Trygve (2015) The importance of current contributions to shielding constants in density-functional theory. Physical Chemistry Chemical Physics, 17 (28 A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.uk J o u r n a l Na me The sources of error in the calculation of nuclear-magnetic-resonance shielding constants determined by density-functional theory are examined. Highly accurate Kohn-Sham wave functions are obtained from coupled-cluster electron density functions and used to define accurate-but current independent-density-functional shielding constants. These new reference values, in tandem with high-accuracy coupled-cluster shielding constants, provide a benchmark for the assessment of errors in common density-functional approximations. In particular the role of errors arising in the diamagnetic and paramagnetic terms is investigated, with particular emphasis on the role of current-dependence in the latter. For carbon and nitrogen the current correction is found to be, in some cases, larger than 10 ppm. This indicates that the absence of this correction in general purpose exchange-correlation functionals is one of the main sources of errors in shielding calculations using density functional theory. It is shown that the current correction improves the shielding performance of many popular approximate DFT functionals.

We study the e↵ects of magnetic fields in the context of magnetic field densityfunctional theory (BDFT), where the energy is a functional of the electron density ⇢ and the magnetic field B. We show that this approach is a worthwhile alternative to current-density functional theory (CDFT) and may provide a viable route to the study of many magnetic phenomena using density-functional theory (DFT). The relationship between BDFT and CDFT is developed and clarified within the framework of the fourway correspondence of saddle functions and their convex and concave parents in convex analysis. By decomposing the energy into its Kohn-Sham components, we demonstrate that the magnetizability is mainly determined by those energy components that are related to the density. For existing density functional approximations, this implies that, for the magnetizability, improvements of the density will be more beneficial than introducing a magnetic-field dependence in the correlation functional. However, once a 1 good charge density is achieved, we show that high accuracy is likely only obtainable by including magnetic-field dependence. We demonstrate that adiabatic-connection (AC) curves at di↵erent field strengths resemble one another closely provided each curve is calculated at the equilibrium geometry of that field strength. In contrast, if all AC curves are calculated at the equilibrium geometry of the field-free system, then the curves change strongly with increasing field strength due to the increasing importance of static correlation. This holds also for density functional approximations, for which we demonstrate that the main error encountered in the presence of a field is already present at zero field strength, indicating that density-functional approximations may be applied to systems in strong fields, without the need to treat additional static correlation.

I joined the Oslo group of theoretical chemistry in my last semester as a bachelor student. Then, I got my master's degree with Trygve Helgaker and Erik Tellgren as my supervisors, and now, finally, my Ph.D. As such, I've been a part of this excellent community for nine years. I've seen the Centre of Theoretical and Computational Chemistry end, and I've seen the Hylleraas Centre of Quantum Molecular Sciences rise. Naming all the generous, kind and interesting people I've interacted with over the years is impossible, but I'll mention a few.My supervisors, Trygve and Erik, have guided me through this project and have granted me more encouragement and patience than I could possibly deserve. Alex Borgoo also acted as unofficial supervisor for a time, and helped me get back on track when things looked bleak. To Glenn B.S. Miller, who started studying chemistry at the same semester as I, and who defended his Ph.D years before me: Thank you for a lasting friendship -and for your linguistic feedback! To Patrick, Volodja, Kai, Chamdan, John, Jostein, Sigbjørn, Julie, Llouis, and all the other temporary inmates of our little office: I will never forget the general atmosphere you created, how helpful you all were, and how enjoyable it has been to be your colleague. So long, and thanks for all the fish! Also a great thank you to Henrik Austad and Vidar Løkken for your indispensable advice on programming, operating systems, backup routines and all the CPU time you have generously granted me on your personal servers. I assure you, there are few privately owned servers out there that have done more number crunching on quantum mechanical systems in magnetic fields.However, there is one person in particular who deserves more credit and praise than anyone else: My wife, Marianne. Being a struggling scientist is hard on the environment in general and on the family in particular. When I was disorganized, she helped me retrieve the loose ends. When I despaired, she encouraged. When I sacrificed all my duties at home and with the family to concentrate on my work, she covered for me. Without her, this would project would be nothing but a dead dream. That is a debt I can never repay. From the bottom of my heart: Thank you! i ii List of Articles I. Kohn-Sham energy decomposition for molecules in a magnetic field, published in Molecular Physics [1].II. Bonding in strong magnetic fields: role of spin and angular momentum, submitted for publication.III. Effects of strong magnetic fields on water from rigorous quantum calculations, to be submitted for publication.iii iv

We present and compare several many-body methods as applied to two-dimensional quantum dots with circular symmetry. We calculate the approximate ground state energy using a harmonic oscillator basis optimized by Hartree-Fock (HF) theory and further improve the ground state energy using two post-HF methods: in-medium similarity renormalization group (IM-SRG) and coupled cluster with singles and doubles (CCSD). With the application of quasidegenerate perturbation theory (QDPT) or the equations-of-motion (EOM) method to the results of the previous two methods, we obtain addition and removal energies as well. Our results are benchmarked against full configuration interaction (FCI) and diffusion Monte Carlo (DMC) where available. We examine the rate of convergence and perform extrapolations to the infinite basis limit using a power-law model.

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