Chapter 1
Computational Methods in Spectroscopy
Andrzej Koleżyński
Abstract Spectroscopy investigates the interaction of electromagnetic radiation
with matter. Along with the development of theoretical methods, increasingly
effective numerical algorithms and computational methods as well as computer
technologies and resulting growing computer power available for scientists, the
so-called in silico experiments—computer simulations of materials and their properties in computer—have become an irreplaceable tool supporting experimental
research, often allowing a better understanding of phenomena taking place during
these interactions, and associated material properties. As a result, it becomes possible in growing number of cases to effectively design new materials with desired
properties and to modify existing ones, to improve their properties. This chapter is
devoted to a brief introduction to issues related to theoretical foundations of quantum
mechanics and density functional theory, both in stationary and time-dependent
form. The key assumptions of these theories are presented, together with the
description of various approximations and simplifications necessary for their practical application to the calculation of properties examined by spectroscopic methods.
The most important practical problems encountered during calculations, resulting
from the complexity of real materials and typical ways of dealing with these problems by means of various simplifications, idealizations, and abstractions in designed
structural models corresponding to real materials, are also presented.
1.1 Introduction
A broadly understood spectroscopy is devoted to the studies of the interactions of
electromagnetic radiation with matter. There are many different spectroscopic
techniques, but all of these techniques are based on the assumption that—when
certain conditions are fulfilled—each material emits or absorbs energy, usually in
A. Koleżyński (&)
Faculty of Materials Science and Ceramics, AGH University of Science
and Technology, 30 Mickiewicza Av., 30-059 Krakow, Poland
e-mail: andrzej.kolezynski@agh.edu.pl
© Springer Nature Switzerland AG 2019
A. Koleżyński and M. Król (eds.), Molecular Spectroscopy—Experiment
and Theory, Challenges and Advances in Computational Chemistry
and Physics 26, https://doi.org/10.1007/978-3-030-01355-4_1
1
Computational Methods in Spectroscopy
Andrzej Koleżyński
Abstract Spectroscopy investigates the interaction of electromagnetic radiation
with matter. Along with the development of theoretical methods, increasingly
effective numerical algorithms and computational methods as well as computer
technologies and resulting growing computer power available for scientists, the
so-called in silico experiments—computer simulations of materials and their properties in computer—have become an irreplaceable tool supporting experimental
research, often allowing a better understanding of phenomena taking place during
these interactions, and associated material properties. As a result, it becomes possible in growing number of cases to effectively design new materials with desired
properties and to modify existing ones, to improve their properties. This chapter is
devoted to a brief introduction to issues related to theoretical foundations of quantum
mechanics and density functional theory, both in stationary and time-dependent
form. The key assumptions of these theories are presented, together with the
description of various approximations and simplifications necessary for their practical application to the calculation of properties examined by spectroscopic methods.
The most important practical problems encountered during calculations, resulting
from the complexity of real materials and typical ways of dealing with these problems by means of various simplifications, idealizations, and abstractions in designed
structural models corresponding to real materials, are also presented.
1.1 Introduction
A broadly understood spectroscopy is devoted to the studies of the interactions of
electromagnetic radiation with matter. There are many different spectroscopic
techniques, but all of these techniques are based on the assumption that—when
certain conditions are fulfilled—each material emits or absorbs energy, usually in
A. Koleżyński (&)
Faculty of Materials Science and Ceramics, AGH University of Science
and Technology, 30 Mickiewicza Av., 30-059 Krakow, Poland
e-mail: andrzej.kolezynski@agh.edu.pl
© Springer Nature Switzerland AG 2019
A. Koleżyński and M. Król (eds.), Molecular Spectroscopy—Experiment
and Theory, Challenges and Advances in Computational Chemistry
and Physics 26, https://doi.org/10.1007/978-3-030-01355-4_1
1