Photoinduced absorption and nonlinear optical properties
of disubstituted polyacetylenes: Theory
Alok Shukla ∗ , Priya Sony
Physics Department, Indian Institute of Technology, Powai, Mumbai 400076, India
Abstract
In this paper, we summarize results of our recent large-scale correlated calculations of nonlinear optical spectra and photoinduced absorption
(PA) spectra of phenyl-disubstituted polyacetylenes (PDPA). Calculations were performed on oligomers of PDPA’s using correlated-electron
Pariser–Parr–Pople (P–P–P) model and configuration interaction (CI) methodology. Computed PA spectra are compared with the recent experiments
of Korovyanko et al., and good agreement is obtained between the two.
Keywords: Semi-empirical models and model calculations; Organic semiconductors based on conjugated molecules; Other conjugated and/or conducting polymers
1. Introduction
Recently discovered conjugated polymer phenyl-disubstituted polyacetylenes (PDPA) [1] exhibits interesting optical
properties such as laser action and photoluminescence (PL) with
large quantum efficiency [2]. Observation of PL in these materials was considered counter-intuitive because of their structural similarities to trans-polyacetylene (t-PA). Since these early
works, a number of experimental studies of the optical properties of PDPA’s have been performed [3,4], including the recent
measurement of photoinduced absorption (PA) spectra of this
polymer [5].
Earlier we had theoretically studied the linear optical properties of this material, and explained its PL in terms of reduced
correlation effects, as compared to t-PA, caused by substitution
of the phenyl rings in place of the side hydrogen atoms [6,7].
However, one of the major limitations of the linear optics is that
in centro-symmetric materials such as PDPA’s, it can connect the
1Ag ground state only to the Bu type excited states, as per dipole
selection rules. Therefore, in order to probe the Ag type excited
states, and higher energy Bu type excited states, it is necessary
to resort to either nonlinear spectroscopies such as the thirdharmonic generation (THG), two-photon absorption (TPA), or
a excited state spectroscopy such as the PA. It is with this aim
in mind, recently, we performed theoretical studies of the TPA
[8], THG [9] and the PA spectra [10] of oligomers of PDPA’s. In
case of our theoretical PA spectra, we obtained good agreement
with the recent experiments of Korovyanko et al. [5], and were
able to explain several peaks of the spectra in terms of important
excited states of the material. In this paper, we present a unified
review of these recent works of ours [8–10].
2. Theory
The unit cell of PDPA oligomers considered in this work is
presented in Fig. 1. Ground state geometry of PDPA’s, to the best
of our knowledge, is still unknown. However, from a chemical
point of view, it is intuitively clear that the steric hindrance would
cause a rotation of the side phenyl rings so that they would no
longer be co-planar with the polyene backbone of the polymer.
The extent of this rotation is also unknown, however, in our
previous works [6,7], we argued that the steric hindrance effects
can be taken into account by assuming that the phenyl rings of
the unit cell are rotated with respect to the y-axis by 30◦ in such
a manner that the oligomers still have inversion symmetry. In
the following, we will adopt the notation PDPA-n to denote a
PDPA oligomer containing n unit cells of the type depicted in
Fig. 1.
The correlated calculations on oligo-PDPA’s were performed
using the Pariser–Parr–Pople (P–P–P) model Hamiltonian:
H = HC + HP + HCP + Hee ,
(1)
369
where κi,j,M,N depicts the dielectric constant of the system which
can simulate the effects of screening, U the on-site repulsion
term and Ri,j is the distance in Å between the ith carbon and the
jth carbon. For Coulomb parameters, we chose the “screened
parameters” of Chandross et al. [11] with values U = 8.0 eV and
κi,i,M,M = 1.0, and κi,j,M,N = 2.0. For hopping matrix elements,
we used t0 = 2.4 eV, t⊥ = 1.4 eV, and t = 0.168 eV. For performing many-body calculations, we used the multi-reference
singles–doubles CI (MRSDCI) method, details pertaining to
which can be found in our earlier works [7–9]. Both longitudinal
(3) ) and transverse (χ(3) ) components corresponding to the
(χxxxx
yyyy
TPA and THG spectra were computed using the sum-over-states
method.
3. Calculation and results
Fig. 1. The unit cell of PDPA. The phenyl rings are rotated with respect to the
y-axis, which is transverse to the axis of the polyene backbone (x-axis).
where HC and HP are the one-electron Hamiltonians for the carbon atoms located on the trans-polyacetylene backbone (chain),
and the phenyl groups, respectively, and HCP is the one-electron
hopping between the chain and the phenyl units. The individual
terms can now be written as:
HC = −
(t0 − (−1)M t)Bk,k ;M,M+1 ,
(2a)
k,k ,M
HP = −t0
Bµ,ν;M,M ,
(2b)
µ,ν,M
and
HCP = −t⊥
Bk,µ,;M,M .
(2c)
k,µ,M
Next, we present the results of our MRSDCI calculations performed on oligomer PDPA-5. Choice of the PDPA-5 was due to
the fact that in both thin film and solution based experimental
samples of PDPA, the mean conjugation length is believed to be
between five to seven repeat units [4]. In Figs. 2–5, we present,
respectively, the TPA, the THG and the PA spectra from the
1Bu and the 2Ag excited states. From the selection rules, it is
obvious that in the TPA and 1Bu –PA spectra only Ag type states
contribute, in 2Ag –PA spectrum only Bu -type states contribute,
while in the THG spectrum both the Ag and the Bu excited states
contribute. It is widely believed that the nonlinear optical (NLO)
properties of conjugated polymers can be described in terms of a
small number excited states called “essential states” [12]. These
states consist of 1Bu , mAg and nBu states (m and n are generic
integers) and make strong contributions to the TPA (mAg ) and
THG (1Bu , mAg , nBu ) spectra. For the case of polyenes, mAg has
strong coupling to the 1Bu state, while nBu has strong coupling
to the mAg state [12]. Thus, one would expect that in polyenes
mAg will also lead to a strong peak in the 1Bu –PA spectrum.
Consistent with the essential state mechanism, it is clear from
In the equation above, k, k are carbon atoms on the polyene
backbone, µ, ν the carbon atoms located on the phenyl groups,
M a unit consisting of a phenyl group and a polyene carbon, · · ·
†
implies nearest neighbors and Bi,j;M,M = σ (ci,M,σ cj,M ,σ +
h.c.). Matrix elements t0 , and t⊥ depict one-electron hops.
In HC , t is the bond alternation parameter arising due to
electron–phonon coupling. In HCP , the sum over µ is restricted
to atoms of the phenyl groups that are directly bonded to backbone carbon atoms. Hee depicts the electron–electron repulsion
and can be written as:
1
Hee = U
ni↑ ni↓ +
Vi,j (ni − 1)(nj − 1),
(3)
2
i
i=j
where i and j represent all the atoms of the oligomer. The
Coulomb interactions are parameterized according to the Ohno
relationship:
Vi,j =
U
1/2
(1 + 0.6117R2i,j ) ,
κi,j
(4)
(3)
Fig. 2. Comparison of imaginary parts of χxxxx (−ω; ω, −ω, ω) (solid lines) and
(3)
χyyyy (−ω; ω, −ω, ω) (dashed lines) of PDPA-5 computed using the screened
parameters and the MRSDCI method. A linewidth of 0.05 eV was assumed for
all the levels.
370
(3)
3. Comparison of χxxxx (−3ω; ω, ω, ω) (solid lines) and
(3)
χyyyy (−3ω; ω, ω, ω) (dashed lines) of PDPA-5 computed using the
Fig.
screened parameters and the MRSDCI method. A linewidth of 0.05 eV was
assumed for all the levels.
the figures that the mAg state leads to strong peaks in the longitudincal components of the TPA and THG spectra, as well
as to the 1Bu –PA spectra, consistent with the observation that
the low-lying excitations in oligo-PDPA’s are essentially based
on the polyene backbone. In polyenes nBu state does not couple strongly to the 2Ag state, and therefore, will be invisible
in their 2Ag –PA spectra. However, in oligo-PDPA’s it couples
rather strongly to the 2Ag state leading to the most intense peak
in their 2Ag –PA spectra. We also note that the 2Ag state contributes a rather strong peak in the longitudinal THG spectrum
of PDPA’s, which is quite unlike the case of polyenes where it
does not contribute at all.
Additionally, we notice from the figures that the essential
states contributing to transverse components of the TPA and
THG spectra my Ag and ky Ag , corresponding to interaction of ypolarized photons, are distinct and are placed at higher energies
as compared to their longitudinal counterparts. In the experimental PA spectra of oligo-PDPA’s, Korovyanko et al. obtained
two features namely PA1 (1.1–1.2 eV) and PA2 (2.0 eV) in
1Bu –PA spectra, and only one prominent feature PAg (1.7 eV)
in the 2Ag –PA spectra. Upon comparing Fig. 4 to the experimental spectrum [5], we identify the mAg state of PDPA-5
located at 1.19 eV with the experimental feature PA1. We predict that the PA1 transition will basically correspond to an
x-polarized photon. Regarding the PA2 feature, we have two possible candidates—my Ag (1.72 eV) and kAg (2.17 eV). Our calculations predict my Ag to have mixed polarization with stronger
y-component, while kAg will be mainly x-polarized. Upon comparing the experimental 2Ag –PA spectrum with Fig. 5, we conclude that the first peak corresponding to the nBu state (1.59 eV)
is a very good description of feature PAg . We predict this feature to be x-polarized. For a discussion of the many-particle wave
functions of all these excited states, we refer the reader to our
recent works [8–10].
4. Conclusions and future directions
Fig. 4. PA spectrum of PDPA-5 from its 1Bu state, computed using the MRSDCI
method. Only the peaks in the experimental energy region have been labeled. A
linewidth of 0.15 eV was assumed.
In conclusion, we have presented calculations of the TPA,
THG, and PA spectra of oligo-PDPA’s and analyzed them in light
of essential state mechanism. Since, no experimental results on
the TPA and THG spectra of these materials exist, our results
could be tested in future experiments. On the other hand, our
results on the PA spectra are found to be in very good quantitative
agreement with the experimental results. These could be put to
an even more stringent test in which the PA-spectra is measured
on the oriented samples, and compared with our predictions on
the polarization of the photons absorbed.
Acknowledgement
This work, in part, was supported by the DST (Government
of India) grant SP/S2/M-10/2000.
References
Fig. 5. PA spectrum of PDPA-5 from its 2Ag excited state, computed using the
MRSDCI method. A linewidth of 0.15 eV was assumed.
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