106
5 Molecular Theory of Local Field
medium [3]. Such classical models deal with the homogeneous bulk medium as
a dielectric continuum. In the inhomogeneous environment of interface, however,
the local field is more complicated than that in the homogeneous medium, and
the theory of dielectric continuum model should become less reliable. Here we
discuss the local field effect at the interface fully from a molecular point of view
[6, 7]. The microscopic theory of local field can accurately describe the effects of
polarization coupling in arbitrary environment, and is straightforwardly applicable
to MD simulation.
In Sect. 5.1 we formulate the general microscopic expressions of dipole moment
and polarizability for the interface system. In Sect. 5.2 these expressions are applied
to the nonlinear susceptibility χ (2) with fully incorporating the local field effect. The
local field effect in inhomogeneous environment is relevant to the dielectric constant
at interfaces ε . Thus, we discuss this issue of ε from the microscopic viewpoint in
Sect. 5.3.
In the following discussion, molecular polarization is represented with the
polarizability α and dipole μ of constituent molecules in a general manner. The
effect of local field can be described with polarizable MD simulations in general,
irrespective of the modeling method of polarization. To implement the present
theory in practical MD simulation, however, one has to resort to a certain kind of
polarizable molecular model. There are a number of kinds of polarizable models,
such as the point dipole [1, 2, 11], fluctuating charge [8, 10, 13], and Drude
oscillator [5, 14, 15], which have their respective ways to represent the electronic
polarization of molecules. The following theory of local field captures the essential
mechanism of polarization interactions and is applicable to the various polarizable
model, though slight modifications may be required for some models to represent
the polarization properties. We present an example of the Charge Response Kernel
(CRK) model in Sect. 6.4.
5.1 Local Field Correction Factor
Self-consistent polarization We discuss the polarization at an arbitrary microscopic configuration of molecules in the interface system. Let us suppose that the
i-th molecule is located at r(i) at an instantaneous moment, whose permanent
dipole moment vector and polarizability tensor are denoted by μ 0 (i) and α(i),
respectively. The polarization of molecules interact each other, and consequently
the total (permanent + induced) dipole moment of the i-th molecule μ(i) and the
electric field at the i-th molecule E(i) are determined in the following form,
μ p (i) = μ
0
p (i) +
x−z
q
α pq (i)E q (i),
(5.1)
E p (i) = E
0
p (i) −
j ( =i)
x−z
q
T pq (ij )μ q (j ),
(5.2)
5 Molecular Theory of Local Field
medium [3]. Such classical models deal with the homogeneous bulk medium as
a dielectric continuum. In the inhomogeneous environment of interface, however,
the local field is more complicated than that in the homogeneous medium, and
the theory of dielectric continuum model should become less reliable. Here we
discuss the local field effect at the interface fully from a molecular point of view
[6, 7]. The microscopic theory of local field can accurately describe the effects of
polarization coupling in arbitrary environment, and is straightforwardly applicable
to MD simulation.
In Sect. 5.1 we formulate the general microscopic expressions of dipole moment
and polarizability for the interface system. In Sect. 5.2 these expressions are applied
to the nonlinear susceptibility χ (2) with fully incorporating the local field effect. The
local field effect in inhomogeneous environment is relevant to the dielectric constant
at interfaces ε . Thus, we discuss this issue of ε from the microscopic viewpoint in
Sect. 5.3.
In the following discussion, molecular polarization is represented with the
polarizability α and dipole μ of constituent molecules in a general manner. The
effect of local field can be described with polarizable MD simulations in general,
irrespective of the modeling method of polarization. To implement the present
theory in practical MD simulation, however, one has to resort to a certain kind of
polarizable molecular model. There are a number of kinds of polarizable models,
such as the point dipole [1, 2, 11], fluctuating charge [8, 10, 13], and Drude
oscillator [5, 14, 15], which have their respective ways to represent the electronic
polarization of molecules. The following theory of local field captures the essential
mechanism of polarization interactions and is applicable to the various polarizable
model, though slight modifications may be required for some models to represent
the polarization properties. We present an example of the Charge Response Kernel
(CRK) model in Sect. 6.4.
5.1 Local Field Correction Factor
Self-consistent polarization We discuss the polarization at an arbitrary microscopic configuration of molecules in the interface system. Let us suppose that the
i-th molecule is located at r(i) at an instantaneous moment, whose permanent
dipole moment vector and polarizability tensor are denoted by μ 0 (i) and α(i),
respectively. The polarization of molecules interact each other, and consequently
the total (permanent + induced) dipole moment of the i-th molecule μ(i) and the
electric field at the i-th molecule E(i) are determined in the following form,
μ p (i) = μ
0
p (i) +
x−z
q
α pq (i)E q (i),
(5.1)
E p (i) = E
0
p (i) −
j ( =i)
x−z
q
T pq (ij )μ q (j ),
(5.2)