treated with classical electrodynamics, and then the field is input to a TDDFT
calculation for the particle.
In a later paper, this approach was extended to include a cluster of metal atoms to
describe the chemical effect in SERS with a separate calculation where classical
electrodynamics is used to describe electromagnetic enhancements, using what was
termed an overlay theory [16].
What is still missing in this previous work is a unified calculation that includes
both chemical and electromagnetic effects for large clusters. A reason for this is that
realistic cluster models of plasmonics are still quite limited. The present study is
therefore motivated by these earlier papers, as the ability of electronic structure
codes to describe silver clusters is crucial to the ultimate goal of including a cluster
of silver atoms in the QM/ED calculation.
Silverstein and Jensen have recently studied the effect of using long-range corrected density functionals on the spectra of Ag n (n = 4–20) [17]. For the smaller
clusters, coupled cluster calculations were also done to provide a higher level reference for comparison with the TDDFT results. Several functionals were considered,
and in general it was found that the corrected functionals give more accurate ionization potentials. The influence of these functionals on the absorption spectra of Ag 20
is more subtle, with only small improvements in the absorption spectra. This also
provides motivation for the present study, where we examine very simple functionals
to see if these might be adequate for the description of absorption spectra.
2 Methods
Time dependent density functional theory has been implemented in two different
ways; in the time domain referred to as real-time TDDFT (RT-TDDFT) and in the
frequency domain (FD-TDDFT). These two methods are equivalent in that they both
solve the time-dependent Kohn-Sham equations using a scheme proposed by Runge
and Gross [18]. However there are differences in their implementation in different
codes, as we show below, such that even the same functional and basis set can give
different results. Below we describe our implementation of these approaches where
we have considered both calculations that make the different codes as close as possible, and where we also consider unique capabilities of each code.
2.1 RT-TDDFT
RT-TDDFT has been implemented using the CP2K molecular simulation software
with pseudopotentials to simplify the electronic description [19]. These pseudopotentials account for 36 core electrons and the nuclear charge in each Ag atom,
thus the potentials are optimized for eleven valence electrons [20]. Two different
types of pseudopotentials were explored: a separable dual-space Gaussian
40
L.R. Madison et al.
calculation for the particle.
In a later paper, this approach was extended to include a cluster of metal atoms to
describe the chemical effect in SERS with a separate calculation where classical
electrodynamics is used to describe electromagnetic enhancements, using what was
termed an overlay theory [16].
What is still missing in this previous work is a unified calculation that includes
both chemical and electromagnetic effects for large clusters. A reason for this is that
realistic cluster models of plasmonics are still quite limited. The present study is
therefore motivated by these earlier papers, as the ability of electronic structure
codes to describe silver clusters is crucial to the ultimate goal of including a cluster
of silver atoms in the QM/ED calculation.
Silverstein and Jensen have recently studied the effect of using long-range corrected density functionals on the spectra of Ag n (n = 4–20) [17]. For the smaller
clusters, coupled cluster calculations were also done to provide a higher level reference for comparison with the TDDFT results. Several functionals were considered,
and in general it was found that the corrected functionals give more accurate ionization potentials. The influence of these functionals on the absorption spectra of Ag 20
is more subtle, with only small improvements in the absorption spectra. This also
provides motivation for the present study, where we examine very simple functionals
to see if these might be adequate for the description of absorption spectra.
2 Methods
Time dependent density functional theory has been implemented in two different
ways; in the time domain referred to as real-time TDDFT (RT-TDDFT) and in the
frequency domain (FD-TDDFT). These two methods are equivalent in that they both
solve the time-dependent Kohn-Sham equations using a scheme proposed by Runge
and Gross [18]. However there are differences in their implementation in different
codes, as we show below, such that even the same functional and basis set can give
different results. Below we describe our implementation of these approaches where
we have considered both calculations that make the different codes as close as possible, and where we also consider unique capabilities of each code.
2.1 RT-TDDFT
RT-TDDFT has been implemented using the CP2K molecular simulation software
with pseudopotentials to simplify the electronic description [19]. These pseudopotentials account for 36 core electrons and the nuclear charge in each Ag atom,
thus the potentials are optimized for eleven valence electrons [20]. Two different
types of pseudopotentials were explored: a separable dual-space Gaussian
40
L.R. Madison et al.