Kaohsiung Medical University Institutional Repository:Item 310902000/14073

Optic nonlinearities of a copper complex of

pyrazinoporphyrazine

L . C . H W A N G , C . Y . T S A I , C . J . T I A O A N D T . C . W E N * School of Chemistry, Kaohsiung Medical College, Kaohsiung, Taiwan, ROC

(*author for correspondence, Prof. Tsai-chuan Wen, Kaohsiung P.O. Box, 72-94, Kaohsiung, Taiwan, E-mail: [email protected])

Abstract. For the copper complex of pyrazinoporphyrazine AzaPhcCu(C(CH3)3)8 in CH2Cl2, we use

nanosecond pulses to measure its third-order nonlinear optic e€ects at 532 nm. The results show that its e€ective third-order nonlinear refractive index neff

2 (ÿ7:85  10ÿ10 esu) is larger than that of the

AzaPhcCu(C12H25)4 and the CuPc(OC5H11)8. The reverse saturable absorption (RSA) of

AzaPhcCu-(C(CH3)3)8is demonstrated by the ratio of e€ective excited state to ground state absorption cross sections.

The observed intersystem crossing lifetime siscof AzaPhcCu(C(CH3)3)8(15 ns) and AzaPhcCu(C12H25)4

(45 ns) are longer than that of CuPc(OC5H11)8(5.0 ns). The aza-substituents are suggested to form a

S1…n; p) state as their lowest excited singlet-states, and their radiationless intersystem crossing rates

(1=sisc) are discussed with the spin-orbit coupling hwSjHSOjwTi and the vibronic coupling hvSjvTi e€ects

between S1and T1states.

Key words: intersystem crossing rate, nonlinear absorption, Z-scan

1. Introduction

Recently, studies have been conducted on the tetrabenzoporphyrazine mac-rocycle system such as phthalocyanine (Pc), naphthalocyanine (Nc), ant-hracenocyanine (Ac) and phenantant-hracenocyanine (Phc), potentially used as nonlinear optical materials (Lezno€ and Lever 1996; Perry et al. 1996; Torre et al. 1998). On the other hand, a number of derivatives of azasubstituted tetrabenzoporphyrazines, such as AzaPhcCu and AzaPhcZn with tert-butyl side chains, and AzaPcSi with axial substituents, are being synthesized by Kudrevich and VanLier (1996) and Kudrevich et al. (1996). Following the methods in Kudrevich et al. (1996), we have prepared several aza-substituted

compounds with side chains of dodecanoyl (as AzaPhcCu(COC11H23)4) and

dodecanyl (as AzaPhcCu(C12H25)4) (Wen et al. 1998). Meanwhile, we also

determined their third-order nonlinear optic e€ects with nanosecond laser pulses at the wavelength of 532 nm (Wen et al. 1998; Tsai et al. 1999). The observed sign and size of the third-order nonlinear refractive indices in both

AzaPhcCu(COC11H23)4 and AzaPhcCu(C12H25)4 solutions are comparable

to that of a phthalocyanine compound of CuPc(OC5H11)8, and the observed

nonlinear absorption is attributed to the reverse saturable absorption (RSA). (Tsai et al. 1999).

The RSA behavior have been investigated for a number of macrocyclic

conjugated organic molecules such as C60 in solutions, (Henari et al. 1992;

Zhang et al. 1994; Smilowitz et al. 1996; Barroso et al. 1998; Riggs and Sun 1999) Aluminophthalocyanine (AlPc) doped xerogels (solid-state silica

ma-trices), (Brunel et al. 1994) and bis-phthalocyanine (LuPc2) in solution (Wen

and Lian 1996). Their intramolecular excitation processes are well described by a six-level system when excited with nanosecond laser pulses. For

exam-ple, for the C60 molecules in toluene (10ÿ5 mol lÿ1), the six-level model

calculations show that the absorption cross sections of the excited states (rT

ex rSex 8  10ÿ16 cm2) are larger than that of the ground state (rgˆ

5:2  10ÿ16 _cm2_{); (Henari et al. 1992) for the materials of LuPc2 in toluene}

(2  10ÿ4_{mol l}ÿ1_{), a similar result is obtained as both r}S

ex(0:9  10ÿ17 cm2)

and rT

ex…4:2  10ÿ17 cm2) are larger than that of rg…2:0  10ÿ18 cm2). (Wen

and Lian 1996) Thus, the above materials have stronger absorption in their excited states than in the ground state. When the input pulse is weak, the materials are relatively transparent, but under intense irradiation, it will create a signi®cant excited-state population; consequently, the transparency will be darkened. This unique property is referred to as RSA.

The characteristics of RSA can be further elucidated with a six-level model

as plotted in Fig. 1, where the parameters assigned s0ˆ 4 ns, siscˆ 5 ns and

rgˆ 10ÿ18cm2 are comparable to the experimental data of those materials

described above. When the size of either rS

exor rTexis increased from 10ÿ18 to

10ÿ16_cm2_{, the transmittance decreased rapidly while input intensity}

in-creased, which is represented by curves 1 to 3 in Fig. 1(a, b), and these curves are calculated according to Equations (6)±(8) in Section 4. Moreover, the

RSA preferably has a short intersystem crossing lifetime sisc as indicated in

Fig. 1(c), because the population on T1 state will be decreased when sisc is

longer than that of the exciting period.

In this paper, we report the nonlinear optic e€ects of a

AzaPhcCu-(C(CH3)3)8 solution. This molecule is synthesized via the condensation of

o-quinones with diaminomaleodinitrile, details of which are described elsewhere (Kudrevich et al. 1996; Wen et al. 1998). Both the Z-scan and the intensity-dependent measurements have been applied to determine their

e€ective third-order nonlinear refractive index (neff

2 ) and lowest excited

singlet- and triplet-states absorption cross-sections (rS

ex and rTex). The

mo-lecular structure and a corresponding UV-visible electronic absorption

spectra with Q-bands absorption appeared at kCH2Cl2

max ˆ 689 nm, as plotted

in Fig. 2. The ground-state absorption cross section rg (rgˆ 1:15 

10ÿ17 _cm2_{) is about an order larger than Groups IIIA and VIA metallo-Pcs}

(2:0  10ÿ18 _cm2_{) (Perry et al. 1994). The one-photon electric dipole}

moment (transition from p…a1u† to p…e9†† of AzaPhcCu(C(CH3)3)8 can be

enhanced largely by the vibronic coupling e€ect of its nonplanar pyrazino rings.

Fig. 1. Calculated transmittance vs. input intensity for a six-level system. The RSA behavior, which is enhanced by enlarging the absorption cross section of either rS

exor rTex, is presented respectively in (a) and

(b). The RSA preferably has a short lifetime siscis shown in (c). The sample concentration is 10ÿ4mol lÿ1,

2. Experiments of nonlinear optical measurements

We perform the intensity-dependent transmittance and the Z-scan measure-ments by using a Q-switched Nd:YAG laser. The laser was frequency dou-bled to 532 nm with 8 ns pulse width for the Gaussian mode.

During the intensity-dependent transmittance measurements, the incident intensity varied without changing the pules polarization by rotating the ®rst waveplate of a two Glan laser polarizer, while a focal lens (76 mm in dia-meter) is mounted 15 cm behind a 2.0 mm sample cuvette setting at the focal

point of the incident laser beam (x0ˆ 12:0 lm). The incident and transmitted

energies are detected simultaneously by two probes Rjp-735 (pyroelectric based, scale ranged from 20 lJ to 1.0 J, and spectral response from 0.25 to 16 lm) and Rjp-765 (silicon based, scale ranged from 20 pJ to 2 lJ, and spectral response from 0.30 to 1.1 lm), then averaged and readout with the RJ-7620 energy meter individually.

Fig. 2. The molecular structure and its UV±Vis spectra of AzaPhcCu(C(CH3†3†8 in CH2Cl2 …1:2 

10ÿ5_{mol l}ÿ1_).

For the Z-scan, an Iris diaphragm, which is adjusted to 2.0 mm (closed aperture) and 42 mm (open aperture) in diameter, is placed in front of an energy probe mounted 110 cm behind the focus of the same incident beam. The input light is kept 4.0  0.4 lJ for each shot, while the sample

(2:0  10ÿ4 _{M in CH}

2Cl2) is contained in a 1 mm quartz cell. Each data

point is an average of over one hundred shots with 1 Hz repetition rate. The experimental errors are estimated to be 20% from the variations of the input laser energies and the concentrations of our sample solution.

3. Results of Z-scan measurements

The data of open- (with open dots) and closed- (with close dots) Z-scans of this compound, together with the division of the close dots by the open dots of each data, are plotted in Fig. 3. This `divided Z-scan' curve reveals the e€ect of the third-order nonlinear refraction alone; therefore, the electric ®eld E…r; z; t† of the input Gaussian beam is a€ected by the nonlinear phase dis-tortion as

Ee…r; z; t† ˆ E…r; z; t† exp ÿa₂L

 

exp…iDU…r; z; t†† …1†

where Ee…r; z; t† is the electric ®eld at the exit surface of the sample, aLis the

linear absorption coecient and DU…r; z; t† is the nonlinear phase shift according to DU…r; z; t† ˆ DU0…z; t†exp ÿ 2r 2 x2_z†   …2† where DU0…z; t† ˆ DU0…t†=…1 ‡ z2=z20†, and DU0…t† is the on-axis phase shift at

the focus. The exponential term exp…iDU…r; z; t†† in Equation (1) can be ex-pressed with the following formula, which is expanded with a Taylor's series as described elsewhere (Weaire et al. 1979).

exp…iDU…r; z; t†† ˆX1 mˆ0 ‰iDU0…z; t†Šm m! exp ÿ2mr2 x2_z†   …3† By applying Equations (1) and (3), the resultant electric ®eld (and intensity) at the far ®eld aperture can be derived theoretically, and then the normalized

transmittance T (T ˆ Iout=Iin) can be expressed simply with the power series

T ˆ 1 ‡_x24DU_{‡ 1†…x}0…t†x_{2‡ 9†}‡_xDU₂0_{‡ 9†}…t†2‡


…4†

where x ˆ z=z0, z0ˆ px20=k. Usually the third term (and higher) on the right

hand side of Equation (4) is negligible when jDU0…t†j  0:1. However, we

need the whole equation to ®t the divided Z-scan data in Fig. 3(b).

The best curve ®tting from Fig. 3 yields the value of DU0…t† as ÿ0:94. By

applying the relation of DU0…t† ˆ kDn0…t†Leff, (Sheik-Bahar et al. 1990) where

Leffˆ …1 ÿ eÿaL†=a (with L the sample length and a the linear absorption

coecient), Dn0ˆ cI (we assume that the nonlinear refraction is mainly due

to the Kerr e€ect), and neff

2 ˆ …cn0=40p†c, we obtain neff2 as ÿ7:85  10ÿ10esu.

This negative nonlinear refraction is induced by a negative lensing e€ect, which will defocus the optic beam as shown in Fig. 4. Consequently the transmittance (observed from the aperture) exhibit a peak (beam

conver-Fig. 3. The Z-scan results of AzaPhcCu(C(CH3†3†8. In (a), close dots: with aperture; open dots: without

aperture; the curves of close dots are moved downward for the clear vision. In (b), is the divided Z-scan data, where the solid line is ®t with Equation (4).

gence) on the negative z=z0 side and a valley (beam divergence) on the

pos-itive side as results.

4. Results of intensity-dependent transmittance

A `six-level' model has been utilized to compute the intensity-dependent transmittance in the present work. As depicted in Fig. 5(a), the excitation processes in this six-level system can be formulated as follows in the rate equation approach: d dt n1 n2 n3 n4 n5 n6 2 6 6 6 6 6 6 4 3 7 7 7 7 7 7 5 ˆ ÿr_hmgI; 0; _s1 0; 0; 1 s5; 0; rgI hm ; ÿs12; 0; 0; 0; 0; 0; _s1 2; ÿ 1 s0ÿ 1 siscÿ rS exI hm ; 1 s3; 0; 0; 0; 0; rSexI hm ; ÿ 1 s3; 0; 0; 0; 0; _s1 isc; 0; ÿ rT exI hm ÿs15; 1 s4; 0; 0; 0; 0; rTexI hm ; ÿ 1 s4; 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 n1 n2 n3 n4 n5 n6 2 6 6 6 6 6 6 4 3 7 7 7 7 7 7 5 …5†

Formula (5) can be simpli®ed according to the facts of

· Equation (1), the term of 1=s5can be neglected as the relaxation process of

S0 T1 takes as long as 100 ls,

Fig. 4. The negative lensing e€ect during the Z-scan of AzaPhcCu(C(CH3†3†8in CH2Cl2. The defocus

property is depicted with dashed lines in (a) and (b), as the sample stands respectively before and after the focal point.

· Equation (2), because of the lifetime of s2…1 ps) is much less than our ns

laser pulse, we obtain …rgI=hm†n1ˆ …1=s2†n2 with the steady-state

ap-proachs of dn2=dt  0, and

· Equation (3), for the reason that the processes of S1 S2 and T1 T2

decay rapidly, we assign …rS

exI=hm†n3ˆ …1=s3†n4and …rTexI=hm†n5ˆ …1=s5†n6

with the steady-state approaches of dn4=dt ˆ dn6=dt  0.

Thus, our level system can be described in good approximation by Equations (6) to (8): dn1 dt ˆ rgI hm n1‡ 1 s0n3 …6† dn3 dt ˆ rgI hm n1ÿ 1 s0n3ÿ 1 siscn3 …7† dn5 dt ˆ 1 siscn3 …8†

In Equations (6)±(8) only the time variation of population densities n1…S0†; n3…S1†, and n5…T1† has been accounted for, because the populations of

levels S1(v), S2 and T2 can be neglected for the very short lifetimes of those

levels. Thus, the variation of light intensity along the propagation direction (z) in the sample can be expressed as

Fig. 5. Energy level diagrams of (a) six-level and (b) four-level systems. The one-photon exciting and relaxing processes are depicted, as irradiate with 532 nm laser pulses.

dI

dz ˆ ÿI…rgn1‡ rSexn3‡ rTexn5†N …9†

where N ˆ n1‡ n3‡ n5 1. The near Gaussian temporal pro®le of input

laser pulses can be expressed as

I…t† ˆ I0exp‰ÿt2=2r2tŠ …10†

where I0 is the peak power of the incident laser pulse, and rt is related to the

fwhm pulse duration tp (8 ns in this work) by tp ˆ 2:36 rt (Barroso et al.

1998).

As usual, the magnitudes of rg; hm; s0; s1, and a proper laser intensity

together with n1ˆ 1; n3ˆ n5ˆ 0 are ®rst assigned in Equations (6)±(8). Then

the time-dependent relative population densities (from t ˆ 0 to t ˆ 8 ns) among the S0…n1†; S1…n3† and T1…n5† states are obtained from the iterative

fourth-order Runge±Kutta simulations. The excited-state cross sections are obtained by integrating Equation (9) to get

T ˆI_Iout in ˆ exp ÿNL…rgn1‡ r S exn3‡ rTexn5†  …11† The nonlinear transmittance data are plotted in Fig. 6, where the solid curves are calculated with Equation (11). The results yield the best ®tting values of rS

ex and rTex as 1:45  10ÿ16 cm2 and 1:45  10ÿ17 cm2, respectively. Other

parameters such as rg, s0 and sisc are all listed in Table 1.

Because our earlier results show that the excited-state absorption of

AzaPhcCu(C12H25†4 is dominated to the excitation channel of S2…m†

S1…m ˆ 0†; …Tsai et al: 1999† a `four-level' system (in Fig. 5(b)) has also been

used to simulate the measurements. In this energy system only the ground state and singlet excited-states are considered, so we just need Equations (6) and (7) to describe the absorbing and relaxing processes, and to evaluate the relative population densities as well. The solid curves in Fig. 7 are the

the-oretical calculations according to T ˆ expfÿNL…rgn1‡ rS_exn3†g, where we

obtain the rS

ex as 1:28  10ÿ16 cm2.

5. Discussion

In the present work we ®nd that the value of neff

2 is ÿ7:85  10ÿ10esu for the

AzaPhcCu(C(CH3†₃†₈. Under the same conditions of Z-scans, we obtain a

value of neff

2 ˆ ÿ2:84  10ÿ10 esu for the AzaPhcCu(C12H25†4 as listed in

Table 1. The larger nonlinear refraction observed in the solution of

has a stronger electron donating e€ect than the dodecanyl alkyl groups (Nalwa 1993).

When excited with picosecond pulses, positive nonlinear refraction is ob-served for a number of metallo-Pcs, which is attributed to the excitation

Fig. 6. The transmittance vs. input intensity of AzaPhcCu(C(CH3†3†8in CH2Cl2. The solid curves are the

theoretical calculations of the six-level model with various sizes of (a) rS

ex, and (b) rTex. Curve Torre et al.

1998 is the best ®tting curve in both (a) and (b).

Table 1. The photophysical parameters and the third-order nonlinear refractive index of AzaPhcCu-(C(CH3)3)8, AzaPhcCu(C12H25)4and CuPc(OC5H11)8in CH2Cl2. rgis evaluated with Tlinˆ exp‰ÿrgN0LŠ,

where N0is the number of molecules per cm3and L is the thickness of sample (2.0 mm). s0is measured with

the time-correlated single-photon method. The parameters of the last two compounds are from Tsai et al. (1999) rg (10)17_cm2₎ n eff 2 (10)10_esu) s_(ns)0 s_(ns)isc r T ex (10)17_cm2₎ r S ex (10)16_cm2₎ AzaPhcCu(C(CH3)3)8 1.15 )(7.85 ‹ 1.57) 0.31 15 ‹ 3 1.45 ‹ 0.29 1.45 ‹ 0.29 AzaPhcCu(C12H25)4 1.50 )(2.84 ‹ 0.57) 0.50 45 ‹ 9 0.03 ‹ 0.006 0.52 ‹ 0.10 CuPc(OC5H11)8 0.18 )(2.24 ‹ 0.45) 4.0 5.0 ‹ 1 4.0 ‹ 0.8 0.48 ‹ 0.09 650 L.C. HWANG ET AL.

processes among metallo-Pc's singlet states (Wei and Huang 1996). For the nanosecond pulses, the negative nonlinear refractions of

AzaPhc-Cu(C(CH3†3†8 and CuPc(OC5H11†8 are due to the population relaxing to

their lowest lying triplet state, according to the Kramer±Kronig relation (Wen and Lian 1996; Sheik-Bahar et al. 1990). Moreover, during the heat released from each radiationless relaxing step, a temperature gradient is formed around the beam axis, taking about 0.15 ns or longer of time; (Wei et al. 1998) therefore, there is an additional refractive index change DnThermalˆ …dn=dT †DT , where DT is the temperature rise due to the heat

released to the solution, and dn=dT is the change of the refractive index with

temperature. The values of dn=dT has been evaluated as ÿ6:01  10ÿ4_kÿ1

for the solution of CH2Cl2, (Tsai et al. 1999) and as ÿ5:9  10ÿ4kÿ1for the

solution of THF (Wood et al. 1995). Thus, this thermal lens e€ect can a€ect the negative nonlinear refractions observed in this work. The quantity of DT will be determined (in our future work) by using the time-resolved thermal lensing technique as described elsewhere (Terazima and Azumi 1987; Castillo et al. 1994).

The theoretical calculation from the six-level system (Fig. 6(a)) yields the

lifetime of intersystem crossing siscˆ 15 ns for AzaPhcCu(C(CH3†3†8, which

is shorter than that of AzaPhcCu(C12H25†4…sisc=45 ns, as listed in Table 1).

Consequently, the triplet state absorption cross section of the former (rT

exˆ 1:45  10ÿ17 cm2) is much larger than that of the later (rTexˆ

0:03  10ÿ17 _cm2_{). The high electron donating behavior of tert-butyl side}

chains could enhance the intersystem crossing rate of AzaPhcCu(C(CH3†3†8.

The magnitude of rS

exˆ 1:45  10ÿ16 cm2 is obtained from the above

calculations. In addition, a similar result of rS

exˆ 1:28  10ÿ16 cm2 is

ob-Fig. 7. The transmittance vs. input intensity of AzaPhcCu(C(CH3†3†8in CH2Cl2. The solid curves are the

theoretical calculations of the four-level model with di€erent values of rS

ex. Curve Torre et al. 1998 is

tained from a four-level system as plotted in Fig. 7. The magnitudes of rS ex

obtained from di€erent models are therefore within the experimental errors

(which is 20%†, and the ratio of rS

ex=rTexis 10 for AzaPhcCu(C(CH3†3†8.

This result indicates that the major excited state absorption belongs to S1…0† ! S2…m†.

Moreover, the relative population densities on the ground state (S0) and

excited-states (S1and T1) are evaluated by applying the parameters of the

absorption cross sections and the life times of each state as listed in Table 1. Examples of these calculations are shown in Fig. 8 at various input intensi-ties. From Fig. 8(a) it is clear that, for the six-level system, the relative

populations on both S1and T1states will remain low at lower input intensity

I ˆ 2:54  10ÿ3 _{GW cm}ÿ2_{. When this intensity increase to I ˆ 4:95 }

10ÿ2 _{GW cm}ÿ2_{, the level population on S1 raises quickly to about 0.29 and}

remains 0.25 at the end of 8 ns pulses, while the level population on T1

reaches to about 0.14 at the end of this period (as in Fig. 8(b)). The

popu-lation on S1and S0states of the four-level system are also plotted in Fig. 8(c)

for the comparison. The results exhibit that, from both models, the

excited-state absorption is attributed to the S2…m† S1…m ˆ 0† at the beginning, then

the intersystem crossing from S1to T1state slowly raises the level population

on T1, as illustrated in Fig. 8(b).

A dynamic property of RSA can be expressed with the ratio of the

excited-state to ground excited-state absorption cross sections rex=rg versus the input

intensity, where rex  n3rSex‡ n5rTex represents the six-level system, and

rex n3rSex represents the four-level system. As usual, the ratio of rex=rg is

very small at low input intensity, and it will increase largely (>1) at high

intensity as shown in Fig. 9, where the ratio of rex=rg 1 is at the input

intensity I  1  10ÿ2 _{GW cm}ÿ2_{, and this ratio increases to about 3.8 when}

the intensity raises to I  5  10ÿ2_{GW cm}ÿ2_.

The results in Table 1 indicated that the intersystem crossing rate (1=sisc)

is CuPc(OC5H11†₈ …2:0  108sÿ1† > AzaPhcCu(C(CH3†₃†₈ …0:66  108sÿ1† >

AzaPhcCu(C12H25†4…0:22  108sÿ1). Usually, the transition from an excited

singlet state (S) to a triplet state (T) is induced by the spin-orbit coupling matrix

hTjHSOjSi: Under the validity of the Born±Oppenheimer approximation,

hTjHSOjSi ˆ hwTjHSOjwSihvTjvSi, where w is the electronic wavefunction and v

is the vibrational wavefunction. The rate equation may thus write (Yardley 1980) knr ˆ 2p_h   jhw_TjHSOjwSij2 X T jhv_Sjv_Tij2d…ESÿ ET† …12†

hw_TjHSOjwSi is the spin-orbit coupling matrix of two excited electronic states,

hv_Sjv_Ti is a vibrational overlap integral and jhv_Sjv_Tij2 is the Franck±Condon

factor, and d…ESÿ ET) is a delta function. The delta function in this equation

assures that only levels for which ET ES will contribute to the intersystem

cross rate.

As we know, compared with naphthalene, the aza-substituted naphthalene (i.e., quinoxaline) have two extra excited-states: one is a S(np_{† state, which is} Fig. 8. Calculated relative population densities N on the levels of S0, S1 and T1. The maximum input

the lowest singlet excited-state of quinoxaline, and the other one is T(np_†,

which is between the S…np_{† and the lowest triplet T…p; p}_{† state (Hadley}

1971). More recently, a (n ! p_{) transition (peaked at 604 nm) is identi®ed}

from the absorption spectra of (CN)ZnPc compound (Mark and Stillman 1995). The relative energy levels of a AzaPhcCu compound are therefore

plotted in Fig. 10; where we assigned tentatively a S(np_{) state (as the lowest}

singlet excited-state) located just below the S(pp_{) state, together with}

a T(np_{), which is above the T(pp}_{). The energy levels of CuPc(OC5H11†}

8

are also depicted in Fig. 10. Thus, the routes of intersystem crossing can

undergo S…np_{† ! T…np}_{† and S…np}_{† ! T…pp}_{† for AzaPhcCu, and it is}

Fig. 9. The ratios of rex=rgas a function of input intensities.

Fig. 10. The energy level diagrams of PcCu and AzaPhcCu.

S…pp_{† ! T…pp}_{† for CuPc(OC5H11†}

8. The rates of these crossover routes are

discussed below.

According to the spin-orbit coupling element jhwTjHSOjwSij2 in Equation

(12), the rates of S…np_{† ! T…pp}_{† has been estimated to be 1000 times}

faster than either S…np_{† ! T…np}_{† or S…pp}_{† ! T…pp}_{†, because of the}

symmetry restrictions, (El-Sayed 1963). The ecient intersystem crossing

route therefore should be S…np_{† ! T…pp}_{† for AzaPcCu, which is much}

faster than the route of S…pp_{† ! T…pp}_{† for CuPc(OC}

5H11†8, as indicated in

Fig. 10. However, our results show clearly that the intersystem crossing rate

of CuPc(OC5H11†8 is three times faster than that of AzaPhcCu(C(CH3†3†8

and nine times faster than that of AzaPhcCu(C12H25†4.

The above discrepancy may be from the Franck±Condon factor in Equation (12). For example, Beddard and et al. (1973) Siebrand (1966) and many other workers have explained that the Franck±Condon integrals

jhvSjvTij2 will decrease rapidly when the energy gap between ES1 and ET1

states increases. Nevertheless, more experimental data are needed to explain the above results.

6. Conclusion

We have investigated the nonlinear absorption cross sections and the

third-order nonlinear refractive index of a newly prepared AzaPhcCu(C(CH3†3†8

molecule in solution under the nanosecond (532 nm) pulses. The results

in-dicated that its e€ective refractive index …neff

2 † and excited-state absorption

cross sections …rS

ex and rTex† are all larger than that of AzaPhcCu(C12H25†4,

and its RSA property is displayed with the high ratio of rex=rg. The

con-tribution to the negative nonlinear refraction from both the radiationless relaxing and heating e€ects are suggested. However, to obtain quantitative data about temperature raise (DT ) during the radiationless decay from the excited states, the time-resolved thermal lens technique is suggested as our

future work. The rates of radiationless intersystem crossing (1/sisc† are

dis-cussed with two important factors in Equation (12), the ®rst is the spin-orbit

coupling element hwTjHSOjwSi, and the second is the vibrational coupling

element hv_Sjv_Ti. The observed rates in this work indicated that the

intra-molecular radiationless transition wS1 ! wT1 of AzaPhcCu could be slow

down by the Franck±Condon factor jhv_Sjv_Tij2, as compared with the PcCu

studied in this work. Acknowledgements

This research was supported by Project NSC 88-2113-M-037-009 of the National Science Council of ROC, Taiwan.

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