222
9 Applications: Aqueous Interfaces
system in that restricted region. This calculation is feasible by MD simulation. By
gradually lowering the threshold z thres and expanding that region, we can observe
the convergence behavior of the calculated χ (2) . Figure 9.1 shows the results of such
analysis. The figure tells us that the positive band at 3700 cm −1 originates from the
region of ˆ
z > −3 Å, since the band amplitude reaches the convergence up to the
region. This result evidences that this positive band at 3700 cm −1 comes from the
top monolayer of the water surface, again supporting the free O–H exposed to the
air. On the other hand, the negative band at 3000∼3600 cm −1 converges at about
ˆ
z > −9 Å, indicating that the band of hydrogen-bonded O–H is attributed to a few
top monolayers of the water surface. This analysis confirms the remarkably acute
selectivity of SFG spectroscopy in the monolayer scale.
Analysis of hydrogen-bonded O–H band: The broad band at 3000∼3600 cm −1
is attributed to hydrogen-bonded O–H, due to the substantial red shift of frequency.
However, further detailed assignment of this band has invoked a number of studies
and often confusions. As seen in the experimental SFG spectrum of water (left panel
of Fig. 1.1), this broad band appears to have two sub-bands, one at about 3200 cm −1
and the other at about 3400 cm −1 . The two sub-bands are often called “ice-like” and
“liquid-like” bands, respectively, in analogy with these spectra of the corresponding
bulk materials. The O–H band at 3200 cm −1 is obviously seen in the infrared and
Raman spectra of ice [79], while the band at 3400 cm −1 is seen in liquid water
[16]. However, the physical origin of these two sub-bands in the SFG spectrum is
still controversial. An intuitive understanding of the two sub-bands comes from the
picture that the water surface is a mixture of ice-like water and liquid-like water.
This idea of two-state mixture model has a long history in bulk water [16], though
there is no consensus to support this idea with microscopic investigation by MD
simulation or other means.
Bonn and co-workers proposed an alternative assignment of the two-band
structure that the two sub-bands are due to Fermi splitting of O–H stretching
vibrational states by the H–O–H bending overtone [98, 99]. Their argument is
supported by the experiment of H-D isotope dilution. By replacing H 2 O with HOD,
they observed that the two sub-bands merge into one. This implies that the two-band
structure should originates from vibrational coupling rather than the structure, since
the isotope dilution little affects on the structure of nuclei.
As we argued in the beginning of this chapter, a main challenge in analyzing O–
H vibration stems from extensive intra- and inter-molecular vibrational couplings,
which delocalize the O–H vibrations and complicates the relation to the molecular
orientation. To disentangle the O–H vibrations, the H-D isotope dilution offers
a useful means. The isotope dilution preserves the structure of nuclei, while it
effectively eliminates the intra- and inter-molecular couplings among nearby O–
H bonds. Therefore, the observed spectrum approaches that of assembly of isolated
O–H bonds in dilute conditions, and the ideal picture about the relation of O–H
orientation and Im[χ (2) ] in Sect. 4.2.1 becomes increasingly reliable in the spectral
analysis.
9 Applications: Aqueous Interfaces
system in that restricted region. This calculation is feasible by MD simulation. By
gradually lowering the threshold z thres and expanding that region, we can observe
the convergence behavior of the calculated χ (2) . Figure 9.1 shows the results of such
analysis. The figure tells us that the positive band at 3700 cm −1 originates from the
region of ˆ
z > −3 Å, since the band amplitude reaches the convergence up to the
region. This result evidences that this positive band at 3700 cm −1 comes from the
top monolayer of the water surface, again supporting the free O–H exposed to the
air. On the other hand, the negative band at 3000∼3600 cm −1 converges at about
ˆ
z > −9 Å, indicating that the band of hydrogen-bonded O–H is attributed to a few
top monolayers of the water surface. This analysis confirms the remarkably acute
selectivity of SFG spectroscopy in the monolayer scale.
Analysis of hydrogen-bonded O–H band: The broad band at 3000∼3600 cm −1
is attributed to hydrogen-bonded O–H, due to the substantial red shift of frequency.
However, further detailed assignment of this band has invoked a number of studies
and often confusions. As seen in the experimental SFG spectrum of water (left panel
of Fig. 1.1), this broad band appears to have two sub-bands, one at about 3200 cm −1
and the other at about 3400 cm −1 . The two sub-bands are often called “ice-like” and
“liquid-like” bands, respectively, in analogy with these spectra of the corresponding
bulk materials. The O–H band at 3200 cm −1 is obviously seen in the infrared and
Raman spectra of ice [79], while the band at 3400 cm −1 is seen in liquid water
[16]. However, the physical origin of these two sub-bands in the SFG spectrum is
still controversial. An intuitive understanding of the two sub-bands comes from the
picture that the water surface is a mixture of ice-like water and liquid-like water.
This idea of two-state mixture model has a long history in bulk water [16], though
there is no consensus to support this idea with microscopic investigation by MD
simulation or other means.
Bonn and co-workers proposed an alternative assignment of the two-band
structure that the two sub-bands are due to Fermi splitting of O–H stretching
vibrational states by the H–O–H bending overtone [98, 99]. Their argument is
supported by the experiment of H-D isotope dilution. By replacing H 2 O with HOD,
they observed that the two sub-bands merge into one. This implies that the two-band
structure should originates from vibrational coupling rather than the structure, since
the isotope dilution little affects on the structure of nuclei.
As we argued in the beginning of this chapter, a main challenge in analyzing O–
H vibration stems from extensive intra- and inter-molecular vibrational couplings,
which delocalize the O–H vibrations and complicates the relation to the molecular
orientation. To disentangle the O–H vibrations, the H-D isotope dilution offers
a useful means. The isotope dilution preserves the structure of nuclei, while it
effectively eliminates the intra- and inter-molecular couplings among nearby O–
H bonds. Therefore, the observed spectrum approaches that of assembly of isolated
O–H bonds in dilute conditions, and the ideal picture about the relation of O–H
orientation and Im[χ (2) ] in Sect. 4.2.1 becomes increasingly reliable in the spectral
analysis.