Two-Color Two-Photon Excited Fluorescence of 2-Methyl-5-tert-butyl-p

Article pubs.acs.org/JPCA

Two-Color Two-Photon Excited Fluorescence of 2‑Methyl-5-tertbutyl‑p‑quaterphenyl (DMQ): Ab Initio Calculations and Experimental Determination of the Molecular Parameters Sebastian Herbrich,*,† Karl-Heinz Gericke,*,† Andrey G. Smolin,‡ and Oleg S. Vasyutinskii‡,§ †

Institut für Physikalische und Theoretische Chemie, TU Braunschweig, Hans-Sommer-Strasse 10, 38106 Braunschweig, Germany Ioffe Institute, Polytechnicheskaya 26, 194021 St. Petersburg, Russia § St. Petersburg State Polytechnic University, Polytechnicheskaya 29, 195251 St. Petersburg, Russia ‡

ABSTRACT: The paper presents experimental and theoretical studies of two-photon excitation dynamics in 2-methyl-5-tert-butyl-p-quaterphenyl (DMQ) dissolved in cyclohexane/paraffin. Experimentally, a two-color two-photon (2C2P) excitation by two femtosecond laser pulses at 800 and 400 nm has been used in combination with the time-resolved detection of polarized molecular fluorescence. The fluorescence decay was found to be two-exponential, resulting in the molecular excited state lifetime of 753 ± 10 ps and the rotational correlation time of 724 ± 45 ps. Control over the excited and fluorescent photons polarization has been used for determination from experiment of seven independent molecular parameters. The experimental data were analyzed on the basis of the recent theoretical approach [Shternin, P. S.; Gericke, K.-H.; Vasyutinskii, O. S. Mol. Phys. 2010, 108, 813−825] supported by ab initio computations of the DMQ electronic structure and transition dipole moments. The results obtained imply that the twophoton absorption tensor S is mostly diagonal and that the Szz tensor component onto the molecular long axis gives the major contribution of 93%. However, it was also found that a number of different symmetry two-photon transitions related to the dipole moment components dxdz and dydz are excited in the conditions of our measurements.

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INTRODUCTION The excitation of polyatomic molecules with multiple photons has attracted wide attention all over the world. It offers certain advantages compared with the one-photon excitation regarding the investigation of complex molecular characteristics such as the molecular structure and dynamics. 1−5 Due to the femtosecond laser spectroscopy and its noninvasive methods of examination of biologically relevant molecules in the real time-domain, this research area has become very attractive and resulted in mutual publications.6−13 McClain, Callis, Johnson, Wan, and others14−17 have established the theoretical background for the two-photon excitation followed by fluorescence (TPEF). They demonstrated how to probe the linear combinations of the elements of the two-photon absorption tensor experimentally. Furthermore, they have developed a theory that describes the decay of the polarized fluorescence in solvents while under the condition of the isotropic rotational diffusion of the molecules. A new timedependent expression for the TPEF intensity has recently been reported by our group.18 It is based upon a spherical tensor approach and valid for any symmetric, or asymmetric top molecule and for any photon polarization under the condition of the isotropic rotational diffusion. The expressions are written in terms of the molecular parameters MKe(R,R′,t) which have clear tensor notation and contain molecular and dynamical © 2014 American Chemical Society

information that can be determined from the TPEF experiments, or calculated from theory. DMQ (2-methyl-5-tert-butyl-p-quaterphenyl) is an important polyphenyl dye that is widely used in laser techniques and in chemical and pharmaceutical industries. Spectral and laser properties of ten selected aromatic compounds from the p- and m-oligophenylenes family were systematically studied almost ten years ago by Nijegorodov et al.19 experimentally at room temperature and theoretically using the PPP-CI method. However, only D2 symmerty p-oligophenylenes were considered in that study and their geometry optimization was not performed. Several polyphenyl molecules have been studied in more detail. In particular, p-terphenyl (PTP) structure and spectral properties were studied intensively theoretically and experimentally during the past 30 years.12,20−25 The infrared and Raman intensities in PTP have been examined by Honda and Furukawa.24 They were connected to two rotational isomers. One is a twisted conformer of the C2h symmetry and the other is a helical conformer of the D2 symmetry. Heimel et al.25 calculated the potential energy surfaces of the electronic ground Received: May 28, 2014 Revised: June 24, 2014 Published: June 25, 2014 5248

dx.doi.org/10.1021/jp505251c | J. Phys. Chem. A 2014, 118, 5248−5255

The Journal of Physical Chemistry A

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molecular parameters were obtained and analyzed. As a result, the elements of the two-photon absorption tensor Sij, the first excited state lifetime τf, and the rotation correlation time τrot were determined from experiment. As shown, the two-photon absorption tensor S is almost diagonal and the Szz component, which is related to the dipole moment components dzdz both parallel to the molecular long axis Z, gives the major contribution of 93%. More, it was found that a number of different two-photon transitions that are different regarding their symmetry are related to the dipole moment components dxdz and dydz and they are also excited under the applied experimental conditions. Furthermore, the previously published value of 760 ps for the fluorescence lifetime in DMQ has been approved. The rotational correlation time value in DMQ is reported for the first time.

and excited states of both PTP rotational conformers utilizing ab initio quantum chemical methods. Furthermore, they were able to analyze the vibronic structure of the emission and absorption bands. Experimental and theoretical study of the 2C2P excited polarized fluorescence in PTP have been reported in our recent papers.12,13 DMQ consists of an aromatic hydrocarbon p-quaterphenyl linked to the methyl and tert-butyl groups. One of the possible DMQ conformers (helical) is shown in Figure 1. As can be

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MOLECULAR ELECTRONIC STRUCTURE AND TRANSITION DIPOLE MOMENTS: AB INITIO CALCULATIONS Transition dipole moments and excitation energies between the ground and excited states in DMQ and p-quaterphenyl molecules have been computed using the GAUSSIAN-0328 package. The computation of the isolated p-quaterphenyl molecule was performed using the ab initio SAC-CI method at the ccpVDZ level. The equilibrium geometries of three stable conformers of the ground state p-quaterphenyl are presented in Figure 2. Full geometry optimization of the rotation

Figure 1. Helical conformer of DMQ.

learned from the results of quantum chemical calculations of pquaterphenyl19 and PTP,24 there are several other stable DMQ conformers related to the rotational isomers of p-quaterphenyl around the inter-ring (C−C) bonds. To the best of our knowledge, no systematic study of different p-quaterphenyl conformers has been done and no comparison between the energy states and optical properties of DMQ and the structure of corresponding p-quaterphenyl conformers has been reported so far elsewhere. Also, no information on the geometry of the relaxed electronic excited states of DMQ has been reported. In the current paper the experimental and theoretical studies of the two-photon excited fluorescence of DMQ dissolved in paraffin/cyclohexane are reported. The two-color two-photon (2C2P) excitation scheme6,12,26,27 was applied. Femtosecond laser pulses were used for the molecular excitation, and the temporal dependence of the polarized molecular fluorescence was detected in the real time domain. Ab initio calculations of the structure of all stable rotational conformers of the pquaterphenyl and DMQ in vacuum and in solution environment were performed. Full geometry optimization for the ground and first excited relaxed electronic states were also performed for vacuum condition and for DMQ dissolved in cyclohexane. In all cases vertical excitation energies and transition dipole matrix elements have been computed. As shown, the first excited state geometry in DMQ is almost planar. Also, comparing the computed energy levels in pquaterphenyl with those in DMQ, we concluded that adjoining of the methyl and tert-butyl groups to p-quaterphenyl shifts down the first excited state energy by only about 0.12 eV, but that it dramatically shifts down the energy of highly excited states, making the energy structure much more dense. As a result, the total experimental two-photon excitation energy of 4.649 eV related to the approximately seventh electronic state in DMQ dissolved in cyclohexane/paraffin. The TPEF polarizations have been studied experimentally in DMQ as a function of each of the two excited photon polarization, and all important molecular parameters MKe(R,R′,t) have been determined using the theory developed in our previous papers.12,18 Utilizing ab initio calculations of the DMQ electronic structure and transition dipole moments the

Figure 2. Three stable rotational conformers of the p-quaterphenyl: (A) helical (left) conformer of the D2 symmetry; (B) chain conformer of the D2 symmetry; (C) twisted conformer of the C2 symmetry. χ is the dihedral angle between the phenyl rings.

conformers has been performed using the SAC-CI method at the D95 level. As shown in Figure 2, these are two conformers of the D2 and one conformer of the C2 symmetry possessing the same dihedral angle χ of χ = |χd| ≃ 33°. The dihedral angle χ value in Figure 2 is in good agreement with the experimental value for PTP, χ ≃ 33° published by Heimel et al.25 The transition dipole moments and the excitation energies computed for three p-quaterphenyl conformers are given in Table 1. Table 1 shows that the first three excited state energies 5249



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energy of highly excited states, making the energy structure much more dense. The ab initio computation of the molecular structure of DMQ dissolved in cyclohexane/paraffin has been performed by applying the polarizable continuum model (PCM) and TDDFT B3LYP method at the D95 level for relaxed and nonrelaxed molecular states. The calculated excitation energies and transition dipole moments are presented in Table 3. One can see that the excited

Table 1. Calculated Energies of First Three Excited States and Transition Dipole Moments from the Ground State for Three p-Quaterphenyl Rotational Conformers in Figure 2a transition

dipole

moment, au

conformer geometry

excited state symmetry

transition energy (eV)

X

Y

Z

helical

B1 B2 B2 B1 B2 B2 A A A

4.1425 4.8115 5.1339 4.1338 4.7868 5.1298 4.1769 5.3509 6.2250

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.1031 0.0577 0.0000 0.0637 0.0768 0.0000 0.0000 0.0000

−3.1065 0.0000 0.0000 3.0852 0.0000 0.0000 2.8712 −0.0186 −0.6152

chain

twisted

Table 3. Calculated Transition Dipole Moments and Excited State Energies for DMQ Dissolved in Cyclohexane/Paraffina

geometry

a

for the twisted conformer of C2 symmetry are significantly larger than the corresponding excited state energies for two other conformers. Full geometry optimization for the ground and the first excited relaxed electronic states in DMQ has also been performed by TD-DFT B3LYP method at the D95 level for vacuum condition and for DMQ dissolved in cyclohexane. In both cases the optimized values of the dihedral angles were found to be practically the same. For the ground state DMQ helical-type conformer they are equal to χd ≃ 33°, 33°, and 51°, where the angle χd ≃ 51° relates to the phenyl ring located at the 2-methyl-5-tert-butyl groups. For two other possible conformers the optimized values of the dihedral angles were found to be very close to those given above within 0.5° accuracy. The optimized values of the dihedral angles in the first excited state (relaxed) were computed according to χd ≃ +0.6°, −1.4°, and +34°. Therefore, the first excited state geometry in DMQ is almost planar. Ab initio calculation of the transition dipole moments and the excitation energy of the DMQ in vacuum has been performed using the TD-DFT B3LYP method at the D95 level. The calculated data are presented in Table 2. Comparing the data in Tables 1 and 2, one can conclude that adjoining of the methyl and tert-butyl groups to p-quaterphenyl loses the molecular state symmetry and shifts down the first excited state energy by only about 0.12 eV, but that it dramatically shifts down the

transition

dipole


X

Y

Z

1 2 3 4 5 6 7 8 9 10

4.02 4.50 4.54 4.68 4.71 4.79 4.93 5.05 5.17 5.25

0.3524 −0.1176 0.0532 −0.0003 0.1441 0.0010 0.0835 −0.2230 −0.0802 −0.3383

−0.0131 0.0070 0.0049 0.0011 −0.0103 0.0210 −0.0043 −0.0390 0.1207 0.0565

3.6729 0.5959 −0.1780 −0.2832 0.3226 −0.0094 −0.0592 0.2342 0.0255 −0.0172

moment, au


X

Y

Z

1 2 3 4 5 6 7 8 9 10 1 2 3

3.58 4.12 4.18 4.32 4.36 4.44 4.53 4.70 4.80 4.88 3.173 3.881 3.985

0.40 −0.1566 0.0530 0.0386 0.1685 −0.0005 0.0979 −0.2614 −0.0666 −0.4194 0.438 −0.1058 0.0551

−0.019 0.0064 0.0068 0.0024 −0.0168 0.0433 −0.0039 −0.0514 0.1275 0.0858 −0.0732 0.0145 0.0132

3.97 0.5613 −0.12 0.2835 0.2432 −0.0070 −0.1806 0.2647 0.0337 −0.0150 4.587 0.783 0.0323

relaxed

a The Z axis is directed along the molecular long axis; the X axis is directed approximately along the right terminal ring plane.

state energies in DMQ in solute in Table 3 are shifted down compared with the corresponding energies in isolated DMQ in Table 2 by 0.4−0.5 eV. Note that the total experimental excitation energy was 4.649 eV (see below), which approximately relates to the nonrelaxed electronic state 7 in Table 3. Antonov et al. have experimentally determined the first excited state energy of 3.65 eV for DMQ dissolved in cyclohexane,29 which is in good agreement with the computed value of E1 = 3.58 eV in Table 3. The computed transition dipole moments and excitation energies in DMQ were found to have approximately the same values for pure cyclohexane C6H12 and paraffin (CnH2n+2) as solutes at 10 < n < 26. As shown in Table 3, the transition dipole moment of the first excited state is almost parallel to the DMQ long the Z axis.

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Table 2. Calculated Transition Dipole Moments and Excited State Energies for DMQ in Vacuum for Optical Excitation from the Ground State of the DMQ Helical Conformer

excited state

dipole

excited state

nonrelaxed

The Z axis is parallel to the molecular long axis and X axis is directed along the molecular symmetry axis.

transition

2C2P EXCITED FLUORESCENCE: THEORETICAL BACKGROUND A convenient spherical tensor based approach for extracting molecular information from 2C2P excited fluorescence experiments has recently been reported and approved by Shternin et al.12,18 Breifly, within this approach the expression describing the fluorescence intensity is written as

moment, au

I = − C e −t / τ f

(2) (fl) ∑ ∑ ∑ ([E(1) K1 ⊗ E K2 ]Ke · E Ke ) Ke K1, K2 R , R ′

×

⎧K K K ⎫ (2K1 + 1)(2K 2 + 1)(2R + 1)(2R′ + 1) ⎪ 1 2 e ⎪ ⎨1 1 R′ ⎬ 2Ke + 1 ⎪ ⎪ ⎩1 1 R ⎭

× M Ke(R ,R′,t ) 5250

(1)



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30 (2) (fl) where E(1) K1Q1, EK2Q2, and EKeQe are the polarization matrices that relate to each of the three photons involved in the photoprocess. The tensor ranks K1, K2, Ke, R, R′ in eq 1 are limited to the values 0, 1, and 2 each. The exponent e−t/τf, where τf is the excited state lifetime responsible for the molecular spontaneous decay. The constant C is proportional to the intensities of light beams with polarization vectors e1 and e2. The term in parentheses is a 9j-symbol.31 The terms MKe(R,R′,t) in eq 1 are molecular parameters that contain all information on the molecular symmetry and structure and on the electronic transitions and can be defined as18

Figure 3. Experimental geometry: exciting photons (red at 800 nm and blue at 400 nm) counterpropagate along X axis and the fluorescence light is detected with respect to the Z axis. The letters Y, Z, R, and L denote the polarization of each of the exciting photons: linearly polarized along the Y axis, linear polarized along the Z axis, right-handed circularly polarized, and left-handed circularly polarized, respectively. Ix and Iy denote the intensities of the fluorescence light in two polarization channels.

M K f (R ,R′,t ) =− 3

∑ ∑ [F1* ⊗ F′1]K q + qK q ′(t )[S′R*′ ⊗ SR ]*K q ′ f

n f , n f′ qe , qe′

f e

f e

e e

(2)

photodetectors with respect to the X axis (Ix) and Y axis (Iy). These changes allowed for more correct adjustment of the two beams polarizations due to the removal of a redundant dichroic mirror. For the excitation a Ti:sapphire femtosecond pulsed laser pumped (Coherent, MIRA 900-B) by the Verdi V-10 laser (Coherent, Santa Clara, CA, USA) with a fundamental output at 800 nm was used. After the fundamental frequency was doubled, the 800 nm beam and the resulting 400 nm beam were split by a dichroic mirror. Temporal synchronization of the pulses was proceeded by an optical delay line in the red beam path. The polarization control was facilitated by λ/2 and λ/4 waveplates in each channel. The degree of light polarization was better than 99% for linear polarized light and 97−98% for circular polarized light. The beams were combined with a second dichroic mirror and focused inside the sample cuvette with an Olympus microscope objective (NA 0.25). To prepare the sample, a solution of DMQ in a 1:1 mixture of cyclohexane and paraffin oil was produced, using a concentration of 500 nM. It is important to use a high viscous sample to be able to resolve the rotational correlation time (750 ps). DMQ (99%) and the solvents (spectroscopic grade, SigmaAldrich) were used without further purification or degassing. The power of the laser beams were 180 and 8.26 mW for the red (800 nm) and the blue (400 nm) beams, respectively. The background consisted of less than 4% of the 2C2P intensity and was generated by the competing three- and two-photon processes. The determination of the M-parameters was not disturbed by the background. No effects of heating of the sample due to the laser beams could be observed because the duration of the measurements was held as short as possible. Combining different excitation beam polarizations with respect to the experimental geometry in Figure 3 lead to four experiments: (YY) both absorbed photons were linearly polarized along the laboratory Y axis, (ZY) one photon was linearly polarized along the Z axis and another was linearly polarized along the Y axis, (RR) both photons had the same circular polarization, and (RL) one photon was right-circularly polarized and another was left-circularly polarized. A sample of the measured signals are presented in Figure 4. The time resolution was about 10 ps, and the actual duration of the femtosecond pulses was about 150 fs. To obtain the seven Mparameters, a set of eight equations is needed because the fluorescence intensity in eq 1 is proportional to the linear

where the first term in the right-hand side is the component of the product of two one-photon fluorescence vectors F and F′, the second term is the rotational diffusion tensor + qK fq ′(t ), and e e

the third term is the component of the product of the twophoton excitation tensors S and S′. Explicit expressions for the fluorescence vector F1, twophoton excitation tensor SR, and rotational diffusion tensor + qK fq ′(t ) are given in refs 12 and 18. The molecular parameters e e

MKf(R,R′,t) are based on the spherical tensor representation, and at t = 0 they are similar to McClain’s1 molecular parameters Q̂ i based on the Cartesian tensor representation. The relationship between the two sets of parameters is tabulated in ref 18. If the electronic excited state is not degenerate, the total number of the molecular parameters is 7:1 three rank K = 0 and four rank K = 2 parameters. All these molecular parameters can be determined from the 2C2P experiment.1,18 The K = 0 molecular parameters M0(0,0), M0(1,1), and M0(2,2) can have only a non-negative values, they describe the isotropic part of the two-photon absorption and following fluorescence.18 The K = 2 parameters M2(1,1,t), M2(1,2,t), M2(0,2,t), M2(2,2,t) at t = 0 describe the anisotropic part of the two-photon absorption tensor dealing with the distribution of the molecular angular momenta. Due to the rotational diffusion the temporal behavior of the K = 2 parameters undergo, in general, a five-exponential anisotropy decay characterized by five different rotation correlation times. Depending on the molecular symmetry, some of the rotation correlation times can be equal to each other.32 In practice, typically only one- or two-exponential decay can be resolved.33

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EXPERIMENTAL SECTION The experimental geometry used is shown in Figure 3. The experimental approach based on the femtosecond-laserexcitation 2C2P scheme and the experimental setup used were described in detail elsewhere.18,34 Contrary to our previously described setup, the two excitation beams at 800 and 400 nm counterpropagated along the X axis while the fluorescence was detected along the Z direction, which is perpendicular to the X and Y axes. The fluorescence signals were split by a polarization prism into two lineary polarized beams. Then they were detected simultaneously using two fast 5251



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Figure 4. Polarized fluorescence intensity as a function of time for all excitation schemes used. The capital letters Y, Z, R, and L at each curve denote the polarization of each of the exciting photons, and the lowercase letters x and y denote the corresponding fluorescence channels. Solid lines are the best fits according to a biexponential decay model.

The parameter Ω can range within 0−3/2 if the excited state |e⟩ is connected to the totally symmetric representation. In case of DMQ, the above rule cannot be directly applied because DMQ has no symmetry properties under the point group transformations. However, the parameter Ω in eq 3 can still be useful for analysis of the molecular properties, as it carries essential information about the two-photon absorption tensor matrix elements. In particular, as can be shown using eqs 2 and 3, the parameter Ω in general ranges within 0 ≤ Ω ≤ 3/2. Moreover, Ω = 3/2 when the following condition is fulfilled:

combination of the M-parameters. Therefore, the four abovementioned polarization combinations are measured with two detection channels x and y so that eight experimental geometries can be obtained. Utilizing Table 1 in ref 12 leads to calculation of the expansion coefficients in these linear combinations for each of the eight experimental geometries. The M-parameters can then be determined from the experiment as a solution of an overestimated system of equations. The isotropic parts of the fluorescence intensity that relate to different excitation schemes are denoted as IYY, IZY, IRR, and IRL. The zero-rank M-parameters regulate these total fluorescence intensities as can be shown from eq 1. Furthermore, these total fluorescence intensities decay single-exponentially with the excited state lifetime τf. The intensities IYY, IRR, and IRL can be directly determined from experiment either by using a linear polarizer installed under the magic angle in front of the fluorescence detector6,7 or by using the relationships IYY = (IYYy + 2IYYx)/3 and IRR(RL) = (Ix + 2Iy)/3. The well-known parameter Ω16 can be described with the help of the M-parameters: Ω=

IRL = IYY

3M 0(2,2) 5 M 0(0,0) + 2M 0(2,2)

∑ |⟨nf |dẑ |ne⟩⟨ne|dẑ |ni⟩ + ⟨nf |dx̂ |ne⟩⟨ne|dx̂ |ni⟩ ne

+ ⟨n f |dŷ |ne⟩⟨ne|dŷ |n i⟩|2 = 0

(4)

Equation 4 shows that Ω has its maximum value when the “parallel” (ZZ) component of the two-photon absorption tensor SR is equal to the sum of the “perpendicular” components (XX + YY) taken with the minus sign. Moreover, if the S21 and S22 components of the two-photon tensor give only the minor contribution to the absorption signal (Table 6 below), the parameter Ω has it minimum value equal to 0 when the “parallel” component of the two-photon absorption tensor is twice the sum of the “perpendicular” components:

(3)

Note that eq 3 contains the intensity IRL in the numerator instead of the intensity IRR in ref 16 of our early paper.12 This difference is because in the studies described in refs 12 and 16 two excitation photons propagated in the same direction, whereas in the conditions of this paper experiment they propagated in opposite directions, Figure 3. The parameter Ω in eq 3 is always equal to 3/2, if the molecular ground state belongs to the totally symmetric representation A1 and the excited state |e⟩ is not connected to the totally symmetric representation as shown by Lakowicz.4

∑ |2⟨nf |dẑ |ne⟩⟨ne|dẑ |ni⟩ − ⟨nf |dx̂ |ne⟩⟨ne|dx̂ |ni⟩ ne

− ⟨n f |dŷ |ne⟩⟨ne|dŷ |n i⟩|2 ≈ 0

(5)

All other relationships between the “parallel” and “perpendicular” components of the two-photon absorption tensor result in intermediate values of the parameter Ω. 5252



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Table 4. Fitted Values of the Anisotropies, Lifetimes, and Total Intensities total intensities r(0)

IYY

IZY

IRR

IRL

1(0.09) 0.5147(0.0040)

0.254(0.033) −0.4859(0.014) [x] 0.2766(0.0058) [y]

0.629(0.018) −0.2389(0.0045)

0.626(0.03) −0.2443(0.0044)

τf τrot Ω

753(10) ps 724(45) ps 0.626(0.037)

indicate the corresponding detection channels, τrot is the rotational correlation time, and τf is the fluorescence lifetime. The molecular parameter values determined from the fit are given in Table 4. The total intensities in Table 4 are normalized by IYY. The [x] and [y] symbols in the third column relate to the partial anisotropies rZYx and rZYy in eqs 9 and 10, respectively. The temporal dependence of the obtained signals was analyzed using a two-exponential fitting procedure that assumes a single fluorescence lifetime τf and a single rotation correlation time τrot. This model was shown to meet perfectly the conditions of our experiment. As can be seen from Table 4, the fluorescence lifetime was found to be τf = 753.4 ± 5.5 ps and the rotational correlation time found to be τrot = 724 ± 45 ps. The values of the M-parameters at the time t = 0 obtained as a solution of linear system given in Table 1 in ref 12 using singular value decomposition35 (SVD) fitting procedure are presented in Table 5. All parameters in Table 5 are normalized

The two-photon anisotropies rl describe the anisotropic part of the fluorescence for the YY, RR, or RL excitation intensities and can be written as

rl =

Ilx − Ily Ilx + 2Ily

(6)

with the index l for YY, RR, or RL. The fluorescence signals in the x and y detection channels can be written as Ilx = Il(t )[1 + 2rl(t )]

(7)

Ily = Il(t )[1 − rl(t )]

(8)

In case of the l = YY excitation geometry the indices x and y in eqs 6−8 should be interchanged. In case of the ZY excitation geometry anisotropy cannot be introduced in the same way. However, it is convenient to define the partial anisotropies rZYx and rZYy so that the fluorescence intensities can be expressed similarly to eqs 7 and 8:12 IZYx = IZY (t )[1 + rZYx(t )]

Table 5. M-Parameters and Ω Determined from Experiment

(9)

IZYy = IZY (t )[1 + rZYy(t )]

M0(0,0) M0(1,1) M0(2,2) M2(1,1) M2(0,2) M2(1,2) M2(2,2) Ω

(10)

The total fluorescence intensities Il(t) = (Ilx + 2Ily)/3 decay single-exponentially whereas, due to the anisotropies rl(t), the fluorescence signals Ilx and Ily show multiexponential behavior. These features of the experimental signal were used in this paper for extracting the anisotropic and isotropic portions of the fluorescence in an individual detection channel of the timeresolved measurements.

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(11)

Fitting of the experimental signals was proceeded using the following intensity expressions (see eqs 7 and 8): t

Ilx(t ) = G

∫−∞ IRF(t′) Il(0)[1 + 2rl(0)e−(t−t′)/τ

rot

]e−(t − t ′)/ τf dt ′ (12)

t

Ily(t ) =

∫−∞ IRF(t′) Il(0)[1 − rl(0)e−(t−t′)/τ

rot

SVD fit of four parameters

1.0 ± 0.15 −0.13 ± 0.17 0.79 ± 0.03 0.25 ± 0.16 1.73 ± 0.1 −0.08 ± 0.5 1.16 ± 0.2 0.620 ± 0.04

1.0 ± 0.16 0 0.82 ± 0.03 0 1.79 ± 0.1 0 1.24 ± 0.22 0.634 ± 0.04

by the value of the parameter M0(0,0). The molecular parameter values obtained by global fit of all seven parameters are given in the second column in Table 5. The signal intensities recalculated using these M-parameters are within the statistical deviation of the experimental values. The molecular parameters MK e(R,R′) carry essential information on the DMQ excitation dynamics and structure. It is easy to see from Table 5 that all M-parameters in the second column containing the index R = 1 are small compared to other parameters and possess large relative errors. More, the parameter M0(1,1) in Table 5 has a nonphysical negative value.18 Thus, we concluded that at the current level of experimental accuracy all values of the parameters containing the index R = 1 can be treated to have zero values. The result obtained by fixing these parameter values to zero: M2(1,2) = M2(1,1) = M0(1,1) = 0 and by proceeding the SVD fit of the rest four molecular parameters is given in the third column in Table 5. The parameters containing the indices R = 0, 2 in the second and third columns in Table 5 do not differ much from each other, which means that the above approximation is appropriate. The result obtained suggests that the two-photon absorption tensor is practically symmetric under the conditions

DATA ANALYSIS AND TWO-PHOTON TENSOR ASSIGNMENT The signals related to different excitation geometries were fitted in a global manner with shared decay times following the procedure described in detail in ref 12 assuming twoexponential decay. The intensity sum rule12 was taken into consideration: IYY + IYZ = IRR + IRL

SVD fit of all seven parameters

]e−(t − t ′)/ τf dt ′ (13)

where factor G is the detector sensitivity, Il(0) is the intensity of the total fluorescence at t ≈ 0, the subscript indices x and y 5253



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occurs through the dzdz components of the transition dipole moment, which are parallel to the molecular long the Z axis. However, there is also evidence for the symmetry-mixing twophoton transitions related to the dipole moment components dxdz and dydz. In future studies the technique developed will be applied to the biologically relevant fluorophores like indole and tryptophan embedded in biological media for investigation of protein dynamics.

of our experiment. Using the explicit expressions for the molecular parameters given in ref 18 the parameter values can in principle be computed on the basis of ab initio quantum chemical method and then compared with experimental data in Table 5. However, this time-consuming computation are out of the scope of this paper. More detailed information can be obtained by considering the two-photon tensor components SRγ which have clear physical interpretation. As shown in ref 12, the tensor component S00 is proportional to the trace of the tensor Tr S. The information about alignment along the direction of the fluorescence polarization (Z axis) is given by the quadruple tensor component S20. The tensor component S22 contains information on the asymmetry of the excitation in the XY molecular plane and the modulus of the tensor component S21 describes the inclination of the major axis of the S tensor with respect to Z axis. The two-photon tensor components SRγ obtained using the relationship between the MK(R,R′) and SRγ given in ref 12 and

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Corresponding Authors

*S. Herbrich. E-mail: [email protected]. *K.-H. Gericke. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.G.S. and O.S.V. acknowledge the financial support from the Russian Science Foundation, grant No. 14-13-00266.

Table 6. Two-Photon Excitation Tensor S Components Determined from Experiment S00 S20 |S21| |S22|

value

standard deviation

1.0 −1.27 0.29 0.17

0.2 0.2 0.07 0.05

REFERENCES

(1) McClain, W. M. Polarization Dependence of Three-Photon Phenomena for Randomly Oriented Molecules. J. Chem. Phys. 1972, 57, 2264−2272. (2) Monson, P. R.; McClain, W. M. Complete Polarization Study of the Two-Photon Absorption of Liquid 1-Chloronaphthalene. J. Chem. Phys. 1972, 56, 4817−4825. (3) Lakowicz, J. R.; Gryczynski, I.; Danielsen, E. Anomalous Differential Polarized Phase Angles for 2-Photon Excitation with Isotropic Depolarizing Rotations. Chem. Phys. Lett. 1992, 191, 47−53. (4) Lakowicz, J. R., Ed. Topics in Fluorescence Spectroscopy. V.5 Nonlinear and Two-Photon-Induced Fluorescence; Plenum Press: New York, 1997. (5) Callis, P. R. Two-Photon-Induced Fluorescence. Annu. Rev. Phys. Chem. 1997, 48, 271−297. (6) Lakowicz, J. R.; Gryczynski, I.; Malak, H.; Gryczynski, Z. TwoColor Two-Photon Excitation of Fluorescence. Photochem. Photobiol. 1996, 64, 632−635. (7) Lakowicz, J. R.; Gryczynski, I.; Malak, H.; Gryczynski, Z. Fluorescence Spectral Properties of 2,5-Diphenyl-1,3,4-Oxadiazole with Two-Color Two-Photon Excitation. J. Phys. Chem. 1996, 100, 19406−19411. (8) Shear, J. B. Multiphoton-Excited Fluorescence in Bioanalytical Chemistry. Anal. Chem. 1999, 71, 598A−605A. (9) Diaspro, A.; Chirico, G.; Collini, M. Two-Photon Fluorescence Excitation and Related Techniques in Biological Microscopy. Q. Rev. Biophys. 2005, 38, 97−166. (10) Ryderfors, L.; Mukhtar, E.; Johansson, L. B. Å. The Symmetry of Two-Photon Excited States as Determined by Time-Resolved Fluorescence Depolarization Experiments. J. Phys. Chem. A 2007, 111, 11531−11539. (11) Opanasyuk, O.; Ryderfors, L.; Mukhtar, E.; Johansson, L. B. Å. Two-Photon Excited Fluorescence Depolarisation and Electronic Energy Migration within Donor−Donor Pairs. Phys. Chem. Chem. Phys. 2009, 11, 7152−7160. (12) Denicke, S.; Gericke, K.-H.; Smolin, A. G.; Shternin, P. S.; Vasyutinskii, O. S. Dynamics of Two-Color Two-Photon Excited Fluorescence of p-Terphenyl: Determination and Analysis of the Molecular Parameters. J. Phys. Chem. A 2010, 114, 9681−9692. (13) Shternin, P. S.; Smolin, A. G.; Vasyutinskii, O. S.; Denicke, S.; Herbrich, S.; Gericke, K.-H. Dynamics of Two-Photon Two-Color Transitions in Fluorophores Excited by Femtosecond Laser Pulses. Proc. SPIE 2012, 85531A1−85531A9. (14) McClain, W. M. Excited State Symmetry Assignment Through Polarized Two-Photon Absorption Studies of Fluids. J. Chem. Phys. 1971, 55, 2789−2796.

normalized by S00 are presented in Table 6. As can be shown from Table 6,

Szz ≈ 0.93 Tr S

AUTHOR INFORMATION

(14)

which implies that the two-photon excitation in DMQ occurs mainly through the dzdz components of the molecular dipole moment whereas the excitation through the dxdx and dydy components gives only minor contribution. The relatively high absolute value of the tensor component | S21| in Table 6 reveals that the dipole moment components dxdz and dydz give appreciable contribution to the two-photon transition. The nonzero values of both S21 and S00 tensor components manifest the contribution from the combined symmetry two-photon excitation. At the same time the tensor component S22 in Table 6 has a relatively small value, indicating that the two-photon excitation tensor is almost totally axially symmetric with respect to the Z axis.

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CONCLUSION We have used the temporal- and polarization-dependent 2C2P excited fluorescence technique as a powerful tool for determination of the full structure of the two-photon excitation tensor in DMQ. By varying the polarization of each of the three photons involved in the photoprocess and using the global fitting procedure, we have determined from experiment seven meaningful molecular parameters, the first excited state lifetime τf, and the rotational correlation time τrot. The results obtained have been interpreted using the theory developed in our recent papers12,18 with the support of ab initio computations of the DMQ electronic structure. Finally, all elements of the twophoton absorption tensor S have been determined and analyzed. As shown, the two-photon excitation preferably 5254



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Two-Color Two-Photon Excited Fluorescence of 2-Methyl-5-tert-butyl-p

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