5.3 Interfacial Dielectric Constant ε
115
The three local field correction factors, f sp (j ), f rq (j ) and f sr (k), in Eq. (5.28) are
associated to the sum-frequency , visible ω 1 , and infrared ω 2 fields, respectively.
The computational analysis of SFG spectra by MD simulation employs the expression of Eq. (5.27).
To summarize the above computational procedure of A eff and M, the calculation
of χ (2) by MD simulation requires the following properties of constituent molecules
at each time:
(i) dipole-dipole coupling tensor T (ij ),
(ii) external field E 0 (j ),
(iii) polarizability tensor α(j ),
(iv) permanent dipole moment vector μ 0 (j ).
Among these properties, (i) and (ii) are readily obtained from the instantaneous
molecular configuration {r(j )}. Conventional force fields for MD simulation allow
for calculating E 0 (j ) at each time step, as it is a necessary quantity to evaluate
electrostatic forces. On the other hand, usual force fields of MD do not provide (iii)
and (iv). We have to obtain the instantaneous values of α(j ) and μ 0 (j ) at each time
step in addition to the force field calculations. The modeling of α(j ) and μ 0 (j ) will
be discussed in the next Chap. 6.
5.3 Interfacial Dielectric Constant ε
The preceding argument on the local field is quite relevant to the microscopic
understanding of the interfacial dielectric constant ε mentioned in Chap. 2. As we
have summarized in Sect. 2.3 the factors to determine the SFG and SHG spectra,
the factors related to interface properties include the nonlinear susceptibility χ (2)
and the dielectric constant of the interface ε . The preceding Sect. 5.2 provided
microscopic formulation of χ (2) on the basis of the molecular theory of local field.
In relation to the above argument, we discuss here the interfacial dielectric constant
ε from the same molecular viewpoint. The microscopic local field is connected to
the concept of ε in the phenomenological three-layer model.
External field vs. local field Let us consider the optical geometry of SFG
measurement in Fig. 2.1. We notice that Fig. 2.1 adopts the three-layer model and
assumes the infinite thin layer of interface at z ≈ 0. However, here we discuss
the structure and properties in the interface layer. In the following discussion the
medium α is assumed to be vacuum for simplicity, and hence ε α = 1, though
extension to other situations is straightforward.
For microscopic treatment of electric fields at the interface, we distinguish the
incident field E I , external field E ext , and local field E loc . Suppose a plane wave
E α
I (ω f ) (f = 1 or 2) in Eq. (2.11) is incident from the medium α (vacuum) to the
interface, the interface region near z ≈ 0 feels the external field of the frequency
ω f , E ext (ω f ). This is a superposition of the incident and reflected radiation fields,
and thus related to the incident field through the optical factor L I (ω f ),
115
The three local field correction factors, f sp (j ), f rq (j ) and f sr (k), in Eq. (5.28) are
associated to the sum-frequency , visible ω 1 , and infrared ω 2 fields, respectively.
The computational analysis of SFG spectra by MD simulation employs the expression of Eq. (5.27).
To summarize the above computational procedure of A eff and M, the calculation
of χ (2) by MD simulation requires the following properties of constituent molecules
at each time:
(i) dipole-dipole coupling tensor T (ij ),
(ii) external field E 0 (j ),
(iii) polarizability tensor α(j ),
(iv) permanent dipole moment vector μ 0 (j ).
Among these properties, (i) and (ii) are readily obtained from the instantaneous
molecular configuration {r(j )}. Conventional force fields for MD simulation allow
for calculating E 0 (j ) at each time step, as it is a necessary quantity to evaluate
electrostatic forces. On the other hand, usual force fields of MD do not provide (iii)
and (iv). We have to obtain the instantaneous values of α(j ) and μ 0 (j ) at each time
step in addition to the force field calculations. The modeling of α(j ) and μ 0 (j ) will
be discussed in the next Chap. 6.
5.3 Interfacial Dielectric Constant ε
The preceding argument on the local field is quite relevant to the microscopic
understanding of the interfacial dielectric constant ε mentioned in Chap. 2. As we
have summarized in Sect. 2.3 the factors to determine the SFG and SHG spectra,
the factors related to interface properties include the nonlinear susceptibility χ (2)
and the dielectric constant of the interface ε . The preceding Sect. 5.2 provided
microscopic formulation of χ (2) on the basis of the molecular theory of local field.
In relation to the above argument, we discuss here the interfacial dielectric constant
ε from the same molecular viewpoint. The microscopic local field is connected to
the concept of ε in the phenomenological three-layer model.
External field vs. local field Let us consider the optical geometry of SFG
measurement in Fig. 2.1. We notice that Fig. 2.1 adopts the three-layer model and
assumes the infinite thin layer of interface at z ≈ 0. However, here we discuss
the structure and properties in the interface layer. In the following discussion the
medium α is assumed to be vacuum for simplicity, and hence ε α = 1, though
extension to other situations is straightforward.
For microscopic treatment of electric fields at the interface, we distinguish the
incident field E I , external field E ext , and local field E loc . Suppose a plane wave
E α
I (ω f ) (f = 1 or 2) in Eq. (2.11) is incident from the medium α (vacuum) to the
interface, the interface region near z ≈ 0 feels the external field of the frequency
ω f , E ext (ω f ). This is a superposition of the incident and reflected radiation fields,
and thus related to the incident field through the optical factor L I (ω f ),