5 Introduction to Quantum Vibrational Spectroscopy
93
The DFT concept is a rigorous re-interpretation of the quantum many-body
problem. It offers a significant improvement in the affordability of calculations.
Unfortunately, its practical implementation needs to include approximated electron
exchange and correlation. The formulation of DFT limits the ability to improve its
quality systematically. Instead, different functionals have been parametrized (i.e.,
calibrated) toward better accuracy when applied to certain systems. Inherent limitations of DFT, e.g., poor description of long-range (dispersive or non-covalent) interactions were recently mitigated by introduction of empirical corrections of dispersion,
e.g., the series of Grimme’s dispersion models (GD). Despite some shortcomings,
DFT offers highly favorable cost versus accuracy level that made it particularly
widely used in spectroscopic studies.
5.3.2.4 Semi-empirical Concept
Semi-empirical quantum chemistry methods are derived by insertion of predetermined parameters into quantum mechanical calculation schemes. The most
straightforward semi-empirical treatment replaces the relatively most timeconsuming calculation procedures in the HF ansatz, i.e., two-electron integrals
are omitted and their values are provided as empirical parameters to produce
the expected results. These parameters are most often obtained from higher-level
quantum mechanical calculations performed for small-scale models, and then used
universally. Semi-empirical methods are significantly more affordable than their
corresponding quantum mechanical frameworks, and thus suitable for the treatment
of large molecules. Conceptually, in some cases semi-empirical schemes are relatively more complete, as empirical parameters may better describe some phenomena
(e.g., electron correlation effects) than the ab initio approach with necessary approximations. Accordingly, as long as the considered system fits the conditions of
the parametrization, semi-empirical calculations may yield more accurate results
than when treated with a pure HF formalism. However, semi-empirical calculations are prone to produce erroneous results if they are applied outside of their
area of parametrization. Therefore, they need to be used with care. Semi-empirical
schemes based on a wavefunction ansatz include the Austin Model 1 (AM1), the
parametric model family of methods (e.g., PM3, PM5) that implement the neglect of
differential diatomic overlap (NDDO) principle (all two-electron integrals involving
two-center charge distributions are neglected) as well as a number of additional
approximations and corrections, depending on the particular method. A similar
concept may also be applied to density-based methods. For example, densityfunctional-based tight-binding (DFTB) inserts pre-calculated parameters into the
DFT calculation scheme, in which a minimal basis and only nearest-neighbor interactions are employed. The resulting deficiency in the description of long-range interactions is corrected with empirical dispersion (analogous to those developed for
DFT functionals). The resulting approach yields reasonably accurate results at a
fraction of the cost of DFT calculations. Although primarily popular decades ago,
when the technology barrier prevented wider use of higher-level quantum methods,
93
The DFT concept is a rigorous re-interpretation of the quantum many-body
problem. It offers a significant improvement in the affordability of calculations.
Unfortunately, its practical implementation needs to include approximated electron
exchange and correlation. The formulation of DFT limits the ability to improve its
quality systematically. Instead, different functionals have been parametrized (i.e.,
calibrated) toward better accuracy when applied to certain systems. Inherent limitations of DFT, e.g., poor description of long-range (dispersive or non-covalent) interactions were recently mitigated by introduction of empirical corrections of dispersion,
e.g., the series of Grimme’s dispersion models (GD). Despite some shortcomings,
DFT offers highly favorable cost versus accuracy level that made it particularly
widely used in spectroscopic studies.
5.3.2.4 Semi-empirical Concept
Semi-empirical quantum chemistry methods are derived by insertion of predetermined parameters into quantum mechanical calculation schemes. The most
straightforward semi-empirical treatment replaces the relatively most timeconsuming calculation procedures in the HF ansatz, i.e., two-electron integrals
are omitted and their values are provided as empirical parameters to produce
the expected results. These parameters are most often obtained from higher-level
quantum mechanical calculations performed for small-scale models, and then used
universally. Semi-empirical methods are significantly more affordable than their
corresponding quantum mechanical frameworks, and thus suitable for the treatment
of large molecules. Conceptually, in some cases semi-empirical schemes are relatively more complete, as empirical parameters may better describe some phenomena
(e.g., electron correlation effects) than the ab initio approach with necessary approximations. Accordingly, as long as the considered system fits the conditions of
the parametrization, semi-empirical calculations may yield more accurate results
than when treated with a pure HF formalism. However, semi-empirical calculations are prone to produce erroneous results if they are applied outside of their
area of parametrization. Therefore, they need to be used with care. Semi-empirical
schemes based on a wavefunction ansatz include the Austin Model 1 (AM1), the
parametric model family of methods (e.g., PM3, PM5) that implement the neglect of
differential diatomic overlap (NDDO) principle (all two-electron integrals involving
two-center charge distributions are neglected) as well as a number of additional
approximations and corrections, depending on the particular method. A similar
concept may also be applied to density-based methods. For example, densityfunctional-based tight-binding (DFTB) inserts pre-calculated parameters into the
DFT calculation scheme, in which a minimal basis and only nearest-neighbor interactions are employed. The resulting deficiency in the description of long-range interactions is corrected with empirical dispersion (analogous to those developed for
DFT functionals). The resulting approach yields reasonably accurate results at a
fraction of the cost of DFT calculations. Although primarily popular decades ago,
when the technology barrier prevented wider use of higher-level quantum methods,