Supplementary Material for
“Excitonic splitting and Vibronic Coupling in 1,2-diphenoxyethane:
Conformation-specific effects in the weak coupling limit”
Evan G. Buchanan, Patrick S. Walsh, David F. Plusquellic and Timothy S. Zwier
Table of contents
1. Dispersed fluorescence spectra of the set of vibrational bands in the first 1100 cm-1 of the tgt
conformer of DPOE (Figures S1).
2. Results of multi-mode modeling of the vibronic structure of the ttt conformer of DPOE using
the Fulton-Gouterman model of vibronic coupling in symmetric bichromophores (Figures
S2-S4).
3. Principal axis orientations of the ttt (top) and tgt conformers of DPOE (Figure S5).
4. Table S1: Parameters from genetic algorithm and linear least squares fits of the origin bands
of DPOE.
1. Dispersed fluorescence spectra of the indicated bands of the tgt conformer of DPOE.
tgt
Origin
-25
+24
-35
+34
+98
+154
-102
-155
Figure S1. Dispersed fluorescence spectra of the totally symmetric fundamentals obtained for the tgt
conformer. The spectra show dominant X11 false origins.
2. Results of the multi-mode modeling of DPOE using the Fulton-Gouterman model.
The FG model has been used to treat symmetric bichromophores with excited electronic
states that can interact to form excitonic states split by an energy, 2VAB. As discussed
elsewhere,1-3 the symmetry adapted electronic basis wavefunctions for each conformer may be
expressed in terms of simple sum and differences as ±e=(1/2)1/2e±e)
whereeq;Q0*qA;QA00qB;QB0 and eq;Q0qA;QA0*qB;QB0 with excitation (*)
and likewise for the normal coordinates, q± = (1/2)1/2 (QA ± QB). The Hamiltonian in
dimensionless elements is given as1-4




1 2
1 2


2
2
bq 
C  2 p   q   2 p   q   bq 

h

1 2
1 2
2
2

bq 
 C  p   q   p   q   bq  
2
2






where C=VAB/ħω, and b=(2ħμω3)-1/2L with linear displacement LQi. The off-diagonal elements,
bq-, mix the lower diagonal block (S-) with the upper block (S+) to give the wavefunctions of the
S1 and S2 states, respectively (the S1/S2 state order is reversed with a simple sign change on C).
_
For a vibrational mode pair, R, R , the eigenfunctions take the following simple forms:
_
S l ( R m R n ) 
_
S l ( R m R n ) 
n

_
i 0 , j 0 ( even )
n

i 0 , j 1( odd )
cl ,i , j l , R i R j 
_
cl ,i , j l , R i R j 
n

i 0 , j 1( odd )
n

i 0 , j 0 ( even )
_
cl  ,i , j l , R i R j
_
cl  ,i , j l , R i R j
The observed excitonic splitting is
∆= 2𝐹𝑉𝐴𝐵
where F is the Franck-Condon quenching factor associated with the geometry change
accompanying electronic excitation of each chromophore.
Figure S1. UV-HB (a) and LIF (b) spectra of DPOE and the FG1-3 model predictions (c) of the R / R
mode pair (46/149 cm-1) of the ttt conformer using the parameters given in Figure S2. It is noted that both
observed spectra are saturated in order to facilitate better comparison with model predictions. The
relative intensities from the model are in good agreement with the unsaturated UVHB spectrum of Figure
2 in the main text.
Figure S2. Observed DFL spectra of the (a) origin and (c) +46 cm-1 bands of DPOE. Shown below each
band in (b) and (d) are the predictions from the FG model for the inter-ring mode pair R/ R and ring
mode pair 6a/ 6a .
Figure S3. Observed DFL spectra of the (a) origin and (c) +46 cm-1 bands of DPOE. Shown below each
band in (b) and (d) are the predictions from the FG model for the inter-ring mode pair R/ R and ring
mode pair 1/ 1 .
Figure S4. Observed DFL spectra of the (a) origin and (c) +46 cm-1 bands of DPOE. Shown
below each band in (b) and (d) are the predictions from the FG model for the inter-ring mode
pair R / R and ring mode pair 12 / 12 .
Figure S5. Principal axis orientations of the ttt (top) and tgt conformers of DPOE.
Table S1.
Parameters from genetic algorithm and linear least squares fits of the origin
bands of DPOE.
tgt
ttt
S0
S1
S2
S0
S2
A / ΔA / MHz
1873.76(7)a
-66.44(3)
-66.16(4)
2508.86(2)
-60.9663 (54)
B / ΔB / MHz
177.85(7)
+0.868(6)
+0.836(6)
157.87(4)
-0.3355 (2)
C / ΔC / MHz
171.08(8)
+0.612(8)
+0.598(3)
148.89(5)
-0.4994 (1)
ΔI / ΔΔI / u·Å2
-157.2(1)
-6.65(8)
-6.88(8)
8.349(20)
-0.413(7)
ΔK / ΔΔK / MHzb
6.2(9)x10-3
2(1)x10-4
2(1)x10-5
---
---
ΔJK / ΔΔJK / MHz
-3.7(9)x10-4
---
---
---
---
36,423.93(2)
36,422.91(2)
36,508.77(2)
100 b
100 b
Origin / cm-1
Band type / %
24(3) a / 76(3) c
υG/υL / MHz
21 / 22
21 / 26
T1 / T2 / wt / Kc
4.1 / 17 / 0.62
4.1 / 17 / 0.47
θ/º
+/-60(2)
90.0
Uncertainties in the final digits correspond to Type A, k=1 or 1σ.
Asymmetric reduction used.
c
Two temperature model: exp(-ΔE / kT1) + wt · exp(-ΔE / kT2).
a
b
References
(1)
(2)
(3)
(4)
Fulton, R. L.; Gouterman, M. VIBRONIC COUPLING .1. MATHEMATICAL
TREATMENT FOR 2 ELECTRONIC STATES, Journal of Chemical Physics 1961, 35,
1059.
Fulton, R. L.; Gouterman, M. VIBRONIC COUPLING .2. SPECTRA OF DIMERS,
Journal of Chemical Physics 1964, 41, 2280.
Fulton, R. L.; Gouterman, M. VIBRONIC COUPLING OF 2 ELECTRONIC STATES,
Spectrochim. Acta 1961, 17, 1093.
Kopec, S.; Ottiger, P.; Leutwyler, S.; Koppel, H. Vibrational quenching of excitonic
splittings in H-bonded molecular dimers: Adiabatic description and effective mode
approximation, Journal of Chemical Physics 2012, 137, 184312.