250
10 Applications: Organic Interfaces
simulation. 1 Full quantum molecular dynamics to allow for resonances is not
feasible in most cases of condense phase simulation. One practical solution of
this problem is to exploit the quantum-classical analogy of resonance phenomena
[16]. Both classical and quantum mechanics can describe resonance phenomena
of vibrations in a qualitatively analogous manner, that an anharmonic coupling
Hamiltonian brings about significant mode mixing of nearly degenerate fundamental and overtone. However, the classical and quantum mechanics do not result in
the same extent of resonance mode mixing [16]. Therefore, one can reasonably
reproduce or mimic the Fermi resonance in the classical mechanics by using an
effective coupling Hamiltonian including a quantum correction, so that the results
of the resonance mixing by the classical mechanics are in accord with those by
the quantum mechanics. This treatment of quantum correction is valid as long as we
reproduce the features of Fermi resonance in the vibrational spectra by classical MD
simulation. The following analysis of the Fermi resonance is based on the treatment.
10.1.3 Methanol C–H Vibrations
Methanol is the smallest alcohol containing only one methyl group, and the
vibrational spectra of C–H band have been experimentally studied by SFG as well as
infrared and Raman. The SFG spectrum in SSP polarization shows two components
of C–H band in Fig. 10.2a, a major low-frequency one at ∼2830 cm −1 and a minor
high-frequency one at ∼2950 cm −1 . It is noteworthy that similar two-band structure
of the C–H band is also seen in the infrared and Raman spectra of liquid methanol
as well, and the assignment of the structure has been argued to date [2, 4, 24, 29].
The widely accepted assignment of the two-band structure is distinct between the
infrared and Raman spectra. The two bands in the IR spectrum are mostly assigned
to the symmetric and asymmetric C–H stretching modes [2], whereas those in
the Raman spectrum to the symmetric C–H stretching and the counterpart of its
Fermi resonance [24, 29]. The different assignments of infrared and Raman spectra
brought about confusion in the assignment of the SFG spectrum. This is a typical
example that straightforward analogy to infrared or Raman spectra is not useful to
interpret SFG spectra.
Band structure The MD analysis provides definite assignment of the SFG spectrum on a common basis to the infrared and Raman spectra, with also elucidating
differences among three vibrational spectroscopies [16, 17]. The basic picture of
vibrational levels of methanol is summarized in Fig. 10.2b. The C–H symmetric
stretching of methyl ν 3 interact with bending overtone 2ν 5 and is split by the Fermi
resonance, while the C–H asymmetric stretching ν 2 , ν 9 overlap with the higherfrequency component of the Fermi splitting in the frequency domain. This scheme
is common among the three vibrational spectroscopies in the case of methanol.
1 The validity of classical mechanics to treat vibrational dynamics of molecules is based on the
equivalence of quantum and classical descriptions of harmonic oscillators [1]. The Fermi resonance
that stems from anharmonic coupling is essentially beyond the classical mechanics.
10 Applications: Organic Interfaces
simulation. 1 Full quantum molecular dynamics to allow for resonances is not
feasible in most cases of condense phase simulation. One practical solution of
this problem is to exploit the quantum-classical analogy of resonance phenomena
[16]. Both classical and quantum mechanics can describe resonance phenomena
of vibrations in a qualitatively analogous manner, that an anharmonic coupling
Hamiltonian brings about significant mode mixing of nearly degenerate fundamental and overtone. However, the classical and quantum mechanics do not result in
the same extent of resonance mode mixing [16]. Therefore, one can reasonably
reproduce or mimic the Fermi resonance in the classical mechanics by using an
effective coupling Hamiltonian including a quantum correction, so that the results
of the resonance mixing by the classical mechanics are in accord with those by
the quantum mechanics. This treatment of quantum correction is valid as long as we
reproduce the features of Fermi resonance in the vibrational spectra by classical MD
simulation. The following analysis of the Fermi resonance is based on the treatment.
10.1.3 Methanol C–H Vibrations
Methanol is the smallest alcohol containing only one methyl group, and the
vibrational spectra of C–H band have been experimentally studied by SFG as well as
infrared and Raman. The SFG spectrum in SSP polarization shows two components
of C–H band in Fig. 10.2a, a major low-frequency one at ∼2830 cm −1 and a minor
high-frequency one at ∼2950 cm −1 . It is noteworthy that similar two-band structure
of the C–H band is also seen in the infrared and Raman spectra of liquid methanol
as well, and the assignment of the structure has been argued to date [2, 4, 24, 29].
The widely accepted assignment of the two-band structure is distinct between the
infrared and Raman spectra. The two bands in the IR spectrum are mostly assigned
to the symmetric and asymmetric C–H stretching modes [2], whereas those in
the Raman spectrum to the symmetric C–H stretching and the counterpart of its
Fermi resonance [24, 29]. The different assignments of infrared and Raman spectra
brought about confusion in the assignment of the SFG spectrum. This is a typical
example that straightforward analogy to infrared or Raman spectra is not useful to
interpret SFG spectra.
Band structure The MD analysis provides definite assignment of the SFG spectrum on a common basis to the infrared and Raman spectra, with also elucidating
differences among three vibrational spectroscopies [16, 17]. The basic picture of
vibrational levels of methanol is summarized in Fig. 10.2b. The C–H symmetric
stretching of methyl ν 3 interact with bending overtone 2ν 5 and is split by the Fermi
resonance, while the C–H asymmetric stretching ν 2 , ν 9 overlap with the higherfrequency component of the Fermi splitting in the frequency domain. This scheme
is common among the three vibrational spectroscopies in the case of methanol.
1 The validity of classical mechanics to treat vibrational dynamics of molecules is based on the
equivalence of quantum and classical descriptions of harmonic oscillators [1]. The Fermi resonance
that stems from anharmonic coupling is essentially beyond the classical mechanics.