Restricted open-shell Kohn-Sham ROKS

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. 

Restricted ensemble Kohn-Sham DFT Alternatively one can perform standard KS-DFT calculations on a collection of determinants with different occupations and take a weighted average of the individual energies to obtain an estimate of the mul-tideterminantal situation. To avoid the independent calculation of several KS determinants, a generalization of this approach was proposed by Filatov and Shaik based on the coupling operator technique developed by Roothaan for restricted open-shell Hartree-Fock. This restricted open-shell Kohn-Sham (ROKS) approach was later extended to situations where fractional occupation numbers are not imposed by the... 

The analysis starts with a restricted open-shell Kohn-Sham (ROKS) calculation on the HS state. If necessary, the magnetic orbitals are transformed to the representation with local orthogonal orbitals a and b, as shown in the first column of Fig. 5.11. Staying within the spin-restricted formalism makes that for each a orbital a orbital can be found which has the same spatial part. In the first step, the direct exchange is estimated from the energy difference of the HS(ROKS) and a BS determinant in which only the spin of one of the unpaired electrons is inverted, but neither the core nor the magnetic orbitals are optimized. 

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

Restricted Open-Shell Kohn-Sham Theory (ROKS)... 

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... 

Hyperfine couplings, in particular the isotropic part which measures the spin density at the nuclei, puts special demands on spin-restricted wave-functions. For example, complete active space (CAS) approaches are designed for a correlated treatment of the valence orbitals, while the core orbitals are doubly occupied. This leaves little flexibility in the wave function for calculating properties of this kind that depend on the spin polarization near the nucleus. This is equally true for self-consistent field methods, like restricted open-shell Hartree-Fock (ROHF) or Kohn-Sham (ROKS) methods. On the other hand, unrestricted methods introduce spin contamination in the reference (ground) state resulting in overestimation of the spin-polarization. 

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