CI method for calculating two-photon cross sections

Journal of Physics and Chemistry of Solids 62 (2001) 1075±1079

www.elsevier.nl/locate/jpcs

A quantum±chemical INDO/CI method for calculating two-photon cross sections Yu-fang Zhou a,b,*, Xiao-mei Wang a, Xian Zhao a, Min-hua Jiang a a

Institute of Crystal Materials, Shandong University, Jinan 250100, P.R. China b Department of Physics, Shandong University, Jinan 250100, P.R. China Received 22 May 2000; accepted 31 October 2000

Abstract Materials with large two-photon absorption (TPA) cross section are now gaining increasing attention since these can be exploited in a number of optical applications. In this paper, on the basis of a quantum±chemical INDO/CI method and by using the sum-over-states (SOS) expression, the theoretical predications on the TPA properties for a series of stilbene derivatives were performed. Some mechanism of effect on the TPA property is discussed and the results will provide theoretical basis for those dyes applied as TPA devices. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: A. Optical materials; A. Organic compounds; D. Electronic structure; D. Optical properties

1. Introduction The research of the materials with large two-photon absorption (TPA) cross section is now gaining increasing attention because of their potential applications in optical data storage [1±3], optical limiting [4] and two-photon pumped up-conversion lasing [5,6]. Two-photon absorption (TPA) in organic materials involves a direct absorption of two photons through a virtual state to access an exited state. The transition probability is proportional to I 2, where I is the intensity of the incident laser pulse and its pump wavelength shifts to longer wavelengths compared to single-photon absorption, where materials are relatively photo-stable. The semiconductor diode lasers can provide required sources, so the costs of two-photon devices can be very low. Because of these advantages, a considerable amount of effort has been devoted to study TPA materials. However, the criteria of design molecules with large two-photon cross section have not been well developed and the full utility of two-photon absorbing materials has not been realized [7,8]. Thus, it is of great importance to make a theoretical study on the mechanism for enhancement of TPA in molecules and give some guidance with materials in applications. Recently, a series of new dyes: CSPI; DPASPI; PSPI; * Corresponding author. E-mail address: [email protected] (Y. Zhou).

DEASPI; HMASPI; and HEASPI were synthesized by Wang's group [9]. These dyes are stilbene chromophores end-capped with the same acceptor but different donors. The linear absorption curves showed their single-photon absorption maximum peaks located from 405 to 475 nm. There is no linear absorption in the spectral range 600± 1300 nm, so TPA can be expected in this range and materials may be used to make two-photon devices, but there are no TPA properties reported. In this paper, on the basis of quantum±chemical calculations, theoretical predications of TPA properties were performed for those chromophores. Some mechanism of effect on the TPA property will be discussed. The results will provide a theoretical basis for their practical applications as TPA devices.

2. Methodology The molecules investigated are shown in Fig. 1, the stilbene chromophores with the same methyl-pyridinium iodide as acceptor and different amino groups as their donors. The frequency dependence of TPA cross section, d (v ), is related to the imaginary part of the second hyperpolarizability, by [10]:

d…v† ˆ

8p2 "v2 Img…2v; v; v; 2v† n2 c2

0022-3697/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0022-369 7(00)00283-3

…1†

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Y. Zhou et al. / Journal of Physics and Chemistry of Solids 62 (2001) 1075±1079

Fig. 1. Structure scheme of compounds.

where n is the index of refraction of medium and c is the speed of light; Img…2v; v; v; 2v† was calculated by using the sum-over-states (SOS) expression; g ijkl Cartesian components are given by [11]: gijkl …2vs ; v1 ; v2 ; v3 † ˆ hX X X m±o n±o p±o

2

1 …P…i; j; k; l; 2vs ; v1 ; v2 ; v3 † 6"3 D ED ED ED E oumi um mumj un numk up puml uo

…vmo 2 vs 2 iG mo †…vno 2 v2 2 v3 2 iG no †…vpo 2 v3 2 iG po †

X X

ED ED ED E D oumi um mumj uo oumk un numl uo

m±o n±o

…vmo 2 vs 2 iG mo †…vno 2 v3 2 iG no †…vno 1 v2 2 iG no †

i

…2† Here P…i; j; k; l; 2vs ; v1 ; v2 ; v3 † is a permutation operator, v1 ; v2 ; v3 denote the frequencies of radiation ®elds and vs ˆ v1 1 v2 1 v3 ; m, n and p denote  excited stated states and o denotes the ground state. omm is the i component of transition dipole ground and m excited

 moment

between

 states and mmj n ˆ mmj n 2 omj o dnm : "vmo is the transition energy between m and o states and G mo is the damping factor of excited state m (in the calculation it is set to 0.l eV for all excited states). The average g is expressed as follows: hgi ˆ

1 1 gyyyy 1 gzzzz 1 2gxxyy 1 2gxxzz 1 2gyyzz † …g 5 xxxx …3†

Full geometry optimizations were performed by using the PM3 quantum chemical method. Then we calculated energies, dipole moments and transition dipole moments by combining the intermediate neglect of differential overlap (INDO) Hamiltonian with the con®guration interaction (CI) technique in zindo program. The CI con®gurations were chosen with 12 occupied energy levels below HOMO and 12 virtual energy levels over LUMO, a total of 145 CI con®gurations. The results from zindo program were inputted into the Eqs. (2) and (3) to calculate the components of g and the average of g . At last, the frequency dependence of twophoton cross sections were obtained with the Eq. (1).

3. Results and discussion To calibrate the calculation method, we chose four compounds as comparison samples whose cross sections have been measured or calculated by Albota et al. [10]. We calculated the TPA cross sections of those samples and compared results with those of Albota et al. [10]. The correlative data is listed in Table 1. We can see from Table 1 that the results we calculated are generally in agreement with those obtained by Ref. [10]. They are in the same order of magnitude, ,10 248 cm 4 s. Although the calculated results in this work are larger than in Ref. [10] by 10±35%, the sequence is the same. So, by using the

Y. Zhou et al. / Journal of Physics and Chemistry of Solids 62 (2001) 1075±1079

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Table 1 Comparison the cross section data with Ref. [10] Compounds

Cross section d £ 10 248 cm 4 s This work

above described method to calculate TPA cross section, one can obtain some information about the TPA properties of the molecules. The TPA spectra for six compounds by considering the 25 lowest excited states is shown in Fig. 2. The magnitudes of maximum TPA cross section range from 1.50 £ 10 248 to 100 £ 10 248 cm 4 s, the corresponding incident ®eld from 1.12 to 1.58 eV (absorption peak wavelengths 1107± 785 nm) suggesting they satisfy the requirement of cross section and peak wavelength for making two-photon devices. The results also show there are considerable differences in cross section and peak wavelength of those samples. This implies that although TPA properties are in¯uenced by many factors the structural features, i.e. the donor and the acceptor, mainly in¯uence TPA. For CSPI (trans-4-[p-(Ncarbazolyl)styryl]-N-methyl pyridinium iodide), at the incident ®eld of 1.16 eV (1068 nm) the TPA reaches its resonance peak, with maximum cross section as high as 36 £ 10 248 cm 4 s. While DPASPI (trans-4-[p-(N,N-diphenyl amino)styryl]-N-methyl pyridinium iodide), its donor is different from that of CSPI only by breaking one C±C bond, there are two absorption peaks, located at 1.41 eV (879 nm) and 1.49 eV (832 nm), the cross sections are 1.5 £ 10 248 and 1.3 £ 10 248 cm 4 s, respectively. A similar

Ref. [10]

2.25

2.024 (Cal.)

2.43

2.10 (Exp.)

9.24

6.805 (Cal.)

11.76

9.95 (Exp.)

character is observed in PSPI (trans-4-[p-(pyrorolidinyl)styryl]-N-methyl pyridinium iodide) and DEASPI (trans-4[p-(N,N-diethyl amino)styryl]-N-methyl pyridinium iodide). The difference of DEASPI from PSPI is also one C±C bond broken, the maximum TPA of PSPI is located at 1.58 eV (785 nm) and the value of d is 34 £ 10 248 cm 4 s. But for DEASPI, two very large peaks occur at 1.1 eV (1127 nm) and 1.2 eV (1033 nm), the values of d are 135 £ 10 248 and 66 £ 10 248 cm 4 s. We can see the TPA properties of the above molecules are violently affected by substituted donors. The following two chromophores of HMASPI (trans-4-[p-(Nhydroxyethyl-N-methyl amino)styryl]-N-methyl pyridinium iodide) and HEASPI (trans-4-[p-(N-hydroxyethyl-N-ethyl amino)styryl]-N-methyl pyridinium iodide), the donors are N-hydroxyethyl-N-methyl amino and N-hydroxyethyl-Nethyl amino, the d of HEASPI is twice as large as that of HMASPI. This is because the electron-donating ability of the donor in HEASPI is stronger than that in HMASPI. The above results indicate that there is a close relationship between TPA property and chromophore structures. But the essential effect on TPA is the micro-electronic distribution as well as the interaction between incident ®eld and electronic states. The electronic distribution of a molecule is decided by its structure, while the incident excited laser

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Y. Zhou et al. / Journal of Physics and Chemistry of Solids 62 (2001) 1075±1079

Fig. 2. Frequency dependent curves of TPA cross section. Data in horizontal coordinate axis represent energies (in eV) of incident photon. Data in longitudinal coordinate axis represent the cross section ( £ 10 250 cm 4 s) of TPA.

Y. Zhou et al. / Journal of Physics and Chemistry of Solids 62 (2001) 1075±1079

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Table 2 The static and transition dipole moments (Debye) of three states

S0 S1 S2 S0!1 S1!2

CSPI

DPASPI

PSPI

DEASPI

HMASPI

HEASPI

2 6.685 2 18.935 2 10.820 2 9.174 2 6.709

7.436 4.632 13.457 8.543 2 8.488

8.387 3.880 15.491 7.842 7.860

2.401 2 8.618 2 18.940 16.489 7.916

6.140 0.423 12.857 7.257 6.883

8.633 3.728 16.277 2 7.770 2 7.681

®eld can change the distribution. When incident ®eld and electronic states meet some match conditions the resonance absorption occurs and extreme electronic transition takes place between favorite states. To understand the mechanism of TPA, we take an examination of dipole transition of electrons. In the push±pull conjugated compounds, the longitudinal component (main component) of cubic polarizability tensor can be described by a simpli®ed model involving the electronic characteristics of three states. In such a model, the contributions to the longitudinal component can be divided into the following three terms [12]:

g/

2 2 2 4 X Mge 0 Mge Dm2ge Mee Mge 1 2 3 2 E 0 3 Ege Ege Ege ge e0

where, Mge is the transition dipole moment from the ground state |gl to the lowest excited state |el, which is strongly coupled to |gl and Mee 0 from |el to the upper-lying excited state |el that is strongly coupled to |el; Dm ge is the difference between the dipole moments in |el and |gl. Ege and Ege 0 denote transition energies, respectively. In the three terms the negative term makes no contribution to the TPA sum, the ®rst and second terms are essential to the TPA process. With such consideration, we choose three main electron states, S0, S1, S2. The static and transition dipole moments are listed in Table 2. We can see from Table 2 that these data in general support the above results and, therefore, can give some explanation for the reason of different TPA. For example, the large d of CSPI compared to DPASPI can be realized by the Dm ge in CSPI, which is evidently larger than that in DPASPI. While the large d of DEASPI compared to PSPI is mainly because it possesses the large transition dipole moment. In the other two molecules, HMASPI and HEASPI, the d in the latter is only twice as large as that in the former. 4. Conclusion We have theoretically investigated the TPA properties of

the above chromophores. With the same backbone and acceptor of those compounds, the TPA cross sections are in¯uenced by their donors sensitively. Although there exists the close relationship between the TPA and structure, the crux of the TPA is decided by the electronic distribution as well as transition under the incident ®eld. The predications show these chromophores possess large TPA cross section and may be applied to design TPA devices.

Acknowledgements This work was supported by a grant for State Key Program of China. We also thank the Institute of Theoretical Chemistry in Shandong University for kindly providing the computer resource.

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