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 : pkdas@ipc.iisc.ernet.in
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 
iiiijj 
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 
 iiiijj 
 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