Restricted Open-Shell Kohn-Sham Theory ROKS

Restricted Open-Shell Kohn-Sham Theory (ROKS) 

ROKS is based on the sum method by Ziegler, Rauk, and Baerends [45], and allows for MD simulations in the first excited singlet state (Sj) [24]. The theoretical framework has been generalized to arbitrary spin states [25], and a new algorithm for solving the self-consistent field equations has been introduced recently [46]. 

The transition of one electron from the HOMO to the LUMO in a closed-shell system leads to four different excited wave functions (Fig. 7.2a). While two states f) and fj) correspond to energetically degenerate triplets, the mixed states mf) and mj) are not eigenfunctions of the total-spin operator. They can be combined to form another triplet state t3) and the singlet state s) (Fig. 7.2b). The total energy of the Sj state is then given by 

These equations can be solved through minimization, using an algorithm for orbital-dependent functionals [46,47]. 

ROKS has been applied to the study of CTI in gas phase [24,48-52]. It has also been combined with a CPMD-QM/MM approach, and thus permits the simulation of the photoisomerization of the RPSB in rhodopsin (Section 7.5), taking into account the protein environment. The computational cost of a ROKS MD simulation is roughly twice as high as a ground-state simulation. It represents therefore the most efficient approach for excited-state MD simulations. 

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Fig. 7.2 Restricted open shell Kohn-Sham theory (ROKS). (a) Four determinants resulting from HOMO-LUMO transition of one electron (b) the mixed states m ) and m2) can be combined to form a triplet state t3) and the singlet state s). The singlet-triplet splitting Ast corresponds to twice the splitting between triplets and mixed states.

ROKS Restricted open-shell Kohn-Sham theory... 

In the present chapter, we will focus on the simulation of the dynamics of photoexcited nucleobases, in particular on the investigation of radiationless decay dynamics and the determination of associated characteristic time constants. We use a nonadiabatic extension of ab initio molecular dynamics (AIMD) [15, 18, 21, 22] which is formulated entirely within the framework of density functional theory. This approach couples the restricted open-shell Kohn-Sham (ROKS) [26-28] first singlet excited state, Su to the Kohn-Sham ground state, S0, by means of the surface hopping method [15, 18, 94-97], The current implementation employs a plane-wave basis set in combination with periodic boundary conditions and is therefore ideally suited to condensed phase applications. Hence, in addition to gas phase reference simulations, we will also present nonadiabatic AIMD (na-AIMD) simulations of nucleobases and base pairs in aqueous solution. 

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