often used, introducing an additional Hubbard U parameter [82] (LDA + U,
GGA + U potentials). In the electronic structure calculations, carried out mainly by
physicists, the PBE potential (or its PBESol variant, optimized for semiconducting
materials) is probably the most widely used, whereas in typical calculations carried
out by chemists, high popularity gained the previously described hybrid functionals,
e.g., B3LYP, in which the parameters are usually fitted for the collection of
experimental data, so one can get very accurate results for similar systems.
Unfortunately, these approximate XC functionals cannot be systematically
improved (KS equations with approximate XC potential do not fulfill the variation
principle); hence, it is not possible to unequivocally estimate errors associated with
the use of a given XC potential, and each time the results of calculations must be
compared with the results obtained by other theoretical methods or experimental
data.
1.2.2 Practical Aspects of the Application of Computational
Methods in Spectroscopy
Computational spectroscopy is a rapidly growing field that provides comprehensive
tools for the simulation, analysis, and interpretation of spectra in the context of
related physical and chemical processes and phenomena. Applied theoretical
approaches can be divided into two groups: time-independent calculations for
stationary states in minimum of the potential energy (e.g., vibrational spectra,
phonon dispersion curves) and time-dependent calculations for electron transitions
and excited states and their electronic properties (electron, NMR, and Mössbauer
spectra). Vibrational spectra of molecules, clusters as well as amorphous and
periodic systems are routinely modeled today and interpreted on the basis of a
harmonic approximation for potential energy near the minimum, normally available
in many programs using very different theory levels, starting from classical
approach with classic interparticle potentials, through hybrid QM/MM approaches,
quantum HF, post-HF, or DFT, up to molecular dynamics [83–87]. Spectroscopic
studies of conformational spaces or reaction pathways in molecular systems are also
broadly supported by routine ab initio and DFT calculations of the potential energy
hypersurface for the ground state, allowing a better understanding of intra- and
intermolecular interactions [88, 89].
1.2.2.1 Harmonic Approximation—Vibrational Spectroscopy
Atoms in molecules, clusters, and solids oscillate with respect to the equilibrium
positions, for which the potential energy of the system is the smallest. Any such
atomic displacement from the equilibrium position is associated with an increase in
potential energy, and the magnitude of these displacements depends on the
22
A. Koleżyński
GGA + U potentials). In the electronic structure calculations, carried out mainly by
physicists, the PBE potential (or its PBESol variant, optimized for semiconducting
materials) is probably the most widely used, whereas in typical calculations carried
out by chemists, high popularity gained the previously described hybrid functionals,
e.g., B3LYP, in which the parameters are usually fitted for the collection of
experimental data, so one can get very accurate results for similar systems.
Unfortunately, these approximate XC functionals cannot be systematically
improved (KS equations with approximate XC potential do not fulfill the variation
principle); hence, it is not possible to unequivocally estimate errors associated with
the use of a given XC potential, and each time the results of calculations must be
compared with the results obtained by other theoretical methods or experimental
data.
1.2.2 Practical Aspects of the Application of Computational
Methods in Spectroscopy
Computational spectroscopy is a rapidly growing field that provides comprehensive
tools for the simulation, analysis, and interpretation of spectra in the context of
related physical and chemical processes and phenomena. Applied theoretical
approaches can be divided into two groups: time-independent calculations for
stationary states in minimum of the potential energy (e.g., vibrational spectra,
phonon dispersion curves) and time-dependent calculations for electron transitions
and excited states and their electronic properties (electron, NMR, and Mössbauer
spectra). Vibrational spectra of molecules, clusters as well as amorphous and
periodic systems are routinely modeled today and interpreted on the basis of a
harmonic approximation for potential energy near the minimum, normally available
in many programs using very different theory levels, starting from classical
approach with classic interparticle potentials, through hybrid QM/MM approaches,
quantum HF, post-HF, or DFT, up to molecular dynamics [83–87]. Spectroscopic
studies of conformational spaces or reaction pathways in molecular systems are also
broadly supported by routine ab initio and DFT calculations of the potential energy
hypersurface for the ground state, allowing a better understanding of intra- and
intermolecular interactions [88, 89].
1.2.2.1 Harmonic Approximation—Vibrational Spectroscopy
Atoms in molecules, clusters, and solids oscillate with respect to the equilibrium
positions, for which the potential energy of the system is the smallest. Any such
atomic displacement from the equilibrium position is associated with an increase in
potential energy, and the magnitude of these displacements depends on the
22
A. Koleżyński