34
Y. Ozaki and Y. Morisawa
The third term of Formula 2.42 has a value other than 0 when (∂
2
μ x / ∂ Q
2 ) =
0 and
ψ n Q
2
ψ m d Q = 0 both hold. The latter integral has a value other than 0
when υ’ = υ and υ ± 2. Therefore, even a first overtone is not forbidden any more
if we include the term of Q
2 . Similarly, second, third… overtones are not forbidden
any more as we take higher-order terms into consideration. However, the intensities
of these overtones are far weaker than those of fundamentals. The frequencies of
first, second, third… overtones are smaller than double, triple, quadruple of the
frequencies of fundamentals, respectively, as already described. This is because the
differences between the vibrational energy levels become narrower as the quantum
number υ increases, as clearly depicted in Fig. 2.12 and indicated by Formula 2.36.
Anharmonicity excludes combination modes as well from those forbidden in a similar
manner. The intensities of combination bands are also weak.
References
1. H. W. Siesler, Y. Ozaki, S. Kawata, H. M. Heise, Near-Infrared Spectroscopy (Wiley-VCH,
2002)
2. Y. Ozaki, W. F. McClure, A. A. Christy, eds., Near-Infrared Spectroscopy in Food Science and
Technology (Wiley, 2007)
3. Y. Ozaki, Near-infrared spectroscopy-Its versatility in analytical chemistry. Anal. Sci. 28, 545–
563 (2012)
4. D. A. Burns, E. W. Ciurczak eds., Handbook of Near-Infrared Analysis, 3rd edn. (Practical
Spectroscopy) (CRC Press, 2007)
5. Y. Ozaki, C. W. Huck, K. B. Be´ c, Near-IR spectroscopy and its applications, in Molecular
and Laser Spectroscopy: Advances and Applications, edited by V. P. Gupta (2017, Elsevier),
pp. 11–38
6. J. Workman, Jr., L. Weyer, Practical Guide and Spectral Atlas for Interpretive Near-Infrared
Spectroscopy, 2nd edn. (CRC Press, 2012)
7. M.A. Czarnecki, Y. Morisawa, Y. Futami, Y. Ozaki, Advances in molecular structure and
interaction studies using near-infrared spectroscopy. Chem. Rev. 115, 9707 (2015)
8. K.B. Bec, D. Karczmit, M. Kwa´ sniewicz, Y. Ozaki, M.A. Czarnecki, Overtones of νC ≡ N
Vibration as a Probe of Structure of Liquid CH 3 CN, CD 3 CN, and CCl 3 CN: Combined Infrared,
Near-Infrared, and Raman Spectroscopic Studies with Anharmonic Density Functional Theory
Calculations. J. Phys. Chem. A 123, 4431–4442 (2019)
9. K.B. Bec, Y. Futami, M.J. Wojcik, Y. Ozaki, Spectroscopic and theoretical study in the
nearinfrared region of low concentration aliphatic alcohols. Phys. Chem. Chem. Phys. 18,
13666–13682 (2016)
10. Y. Morisawa, S. Nomura, K. Sanada, Y. Ozaki, Monitoring of a calcination reaction of high
reflective green-black (HRGB) pigments by using near-infrared electronic spectroscopy: calcination temperature-dependent crystal structural changes of their components and calibration
of the extent of the reaction. Appl. Spectrosc. 66, 666–676 (2012)
11. Y. Hu, J. Zhang, H. Sato, Y. Futami, I. Noda, Y. Ozaki, C-H···O = C hydrogen bonding and
isothermal crystallization kinetics of poly(3-hydroxybutyrate) investigated by near-infrared
spectroscopy. Macromolecules 39, 3841–3847 (2006)
12. H. Sato, M. Nakamura, A. Padermshoke, H. Yamaguchi, H. Terauchi, S. Ekgasit, I.
Noda, Y. Ozaki, Thermal behavior and molecular interaction of poly(3-hydrobutyrate-cohydroxyhexanoate) studied by wide-angle X-ray diffraction. Macromolecules 37, 3763–3769
(2004)
Y. Ozaki and Y. Morisawa
The third term of Formula 2.42 has a value other than 0 when (∂
2
μ x / ∂ Q
2 ) =
0 and
ψ n Q
2
ψ m d Q = 0 both hold. The latter integral has a value other than 0
when υ’ = υ and υ ± 2. Therefore, even a first overtone is not forbidden any more
if we include the term of Q
2 . Similarly, second, third… overtones are not forbidden
any more as we take higher-order terms into consideration. However, the intensities
of these overtones are far weaker than those of fundamentals. The frequencies of
first, second, third… overtones are smaller than double, triple, quadruple of the
frequencies of fundamentals, respectively, as already described. This is because the
differences between the vibrational energy levels become narrower as the quantum
number υ increases, as clearly depicted in Fig. 2.12 and indicated by Formula 2.36.
Anharmonicity excludes combination modes as well from those forbidden in a similar
manner. The intensities of combination bands are also weak.
References
1. H. W. Siesler, Y. Ozaki, S. Kawata, H. M. Heise, Near-Infrared Spectroscopy (Wiley-VCH,
2002)
2. Y. Ozaki, W. F. McClure, A. A. Christy, eds., Near-Infrared Spectroscopy in Food Science and
Technology (Wiley, 2007)
3. Y. Ozaki, Near-infrared spectroscopy-Its versatility in analytical chemistry. Anal. Sci. 28, 545–
563 (2012)
4. D. A. Burns, E. W. Ciurczak eds., Handbook of Near-Infrared Analysis, 3rd edn. (Practical
Spectroscopy) (CRC Press, 2007)
5. Y. Ozaki, C. W. Huck, K. B. Be´ c, Near-IR spectroscopy and its applications, in Molecular
and Laser Spectroscopy: Advances and Applications, edited by V. P. Gupta (2017, Elsevier),
pp. 11–38
6. J. Workman, Jr., L. Weyer, Practical Guide and Spectral Atlas for Interpretive Near-Infrared
Spectroscopy, 2nd edn. (CRC Press, 2012)
7. M.A. Czarnecki, Y. Morisawa, Y. Futami, Y. Ozaki, Advances in molecular structure and
interaction studies using near-infrared spectroscopy. Chem. Rev. 115, 9707 (2015)
8. K.B. Bec, D. Karczmit, M. Kwa´ sniewicz, Y. Ozaki, M.A. Czarnecki, Overtones of νC ≡ N
Vibration as a Probe of Structure of Liquid CH 3 CN, CD 3 CN, and CCl 3 CN: Combined Infrared,
Near-Infrared, and Raman Spectroscopic Studies with Anharmonic Density Functional Theory
Calculations. J. Phys. Chem. A 123, 4431–4442 (2019)
9. K.B. Bec, Y. Futami, M.J. Wojcik, Y. Ozaki, Spectroscopic and theoretical study in the
nearinfrared region of low concentration aliphatic alcohols. Phys. Chem. Chem. Phys. 18,
13666–13682 (2016)
10. Y. Morisawa, S. Nomura, K. Sanada, Y. Ozaki, Monitoring of a calcination reaction of high
reflective green-black (HRGB) pigments by using near-infrared electronic spectroscopy: calcination temperature-dependent crystal structural changes of their components and calibration
of the extent of the reaction. Appl. Spectrosc. 66, 666–676 (2012)
11. Y. Hu, J. Zhang, H. Sato, Y. Futami, I. Noda, Y. Ozaki, C-H···O = C hydrogen bonding and
isothermal crystallization kinetics of poly(3-hydroxybutyrate) investigated by near-infrared
spectroscopy. Macromolecules 39, 3841–3847 (2006)
12. H. Sato, M. Nakamura, A. Padermshoke, H. Yamaguchi, H. Terauchi, S. Ekgasit, I.
Noda, Y. Ozaki, Thermal behavior and molecular interaction of poly(3-hydrobutyrate-cohydroxyhexanoate) studied by wide-angle X-ray diffraction. Macromolecules 37, 3763–3769
(2004)