Chapter 6
Charge Response Kernel for Electronic
Polarization
Abstract The charge response kernel (CRK) is a non-empirical and universal
method to represent polarization of molecules. It is particularly powerful to the
MD calculations of SFG spectroscopy. This chapter explains the CRK theory and
its application to polarizable MD simulation. The CRK is rigorously formulated as
a second-order derivative of electronic energy on the basis of electronic structure
theory, either the ab initio molecular orbital or density functional theory. The calculated CRK offers a general method of fluctuation charges to MD simulation, and also
represents the dipole, polarizability and second-order nonlinear susceptibility on the
same footing with equivalent accuracy to the underlying ab initio calculations.
Keywords Charge response kernel (CRK) · Electrostatic potential (ESP) charge ·
Coupled perturbed Hartree-Fock (CPHF) · Polarizable force field
This chapter deals with molecular modeling methods of A eff and M in Eq. (5.28)
for actual interface systems. To construct A eff and M from molecular simulation,
we need the molecular polarizability tensor α(j ) and dipole moment vector μ(j ).
These molecular properties should be defined at instantaneous configuration, as they
vary with molecular rotation and vibration. Since conventional force fields of MD
do not offer these properties, we need to evaluate them at each time step in addition
to the force field calculations. The modeling of α(j ) and μ(j ) is the heart of the SFG
calculation by MD simulation, and the reliability of the results critically depends on
the accuracy of this modeling. One straightforward method to describe them would
be to carry out direct electronic structure calculation of these quantities at each time
step of MD simulation like the ab initio MD simulation [4, 12, 14]. It could obviate
the modeling in principle, whereas the computational cost is substantially larger
than that of the usual ab initio MD simulation, since computation of polarizability
is more demanding than that of energy or force.
Here we present a general solution for the modeling of α(j ) and μ(j ) on
the basis of the charge response kernel (CRK) theory [3, 7, 9]. This theory
provides a universal method to describe molecular polarization from non-empirical
© 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_6
123
Charge Response Kernel for Electronic
Polarization
Abstract The charge response kernel (CRK) is a non-empirical and universal
method to represent polarization of molecules. It is particularly powerful to the
MD calculations of SFG spectroscopy. This chapter explains the CRK theory and
its application to polarizable MD simulation. The CRK is rigorously formulated as
a second-order derivative of electronic energy on the basis of electronic structure
theory, either the ab initio molecular orbital or density functional theory. The calculated CRK offers a general method of fluctuation charges to MD simulation, and also
represents the dipole, polarizability and second-order nonlinear susceptibility on the
same footing with equivalent accuracy to the underlying ab initio calculations.
Keywords Charge response kernel (CRK) · Electrostatic potential (ESP) charge ·
Coupled perturbed Hartree-Fock (CPHF) · Polarizable force field
This chapter deals with molecular modeling methods of A eff and M in Eq. (5.28)
for actual interface systems. To construct A eff and M from molecular simulation,
we need the molecular polarizability tensor α(j ) and dipole moment vector μ(j ).
These molecular properties should be defined at instantaneous configuration, as they
vary with molecular rotation and vibration. Since conventional force fields of MD
do not offer these properties, we need to evaluate them at each time step in addition
to the force field calculations. The modeling of α(j ) and μ(j ) is the heart of the SFG
calculation by MD simulation, and the reliability of the results critically depends on
the accuracy of this modeling. One straightforward method to describe them would
be to carry out direct electronic structure calculation of these quantities at each time
step of MD simulation like the ab initio MD simulation [4, 12, 14]. It could obviate
the modeling in principle, whereas the computational cost is substantially larger
than that of the usual ab initio MD simulation, since computation of polarizability
is more demanding than that of energy or force.
Here we present a general solution for the modeling of α(j ) and μ(j ) on
the basis of the charge response kernel (CRK) theory [3, 7, 9]. This theory
provides a universal method to describe molecular polarization from non-empirical
© 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_6
123