Density functional theory , open-shell

The determination of the electronic structure of lanthanide-doped materials and the prediction of the optical properties are not trivial tasks. The standard ligand field models lack predictive power and undergoes parametric uncertainty at low symmetry, while customary computation methods, such as DFT, cannot be used in a routine manner for ligand field on lanthanide accounts. The ligand field density functional theory (LFDFT) algorithm23-30 consists of a customized conduct of nonempirical DFT calculations, extracting reliable parameters that can be used in further numeric experiments, relevant for the prediction in luminescent materials science.31 These series of parameters, which have to be determined in order to analyze the problem of two-open-shell 4f and 5d electrons in lanthanide materials, are as follows. 

What is obviously needed is a generally accepted recipe for how atomic states should be dealt with in approximate density functional theory and, indeed, a few empirical rules have been established in the past. Most importantly, due to the many ways atomic energies can be obtained, one should always explicitly specify how the calculations were performed to ensure reproducibility. From a technical point of view (after considerable discussions in the past among physicists) there is now a general consensus that open-shell atomic calculations should employ spin polarized densities, i. e. densities where not necessarily... 

Grafenstein, J., Kraka, E., Cremer, D., 1998, Density Functional Theory for Open-Shell Singlet Biradicals , Chem. Phys. Lett., 288, 593. 

The identification of unknown chemical compounds isolated in inert gas matrices is nowadays facilitated by comparison of the measured IR spectra with those computed at reliable levels of ab initio or density functional theory (DFT). Furthermore, the observed reactivity of matrix isolated species can in some instances be explained with the help of computed reaction energies and barriers for intramolecular rearrangements. Hence, electronic structure methods developed into a useful tool for the matrix isolation community. In this chapter, we will give an overview of the various theoretical methods and their limitations when employed in carbene chemistry. For a more detailed qualitative description of the merits and drawbacks of commonly used electronic structure methods, especially for open-shell systems, the reader is referred to the introductory guide of Bally and Borden.29... 

For quantum chemistry, first-row transition metal complexes are perhaps the most difficult systems to treat. First, complex open-shell states and spin couplings are much more difficult to deal with than closed-shell main group compounds. Second, the Hartree—Fock method, which underlies all accurate treatments in wavefunction-based theories, is a very poor starting point and is plagued by multiple instabilities that all represent different chemical resonance structures. On the other hand, density functional theory (DFT) often provides reasonably good structures and energies at an affordable computational cost. Properties, in particular magnetic properties, derived from DFT are often of somewhat more limited accuracy but are still useful for the interpretation of experimental data. 

ROSS Restricted open-shell singlet density functional theory... 

Wang, F. and Ziegler T., Excitation energies of some dl systems calculated using time-dependent density functional theory an implementation of open-shell TDDFT theory for doublet-doublet excitations. Mol.Phys (2004) 102 2585 -2595. 

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. 

Density-functional theory and Kohn—Sham orbitals The energies of the two states for this open-shell configuration are... 

M. Odelius, D. Laikov, and J. Butter (2003) Excited state geometries within time-dependent and restricted open-shell density functional theories. J. Mol. 

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