Kohn-Sham models for quasi-relativistic N-electron Coulomb systems; that is, systems where the kinetic energy of the electrons is given by the quasi-relativistic operator $$sqrt{-alpha^{-2}Delta_{x_n}+alpha^{-4}}-alpha^{-2}.$$ For spin-unpolarized systems in the local density approximation, we prove existence of a ground state (or minimizer) provided that the total charge $Z_{m tot}$ of K nuclei is greater than N-1 and that $Z_{m tot}$ is smaller than a critical charge $Z_{m c}=2 alpha^{-1} pi^{-1}$

Abstract Criteria for Multiple Solutions to Nonlinear Coupled Equations Involving Magnetic Schrodinger Operators

We consider a system of nonlinear coupled equations involving magnetic Schrodinger operators and general potentials. We provide a criteria for the existence of multiple solutions to these equations. As special cases we get the classical results on existence of innitely many distinct solutions within Hartree and Hartree-Fock theory of atoms and molecules subject to an external magnetic fields. We also extend recent results within this theory, including Coulomb system with a constant magnetic field, a decreasing magnetic field and a physically measurable magnetic field

Advancing relativistic electronic structure methods for solids and in the time domain

Paper I and III are not available in Munin Paper I: Repisky, M., Konecny, L., Kadek, M., Komorovsky, S., Malkin, O.L., Malkin, V.G. & Ruud, K. (2015). Excitation Energies from Real-Time Propagation of the Four-Component Dirac–Kohn–Sham Equation. Available in Journal of Chemical Theory and Computation, 11(3), 980-991. Paper III: Konecny, L., Kadek, M., Komorovsky, S., Malkina, O.L., Ruud, K. & Repisky, M. (2016). Acceleration of Relativistic Electron Dynamics by Means of X2C Transformation: Application to the Calculation of Nonlinear Optical Properties. Available in Journal of Chemical Theory and Computation, 12(12), 5823-5833.Effects arising from the special theory of relativity significantly influence the electronic structure and properties of molecules and solid-state materials containing heavy elements. At the same time, the inclusion of the relativistic effects in theoretical and computational models increases their methodological complexity and the computational cost. In the solid state, additional challenges to the mathematical and algorithmic robustness of methods arise due to the infinite extent of the systems. In this thesis, I present two extensions of quantum-chemical relativistic methods based on Gaussian-type basis functions in the study of the electronic ground-state of molecules: band-structure calculations of materials in the solid state, and simulations of the response of molecules that are subjected to an external time-dependent field by propagating their perturbed state in real time. The development of the relativistic methods for solids was preceded by an independent implementation of the theory at the nonrelativistic level. In comparison to methods based on plane waves, the use of Gaussian-type basis functions in the solid-state community is limited. The relativistic method presented here is the first ever implementation of the Dirac-type equations using Gaussian-type basis functions for solid-state systems, and can be used to study one-, two-, and three-dimensional periodic systems on an equal footing for the entire periodic table. The time propagation method is a technically simpler alternative to perturbation approaches, and is applied here to probe relativistic effects on absorption and X-ray spectra, and nonlinear optical and chiroptical properties of molecules. Our work in the both areas provides a technology with the potential to predict properties of novel materials, and to support the interpretation of experiments

Theory for Molecular Tests of Fundamental Physics

Even today, fundamental difficulties remain in the understanding of our universe. Among those are inexplicable phenomena like the enormous excess of matter over anti-matter (baryon asymmetry) — connected to the question why is there matter at all — or dark matter (DM) and dark energy which are invoked to explain the structure and evolution of our universe, and problems like the unification of quantum theory with gravity. In order to take a step closer to resolving such issues, it is important to test the known laws of physics, summarized in the standard models of particle physics (SM) and cosmology (ΛCDM model), as accurately as possible. Direct experimental tests of the SM can be carried out with high energies at large colliders like the LHC at CERN, and direct tests of the ΛCDM model are usually performed at large observatories like LIGO. In contrast, the theoretical foundations of chemistry are mostly well understood. Hence, molecules are theoretically and experimentally well controllable. Thus, measurements in standard-sized laboratories with ultra-high precision are possible, so that the less well understood laws of physics can be tested. Such low-energy experiments provide indirect tests of the standard models in the realm of chemistry by probing the fundamental symmetries of nature. Therewith, these tests are complementary to direct tests of the laws of physics in cosmology or high-energy physics. In this cumulative thesis quantum chemical methods are developed and applied to design new experiments and improve existing experiments that employ molecules for tests of fundamental symmetries and, therewith, search for new physics beyond the standard models (BSM). A simultaneous violation of parity and time-reversal symmetry (P,T) is closely connected to baryon asymmetry. P,T-violation appears in a larger amount in unifying BSM theories than in the SM itself. P,T-violation on the elementary particle level is relativistically enhanced in heavy atoms and heavy-elemental molecules and results in permanent electric dipole moments (EDMs) of atoms and molecules which are non-vanishing in the limit of vanishing electric fields. In the first part of this thesis, P,T-violations in diatomic and small polyatomic molecules are studied in order to find well-suited candidates for a first measurement of a permanent EDM. Within this study relativistic effects as well as effects due to the chemical environment of the heavy atom are systematically analyzed. Furthermore, the effects of various fundamental sources of P,T-violation that contribute to the P,T-odd EDM of a molecule are studied. It is discussed, how these sources can be disentangled from experiments that aim to measure the permanent EDMs of different molecules. Among this research one of the first calculations of P,T-odd effects in polyatomic molecules is presented. In the second part of this thesis, the applicability of chiral molecules as sensitive probes for P-violating cosmic fields is demonstrated. P-violating cosmic fields are predicted in several cold DM (CDM) models as well as in the standard model extension (SME) that allows for local Lorentz invariance violation (LLIV). LLIV appears in several theories that aim to unify quantum theory and gravity. It is shown that well-chosen chiral molecules containing heavy elements can improve present limits on P-odd interactions of electrons with cosmic fields by at least two orders of magnitude. This renders chiral molecules particularly interesting for searches for BSM physics. In order to guide future searches for candidate molecules, challenges that may appear in the theoretical description or the design of experiments are discussed. In the last part of this thesis, the possibilities to use a clock transition in the iodine molecule to limit LLIV are explored in cooperation with the BOOST collaboration. Quantum chemical studies of such effects in iodine are presented. These calculations are essential for an estimate of the expected sensitivity of the BOOST satellite mission, which employs the iodine molecular clock as probe for LLIV

The removal of radionuclides from contaminated water samples using graphene oxide nano-flakes

One of the main challenges currently facing the nuclear industry is the management, removal and disposal of radioactive material from aqueous environments. Water contaminated with nuclear material has arisen in a number of ways. The majority of nuclear material in aqueous environments is from normal nuclear activities and is currently stored in ponds, silos and tanks. Many of the waste storage facilities in the UK are however nearing the end of their intended lifetime so will shortly need processing. The contamination of water with nuclear material is also not confined directly to activities in a nuclear site, activities such as uranium mining can significantly increase the concentration of radionuclides and other heavy metals in groundwater. There are solutions within the nuclear industry to remediate contaminated water, there is also an ongoing need for more efficient and low-cost solutions. Graphene oxide (GO) has been shown under laboratory conditions to be a highly effective sorbent material for the removal of cations from aqueous environments. The research presented in this thesis is a computational study to better understand the binding interactions between GO and cations to influence its development as a decommissioning solution in the nuclear industry. The research begins in Chapter 3 where a model of GO is developed in density functional theory (DFT) and an insensitivity to the lateral size of the nano-flake for functional group stability on the surface at high level of oxidation is revealed, which had not been reported previously. It was also found from calculations that the formation of epoxy groups is unlikely at low levels of surface oxidation and functional groups tend to aggregate on GO surfaces, which is consistent with experimental observations. The research then continues in Chapter 4 with an investigation into the binding interactions between GO and radionuclide cations. It is found, in agreement with experimental results that tetravalent cations mostly form inner-sphere complexes with GO and divalent cations mostly form outer-sphere complexes. A correlation between formal charge and binding energy is also revealed which is consistent with experimental results. Th(IV) is found to have a low affinity towards the neutral COOH group which exists on GO edges in low pH environments, which is identified as a potential route towards radionuclide selectivity using chemically modified GO. An investigation into the effect of defects in the GO lattice on sorption ability is presented in Chapter 5. It is found that defects have little to no effect on binding to the edge of the GO nano-flake and binding to the surface of defected GO is broadly similar to binding to the surface of defected-free GO. It is found however that the presence of a pore in the GO lattice can promote the hydrolysis of the Th(IV) aquocomplex which significantly increases the stability of the system. Binding to areas of the GO surface containing Stone-Wales defects is also enhanced by a greater density of functional groups. The thesis then concludes in Chapter 6 with a summary of results and a discussion of the potential applications of GO in nuclear decommissioning

Simulating Self-Assembly of Organosulfur Species on Gold Nanoparticles

This Thesis aims to establish an accurate but computationally effective method for simulating self-assembly of organosulfurs on gold nanoparticles (AuNPs), a process resulting in their functionalisation. A second gold rush is currently rekindling chemists’ interest in the synthesis of novel functionalised AuNPs: these can bear the most chemically diverse functional groups, making them employable in a wide variety of applications, from optoelectronics to catalysis. Some aspects of self-assembly remain experimentally unclear at the mechanistic and electronic levels: achieving its accurate reproduction in silico would indeed represent an important contribution in the synthesis of functionalised AuNPs. This task, however, has so far proven difficult to achieve. In this work, I set out and review four fundamental challenges facing the computational chemist aiming to simulate self-assembly, and describe the strategy chosen to overcome them, using thiols (RSH) as the reference organosulfur. These challenges involve proper reproduction of: I) gold’s relativistic effects and aurophilicity; II) the extensive surface reconstruction occurring upon self-assembly, with formation of RS–Au–SR staples and hydrogen loss; III) the large scale ligands involved in the process and their interactions; and IV) the fluctuating solvent environment in which it occurs. Confined to the AuNP core and RSH headgroups, challenges I and II involve complex electronic properties and entail electronic change, with bonds being cleaved (S–H) and reformed (S–Au, possibly H–H): overcoming them requires explicit simulation of electrons with a QM method (DFT). Challenges III and IV involve the entire RSH-AuNP system, including RSH tails of typically ∼10^2 atoms: QM methods become impracticable at these system sizes, and a less costly classical forcefield treatment (MM) is necessary in this case, at least in part. The work presented here then proceeds towards the stated aim by attempting to resolve each of these challenges I–IV. The eventually devised solution proposes a combination of classical molecular dynamics (MD), followed by the hybrid QM/MM method ONIOM, which allows to combine the ‘best of the QM and MM worlds’ and is well established for other systems. To overcome challenge I, various effective core potentials (ECPs); basis sets; and density functionals are evaluated based on their ability to predict properties and geometries of several pristine AuNPs. These properties and geometries are either derived experimentally, or from high-level ab initio calculations. The chosen QM method PBE/LANL2DZ is then further tested on various systems, assessing its ability (challenge II) to reproduce hydrogen loss and staple formation. Upon proposing to tackle challenge III using ONIOM (with the OPLS-AA forcefield for the MM part), the method’s performance is first compared to that of full QM (PBE/LANL2DZ) in terms of accuracy and efficiency, and in a variety of contexts, including on AuNPs featuring a 38-atom gold core. Once these calculations confirm the considerable time gains afforded by the introduction of ONIOM, I then demonstrate its full applicability in the optimisation of a large, experimentally plausible functionalised AuNP. Finally, I propose to tackle challenge IV by introducing a classical MD simulation stage to precede QM/MM optimisation. As a test, MD is used to generate statistically significant sets of 8-atom AuNPs coated with alkylthiols of different chain lengths, which are then optimised, thereby successfully reproducing the early stages of reconstruction. I then conclude by successfully testing this MD + ONIOM approach on two much larger functionalised AuNPs, having 20-atom gold cores and sixteen or seventeen 64-atom ligands. My Thesis highlights both the strengths and limitations of the ONIOM approach in simulating such a complex process as organosulfur self-assembly on AuNPs. Nonetheless, the chosen MD + ONIOM strategy can indeed reproduce key aspects of self-assembly with increased CPU-efficiency, and, importantly, makes electronically plausible predictions: it therefore represents a viable route for the in silico investigation of this process, and an encouraging fulfilment of my initial aim.Open Acces