Interference between Charge-Transfer and Intermediate - American

9802

J. Phys. Chem. B 2006, 110, 9802-9814

Strong Two-Photon Absorption in New Asymmetrically Substituted Porphyrins: Interference between Charge-Transfer and Intermediate-Resonance Pathways Mikhail Drobizhev,† Fanqing Meng,‡ Aleksander Rebane,*,† Yuriy Stepanenko,†,§ Eric Nickel,| and Charles W. Spangler‡ Departments of Physics and Chemistry and Biochemistry, Montana State UniVersity, Bozeman, Montana 59717, Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland, and Synar Technologies, Inc., 1267 Briarwood DriVe, Atlanta, Georgia 30306 ReceiVed: September 13, 2005; In Final Form: March 20, 2006

We study two-photon absorption (2PA) in two series of new free-base porphyrins with 4-(diphenylamino)stilbene or 4,4′-bis-(diphenylamino)stilbene (BDPAS) attached via π-conjugating linkers at the porphyrin meso-position. We show that this new substitution modality increases the 2PA cross section in the Soret band region (excitation wavelength 750-900 nm) of the core porphyrin by nearly 2 orders of magnitude, from σ2 ≈ 10 GM for the meso-phenyl-substituted analogue to σ2 ≈ 103 GM for the ethynyl-linked BDPASporphyrin dyad. The 2PA properties are quantitatively described by considering two different and interfering 2PA quantum transition pathways. The first path involves virtual transition via intermediate one-photon resonance. The second path bypasses the intermediate resonance and occurs due to a large permanent dipole moment difference between the ground and the final electronic states. To our best knowledge, this is the first experimental observation of the combined effect of these two pathways on one particular two-photon transition, resulting in quantum-interference-modulated 2PA strength.

1. Introduction Two-photon absorption (2PA) is increasingly used in various areas of photonics, such as high-resolution microscopy,1 microand nanofabrication,2 optical power limiting,3 high-density optical storage,4 and photodynamic therapy.5,6 These applications often rely on special organic compounds, which unite a large value of the 2PA cross section at particular wavelength(s) with a specific molecular functionality. Porphyrins are unique among organic chromophores because they possess many important properties, including large excited-state absorption, long triplet lifetime, intrinsic ability of photochemical switching between tautomeric forms, as well as good biological compatibility. Unfortunately, the generally known porphyrins are notorious for having a rather low 2PA cross section, σ2 ≈ 1-10 GM. This has so far greatly limited the practical utility of tetrapyrroles as multiphoton sensitizers. In a series of papers7,8 we reported a detailed study of the absolute 2PA spectra of different centrosymmetric tetrapyrrole compounds and identified different mechanisms that contribute to the enhancement of their 2PA cross section in the near-IR spectral region of excitation, λex ) 700-1000 nm. In particular, we have shown that in some tetraazaporphyrins with symmetric electron-accepting peripheral substitution7b and also in conjugated porphyrin dimers8 the two-photon transition into onephoton-forbidden gerade states can have a cross section as large as σ2 ≈ 103-104 GM. However, one can expect that an asymmetric π-conjugated substitution of porphyrin with electron donating and/or accepting * Author to whom correspondence should be addressed. Phone: (406) 994-7831. Fax: (406) 994-4452. E-mail: [email protected]. † Department of Physics, Montana State University. ‡ Department of Chemistry and Biochemistry, Montana State University. § Polish Academy of Sciences. | Synar Technologies, Inc.

groups can break the center of inversion and trigger two-photon transition into the one-photon-allowed Soret band. This type of transition can be particularly intensified if it is of a strong charge-transfer (CT) character.9 This means that in such a molecule there appears an additional channel of 2PA, which is based upon the difference between permanent dipole moments in the ground and final states. At the same time, one can expect that this transition can also be resonantly enhanced due to the intermediate one-photon Q-state(s), occurring near one-half of the 2PA transition energy, similarly to the case of centrosymmetric tetrapyrroles.7,8 In this article we consider a family of new non-centrosymmetric porphyrins, bearing at the meso-position special electrondonating groups (D) with 4-diphenylaminostilbene (DPAS) or 4,4′-bis-(diphenylamino)stilbene (BDPAS) motifs. Such substitution can result in two different mechanisms of efficient twophoton-induced excitation of the porphyrin moiety. First, when electronic π-conjugation between the porphyrin and the substituent is broken, the porphyrin part (Por) of the molecule can be excited as a result of resonant energy transfer from initially two-photon-excited substituent groups. This mechanism of 2PA excitation in Por-D dyads and porphyrin-core dendrimers grafted with several 2PA-absorbing groups was considered previously.10-13 Here we focus on the second mechanism, where the substituent is strongly π-conjugated to a porphyrin macrocycle, thus resulting in a dramatic change of the optical spectra of the latter. We show here that this can be achieved by using ethenyl- and ethynyl-bonding of the porphyrin and D substituent. As a result, we find for these molecules two very strong (σ2 ≈ 103 GM) 2PA bands in the Soret region, one at λex ) 810-830 nm and the other at λex ≈ 915 nm. In comparison to centrosymmetric tetrapyrrole systems, these bands cover a much broader spectral region, which can find use in optical limiting applications. We further demonstrate that for the lower-energy

10.1021/jp0551770 CCC: $33.50 © 2006 American Chemical Society Published on Web 05/02/2006

2PA in Asymmetrically Substituted Porphyrins

J. Phys. Chem. B, Vol. 110, No. 20, 2006 9803

1 Rf0(2) ) σ2I2 2

Figure 1. Two alternative pathways for two-photon absorption in a three-level system. (a) The virtual path involves a real intermediate resonance (i). (b) The dipole path bypasses intermediate resonance and consists of two amplitudes, each depending on the permanent dipole moment, one in the ground state (0) and another in the final state (f). Hollow arrows show the transition dipole moments, and filled arrows show the photon energies.

transition, i.e., near λex ) 915 nm, a large permanent dipole change is most important in determining strong 2PA, whereas the higher-energy transition comprises two competing quantummechanical 2PA pathways with comparable amplitudes: One involves a transition in a three-level system via intermediate one-photon resonance, and the other connects the same initial and final states but does not need an intermediate level because of appreciable change of the permanent dipole moment upon excitation. Since the overall probability of 2PA is a square of the modulus of the sum of two pathway amplitudes, the interference term will be nonnegligible if the amplitudes are of comparable magnitudes. Such “2 + 2” type of interference has previously been predicted theoretically in refs 9 and 14-18. Furthermore, a possibility of quantum control of 2PA efficiency by varying frequencies and relative polarizations of two laser beams has also been discussed.15,17 However, this effect has not been shown experimentally so far. This article presents, to the best of our knowledge, a first demonstration of quantum interference between permanent dipole moment change and intermediate-resonance pathways in two-photon absorption. 2. Theoretical Background: Three-Level Model for 2PA in Nonsymmetrical Molecules Let us consider a three-level system for a nonsymmetrical molecule, with the ground, 0, intermediate, i, and final, f, states (Figure 1a). Second-order perturbation theory with the summation over all intermediate states, including 0 and f, gives for the 2PA cross section19

〈|

ν σ2(ν) ) A (e‚µfi)(e‚µi0) + (e‚µf0)(e‚∆µf0) νi0 - ν

|〉 2

g(2ν) (1)

where A ) 2(2πL)4/(hcn)2, h is the Planck constant, c is the speed of light, n is the refractive index of the solution, L ) (n2 + 2)/3 is the Lorentz local field factor, ν is the laser excitation frequency (in Hz), e is the unit electric field polarization vector, µkl are the transition dipole moments between states k and l, νkl are the corresponding transition frequencies, ∆µf0 ) µf - µ0 is the difference between permanent dipole moments in the states f and 0, and g(2ν) is the 2PA line shape function (in Hz-1), ∞ g(2ν) d(2ν) ) 1. The angle brackets normalized such that ∫-∞ denote the averaging over all molecular orientations. In derivation of eq 1 one uses the commonly accepted in the experimental literature20 definition of the two-photon cross section

(2)

where Rf0(2) is the molecular transition rate (in s-1) and I is the photon flux (in photon s-1 cm-2). Note that the permanent dipole difference in eq 1 is due to the fact that the summation in perturbation expansion includes not only the intermediate energy level i but also both the initial and the final states.21 The permanent dipole can be neglected in symmetrical molecules, but in nonsymmetrical systems, such as discussed in this paper, it may have a significant impact on 2PA properties.9,14-18 In fact, the two terms in eq 1 can be viewed as representing two alternative quantum transition pathways. The first, so-called “virtual” path, connects the ground state, g, to the final excited state, f, via intermediate state i (Figure 1a). The second, so-called “dipole” path, directly connects g to f (Figure 1b). Note that while the virtual path is strongly dependent on the detuning between the laser frequency and the intermediate resonance, ∆ν ) νi0 - ν, the dipole path bypasses the intermediate resonance and is, therefore, independent of ∆ν. Below we will use this important distinction to separate the two contributions in measured 2PA spectra. Isotropic spatial averaging in eq 1 gives the following result14,22

{[

(

1 ν (2(µfi‚µi0)2 + |µfi|2|µi0|2) σ2(ν) ) A 15 νi0 - ν

[

)] 2

+

[2(∆µf0‚µf0)2 + |∆µf0|2|µf0|2] + ((∆µf0‚µf0)(µfi‚µi0) +

(

(∆µf0‚µfi)(µf0‚µi0) + (∆µf0‚µi0)(µf0‚µfi))

2ν νi0 - ν

)]}

(3)

Here, square brackets collect similar terms in three groups. The first group corresponds to the virtual pathway, the second to the dipole pathway, and the third to the interference between these two pathways. If all the dipole moments are either parallel or antiparallel to a particular molecular axis, say x, then eq 3 recombines to

[ (

)

]

2 ν 1 σ2(ν) ) A µi0µfi + ∆µf0µf0 g(2ν) 5 νi0 - ν

(4)

where µi0, µfi, µf0, and ∆µf0 represent the projections of all dipole moment vectors on the positive direction of the x-axis. Depending on the relative magnitude of different molecular dipole moments, as well as the reverse detuning factor X ) ν/(νi0 ν), one of the terms in eq 4 can be stronger or weaker than the other. For example, if |µi0µfi|X . |∆µf0µf0|, then the virtual pathway dominates, and we obtain a known result8b,c,19 for the three-level system without a permanent dipole 2 2 1 µi0 µfi 2 ν g(2ν) σ2(ν) ) A 5 (ν - ν)2

(5)

i0

In the opposite situation, when |µi0µfi|X , |∆µf0µf0|, the dipole term dominates, and the cross section can be described in the framework of a two-level system

1 σ2(ν) ) A ∆µf02µf02g(2ν) 5

(6)

In the intermediate case, when |µi0µfi|X ≈ |∆µf0µf0|, nonlinear absorption should exhibit quantum interference, and the corresponding absorption will depend on the relative phase between the two paths (cf. refs 15-18, 23, and 24). In particular, if one

9804 J. Phys. Chem. B, Vol. 110, No. 20, 2006

Drobizhev et al.

of the four dipole vectors is directed opposite to the other three, then the two terms in eq 4 will have opposite signs (we consider only the situation where νi0 > ν), and the 2PA cross section will be lower than the sum of two contributions resulting from separate 2PA pathways. At a particular combination of molecular parameters and laser frequency this can even result in a complete cancellation of two-photon absorptivity. In all other arrangements of dipoles (the dipoles are pointing to the same direction all together or by pairs) one will obtain a constructive interference and enhancement of the 2PA cross section. 3. Experimental Section Figure 2 shows the chemical structure of the porphyrins studied in this work. The compounds were obtained by condensing 10-(2′,6′-dichlorophenyl) bilane with a corresponding aldehyde under acidic conditions, followed by oxidation with 2,3-dichloro-5,6-cyano-1,4-benzoquinone (DDQ). All of the porphyrins were purified by column chromatography on silica gel using 40-50% methylene chloride and hexanes as eluent and were obtained in yields higher than 30%. All of the target porphyrin structures were confirmed by NMR and matrixassisted laser desorption ionization time-of-flight (MALDI-TOF) mass spectrometry. A more detailed synthetic procedure is described in ref 6c. Linear absorption spectra of the solutions were measured using a UV-vis spectrophotometer (Perkin-Elmer Lambda 900). Fluorescence emission, excitation, and excitation polarization spectra were recorded with a luminescence spectrometer (PerkinElmer LS 50B). Fluorescence anisotropy was measured with the standard single-channel method.25 Fluorescence quantum yields ΦF were evaluated by integrating the fluorescence intensity of the unknown and reference samples and using the relation26

ΦF )

∫ F(ν˜ ) dν˜ 1 - 10-OD Φ -OD FR nR2 ∫ FR(ν˜ ) dν˜ 1 - 10 n2

R

(7)

where the index R denotes the reference solution and no index designates the solution under investigation, F(ν˜ ) is the fluorescence spectrum, ν˜ is the frequency (in cm-1), and OD is the optical density at the excitation wavelength. This wavelength was chosen such that the condition OD e 0.2 was satisfied simultaneously for the measured solution and for the reference sample, which in our case was tetraphenylporphyrin free base in toluene at ambient conditions (for which ΦFR ) 0.06127). Time-resolved fluorescence decay kinetics was measured with the standard time-correlated single-photon counting technique, as described in refs 28 and 29. Our laser system for two-photon absorption measurements comprised a Ti:sapphire femtosecond oscillator (Coherent Mira 900) pumped by a 5 W continuous wave frequency-doubled Nd:YAG laser (Coherent Verdi) and a 1 kHz repetition rate Ti:sapphire femtosecond regenerative amplifier (CPA-1000, Clark MXR). The pulses from the amplifier were downconverted with an optical parametric amplifier, OPA (TOPAS, Quantronix), whose output can be continuously tuned from 1100 to 2000 nm. The fundamental of the signal and the second harmonic of the idler were used for two-photon excitation in the Q- and Soret regions, respectively. The OPA output signal pulse energy was 100-200 µJ (5-10 µJ after frequency doubling of the idler), and the pulse duration was 100 fs. The excitation laser beam was slightly focused and directed to the sample dichloromethane solution contained in 1 cm

spectroscopic cell. A small fraction of the beam was split off by a thin glass plate, placed just before the sample, and was directed to the reference detector (Molectron). The sample fluorescence was collected with a spherical mirror and focused on the entrance slit of an imaging grating spectrometer (Jobin Yvon Triax 550). The 2PA spectrum (in relative units) was obtained by tuning the wavelength of the OPA and measuring the corresponding intensity of two-photon-excited fluorescence. The wavelength tuning of OPA and data collection were computer-controlled with a LabView routine. At each wavelength, the fluorescence intensity was normalized to the square of the excitation photon flux, measured in the reference channel. To exclude possible artifacts due to linear absorption at wavelengths close to intermediate resonance and any population saturation, we checked that at each measured wavelength the fluorescence signal increased as a square of excitation intensity. Absolute 2PA cross sections in the Q-band region were measured using a fluorescence technique8c relative to free-base tetraphenylporphyrine in toluene, for which σ2 ) 3.5 GM at 1180 nm.7c Two-photon absorption cross sections in the Soret region (λex ) 795 nm) were determined in our previous paper.10 To obtain absolute 2PA spectra in GM units, all raw 2PA spectra were calibrated to the known (at one wavelength) absolute cross section value. 4. Results 4.1. One-Photon Absorption Spectra. Figure 2 shows the UV-vis absorption spectra of the two series of porphyrins with (diphenylamino)stilbene (DPAS) (2, 4, and 6) and 4,4′-bis(diphenylamino)stilbene (BDPAS) (3, 5, and 7) attached at the meso-position. In both series, the Q-band as well as B-band regions undergo a systematic change when going from the parent 1 and single-bond-linked 2 and 3 to double-bond-linked 4 and 5 and triple-bond-linked 6 and 7. First, we see that the classical porphyrin four-band spectrum in the Q-region suddenly transforms into a two-band spectrum in 4-7 (by analogy with usual porphyrins we call these new features also Q-bands). This fact alone implies that the electronic structure of the porphyrin is strongly influenced by conjugation to the substituent, since in the absence of strong π-conjugation the absorption spectra would be just a superposition of that of the porphyrin and the substituent. Second, the intensity of the lowest-energy Q(1)-transition increases, while its maximum shifts to the red (650-660 nm). The next Q(2)-band is also integrally much stronger than any Q-band of 1-3. Note also that while generally similar the peaks of the triple-bonded 6 and 7 are almost twice as intense and somewhat narrower compared to those of double-bond-linked 4 and 5. Because neither DPAS nor BDPAS absorb in the red part of the spectrum,30,31 all these spectral changes of the Q-bands unambiguously demonstrate that the ethenyl and ethynyl linkers are responsible for increasing π-conjugation. Upon going from 1 to single-bonded 2 and 3, the Soret band slightly broadens but does not shift (λmax ) 405-410 nm). This broadening can be due to a partial overlap of the nondisturbed porphyrin Soret band with a substituent absorption band. In ethenyl- and ethynyl-linked dyads 4-7, we observe both a broadening and a red shift of the Soret band to λmax ) 415425 nm and also an appearance of a very smooth shoulder on its long-wavelength side near 460-470 nm. We relate the red shift to the porphyrin-substituent conjugation effect and assign the shoulder to the CT state (see section 4.6 below for the proof). Fluorescence excitation spectroscopy of 2-7 show that the B-band region comprises two different types of transitions: At



Figure 2. One-photon (full line) and two-photon (symbols) absorption spectra of a series of new modified porphyrins studied in this paper. The bottom abscissa axis represents the transition frequency, and the top one the transition wavelength. The left ordinate axis shows the 2PA cross section, and the right one the 1PA extinction coefficient.


Drobizhev et al.

TABLE 1: Two-Photon Absorption Peak Cross Section (σ2) with Corresponding Laser Excitation Wavelengths (λex) in the Q- and Soret Band Regions Qx(1) (S0 f S1)

Qx(2) (S0 f S2)

Bx(1) (S0 f S3)

Bx(2) (S0 f S4)

λex σ2 λex σ2 λex σ2 λex σ2 molecule (GM) (nm) (GM) (nm) (GM) (nm) (GM) (nm) 4 5 6 7

8.5 20 19 49

1290 1284 1288 1280

64 130 160 250

1142 1149 1141 1153

560 880 500 1100

914 916 907 915

480 810 730 910

816 826 820 803

high excitation frequencies, νex > 25 000 cm-1 (λex < 400 nm) a dual emission from both D (green) and porphyrin (red) can be detected in 2 and 3 and to a lesser extent in 4-7. At lower excitation frequencies, νex < 25 000 cm-1 (λex > 400 nm), only porphyrin fluorescence is present. We therefore conclude that at νex > 25 000 cm-1 the absorption transition is predominantly localized on the D (DPAS or BDPAS) fragment, while at lower frequency the absorption is due to an extended, porphyrin-based, conjugation system. The same dividing line in transition frequencies (i.e., 25 000 cm-1) can also be applied for 2PA spectra, because for stronger conjugated dyads 4-7 the inversion symmetry of D is broken and its 2PA spectrum will follow the 1PA spectrum, whereas for nonconjugated systems 2 and 3, 2PA of both DPAS and BDPAS occurs not lower in energy than 1PA.32,33 In what follows, we will study the region of transition frequencies, lower than 25 000 cm-1, which corresponds to the excitation of the π-electron system of a porphyrin macrocycle, at least partially conjugated with D. The spectral features described here for porphyrins 4-7 agree with earlier reports of meso-alkenyl- or meso-alkynyl-linked porphyrins, where an increase of the Q-band absorption as well as a red shift of both Q- and Soret transitions34-47 were also observed. In those cases where either electron donating or accepting (or both, connected to opposite sides) groups were used for substitution, a red shoulder or even separate peak split off the Soret band was observed and in some cases ascribed to CT states.34,37,39,40,42,44,45 4.2. Two-Photon Absorption Spectra. Figure 2 shows the 2PA spectra of 1, 2, and 4-7, and Table 1 summarizes the observed 2PA cross sections in the corresponding peaks of strongly conjugated 4-7. From these data we can conclude that for enhancement of 2PA the ethynyl linker is better than the ethenyl one and the longer substituent (BDPAS) is almost always better than the shorter (DPAS). We relate the first effect to a weaker conjugation between D and Por parts in ethenyllinked molecules due to a steric hindrance between the porphyrin β and the linker ethenyl protons. Since all of these molecules do not possess a center of inversion, one can anticipate that the 2PA transitions will roughly coincide with the 1PA transitions, although the intensity distribution should not necessarily be the same in 2PA and 1PA. Figure 3 shows a detailed 2PA spectrum in the Q-region of 4-7. As expected, 2PA basically follows the 1PA spectra. Note that the absolute 2PA cross sections of all the molecules in the lowest, Q(1), band are much larger than those obtained earlier7c for different symmetrically substituted porphyrins, i.e., σ2 ) 10-70 GM vs 0.5-2 GM. 2PA spectra of 4-7 in the Soret region (Figure 2) are, however, intriguingly distinct from the corresponding 1PA spectra. While the 1PA spectrum consists of one broad band, the 2PA spectrum shows at least two spectrally resolved peaks. Note that both 2PA peak cross section values are particularly large σ2 ) 500-1000 GM, which is much larger than ∼10 and

110 GM, found in this region for 1 and 2, respectively.6a One 2PA peak almost coincides with the 1PA maximum (at λ2PA/2 ≈ 410-415 nm), and another is shifted to lower frequencies (λ2PA/2 ≈ 460-470 nm). The nature of this latter 2PA transition is not so obvious, but the above-mentioned shoulder in the longwavelength side of the 1PA Soret envelope gives us a possible hint that its CT character can be strongly revealed in 2PA. To further elucidate the nature of 2PA transitions presented here and quantitatively describe their intensities with the model equations of section 2, we accomplish in the following sections a series of additional measurements. First we study fluorescence polarization as a function of excitation wavelength to spectrally resolve a number of otherwise hidden, strongly overlapping absorption transitions. Then, using fluorescence lifetime and polarization measurements in different solvents, we obtain effective molecular cavity volume, which is necessary for ultimate evaluation of the permanent dipole moment change from solvatochromic data for each polarization-resolved transition. These data allow us to explain strong two-photon absorption and demonstrate the effect of quantum interference introduced above in section 2. Because of the qualitative similarity of 2PA features in 4-7, we selected for such a detailed analysis molecule 7, which shows the strongest 2PA. 4.3. Fluorescence Polarization as a Function of Excitation Wavelength: Resolution of Hidden 1PA Transitions. Fluorescence anisotropy, r, was measured as a function of excitation frequency, while the emission detection wavelength was set at the red side of the 0-0 fluorescence peak. Figure 4 (upper part) presents the anisotropy spectrum of 7 in dichloromethane. First of all, we see that the maximum anisotropy, rmax, is attained at the lowest frequency, whereas minimum value, rmin, is observed at high frequencies (wavelength region, 390-410 nm), and that r is always positive. According to ref 25, fluorescence anisotropy depends on the angle R between excitation and emission transition dipoles as follows

r ) rmax

3 cos2 R - 1 2

(8)

where rmax corresponds to a collinear arrangement of excitation and emission dipoles. Using the experimentally measured ratio rmin/rmax ≈ 0.25, we can conclude that rmin corresponds to the excitation of the dipole, directed at R ≈ 45° with respect to the longest-wavelength transition. This conclusion is reasonable, especially if we take into account that mono- and di-mesosubstituted porphyrins possess two coordinate frames rotated about the axis perpendicular to the tetrapyrrole plane with respect to each other by 45°. One frame is built on the x-axis connecting meso-meso substituents, and the y-axis is perpenidicular to it. Another frame involves axis x′, parallel to the NH-HN direction inside the tetrapyrrole ring, and axis y′ is perpendicular to it. Note that R ≈ 45° between different electronic transitions was found previously for mono- and diaza-substituted porphyrins,48 possessing similar symmetry. Since the excitation anisotropy measurements give only relative orientations of absorption transitions, we cannot unambiguously assign all of the observed transition polarizations to particular directions within the molecular frame. However, it is reasonable to assume that the longest-wavelength Qtransition is polarized along the x-axis because of the strongly extended π-conjugation in this direction. This assumption is also corroborated by the data obtained for a number of other mesomeso donor-acceptor-substituted porphyrins on the basis of quantum-chemical calculations.35,36,40



Figure 3. Two-photon absorption spectra of 4-7 in the Q-band region (symbols). The dashed line is a guide to the eye. Normalized one-photon absorption is also shown for comparison (solid line).

The fact that in 7 the anisotropy is positive, and even stays larger or equal to 0.25rmax, can imply that all of the observed transition dipoles are either parallel to the x-axis or directed at 45° to it. With this information in hand, we now are going to resolve the absorption spectrum into two contributions, polarized at 0° and 45° with respect to the x-axis. From the approach described in ref 25, the measured anisotropy can be written as a sum of two terms

r(ν) ) f0(ν)r0 + f45(ν)r45

(9)

where fR (ν) represents a fractional contribution of the transition with polarization R to the total absorption and rR represents the anisotropy of this transition. In our case, r0 ) rmax and r45 ) 0.25rmax. Since, by definition, f0(ν) + f45(ν) ) 1, one can easily obtain

f0(ν) )

r(ν) - r45 r(ν) - 0.25rmax ) f45(ν) ) 1 - f0(ν) r0 - r45 0.75rmax (10)

The contributions to the total absorption spectrum A(ν), polarized at 0° and 45° are given by

A0(ν) ) f0(ν)A(ν) A45(ν) ) f45(ν)A(ν)

(11)

Figure 4 shows both A0(ν) (solid thin line) and A45(ν) (dashed line) as well as the total absorption spectrum (solid bold line) for 7 in dichloromethane, obtained by using eqs 10 and 11. As one can see, there are four moderately strong absorption bands polarized along the x-axis, two in the Q-region and two in the Soret region. The two parallel polarized Q-bands, Qx(1) at 660 nm and Qx(2) at 578 nm, almost completely dominate in the red part of the absorption spectrum. The first x-polarized Bx(1)transition (at 470 nm) makes up the long-wavelength shoulder of the complex and broad Soret band, and the second one, Bx(2) at 418 nm, is responsible for a narrow peak on the top of that band. The strongest contribution to the Soret band comes from transitions polarized at 45° to the x-axis, Bx′ and By′. They constitute a very broad distribution (centered at 415 nm), which is probably composed of transitions localized on the porphyrin nucleus. Note that at λ < 400 nm the transitions localized on the substituent moiety also start to contribute to the absorption spectrum (see above). 4.4. Time-Resolved and Steady-State Fluorescence Spectrsocopy: Fluorescence Lifetime in Different Solvents. Here we determine fluorescence lifetime values in different solvents,


Figure 4. Absorption anisotropy of 7. Top part: Fluorescence anisotropy as a function of excitation frequency. Horizontal dashed lines show minimum and maximum limits of r. Bottom part: Decomposition of the absorption spectrum (bold solid line) into two components: one polarized at 0° (thin solid line) and another at 45° (dashed line) to the fluorescence dipole moment. The inset shows the orientation of the molecular axes.

Drobizhev et al.

Figure 6. Fluorescence spectra of 7 in different solvents. Excitation wavelength λex ) 578 nm. All spectra are normalized to the optical density at the excitation wavelength.

phenyl group). This process is facilitated in polar solvents by stronger solvation of emerging ions, thus resulting in lowering of the energy of the final charge-transfer (CT) state. Such a CT state rapidly recombines nonradiatively to give the ground state. A similar quenching effect was observed for a number of other porphyrins bearing strong electron-withdrawing substituents.49-54 The radiative lifetime value, τR, of 7 has been calculated according to the Strickler-Berg equation55

1 ) 2.88 × 10-9n2〈νjF-3〉Aν-1 τR

∫

(νj) dνj νj

(12)

where

〈νjF-3〉Aν-1 )

Figure 5. Fluorescence decay kinetics of 1, 7, and BDPAS, curves from top to bottom, respectively, measured in benzene and presented in a logarithmic scale.

which will be used in the following for evaluation of effective molecular volume and permanent dipole moment changes. Figure 5 demonstrates the fluorescence decay kinetics of 7 and that of its separate constituent parts, BDPAS and 1, in benzene solution upon excitation at 401 nm. All three curves are well described by a single exponent with lifetimes of 2.73, 1.26, and 3.61 ns, respectively. Steady-state fluorescence spectra and fluorescence quantum efficiencies of 7 were measured (at λex ) 578 nm) in a number of solvents with different polarities, and the results are presented in Figure 6 and Table 2. We find strong fluorescence quenching in polar solvents. For instance, the quantum yield of fluorescence decreases by more than an order of magnitude when going from benzene to acetone. Note that in the same conditions the fluorescence quantum yield of parent molecule 1 changes from ΦF ) 0.023 to 0.017, i.e., only by 25%. Since 1 does not bear a D substituent group, we attribute the above strong quenching effect in 7 to a complete intramolecular electron transfer from the BDPAS part to the porphyrin core (including the dichloro-

∫ F(νj) dνj ∫

F(νj) dν

(13)

νj3

(νj) is the absorption spectrum presented as an extinction coefficient (in M-1 cm-1) versus frequency νj (in cm-1) and F(νj)is the fluorescence spectrum. The fluorescence spectrum of 7 in dicholoromethane consists of three Gaussian peaks, Figure 7, which correspond to the strong pure electronic transition, at νjF(0-0) ) 15 040 cm-1, and two weaker vibronic peaks, shifted by Ω1 ) 460 cm-1 and Ω2 ) 1200 cm-1 to lower frequencies. Therefore, to apply the Strickler-Berg equation, we first simulate the absorption spectrum in the region of the Q-bands with four Gaussian peaks (Figure 7): one corresponding to the Qx(1)(0-0) transition with the central frequency at νjA(0-0) ) 15 160 cm-1, two others corresponding to vibronic satellites, Qx(1)(0-1) and Qx(1)(0-1′), with the frequencies fixed at νjA(0-0) + 460 cm-1 and νjA(0-0) + 1200 cm-1, respectively, and the fourth peak, corresponding to the whole Qx(2)-band. The first three absorption peaks taken together represent a rather good mirror image of the fluorescence spectrum. By substituting the integral intensity of these three peaks and the quantity from eq 13 obtained from the fluorescence spectrum into eq 12, we obtain τR ) 38 ns. Table 2 presents fluorescence lifetimes τ in different solvents, which were obtained from steady-state measurements using the relation τ ) τRΦF. We note a very good correlation between the fluorescence lifetime value obtained for 7 in benzene from



TABLE 2: Optical Properties of 7 in Different Solvents

solvent

a

nb

ηc (cP)

n-octane n-hexane benzene butyl-ether soybean oil chloroform tetrahydrofuran 2-chlorobutane dichloromethane 4-methyl-pentanone acetone acetonitrile

2.0 2.02 2.27 3.08 3.2 4.81 7.58 8.06 8.93 13.1 20.7 37.5

1.398 1.375 1.501 1.398 1.466 1.446 1.407 1.396 1.424 1.396 1.359 1.344

0.546 0.307 0.65 0.691 69 0.57 0.48 0.412 0.425 0.59 0.325 0.357

λabsd (Qx(1)) (nm)

λfluoe (Qx(1)) (nm)

ΦFf

τg (ns)

rmaxh

662 662 662 660 662 660 660 660 660 660 658 658

663.5 663 666.5 664.5 666 667 666 665 664.5 665 663.5 662

0.063 0.063 0.075 0.068 0.069 0.068 0.031 0.044 0.011 0.012 0.0068 0.010

2.39 2.39 2.85 2.58 2.62 2.58 1.18 1.67 (0.42) (0.46) (0.26) (0.38)

0.049 0.031 0.055 0.057 0.28 0.057 0.085 0.062 0.065 0.111 0.060 0.045

a Dielectric constant. b Index of refraction. c Viscosity. d Absorption maximum of the first Q-band envelope. e Fluorescence maximum. f Fluorescence quantum yield. The fluorescence quantum yield was measured relative to H2TPP in toluene, for which ΦF ) 0.061.27 g Fluorescnce lifetime. Effective fluorescence lifetimes values are given in parentheses in those cases where the decay kinetics is expected to be not monoexponential (section 4.4). h Maximum value of the fluorescence anisotropy.

Figure 7. Normalized absorption (solid circles) and fluorescence (empty circles) spectra of 7 in dichloromethane in the region of the Qx(1)-transition. Both spectra consist of three vibronic components, shown by dotted (0-0), dashed (0-1), and dash-dotted (0-1′) lines. The onset of a broad, unresolved Qx(2) absorption band is shown by the solid line.

these steady-state measurements (τ ) 2.85 ns, Table 2) and that measured directly from fluorescence decay kinetics (τ ) 2.73 ns). 4.5. Fluorescence Polarization as a Function of Solvent Viscosity. We now measure the dependence of fluorescence anisotropy as a function of solvent viscosity to evaluate the effective molecular volume. The last column of Table 2 presents the limiting fluorescence anisotropy value, rmax, measured upon exciting the Qx(1)(0-0) band of 7 and recording the fluorescence in the same transition (at a slightly longer wavelength). For isotropic rotational motion of a molecule in a solvent with viscosity η and in the case of monoexponential decay of fluorescence with time τ, this anisotropy value will obey the Perrin equation25

rmax )

0.4 τkT 1+ ηV

(14)

where k is the Boltzmann constant, T is the temperature, and V is the effective molecular volume which has to be found.

Figure 8. Perrin plot for the anisotropy of fluorescence in the Qx(1)transition of 7 measured in a series of nonpolar solvents. The best linear regression passing through the origin is shown by the solid line.

Fluorescence decay kinetics in nonpolar solvents (with < 8) is described by monoexponential decay; see Figure 5. In more polar solvents, a photoinduced charge separation can result in biexponential decay, which is related to two different decay times of thermally equilibrated charge-separated and singletexcited porphyrin states (ref 54 and references therein). Therefore, eq 14 can be applied directly to a set of data in nonpolar solvents only. Representation of experimental data in 0.4/rmax - 1 vs τ/η coordinates is shown in Figure 8. The slope of the corresponding linear regression is found to be kT/V ) (1.72 ( 0.04) × 107 erg/cm3. This corresponds to the volume of a molecular equivalent sphere V ) 2350 ( 50 Å3 with the radius a ) 8.25 ( 0.06 Å. 4.6. Solvatochromic Shifts of Absorption and Fluorescence Peaks: Permanent Dipole Moment Changes. The measurements of solvatochromic shifts, presented below, provide the values of the permanent dipole moment changes, associated with each particular absorption transition. We concentrate on solvatochromism of optical transitions polarized only along the x-axis, because they are much better resolved than those polarized at 45° to the x-axis (Figure 4). In our practical approach we first resolve x-polarized transitions, as described in section 4.3, in each particular solvent, and then follow their maxima shifts as


Drobizhev et al.

a function of polarity. Usually in such measurements one uses solvents with equal refractive indices to simplify the analysis to consideration of only dipole-dipole interactions.56 We use here a series of preselected solvents with different but very similar n values, which were shown previously to interact with tetrapyrrolic molecules only nonspecifically (via dipole-dipole interactions).57,58 We first consider the lowest Qx(1)(0-0) transition. If νjS is the Stokes’ shift (in cm-1) between absorption νjA(0-0) and fluorescence νjF(0-0) pure electronic transition maxima, νjS ) νjA(0-0) - νjF(0-0), then according to the theory (ref 56 and references therein), the difference in fluorescence Stokes’ shifts ∆νjS, observed in two solvents with different dielectric constants is given by

hc∆νjS ) |∆µf0|2a-3∆f()

(15)

where f() is the Onsager polarity function: f() ) 2( - 1)/ (2 +1). Figure 9a shows the dependence of the Stokes shift of 7 on f(), which is described quite well by a straight line with the slope |∆µ10|2/hca3 ) 177 ( 12 cm-1. Using the molecular radius, a ) 8.25 Å, determined in the previous section, we calculate |∆µ10| ) 4.5 ( 0.4 D. This latter value implies that the lowest electronic transition (Qx(1)(0-0)) is accompanied by an appreciable charge transfer. Equation 15 can be applied to the lowest S0 f S1 transition only. For higher absorption transitions, one can use another equation, which relates the shift of the absorption maximum to solvent polarity56

hc∆νjA ) -(µ0‚∆µf0)a-3∆f()

(16)

where µ0 is the permanent dipole moment in the ground state and the parentheses designate the scalar product of the two vectors involved. To find the |∆µf0| values for higher-lying transitions, we first need to determine the value of permanent dipole moments in the ground state. This can be done by measuring the absorption solvatochromic shift (eq 16) of the Qx(1)-band and employing the value of |∆µ10| already known from the Stokes shift data. Figure 9b, lower plot, presents the frequency shift of the Qx(1)band absorption maximum. The slope of the corresponding linear regression is -(µ0‚∆µ10)/hca3 ) 90 ( 19 cm-1. From the specific molecular geometry of 7 it is reasonable to assume that the angle between µ0 and ∆µ10 is either 0° or 180°, and therefore, we can find the molecular dipole moment in the ground state from the above slope and known values of a and ∆µ10: |µ0| ) 2.3 ( 0.5 D. The positive sign of the slope implies opposite directions of ∆µ10 and µ0. Figure 9b, upper plot, demonstrates that the next Qx(2)-band has almost vanishing solvatochromic shift falling within the error margins of our measurements. The frequency shifts for Bx(1)- and Bx(2)-transitions as a function of solvent polarity are shown in Figure 9c. As one can see, the slope of the Bx(1)-transition is quite large, with -(µ0‚ ∆µ30)/hca3 ) -400 ( 90 cm-1, thus resulting in a large value of the permanent dipole moment change |∆µ30| ) 20.0 ( 4.5 D with coinciding directions of µ0 and ∆µ30. Note that the similarly large values of |∆µ| for the lowest component of the Soret manifold were also found in some other A-Por and A-Por-D structures.40,52 However, the Bx(2)-band maximum changes nonsystematically, and the best linear fit to the data gives a moderate solvatochromic shift with large error margins, -(µ0‚∆µ30)/hca3

Figure 9. Fluorescence and absorption peak positions of 7 as a function of the Onsager solvent polarity function: Stokes’ shift (a), frequency of the x-polarized absorption maxima in the Q-band region and the Soret band region (c). The symbols at data points designate the following solvents: o, octane; be, butyl ether; ii, isobutyl isobutyrate; ia, isobutyl acetate; cb, 2-chlorobutane; mp, 4-methyl-2-pentanone; thf, tetrahydrofurane; a, acetone. The best linear regression is shown by solid lines.

) 75 ( 150 cm-1, allowing only an approximate estimation of the possible range of dipole moment change: |∆µ40| ) 3.7 ( 7.4 D.



TABLE 3: Some Ground- and First-Excited-State Molecular Parameters of 7 parameter

τRa (ns)

ab (Å)

µ0c (D)

value

38 ( 4

8.25 ( 0.06

2.3 ( 0.5

a

Radiative lifetime. b Effective molecular radius. c Ground-state permanent dipole moment.

TABLE 4: Linear Optical Properties of the First Five Excited States of 7 in Dichloromethane transition

λmaxa (nm)

maxb (104 M-1cm-1)

∆µf0c (D)

µf0d (D)

Qx(1) (S0 f S1) Qx(2) (S0 f S2) Bx(1) (S0 f S3) Bx(2) (S0 f S4) Bx′-y′

660 578 470 418 415

2.2 5.3 4.8 6.6 19.4

-4.5 ( 0.4 -0.9 ( 1.2 20 ( 4.5 -3.7 ( 7.4

3.0 4.9 6.6 5.1

a Peak wavelength. b Peak extinction coefficient. c Change of permanent dipole moment upon excitation (projection to direction of µ0). d Transition dipole moment.

Tables 3 and 4 summarize the main molecular parameters determined in the previous three sections for 7. 5. Quantitative Comparison of the 2PA Spectrum of 7 with the Theoretical Model 5.1. 2PA in the Q-Band Region. We have previously shown7b,c,f,59 that by comparing 1PA and 2PA spectra in the region of the lowest pure electronic, Q(0-0), transition one can conclude whether a molecule possesses the center of inversion or not. In centrosymmetric molecules the 2PA of laser photons tuned to one-half of the Q(0-0) transition frequency will be strongly forbidden. However, in non-centrosymmetric molecules the 1PA and 2PA peaks should coincide because there are no intermediate states any closer to the laser frequency, and therefore, there is no shift of the 2PA peak due to resonance enhancement effects. In this latter case the Q(0-0) 2PA transition can be described within the framework of the twolevel model. Since the structures of 4-7 are strongly asymmetric, at first glance it is quite surprising that their lowest 2PA transition does not exactly coincide with the Qx(1) 1PA peak. However, as we already know, the observed Qx(1)-band is composed of two overlapping peaks, Qx(1)(0-0) and Qx(1)(01), the latter shifted in the case of 7 by only Ω1 ) 460 cm-1 to higher frequencies. Therefore, we can easily explain a blue shift and a broadening of the Qx(1)-peak in 2PA, compared to 1PA, if we suppose that the vibronic Qx(1)(0-1) 2PA transition may borrow its intensity from the 0-0 2PA transition, the effect known for different non-centrosymmetric molecules,60 including tetrapyrroles.59 In fact, the 2PA spectrum can be well described by a sum of two Gaussians (Figure 10), which have the same central frequencies and widths as Qx(1)(0-0) and Qx(1)(0-1) 1PA transitions but a different intensity ratio. This decomposition gives us the maximum 2PA cross section of the Qx(1)(0-0) transition, σ2 ) 23 ( 5 GM. Now we can check the applicability of the two-level approximation to the Qx(1)(0-0) 2PA transition even quantitatively. Using eq 6 and noticing that7a

µf02g(νjf0) )

3 × 103 ln 10 h f0(νjf0) νjf0 (2π)3NA

where NA is Avogadro’s number, one can obtain

(17)

Figure 10. One-photon absorption (bold solid line) and two-photon absorption (symbols) spectra of 7 in the region of the Qx(1)-transition. The 1PA spectrum is decomposed into 0-0 (dotted), 0-1, (dashed), and 0-1′ (dash-dotted) transitions. The best fit of the 2PA band (solid line) consists of two Gaussians: The first coincides with the 0-0 peak of the 1PA spectrum (same dotted line as for the 1PA), and the second with the 0-1 peak (dash-dot-dotted) with the same central frequency and width as the corresponding 1PA peak, but with different amplitude. The difference in the amplitude ratio between the 0-0 and the 0-1 peaks in the 1PA and 2PA spectra explains a blue shift of 2PA with respect to 1PA.

( )

σ2

νjf0 f0(νjf0) 12 ln 10 π 103 L4 ) ∆µf02 ) 2 2 2 5 νjf0 N hc n A

f0(νjf0) L4 (18) 4.84 × 10-15 2∆µf02 νjf0 n This last equation contains in its right-hand side only the 1PA parameters, the change of the permanent dipole moment of the molecule, and the solvent refractive index. Substituting the data previously obtained for 7, |∆µ10| ) 4.5 D, 10(νj10) ) 2.2 × 104 M-1 cm-1, and νj10 ) 15 150 cm-1 and using n ) 1.424 and L ) 1.34 for dichloromethane, we obtain for the Qx(1)(0-0) transition: σ2(νjf0) ) 23 ( 4 GM. Very good agreement of this value with σ2 found directly from the 2PA experiment supports the validity of the two-level approximation (eq 6) for the lowest pure electronic transition. It also justifies our method of resolving the lowest 2PA peak into two components (Figure 10) and our assumption that the angle between ∆µ10 and µ10 is close to 180°. Furthermore, this result demonstrates that the 2PA cross section in a two-level system can be predicted a priori by measuring the 1PA extinction coefficient and the change in the permanent dipole moment. Strong intensification of the second, Qx(2), band in 2PA spectrum cannot be quantitatively explained at this moment. Since the change of the permanent dipole moment is small for this transition, we assume that the effect of strong resonance enhancement is due to intermediate level(s). Also, higherfrequency vibronic transitions of the Qx(1)-manifold can contribute considerably to 2PA of Qx(2). 5.2. 2PA in the Soret Region. We are now in a position where we can quantitatively compare the theoretical three-level model, described in section 2, with the 2PA spectra measured in our experiment. Figure 11a shows the 2PA spectrum of 7 in the Soret region, plotted together with the 1PA spectral component polarized parallel to the x-axis (as found in section 4.3). Note a rather good general correspondence of the two spectra, especially in the region of the Bx(1)-band. We explain


Drobizhev et al. Suppose that the general eq 4 can be applied separately for Bx(1)- and Bx(2)-transitions. Since the 1PA and 2PA are simultaneously allowed for each transition, we can substitute in eq 4 g(2ν) ) g1(2ν) + g2(2ν), where g1(2ν) and g2(2ν) are (separately) normalized 1PA profiles of Bx(1)- and Bx(1)-peaks, respectively, and 2ν ) ν1PA, where ν1PA is a variable 1PA frequency. To compare the dipole and virtual contributions for each particular transition, we regroup eq 4 as follows

x

5σ2(ν)

ν + ∆µf0µf0 (19) ) µi0µfi ν A(g1(ν1PA) + g2(ν1PA)) i0 - ν

Figure 11. (a) Two-photon absorption spectrum of 7 in the region of the Soret band (symbols). The one-photon absorption component polarized along the x-axis (bold solid line) is also shown for comparison. The 1PA spectrum is fitted (thin solid line) with a sum of two Gaussians (dashed lines). (b) The same spectrum presented in linearizing coordinates (see text for details). The best linear regressions of the 2PA spectrum in the regions of the Bx(1)- and Bx(2)-peaks are shown by straight line segments.

the fact that the 2PA spectrum qualitatively follows the x-polarized 1PA component but not the whole 1PA spectrum by a large charge shift and an extension of the π-conjugated system along the Por-D (x-) direction. As a result, the σ2 value amounts to several hundred GM, which is at least an order of magnitude larger than that expected for transitions localized on the tetrapyrrole macrocycle alone (Bx′ and By′). Our solvatochromism analysis presented above has shown that the two strongly 2PA-allowed states in the Soret region demonstrate either very strong (Bx(1)) or moderately weak (Bx(2)) charge-transfer character. However, from our previous studies7,8 it is known that the 2PA of symmetric porphyrins is often dominated in this spectral region by a virtual mechanism, in which the Q-state plays a role of a real intermediate level, thus resulting in strong resonant enhancement of 2PA.7,8 This suggests that, in principle, both dipole and virtual mechanisms of 2PA could be operative in the nonsymmetric porphyrins studied here. If both mechanisms (quantum pathways) have comparable amplitudes, then they will interfere with each other. Therefore, to prove the presence of this kind of interference we should compare the corresponding relative amplitudes. One possible approach to this problem is presented in what follows.

Presentation of the left-hand side of the above equation, as ordinate, Y, against ν/(νi0 - ν), as abscissa, X, should give a straight line in the region where g1(ν1PA) and g2(ν1PA) do not considerably overlap. The slope of this line gives µi0µfi, and the Y-intercept is equal to ∆µf0µf0. Therefore, by comparing the slope (multiplied by X) and intercept values, one can eventually estimate the relative contribution of the amplitudes of virtual and dipole quantum pathways. Knowing σ2(ν), g1(2ν), and g2(2ν) from experiment and assuming that νi0 corresponds to the frequency of the Qx(1)transition, we can now plot Y versus X, as presented in Figure 11b. Note that Bx(1) and Bx(2) overlap only in the limited interval, 2.8 < X < 3.5, whereas outside of this region 1PA can be well described with a single Gaussian function, corresponding to either Bx(1) or Bx(2) (dashed lines in Figure 11b). As one can also see, outside the overlap region, our plot can indeed be well approximated with two straight line segments. In the Bx(1)transition, the best fit gives a slope value µ10µ31 ) 10 ( 8 D2 and Y-intercept value ∆µ30µ30 ) 127 ( 19 D2. From these data we can immediately conclude that the dipole path contributes much more to the overall 2PA than the virtual path. Although, because of the large experimental error, the exact ratio between two amplitudes is difficult to obtain; we can still estimate that the transition probability amplitude due to the dipole path is ca. 5 times larger than that of the virtual path. In this case, we can neglect the interference between the two paths. Further, by using µ30 ) 6.6 D, which was measured independently from linear absorption (Table 4), we find ∆µ30 ) 19 ( 4 D, which is very close to what was found from solvatochromic shift measurements (20 ( 4.5 D, Table 4). This good agreement between the two ∆µ30 values proves the quantitative validity of our model (eqs 4-6) and the assumption that the angles between ∆µ30 and µ30 as well as between ∆µ30 and µ0 are close to 0° (or 180°). The situation is different in the Bx(2)-transition, where the linear fit has a slope value µ10µ41 ) 53 ( 10 D2, and the Y-intercept value is ∆µ40µ40 ) -83 ( 38 D2. Here, the two pathways have comparable probabilities, with the virtual amplitude about 2.5 times larger than the dipole one. This implies that quantum interference between the two paths cannot be discarded for this transition. Also, because the two amplitudes have opposite signs, this must be destructive interference. Using the slope and µ10 values (Table 4), we can estimate the excited-state transition dipole moment, µ41 ) 18 ( 4 D. This last value is rather high, thus explaining why even with destructive interference the 2PA remains so strong. Note that we have recently observed similarly large excited-state transition dipole moments for a number of π-conjugated porphyrin dimers and explained this effect by very large electron-hole separation in their fully delocalized excited state.8b,c A similar mechanism can apply to the Por-D molecules considered here, because of their specific quasi-one-dimensional extension of the π-electron

2PA in Asymmetrically Substituted Porphyrins system along the x-axis. Therefore, a quite large value of µ41 suggests that µ41 is most probably oriented along the x-axis, which in turn indirectly supports an assumption made in derivation of eq 4 that all four dipole moments involved in 2PA are either parallel or antiparallel to each other. As for the permanent dipole change, by taking µ40 ) 5.1 D (Table 4), we find ∆µ40 ) 16 ( 7 D. Despite the rather large error limits, the allowed ranges of ∆µ40 values found from the 2PA spectrum and independently from solvatochromic shift (Table 4) do overlap at ∆µ40 ) 9 ( 11 D, and therefore the two methods give consistent results. 6. Conclusion We have shown that the new porphyrins with 4-(diphenylamino)stilbene (DPAS) or 4,4′-bis-(diphenylamino)stilbene (BDPAS) attached via π-conjugating ethenyl or ethynyl linkers at the meso-position show very strong intrinsic two-photon absorption in a broad near-IR region: σ2 > 100 GM (at 8001200 nm) and σ2 ) 500-1000 GM (at 800-975 nm). Two strong 2PA transitions in the Soret region are explained by a very large change of the permanent dipole moment (CT transition) and a strong resonance enhancement effect. We demonstrate, to our best knowledge, for the first time the effect of quantum interference between the dipole and the virtual pathways, leading to the same final 2PA state in the highfrequency region of the Soret band. The very advantageous combination of strong 2PA with other special molecular features may facilitate the use of these new porphyrins in photodynamic therapy and imaging of biological processes. Acknowledgment. We thank Joy Rogers and Paul Fleitz for providing the fluorescence lifetime data. This work was supported by the Air Force Office for Scientific Research Grant No. FA9550-05-1-0357, the Department of Energy EPSCoR grant, and the MBRCT Grant No. Z3781. References and Notes (1) (a) Zipfel, W. R.; Williams, R. M.; Webb, W. W. Nat. Biotechnol. 2003, 21, 1369 and references therein. (b) Blanchard-Desce, M. C. R. Phys. 2002, 3, 439 and references therein. (2) (a) Cumpston, B. H.; Ananthavel, S. P.; Barlow, S.; Dyer, D. L.; Ehrlich, J. E.; Erskine, L. L.; Heikal, A. A.; Kuebler, S. M.; Lee, I.-Y. S.; McCord-Maughon, D.; Qin, J.; Ro¨ckel, H.; Rumi, M.; Wu, X.-L.; Marder, S. R.; Perry, J. W. Nature 1999, 398, 51. (b) Zhou, W.; Kuebler, S. M.; Braun, K. L.; Yu, T.; Cammack, J. K.; Ober, C. K.; Perry, J. W.; Marder, S. R. Science 2002, 296, 1106. (3) Spangler, C. W. J. Mater. Chem. 1999, 9, 2013 and references therein. (4) (a) Parthenopoulos, D. A.; Rentzepis, P. M. Science 1989, 245, 843. (b) Burr, G. W. Volumetric Storage. In Encyclopedia of Optical Engineering; Driggers R. G., Ed.; Marcel Dekker: New York, 2003 and references therein. (5) Bhawalkar, J. D.; Kumar, N. D.; Zhao, C.-F.; Prasad, P. N. J. Clin. Lasers Med. Surg. 1997, 15, 201. (6) (a) Karotki, A.; Kruk, M.; Drobizhev, M.; Rebane, A.; Nickel, E.; Spangler, C. W. IEEE J. Sel. Top. Quantum Electron. 2001, 7, 971. (b) Spangler, C. W.; Starkey, J. R.; Meng, F.; Gong, A.; Drobizhev, M.; Rebane, A.; Moss, B. Proc. SPIE-Int. Soc. Opt. Eng. 2005, 5689, 141. (c) Nickel, E.; Spangler, C. W.; Rebane, A. Porphyrins with enhanced multi-photon absorption cross-sections for photodynamic therapy. U. S. Patent 6,953,570 B2, Oct 11, 2005. (7) (a) Drobizhev, M.; Karotki, A.; Kruk, M.; A. Rebane, Chem. Phys. Lett. 2002, 355, 175. (b) Drobizhev, M.; Karotki, A.; Kruk, M.; Mamardashvili, N. Zh.; Rebane, A. Chem. Phys. Lett. 2002, 361, 504. (c) Karotki, A.; Drobizhev, M.; Kruk, M.; Spangler, C.; Nickel, E.; Mamardashvili, N.; Rebane, A. J. Opt. Soc. Am. B 2003, 20, 321. (d) Drobizhev, M.; Karotki, A.; Kruk, M.; Krivokapic, A.; Anderson, H. L.; Rebane, A. Chem. Phys. Lett. 2003, 370, 690. (e) Kruk, M.; Karotki, A.; Drobizhev, M.; Kuzmitsky, V.; Gael, V.; Rebane, A. J. Lumin. 2003, 105, 45. (8) Karotki, A.; Drobizhev, M.; Dzenis, Y.; Taylor, P. N.; Anderson, H. L.; Rebane, A. Phys. Chem. Chem. Phys. 2004, 6, 7. (b) Drobizhev, M.; Stepanenko, Y.; Dzenis, Y.; Karotki, A.; Rebane, A.; Taylor, P. N.;

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