An Extended CCSD Model Including Triple Excitations for Core-Ionization Energies

A model for calculation of core-ionization energies is developed within the equations-of-motion coupled cluster framework with application of the CVS approximation. The model deviates from EOM-CCSD by inclusion of triple projection manifold and triple excitation operators, as well as triple excitation amplitudes. However, the triple projection manifold is restricted to only include states involving a specific core excitation, namely an excitation to a super-diffuse orbital. As the super-diffuse orbital does not interact with the molecule orbitals, the model produces core-ionization energies. The truncation level of the cluster operator remains as in EOM-CCSD, but a trivial zero triple cluster operator is added. There are still some minor errors present in the pilot code, but it is expected that the model produces results at an accuracy level close to EOM-CCSDT. The computational cost, however, is reduced to n7 compared to EOM-CCSDT, which scales as n8, and could be further reduced to n6, n denoting the number of basis functions. Since the proposed model is the theoretical equivalent to the experimental procedure XPS, it is named XPS-CCSD. Theoretical spectra may be constructed by core-ionization energies obtained by the XPS-CCSD model, where these are helpful in the interpretation of their experimental counterpart. Sammendrag. En modell for beregning av kjerneioniseringsenergier er utledet ved hjelp av equations-of-motion coupled cluster teori hvor CVS approksimasjonen er benyttet. Forskjellen mellom denne modellen og eksisterende metoder som EOM-CCSDT og EOM-CCSD er størrelsen p̊a projeksjonsmanifoldet og trunkeringsniv̊aet av cluster-operatoren. Modellen inkluderer de samme elektroninteraksjonene som CCSD, men tar ogs̊a høyde for trippeleksitasjoner som resulterer i kjerneionisering. En superdiffus orbital er inkuldert i basissettet, slik at kjerneeksitasjon til denne orbitalen resulterer i kjerneionisering. Pilotkoden innholder fremdeles noen små feil, men det er forventet at modellen vil gi resultater som er sammenliknbare med EOM-CCSDT n̊ar det kommer til nøyaktighet. Beregningskostnaden er imdilertid redusert til n7 sammenlignet med EOM-CCSDT som skalerer som n8, og kan ytterligere reduseres til n6, hvor n betegner antall basisfunksjoner. Modellen kan brukes til å konstruere teoretiske spekter, hvor et eksperimentelt spekter fra XPS-metoden kan tolkes ved hjelp av det teoretiske spekteret. Derfor har modellen f̊att navnet XPSCCSD. Preface. This thesis concludes the master program Chemical Engineering and Biotechnology with specialization in Applied Theoretical Chemistry at NTNU. It was supervised by Professor Henrik Koch and co-supervised by Sarai D. Folkestad, and written during the spring of 2018. The work was conducted in Trondheim at NTNU, while March was spent at Scuola Normale Superiore di Pisa. I would like to thank Professor Henrik Koch for his help and advice during this process, as well as the invitation to Pisa. I would also like to thank Sarai D. Folkestad for equation-proofreading, debugging help and all the knowledge she has shared with me over the past months. I am truly grateful for all the hours she has invested in me, without her guidance the work presented would not have come this far.