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THE JOURNAL OF CHEMICAL PHYSICS 124, 044301 共2006兲

Ab initio study of optical properties of rhodamine 6G molecular dimers V. I. Gavrilenkoa兲 and M. A. Noginov Center for Materials Research, Norfolk State University, Norfolk, Virginia 23504

共Received 6 October 2005; accepted 29 November 2005; published online 23 January 2006兲 Equilibrium atomic geometries of rhodamine 6G 共R6G兲 dye molecule dimers are studied using density-functional theory. Electron-energy structure and optical properties of R6G H and J dimers are calculated using the generalized gradient approximation method with ab initio pseudopotentials. Our theory predicts substantial redshifts or blueshifts of the optical absorption spectra of R6G dye molecules after aggregation in J or H dimers, respectively. Predicted optical properties of R6G dimers are interpreted in terms of interatomic and intermolecular interactions. Results of the calculations are discussed in comparison with experimental data. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2158987兴 I. INTRODUCTION

The use of dyes in dye lasers and various photoinduced reactions caused extensive studies of their electronic and optical properties.1–3 More recently, dyes have become the subject of renewal interest, which has been focused on the phenomenon of molecular aggregation.4–7 Rhodamine 6G 共R6G兲 dye is one of the most efficient laser dyes characterized by a high-efficiency luminescence band around 560 nm 共see, e.g., Ref. 6 and references therein兲. However, optical properties of high-concentrated R6G dyes differ from those of isolated dye molecules.1,3,5,7,8 The R6G dye has a high tendency to form H-type nonluminescent dimer sandwichlike aggregates with parallel-aligned molecular axes.1,5,7,8 Another configuration of R6G molecules with head-to-tail aligned dipole moments 共J-type dimers兲 was normally observed in the presence of an additional external potential 共by intercalation, on solid surfaces, etc.兲.1,5,7,8 H-type R6G dimers are associated with a remarkable blueshift in the optical absorption band with respect to R6G monomers.5,8 On the other hand, J-type R6G dimers are characterized by a redshifted luminescence band.5,7,8 It has been demonstrated for decades that Kohn-Sham density-functional theory 共DFT兲 realistically predicts the electronic structure of different systems, such as atoms, molecules, and solids.9–11 Various generalized gradient approximation 共GGA兲 methods describing exchange and correlation 共XC兲 interaction have been shown to systematically improve the local density approximation 共LDA兲 predictions of equilibrium atomic geometries.10 In atomic systems 共such as large single molecules, inorganic solids, etc.兲 the geometry optimization study primarily requires accurate prediction of the short-range interatomic interaction which is well reproduced within a standard DFT approach 共see, e.g., Refs. 10 and 11兲. However, in addition to the short-range interaction, a geometry optimization study in the molecular system requires also realistic predictions of the long-range 共electrostatic兲 interaction12 which is not straightforward within a DFT. In order to be able to realistically calculate the dipolea兲

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dipole 共van der Waals兲 term of the interaction energy one needs to reliably predict a charge distribution in the system. This is a many-body effect which requires realistic modeling of the XC interaction, and it is more challenging for the DFT-GGA.13 The Perdew-Wang 共PW兲 model for XC has been used in Ref. 14 to study simple organic molecular dimers. The Perdew-Burke-Ernzerhof 共PBE兲 functional15 accounting for XC interaction leads to further improvements against PW in predictions of equilibrium geometry and electronic properties of molecular systems. The PBE model of XC interaction was modified in Ref. 16 by introduction of several new formal parameters into the original PBE-XC functional, the extended PBE 共xPBE兲 method, which shows some improvement for simple molecular systems. The last method, however, is less transparent for understanding the physics of the interaction because of the new parameters which could not be easily interpreted. Comparative study of predicted equilibrium distances and bonding energies17 clearly indicated that the PBE 共and xPBE兲 methods predict these parameters with better than 10% accuracy for a number of simple molecular dimers. However, for more complex molecular systems these methods could result in bigger deviations, consequently the predicted values should be taken cautionary. This point is addressed below in this work by discussing equilibrium geometries of R6G dimers predicted in this work. Electronic excitations are key points of most of the commonly measured optical spectra. The first-principle studies of excited states, however, require much larger effort than computations of the ground state. Theoretical approaches for computation optics could be roughly separated into two large groups. In first group methods the system of independent particles excited by an external light field is considered within perturbation theory 关the random phase approximation RPA兴. The DFT is used as a zero-order solution and other corrections to the electron self-energies 共such as many-body, local-field effects, quasi particle 共QP兲 shifts18兲 are applied. Optical response functions are calculated by solving a set of Green’s function equations.17 An alternative approach to predict electronic excitation energies is the time-dependent den-

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V. I. Gavrilenko and M. A. Noginov

sity functional theory 共TDDFT兲.17 For many systems the last approach offers practical advantages 共e.g., excitonic effects in both organic and inorganic materials兲. Comparative analysis of both approaches is given in a recent review.17 For predictions of linear and nonlinear optical respons both approaches are equivalent as demonstrated in Ref. 19. Nonradiative and luminescent characters of H and J dimers, respectively, have been semiqualitatively interpreted in the literature using excitonic theory.20 It has been argued3–8 that observed blueshifts 共H type兲 or redshifts 共J type兲 in optical absorption spectra are due to the interplay of optical selection rules modified through intermolecular interactions. Recently, first-principle theories have been used for the study dimers of some simple molecules.13,16,21–23 Due to the complexity of the system, the quantitative analysis of more complex organic molecular dimers is still challenging for the first-principle theory. In this case a reasonable compromise could be the development of analytical models to study linear and nonlinear optical properties of molecular dimers.12 To our knowledge, despite remarkable interest and experimental activity, no systematic ab initio theoretical study of the optical properties of dye molecular dimers has been presented in the literature. The purpose of the present work is to fill this gap. In this study, we present the results of the numerical analysis of electron-energy structure and optical properties associated with molecular R6G dimers based on the state-ofthe-art first-principle methods in computational physics and chemistry. II. METHOD

We have used both commercial24 and research25 computational packages based on ab initio pseudopotentials 共PP兲. The electron-energy structure and eigenfunctions of R6G single molecules and molecular dimers were calculated within DFT-GGA using fully separable ab initio PP generated according to the Troullier-Martins scheme.26 An energy cutoff up to 60 Ry is taken for a generated fully separable PP.25 Convergence of the ground state has been proved by test calculations with an energy cutoff 共Ecut兲 up to 100 Ry for the R6G single molecule. An accuracy of better than 10% for eigenvalues is achieved with Ecut = 45 Ry. The QP corrections are calculated as in Ref. 18 only for the monomer. For the atomic relaxation of single-molecule and molecular dimers the supercell method is used. The GGA-PBE functional was used to model XC interaction.15 Dimensions of the supercell are determined from the following consideration. The main purpose to introduce the super cell is to simulate a virtual crystal in order to define periodical pseudopotentials. On the other hand, it should be large enough to avoid additional intermolecular interactions between molecules from the neighboring cells. However, increase of the supercell dimensions immediately results in a dramatic increase of the plane wave numbers in the evaluation of the PPs. No effect on the results has been found for the systems studied if the volume of the supercell exceeds 20⫻ 15⫻ 15 A3. The optimized geometries of the dimers were obtained in

a few steps. First, the equilibrium atomic geometry of the single molecule was determined. Then every single molecule was kept frozen in order to get the molecular dimer configuration. After that boundary atoms were allowed to relax. The last steps were repeated until the full convergence of the geometry of dimers. Optical absorption spectra were calculated within RPA approach19,27–29 according to

␣共␻兲 = 2␻k共␻兲.

共1兲

The extinction coefficient k was determined through real and imaginary parts of the dielectric permittivity function ␧共␻兲 = ␧1共␻兲 + i␧2共␻兲 according to the formula k共␻兲 =

1

冑2

冑冑␧21 + ␧22 − ␧1 .

共2兲

The isotropic dielectreic susceptibililty functio ␧共␻兲 is given through the components of the second-rank dielectric tensor ␧␣␤共␻兲共␣ , ␤ = x , y , z兲, ␧ = 31 共␧xx + ␧yy + ␧zz兲.

共3兲

The evaluation of ␧␣␤共␻兲 in this work is based on the independent particle approximation. The time-dependent linear optical susceptibility function follows from the equation of motion for the density matrix 共the RPA picture兲.27 The function of ␧␣␤共␻兲 is given by ␧␣␤共␻兲 = 1.0 + 8␲ 兺

n,m

f nm 具n兩␯␣兩m典具m兩␯␤兩n典 , 2 共␻nm − ␻ + i⌫兲 ␻nm

共4兲

where ␯␣ and ␯␤ are Cartesian components 共␣ , ␤ = x , y , z兲 of the velocity operator, ␻nm = En − Em, f nm is electron occupation function 共taken here at zero temperature兲, and indices n and m denote empty and filled electronic states. The intraband electron transitions are excluded in this study because of the negligible contributions. Note, that we use atomic system units: m0 = ប = e = c = 1. We also neglected the optical momentum nonlocality effects28 and replaced velocity operator ␯ˆ for momentum operator 共␯ˆ = pˆ = −i ⵱ 兲. In this case Eq. 共4兲 agrees with that given in Ref. 19 for linear optical response. Neglect of the effects of nonlocality may cause errors in the predictions of the shape of optical spectra, which could be not small in molecular systems.28,29 However, this point is beyond the scope of the present study and will be addressed explicitly elsewhere.

III. RESULTS AND DISCUSSION

Equilibrium atomic configuration of the single R6G molecule was determined by geometry optimization as described above. Comparison with the results provided by other commercial packages 关GAUSSIAN-03 and JAGUAR 4.2 共Refs. 30 and 31兲兴 indicate that the latter packages, based on quantum chemistry methods, are faster for this system than the PP method in producing equilibrium geometries of the single molecule. The ab initio PP theory is more often used for crystals. For molecular systems, it is applied in a supercell version, which requires more extensive computational work. However, agreement of the results predicted by PP theory


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Optical properties of rhodamine dimers

FIG. 1. Predicted equilibrium geometry of H-type dimers of R6G molecules. Note the predicted twisted angle of 28° and the opposite orientation of dipole moments of neighboring molecules. The atom type is indicated on a gray scale as follows: hydrogen 共white兲, carbon 共gray兲, oxygen 共dark gray兲, and nitrogen 共black兲.

with experimental optical data is better, as it has been proven in this work. We found that the H-type configuration is energetically favorable against the J type, H J − Etot = − 0.064 eV. ⌬Etot = Etot

共5兲

The relatively small energy difference 共⌬Etot 艋 3kT兲 indicates that both configurations of free standing R6G dimers could coexist at room temperature with a concentration ratio of H- to J-type dimers of at least one order of magnitude. In Figs. 1 and 2, fully relaxed atomic configurations of H- and J-type R6G molecular dimers are shown. The molecular axes in H type are antiparallel with a twisted angle ␪H = 28°. The predicted angular value perfectly matches the experimental exp = 29° 兲 recently reported in Ref. 5 for R6G molone 共␪H ecules intercalated in fluor-taeniolite 共TN兲 film. For J-type dimers, our analysis predicts only one equilibrium configuration with the angle between molecular axes ␪J = 93° 共T-shape configuration shown in Fig. 2兲. This value is in reasonable agreement with reported torsion angle values of 105° and 109° obtained in Ref. 7 using excitonic theory20 from optical absorption spectra of R6G dimers intercalated in Laponite Clay. The predicted distance between geometrical centers of the molecules in J dimer, 0.803 nm, is lower than the value of 0.95 nm obtained from the optical absorption in Ref. 7. However, the predicted intermolecular distance of the free standing H-type dimer, ⌬R ⬵ 0.24 nm, is much smaller than the reported experimental value of 0.71 nm of intercalated dimers.5 These discrepancies require some comments. On one hand experimental data in Refs. 5 and 7 were obtained from optical absorption using semiquantitative analysis based on the excitonic theory.20 Within this model intermolecular interaction is assumed of pure van de Waals type, and neglect of the short-range interaction may cause errors. The intermolecular distance may also increase by intercalation in the TN system5 or in Laponite Clay.7 On the

FIG. 2. Predicted equilibrium atomic geometry of the R6G J-type dimer. The atom type is indicated on a gray scale as follows: hydrogen 共white兲, carbon 共gray兲, oxygen 共dark gray兲, and nitrogen 共black兲.

other hand, the predicted value of intermolecular distances should also be taken cautionary. Our model incorporates both short- and long-range 共dipole-dipole兲 interactions. The short-range interaction is determined straightforward from DFT-GGA electronic structure through the calculations of corresponding overlap integrals. However, dipole-dipole interaction is incorporated through self-consistent calculations of the charge distribution over molecules in dimers. This essentially many-body part requires a realistic description of XC interaction, and it is still challenging for the DFT-GGA approach. Several models for XC were proposed within the last decades. In this work we used the PBE 共Ref. 15兲 approach for XC interaction which was proved in Ref. 16 by a geometry optimization study of the dimers formed from relative small molecules. The limitations of this approach may result in discrepancies observed. One can expect that further development of the XC model will result in better agreement between predictions and experiment. For a better understanding of the numerical results, it is instructive to refer to the electrostatic theory. The calculated static dipole moment 共␮兲 is found to be parallel to the molecular axis oriented along benzene rings of the R6G molecule. Assuming all molecules have been identical, the attractive potential energy describing dipole-dipole interaction is given by29


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FIG. 3. Predicted optical absorption spectrum of the single R6G molecule 共solid line兲 in comparison with experimental data 共dots兲共Ref. 31兲.

V共r兲 =

兩␮兩2 f共␪兲, 兩r兩3

with f共␪兲 = 共1 − 3 cos3 ␪兲,

共6兲

where ␪ is an angle between r 共location in direct space兲 and ␮. The energy of the dipole-dipole interaction is determined through a calculation of overlap integrals with the potential 共6兲 after integration over entire space. It is proportional to 兩r兩−6, which represents the van der Waals type of interaction. Equation 共6兲 demonstrates that a strong attractive 共negative兲 value is expected for dipoles aligned antiparallel if aggregated in H-type dimers which should be the most energetically favorable configuration resulting in quenching the radiation. This is in agreement with direct computations of this work: total energy of the H dimer is lower than that of the J dimer 关see Eq. 共5兲兴, and the predicted value of ␮ for the H-type dimer is 34 times smaller than that of the J dimer. Optical absorption spectra of the R6G single molecule as well as those of molecular dimers are calculated from Eqs. 共1兲–共4兲. The self-consistently calculated eigenfunctions and eigenenergies of dimers include QP shift of monomer.18 Calculated optical absorption spectrum for the isolated R6G molecule is shown in Fig. 3 in comparison with the experimental data.32 Absolute values of the absorption coefficient are normalized according to the molecular concentration followed from the dimension of the supercell.28 Electronic eigenvalues related to singlet-type electronic states are represented with better than 10% accuracy. The theoretically calculated absorption spectrum shown in Fig. 3 reproduces most of characteristic features measured experimentally. Thus, the dominant calculated absorption peak is located at 511 nm, while the same peak is seen in the experimental absorption spectrum at about 528 nm.5,30,33 The predicted optical absorption spectrum corresponding to the singlet transitions of H-type dimers shows the dominant peak located at 483 nm 共2.567 eV兲; see Fig. 4. There is also another small peak located at 526 nm 共2.357 eV兲. The splitting 共⌬EH = 0.210 eV兲 is caused by the strong intermolecular interaction between ␲-type electrons of the neighboring molecules in H dimer. In terms of excitonic theory20 these peaks correspond to antibonding 共dipole-allowed兲 and

FIG. 4. Calculated optical absorption spectra of H-type R6G dimers 共bold line兲 in comparison with that of the single R6G molecule 共dotted line兲. Weakly allowed transitions to the antisymmetrical states 共due to the twisting兲 result in a small redshifted peak indicated by the arrow.

bonding 共dipole-forbidden兲 electronic states, respectively. Due to the twisting of the molecular axes 共see Fig. 1兲, optical transitions to a dipole-forbidden unoccupied electronic state in H-type dimers are weakly allowed 共see also Refs. 3 and 6兲. The predicted absorption maximum of R6G monomers 共Fig. 3兲 is located at 511 nm. Therefore, our theory predicts a strong blueshift 共⌬␭ = 28 nm兲 in optical absorption of R6G due to the creation of H-type dimers. Very close to this value are reported experimental data of absorption maxima at 501 nm 共Ref. 5兲 and 500 nm 共Ref. 7兲关as compared to a 528 nm maximum in initial spectrum 共Refs. 5 and 7兲兴 of R6G molecules intercalated in a fluor-taeniolite film5 or in a Laponite Clay,7 which were interpreted as an indication of H-type dimers. On the other hand, our recent study33 does not reveal any remarkable changes in optical absorption with increase of the concentration of R6G molecules in methanol solution from 0.1 to 3.8 g / l. One can speculate that intercalation substantially increases the probability of aggregation of R6G molecules. For T-shaped J-type R6G dimers, our theory predicts splitting of the main absorption peak into two maxima located at 527 nm 共2.353 eV兲 and at 506 nm 共2.451 eV兲; see Fig. 5. The splitting 共⌬EJ = 0.098 eV兲 is caused by the hydrogen-bonding interaction of boundary atoms from one molecule with delocalized ␲ electrons from the other molecule in the J dimer. In terms of the excitonic theory,20 this situation corresponds to the oblique mutual orientation of molecular dipoles when electronic transitions to both electronic unoccupied levels are allowed 共see discussion in Refs. 3, 6, and 7兲, in agreement with our results. Obtained values of the total energy minima as well as values of ⌬EH and ⌬EJ clearly indicate that intermolecular interaction in H type is substantially stronger then that in J-type R6G dimers. Theoretical results above are consistent with the experimental data presented in our recent publication.33 In Ref. 33, optical absorption, emission, and excitation spectra of a pure solution of R6G in methanol at a concentration of the mixture in the range from 0.1 to 16.7 g / l have been measured.


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Optical properties of rhodamine dimers

FIG. 5. Calculated optical absorption spectra of J-type R6G dimers 共bold line兲 in comparison with that of the single R6G molecule 共dotted line兲.

With the increase of the R6G dye molecular concentration, we observed the appearance of the second emission band 共at ⬃600 nm兲, which was redshifted with respect to the ⬃565 nm luminescence band presented in low-concentrated dye solution; see Fig. 6. However, practically no changes in the absorption spectrum were observed.33 A theoretical prediction of the light-emission spectrum requires incorporation of temperature-dependent distribution functions in Eq. 共4兲 and microscopic modeling of energy transfer in the system, which is beyond the scope of the present study. However, results of our calculations could be used for semiquantitative analysis of the luminescence from R6G dye aggregates. First of all, it is reasonable to expect that photon energy shifts in absorption and emission bands related to the same singlet-type optical transitions should be close to each other. Thus, the redshifted ⬃600 nm luminescence band observed in the high-concentrated R6G solution33 could be related to J-type dimers. Below, we qualitatively explain the experimental results of Ref. 33 and answer several naturally arising questions based on two additionally taken assumptions. Why

did we not see the presence of dimers in absorption while we observed J dimers in emission? To answer the first half of this question, we use assumption 1: the concentration of dimers was low. Our prediction of a strong blueshift in optical absorption spectra due to H dimers 共see Fig. 4兲 agrees with experiment of intercalated R6G.5,7 On the other hand in Ref. 33 we have not observed any new blueshifted peaks in the optical absorption of free-standing R6G aggregates even at a very high concentration of R6G where well-pronounced splitting in luminescence has been measured 共at 16.7 g / l; see also Fig. 6兲. One can speculate that the stability of freestanding dimers at room temperature is very low, but it could be enhanced through surface adsorption and/or intercalation. In order to answer the second half of the question above, why in this case there is a relatively strong second band 共the J band because H dimers are nonradiative, as discussed above兲 in the emission,1,3,5,7,8,33 we use assumption 2: there is an efficient energy transfer from monomers to dimers. In support of this assumption, we estimated the energy transfer in R6G aggregates. Our approach exploits the readily achievable coupling via incoherent long-range dipolar interaction, which allows intermolecular communication via Förster energy transfer 共see, e.g., Ref. 34 and references therein兲. The intermolecular distance R0 at which the efficiency of the energy transfer is equal to 50% 共Förster radius兲 is given by34 R60 =

3 ␩0 2共2␲兲5 n4

=

3 ␩0 2共2␲兲5 n4

冕冕

F共˜␯兲␴abs共˜␯兲

d˜␯ ˜␯4

F共␭兲␴abs共␭兲␭5d␭,

共7兲

where ˜␯ = ␻ / 2␲c is the wave number 共cm−1兲, ␴abs共˜␯兲 is the effective cross section of acceptor absorption, n is the refractive index 关dispersion of n is neglected in Eq. 共7兲兴, ␩0 is the quantum yield of luminescence of the donor, and F共˜␯兲 is the normalized radiation spectrum expressed as the number of quanta per unit frequency range,

冕

F共˜␯兲d˜␯ =

冕

F共␭兲␭d␭ = 1.

共8兲

In expressions 共7兲 and 共8兲, we used a conventional relationship of argument scale conversion for radiation spectrum 共see, e.g., Ref. 35兲. Following Ref. 36, the effective emission cross section ␴em共␭兲 can be calculated as

␴em共␭兲 =

1 ␩0 ␭5F共␭兲, 8␲ n2c␶em

共9兲

where ␶em is the emission lifetime, and c is the light speed. Combining Eqs. 共7兲 and 共8兲, we obtain a convenient formula for calculating the Förster radius, R60 =

FIG. 6. Emission spectra of a pure solution of R6G in methanol at concentrations of dye equal to 0.1 g / l 共1兲, 3.8 g / l 共2兲, and 16.7 g / l 共3兲. The emission intensity of trace 3 is twentyfold increased 共after Ref. 32兲.

3 c␶em 8␲4 n2

冕

␴em共␭兲␴abs共␭兲d␭.

共10兲

Based on the emission and absorption spectra of R6G dye in 0.1 g / l methanol solution 共recorded using straightforward procedures described in Ref. 33兲 and the luminescence decay time of a low-concentrated R6G, ␶em = 5 ⫻ 10−9 s


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absorption spectra. The results of this work are discussed in comparison with available experimental data. ACKNOWLEDGMENTS

This research was supported by the NASA URC Grant No. NCC-3-1035 and the NSF CREST Grant No. HRD9805059. The authors cordially thank V. P. Drachev, C. Davison, P. Nyga, and V. M. Shalaev for providing the results of the lifetime measurements and G. Zhu for the help with the processing experimental data. F. del Monte and D. Levy, J. Phys. Chem. 102, 8036 共1998兲. J. E. Selwyn and J. I. Steinfeld, J. Phys. Chem. 76, 762 共1972兲. 3 R. W. Chambers, T. Kajiwara, and D. R. Kearns, J. Phys. Chem. 78, 380 共1974兲. 4 J. Bujdak, N. Iyi, and R. Sasai, J. Phys. Chem. B 108, 4470 共2004兲. 5 R. Sasai, T. Fujita, N. Iyi, H. Itoh, and K. Takagi, Langmuir 18, 6578 共2002兲. 6 T. Kikteva, D. Star, Z. Zhao, T. L. Baislev, and G. W. Leach, J. Phys. Chem. B 103, 1124 共1999兲. 7 V. Martinez, F. Lopez Arbeola, T. Banuelos, T. Arbeola Lopez, and I. Lopez Arbeola, J. Phys. Chem. B 108, 20030 共2004兲; 109, 7443 共2005兲. 8 R. Sasai, N. Iyi, T. Fujita, F. L. Arbeloa, V. M. Martinez, K. Takagi, and H. Itoh, Langmuir 20, 4715 共2004兲. 9 W. Kohn and L. Sham, Phys. Rev. 140, A1133 共1965兲. 10 T. Ziegler, Chem. Rev. 共Washington, D.C.兲 91, 651 共1991兲. 11 W. Kohn, A. D. Becke, and R. G. Parr, J. Phys. Chem. 100, 12974 共1996兲. 12 Yu. Pereverzev, O. V. Prezhdo, and L. R. Dalton, J. Chem. Phys. 117, 3354 共2002兲. 13 Y. Zhang, W. Pan, and W. Yang, J. Chem. Phys. 107, 7921 共1997兲. 14 J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 共1992兲. 15 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 共1996兲. 16 X. Xu and W. A. Goddard III, J. Chem. Phys. 121, 4068 共2004兲. 17 G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 共2002兲. 18 G. Cappellini, R. Del Sole, L. Reining, and F. Bechstedt, Phys. Rev. B 47, 9892 共1993兲. 19 R. Leitsmann, W. G. Schmidt, P. H. Hahn, and F. Bechstedt, Phys. Rev. B 71, 195205 共2005兲. 20 M. Kasha, Rev. Mod. Phys. 31, 162 共1959兲. 21 M. O. Sinnokrot and C. D. Sherill, J. Phys. Chem. A 108, 10200 共2004兲. 22 R. L. Jaffe and G. D. Smith, J. Chem. Phys. 105, 2780 共1996兲. 23 S. Tsuzuki and H. P. Luthi, J. Chem. Phys. 114, 3949 共2001兲. 24 Material studio modeling 3.2, Accelrys Software Inc. 2004. 25 M. Fuchs and M. Schefler, Comput. Phys. Commun. 16, 1 共1999兲. 26 N. Troullier and J. L. Martins, Phys. Rev. B 43, 1993 共1991兲. 27 V. I. Gavrilenko, Phys. Status Solidi A 188, 1267 共2001兲. 28 B. Adolph, V. I. Gavrilenko, K. Tenelsen, F. Bechstedt, and R. Del Sole, Phys. Rev. B 53, 9797 共1996兲. 29 A. S. Davydov, Solid State Theory 共Academic, New York, 1980兲. 30 Computer code GAUSSIAN-03, Gaussian Inc., Wallingford, CT, 2003. 31 Computer code JAGUAR 4.2, Schrodinger Inc., Portland, OR, 2002. 32 U. Backmann, Lambdachrome Laser Dyes, 2nd ed. 共Lambda Physik GmbH, Goettingen, Germany, 1994兲, pp. 150 and 151. 33 M. A. Noginov, M. Vondrova, S. M. Williams, M. Bahoura, V. I. Gavrilenko, S. M. Black, V. P. Drachev, V. M. Shalaev, and A. Sykes, J. Opt. A, Pure Appl. Opt. 7, 219 共2005兲. 34 V. M. Agranovich and M. D. Galanin, Electronic Excitation Energy Transfer in Condensed Matter 共North-Holland, Amsterdam, 1982兲. 35 S. J. Strickler and R. A. Berg, J. Chem. Phys. 37, 814 共1962兲. 36 O. Svelto, Principles of Lasers 共Plenum, New York, 1998兲. 37 The experiments were performed by V. P. Drachev, C. Davison, P. Nyga V. M. Shalaev and will be published elsewhere. 1 2

FIG. 7. Absorption 共dotted line兲 and emission 共solid line兲 cross-section spectra of R6G dye solution in methanol, 0.1 g / l.

共measured in 1-mm-thick cuvette under 2.5 ps excitation at 530 nm by Drachev et al. at Purdue University37兲, we calculated the absorption and emission cross sections of R6G dye; see Fig. 7. Using these experimental data, we calculated the overlap integral 兰␴em共␭兲␴abs共␭兲d␭ = 2.15⫻ 10−38 cm5 and the Förster radius R0 = 4.4⫻ 10−7 cm. Note that using the emission and absorption cross section spectra of R6G given in Ref. 36, one can calculate a substantially higher value of the overlap integral 兰␴em共␭兲␴abs共␭兲d␭ = 6.01⫻ 10−38 cm5, which results in a bigger value of the Förster radius R0 = 5.0⫻ 10−7 cm. The emission spectra depicted in Fig. 6 correspond to three different average intermolecular distances, R1 = 2.0⫻ 10−6 cm, R2 = 6.0⫻ 10−7 cm, and R3 = 3.6⫻ 10−7 cm. From this figure follows that only one luminescence band is present at Ri ⬎ R0, and two bands are observed at Ri ⬇ R0, which is in a good agreement with the qualitative consideration above. Therefore optical absorption spectrum of free-standing aggregates is determined through R6G monomers, and the luminescence of J dimers is observed due to efficient energy transfer and to the high radiative cross section. IV. CONCLUSION

Electron-energy structure and optical properties of R6G H and J dimers are calculated using the DFT-GGA method with ab initio pseudopotentials. The substantial redshift of optical absorption spectra of R6G dye molecules after aggregation in J dimers is caused by hydrogen-bonding interaction of boundary atoms from one molecule with delocalized ␲ electrons from the other molecule. The H-type configuration is characterized by a strong interaction of ␲ electrons from neighboring molecules, which results in substantial splitting of the singlet electron state and in the predicted blueshift in
