10.2 Benzene: SFG from Centrosymmetric Molecules
253
10.2 Benzene: SFG from Centrosymmetric Molecules
The SFG of benzene poses an intriguing issue. The liquid benzene surface generates
intense C–H signal in the SFG spectrum, although each benzene molecule is centrosymmetric and thus it should have null hyperpolarizability [13, 25]. Elucidating
the SFG mechanism of liquid benzene is pertinent to the fundamental mechanism
of SFG and symmetry breaking.
First, let us recall the SFG from other ordinary non-centrosymmetric molecules,
as we discussed in Sect. 3.3. These molecules have finite non-zero hyperpolarizabilities, and nevertheless the susceptibility of their bulk materials vanishes. This
is because the molecular orientation is random and isotropic in the bulk, so that
the contributions of hyperpolarizabilities cancel each other by taking the statistical
average. On the other hand, the susceptibility of their interfaces is not necessarily
zero due to anisotropic molecular orientation. However, such typical scenario for
the SFG activity of interfaces does not elucidate the SFG signal from benzene,
because the benzene itself has no hyperpolarizability regardless of its orientation.
Consequently, there remain two possible scenarios in order to elucidate the SFG of
benzene:
(i) symmetry breaking: the symmetry of benzene molecules is broken at the
inhomogeneous environment at the interface so that the SFG becomes allowed
there.
(ii) quadrupole: the quadrupole mechanism of SFG is invoked beyond the conventional dipole mechanism.
The MD simulation was fully utilized to examine these mechanisms [18], and found
that both mechanisms are actually involved in the SFG from liquid benzene.
Regarding (i) symmetry breaking, the benzene molecule has six equivalent C–H
groups, whose vibrations are degenerated in the zero-th order approximation. The
C–H groups construct the normal modes of C–H stretching under the D 6h symmetry
of benzene (i.e. ν 2 (A 1g ), ν 7 (E 2g ), ν 13 (B 1u ), and ν 20 (E 1u )), and these normal
modes have nearly degenerate frequencies. Therefore, these C–H normal modes can
be readily mixed each other by a small external perturbation. At the surface of liquid
benzene, the nonuniform solvation environment acts as the perturbation to break
the symmetry of the C–H modes. This mechanism implies that a centrosymmetric
molecule can readily become SFG active at interface. Figure 10.3a shows the
calculated result of Im[χ (2) ] spectrum (red line) of benzene by the standard time
correlation function formula of Eq. (5.27). The Im[χ (2) ] spectrum shows a bipolar
band at about 3100 cm −1 region. The positive and negative components are
attributed to the upward and downward local C–H modes. These local modes are
slightly split in frequency due to the distinct solvation environments.
(ii) The quadrupole mechanism turned out to be also significant in the SFG
spectrum of benzene. The MD analysis was applied to examine all possible
quadrupole contributions discussed in Chap. 7, and consequently revealed that the
χ IQB term has a particularly large contribution. Figure 10.3a shows the Im[χ IQB ]
253
10.2 Benzene: SFG from Centrosymmetric Molecules
The SFG of benzene poses an intriguing issue. The liquid benzene surface generates
intense C–H signal in the SFG spectrum, although each benzene molecule is centrosymmetric and thus it should have null hyperpolarizability [13, 25]. Elucidating
the SFG mechanism of liquid benzene is pertinent to the fundamental mechanism
of SFG and symmetry breaking.
First, let us recall the SFG from other ordinary non-centrosymmetric molecules,
as we discussed in Sect. 3.3. These molecules have finite non-zero hyperpolarizabilities, and nevertheless the susceptibility of their bulk materials vanishes. This
is because the molecular orientation is random and isotropic in the bulk, so that
the contributions of hyperpolarizabilities cancel each other by taking the statistical
average. On the other hand, the susceptibility of their interfaces is not necessarily
zero due to anisotropic molecular orientation. However, such typical scenario for
the SFG activity of interfaces does not elucidate the SFG signal from benzene,
because the benzene itself has no hyperpolarizability regardless of its orientation.
Consequently, there remain two possible scenarios in order to elucidate the SFG of
benzene:
(i) symmetry breaking: the symmetry of benzene molecules is broken at the
inhomogeneous environment at the interface so that the SFG becomes allowed
there.
(ii) quadrupole: the quadrupole mechanism of SFG is invoked beyond the conventional dipole mechanism.
The MD simulation was fully utilized to examine these mechanisms [18], and found
that both mechanisms are actually involved in the SFG from liquid benzene.
Regarding (i) symmetry breaking, the benzene molecule has six equivalent C–H
groups, whose vibrations are degenerated in the zero-th order approximation. The
C–H groups construct the normal modes of C–H stretching under the D 6h symmetry
of benzene (i.e. ν 2 (A 1g ), ν 7 (E 2g ), ν 13 (B 1u ), and ν 20 (E 1u )), and these normal
modes have nearly degenerate frequencies. Therefore, these C–H normal modes can
be readily mixed each other by a small external perturbation. At the surface of liquid
benzene, the nonuniform solvation environment acts as the perturbation to break
the symmetry of the C–H modes. This mechanism implies that a centrosymmetric
molecule can readily become SFG active at interface. Figure 10.3a shows the
calculated result of Im[χ (2) ] spectrum (red line) of benzene by the standard time
correlation function formula of Eq. (5.27). The Im[χ (2) ] spectrum shows a bipolar
band at about 3100 cm −1 region. The positive and negative components are
attributed to the upward and downward local C–H modes. These local modes are
slightly split in frequency due to the distinct solvation environments.
(ii) The quadrupole mechanism turned out to be also significant in the SFG
spectrum of benzene. The MD analysis was applied to examine all possible
quadrupole contributions discussed in Chap. 7, and consequently revealed that the
χ IQB term has a particularly large contribution. Figure 10.3a shows the Im[χ IQB ]