42. Near infrared spectrum
Applicability of near-infrared reflectance spectroscopy (NIRS) for determination of crude protein
content in cowpea (Vigna unguiculata) leaves (pages 45–53) 2012 Erick K. Towett, Merle Alex, Keith D.
Shepherd, Severin Polreich, Ermias Aynekulu and Brigitte L. Maass
76. • Although the harmonic model can help understanding vibrational
spectroscopy, it produces some disappointing restrictions for NIR
spectroscopy because it can not permit transitions where ∆υ is
greater than 1 (selection rule of n ± 1 ).
• Transitions with ∆υ = 2 or greater (absorption frequencies of 2n, 3n
etc.) are forbidden by the harmonic/quantum model and, in this
way, most of the observable phenomena in the NIR region, the
overtones bands, should not exist.
• Also, the vibrations in the harmonic model are independent and
their combinations would not exist under the restrictions imposed
by the model.
• Nevertheless, both overtones and combination bands exist.
Pasquini Near Infrared Spectroscopy: Fundamentals, Practical Aspects and Analytical Applications
J. Braz. Chem. Soc., Vol. 14, No. 2, 198-219, 2003.
77. Anharmonic VibrationsAnharmonic Vibrations
• The fact that springs eventually loose their elasticity and
break has its correspondence in the quantum chemical
oscillator.
• The key to a correct description is the use of an anharmonic
potential.
• A consequence of anharmonicity is, that the vibratory levels
are now not evenly spaced but tend to become closer with
increasing quantum numbers.
• One way to address this issue is to assume that the individual
energies En from the harmonic case are only the first linear
term of a series that comprises terms of higher order.
78. ν = 0
ν = 3
ν = 2
ν = 1
ν = 0
ν = 3
ν = 2
ν = 1
de de
Interatomic Distance
PotentialEnergy(V)
A
Harmonic Potential
B
Anharmonic Potential
Dissociation
Fundamental
First overtone
Second overtone
2
2
1
kxV =
νυυ hE
+=
2
1 )
2
1
()
2
1
(1)
2
1
()
2
1
( 2
+
+−≅+−+≅ υυνυνυν mm xhhxhE
( )2)(
1 erra
e eDV −−
−=
การสั่นของพันธะที่ประกอบด้วยการสั่นของพันธะที่ประกอบด้วย 22 อะตอมอะตอม
De
91. Absorption due to overtoneAbsorption due to overtone
νn
= nν0
[1 – (n + 1)X]
Where
n = positive integer
ν0
= wave number of the fundamental vibration
X = anharmonicity constant
92. Absorption due to combinationAbsorption due to combination
νn
= n1ν1
+ n2ν2
Where
n1, n2 = positive integers
ν1 ,
ν2
= wave number of the fundamental vibration
Simultaneous excitation of more than one
quantum number gives rise to a combination band.
95. Bond vibrationBond vibration Wavenumber
(cm-1)
Wavelength
(nm)
Asymmetrical stretching of NH 3400 2941
Symmetrical stretching of NH 3300 3030
Overtone of asymmetrical stretching of
NH
6803 1470
Overtone of symmetrical stretching of NH 6536 1530
Combination of symmetrical stretching
and asymmetrical stretching of NH
6666 1500
Fundamental, overtone andFundamental, overtone and
combination vibrations of ureacombination vibrations of urea
