106
K. B. Be´ c et al.
of intermode coupling contributions in addition to the adequate treatment of anharmonic effects. Especially when combined with sparse matrix algebra routines and
advanced interpolation techniques to reduce the associated computational effort, gridbased methods are capable of delivering a highly accurate description of complex
quantum mechanical systems.
5.6 Applications of Anharmonic Approaches in NIR
Spectroscopy
Applications of VSCF theory in investigations of mid-infrared (MIR) spectra are
reasonably popular in literature [12], yet relatively few examples aimed at the NIR
region can be found. Although even the basic VSCF approach is capable of predicting
up to third-order overtones and combination bands, it seems that an improved description of mode correlations (e.g., by means of PT2-VSCF, or VCI) is often necessary
to yield a qualitatively correct prediction of NIR modes [13]. These approaches
frequently prove to be prohibitively expensive for treating larger molecules, although
examples exist of successful applications of the PT2-VSCF approach to molecules
counting ca. 15 atoms (e.g., malic acid), when certain approximations are assumed
(e.g., the application of a quartic force field, QFF) [13]. The anharmonic frameworks featuring a robust treatment of mode correlations (i.e., VSCF-VCI, VCC) are
far more expensive. The applicability of these methods may improve in the future,
however.
The primary advantage of the DVPT2-GVPT2 approach is efficiency and applicability to molecules that are in the center of attention of applied NIR spectroscopy. Additionally, the GVPT2 framework fully mitigates the typical shortcoming of perturbation theory being prone to produce meaningless description of
tightly coupled modes that becomes increasingly probable upon an increase of the
system size. Therefore, this framework finds a remarkably widening application area
in solving spectroscopic problems. A good example is a recent investigation of the
NIR spectroscopic properties of melamine [14]. This compound is of key interest to
analytical NIR spectroscopy in the context of food quality control. However, as in
many other cases, the NIR spectrum of melamine remained shallowly understood
before. Spectra calculations by means of the DVPT2 and GVPT2 methods performed
at B3LYP-GD3BJ/SNST level were able to accurately reconstruct all essential NIR
absorption bands of melamine (Fig. 5.7). This yielded detailed and unambiguous
band assignments for the compound, enhancing the ability to interpret the essential features of the multivariate models used for analyzing melamine content. It is
noteworthy that at the same time, an interesting comparison was made. The present
implementation of GVPT2 includes the ability to predict three quanta transitions
(i.e., second overtones, ternary combination bands). The appearance of such bands
in the experimental NIR spectrum of melamine could be directly assessed. As demonstrated in Fig. 5.7, this improves the interpretability of minor bands. However, the
K. B. Be´ c et al.
of intermode coupling contributions in addition to the adequate treatment of anharmonic effects. Especially when combined with sparse matrix algebra routines and
advanced interpolation techniques to reduce the associated computational effort, gridbased methods are capable of delivering a highly accurate description of complex
quantum mechanical systems.
5.6 Applications of Anharmonic Approaches in NIR
Spectroscopy
Applications of VSCF theory in investigations of mid-infrared (MIR) spectra are
reasonably popular in literature [12], yet relatively few examples aimed at the NIR
region can be found. Although even the basic VSCF approach is capable of predicting
up to third-order overtones and combination bands, it seems that an improved description of mode correlations (e.g., by means of PT2-VSCF, or VCI) is often necessary
to yield a qualitatively correct prediction of NIR modes [13]. These approaches
frequently prove to be prohibitively expensive for treating larger molecules, although
examples exist of successful applications of the PT2-VSCF approach to molecules
counting ca. 15 atoms (e.g., malic acid), when certain approximations are assumed
(e.g., the application of a quartic force field, QFF) [13]. The anharmonic frameworks featuring a robust treatment of mode correlations (i.e., VSCF-VCI, VCC) are
far more expensive. The applicability of these methods may improve in the future,
however.
The primary advantage of the DVPT2-GVPT2 approach is efficiency and applicability to molecules that are in the center of attention of applied NIR spectroscopy. Additionally, the GVPT2 framework fully mitigates the typical shortcoming of perturbation theory being prone to produce meaningless description of
tightly coupled modes that becomes increasingly probable upon an increase of the
system size. Therefore, this framework finds a remarkably widening application area
in solving spectroscopic problems. A good example is a recent investigation of the
NIR spectroscopic properties of melamine [14]. This compound is of key interest to
analytical NIR spectroscopy in the context of food quality control. However, as in
many other cases, the NIR spectrum of melamine remained shallowly understood
before. Spectra calculations by means of the DVPT2 and GVPT2 methods performed
at B3LYP-GD3BJ/SNST level were able to accurately reconstruct all essential NIR
absorption bands of melamine (Fig. 5.7). This yielded detailed and unambiguous
band assignments for the compound, enhancing the ability to interpret the essential features of the multivariate models used for analyzing melamine content. It is
noteworthy that at the same time, an interesting comparison was made. The present
implementation of GVPT2 includes the ability to predict three quanta transitions
(i.e., second overtones, ternary combination bands). The appearance of such bands
in the experimental NIR spectrum of melamine could be directly assessed. As demonstrated in Fig. 5.7, this improves the interpretability of minor bands. However, the