Supplementary material

Effect of the Position of Auxiliary Acceptor in D-A-π-A Photosensitizes on Photovoltaic Performances of Dye-sensitized Solar Cells

Pei Yu, Fengying Zhang, Ming Li, Rongxing He[*]

The three parameters related charge separation is evaluated as follows.

For DSSCs, the η would be decreased due to the incomplete charge separation. Therefore, quantifying the length and magnitude of the CTis of much concern to evaluate the performance of sensitizer. In this work, three parameters of CT mentioned above are used to quantify the degree of electron transfer. The total electron densities of initial and final states and their centroids should be calculated.[1,2]

The CT distance (L) is defined by two barycenters of the electronic density depletion (R-) and increment (R+) zones upon excitation.

(1)

The barycenters of electronic density depletion (R-) region and the electronic density increment (R+) region associated with electronic transition should be defined byρ+(r) and ρ-(r):

(2)

and

(3)

To calculate the two barycenters, the increase ρ+(r)/decrease ρ-(r) of the density due to the electronic transition is expressed as:

(4)

and

(5)

In Equation (3), Δρ(r) is defined as:

(6)

WhereρES(r) and ρGS(r) are the electronic densities associated to excited and ground states. The fraction of electron exchange can be expressed as:

(7)

The overlap (Ω) between the zones of density depletion and increment is written as:

(8)

H is defined as half of the sum of the centroids axis (σ) along electron transfer direction. For instance, if the electron transfer direction is along the x axis, H is given by:

(9)

Table Captions

Table S1 Effects of functional on the estimated vertical excitation energy (units in eV) of dye WS-1 in dichloromethane solution.

Table S2Effects of basis set on transition energy (in eV) of dye WS-1 in dichloromethane solution (the BHandHLYP functional was used)

Table S3 Electronic transition data obtained by the TD-BHandHLYP/6-31+G* level for all free dyes in Dichloromethane solution with PBE0/6-311G** geometries

Table S1Effects of functional on the estimated Vertical excitation energy (units in eV) of dye WS-1 in dichloromethane solution

M062X / BHandHLYP / BMK / PBE0 / B3LYP / O3LYP / Exp.a
WS-1 / 522.0(2.37) / 534.0(2.32) / 572.1(2.17) / 675.3(1.83) / 726.2(1.71) / 826.8(1.50) / 545.0(2.27)
416.3(2.98) / 419.0(2.96) / 445.5(2.78) / 533.7(2.32) / 579.4(2.14) / 539.4(2.30) / 462.0(2.68)

afrom reference {Zhu, 2014 #339}[3]

Table S2Effects of basis set on transition energy (in eV)of dye WS-1 in dichloromethane solution (the BHandHLYP functional was used)

Basis set / 6-31+G* / 6-31+G** / 6-31G* / 6-311+G* / 6-31++G* / Exp.a
Cal. / 547.8(2.26) / 548.6(2.26) / 534.0(2.32) / 548.9(2.26) / 547.8(2.26) / 545.0(2.27)
430.9(2.88) / 431.5(2.33) / 419.3(2.95) / 432.1(2.87) / 430.9(2.88) / 462.0(2.68)

afrom reference [3]

Table S3 Electronic transition data obtained by the TD-BHandHLYP/6-31+G* level for all free dyes in Dichloromethane solution with PBE0/6-311G** geometries

Compounds / S0→Sn (eV) / Wavelength/nm / ƒ/LHE / Wavelength
WS-1 / 2.263(S0→S1) / 547.8 / 1.838/0.985 / H-1->LUMO (14%), HOMO->LUMO (72%), HOMO->L+1 (10%)
2.877(S0→S2) / 430.9 / 0.255/0.444 / H-1->LUMO (32%), HOMO->L+1 (54%), H-1->L+1 (5%)
3.698(S0→S4) / 335.2 / 0.108/0.220 / H-1->L+1 (63%), HOMO->L+1 (14%), H-2->LUMO (8%), HOMO->LUMO (5%)
4.066(S0→S5) / 305.0 / 0.361/0.564 / H-5->L+1 (14%), H-2->L+2 (52%), H-1->L+2 (15%), HOMO->L+6 (6%)
WS-11 / 2.172(S0→S1) / 570.9 / 1.590/0.974 / H-1->LUMO (19%), HOMO->LUMO (75%)
3.022(S0→S2) / 410.3 / 0.257/0.447 / H-2->LUMO (10%), H-1->LUMO (68%), HOMO->LUMO (16%)
3.216(S0→S3) / 385.5 / 0.135/0.267 / H-1->L+1 (27%), HOMO->L+1 (62%)
3.688(S0→S4) / 336.2 / 0.763/0.827 / HOMO->L+2 (80%)
WS-12 / 2.054(S0→S1) / 603.6 / 1.618/0.976 / H-1->LUMO (18%), HOMO->LUMO (76%)
3.307(S0→S3) / 375.0 / 0.589/0.742 / HOMO->L+2 (73%), HOMO->L+1 (9%)
3.703(S0→S4) / 334.9 / 0.172/0.327 / H-1->L+1 (25%), HOMO-> L+1 (54%), H-2->L+1 (5%), HOMO->L+2 (7%)H-
3.776(S0→S5) / 328.3 / 0.118/0.238 / H-5->LUMO (15%), H-2->LUMO (57%), H-1->LUMO (10%)

References

1. Guo M, He R, Dai Y, Shen W, Li M, Zhu C, Lin SH (2012) Electron-Deficient Pyrimidine Adopted in Porphyrin Sensitizers: A Theoretical Interpretation of π-Spacers Leading to Highly Efficient Photo-to-Electric Conversion Performances in Dye-Sensitized Solar Cells. The Journal of Physical Chemistry C 116 (16):9166-9179

2. Le Bahers T, Adamo C, Ciofini I (2011) A qualitative index of spatial extent in charge-transfer excitations. Journal of Chemical Theory and Computation 7 (8):2498-2506

3. Zhu H, Li W, Wu Y, Liu B, Zhu S, Li X, Ågren H, Zhu W (2014) Insight into Benzothiadiazole Acceptor in D–A− π–A Configuration on Photovoltaic Performances of Dye-Sensitized Solar Cells. ACS Sustainable Chemistry & Engineering 2 (4):1026-1034

Pei Yu, Fengying Zhang, MingLi, Rongxing He()

Key Laboratory of Luminescence and Real-Time Analytical chemistry (Southwest University), Ministry of Education, College of Chemistry and Chemical Engineering, Southwest University, Chongqing 400715, China

e-mail:,phone: +86-023-68253023