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Theoretical investigation on a series of heterocycle-based compounds with large two-photon absorption cross-sections
Journal of Molecular Structure: THEOCHEM 719 (2005) 207–212 www.elsevier.com/locate/theochem
Theoretical investigation on a series of heterocycle-based compounds with large two-photon absorption cross-sections Xiang-Biao Zhanga, Ji-Kang Fenga,b,*, Xin Zhoua, Ai-Min Rena a
State Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, Institute of Theoretical Chemistry, NO2 Liutiao Road, Changchun 230021, China b College of Chemistry, JiLin University, Changchun 130023, China Received 27 October 2004; revised 14 January 2005; accepted 2 February 2005
Abstract A series of heterocycle-based molecules using p-deficient (pyridinium) and p-excessive (pyrrole) heteroaromatic rings as acceptor and donor, respectively, have been designed and their two-photon absorption properties have been investigated theoretically by using the AM1 and ZINDO methods. On the basis of correct geometries and UV-VIS spectra, the positions and strengths of two-photon absorption of these molecules were reported. Our calculated results reveal that molecule F, which has the largest two-photon cross-section (2457.29! 10K50 cm4 s photonK1) among studied molecules, is a more promising two-photon absorption material. q 2005 Elsevier B.V. All rights reserved. Keywords: Two-photon absorption; AM1 and ZINDO methods; Heterocycle-based molecules
1. Introduction Presently, more and more theoretical predictions and experimental observations on the phenomenon of twophoton absorption (TPA) have been reported. It results from the fact that the molecules with large TPA crosssections d(u) can be exploited in a number of applications, such as upconverted lasing [1–3], optical power limiting [4–6], photodynamic therapy [7], and three-dimensional (3D) microfabrication [8–10]. Various design strategies have successfully been used to synthesize organic molecules with large TPA cross-sections. One strategy is to synthesize a variety of donor-conjugated bridge-acceptor (D–p–A), donor-conjugated bridge-donor (D–p–D) and acceptorconjugated bridge-acceptor (A–p–A) derivatives, in which * Corresponding author. Corresponding author. Address: State Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, Institute of Theoretical Chemistry, NO2 Liutiao Road, Changchun 230021, China. Tel.: C86 431 849 9856; fax: C86 431 894 5942. E-mail address: [email protected] (J.-K. Feng).
0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.02.001
increase of the donor strength, acceptor strength and the conjugation length of the molecules can improve TPA crosssections [11–15]. On the other hand, many researches have focused on octupolar, multi-branched or dendrimer molecules [16–22], whose TPA cross-sections can be significantly improved by the increased chromophore density of the molecules without causing any aggregation [23,24]. Abbotto et al. [25] have reported highly efficient heteroaromatic-based TPA dyes presenting a A–p–D–p– A, where A (p-acceptor) is a p-deficient heteroaromatic ring (pyridine, quinoline, benzothiazole), D (p-donor) a pexcessive pyrrolyl moiety and octupolar heterocyclic compounds having good TPA property [19,25–28]. In literature [19,25], they have described a heterocycle-based branched quasi-octupolar TPA dye, using p-deficient (pyridinium) and p-excessive (pyrrole) heteroaromatic rings as A and D units, respectively. This chromophore presents a very large TPA cross-section in the femtosecond regime. Comparison of the TPA cross-sections between the branched system and the corresponding ‘monomeric unit’ shows a strong cooperative enhancement. In order to obtain better heteroaromatic-based TPA chromophores, we designed molecules B–F on the basis of their works and performed CI calculations.
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2. Computational methods The TPA process corresponds to simultaneous absorption of two photons. The TPA efficiency of an organic molecule, at optical frequency u/2p, can be characterized by the TPA cross-section d(u). It can be directly related to the imaginary part of the second hyperpolarizability g(Ku; u, u, u) by Ref. [29] dðuÞ Z
3Zu2 4 L Im½gðKu; u; Ku; uÞ 2n2 c2 30
(1)
where Zu the energy of the incoming photons, c the speed of light, and 30 the vacuum electric permittivity. n denotes the refractive index of the medium and L corresponds to the local-field factor. In the calculations presented here, n, L are set to 1 (isolated molecule in vacuum). The sum-over-states (SOS) expression to evaluate the components of the second hyperpolarizability gabgd can be educed out using perturbation theory and density matrix method. By considering a power expansion of the energy with respect to the applied field, the gabgd Cartesian components are given by Refs. [30,31]:
The primes on the summation over the electronic states indicate exclusion of the ground state. GK is the damping factor of excited state K, and in the present work, all damping factors Gs are set 0.1 eV. To compare the calculated d value with experimental value measured in solution, the orientationally averaged (isotropic) value of g is evaluated, which is defined as: 1 X hgi Z i; j Z x; y; z (4) giijj C gijij C gijji 15 i;j In principle, any kind of self-consistent field molecular orbital procedure combined with configuration interaction (CI) can be used to calculate the physical values in the above expressions. In this paper, the AM1 [32] method was firstly used to calculate molecular equilibrium geometries. Then the properties of electronic excited states were obtained by single and double electronic excitation configuration interaction using ZINDO [33] program. Furthermore, onephoton absorption (OPA) parameters, which were need to predict TPA properties were provided. Then according to the formula (1)–(4), the second hyperpolarizabilities g and the TPA cross-sections d(u) were calculated.
gabgd ðKus ; u1 ; u2 ; u3 Þ Z ZK3
X
P1;2;3
X X X 0 0 0 K
L
M
h0jma jKihKjmb jLihLjmg jMihMjmd j0i ðuK K iGK =2 K us ÞðuL K iGL =2 K u2 K u3 ÞðuM K iGM =2 K u3 Þ
h0jmb jKihKjma jLihLjmg jMihMjmd j0i C ðuK C iGK =2 C u1 ÞðuL K iGL =2 K u2 K u3 ÞðuM K iGM =2 K u3 Þ h0jmb jKihKjmg jLihLjma jMihMjmd j0i C ðuK C iGK =2 C u1 ÞðuL C iGL =2 C u1 C u2 ÞðuM K iGM =2 K u3 Þ h0jmb jKihKjmg jLihLjmd jMihMjma j0i C ðuK C iGK =2 C u1 ÞðuL C iGL =2 C u1 C u2 ÞðuM C iGM =2 C us Þ X X h0jma jKihKjmb j0ih0jmg jLihLjmd j0i 0 0 K ðuK K iGK =2 K us ÞðuK K iGK =2 K u1 ÞðuL K iGL =2 K u3 Þ K L h0jma jKihKjmb j0ih0jmg jLihLjmd j0i ðuK K iGK =2 K u1 ÞðuL C iGL =2 C u2 ÞðuL K iGL =2 K u3 Þ h0jmb jKihKjma j0ih0jmg jLihLjmd j0i C ðuK C iGK =2 C u1 ÞðuK C iGK =2 C us ÞðuL C iGL =2 C u2 Þ h0jmb jKihKjma j0ih0jmg jLihLjmd j0i C ðuK C iGK =2 C u1 ÞðuL C iGL =2 C u2 ÞðuL K iGL =2 K u3 Þ C
In this formula a, b, g and d refer to the molecular axes; u1, u2 and u3 are optical frequencies and usZu1Cu2Cu3 is the polarization response frequency; SP1,2,3 indicates a sum over the terms obtained by the six permutations of the pairs (u1/mb), (u2/mg) and (u3/md); K, L, and M denote excited states and 0, the ground state; jKi is an electronic wavefunction with energy Zuk relative to the ground electronic state; ma is the ath (Zx, y, z) component of the dipole operator hKjma jLi Z hKjma jLi K h0jma j0i
(3)
ð2Þ
3. Results and discussion 3.1. Structural design and geometry optimization In order to obtain better TPA materials, introducing amido groups into molecule A (have been synthesized) [19] and replacing the center of A by pyrylium, we have built molecules B–F (as shown in Fig. 1). Using AM1 method, the geometries of molecules were optimized. For A–D, because of the effect of methyl in
X.-B. Zhang et al. / Journal of Molecular Structure: THEOCHEM 719 (2005) 207–212
A
B
H2N
H3C N
H3C N
CH3
N N
CH3
N
N
CH3 H2N
CH3
C
CH3
H3C N
CH 3
N
NH2
CH3
NH2 N
N
CH 3 NH 2
H2N
CH3
E
F
N
CH3
N
CH 3
H 2N
H 3C N
H 3C N
CH 3 O
NH2
CH3
N
H 3C N
N
N
D
NH 2
H 2N
209
CH 3 O
N
N
H 2N
CH 3
N
NH 2
N CH 3
Fig. 1. The molecular structures of studied compounds.
pyridinium on molecular structure, two branches at the side of it and pyridinium are not in the same plane; the arm that faces to it and molecular center are coplanar only for A, for B–D, the sort of coplanarity was broken to some extent due to barrier between methyl and amido group in the pyrrole. The molecules E and F have a good coplanarity except methyls and amido groups in molecular structure.
using the ZINDO method. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energies as well as energy gaps between them (DEg) for molecules A–F were summarized in Table 1. One can find that the order of energy gaps: AOEODOCO BOF. 3.3. One-photon absorption
3.2. Electronic structure On the basis of equilibrium geometries optimized by AM1, we calculated the electronic structures of molecules
In order to obtain OPA property, we used the ZINDO program to calculate CI on the basis of equilibrium geometries optimized by AM1 method. The CI calculations
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Table 1 Energies of the HOMO and LUMO for A–F and their energy gaps (DEg, ev)
LUMO HOMO DEg
A
B
C
D
E
F
K0.149266 K0.348493 0.199227
K0.138507 K0.324594 0.186087
K0.149201 K0.336758 0.187557
K0.140241 K0.334951 0.194710
K0.151688 K0.347289 0.195601
K0.137926 K0.323241 0.185315
include 196 singly (SCI) and 54 doubly (DCI) excited configurations, a total of 251 configurations including the ground state. Table 2 collects main OPA wavelengths l(1), oscillator strengths (lager than 0.6), transition natures and experimental results or molecules. We can see from Table 2 that our calculated OPA wavelength for A is in good agreement with corresponding experimental value. It indicates that our computational method is reliable. All the studied molecules have two OPA peaks corresponding to final states S1 and S2, respectively. Comparing OPA wavelengths corresponding to from S0 to S1, we can see that the OPA wavelengths of molecules B–D, which have a large red-shift with respect to A due to electron-accepting effect of amido groups, change ð1Þ ð1Þ with positions of aimino groups. lð1Þ B , lC and lD are 546.9, 530.7 and 517.2, respectively. It indicates that amido group
of different position has different electron-donating ability. Due to the difference of electron-accepting abilities of pyridinium and pyrylium, OPA wavelength of E is shifted by 17.9 nm with respect to A. F has the largest OPA wavelength. OPA corresponding to final state S2 has similar features. 3.4. Two photon absorption In this section, we will set out calculated results of TPA properties of molecules. According to expressions (1)–(4), we compiled a program of calculating TPA cross-section. Using the program, we have calculated TPA cross-sections for investigated compounds. Table 3 displays the positions of TPA peak (lð2Þ max ) in the range of 700–800 nm, the corresponding TPA cross-sections d(u)max and transition
Table 2 The OPA wavelengths and corresponding transition natures for compounds A–F Compound
l(1) (nm)
f
Final state Sm
Configurations and weights
A
482.0 (475) [19]
1.44570
1
478.4
0.91745
2
546.9 532.1 530.7
1.05477 1.16908 1.07289
1 2 1
523.4
0.92649
2
517.2 512.1 499.9 480.8 545.4
0.85037 1.08069 0.95543 0.61004 1.10618
1 2 1 2 1
533.6
1.56531
2
(HOMO,0)/(LUMO,0) 46.2% (HOMO-1,0)/(LUMO,0) 38.6% (HOMO,0)/(LUMO,0) 36.1% (HOMO-1,0)/(LUMO,0) 46.6% (HOMO-1,0)/(LUMO,0) 82.9% (HOMO,0)/(LUMO,0) 79.7% (HOMO,0)/(LUMO,0) 28.3% (HOMO-1,0)/(LUMO,0) 51.2% (HOMO,0)/(LUMO,0) 50.0% (HOMO-1,0)/(LUMO,0) 28.5% (HOMO-1,0)/(LUMO,0) 77.1% (HOMO,0)/(LUMO,0) 74.1% (HOMO,0)/(LUMO,0) 81.2% (HOMO,-1)/(LUMO,0) 82.3% (HOMO,-1)/(LUMO,0) 23.29% (HOMO,0)/(LUMO,0) 58.70% (HOMO,-1)/(LUMO,0) 60.19% (HOMO,0)/(LUMO,0) 21.54%
B C
D E F
Note: the figure in parentheses are experimental values. Table 3 The TPA wavelengths, TPA cross-sections and transition natures for studied compounds Molecules
lð2Þ max (nm)
d (u)max!10K50 (cm4 s photonK1)
Transition nature
Configurations and weights
A B C D E F
763.5 826.1 860.1 794.5 729.3 790.9
1366.96 2207.29 1554.37 1376.86 1817.14 2457.29
s0/s3 s0/s3 s0/s3 s0/s3 s0/s3 s0/s3
(HOMO-2,0)/(LUMO,0) 84.17% (HOMO-2,0)/(LUMO,0) 84.96% (HOMO-2,0)/(LUMO,0)79.41% (HOMO-2,0)/(LUMO,0)85.14% (HOMO-2,0)/(LUMO,0)74.01% (HOMO-2,0)/(LUMO,0)74.46%
X.-B. Zhang et al. / Journal of Molecular Structure: THEOCHEM 719 (2005) 207–212
natures for studied compounds. In this paper, we have depicted the TPA spectra (as shown in the Fig. 2) one by one point and ensured d(u)max and lð2Þ max . This method consists of two conditions: (1) for the molecule that has central symmetry, a change in the parity between the initial and final states (wave functions) is required for every photon involved in the transition for electric dipole transition. Thus the selection rule for TPA is different from that of OPA; (2) for the molecule without a center of inversion symmetry, every state is of mixed parity A
211
and hence transitions between all electronic states involving any number of photons are allowed. Here, all the molecules belong to (2), in principle, there is no limit on the symmetries of the ground and excited states of the oneand two-photon transitions. From Fig. 2 and literature [19], we have known that theoretical and experimental values of TPA cross-section of A at 800 nm are 544 and 113!10K50 cm4 s photonK1 (femtosecond value measured in DMSO), respectively. Structure of A can be pictured as a compromise between its B
C D
E F
Fig. 2. TheTPA spectra of studied compounds.
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resonance forms. In nonpolar solvent, quinoid form dominates whereas the benzenoid form is stable in polar solvent [34,35]. Enhancement of TPA cross-section of the former with respect to that of the latter can be as larger as a factor of 5 [36]. It is obvious that calculated value in vacuum and experimental values in DMSO (polar solvent) agree with this rule. On the other hand, it also examined our computational method. As can be seen in Table 3, TPA cross-sections of molecules B, C and D have an obvious enhancement while amido groups are introduced into A due to increase of length of effective conjugation chain. Molecules B, C and D have similar structure, but there exist a larger difference between their TPA cross-sections. It is ascribed to amido group of different position in pyrrole ring has different electrondonating ability. Cross-section of molecule E increases by 450!10K50 cm4 s photonK1 with respect to that of A due to that pyrylium has a stronger electron-accepting ability than pyridinium. It is reasonable that F has the largest TPA cross-section, which is 2457.29!10K50 cm4 s photonK1 (as shown in Table 3).
4. Conclusions In this paper, on the basis of Abbotto et al. works, a heterocycle-based branched quasi-octupolar TPA dye has been improved and their electronic structures, OPA and TPA properties have been calculated using the AM1 and ZINDO methods. Molecule F has the largest TPA crosssection (2457.29!10K50cm4 s photonK1), is a promising material.
Acknowledgements This work was supported by the National Nature Science Foundation of China (20273023) and the University Doctoral Subject Foundation of China.
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Theoretical investigation on a series of heterocycle-based compounds with large two-photon absorption cross-sections Xiang-Biao Zhanga, Ji-Kang Fenga,b,*, Xin Zhoua, Ai-Min Rena a
State Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, Institute of Theoretical Chemistry, NO2 Liutiao Road, Changchun 230021, China b College of Chemistry, JiLin University, Changchun 130023, China Received 27 October 2004; revised 14 January 2005; accepted 2 February 2005
Abstract A series of heterocycle-based molecules using p-deficient (pyridinium) and p-excessive (pyrrole) heteroaromatic rings as acceptor and donor, respectively, have been designed and their two-photon absorption properties have been investigated theoretically by using the AM1 and ZINDO methods. On the basis of correct geometries and UV-VIS spectra, the positions and strengths of two-photon absorption of these molecules were reported. Our calculated results reveal that molecule F, which has the largest two-photon cross-section (2457.29! 10K50 cm4 s photonK1) among studied molecules, is a more promising two-photon absorption material. q 2005 Elsevier B.V. All rights reserved. Keywords: Two-photon absorption; AM1 and ZINDO methods; Heterocycle-based molecules
1. Introduction Presently, more and more theoretical predictions and experimental observations on the phenomenon of twophoton absorption (TPA) have been reported. It results from the fact that the molecules with large TPA crosssections d(u) can be exploited in a number of applications, such as upconverted lasing [1–3], optical power limiting [4–6], photodynamic therapy [7], and three-dimensional (3D) microfabrication [8–10]. Various design strategies have successfully been used to synthesize organic molecules with large TPA cross-sections. One strategy is to synthesize a variety of donor-conjugated bridge-acceptor (D–p–A), donor-conjugated bridge-donor (D–p–D) and acceptorconjugated bridge-acceptor (A–p–A) derivatives, in which * Corresponding author. Corresponding author. Address: State Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, Institute of Theoretical Chemistry, NO2 Liutiao Road, Changchun 230021, China. Tel.: C86 431 849 9856; fax: C86 431 894 5942. E-mail address: [email protected] (J.-K. Feng).
0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.02.001
increase of the donor strength, acceptor strength and the conjugation length of the molecules can improve TPA crosssections [11–15]. On the other hand, many researches have focused on octupolar, multi-branched or dendrimer molecules [16–22], whose TPA cross-sections can be significantly improved by the increased chromophore density of the molecules without causing any aggregation [23,24]. Abbotto et al. [25] have reported highly efficient heteroaromatic-based TPA dyes presenting a A–p–D–p– A, where A (p-acceptor) is a p-deficient heteroaromatic ring (pyridine, quinoline, benzothiazole), D (p-donor) a pexcessive pyrrolyl moiety and octupolar heterocyclic compounds having good TPA property [19,25–28]. In literature [19,25], they have described a heterocycle-based branched quasi-octupolar TPA dye, using p-deficient (pyridinium) and p-excessive (pyrrole) heteroaromatic rings as A and D units, respectively. This chromophore presents a very large TPA cross-section in the femtosecond regime. Comparison of the TPA cross-sections between the branched system and the corresponding ‘monomeric unit’ shows a strong cooperative enhancement. In order to obtain better heteroaromatic-based TPA chromophores, we designed molecules B–F on the basis of their works and performed CI calculations.
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2. Computational methods The TPA process corresponds to simultaneous absorption of two photons. The TPA efficiency of an organic molecule, at optical frequency u/2p, can be characterized by the TPA cross-section d(u). It can be directly related to the imaginary part of the second hyperpolarizability g(Ku; u, u, u) by Ref. [29] dðuÞ Z
3Zu2 4 L Im½gðKu; u; Ku; uÞ 2n2 c2 30
(1)
where Zu the energy of the incoming photons, c the speed of light, and 30 the vacuum electric permittivity. n denotes the refractive index of the medium and L corresponds to the local-field factor. In the calculations presented here, n, L are set to 1 (isolated molecule in vacuum). The sum-over-states (SOS) expression to evaluate the components of the second hyperpolarizability gabgd can be educed out using perturbation theory and density matrix method. By considering a power expansion of the energy with respect to the applied field, the gabgd Cartesian components are given by Refs. [30,31]:
The primes on the summation over the electronic states indicate exclusion of the ground state. GK is the damping factor of excited state K, and in the present work, all damping factors Gs are set 0.1 eV. To compare the calculated d value with experimental value measured in solution, the orientationally averaged (isotropic) value of g is evaluated, which is defined as: 1 X hgi Z i; j Z x; y; z (4) giijj C gijij C gijji 15 i;j In principle, any kind of self-consistent field molecular orbital procedure combined with configuration interaction (CI) can be used to calculate the physical values in the above expressions. In this paper, the AM1 [32] method was firstly used to calculate molecular equilibrium geometries. Then the properties of electronic excited states were obtained by single and double electronic excitation configuration interaction using ZINDO [33] program. Furthermore, onephoton absorption (OPA) parameters, which were need to predict TPA properties were provided. Then according to the formula (1)–(4), the second hyperpolarizabilities g and the TPA cross-sections d(u) were calculated.
gabgd ðKus ; u1 ; u2 ; u3 Þ Z ZK3
X
P1;2;3
X X X 0 0 0 K
L
M
h0jma jKihKjmb jLihLjmg jMihMjmd j0i ðuK K iGK =2 K us ÞðuL K iGL =2 K u2 K u3 ÞðuM K iGM =2 K u3 Þ
h0jmb jKihKjma jLihLjmg jMihMjmd j0i C ðuK C iGK =2 C u1 ÞðuL K iGL =2 K u2 K u3 ÞðuM K iGM =2 K u3 Þ h0jmb jKihKjmg jLihLjma jMihMjmd j0i C ðuK C iGK =2 C u1 ÞðuL C iGL =2 C u1 C u2 ÞðuM K iGM =2 K u3 Þ h0jmb jKihKjmg jLihLjmd jMihMjma j0i C ðuK C iGK =2 C u1 ÞðuL C iGL =2 C u1 C u2 ÞðuM C iGM =2 C us Þ X X h0jma jKihKjmb j0ih0jmg jLihLjmd j0i 0 0 K ðuK K iGK =2 K us ÞðuK K iGK =2 K u1 ÞðuL K iGL =2 K u3 Þ K L h0jma jKihKjmb j0ih0jmg jLihLjmd j0i ðuK K iGK =2 K u1 ÞðuL C iGL =2 C u2 ÞðuL K iGL =2 K u3 Þ h0jmb jKihKjma j0ih0jmg jLihLjmd j0i C ðuK C iGK =2 C u1 ÞðuK C iGK =2 C us ÞðuL C iGL =2 C u2 Þ h0jmb jKihKjma j0ih0jmg jLihLjmd j0i C ðuK C iGK =2 C u1 ÞðuL C iGL =2 C u2 ÞðuL K iGL =2 K u3 Þ C
In this formula a, b, g and d refer to the molecular axes; u1, u2 and u3 are optical frequencies and usZu1Cu2Cu3 is the polarization response frequency; SP1,2,3 indicates a sum over the terms obtained by the six permutations of the pairs (u1/mb), (u2/mg) and (u3/md); K, L, and M denote excited states and 0, the ground state; jKi is an electronic wavefunction with energy Zuk relative to the ground electronic state; ma is the ath (Zx, y, z) component of the dipole operator hKjma jLi Z hKjma jLi K h0jma j0i
(3)
ð2Þ
3. Results and discussion 3.1. Structural design and geometry optimization In order to obtain better TPA materials, introducing amido groups into molecule A (have been synthesized) [19] and replacing the center of A by pyrylium, we have built molecules B–F (as shown in Fig. 1). Using AM1 method, the geometries of molecules were optimized. For A–D, because of the effect of methyl in
X.-B. Zhang et al. / Journal of Molecular Structure: THEOCHEM 719 (2005) 207–212
A
B
H2N
H3C N
H3C N
CH3
N N
CH3
N
N
CH3 H2N
CH3
C
CH3
H3C N
CH 3
N
NH2
CH3
NH2 N
N
CH 3 NH 2
H2N
CH3
E
F
N
CH3
N
CH 3
H 2N
H 3C N
H 3C N
CH 3 O
NH2
CH3
N
H 3C N
N
N
D
NH 2
H 2N
209
CH 3 O
N
N
H 2N
CH 3
N
NH 2
N CH 3
Fig. 1. The molecular structures of studied compounds.
pyridinium on molecular structure, two branches at the side of it and pyridinium are not in the same plane; the arm that faces to it and molecular center are coplanar only for A, for B–D, the sort of coplanarity was broken to some extent due to barrier between methyl and amido group in the pyrrole. The molecules E and F have a good coplanarity except methyls and amido groups in molecular structure.
using the ZINDO method. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energies as well as energy gaps between them (DEg) for molecules A–F were summarized in Table 1. One can find that the order of energy gaps: AOEODOCO BOF. 3.3. One-photon absorption
3.2. Electronic structure On the basis of equilibrium geometries optimized by AM1, we calculated the electronic structures of molecules
In order to obtain OPA property, we used the ZINDO program to calculate CI on the basis of equilibrium geometries optimized by AM1 method. The CI calculations
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Table 1 Energies of the HOMO and LUMO for A–F and their energy gaps (DEg, ev)
LUMO HOMO DEg
A
B
C
D
E
F
K0.149266 K0.348493 0.199227
K0.138507 K0.324594 0.186087
K0.149201 K0.336758 0.187557
K0.140241 K0.334951 0.194710
K0.151688 K0.347289 0.195601
K0.137926 K0.323241 0.185315
include 196 singly (SCI) and 54 doubly (DCI) excited configurations, a total of 251 configurations including the ground state. Table 2 collects main OPA wavelengths l(1), oscillator strengths (lager than 0.6), transition natures and experimental results or molecules. We can see from Table 2 that our calculated OPA wavelength for A is in good agreement with corresponding experimental value. It indicates that our computational method is reliable. All the studied molecules have two OPA peaks corresponding to final states S1 and S2, respectively. Comparing OPA wavelengths corresponding to from S0 to S1, we can see that the OPA wavelengths of molecules B–D, which have a large red-shift with respect to A due to electron-accepting effect of amido groups, change ð1Þ ð1Þ with positions of aimino groups. lð1Þ B , lC and lD are 546.9, 530.7 and 517.2, respectively. It indicates that amido group
of different position has different electron-donating ability. Due to the difference of electron-accepting abilities of pyridinium and pyrylium, OPA wavelength of E is shifted by 17.9 nm with respect to A. F has the largest OPA wavelength. OPA corresponding to final state S2 has similar features. 3.4. Two photon absorption In this section, we will set out calculated results of TPA properties of molecules. According to expressions (1)–(4), we compiled a program of calculating TPA cross-section. Using the program, we have calculated TPA cross-sections for investigated compounds. Table 3 displays the positions of TPA peak (lð2Þ max ) in the range of 700–800 nm, the corresponding TPA cross-sections d(u)max and transition
Table 2 The OPA wavelengths and corresponding transition natures for compounds A–F Compound
l(1) (nm)
f
Final state Sm
Configurations and weights
A
482.0 (475) [19]
1.44570
1
478.4
0.91745
2
546.9 532.1 530.7
1.05477 1.16908 1.07289
1 2 1
523.4
0.92649
2
517.2 512.1 499.9 480.8 545.4
0.85037 1.08069 0.95543 0.61004 1.10618
1 2 1 2 1
533.6
1.56531
2
(HOMO,0)/(LUMO,0) 46.2% (HOMO-1,0)/(LUMO,0) 38.6% (HOMO,0)/(LUMO,0) 36.1% (HOMO-1,0)/(LUMO,0) 46.6% (HOMO-1,0)/(LUMO,0) 82.9% (HOMO,0)/(LUMO,0) 79.7% (HOMO,0)/(LUMO,0) 28.3% (HOMO-1,0)/(LUMO,0) 51.2% (HOMO,0)/(LUMO,0) 50.0% (HOMO-1,0)/(LUMO,0) 28.5% (HOMO-1,0)/(LUMO,0) 77.1% (HOMO,0)/(LUMO,0) 74.1% (HOMO,0)/(LUMO,0) 81.2% (HOMO,-1)/(LUMO,0) 82.3% (HOMO,-1)/(LUMO,0) 23.29% (HOMO,0)/(LUMO,0) 58.70% (HOMO,-1)/(LUMO,0) 60.19% (HOMO,0)/(LUMO,0) 21.54%
B C
D E F
Note: the figure in parentheses are experimental values. Table 3 The TPA wavelengths, TPA cross-sections and transition natures for studied compounds Molecules
lð2Þ max (nm)
d (u)max!10K50 (cm4 s photonK1)
Transition nature
Configurations and weights
A B C D E F
763.5 826.1 860.1 794.5 729.3 790.9
1366.96 2207.29 1554.37 1376.86 1817.14 2457.29
s0/s3 s0/s3 s0/s3 s0/s3 s0/s3 s0/s3
(HOMO-2,0)/(LUMO,0) 84.17% (HOMO-2,0)/(LUMO,0) 84.96% (HOMO-2,0)/(LUMO,0)79.41% (HOMO-2,0)/(LUMO,0)85.14% (HOMO-2,0)/(LUMO,0)74.01% (HOMO-2,0)/(LUMO,0)74.46%
X.-B. Zhang et al. / Journal of Molecular Structure: THEOCHEM 719 (2005) 207–212
natures for studied compounds. In this paper, we have depicted the TPA spectra (as shown in the Fig. 2) one by one point and ensured d(u)max and lð2Þ max . This method consists of two conditions: (1) for the molecule that has central symmetry, a change in the parity between the initial and final states (wave functions) is required for every photon involved in the transition for electric dipole transition. Thus the selection rule for TPA is different from that of OPA; (2) for the molecule without a center of inversion symmetry, every state is of mixed parity A
211
and hence transitions between all electronic states involving any number of photons are allowed. Here, all the molecules belong to (2), in principle, there is no limit on the symmetries of the ground and excited states of the oneand two-photon transitions. From Fig. 2 and literature [19], we have known that theoretical and experimental values of TPA cross-section of A at 800 nm are 544 and 113!10K50 cm4 s photonK1 (femtosecond value measured in DMSO), respectively. Structure of A can be pictured as a compromise between its B
C D
E F
Fig. 2. TheTPA spectra of studied compounds.
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resonance forms. In nonpolar solvent, quinoid form dominates whereas the benzenoid form is stable in polar solvent [34,35]. Enhancement of TPA cross-section of the former with respect to that of the latter can be as larger as a factor of 5 [36]. It is obvious that calculated value in vacuum and experimental values in DMSO (polar solvent) agree with this rule. On the other hand, it also examined our computational method. As can be seen in Table 3, TPA cross-sections of molecules B, C and D have an obvious enhancement while amido groups are introduced into A due to increase of length of effective conjugation chain. Molecules B, C and D have similar structure, but there exist a larger difference between their TPA cross-sections. It is ascribed to amido group of different position in pyrrole ring has different electrondonating ability. Cross-section of molecule E increases by 450!10K50 cm4 s photonK1 with respect to that of A due to that pyrylium has a stronger electron-accepting ability than pyridinium. It is reasonable that F has the largest TPA cross-section, which is 2457.29!10K50 cm4 s photonK1 (as shown in Table 3).
4. Conclusions In this paper, on the basis of Abbotto et al. works, a heterocycle-based branched quasi-octupolar TPA dye has been improved and their electronic structures, OPA and TPA properties have been calculated using the AM1 and ZINDO methods. Molecule F has the largest TPA crosssection (2457.29!10K50cm4 s photonK1), is a promising material.
Acknowledgements This work was supported by the National Nature Science Foundation of China (20273023) and the University Doctoral Subject Foundation of China.
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