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Supplementary Material Geometry and quadratic nonlinearity of charge transfer complexes in solution using depolarized hyper-Rayleigh scattering Ravindra Pandey1, Sampa Ghosh1, S. Mukhopadhyay2, S. Ramasesha2 and Puspendu K. Das1* 1 Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India 2 Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India *Corresponding author Email : [email protected] Fax : 91-80-2360 0683 1 Content 1. Determination of the molar extinction coefficient and the association constants of the CT complexes by Benesi-Hildebrand method 2. Calculation of total HRS intensity for the linearly polarized and the circularly polarized incident light 3. Absorption spectra of the donors and acceptors 4. Absorption spectra of the CT complexes as a function of donor concentration 5. Plots of HRS intensity (normalized with respect to the incident beam intensity) vs. the concentration of the CT complex 6. Quadratic dependence of the HRS intensity on the incident beam intensity have been shown for two representative complexes 2 1. Determination of the molar extinction coefficient and the association constants of the CT complexes by Benesi-Hildebrand method Association constants of the complexes were determined by UV-visible spectroscopic titration, as described below, using the Benesi-Hildebrand (BH) analysis method. Intensities of the absorption peaks of the components and the complex in the visible region have been used to obtain the association constant by this method. Such complexes are, in most cases, characterized by the appearance of a new peak in the absorption spectra. The equilibrium between donor (D) and acceptor (A) 1:1 complex can be represented as, A + D⇌ AD (S1) The association constant of the complex AD is given by, K [AD] [AD] [A] f [D] f ([D] 0 [AD])([A] 0 [AD]) (S2) where the parentheses indicate the molar concentrations of the donor, acceptor and the complex. Subscript f refers to the free acceptor/donor in solution, while the subscript 0 indicates the initial concentration of the acceptor and the donor. Equation (2) can be rearranged as, [A] 0 [A] 0 1 1 [AD] 1 [AD] K [D] 0 [D] 0 [D] 0 (S3) In the BH method if the optical absorption in the region of measurement is only due to the complex, for a 1 cm path length, the absorbance of the complex () is given by, Λ ε AD λ [AD] (S4) 3 where AD is the molar extinction coefficient of AD at the wavelength . Equation (3) then becomes [A] 0 [A] 0 1 1 1 [AD] AD AD AD Λ Kε λ [D] 0 [D] 0 ε λ ελ [D] 0 ε AD λ (S5) If [D]0 [A]0, the second and fourth terms on the right hand side of eqn. (5) can be neglected and written as, [A] 0 1 1 1 AD AD Λ [D] 0 ε λ Kε λ (S6) The above equation can be rearranged to give the final form of the Benesi-Hildebrand equation as Q [A] 0 [D] 0 [D] 1 AD0 AD Λ Kε λ ελ (S7) For a series of solutions, the left hand side of equation (7) denoted by Q, if plotted against [D]0, the slope of the line will give the reciprocal of the molar extinction coefficient of the complex and the ratio of the slope to intercept will yield the reciprocal of the association constant. For the case, where the acceptor absorbs in the region of measurement, for a path length of 1 cm, the absorbance is given by, A AD A Λ ' ε AD λ [AD] ε λ [A] f ε λ [AD] ε λ ([A] 0 [AD]) (S8) where A is the molar coefficient of the acceptor at the wavelength, . An apparent molar absorptivity of A at , a may be defined as ε aλ Λ' [A] 0 (S9) 4 For the condition [D]0 [A]0, using equations (8) and (9), we can write the final form of Q as, Q' [D]0 (ε aλ ε λA ) 1 K(ε λAD ε λA ) [D]0 (S10) (ε λAD ε λA ) Plot of Q vs. [D]0 is linear whose slope yields the value of (AD - A ). With the knowledge of A from the absorption spectra of the acceptor alone, the value of AD can be obtained. The intercept gives the value of K, for the complex. Equation (10) is also known in the literature as Ketelaar equation. For the series of complexes of donors with chloranil as the acceptor, solutions were prepared in pure chloroform and with DDQ in pure dichloromethane. Absorption spectra were taken in a UV-vis spectrometer (Hitachi U3000). To maintain [D]0 [A]0, the donor concentrations were kept at least 100 times greater than the acceptor concentrations. The acceptor concentrations were of the order of 10-3 M. The donor concentrations were varied from 0.1 - 4.0 M. The plots of Q (or Q) vs. [D]0 of all the complexes are shown below. 0.0018 0.0042 Q' vs [D]0plot for CHL-durene complex 0.0017 Q' vs [D]0 plot for CHL-Mesitylene complex 0.0040 0.0016 M ) 2 0.0036 -1 0.0014 0.0013 -1 = 561.29 cm M K = 1.74 M 0.0012 Q'(cm Q'(cm -1 2 M ) 0.0038 0.0015 -1 0.0034 -1 = 1080.5 cm M 0.0032 -1 K = 0.45 M 0.0030 -1 -1 0.0011 0.0028 0.0010 0.05 0.10 0.15 0.20 0.25 [D]0 ( M ) 0.30 0.35 0.40 0.45 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 [D]0 ( M ) 5 0.000095 Q' vs [D]0 plot for CHL- p-Xylene complex 0.014 Q vs. [D]0 plot for DDQ-Durene complex 0.000090 0.013 Q (cm M ) 2 2 Q' ( cm M ) 0.000085 0.000080 -1 -1 0.012 0.011 -1 = 895 cm M -1 0.000075 0.000070 -1 0.010 K = 0.29 M = 1663.5 cm M 0.000065 -1 K = 12.1 M -1 -1 0.000060 0.009 0.000055 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0.01 0.02 0.03 [D]0 ( M ) 0.000120 0.000105 0.0011 0.07 2 M ) 0.0012 -1 2 Q (cm M ) 0.06 Q' vs. [D]0 plot for DDQ-pxylene complex 0.0013 0.000110 Q'(cm -1 0.000100 0.000095 = 1772.9 cm M 0.000090 K = 7.1 M -1 0.0010 0.0009 -1 = 1755.8 cm M 0.0008 -1 0.000085 K = 1.29 M -1 -1 0.0007 0.000080 0.00 0.0006 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.3 0.6 0.9 [D]0( M ) 1.2 1.5 [D]0 (M) 0.0024 20 TOL-DDQ complex in CH2Cl2 0.0022 AD -1 = 2552.5 cm M Ka= 1.02 M HMB-CHL complex in CHCl3) -1 18 DA -1 = 2708 cm M -1 Ka = 7.8 M -1 -1 16 -2 Q x 10 (cm M ) -2 0.0020 14 -2 -3 0.05 0.0014 Q vs. [D]0 plot for DDQ- mesitylene complex 0.000115 Q' x 10 ( cm M ) 0.04 [D]0 ( M ) 0.0018 12 0.0016 10 0.0014 2.2 2.4 2.6 2.8 3.0 3.2 0 CD (M) 3.4 3.6 3.8 4.0 4.2 8 8 16 24 0 32 40 -2 CD x 10 (M) 6 2. Calculation of total HRS intensity for the linearly polarized and the circularly polarized incident light The total HRS intensity for the linearly polarized and the circularly polarized incident light are given in the laboratory frame (XYZ), respectively, as 2 2 I 2 GN XXX ZXX I 2 I 2 2 2 2 2 2 ZYY ZXX XYY XXX ZYX ZXY 2 I GN 2 ZYY ZXX XYX XXY 2 2 XYY XXX (S11) (S12) where G is a parameter that accounts for the instrument and local field factors, N is the number density of the CT complexes as defined in equation 1 of the main text. The different β components in the laboratory frame can be related to the β tensor elements in the molecular frame, (i) where i can vary from 1 to 3. 2 XXX 1 6 9 6 12 2 iii2 iii ijj ijj2 ijj ikk 123 7 i 35 i j 35 i j 35 i j k 35 (S13) 2 ZXX 1 2 11 2 8 2 iii2 iiiijj ijj2 ijj ikk 123 35 i 105 i j 105 i j 105 i j k 35 (S14) ZYX ZXY ( ZXX ZYY ) 2 1 4 1 4 20 2 iii2 iii ijj ijj2 ijj ikk 123 105 i 105 i j 105 i j 105 i j k 35 XYX XXY 2 ( XXX XYY ) 4 12 24 12 20 2 iii2 iiiijj ijj2 ijj ikk 123 (S15) 105 i 105 i j 105 i j 105 i j k 35 4 8 44 8 32 2 iii2 iii ijj ijj2 ijj ikk 123 35 i 105 i j 105 i j 105 i j k 35 1 12 3 4 6 2 iii2 iii ijj ijj2 ijj ikk 123 35 i 105 i j 105 i j 35 i j k 35 (S16) (S17) (S18) From all these, the depolarization ratios as defined in the main text can be obtained. 7 3. Absorption spectra of the donors and acceptors 6 0.7 0.0005 M HMB in CHCl3 0.001(M) Durene in CHCl3 max = 242 nm 0.6 5 Absorbance Absorbance 0.5 0.4 0.3 max = 271 nm 4 3 2 0.2 271 nm 1 0.1 0.0 200 0 225 250 275 300 325 200 350 250 300 350 400 450 500 Wavelength (nm) Wavelength (nm) 2.0 1.4 0.001(M) Mesitylene in CHCl3 Absorbance Absorbance 1.2 max = 265 nm 1.5 0.006(M) Xylene in CHCl3 1.0 max = 263 nm 1.0 0.8 0.6 0.4 0.5 0.2 0.0 0.0 240 255 270 285 300 315 330 240 345 260 Wavelength (nm) 300 320 340 360 380 Wavelength (nm) 0.30 0.20 0.0008(M) Chloranil in CHCl3 0.0004 (M) DDQ in CH2Cl2 max = 375 nm 0.25 max = 387 nm Absorbance 0.15 Absorbance 280 0.10 0.20 0.15 0.10 0.05 0.05 0.00 0.00 300 350 400 450 500 Wavelength (nm) 550 600 350 400 450 500 550 600 Wavelength (nm) 8 0.006(M) Toluene in CHCl3 1.4 max= 262 nm Absorbance 1.2 1.0 0.8 0.6 0.4 0.2 0.0 240 260 280 300 320 340 360 Wavelength (nm) 4. Absorption spectra of the CT complexes as a function of donor concentration 1.2 CHL Conc. = 0.0005 M Durene Conc. 0.05 M 0.10 M 0.20 M 0.31 M 0.40 M 0.51 M 0.4 Absorbance 0.9 Absorbance CT = 476 nm CHL Conc. = 0.0005 M HMB Conc. 0.10 M 0.20 M 0.25 M 0.35 M 0.40 M CT = 515 nm 0.6 0.3 0.3 0.2 0.1 0.0 0.0 400 500 600 700 800 400 Wavelength (nm) 500 600 700 Wavelength (nm) 0.8 -4 CHL Conc. 5x10 M Mes Conc. 0.6 M 0.8 M 1.0 M 1.4 M 1.8 M 2.0 M 2.2 M CT = 424 nm 0.4 CHL Conc. = 0.0005 M PX Conc. 1.0 M 1.5 M 2.0 M 2.5 M 3.0 M 3.5 M 4.0 M PX-CHL CT = 414 nm 0.6 0.4 0.2 0.2 0.0 400 500 0.0 600 350 Wavelength (nm) 400 450 500 550 600 Wavelength (nm) 1.2 1.2 DDQ Conc. = 0.0005M 0.02 M 0.03 M 0.04 M 0.05 M 0.06 M 0.07 M 0.10 M 0.12 M CT = 587 nm 0.8 0.6 DDQ Conc. = 0.0005M PX conc. 0.5 M 1.0 M 1.5 M 2.0 M 2.5 M 0.8 0.6 0.4 0.4 0.2 0.2 0.0 400 CT = 520 nm 1.0 Absorbance 1.0 Absorbance Absorbance 0.6 0.8 Absorbance MES- CHL Complex 0.0 500 600 700 Wavelength (nm) 800 400 500 600 700 800 Wavelength (nm) 9 1.0 CT = 440 nm DDQ Conc. = 0.0005M Toluene Conc. 2.5 M 3.0 M 3.5 M 4.0 M 4.5 M 5.0 M Absorbance 0.8 0.6 0.4 0.2 0.0 350 400 450 500 550 600 650 700 Wavelength (nm) 5. HRS intensity (normalized with respect to incident beam intensity) vs. the concentration of the complex: slopes of these graphs are used to determine the first hyperpolarizabilities of various complexes 0.50 1.4 HMB-CHL -30 = 26.9 X10 esu 0.48 DUR-CHL -30 = 21.9 X10 esu 0.46 1.2 0.44 1.0 I2/I I2/I 2 2 0.42 0.8 0.40 0.38 0.6 0.36 0.34 0.4 0.32 0.2 0.30 -5 -4 2.0x10 -4 -4 4.0x10 6.0x10 -4 8.0x10 -3 -3 1.0x10 1.2x10 5.0x10 -3 -4 1.0x10 -4 -4 2.0x10 2.5x10 -4 3.0x10 -4 3.5x10 Conc. (M) Conc. (M) 0.35 -4 1.5x10 1.4x10 0.135 MES-CHL -30 = 15.79 X10 esu 0.130 XYl-CHL -30 = 14.3 X10 esu 0.34 0.125 0.33 0.120 I2/I I2/I 2 2 0.32 0.31 0.115 0.110 0.105 0.30 0.100 0.29 0.095 0.28 0.090 -5 -5 -5 -5 -4 -4 -4 -4 -5 -4 -4 -4 -4 -4 -4 -4 2.0x10 4.0x10 6.0x10 8.0x10 1.0x10 1.2x10 1.4x10 1.6x10 8.0x10 1.0x10 1.2x10 1.4x10 1.6x10 1.8x10 2.0x10 2.2x10 Conc. (M) Conc. (M) 10 4.25 Durene DDQ complex -30 = 34.8 x 10 esu 0.94 Xylene DDQ -30 = 13.6 X10 esu 4.20 0.92 4.15 2 I2/I I2/I 2 0.90 0.88 4.10 0.86 4.05 0.84 4.00 -5 5.0x10 -4 1.0x10 -4 -4 1.5x10 -4 2.0x10 2.5x10 -4 3.0x10 -4 -5 3.5x10 -5 -5 -5 Conc. (M) 0.870 -4 -4 -4 -4 -4 -4 2.0x10 4.0x10 6.0x10 8.0x10 1.0x10 1.2x10 1.4x10 1.6x10 1.8x10 2.0x10 Conc. (M) TOL-DDQ Complex -30 = 7.7 X10 esu 0.865 I2/I 2 0.860 0.855 0.850 0.845 0.840 -4 -4 -4 -4 -4 -4 -4 -4 -4 1.0x10 2.0x10 3.0x10 4.0x10 5.0x10 6.0x10 7.0x10 8.0x10 9.0x10 Conc. (M) 6. Quadratic dependence of the HRS intensity on the incident beam intensity is shown for two representative complexes 1.70 2.4 Durene- CHL complex 1.65 Durene- DDQ complex slope= 2.1 slope= 1.98 1.60 2.3 1.55 log I2 log I2 2.2 2.1 1.50 1.45 1.40 2.0 1.35 1.9 1.30 1.15 1.20 1.25 1.30 log I 1.35 1.40 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 log I 11