most of the system’s properties of interest can be derived from first-order changes
of electron density q
1 r; t
ð Þ [107, 115, 116] (in some cases, however, it is also
necessary to take into account the corrections of higher orders). Despite the obvious
advantages of the discussed approximations (adiabatic and linear response function)
allowing the study of many processes related to excitations from the ground state of
the system, there are still a number of problems requiring solutions and phenomena
that are still impossible to study within TD-DFT formalism (e.g., electronic transitions with substantial contributions from double excitations or non-adiabatic
effects) [107]. Thus, there is ongoing work on the development of new, better and
better and more accurate exchange–correlation functionals, especially suitable for
excited states and enabling the description of more complex phenomena within the
TD-DFT formalism, which will allow in the near future for a correct description of
intermingled optical properties using more realistic models and thus significant
broadening of various complex spectroscopic processes possible to be described
and analyzed within TD-DFT approach.
1.3 The Problem of Computational Complexity
and the Resulting Necessary Simplifications
and Approximations
The above-mentioned, obviously very brief description of the most popular theoretical methods used to model material properties shows how much can be modeled
today, but at the same time indicates many limitations that prevent effective and
accurate study of many phenomena and processes, including those that are the
domain of spectroscopy. Nevertheless, the development of theoretical methods, the
emergence of new theoretical models of various phenomena, new approaches to
difficult theoretical issues as well as the continuous development of the existing
ones, together with the involvement of many research teams around the world in the
development of computational chemistry, physics, and materials science, allows
hoping that in the coming years it will be possible to conduct more and more
accurate computer simulations of a growing number of applicationally important
processes and physicochemical phenomena.
The second barrier, besides the need to develop theoretical methods, that inhibits
the effective and widespread use of computational methods in the analysis of the
properties and in materials characterization is the complexity of many physical
systems, which still prevents the ability to obtain the results which are correct
quantitatively, and in many cases even just qualitatively. These problems result
from the complexity on the two separate levels—the structural (non-stoichiometric
composition, point defects, admixtures, partial occupation of some crystal lattice
sites, local compositional disorder, etc.) and the microstructural, important in
polycrystalline solids (grain size distribution, structure and properties of grain
boundaries, segregation of admixtures and defects at grain and phase boundaries,
1 Computational Methods in Spectroscopy
31
of electron density q
1 r; t
ð Þ [107, 115, 116] (in some cases, however, it is also
necessary to take into account the corrections of higher orders). Despite the obvious
advantages of the discussed approximations (adiabatic and linear response function)
allowing the study of many processes related to excitations from the ground state of
the system, there are still a number of problems requiring solutions and phenomena
that are still impossible to study within TD-DFT formalism (e.g., electronic transitions with substantial contributions from double excitations or non-adiabatic
effects) [107]. Thus, there is ongoing work on the development of new, better and
better and more accurate exchange–correlation functionals, especially suitable for
excited states and enabling the description of more complex phenomena within the
TD-DFT formalism, which will allow in the near future for a correct description of
intermingled optical properties using more realistic models and thus significant
broadening of various complex spectroscopic processes possible to be described
and analyzed within TD-DFT approach.
1.3 The Problem of Computational Complexity
and the Resulting Necessary Simplifications
and Approximations
The above-mentioned, obviously very brief description of the most popular theoretical methods used to model material properties shows how much can be modeled
today, but at the same time indicates many limitations that prevent effective and
accurate study of many phenomena and processes, including those that are the
domain of spectroscopy. Nevertheless, the development of theoretical methods, the
emergence of new theoretical models of various phenomena, new approaches to
difficult theoretical issues as well as the continuous development of the existing
ones, together with the involvement of many research teams around the world in the
development of computational chemistry, physics, and materials science, allows
hoping that in the coming years it will be possible to conduct more and more
accurate computer simulations of a growing number of applicationally important
processes and physicochemical phenomena.
The second barrier, besides the need to develop theoretical methods, that inhibits
the effective and widespread use of computational methods in the analysis of the
properties and in materials characterization is the complexity of many physical
systems, which still prevents the ability to obtain the results which are correct
quantitatively, and in many cases even just qualitatively. These problems result
from the complexity on the two separate levels—the structural (non-stoichiometric
composition, point defects, admixtures, partial occupation of some crystal lattice
sites, local compositional disorder, etc.) and the microstructural, important in
polycrystalline solids (grain size distribution, structure and properties of grain
boundaries, segregation of admixtures and defects at grain and phase boundaries,
1 Computational Methods in Spectroscopy
31