Chapter 7
Quadrupole Contributions from
Interface and Bulk
Abstract This chapter provides the comprehensive argument on quadrupole contributions in SFG spectroscopy. Though the preceding chapters have dealt with
the induced dipole contribution, the accurate theory of SFG and SHG should take
account of the induced quadrupole beside the dipole. The former can arise from the
bulk region, while the latter stems only from the interface. We clarify three kinds of
quadrupole contributions, namely χ IQ , χ IQB and χ B , in addition to the dipole one
χ ID . The four terms have different roles in SFG and SHG spectra, as summarized
in Sect. 7.5. The following discussion elucidates these quadrupole mechanisms and
characters, and derives their microscopic formulas for calculating them.
Keywords Quadrupole · Bulk contribution · χ IQB and χ B
The present chapter provides comprehensive argument on the quadrupole contributions to the SFG spectroscopy. In the preceding chapters, we have assumed
that the sum frequency signal originates from the second-order susceptibility
χ (2) ((, ω 1 , ω 2 ) at the interface. We have argued in Problem 1.1 that the χ (2)
vanishes in isotropic bulk media, and this property renders the SFG spectroscopy
the surface selectivity.
We recall that this argument dealt with the induced electric dipole P (2) in
Eq. (1.4), which exclusively arises from a region where the inversion symmetry
is broken. However, the sources of the sum frequency signal may include higherorder, electric quadrupole and magnetic dipole contributions in addition to the
electric dipolar polarization of Eq. (1.4). These higher-order contributions are not
necessarily forbidden in isotropic media for symmetry reason, and thus affect the
surface selectivity of SFG spectroscopy. Even if the intrinsic quadrupole signal
in the bulk is weaker than the dipole at the surface, the overwhelmingly larger
volume of the bulk could compensate for the weak quadrupole signal [10]. Rigorous
quantitative theory of SFG should take account of these contributions. 1
1 The general “quadrupole” term incorporates the electric quadrupole and the magnetic dipole
contributions, as we argue later.
© Springer Nature Singapore Pte Ltd. 2018
A. Morita, Theory of Sum Frequency Generation Spectroscopy,
Lecture Notes in Chemistry 97, https://doi.org/10.1007/978-981-13-1607-4_7
151
Quadrupole Contributions from
Interface and Bulk
Abstract This chapter provides the comprehensive argument on quadrupole contributions in SFG spectroscopy. Though the preceding chapters have dealt with
the induced dipole contribution, the accurate theory of SFG and SHG should take
account of the induced quadrupole beside the dipole. The former can arise from the
bulk region, while the latter stems only from the interface. We clarify three kinds of
quadrupole contributions, namely χ IQ , χ IQB and χ B , in addition to the dipole one
χ ID . The four terms have different roles in SFG and SHG spectra, as summarized
in Sect. 7.5. The following discussion elucidates these quadrupole mechanisms and
characters, and derives their microscopic formulas for calculating them.
Keywords Quadrupole · Bulk contribution · χ IQB and χ B
The present chapter provides comprehensive argument on the quadrupole contributions to the SFG spectroscopy. In the preceding chapters, we have assumed
that the sum frequency signal originates from the second-order susceptibility
χ (2) ((, ω 1 , ω 2 ) at the interface. We have argued in Problem 1.1 that the χ (2)
vanishes in isotropic bulk media, and this property renders the SFG spectroscopy
the surface selectivity.
We recall that this argument dealt with the induced electric dipole P (2) in
Eq. (1.4), which exclusively arises from a region where the inversion symmetry
is broken. However, the sources of the sum frequency signal may include higherorder, electric quadrupole and magnetic dipole contributions in addition to the
electric dipolar polarization of Eq. (1.4). These higher-order contributions are not
necessarily forbidden in isotropic media for symmetry reason, and thus affect the
surface selectivity of SFG spectroscopy. Even if the intrinsic quadrupole signal
in the bulk is weaker than the dipole at the surface, the overwhelmingly larger
volume of the bulk could compensate for the weak quadrupole signal [10]. Rigorous
quantitative theory of SFG should take account of these contributions. 1
1 The general “quadrupole” term incorporates the electric quadrupole and the magnetic dipole
contributions, as we argue later.
© Springer Nature Singapore Pte Ltd. 2018
A. Morita, Theory of Sum Frequency Generation Spectroscopy,
Lecture Notes in Chemistry 97, https://doi.org/10.1007/978-981-13-1607-4_7
151