306
M. A. Czarnecki et al.
The theory of hydrogen bonding and the role of anharmonicity remained a matter
of intense research. With the availability of advanced quantum mechanical calculations further progress in the understanding of the relation between hydrogen bonding
and anharmonicity could be achieved. By applying the methodologies described in
the chapter “Introduction to Quantum Vibrational Spectroscopy,” detailed information on the change in the anharmonicity of the vibrational potential and the transition
dipole moments upon the formation of hydrogen bonding can be obtained. A number
of examples have been discussed in the recent literature, for instance, a systematic
research by Futami and co-workers [3]. These investigations yielded deep insights
into the discussed phenomenon by studying NIR and IR spectra of pyrrole, pyridine,
and pyrrole–pyridine complex in solution phase (CCl 4 ). The foundation for the study
was formed by the observation that the first overtone of the NH stretching vibration
of a non-bonded pyrrole molecule appears as a well-resolved band at 6856 cm
−1 ;
however, it is not observed for a pyrrole–pyridine complex. The theoretical calculations by Futami et al. used Johnson’s reformulation of the Numerov approach and
yielded detailed information on the vibrational levels and the dipole moment functions of the ν(NH) mode in a non-bonded pyrrole molecule as well as the pyrrole–
pyridine complex. Those results explained why the 2ν(NH) transition of pyrrole is
weakened upon the formation of a NH–N hydrogen bond in the pyrrole–pyridine
complex. Firstly, reproduction of the shift observed for the experimental peak as
well as the variation in its intensity was achieved. Further insight was obtained from
the analysis of the one-dimensional vibrational wave functions of the two molecular
systems. The conclusion was drawn that upon the formation of hydrogen bonding,
the transition dipole moment diminishes while at the same time the overlap integral
of the wave function is enhanced. This leads to a dramatic decrease in the intensity
of the 2ν(NH) band of pyrrole to a level at which it is hardly detectable by the experiment. Therefore, the study revealed a significant decrease in the 2ν(NH) transition
dipole moment upon formation of the pyrrole–pyridine complex. This in turn results
in a remarkably weak intensity of the first overtone band observed experimentally
for the hydrogen–bonded NH group [3].
The investigation of the changes caused by hydrogen bonding to the anharmonicity of vibrational potential and transition dipole moment has been continued
with a number of different systems [3]. Those included complexes featuring NH–π
hydrogen bonding such as pyrrole–ethylene and pyrrole–acetylene. This investigation revealed that the stabilization energy of NH–π hydrogen bond is almost twothirds lower than the stabilization energy of a typical NH–N bond. Furthermore, the
formation of NH–π hydrogen bonding induces a comparably small red-shift in the
fundamental and first overtone of ν(NH) bands. It was concluded that the energy
shift depends on the intermolecular force between the hydrogen–bonded molecules.
On the other hand, Futami et al. also observed an increasing trend in the intensity
of the ν(NH) fundamental absorption but a decreasing trend in the intensity of the
ν(NH) first overtone band. Consequently, this observation made for NH–π hydrogen
bonding remained in full agreement with earlier results for the pyrrole–pyridine case,
in which NH–N hydrogen bonding is present.
M. A. Czarnecki et al.
The theory of hydrogen bonding and the role of anharmonicity remained a matter
of intense research. With the availability of advanced quantum mechanical calculations further progress in the understanding of the relation between hydrogen bonding
and anharmonicity could be achieved. By applying the methodologies described in
the chapter “Introduction to Quantum Vibrational Spectroscopy,” detailed information on the change in the anharmonicity of the vibrational potential and the transition
dipole moments upon the formation of hydrogen bonding can be obtained. A number
of examples have been discussed in the recent literature, for instance, a systematic
research by Futami and co-workers [3]. These investigations yielded deep insights
into the discussed phenomenon by studying NIR and IR spectra of pyrrole, pyridine,
and pyrrole–pyridine complex in solution phase (CCl 4 ). The foundation for the study
was formed by the observation that the first overtone of the NH stretching vibration
of a non-bonded pyrrole molecule appears as a well-resolved band at 6856 cm
−1 ;
however, it is not observed for a pyrrole–pyridine complex. The theoretical calculations by Futami et al. used Johnson’s reformulation of the Numerov approach and
yielded detailed information on the vibrational levels and the dipole moment functions of the ν(NH) mode in a non-bonded pyrrole molecule as well as the pyrrole–
pyridine complex. Those results explained why the 2ν(NH) transition of pyrrole is
weakened upon the formation of a NH–N hydrogen bond in the pyrrole–pyridine
complex. Firstly, reproduction of the shift observed for the experimental peak as
well as the variation in its intensity was achieved. Further insight was obtained from
the analysis of the one-dimensional vibrational wave functions of the two molecular
systems. The conclusion was drawn that upon the formation of hydrogen bonding,
the transition dipole moment diminishes while at the same time the overlap integral
of the wave function is enhanced. This leads to a dramatic decrease in the intensity
of the 2ν(NH) band of pyrrole to a level at which it is hardly detectable by the experiment. Therefore, the study revealed a significant decrease in the 2ν(NH) transition
dipole moment upon formation of the pyrrole–pyridine complex. This in turn results
in a remarkably weak intensity of the first overtone band observed experimentally
for the hydrogen–bonded NH group [3].
The investigation of the changes caused by hydrogen bonding to the anharmonicity of vibrational potential and transition dipole moment has been continued
with a number of different systems [3]. Those included complexes featuring NH–π
hydrogen bonding such as pyrrole–ethylene and pyrrole–acetylene. This investigation revealed that the stabilization energy of NH–π hydrogen bond is almost twothirds lower than the stabilization energy of a typical NH–N bond. Furthermore, the
formation of NH–π hydrogen bonding induces a comparably small red-shift in the
fundamental and first overtone of ν(NH) bands. It was concluded that the energy
shift depends on the intermolecular force between the hydrogen–bonded molecules.
On the other hand, Futami et al. also observed an increasing trend in the intensity
of the ν(NH) fundamental absorption but a decreasing trend in the intensity of the
ν(NH) first overtone band. Consequently, this observation made for NH–π hydrogen
bonding remained in full agreement with earlier results for the pyrrole–pyridine case,
in which NH–N hydrogen bonding is present.