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Context & Aims .

Difficulties in describing the excited states of open-shell molecules using the very popular time-dependent density-functional theory (TD-DFT) method [HC12] were raised as early as 2005 [C05]. In particular, there was no automatic assignment of spin-states at that time. We therefore proposed a formula [CIC06] for calculating the spin of a TD-DFT excited state and this formula is, for example, currently used in the popular quantum chemistry program Gaussian [MC17]. Yet much remains to be done in applying TD-DFT, and in developing better tools for applying TD-DFT, to the study of open-shell excited states in biochemistry, for molecular machines involving electron transfer, and in nanoelectronics. The objective of this thesis will be to reformulate, implement, and apply TD-DFT in order to eliminate any spin-contamination of spin, thereby adding new rigor to a large class of important calculations. A solution has been proposed in the literature by Li and Liu and co-workers [LL10,LL11] which seems promising. We propose to improve it by including the double excitations [HIRC11,CH15], to program it, and to validate the method by comparisons with CASSCF multiconfiguration calculations. In parallel and in relation with the progress of the developments, we will study the dimerization of viologen. Viologene has the particularity of easily being reduced to a doublet which caCM Typewritern then dimerize forming either a triplet state or a singlet state. This particularity is at the origin of many molecular machines. Another application concerns the biochemical processes involved in oxidations, specifically we will study Cu(II)-Cu(III) complexes. The results obtained thanks to the developments in the TD-DFT framework, will allow a better interpretation and understanding of the mechanisms involved which is a pre-requisite to a design of new bio-inspired catalysts, as well as molecular machines and certain types of nanoelectronics applications. 

Bibliography

[MC17] Hemanadhan Myneni and Mark E. Casida, Comput. Phys. Comm. 213, 72 (2017). [CH15] Mark E. Casida and Miquel Huix-Rotllant, Topics in Current Chemistry, special volume on Density-Functional Methods for Excited States, edited by Nicolas Ferré, Michael Filatov, and Miquel Huix-Rotllant (Springer, 2015), p. 1. [CH12] M.E. Casida and Miquel Huix-Rotllant, Annu. Rev. Phys. Chem. 63, 287 (2012). [HIRC11] M. Huix-Rotllant, A. Ipatov, A. Rubio, and M.E. Casida, Chem. Phys. 391, 120 (2011). [LL11] Z. Li and W. Liu, J. Chem. Phys. 135, 194106 (2011); Z. Li and W. Liu, J. Chem. Phys. 138, 029904 (2013). [LL10] Z. Li and W. Liu, J. Chem. Phys. 133, 064106 (2010). [CIC06] M.E. Casida, A. Ipatov, and F. Cordova, in Time-Dependent Density-Functional Theory, edited by M.A.L. Marques, C. Ullrich, F. Nogueira, A. Rubio, and E.K.U. Gross, Lecture Notes in Physics (Springer: Berlin, 2006), pp. 243. [C05] M.E. Casida, J. Chem. Phys. 122, 054111 (2005).