Excited-state theory

There are other noteworthy single excited-state theories. Gorling developed a stationary principle for excited states in density functional theory [41]. A formalism based on the integral and differential virial theorems of quantum mechanics was proposed by Sahni and coworkers for excited state densities [42], The local scaling approach of Ludena and Kryachko has also been generalized to excited states [43]. 

Abstract Excited-state theories in the single-reference, linear-response framework and their deriva-... 

This chapter, therefore, encompasses two extremes of excited-state theories within the single-reference, linear-response framework One that aims at high and controlled accuracy for relatively small gas-phase molecules such as EOM-CC and the other with low to medium accuracy for large molecules and solids represented by CIS and TDDFT. We aim at clarifying the mutual relationship among these excited-state methods including the two extremes, while delegating a more complete exposition of EOM-CC to the next chapter contributed by Watts. 

Both CIS and TDHF have the correct size dependence and can be applied to large molecules and solids (we will shortly substantiate what is meant by the correct size dependence ) [42-51], It is this property and their relatively low computer cost that render these methods unique significance in the subject area of this book despite their obvious weaknesses as quantitative excited-state theories. They can usually provide an adequate zeroth-order description of excitons in solids [50], Adapting the TDHF or CIS equations (or any methods with correct size dependence, for that matter) to infinitely extended, periodic insulators is rather straightforward. First, we recognize that a canonical HF orbital of a periodic system is characterized by a quantum number k (wave vector), which is proportional to the electron s linear momentum kh. In a one-dimensional extended system, the orbital is... 

A finite-temperature DFT is, in effect, an excited-state theory. As the temperature increases, more and more excited states are mixed in with the ground state. The excited states of greatest chemical importance are the electronic ones, including the ionized states M+ and M. Excited vibrational states will also play a role since the equilibrium electron density function, which determines all the properties, depends on the mix of electron density functions for all the excited states, as well as the ground state. 

Fifth Stage Potential Functionals and Excited State Theories (1985-1995)... 

Science during this period was led by nanomaterials design, inspired by the discovery of Ceo fullerene in 1985 and by photochemistry inspired by the development of femtosecond time-resolved spectroscopy in 1987. This scientific tide may have had an important impact on quantum chemistry during the latter half of this period DFT, enabling fast calculations, rapidly grew in use, and many excited state theories were developed for photochemical reaction calculations. 

We mention that there are other noteworthy single excited-state theories the stationary-principle theory of Gorling [33], the formalism of Sahni [34] or the local scaling approach of Ludena and Kryachko [35]. Beyond the time-independent theories mentioned above the time-dependent density functional theory [36] provides... 

K. B. Bravaya, D. Zuev, E. Epifanovsky, and A. I. Krylov,/. Chem. Phys., 138,124106 1-15 (2013). Complex-Scaled Equation-of-Motion Coupled-Cluster Method with Single and Double Substitutions for Autoionizing Excited States Theory, Implementation, and Examples. 

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