O presente trabalho descreve a investigação de funcionais de densidade para os cálculos das constantes escalares de acoplamento indireto spin-spin para diferentes tipos de átomos. 26 DFTs são inicialmente avaliados para um conjunto de calibração contendo constantes de acoplamento indireto spin-spin das moléculas HF, CO, H2O, NH3, PH3, PF3, BHF2, BF3, F2O, CH4, C2H2, C2H4 e C2H6. As estratégias utilizadas envolvem principalmente o ajuste da porcentagem de troca orbital Hartree-Fock (EXHF), a fim de melhorar a precisão. Estudos anteriores sugeriram que a utilização de uma certa porcentagem de troca exata contribui para obter resultados mais precisos para as constantes de acoplamento. Do total, BHandH, B1B95, a família B97 e a família ωB97 forneceram bons resultados para o conjunto de calibração. Em geral, DFTs híbridos contendo entre 30% e 50% de EXHF em sua composição apresentam valores mais precisos para as constantes de acoplamento. Os funcionais modificados B1B95 40% EXHF, BHandH 40% EXHF e B972B95 60% EXHF apresentam ótima precisão para rotinas de otimização de geometria e cálculo da constante de acoplamento. Para funcionais corrigidos no longo alcance, a porcentagem EXHF não é bem definida, mas pode ser ajustada em termos de três parâmetros. Uma versão de ωB97XD com γ incrementado para 0,35 tem ótima precisão, assim como umaversão de ωB97X com α incrementado para 0,2. Versões corrigidas no longo alcance de B1B95 e BHandH fornecem excelentes precisões com α =0,4, α + β =1,0 e γ ajustado ao funcional. Os funcionais de longo alcance e o B972B95 60% EXHF desafiam os níveis de teoria SOPPA(CCSD) e SOPPA(CC2), que apresentam boa precisão independente do tipo de núcleo envolvido no acoplamento. O termo do contato de Fermi está principalmente associado às diferenças nos resultados para as constantes de acoplamento calculadas entre os métodos. Segundo o teorema de Janak, os funcionais de longo alcance estão mais próximos do comportamento exato de um funcional; o aumento da troca exata em DFTs híbridos leva a um aumento da localização eletrônica, levando a concavidades menores. A utilização de um conjunto teste com mais tipos de acoplamento reforça a ótima precisão obtida com B1B95 40% EXHF, BHandH 40% EXHF e suas versões de longo alcance. / This work seeks to describe the investigation of density functionals for calculating indirect spin-spin scalar coupling constants for different types of atoms. 26 DFTs are initially evaluated for a calibration set containing HF, CO, H2O, NH3, PH3, PF3, BHF2, BF3, F2O, CH4, C2H2, C2H4 and C2H6 indirect spin-spin coupling constants. The strategies used mainly involve adjusting the percentage of Hartree-Fock orbital exchange (EXHF) in order to increase accuracy. Previous studies have suggested that the use of a certain percentage of exact exchange contributes to obtain more accurate results for coupling constants. Overall, BHandH, B1B95, B97 family and ωB97 family have provided good results for the calibration set. In general, hybrid DFTs containing between 30% and 50% EXHF in their composition show more accurate values for the coupling constants. The modified functionals B1B95 40% EXHF, BHandH 40% EXHF and B972B95 60% EXHF have optimal accuracy for geometry optimization and coupling constant calculation routines. For long-range corrected functionals, EXHF percentage is not well defined but can be adjusted in terms of three parameters. A version of ωB97XD with γ increased to 0.35 has great accuracy, as well as a version of ωB97X with α increased to 0.2. Long-range corrected versions of B1B95 and BHandH provided excellent accuracies with α =0.4, α + β =1.0 and γ adjusted to the functional. Long-range functionals and B972B95 60% EXHF challenge SOPPA(CCSD) and SOPPA(CC2) levels of theory, which have good accuracy regardless of the core type involved in the coupling. Fermi-contact term is mainly associated with the differences from results of calculated coupling constants between methods. According to Janaks theorem, long-range functionals are closest to the exact behavior of a functional; increasing exact exchange in hybrid DFTs leads to an increased electronic localization, leading to lower concavities. Using a test set with more coupling types reinforces the optimum accuracy obtained with B1B95 40% EXHF, BHandH 40% EXHF and their long-range versions.

Abstract In this thesis, the theory of static magnetic resonance spectral parameters of nuclear magnetic resonance (NMR) and electron spin resonance (ESR) spectroscopy is investigated in terms of the molecular Breit-Pauli Hamiltonian, which is obtained from the relativistic Dirac equation via the Foldy-Wouthuysen transformation. A leading-order perturbational relativistic theory of NMR nuclear shielding and spin-spin coupling tensors, and ESR electronic g-tensor, is presented. In addition, the possibility of external magnetic-field dependency of NMR parameters is discussed. Various first-principles methods of electronic structure theory and the role of one-electron basis sets and their performance in magnetic resonance properties in terms of their completeness profiles are discussed. The presented leading-order perturbational relativistic theories of NMR nuclear shielding tensors and ESR electronic g-tensors, as well as the theory of the magnetic-field dependent NMR shielding and quadrupole coupling are evaluated using first-principles wave function and density-functional theories.