Letter pubs.acs.org/JPCL
The Effect of the π-Electron Delocalization Curvature on the TwoPhoton Circular Dichroism of Molecules with Axial Chirality Carlos Diaz,† Na Lin,‡,§ Carlos Toro,† Remy Passier,† Antonio Rizzo,∥ and Florencio E. Hernández*,†,⊥ †
Department of Chemistry, University of Central Florida, P.O. Box 162366, Orlando, Florida 382616-2366, United States State Key Laboratory of Crystal Materials, Shandong University, 250100 Jinan, Shandong, People’s Republic of China § Center for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø, N-9037 Tromsø, Norway ∥ CNR - Consiglio Nazionale delle Ricerche, Istituto per i Processi Chimico Fisici (IPCF-CNR), UoS di Pisa, Area della Ricerca, Via G. Moruzzi 1, I-56124 Pisa, Italy ⊥ The College of Optics and Photonics, CREOL University of Central Florida, P.O. Box 162366, Orlando, Florida 382616-2366, United States ‡
S Supporting Information *
ABSTRACT: Herein we report on the theoretical-experimental study of the effect of curvature of the π-electron delocalization on the two-photon circular dichroism (TPCD) of a family of optically active biaryl derivatives (S-BINOL, S-VANOL, and S-VAPOL). The comparative analysis of the influence of the different transition moments to their corresponding TPCD rotatory strength reveals an enhanced contribution of the magnetic transition dipole moment on VAPOL. This effect is hereby attributed to the additional twist in the π−electron delocalization on this compound. TPCD measurements were done using the double L-scan technique in the picosecond regime. Theoretical calculations were completed using modern analytical response theory, within a time-dependent density functional theory (TD-DFT) approach, at both, B3LYP and CAM-B3LYP levels, with the aug-cc-pVDZ basis set for S-BINOL and S-VANOL, and 6-31G* for S-VAPOL. Solvent effects were included by means of the polarizable continuum model (PCM) in CH2Cl2. SECTION: Spectroscopy, Photochemistry, and Excited States
T
he understanding of chiral systems has been the aim of study of many scientists in our community during the last two decades. This effort has been mainly motivated by the central role this type of molecule plays in biological processes,1 their implications in the drug and food industry,2,3 and their applications in nanotechnology,4 optics and photonics,5 and in asymmetric catalysis.6 The understanding of chiral systems has been mainly driven by the development of circular dichroism (CD) and optical rotatory dispersion (ORD).7 The former is defined as the difference in absorption using right (RCPL) and left (LCPL) circularly polarized light.8,9 During the past 20 years, electronic circular dichroism (ECD), i.e., the CD associated with transitions between electronic states, has been the technique par excellence for the study of the conformational and physicochemical properties of optically active molecules.7 This method is based on the one-photon absorption (OPA) of chiral compounds, which typically takes place in the far and near UV region of the electromagnetic spectrum. Since OPA of standard aqueous buffer solutions and common solvents reside in the same spectral region, and the scattering present in some specific samples becomes critical at shorter wavelengths, ECD has intrinsic limitations for the study of optically active molecules in solution and in inhomogeneous media in the UV region.10 © 2012 American Chemical Society
In order to bypass these obstacles, several approaches such as synchrotron radiation circular dichroism (SRCD),11 magnetic circular dichroism (MCD),12 vibrational circular dichroism (VCD),13 and vibrational Raman optical activity (VROA),14 have been proposed. Among these methods, VCD and VROA have made the most significant contributions to the determination of the configuration of small molecules and the secondary structure of proteins.13,14 However, the deeper understanding of attractive biological systems such as natural amino acids structures and proteins, and the innovative development of chiral molecules with distinctive functionalities for practical asymmetric catalysis, among others, requires the development of novel approaches that can reveal spectroscopic fingerprints and structural features at shorter wavelengths. With the aim of overcoming the existent barriers, nonlinear optical processes such as second harmonic generation (SHG), sum-frequency generation (SFG), multiphoton optical rotation, and nonlinear optical activity have been exploited lately.15,16 Although these original optical methods have started making important contributions to the field of chirality,15,16 none of Received: May 7, 2012 Accepted: June 20, 2012 Published: June 20, 2012 1808
dx.doi.org/10.1021/jz300577e | J. Phys. Chem. Lett. 2012, 3, 1808−1813
The Journal of Physical Chemistry Letters
Letter
them refers to truly polarization-dependent multiphoton excitation processes comparable to ECD that would allow to work in that obscure region of the UV. A few years ago, and after developing the double L-scan technique,17 we demonstrated experimentally two-photon circular dichroism (TPCD) in S-1,1′-bi(2-naphthol) (SBINOL) and R-1,1′-ni(2-naphthol) (R-BINOL). These remarkable results proved the theoretical predictions done first by Tinoco and Power in the 1970s,18,19 and which was revitalized 30 years later by Rizzo and co-workers.20 TPCD, defined in the degenerate case as ΔδTPCD(λ) = δTPA L (λ) − TPA TPA δTPA R (λ) [δL (λ) and δR (λ) are the TPA cross sections for LPCL and RCPL, respectively, measured at a specific wavelength λ], is the nonlinear counterpart of ECD.21 Because the typical wavelength for two-photon excitation is approximately 2-fold longer than that required for OPA, the linear absorption in the TPA region is negligible, and scattering can be minimized.22,23 Therefore, the study of optically active molecules at shorter wavelengths using TPCD becomes an open possibility that can lead to new and/or complementary structural and conformational understanding of biological and chemical systems. Although we have already revealed the complex contribution of the excited states to the overall TPCD rotatory strength, i.e., the parameter that determines the TPCD signal of chiral systems,21 TPCD is still in its infancy. Therefore, there is still a great need of more systematic studies to truly understand the structure−property relationship of this phenomenon. In this Letter, we report on the theoretical-experimental study of the TPCD on a series of optically active biaryl derivatives. We highlight the effect of curvature of the π− electron delocalization on the observable. The comparative analysis of the different transition moments that contribute to their TPCD rotatory strength reveals a boost in the contributions related to the magnetic transition dipole moment on VAPOL. This enhancement is associated with the additional twist present in the π-electron delocalization of this molecule. S-BINOL, S-3,3′-diphenyl-[2,2′-binaphthalene]-1,1′-diol (SVANOL), and S-2,2′-siphenyl-[3,3′-biphenanthrene]-4,4′-diol (S-VAPOL) were chosen for this investigation because of their molecular structures (see Figure 1) and their great applicability
Figure 2. TPA spectra of S-BINOL (a), S-VANOL (b), and S-VAPOL (c), plotted at half of the excitation wavelength. Theoretical electronic transitions with Lorentzian convolution [line width 0.20 eV FWHM] (scattered spheres and dashed lines), and experimental TPA spectra (solid line with filled squares). The theoretical spectra are shifted +18 nm, −17 nm, and −3 nm for S-BINOL, S-VANOL, and S-VAPOL, respectively.
spectra were slightly shifted by +18 nm, −17 nm, and −3 nm for S-BINOL, S-VANOL, and S-VAPOL, respectively. The first observation is the theoretical−experimental spectral matching in all the spectra. The matching is excellent in S-BINOL (bands at ca. 230 and 275 nm). The features get more intricate for SVANOL and S-VAPOL. For S-VANOL, the experiment shows a broad band at 270 nm, followed by an increase in absorption arising below 240 nm. Our calculations yield some intensity above 280 nm, then a couple of states absorbing around 240 nm and a strong increase in absorption for our frontier states (the 19th and the 20th). It is likely that further TPA strengths might be produced by states beyond the 20th, which would contribute then to the sharp increase in the experiment. In the range of wavelengths explored in the experiment, the TPA absorption of S-VANOL is therefore reasonably reproduced by theory. For S-VAPOL, the distribution of two-photon strengths is more complex, with a sequence of two-photon absorption strengths of different intensities lying between 330 and 220 nm. The bands seen in the experiment at 320 and 280 nm and the increase in intensity at the low wavelength end of the interval (220 nm) are all in correspondence with electronic states that are particularly active in two-photon absorption. The second observation is related to the differences in magnitude between
Figure 1. Molecular structures of S-BINOL (left), S-VANOL (center) and S-VAPOL (right). The arrows inside the molecules display the direction of the π-electron delocalization. The numbering for some carbon atoms is shown.
as chiral auxiliaries in asymmetric catalysis.24 In addition, they are all commercially available in high enantiomeric excess (enantiomeric ratio R:S ≥ 99:1). The theoretical (DFT/B3LYP) and experimental TPA spectra of S-BINOL,25 S-VANOL, and S-VAPOL, using linearly polarized light (LPL) and plotted at half of their excitation wavelength, are displayed in Figure 2. In order to show a better overlapping between experiment and theory, the theoretical 1809
dx.doi.org/10.1021/jz300577e | J. Phys. Chem. Lett. 2012, 3, 1808−1813
The Journal of Physical Chemistry Letters
Letter
the theory and the experiment. While in S-BINOL and SVANOL the two magnitudes differ by approximately 8- and 4fold, respectively, the difference increases for S-VAPOL. The difference in magnitude between the theory and experiment was already attributed, in ref 21, to exciton coupling for dimers undergoing electrically allowed transitions,26,27 and excitation pulse width of the excitation source, which can lead to excitedstate absorption. The contribution of the latter, in measurements of polarization-dependent optical properties of organics, was recently reported in the literature.28,29 The third and perhaps the most relevant observation in Figure 2 is the fact that the theoretical and experimental TPA cross sections show TPA TPA the same trend: δTPA S‑BINOL(λ) < δS‑VAPOL(λ) < δS‑VANOL(λ). This tendency suggests the existence of a weaker charge transfer in S-BINOL compared to that in the other two compounds due to the position of the external phenyl ring in the naphthalene and phenanthrene systems. This statement is supported by the position of the theoretical and experimental maximum of the linear absorption spectra of all three compounds (λMax,S‑BINOL ≈ 229 nm, λMax,S‑VANOL ≈ 248 nm, and λMax,S‑VAPOL ≈ 266 nm), which indicates a shorter effective extent of the π-electron delocalization in S-BINOL (see spectra in the Supporting (λ) between Information, SI). However, the difference in δTPA i the last two is less important. This implies that the conjugation through the π-system is not effectively increased going from SVANOL to S-VAPOL because of the twist in the π-electron delocalization found in the latter (see Figure 1). This result is consistent with the extensive theoretical−experimental evidence given in the literature sustaining that the dependence of the TPA cross-section of conjugated systems with respect to the π-electron delocalization length is more effective in molecules with one-dimensional (linear) charge transfer.30 Note: Electron delocalization to the phenyl rings attached in positions 3,3′ in S-VANOL and 2,2′ in S-VAPOL is considered negligible because of the large dihedral angle (∼ 53°) existent between the two systems.31,32 In Figure 3 we present the theoretical (DFT/B3LYP) and experimental TPCD spectra of S-BINOL,21 S-VANOL, and SVAPOL, plotted at half of their excitation wavelength. In these plots the suitable spectral agreement between the theory and (ω0f) have the experiment is noticeable (All theoretical RTPCD 0f the same spectral shift utilized in Figure 2). In S-BINOL, RTPCD 0f over the entire spectrum clearly sums-up to reproduce the main spectral features, i.e., overall negative signal and a negative band at 225 nm. In S-VANOL, a series of negative transitions spanning from 240 to 320 nm are in agreement with the sum of negative bands within the same region. The experimental positive band centered at 245 nm is not observed in the theoretical spectrum. Again, it is likely that further RTPCD might 0f be produced by states beyond the 20th, which would reproduce the mentioned positive band. Although states 18 and 19 have cancels the strongest intensity, their net contribution to RTPCD 0f almost completely because of their spectral proximity as explained in ref 21. Experiment and theory display a series of positive and negative contributions in S-VAPOL. Positive transitions at 255, 270, 285, 302 and 328 nm reproduce the positive bands centered at 250, 280, and 330 nm. Negative transitions at 250, 272, 280, 294, 299, and 305 nm, are in agreement with negative bands centered at 245, 270, and 290 nm. The moderate theoretical-experimental agreement in SVAPOL could perhaps be attributed to the quality of the chosen basis set (6-31G*). Using the aug-cc-pVDZ in this molecule represented a very expensive computational challenge
Figure 3. TPCD spectra of S-BINOL (a), S-VANOL (b), and SVAPOL (c), plotted at half of the excitation wavelength. Theoretical electronic transitions with Lorentzian convolution [line width 0.20 eV FWHM] (scattered spheres and dashed lines), and experimental TPA spectra (solid line with filled squares). The theoretical spectra are shifted +18 nm, −17 nm, and −3 nm for S-BINOL, S-VANOL, and SVAPOL, respectively. The numbers in the plots refer to some of the most important excited states to the TPCD signal.
for us. Nevertheless, since our level of theory has been proven to predict,33 at least qualitatively, the behaviors and trends in systems exhibiting axial chirality, the use of the chosen functional and basis set for S-VAPOL is justified. Another interesting observation in Figure 3 is the resultant trend in the TPCD signal magnitude of these three biaryl TPCD TPCD TPCD derivatives, i.e., δS‑BINOL (λ) < δS‑VANOL (λ) < δS‑VAPOL (λ). Although there is a difference in magnitude between the theoretical and the experimental values, the observed tendency is the same in both cases. Knowing that the TPCD signal directly depends on the different contributions from the electric transition quadrupole moment and the magnetic transition dipole moment through RTPCD (see eq 2), a comparison of the 0f weight of each of these parameters to ΔδTPCD, in all three molecules, was performed by theoretical means. Figure 4 displays the contribution of the electric transition quadrupole moment [B2 vs λ] and the magnetic transition dipole moment [(B1 + B3) vs λ ] to RTPCD , between 200 and 0f 350 nm. In Figure 4a one can observe an overwhelming influence of the electric transition quadrupole moment (B2S‑BINOL < B2S‑VANOL < B2S‑VAPOL) onto the TPCD on S1810
dx.doi.org/10.1021/jz300577e | J. Phys. Chem. Lett. 2012, 3, 1808−1813
The Journal of Physical Chemistry Letters
Letter
transition dipole moment to the TPCD signal of this molecule compared to the other two. The apparent large contribution of (B1 + B3) to the TPCD of S-VANOL, at 255 nm, is broadly canceled by the two, opposite in sign but relatively close in amplitude, transitions (states 18 and 19) observed at virtually the same wavelength (Figure 4.b). The effect of cancellation of contributions that affect the shape and amplitude of the TPCD spectrum of chiral molecules has already been observed by Rizzo and co-workers in S-BINOL (e.g., excited states 5 and 6).21 In order to corroborate this outcome, a comparison between the summations over the absolutes values of both contributions, independently to the TPCD signal in each molecule was performed (see Table 1). In this comparison, we have also Table 1. Summation over the Absolute Values of the Theoretical Molecular Parameters |B2| and |B1 + B3| in SBINOL, S-VANOL, and S-VAPOL, from 200 to 350 nm, Using B3LYP S-BINOL S-VANOL S-VAPOL
∑20 i=1|B2|
∑20 i=1|B1 + B3|
347.80 1402.89 2770.71
1190.04 3654.55 5421.73
included the absolute values of those contributions in SVANOL (255 nm) that canceled in the TPCD spectrum to make a fair evaluation of the effect. First, values displayed in Table 1 show a clear augmentation of both contributionsthe electric transition quadrupole moment and the magnetic transition dipole momentgoing from S-BINOL to SVAPOL. The greater increase of the contribution of the latter to RTPCD is evident. This comparative analysis is in agreement 0f with the explanation given above. Therefore, the contribution of the magnetic transition dipole moment to the TPCD signal in S-VAPOL is enhanced as a result of the extra twist present in the π-electron delocalization in this vaulted structure. Our explanation is supported by previous theoretical works on photoinduced electric currents in ring-shape molecules,35 and chiral control of electron transfer in helical molecular bridges, both using circularly polarized radiation.36 While in the former the authors demonstrate that ring currents, originated by a second-order nonlinear optical response, produce a magnetic dipole moment in aromatic molecules, in the latter, Skourtis et al. describe the effect in the framework of a general novel phenomenon of transfer of charge with its momentum information. Our statement is also supported by the simplified analysis of the excited states, electronic transitions and molecular orbitals given in the SI, performed using Gaussian 09.37 In summary, the comparative analysis of the measured and calculated TPA and TPCD spectra on a series of compounds with axial chirality led us to a better understanding of the molecular structure−property relationships of TPCD. The TPCD TPCD signal varied according to ΔδTPCD S‑BINOL < ΔδS‑VANOL < TPCD ΔδS‑VAPOL. This trend obeys the contributions of the different transition moments to the TPCD signal. On one hand, we found that the influence of the electric transition quadrupole moment to the TPCD becomes more important in a molecule in which the charge transfer away from the center of the molecule or vice versa, is favored. On the other hand, we determined that the effect of the magnetic transition dipole moment to the TPCD rotatory strength, and thus the TPCD
Figure 4. Plot of molecular parameter B2 vs λ (a) and B1 + B3 vs λ (b); λ is half of the excitation wavelength. S-BINOL (patterned columns), S-VANOL (solid orange columns), and S-VAPOL (solid black columns).
VAPOL (mainly within the strongest TPA region), followed by that of S-VANOL in the spectral region above 250 nm. The weight of B2 in S-BINOL is very small. This outcome was anticipated after examining the molecular structure of all three molecules and realizing that the position of the external ring in S-VANOL and S-VAPOL, compared to that in S-BINOL, favors a larger charge transfer away from the center of the molecule or vice versa (in S-BINOL the spherically symmetrical electronic charge distribution is mostly retained).34 The most remarkable finding, however, is the overpowering contribution of the magnetic transition dipole moment to the TPCD signal in S-VAPOL (see Figure 4b). The observed trend of this effect turns out to be (B1 + B3)S‑BINOL < (B1 + B3)S‑VANOL < (B1 + B3)S‑VAPOL. (B1 + B3)S‑BINOL < (B1 + B3)S‑VANOL is the result of the relative position of the two naphthalene moieties with respect to the center of the molecule. While in S-BINOL, the π-electron delocalization, considering both moieties, takes place at a normal angle (∼89°), in S-VANOL it happens at approximately 125° (see Figure 1). Therefore, a stronger contribution of the magnetic transition dipole moment to the TPCD signal in S-VANOL, compared to that S-BINOL, can be expected due to the slight helicity found in the former. In SVAPOL this effect is even stronger. In addition to having the two phenanthrene structures in a similar relative orientation as the two naphthalenes in S-VANOL, S-VAPOL has its third and most external phenyl ring in the aromatic system in a position that imposes an additional curvature to the π−electron delocalization (see Figure 1). This twist in the π-electron delocalization induces a stronger contribution of the magnetic 1811
dx.doi.org/10.1021/jz300577e | J. Phys. Chem. Lett. 2012, 3, 1808−1813
The Journal of Physical Chemistry Letters
Letter
signal, is strongly enhanced by the twist in the π-electron delocalization of the chiral molecules. S-VANOL, S-VAPOL, and tetrahydrofuran (THF) were purchased from Sigma-Aldrich and used without further purification. The linear absorption spectra of all solutions were measured in 0.2 mM/THF solutions placed in a 1 mm quartz cell, using a single beam Agilent 8453 spectrometer (contributions from the solvent and the cell were always subtracted). The nonlinear optical characterization of these compounds was performed using the double L-scan technique17 in THF solutions at a concentration of 0.1 M. Twophoton excitation was induced with an optical parametric generator, pumped by the third harmonic of a mode-locked Nd:YAG laser, operating at 10 Hz repetition rate and a pulse width of 25 ps (full width at half-maximum (FWHM)). The covered spectral range was from 440 to 700 nm. The absence of molecular aggregates in solution at such a high concentration was corroborated by examining the UV−vis spectra and comparing the two-photon absorption cross sections of two different solutions (0.1 and 0.001 M). The UV−vis spectra and the cross sections did not change with the concentration. In addition, the visible inspection of the solutions did not reveal the formation of clusters. The theoretical background involved in this research has been given in detail elsewhere.38−43 The necessary formulas and computational details are summarized in the SI. The reader is also referred to the SI for definitions, symbols, and convention adopted in this manuscript. Geometry optimizations were carried out using Gaussian 09.37 UV−vis, ECD, TPA, and TPCD spectra were simulated using Dalton 2.0.44 Herein, we only present the main equations of TPCD to show the molecular parameters that carry out the information regarding the contributions from the different transition moments to the TPCD signal. TPCD is given here (in units of GM, Göppert-Mayer, 10−50 cm4 sec molecule−1 photon−1) as18,19,43
DFT),45,46 both at DFT/B3LYP47−49 and DFT/CAMB3LYP,50,51 with the aug-cc-pVDZ basis set for S-BINOL and S-VANOL, and 6-31G* for S-VAPOL. Solvent effects were included by means of the polarizable continuum model (PCM) in CH2Cl2. (see the SI for additional details on the calculations and in particular for the justification of the preference given to DFT/B3LYP in the discussion).
■
ASSOCIATED CONTENT
S Supporting Information *
Theoretical and computational approach, tables with TPCD molecular parameters, HOMO−LUMO analysis, and UV−vis, ECD, TPA, and TPCD spectra. This material is available free of charge via the Internet http://pubs.acs.org.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail: fl
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work was partially supported by the National Science Foundation through Grant Number CHE-0832622.
■
REFERENCES
(1) Tamura, K. Origin of Amino Acid Homochirality: Relationship with the RNA World and Origin of tRNA Aminoacylation. BioSystems 2008, 92, 91−98. (2) Simó, C.; Barbas, C.; Cifuentes, A. Chiral Electromigration Methods in Food Analysis. Electrophoresis 2003, 24, 2431−2441. (3) McConnell, O.; Bach, A.; Balibar, C.; Byrne, N.; Cai, Y.; Carter, G.; Chlenov, M.; Di, L.; Fan, K.; Goljer, I.; et al. Enantiomeric Separation and Determination of Absolute Stereochemistry of Asymmetric Molecules in Drug DiscoveryBuilding Chiral Technology Toolboxes. Chirality 2007, 19, 658−682. (4) Zhang, J.; Albelda, M.; Liu, T.; Canary, Y.; Chiral, J. W. Nanotechnology. Chirality 2005, 17, 404−420. (5) Haupert, L. M.; Simpson, G. J. Chirality in Nonlinear Optics. Annu. Rev. Phys. Chem. 2009, 60, 345−365. (6) Noyori, R. Asymmetric Catalysis: Science and Opportunities (Nobel Lecture). Angew. Chem., Int. Ed. 2002, 41, 2008−2022. (7) Nakanishi, K., Berova, N., Woody, R. W., Eds. Circular Dichroism: Principles and Applications; VCH: New York, 1994. (8) Condon, E. U. Theories of Optical Rotatory Power. Rev. Mod. Phys. 1937, 9, 432−457. (9) Caldwell, D. J.; Eyring, H. The Theory of Optical Activity; WileyInterscience: New York, 1971. (10) Tinoco, I.; Mickols, W. Absorption, Scattering, and Imaging of Biomolecular Structures with Polarized Light. Annu. Rev. Biophys. Bio. 1987, 16, 319−349. (11) Miles, A. J.; Wallace, B. A. Synchrotron Radiation Circular Dichroism Spectroscopy of Proteins and Applications in Structural and Functional Genomics. Chem. Soc. Rev. 2006, 35, 39−51. (12) Mason, W. R. A Practical Guide to Magnetic Circular Dichroism Spectroscopy; John Wiley & Sons: Hoboken, NJ, 2007. (13) Devlin, F. J.; Stephens, P. J.; Scafato, P.; Superchi, S.; Rosini, C. Determination of Absolute Configuration Using Vibrational Circular Dichroism Spectroscopy: The Chiral Sulfoxide 1-Thiochromanone SOxide. Chirality 2002, 14, 400−406. (14) Barron, L. D. Molecular Light Scattering and Optical Activity; Cambridge University Press: Cambridge, U.K., 2004. (15) Fischer, P.; Hache, F. Nonlinear Optical Spectroscopy of Chiral Molecule. Chirality 2005, 17, 421−437.
Δδ TPCD(ω) ≈ 4.87555 × 10−5 × ω2 ∑ g (2ω , ω0f , Γ)·R 0TPCD (ω0f ) f f
(1)
Here (g(2ω,ω0f,Γ)) is a normalized Lorentzian line shape function with a 0.20 eV FWHM (Γ) and RTPCD (ω0f) is the 0f TPCD rotatory strength, in atomic units, as for the circular frequency. RTPCD (ω0f) is obtained through, 0f R 0TPCD (ω0f ) = −b1B1TI (ω0f ) − b2B2TI (ω0f ) − b3B3TI (ω0f ) f (2)
where b1, b2, and b3 are scalars that depend on the experimental setup. For our experimental configuration using two colinear photons with identical polarization state (RCPL or LCPL), circular frequency ω and traveling direction, b1 = 6, b2 = 2, and TI b3 = −2. The molecular parameters BTI 1 (ω0f), B2 (ω0f), and TI B3 (ω0f) are defined as a function of the two-photon p ,0f p,0f +,0f generalized tensors: Pρσ * (ω0f), Mρσ (ω0f) and Tρσ (ω0f). p ,0f While Pρσ* (ω0f) involves only the velocity operator, Mp,0f ρσ (ω0f) and T+,0f ρσ (ω0f) include the magnetic dipole and the velocity form of the electric quadrupole operator, respectively (see the SI for more details). B1TI(ω0f) and B3TI(ω0f) depend on TI +,0f Mp,0f ρσ (ω0f), while B2 (ω0f) depends only on Pρσ (ω0f). OPA, ECD, TPA and TPCD were calculated for the first 20 electronic excited states of the B3LYP/6-31G* optimized structures using time-dependent density functional theory (TD1812
dx.doi.org/10.1021/jz300577e | J. Phys. Chem. Lett. 2012, 3, 1808−1813
The Journal of Physical Chemistry Letters
Letter
B.; Petersson, G. A., et al. Gaussian 09, revision A.1; Gaussian, Inc.: Wallingford, CT, 2009. (38) Rizzo, A.; Jansík, B.; Pedersen, T. B.; Ågren, H. Origin Invariant Approaches to the Calculation of Two-Photon Circular Dichroism. J. Chem. Phys. 2006, 125, 064113-1−064113-11. (39) Jansík, B.; Rizzo, A.; Ågren, H. Ab Initio Study of the TwoPhoton Circular Dichroism in Chiral Natural Amino Acids. J. Phys. Chem. B 2007, 111, 446−460. (40) Jansík, B.; Rizzo, A.; Ågren, H.; Champagne, B. Strong TwoPhoton Circular Dichroism in Helicenes: a Theoretical Investigation. J. Chem. Theory Comput. 2008, 4, 457−467. (41) Rizzo, A.; Lin, N.; Ruud, K. Ab Initio Study of the One- and Two-Photon Circular Dichroism of R-(+)-3-Methyl-cyclopentanone. J. Chem. Phys. 2008, 128, 164312-1−164312-17. (42) Lin, N.; Santoro, F.; Rizzo, A.; Luo, Y.; Zhao, X.; Barone, V. Theory for Vibronically Resolved Two-Photon Circular Dichroism Spectra. Application to (R)-(+)-3-Methyl-cyclopentanone. J. Phys. Chem. A 2009, 113, 4198−4207. (43) Guillaume, M.; Ruud, K.; Rizzo, A.; Monti, S.; Lin, Z.; Xu, X. Ab Initio Study of the One- and Two-Photon Circular Dichroism of (L)Tryptophan. J. Phys. Chem. B 2010, 114, 6500−6512. (44) DALTON 2.0, a molecular electronic structure program, 2005; see http://www.kjemi.uio.no/software/dalton/dalton.html. (45) Runge, E.; Gross, E. K. U. Density-Functional Theory for TimeDependent Systems. Phys. Rev. Lett. 1984, 52, 997−1000. (46) Dierksen, M.; Grimme, S. A Theoretical Study of the Chiroptical Properties of Molecules with Isotopically Engendered Chirality. J. Chem. Phys. 2006, 124, 174301-1−174301-12. (47) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (48) Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A. 1988, 38, 3098−3100. (49) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle− Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (50) Yanai, T.; Tew, D. P.; Handy, N. C. A New Hybrid ExchangeCorrelation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP). Chem. Phys. Lett. 2004, 393, 51−57. (51) Peach, M. J. G.; Helgaker, T.; Sałek, P.; Keal, T. W.; Lutnaes, O. B.; Tozer, D. J.; Handy, N. C. Assessment of a Coulomb-Attenuated Exchange-Correlation Energy Functional. Phys. Chem. Chem. Phys. 2006, 8, 558−562.
(16) Ji, N.; Ostroverkhov, V.; Belkin, M; Shiu, Y-J; Shen, Y.-R. Toward Chiral Sum-Frequency Spectroscopy. J. Am. Chem. Soc. 2006, 128, 8845−8848. (17) De Boni, L.; Toro, C.; Hernandez, F. E. Synchronized Double L-Scan Technique for the Simultaneous Measurement of PolarizationDependent Two-Photon Absorption in Chiral Molecules. Opt. Lett. 2008, 33, 2958−2960. (18) Tinoco, I. Two-Photon Circular Dichroism. J. Chem. Phys. 1975, 62, 1006−1009. (19) Power, E. A. Two-Photon Circular Dichroism. J. Chem. Phys. 1975, 63, 1348−1350. (20) Jansik, B.; Rizzo, A; Agren, H Response Theory Calculations of Two-Photon Circular Dichroism. Chem. Phys. Lett. 2005, 414, 461− 467. (21) Toro, C.; De Boni, L.; Lin, N.; Santoro, F.; Rizzo, A.; Hernandez, F. E. Two-Photon Absorption Circular Dichroism: A New Twist in Nonlinear Spectroscopy. Chem.Eur. J. 2010, 16, 3504− 3509. (22) Denk, W.; Strickler, J. H.; Webb, W. W. Two-Photon Laser Scanning Fluorescence Microscopy. Science 1990, 248, 73−76. (23) 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.; et al. Two-Photon Polymerization Initiators for Three-Dimensional Optical Data Storage and Microfabrication. Nature 1999, 348, 51−54. (24) Loncaric, C.; Wulff, W. D. An Efficient Synthesis of (−)-Chloramphenicol via Asymmetric Catalytic Aziridination: A Comparison of Catalysts Prepared from Triphenylborate and Various Linear and Vaulted Biaryls. Org. Lett. 2001, 3, 3675−3678. (25) Toro, C.; De Boni, L.; Lin, N.; Santoro, F.; Rizzo, A.; Hernandez, F. E. Two-Photon Absorption Circular−Linear Dichroism of Axial Enantiomers. Chirality 2010, 22, E-202−210. (26) Woody, R. W. The Exciton Model and the Circular Dichroism of Polypeptides. Monatsh. Chem. 2005, 136, 347−366. (27) Di Bari, L.; Pescitelli, G.; Salvadori, P. Conformational Study of 2,2′-Homosubstituted 1,1′-Binaphthyls by Means of UV and CD Spectroscopy. J. Am. Chem. Soc. 1999, 121, 7998−8004. (28) Zhang, S.; Zhang, H.; Lu, C.; Jia, T.; Wang, Z.; Sun, Z. Mechanism of Polarization-Induced Single-Photon Fluorescence Enhancement. J. Chem. Phys. 2010, 133, 214504−1−214504−6. (29) Nag, A.; Goswami, D. Polarization Induced Control of Single and Two-Photon Fluorescence. J. Chem. Phys. 2010, 132, 154508−1− 154508−5. (30) Nalwa, H. S.; Miyata, S. Nonlinear Optics of Organic Molecules and Polymers; CRC Press: New York, 1996. (31) Prasad, L.; Polavarapu, P. L.; Petrovic, A. G.; Vick, S. E.; Wulff, W. D.; Ren, H.; Ding, Z.; Staples, R. J. Absolute Configuration of 3,3′Diphenyl-[2,2′-binaphthalene]-1,1′-diol Revisited. J. Org. Chem. 2009, 74, 5451−5457. (32) Petrovic, A. G.; Vick, S. E.; Polavarapu, P. L. Determination of the Absolute Stereochemistry of Chiral Biphenanthryls in Solution Phase Using Chiroptical Spectroscopic Methods: 2,2′-Diphenyl-[3,3′biphenanthrene]-4,4′-diol. Chirality 2008, 20, 501−510. (33) Lin, N.; Santoro, F.; Zhao, X.; Toro, C.; De Boni, L.; Hernandez, F. E.; Rizzo, A. Computational Challenges in Simulating and Analyzing Experimental Linear and Nonlinear Circular Dichroism Spectra. R-(+)-1,1′-Bis(2-naphthol) as a Prototype Case. J. Phys. Chem. B 2011, 115, 811−824. (34) Calvert, R. L.; Ritchie, G. L. D. Molecular Quadrupole Moment of Naphthalene. J. Chem. Soc., Faraday Trans. 2 1980, 76, 1249−1253. (35) Nobusada, K. Photoinduced Electric Currents in Ring-Shaped Molecules by Circularly Polarized Laser Pulses. Phys. Rev. A 2007, 75, 032518-1−032518-7. (36) Skourtis, S. S.; Beratan, D. N.; Naaman, R.; Nitzan, A.; Waldeck, D. H. Chiral Control of Electron Transmission through Molecules. Phys. Rev. Lett. 2008, 101, 238103-1−238103-4. (37) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, 1813
dx.doi.org/10.1021/jz300577e | J. Phys. Chem. Lett. 2012, 3, 1808−1813
