<p>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 <italic>N&plusmn;2</italic> 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, <italic>ab initio</italic> 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.</p> / Dissertation

Abstract In this thesis, the classic Kurland-McGarvey theory for the nuclear magnetic resonance (NMR) chemical shift is presented in a modern framework for paramagnetic systems containing one or more unpaired electrons. First-principles computations are carried out for the NMR shielding tensors in paramagnetic transition-metal complexes. A combined ab initio/density-functional theory (DFT) approach is applied to obtain the necessary electron paramagnetic resonance (EPR) property tensors, i.e., the g-tensor, zero-field splitting tensor (D) and hyperfine coupling tensors (A). In DFT, both the generalised-gradient approximation and hybrid DFT are applied to calculate A. The complete active space self-consistent field theory (CASSCF) and N-electron valence-state perturbation theory (NEVPT2) are applied to calculate the g- and D-tensors. Scalar relativistic effects are included at the second-order Douglas-Kroll-Hess level for the g- and D-tensors and, for A, at the fully relativistic four-component matrix-Dirac-Kohn-Sham level. This methodology is applied to study ¹³C and ¹H chemical shifts and shielding anisotropies in a series of Co(II) pyrazolylborate complexes, a Cr(III) quinolyl-functionalised cyclopentadienyl complex, Ni(II) acetylacetonate complexes and various metallocenes. The results obtained from these calculations are generally in a good agreement with the experimental data, in some cases, for Ni(II) complexes, allowing to correct the experimental spectral signal assignment. CASSCF/NEVPT2 computations (especially for the D-tensor) are more accurate than DFT, which is useful for the purpose of obtaining the NMR chemical shifts. The computational results obtained are dependent on the choice of molecular geometry (experimental X-ray or computationally optimised), wavefunction used for g and D (CASSCF or NEVPT2), DFT functional for A, and the quality of the basis sets. The locally dense basis method used for the CASSCF/NEVPT2 computations is less expensive and gives equally good results for g and D as fully balanced basis sets. The scalar relativistic influences are usually small for g and D, but are large for A. Due to that, scalar relativistic effects are important for the chemical shift and shielding anisotropy, especially for carbon nuclei. These first-principles computations based on combined ab initio/DFT methodology are promising for the treatment of important electron correlation and scalar relativistic effects in the calculation of pNMR chemical shifts and shielding anisotropies. This work provides a straightforward platform for further development of pNMR shielding theory in terms of first-principles wavefunctions, as well as for applications in current problems in bio- and materials sciences, including low-temperature experiments. / Original papers The original papers are not included in the electronic version of the dissertation. Vaara, J., Rouf, S. A., &amp; Mareš, J. (2015). Magnetic Couplings in the Chemical Shift of Paramagnetic NMR. Journal of Chemical Theory and Computation, 11(10), 4840–4849. https://doi.org/10.1021/acs.jctc.5b00656 Rouf, S. A., Mareš, J., &amp; Vaara, J. (2015). ¹H Chemical Shifts in Paramagnetic Co(II) Pyrazolylborate Complexes: A First-Principles Study. Journal of Chemical Theory and Computation, 11(4), 1683–1691. https://doi.org/10.1021/acs.jctc.5b00193 Rouf, S. A., Jakobsen, V. B., Mareš, J., Jensen, N. D., McKenzie, C. J., Vaara, J., &amp; Nielsen, U. G. (2017). Assignment of solid-state ¹³C and ¹H NMR spectra of paramagnetic Ni(II) acetylacetonate complexes aided by first-principles computations. Solid State Nuclear Magnetic Resonance, 87, 29–37. https://doi.org/10.1016/j.ssnmr.2017.07.003 Rouf, S. A., Mareš, J., &amp; Vaara, J. (2017). Relativistic Approximations to Paramagnetic NMR Chemical Shift and Shielding Anisotropy in Transition Metal Systems. Journal of Chemical Theory and Computation, 13(8), 3731–3745. https://doi.org/10.1021/acs.jctc.7b00168 http://jultika.oulu.fi/Record/nbnfi-fe201801031039

Im Rahmen der vorliegenden Arbeit wird eine Tight-Binding-Formulierung der Korringa-Kohn-Rostoker-Greenschen-Funktionsmethode vorgestellt. Dabei werden mittels eines geeignet gewählten Referenzsystems abgeschirmte Strukturkonstanten konstruiert. Es werden die Vorteile und Grenzen dieser Transformation des Formalismus diskutiert. Es wird gezeigt, daß der numerische Aufwand zur erechnung der Elektronenstruktur von Systemen mit langgestreckter Elementarzelle linear mit der Systemgröße wächst. Damit ist eine Behandlung von Systemen mit 500 und mehr Atomen pro Elementarzelle möglich. Anhand von umfangreichen Testrechnungen kann demonstriert werden, daß das neue Verfahren bezüglich seiner Genauigkeit mit dem traditionellen KKR-Verfahren vergleichbar ist. Es werden Anwendungen zur Berechnung der Elektronenstruktur sowie zur Zwischenlagenaustauschkopplung von Co/Cu(100)-Vielfachschichten vorgestellt. / A newly developed ab initio tight-binding-formulation of the Korringa-Kohn-Rostoker-Green's function method for layered systems is presented. Screened structure constants are calculated by means of a repulsive reference system. Advantages and limits of this transformation of the formalism are discussed in detail. The numerical effort for self consistent electronic structure calculations of systems with a large prolonged supercell scales linearly with the system size. Systems with up to 500 atoms per unit cell can be treated easily. The accuracy of the new method is of the same order as the traditional KKR method. Applications to electronic structure calculations and magnetic interlayer exchange coupling in Co/Cu(100) multilayers are presented.

Weak intermolecular interactions have very strong impact on the structures and properties of life giving molecules like H2O, DNA, RNA etc. These interactions are responsible for many biological phenomena. The directional preference of some of these interactions is used for designing different synthetic approaches in the supramolecular chemistry. The work reported in this Thesis comprises of investigations of weak intermolecular interactions in gas phase using home-built Pulsed Nozzle Fourier Transform Microwave (PN-FTMW) spectrometer as an experimental tool and ab-initio and Atoms in Molecules (AIM) theory as theoretical tools. The spectrometer which is coupled with a pulsed nozzle is used to record pure rotational spectra of the molecular clusters in a jet cooled molecular beam. In the molecular beam molecules/complexes are free from interactions with other molecules/complexes and thus, spectroscopy in the molecular beams provides information about the 'isolated' molecule/complex under investigation. The rotational spectra of the molecules/complexes in the molecular beam provide their geometry in the ground vibrational states. These experimental geometries can be used to test the performance and accuracy of theoretical models like ab-initio theory, when applied to the weakly bound complexes. Further the AIM theory can be used to gain insights into the nature and strength of the intermolecular interactions present in the system under investigation. Chapter I of this Thesis gives a brief introduction of intermolecular interactions. Other than hydrogen bonding, which is considered as the most important intermolecular interaction, many other intermolecular interactions involving different atoms have been observed in past few decades. The chapter summarizes all these interactions. The chapter also gives a brief introduction to the experimental and theoretical methods used to probe these interactions. In Chapter II, the experimental and theoretical methods used in this work are summarized. Details of our home-built PN-FTMW spectrometer are given in this chapter. The chapter also discusses briefly the theoretical methods like ab-initio, AIM and Natural bond orbital (NBO) analysis. We have made few changes in the mode of control of one of our delay generators which have also been described. Chapter III and Chapter V of this Thesis are dedicated to the propargyl alcohol complexes. Propargyl alcohol (PA) is a molecule of astrophysical interest. It is also important in combustion chemistry since propargyl radical is considered as the precursor in soot formation. Moreover, PA is a multifunctional molecule, having a hydroxyl (-OH) and an acetylenic (-C≡C-H) group. Both of the groups can individually act as hydrogen bond acceptor as well as donor and thus PA provides an exciting possibility of studying many different types of weak interactions. Due to internal motion of -OH group, PA monomer can exist in gauche as well as trans form. However, rotational spectra of PA-monomer show the presence of only gauche conformer. In Chapter III, rotational spectra of Ar•••PA complex are discussed. The pure rotational spectra of the parent Ar•••PA complex and its two deuterated isotopologues, Ar•••PA-D (OD species) and Ar•••PA-D (CD species), could be observed and fitted within experimental uncertainty. The structural fitting confirmed a structure in which PA is present as gauche conformer and argon interacts with both the O-H group and the acetylenic group leading to Ar•••H-O and Ar•••π interactions respectively. Presence of these interactions was further confirmed by AIM theoretical analysis. In all the three isotopologues c-type rotational transitions showed significant splitting. Splitting patterns in the three isotopologues suggest that it originates mainly due to the large amplitude motion of the hydroxyl group and the motion is weakly coupled with the carbon chain bending motion. No evidence for the complex with trans conformer of PA was found. Although, we could not observe Ar•••trans-PA complex experimentally, we decided to perform ab-initio and AIM theoretical calculations on this complex as well. AIM calculations suggested the presence of Ar•••H-O and a unique Ar•••C interaction in this complex which was later found to be present in the Ar•••methanol complex as well. This prompted us to explore different possible interactions in methanol, other than the well known O-H•••O hydrogen bonding interactions, and eventually led us to an interesting interaction which we termed as carbon bond. Chapter IV discusses carbon bonding interaction in different complexes. Electrostatic potential (ESP) calculations show that tetrahedral face of methane is electron-rich and thus can act as hydrogen/halogen bond acceptor. This has already been observed in many complexes, e.g. CH4•••H2O/HF/HCl/ClF etc., both experimentally and theoretically. However, substitution of one of the hydrogens of methane with -OH leads to complete reversal of the properties of the CH3 tetrahedral face and this face in methanol is electron-deficient. We found that CH3 face in methanol interacts with electron rich sites of HnY molecules and leads to the formation of complexes stabilized by Y•••C-X interactions. This interaction was also found to be present in the complexes of many different CH3X (X=OH/F/Cl/Br/NO2/NF2 etc.) molecules. AIM, NBO and C-X frequency shift analyses suggest that this interaction could be termed as "carbon bond". The carbon bonding interactions could be important in understanding hydrophobic interactions and thus could play an important role in biological phenomena like protein folding. The carbon bonding interaction could also play a significant role in the stabilization of the transition state in SN2 reactions. In Chapter V of this Thesis rotational spectra of propargyl alcohol dimer are discussed. Rotational spectra of the parent dimer and its three deuterated (O-D) isotopologues (two mono-substituted and one bi-substituted) could be recorded and fitted within experimental uncertainty. The fitted rotational constants are close to one of the ab-initio predicted structure. In the dimer also propargyl alcohol exists in the gauche form. Atoms in molecules analysis suggests that the experimentally observed dimer is bound by O-H•••O, O-H•••π and C-H•••π interactions. Chapter VI of the thesis explores the 'electrophore concept'. To observe the rotational spectra of any species and determine its rotational constant by microwave spectroscopy, the species should have a permanent dipole moment. Can we obtain rotational constants of a species having no dipole moment via microwave spectroscopy? Electrophore concept can be used for this purpose. An electrophore is an atom or molecule which could combine with another molecule having no dipole moment thereby forming a complex with a dipole moment, e.g. Argon atom is an electrophore in Ar•••C6H6 complex. The microwave spectra of Ar•••13CC5H6 and Ar•••C6H5D complexes were recorded and fitted. The A rotational constant of these complexes was found to be equal to the C rotational constant of 13CC5H6 and C6H5D molecules respectively and thus we could determine the C rotational constant of microwave 'inactive' 13CC5H6. This concept could be used to obtain the rotational spectra of parallel displaced benzene-dimer if it exists. We recently showed that the square pyramidal Fe(CO)5 can act as hydrogen bond acceptor. Appendix I summarizes the extension of this work and discusses interactions of trigonal bipyramidal Fe(CO)5 with HF, HCl, HBr and ClF. Our initial attempts on generating a chirped pulse to be used in a new broadband spectrometer are summarized in Appendix II. Preliminary investigations on the propargyl•••water complex are summarized in Appendix III.

Im Rahmen der vorliegenden Arbeit wird eine Tight-Binding-Formulierung der Korringa-Kohn-Rostoker-Greenschen-Funktionsmethode vorgestellt. Dabei werden mittels eines geeignet gewählten Referenzsystems abgeschirmte Strukturkonstanten konstruiert. Es werden die Vorteile und Grenzen dieser Transformation des Formalismus diskutiert. Es wird gezeigt, daß der numerische Aufwand zur erechnung der Elektronenstruktur von Systemen mit langgestreckter Elementarzelle linear mit der Systemgröße wächst. Damit ist eine Behandlung von Systemen mit 500 und mehr Atomen pro Elementarzelle möglich. Anhand von umfangreichen Testrechnungen kann demonstriert werden, daß das neue Verfahren bezüglich seiner Genauigkeit mit dem traditionellen KKR-Verfahren vergleichbar ist. Es werden Anwendungen zur Berechnung der Elektronenstruktur sowie zur Zwischenlagenaustauschkopplung von Co/Cu(100)-Vielfachschichten vorgestellt. / A newly developed ab initio tight-binding-formulation of the Korringa-Kohn-Rostoker-Green's function method for layered systems is presented. Screened structure constants are calculated by means of a repulsive reference system. Advantages and limits of this transformation of the formalism are discussed in detail. The numerical effort for self consistent electronic structure calculations of systems with a large prolonged supercell scales linearly with the system size. Systems with up to 500 atoms per unit cell can be treated easily. The accuracy of the new method is of the same order as the traditional KKR method. Applications to electronic structure calculations and magnetic interlayer exchange coupling in Co/Cu(100) multilayers are presented.