usually a fairly limited choice of methods of calculating IR intensity and Raman
activity, their detailed description will not be presented here.
Harmonic approximation is very useful and in many cases allows obtaining
accurate data on vibrations in the system. In many cases, however, in systems in
which anharmonic interactions have a significant effect on properties and thus
cannot be neglected, this approximation is insufficient, and there is a need to
consider the higher-order terms of Taylor series expansion. In this case, the
vibrational spectrum calculations are significantly more complex and computationally demanding, hence limited to relatively small systems—in the case of
medium and large systems, such calculations are still in practice impossible and we
have to use harmonic approximation or classical methods based on interatomic
potentials.
1.2.2.2 Time-Dependent DFT
Calculations of the energy for excited states of the systems and their electronic
properties have also become an irreplaceable auxiliary tool in the interpretation of
electronic spectra and dynamics of excited systems. While the calculations with the
so-called chemical accuracy for systems in the ground state have become in last
years relatively simple, the accurate estimation of energy of excited states is still
quite a challenge, both from theoretical and computational complexity point of view
(excited states are often close to each other, hence very high precision of calculations is necessary, associated with a high level of theory, often also with additional
geometry optimization for excited states, which is associated with extremely
time-consuming calculations, impossible to do in the case of large systems).
Currently, there are a number of different quantum mechanical methods for calculating different properties of excited states. A detailed discussion of such methods
goes far beyond the scope of this chapter and is available in many studies [e.g.,
101–105]. Generally, these methods can be divided into two groups: The first is the
previously mentioned classical, post-HF-based “configuration” methods (single
configuration CI, multi-configuration MCSCF, CASSCF, CASPT2, or
multi-reference MRCI, in which any electron state is defined in the form of a linear
combination of a number of Slater determinants corresponding to various electronic
configurations) or derived from the coupled cluster (CC) family. However, these
methods are very computationally demanding, and hence, they cannot be used for
larger molecules or more complex solids.
The second group consists of methods based on electron density. In classical
DFT, the effects of exchange and correlation are taken into account approximately
by means of XC functionals, usually obtained by fitting functional parameters to
experimental data or by imposing physical constraints on the shape of XC potential
well, based on the properties of the theoretical model system.
The extension of classical DFT approach for excited systems is the TD-DFT
method [105–109], which proved to be an extremely effective and useful tool, with
precision comparable to the most sophisticated post-HF methods, but with
26
A. Koleżyński
activity, their detailed description will not be presented here.
Harmonic approximation is very useful and in many cases allows obtaining
accurate data on vibrations in the system. In many cases, however, in systems in
which anharmonic interactions have a significant effect on properties and thus
cannot be neglected, this approximation is insufficient, and there is a need to
consider the higher-order terms of Taylor series expansion. In this case, the
vibrational spectrum calculations are significantly more complex and computationally demanding, hence limited to relatively small systems—in the case of
medium and large systems, such calculations are still in practice impossible and we
have to use harmonic approximation or classical methods based on interatomic
potentials.
1.2.2.2 Time-Dependent DFT
Calculations of the energy for excited states of the systems and their electronic
properties have also become an irreplaceable auxiliary tool in the interpretation of
electronic spectra and dynamics of excited systems. While the calculations with the
so-called chemical accuracy for systems in the ground state have become in last
years relatively simple, the accurate estimation of energy of excited states is still
quite a challenge, both from theoretical and computational complexity point of view
(excited states are often close to each other, hence very high precision of calculations is necessary, associated with a high level of theory, often also with additional
geometry optimization for excited states, which is associated with extremely
time-consuming calculations, impossible to do in the case of large systems).
Currently, there are a number of different quantum mechanical methods for calculating different properties of excited states. A detailed discussion of such methods
goes far beyond the scope of this chapter and is available in many studies [e.g.,
101–105]. Generally, these methods can be divided into two groups: The first is the
previously mentioned classical, post-HF-based “configuration” methods (single
configuration CI, multi-configuration MCSCF, CASSCF, CASPT2, or
multi-reference MRCI, in which any electron state is defined in the form of a linear
combination of a number of Slater determinants corresponding to various electronic
configurations) or derived from the coupled cluster (CC) family. However, these
methods are very computationally demanding, and hence, they cannot be used for
larger molecules or more complex solids.
The second group consists of methods based on electron density. In classical
DFT, the effects of exchange and correlation are taken into account approximately
by means of XC functionals, usually obtained by fitting functional parameters to
experimental data or by imposing physical constraints on the shape of XC potential
well, based on the properties of the theoretical model system.
The extension of classical DFT approach for excited systems is the TD-DFT
method [105–109], which proved to be an extremely effective and useful tool, with
precision comparable to the most sophisticated post-HF methods, but with
26
A. Koleżyński