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Molecular Simulation
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Quantum mechanical modelling and calculation of two-photon absorption properties of new class 'Λ'-shaped conjugated molecules Zhong Hua; Wei Wangb; Vedbar Singh Khadkaa; David W. Galipeaua; Xingzhong Yana a Applied Photovoltaic Center, The College of Engineering, South Dakota State University, Brookings, SD, USA b Department of Mechanical Engineering, Binghamton University, State University of New York, Binghamton, NY, USA Online publication date: 05 May 2011
To cite this Article Hu, Zhong , Wang, Wei , Khadka, Vedbar Singh , Galipeau, David W. and Yan, Xingzhong(2011)
'Quantum mechanical modelling and calculation of two-photon absorption properties of new class 'Λ'-shaped conjugated molecules', Molecular Simulation, 37: 6, 431 — 439 To link to this Article: DOI: 10.1080/08927022.2010.550287 URL: http://dx.doi.org/10.1080/08927022.2010.550287
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Molecular Simulation Vol. 37, No. 6, May 2011, 431–439
Quantum mechanical modelling and calculation of two-photon absorption properties of new class ‘L’-shaped conjugated molecules Zhong Hua*, Wei Wangb, Vedbar Singh Khadkaa, David W. Galipeaua and Xingzhong Yana a
Applied Photovoltaic Center, The College of Engineering, South Dakota State University, Brookings, SD 57007, USA; bDepartment of Mechanical Engineering, Binghamton University, State University of New York, Binghamton, NY 13902, USA
Downloaded By: [Hu, Zhong][South Dakota State University] At: 19:31 10 May 2011
(Received 7 October 2010; final version received 15 December 2010) Organic material with high intensity of two-photon absorption (TPA)-induced fluorescence can be used as the up-converter material for photovoltaic devices. In this work, quantum mechanics modelling techniques were applied to theoretically investigate one- and two-photon absorption properties of new ‘L’-shaped conjugated molecules. Fluorene and diphenylmethylene analogues as the p centres were chosen for building the p-conjugated bridges to connect the two types of strong electron donors, N,N-diphenylamino and carbazole groups. In these molecular structures, cyano and ketone groups were also selected to modify the p centres as electron acceptors. The TPA cross sections of these derivatives were calculated using two-state, three-state and sum-over-state models, respectively. Geometrical structures of these molecules were optimised using Hartree– Fock theory, and properties of excited states of these molecules were obtained based on configuration interaction with single excitations method. The effects of donor, acceptor and p centre on the TPA behaviours of these designed molecules were investigated. Several of these molecules have attractive TPA properties, which may have potential for photovoltaic device applications. Keywords: two-photon absorption; frequency up-conversion; organic conjugated materials; quantum mechanics modelling; donor and acceptor
1. Introduction Recently, frequency up-converted emission has been utilised for improving the conversion efficiency of conventional solar cells [1 –4]. Frequency up-converted emission, the so-called up-conversion, is a physical process in which incident photons with low energies can be converted into photons with higher energies. Thus, the sub-band gap photons, which are transmitted by a conventional solar cell, maybe converted to photons with the energies above the band gap via the up-conversion process. Two-photon absorption (TPA)-induced emission is one of the mechanisms in up-conversion. The phenomenon of TPA was theoretically predicted by Go¨ppert-Mayer [5] and experimentally observed by Kaiser and Garrett [6]. The TPA is a nonlinear optical process, which involves the simultaneous absorption of two photons [7]. Today, organic materials with large TPA cross section have attracted great attention in a number of applications including frequency up-conversion lasing [8,9], 3D microfabrication [10 –12] and 3D optical data storage [13,14]. Organic materials with large TPA cross sections have the potential application in up converters for solar cells as well. The up converters will introduce efficient photon management, and carry out frequency up conversion of low-energy photons towards higher energy ones over the band gap of the photovoltaic materials in
*Corresponding author. Email:
[email protected] ISSN 0892-7022 print/ISSN 1029-0435 online q 2011 Taylor & Francis DOI: 10.1080/08927022.2010.550287 http://www.informaworld.com
solar cells. Obviously, cell efficiency will be expected if organic up-converter materials with large TPA cross section are applied to existing solar cell technologies. As a nonlinear optical behaviour, TPA properties are studied theoretically and experimentally in many organic molecules including dendrimers [15 –19]. It is noted that the value of TPA cross section (s) determines the TPA properties and highly depends on the molecular structures. Organic molecules with various electron donor (D) and electron acceptor (A) attached symmetrically or asymmetrically to a conjugated bridge (p centre) are possible to have large s values [20]. For example, a series of organic molecules with different electron donor and acceptor combinations attached to a trans-stilbene type of p centre have shown effects from the symmetry, the strength of electron donors and acceptors, as well as the conjugation lengths of the molecules [20,21]. Meanwhile, the crucial effect of p centre on the TPA properties was also observed for the TPA molecules. For instance, the dithienothiophene p centre plays an important role in the new TPA chromophores [22]. There is possible structure-to-property relation for molecular TPA. Varying D or A end groups, varying p-conjugated centre and varying effective conjugated length were proved to be efficient ways for the design of molecules with large TPA cross section [23,24]. In the last decade, molecules with extending
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432 Z. Hu et al. conjugated electronic structures from one to two or even three dimensions have been tested with high-TPA activity. For example, linear quadrupolar molecules and octupolar multi-branched (dendritic) structures have been the focus over recent years, and largest TPA s values (even access , 10,000 GM) were found in symmetric and multi-branched p electron conjugation framework [25,26]. Enhancements were observed for the dendron from the electronic effects of the structures. It is disclosed that organic molecule compounds with high-efficiency multiphoton absorption properties generally include a bridge of p -conjugated bonds connecting electron donor groups or electron acceptor groups. However, it is unclear about what kind of functional groups or linkages is appropriate for having a large TPA cross section. In this work, a new group of organic molecules is studied. Since fluorene- or diphenylmethylene-based compounds possess some general peculiarities in TPA processes due to their one- and two-photon fluorescence anisotropy and low dielectric constant [27,28], they are used as p-conjugated bridges to connect the electron donor and electron acceptor. N,Ndiphenylamino- or carbazole-based groups, as effective electron donor groups through electropolymerisation and electro-optic poled properties, are used as donors [29,30]. Cyano- or ketone-based groups, due to the enhancement of the electron affinities, are used as acceptors [31,32]. The new group of organic molecules forms quadrupolar ‘L’-shaped structures, which possess certain permanent dipole momentum and C2V symmetry. The motivation of this work stems from that molecular TPA is very promising for light harvesting of near-infrared photons in solar cells. Quantum mechanics calculations are expected to develop new structure–property relations in these specific structures and provide information for the design of up-converter materials.
2. Theory 2.1 TPA process TPA is a nonlinear optical phenomenon. A simplified TPA process is shown in Figure 1. TPA occurs in two ways. The electron of a molecule can be excited from
(a)
(b) f
hU2
hU1
Virtual level hU1 + hU2 0
Figure 1.
f
hU2
TPA process.
i
ground state j0l to excited state j f l (final state) by the simultaneous absorption of two photons via a virtual level (as shown in Figure 1(a)) [7,33]. The so-called virtual level is not real intermediate level, its existence is allowed by quantum mechanics [33,34]. The excited state can also be reached by stepwise TPA [7,33], which includes two distinctive one-photon absorption processes (as shown in Figure 1(b)). The electron is firstly excited from the ground state to a real intermediate state jil by the absorption of one photon with an energy of hn1 , and then it is excited from this intermediate state to final state by the absorption of another photon with an energy of hn2 . Such a nonlinear process is related to the second hyperpolarisability of the molecule.
2.2 Polarisabilities and hyperpolarisabilities The electronic and structural properties of a molecule are influenced if the molecule is exposed to an electric field. The changes of these properties can be quantified by the changes of the dipole moment of the molecule [35,36]. When a static (direct current, DC) field is applied to a molecule, this dipole moment can be written in the terms of a Taylor series [35,37], X X X mi ¼ mð0Þ aij Ej þ bijk Ej Ek þ gijkl Ej Ek El þ · · ·; i þ j
jk
jkl
ð1Þ where the field and the dipole moment are described in the vector representation, ~ ¼ ðEx ; Ey ; Ez Þ; E
m~ ¼ ðmx ; my ; mz Þ:
ð2Þ
In Equation (1), mð0Þ is the static dipole moment i independent of external field. The coefficient a is the molecular linear polarisability, and b and g are the molecular nonlinear polarisabilities which are also called the first hyperpolarisability and the second hyperpolarisability, respectively. The hyperpolarisabilities are important to quantify the response ability of the molecule, when it is exposed to an external electric field. Here, the indices i, j, k, l correspond to the molecular coordinates (i.e. x, y, z). Equation (1) becomes frequency dependent, when the static DC field is replaced by the alternating current (AC) field [35], X mi ðv0 Þ ¼ mð0Þ aij ðv0 ; vj ÞEj ðvj Þ i ðv0 Þ þ þ
X
j
bijk ðv0 ; vj ; vk ÞEj ðvj ÞEk ðvk Þ
jk
hU1 hU1 + hU2 0
þ
X
gijkl ðv0 ; vj ; vk ; vl ÞEj ðvj ÞEk ðvk ÞEl ðvl Þ
jkl
þ · · ·:
ð3Þ
Molecular Simulation 433 For macroscopic system, the polarisation instead of the dipole moment is used to describe the response of a molecule within an electric field [35,37,38], X ð1Þ Pi ðv0 Þ ¼ Pð0Þ xij ðv0 ; vj ÞEj ðvj Þ i ðv0 Þ þ þ
X
þ
X
j
xð2Þ ijk ðv0 ; vj ; vk ÞE j ðvj ÞEk ðvk Þ
jk
xð3Þ ijkl ðv0 ; vj ; vk ; vl ÞE j ðvj ÞEk ðvk ÞE l ðvl Þ þ · · ·;
jkl
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ð4Þ where P ð0Þ is the permanent polarisation independent of the field and x is the susceptibilities. x ð1Þ is the linear optical susceptibility, x ð2Þ is the second-order nonlinear optical susceptibility and x ð3Þ is the third-order nonlinear optical susceptibility. The (hyper-)polarisability describes the response of molecular system per molecule, whereas the susceptibilities describe the response per volume unit. The second hyperpolarisability can be used to calculate the TPA cross section of molecule.
2.3 TPA cross section The efficiency of the TPA process can be characterised by the TPA cross section [7,20,21,34,39]. The TPA cross section is related to the imaginary part of the third-order susceptibility (or the second hyperpolarisability), through [21,40 – 42]
s¼
8p 2 " v 2 8p 2 "v 2 Imðx ð3Þ Þ ¼ ImðgÞ; 2 2 n c N n 2c 2
ð5Þ
where " is the Planck constant divided by 2p; v is the frequency of photon; n is the refractive index; c is the speed of light and N is the number density of molecules. By considering a power expansion of the energy with respect to the applied field, the sum-over-state (SOS) expression used to evaluate the Cartesian components of gijkl is given by [42 –45]
gijkl ð2vs ; v1 ; v2 ; v3 Þ ¼
polarisation response frequency; v1 , v2 and v3 indicate the frequencies of the perturbing radiation fields (considering the degenerate TPA, v1 ¼ v2 ¼ v and v3 ¼ 2v), i, j, k and l correspond to the molecular axes x, y and z; m, n and p denote excited states and 0, the ground state. mj is the j(x, y, z)th component of the dipole operator kmjmj jnl ¼ kmjmj jnl 2 kojmj jolÞ; ðh=2pÞvmo is the transition energy between the m and o states. Gmo is the damping factor of the excited state m. The TPA cross section can be obtained by evaluating the two-photon transition matrix elements Sab as well. They are defined as [20,46,47], Sab ¼
Xh0jm a jii ijm b j f i
DEi
h0jm b ji hijm a j f i þ ; DEi
where DEi ¼ "vi 2 "vf =2, m a and m b are the Cartesian components of the dipole moment operator m and a; b [ ðx; y; zÞ. The summation runs over all the intermediate states jil, the ground state j0l and the final state j f l. The TPA cross section that is directly comparable with the experiments is defined as [20,40,47]
stp ¼
4p 2 a50 a v 2 L 4 dtp ; 15c Gf n 2
ð8Þ
where a0 is the Bohr radius; a is the fine structure constant; Gf is the lifetime broadening of the final state, which can be commonly assumed to be 0.1 eV, corresponding to a lifetime of a few femtoseconds. L is the Lorentz field factor and n is the refractive index. The unit of stp is GM (1 GM ¼ 10250 cm4 s mol21 photon21). dtp is the TPA probability. In addition to the SOS Equation (6) used to obtain the two-photon transition matrix element, a simplified approach called few-state model [20,25,48,49], including two-state and three-state models, can be used to calculate two-photon transition matrix elements of some special molecular systems. For asymmetrical charge-transfer molecules with donor–acceptor pattern [49], a two-state
4p 3 Pði; j; k; l; 2vs ; v1 ; v2 ; v3 Þ 3h"3 XXX hojmi jmihmjmj jn hnjmk j pih pjml joi £ ðvmo 2 vs 2 iGm0 Þðvno 2 v2 2 v3 2 iGn0 Þðvpo 2 v3 2 iGp0 Þ m–0 n–0 p–0 # XX hojmi jmihmjmj jo hojmk jnihnjml joi 2 ; ðvmo 2 vs 2 iGm0 Þðvno 2 v3 2 iGn0 Þðvno þ v2 2 iGn0 Þ m–0 n–0
where Pði; j; k; l; 2vs ; v1 ; v2 ; v3 Þ is a permutation operator defined in such a way that for any permutation of ði; j; k; lÞ, an equivalent permutation of ð2vs ; v1 ; v2 ; v3 Þ is made simultaneously. vs ¼ v1 þ v2 þ v3 is the
ð7Þ
ð6Þ
model, which includes only the ground state and the final state, can be used to describe the TPA behaviour of molecules. The TPA cross section of 1D molecules is completely dominated by the component along the
434 Z. Hu et al.
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molecular axis Sxx [20]. In this case, the SOS Equation (6) can be simplified to ff 00 2m0f x mx 2 mx ; ð9Þ Sxx ¼ DE where m0f x is the transition dipole moment between the ground state j0l and the final state j f l; mffx 2 m00 x is the dipole moment difference between the ground state and the final state; DE ¼ "vf 2 "vf =2 ¼ "vf =2. A three-state model, which includes the first lowest singlet states, appropriately describes the TPA of symmetric molecules. In this case, the SOS Equation (6) can be simplified to [20,49] 2m01 m1f 2m0f mffx 2 m00 x Sxx ¼ x x þ x ; ð10Þ DE2 DE1 where DE1 ¼ "v1 2 "vf =2 and DE2 ¼ "vf 2 "vf =2 ¼ "vf =2.
3.
Results and discussion
3.1 Molecule design Linear molecules with appropriate electron donor group and electron acceptor group attached symmetrically or asymmetrically to a p-conjugated linker (p centre) show large nonlinear optical response and large TPA cross section [21,23,24]. The electronic effects from electron donors, acceptors and p centres can significantly impact on the TPA behaviours. On this guiding line, fluorene (FR) and diphenylmethylene (BZ) analogues as the p centres were chosen for building the p-conjugated bridges to connect the two types of strong electron donors, N,Ndiphenylamino and carbazole groups (Figure 2). In these structures, cyano and ketone groups were also selected to modify the p centres as electron acceptors. The structures of the molecules based on the combinations of the proposed donors, acceptors and p centres were designed and studied (Figure 3). Thus, these structures show ‘L’ shapes with C2v symmetry. The designed molecules are denoted as BZ(I), BZ(II), BZ-K(I), BZ-K(II), BZ-DC(I), BZ-DC(II), FR(I), FR(II), FR-K(I), FR-K(II), FR-DC(I) and FR-DC(II), respectively.
3.2 Computational details The software package Gaussian 03W is used to calculate molecular electronic structure and properties throughout this theoretical work [50]. The geometric structure of each molecule was optimised at the Hartree –Fock (HF) level. Configuration interaction singlets (CIS) method was applied for investigating the important parameters of the excited states. These include excitation energies, transition dipole moments between the ground and excited states,
H
H
N
N
N, N-diphenylamino
Carbazole
Fluorene (FR)
Diphenylmethylene (BZ)
Donors
π centre
Acceptor
CN
O
Cyano
Ketone
Figure 2. Structures of p centres, electron donors and electron acceptors.
transition dipole moments between different excited states and the dipole moment difference between the ground and the excited states. All calculations were carried out by using the Gaussian 03W quantum chemistry program based on a basis set of 6-31 G(d). Two- and three-state models (Equations (9) and (10)), as well as SOS formula (Equation (7)) which involves the four lowest excited states, were applied for calculating the TPA cross section of each molecule.
3.3
HOMO, LUMO, energy gaps and charge transfer
The calculated energy eigenvalue of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) and the energy-gaps (the energy difference between HOMO and LUMO orbitals) of the designed molecules are listed in Table 1, in which the photons with the up-converted energy gap can be absorbed by most solar cells. The HOMO and LUMO orbital contour plots in Figure 4 show the charge transfer direction. From Figure 4, it can be clearly seen that molecules BZ-DC(II), BZ-DC(I), BZ-K(II), FR-DC(I), FR-DC(II) and FR-K(II) have significant difference of molecular orbital distributions between HOMO and LUMO. The molecular orbitals of HOMO are distributed mainly on donors or donors to linkers, and the molecular orbitals of LUMO are distributed mainly on p-centres or acceptor centres, so that the charges are transferred from donors to the centres with the aid of the bridge (linker). On the other hand, molecules BZ(II), BZ(I), FR(I) and FR(II) have much less difference of molecular orbital distributions between HOMO and LUMO. The HOMO and LUMO are distributed almost over the entire molecules, which gives no clear charge-transferring directions. Although quantum-chemical calculations show that the ground-state transition to the first excited-state transition is connected with the electron transfer between the HOMO and LUMO, as well as the TPA property, Figure 4 does not
Molecular Simulation 435 O
D
BZ
D D=
N
CN
NC
BZ-K
D
N , I;
, II
N
D= BZ(I), BZ(II)
D N
, I;
, II
D
BZ-DC
D D=
N
N
, I;
, II
B BZ-DC(I), BZ-DC(II)
Z-K(I), BZ-K(II)
NC
O
CN
X
X
X
X
X
X
FR
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FR-K
N
N X=
,I
X= , II
FR(I), FR(II)
Figure 3.
N
N X=
,I
,I , II
, II
FR-DC(I), FR-DC(II)
FR-K(I), FR-K(II),
Molecular structure of the D-p-D and D-A-D compounds.
give a quantitative representation, and detailed calculation should follow the equations listed above.
3.4
FR-DC N
N
Two-photon absorption
The TPA cross sections of the designed molecules are calculated using two-state, three-state and SOS models up to the fourth lowest excited state, respectively. The major results are listed in Table 2, including the excitation energy, E (eV), from the ground state to the current excited state up to the fourth excited state, the two-photon wavelength, ltp (nm), of the fundamental light which is twice the wavelength corresponding to the transition and the TPA cross section, stp (GM), of the four lowest excited states. The maximum TPA cross section of each compound corresponding to its wavelength is shown in Figure 5. The computed two-photon wavelengths, ltp, of the designed 12 molecules are in the range of 450– 650 nm, and they are falling into the visible part of the electromagnetic spectra. Thus, the emitted photons could be in the UV region (half of the wavelengths) which will not be absorbed by most of the existing solar cell. To find the TPA in near-IRconjugated molecules, further work on design strategy and structure –property relations needs to be done to be closer to the ultimate goal [51,52]. Since the compounds designed are all symmetric, the three-state model can primarily be used to describe the effects of the molecular structures on the TPA properties of the designed molecules, i.e. most of the calculations were involving the ground, the first excited and the second excited states, see the number in bold in the column of the TPA cross section, stp, in Table 2 [20].
3.4.1 Effects of conjugated length It is noticed that the increase in the conjugation length has an effect on the TPA cross section. The maximum TPA cross section of FR(I) compound is about 33.68 GM. By adding another two carbon– carbon double bonds into the bridge of FR(I), FR(II) is then formed. The maximum TPA cross section of FR(II) is about 45.61 GM, which is 35% larger than that of FR(I). Similarly, FR-K(II) has a maximum TPA cross section of 101.4 GM, which is 13% less than the value of 116.4 GM for FR-K(I). The maximum TPA cross section of FR-DC(II) is 186.3 GM, which is only about 40% of that of FR-DC(I) (312.2 GM). So, the increase in the conjugation length cannot promise the improvement of the TPA cross section of the molecules with a ‘L’ shape.
Table 1. Energy eigenvalue (Hartree) of HOMO and LUMO and energy gaps (eV) of designed molecules. Molecules
HOMO (Ha)
LUMO (Ha)
Energy-gap (eV)
BZ(I) BZ(II) BZ-K (I) BZ-K (II) BZ-DC (I) BZ-DC (II) FR (I) FR (II) FR-K (I) FR-K (II) FR-DC (I) FR-DC (II)
2 0.25176 2 0.27406 2 0.25844 2 0.27791 2 0.26052 2 0.27950 2 0.25245 2 0.25191 2 0.25826 2 0.25587 2 0.26181 2 0.25811
0.08472 0.07484 0.05422 0.04487 0.03158 0.02385 0.08405 0.07971 0.03640 0.03980 0.00336 0.00422
4.340 4.913 4.123 4.616 4.420 4.637 4.734 4.641 4.117 4.314 3.727 3.919
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436 Z. Hu et al.
HOMO of BZ(I)
LUMO of BZ(I)
HOMO of FR(I)
LUMO of FR(I)
HOMO of BZ(II)
LUMO of BZ(II)
HOMO of FR(II)
LUMO of FR(II)
HOMO of BZ-K(I)
LUMO of BZ-K(I)
HOMO of FR-K(I)
LUMO of FR-K(I)
HOMO of BZ-K(II)
LUMO of BZ-K(II)
HOMO of FR-K(II)
LUMO of FR-K(II)
HOMO of BZ-DC(I)
LUMO of BZ-DC(I)
HOMO of FR-DC(I)
LUMO of FR-DC(I)
HOMO of BZ-DC(II)
LUMO of BZ-DC(II)
HOMO of FR-DC(II)
LUMO of FR-DC(II)
Figure 4. HOMO and LUMO of designed molecules.
3.4.2
Effects of acceptor
BZ-K(I) and BZ-DC(I) are formed by adding the acceptor groups (ketone or cyano) into BZ(I). Similarly, BZ-K(II) and BZ-DC(II) are created by adding the acceptors into BZ(II). In Table 2, it is found that the maximum TPA cross sections of BZ(I), BZ-K(I) and BZ-DC(I) are 50.62, 107.4 and 330.2 GM, respectively, and that of BZ(II), BZ-K(II) and BZ-DC(II) are 1.725, 68.74 and 739.9 GM, respectively. In the same way, FR-K(I) and FR-DC(I) are formed by adding the acceptor groups (cyano or ketone) into FR(I), and similar FR-K(II) and FR-DC(II) are created by adding the acceptors into FR(II). These six molecules have the same trend, i.e. the molecules with cyano acceptor (BZ-DC(I), BZ-DC(II), FR-DC(I) and FR-DC(II)) have the highest TPA cross sections, and the molecules with ketone acceptor (BZ-K(I), BZ-K(II), FR-K(I) and FR-
K(II)) have relatively higher TPA cross sections. Therefore, cyano is a better acceptor among these 12 molecules. However, the molecules only have p-centres (fluorene or diphenylmethylene) have lowest TPA cross sections. Thus, for the designed molecules with a ‘L’ shape, the TPA cross sections of the ones with D-p-D structure can be enhanced by adding the acceptor groups into them. In other words, the TPA behaviours of these molecules can be improved by changing the D-p-D molecular structure to D-A-D structure.
3.4.3
Effects of donor
The effects of donor on the TPA behaviours of the designed molecules are analysed by comparing the TPA cross sections between BZ(I) and BZ(II), BZ-K(I) and
Molecular Simulation 437 Table 2. Calculated TPA cross sections stp (GM) of the four lowest excited states, together with the excitation energy from ground state E (eV), oscillator strength ( f) and the two-photon wavelength ltp (nm) of the fundamental light which is twice the wavelength corresponding to the transition.
BZ(I)
BZ(II)
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BZ-K(I)
BZ-K(II)
BZ-DC(I)
BZ-DC(II)
FR(I)
FR(II)
FR-K(I)
FR-K(II)
FR-DC(I)
FR-DC(II)
Excited state
E (eV)
f
ltp (nm)
stp (GM)a
1st 2nd 3rd 4th 1st 2nd 3rd 4th 1st 2nd 3rd 4th 1st 2nd 3rd 4th 1st 2nd 3rd 4th 1st 2nd 3rd 4th 1st 2nd 3rd 4th 1st 2nd 3rd 4th 1st 2nd 3rd 4th 1st 2nd 3rd 4th 1st 2nd 3rd 4th 1st 2nd 3rd 4th
4.340 4.555 5.542 5.543 4.913 5.146 5.579 5.580 4.123 4.251 4.410 5.497 4.616 4.739 5.021 5.583 4.420 4.457 5.274 5.609 4.637 4.683 5.562 5.585 4.734 4.916 5.491 5.683 4.641 4.737 5.505 5.706 4.117 4.317 4.719 4.828 4.314 4.325 4.676 4.681 3.727 4.209 4.571 5.144 3.919 4.411 4.562 4.901
2.464 1.102 0.021 0.061 2.600 0.819 0.063 0.023 2.579 0.232 1.002 0.002 0.027 2.725 0.808 0.085 2.638 1.447 0.001 0.008 1.344 2.537 0.058 0.081 1.963 1.315 0.606 0.001 2.024 2.310 0.252 0.198 0.707 0.000 1.414 1.717 0.000 0.498 1.760 2.681 0.475 1.871 1.749 0.095 0.173 2.950 2.045 0.225
571.4 544.3 447.4 447.3 504.8 481.9 444.4 444.3 601.4 583.4 562.3 451.1 537.2 523.2 493.8 444.2 561.0 556.3 470.1 442.1 534.8 529.6 445.8 444.0 523.8 504.4 451.6 436.3 534.3 523.4 450.5 434.6 602.3 574.4 525.5 513.6 574.8 573.4 530.3 529.7 665.3 589.1 542.4 482.1 632.7 562.2 543.6 506.0
10.23 50.62 0.023 3.497 0.567 1.725 0.133 0.636 107.4 17.31 98.23 2.934 0.380 8.635 68.74 0.373 92.00 330.2 3.496 56.18 11.74 134.8 739.9 1.391 5.060 33.68 5.948 16.17 10.16 45.61 3.408 27.71 16.01 0.011 116.4 48.09 0.001 11.06 7.955 101.4 49.79 312.2 175.4 124.9 18.34 186.3 105.6 18.91
BZ-DC(II)
600 σtp (GM)
Molecule
800
400 BZ-DC(I)
FR-DC(I)
FR-DC(II)
200 FR-K(I) FR-K(II) BZ-K(II) BZ(I) FR(II) FR(I) BZ(II)
0 425
475
525
BZ-K(I)
575
625
Wavelength (nm)
Figure 5. Maximum TPA cross sections of the studied molecules.
BZ-K(II), or between BZ-DC(I) and BZ-DC(II), respectively. In each pair of group, the molecules have the same centre and linker (bridge), only change the donors. From the simulation results, it indicates that the TPA cross section of the designed molecules can be enhanced by changing the electron donor, and the effects of the donor depends not only on the strength of the donor itself, but also on the combinations of the molecular linker and acceptor. So, both donor groups could be good candidates for having high-TPA cross section.
3.4.4
Effects of p centre
For compounds BZ(I) and FR(I) having the same donor but different p centres, the TPA cross sections are 50.62 and 33.68 GM, respectively. Similarly, for compounds BZK(I) and FR-K(I) having the same donor but different p centres, the TPA cross sections are 107.4 and 116.4 GM, respectively, and for BZ-DC(I) and FR-DC(I), 330.2 and 312.2 GM, respectively. These results indicate that these two different p centres have no significant impact on the TPA behaviour. The simulation results show that within the 12 designed molecules, BZ-DC(II) has the largest TPA cross section of 739.9 GM. The compounds FR-DC(I), BZ-DC(I) and BZ-DC(II) have more attractive TPA properties than others. Besides, the TPA behaviours of the designed molecules with D-A-D structure are more active than that of molecules with D-p-D structure. It is noticeable that the maximum TPA cross section of different molecules is obtained at different frequencies.
a
The TPA cross section of each molecule was calculated four times and has four TPA cross sections, see the last column, in which the first TPA cross-sectional value (stp) involves two states (ground state and first excited state) and was calculated by two-state model (Equation (9)), the second stp value involves three states (ground state, first excited state and the second excited state) and was calculated by threestate model (Equation (10)) and the third and fourth stp values involve three and four states, respectively, and were calculated by SOS model (Equation (7)). The maximum TPA cross sections stp values are in bold in the table.
4.
Conclusions
The nonlinear optical response properties of organic compounds, which can be potentially used as the up converter to enhance the efficiencies of solar cells, were modelled and theoretically investigated. Twelve new
Downloaded By: [Hu, Zhong][South Dakota State University] At: 19:31 10 May 2011
438 Z. Hu et al. organic molecules with ‘L’ shape were designed, and the relationships between the molecular structure and TPA behaviour were investigated. Different factors affecting the TPA behaviours of these compounds were studied. Ab initio quantum chemistry methods, such as HF and CIS, were used to study the TPA properties of the designed molecules. The TPA cross sections of the designed molecules were calculated based on the few-state and SOS models. For most of the designed molecules, it is found that the three-state model is very useful for describing the TPA behaviours and for qualitative analyses of the effects of donor, acceptor and conjugated bridge on the TPA cross sections of these molecules. However, for some molecules, the SOS model, which involves more excited states, should be employed to study the TPA behaviours. The TPA behaviours of molecules with D-A-D structure seem to be more active than that of the molecules with D-p-D structure. The molecular length has effects on the TPA behaviour of the molecule, while the increase in molecular length cannot promise the increase in TPA cross section. The p-conjugated bridges have great effects on the TPA cross sections of the designed molecules, and the effects of donor and acceptor on the TPA properties of all the molecules were also discussed. It was found that the compounds BZ-DC(II), BZ-DC(I), FR-DC(I) and FRDC(II) have attractive TPA properties which implies that cyano is a better acceptor among these 12 molecules. Further work on design strategy and structure –property relations needs to be done to modify the conjugated molecule structures with TPA in near-IR to be potentially used as the up-converter materials.
Acknowledgements This work was supported by the NSF/SD EPSCoR PANS Funds #0554609 and the State of South Dakota.
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