Density Functional Theory-Based Molecular Modeling

energies

Article Density Functional Theory-Based Molecular Modeling: Veriﬁcation of Decisive Roles of Van der Waals Aggregation of Triiodide Ions for Eﬀective Electron Transfer in Wet-Type N3-Dye-Sensitized Solar Cells

Susumu Yanagisawa 1,* and Shozo Yanagida 2,* 1 Department of Physics and Earth Sciences, Faculty of Science, University of the Ryukyus, Senbaru, Nishihara, Okinawa 903-0213, Japan 2 M3 Laboratory, Inc., Osaka University, ISIR, 8-2, Ibaraki, Osaka 567-0047, Japan * Correspondence: [email protected] (S.Y.); [email protected] (S.Y.)

Received: 18 May 2020; Accepted: 5 June 2020; Published: 11 June 2020

Abstract: Density functional theory-based molecular modeling (DFT/MM) validates that KI and I2 undergo exothermic van der Waals (vdW) aggregation in acetonitrile (AN) or in the presence of 4-tert-butylpyridine (TBP), forming potassium triiodide (KI3) and, further mutual vdW aggregation leads to the formation of (KI3)2 and AN, (KI3)2 and (AN)2 and (KI3)2 and TBP in the AN-based Dye sensitized solar cells (DSSC) electrolytes. All KI3 aggregates have a very low energy gap, 0.17 eV, 0.14 eV and 0.05 eV of lowest unoccupied molecular orbital (LUMO) + 1 and LUMO, respectively, verifying efficient electron diffusion in µm-thick DSSC electrolytes. Hydrogen-bonding aggregation of anatase TiO2 model, Ti9O18H and OH, with N3 (proton) dye is also validated by DFT/MM, and the energy structure verifies unidirectional electron flow from highest occupied molecular orbital (HOMO) on thiocyanide (SCN) groups of N3 dye to LUMO on the TiO2 model at the aggregates. + Further, DFT/MM for the aggregation of K I3− with N3 verifies the most exothermic formation of the + + aggregate of N3 (proton) and K I3−. The UV-Vis spectra of N3 (proton) and K I3− is consistent with reported incident photocurrent efficiency (IPCE) action spectra (λ = 450–800 nm) of N3-sensitized + DSSC, verifying that the N3 dye of N3 (proton) and K I3− becomes an effective sensitizer in the anode / TiO2 / N3 (proton) / KI/I2 / acetonitrile (AN) / cathode structured DSSC. The energy structure of + LUMO and LUMO + 1 of the aggregates, Ti9O18H and OH and N3 (proton), N3 and K I3−, (KI3)2 and AN and (KI3)2 and TBP verifies high IPCE photocurrent and effective electron diffusion via + KI3-aggregates in the DSSC of Ti9O18H and OH and N3 (proton) and K I3−.

Keywords: density functional theory; van der Waals Coulomb interactions; triiodide ion; electrostatic potential map

1. Introduction As reported in the preceding papers [1–6], quantum chemistry molecular modeling, i.e., density functional theory-based molecular modeling (DFT/MM) can be regarded as theory-based “experiments”. DFT/MM can be carried out very quickly using high-end supercomputer-like personal computers. DFT/MM are applicable to molecular aggregates which are induced by van der Waals (vdW) force (including hydrogen bonding and Coulomb interactions). DFT/MM for the structuring of aggregates gives the heat of formation, dipole moment for understanding solubility in polar solvent like water and acetonitrile (AN) and the energy structures of aggregates, i.e., surface orbital electron energy structures [almost degenerate highest molecular orbitals [HOMO (n), n = 0–4)] and the lowest unoccupied molecular orbitals [LUMO + n, n = 0–2)]. Their molecular orbital conﬁgurations are

Energies 2020, 13, 3027; doi:10.3390/en13113027 www.mdpi.com/journal/energies Energies 2020, 13, x FOR PEER REVIEW 2 of 15

Energiesorbital2020 electron, 13, 3027 energy structures [almost degenerate highest molecular orbitals [HOMO (n), 2n of = 14 0– 4)] and the lowest unoccupied molecular orbitals [LUMO + n, n = 0–2)]. Their molecular orbital configurations are evaluated as theory-based “experimental” data for verification and prediction of evaluated as theory-based “experimental” data for verification and prediction of interacting molecules. interacting molecules. Semiconducting property of the aggregates can be verified by the orbital Semiconducting property of the aggregates can be verified by the orbital energy gap between LUMO energy gap between LUMO and LUMO + 1 [2,3]. We performed DFT/MM using the B3LYP exchange and LUMO + 1 [2,3]. We performed DFT/MM using the B3LYP exchange correlation functional and correlation functional and the 6–31G(d) basis set with Spartan’18 (Wavefunction, Inc. Irvine, CA). the 6–31G(d) basis set with Spartan’18 (Wavefunction, Inc. Irvine, CA). Prior to the DFT calculation for Prior to the DFT calculation for electronic properties, the geometries of the molecular aggregates were electronic properties, the geometries of the molecular aggregates were determined by the molecular determined by the molecular mechanics employing the Merck molecular force field (MMFF). mechanics employing the Merck molecular force field (MMFF). Since the first report of its high-performance by O’Regan and Grätzel [7], the dye-sensitized solar Since the first report of its high-performance by O’Regan and Grätzel [7], the dye-sensitized solar cell (DSSC) using KI / I2 / acetonitrile electrolyte has been a focus for a fundamental understanding cell (DSSC) using KI / I2 / acetonitrile electrolyte has been a focus for a fundamental understanding of of microscopic electronic phenomena of TiO2, dye molecules and electrolytes [8]. As for wet-type microscopic electronic phenomena of TiO , dye molecules and electrolytes [8]. As for wet-type DSSC 2 −/ − DSSC electrolytes of acetonitrile (AN), KI and I2, redox couple/ of I I3 was introduced to explain electrolytes of acetonitrile (AN), KI and I2, redox couple of I− I3−was introduced to explain electron electron diffusion by electron hopping and exchange mechanisms [9]. Recently, we reported that diffusion by electron hopping and exchange mechanisms [9]. Recently, we reported that DFT/MM DFT/MM verifies the semiconducting properties for quasi-solid state I5−N(CH3)4+ -based electrolytes verifies the semiconducting properties for quasi-solid state I N(CH ) + -based electrolytes of DSSC [1]. 4− +5 − 3 4 of DSSC [1]. In addition, we clarified4 that PbI+ 6 /MeNH3 -based perovskite solar cells have excellent In addition, we clarified that PbI6 −/MeNH3 -based perovskite solar cells have excellent electron electron diffusion among panchromatic PbI64−/MeNH3+ matrixes in the solar cells [2,3]. We have diffusion among panchromatic PbI 4 /MeNH + matrixes in the solar cells [2,3]. We have ascribed 6 − 3 4− + ascribed excellence of perovskite solar4 cells to PbI+ 6 /MeNH3 -induced vdW aggregation. Here, we excellence of perovskite solar cells to PbI6 −/MeNH3 -induced vdW aggregation. Here, we corroborate corroborate that the iodine element-based vdW aggregations also play an important role in that the iodine element-based vdW aggregations also play an important role in unidirectional electron unidirectional electron diffusion in wet-type DSSC using KI / I2 / acetonitrile electrolytes. diffusion in wet-type DSSC using KI/I2/acetonitrile electrolytes.

2.2 Results. Results

2.1.2.1. DFT-Based DFT-Based Electrostatic Electrostatic Potential Potential Map Map (EPM) (EPM) and and Van Van der der Waals Waals Aggregation Aggregation

FigureFigure1 shows1 shows the the EPM EPM of of I 2 I,2 KI,, KI, and and AN. AN.

(a) (b) (c)

Figure 1. Electrostatic potential map with dipole as a measure of solubility: (a)I2;(b) KI; (c) acetonitrile (AN). Figure 1. Electrostatic potential map with dipole as a measure of solubility: (a) I2; (b) KI; (c) acetonitrile In(AN) the. colorful electrostatic potential map (ESPM), the property range (kJ/mol, eV) indicates potential energy of surface electron density of molecules and of vdW aggregates. Blue surface color is particularlyIn the colorful electron electrostatic poor and subject potential to electrophilic map (ESPM), attack the (electronproperty poor range vdW (kJ/mol, surface), eV) and indicate red s surfacepotential color energy is particularly of surface electronelectron rich,density subject of molecules to nucleophilic and of attackvdW aggregates. (electron rich Blue vdW surface surface). color Asis quantitativeparticularly electron structured poor activity, and subject volume to electrophilic (Å3) of molecules attack (electron is determined poor vdW by the surface), CPK model,and red reflectingsurface color surface is particularly electron number electron of molecules rich, subject and to aggregates. nucleophilic It mayattack be (electron added that rich the vdW blue surface). region correspondsAs quantitative to the structure LUMO richd activity, region, andvolume the red (Å3) region of molecules to the HOMO is determined rich region. by the CPK model, reflectingPale blue surface EPM electron of I2 indicates number its electrophilicof molecules nature and aggregates. and the top It surface may be is added particularly that the electrophilic. blue region Colorfulcorresponds EPM ofto KI the and LUMO AN indicate rich region, the presence and the of red both region electrophilic to the HOMO and nucleophilic rich region. surface, reflecting large dipole,Pale blue 10.68 EPM debye of and I2 indicates 3.81 debye, its respectively. electrophilic It nature is worth and noting the that top the surface volumes is particularly of I2 and electrophilic. Colorful EPM of KI and AN indicate the presence of both electrophilic and nucleophilic Energies 2020, 13, x FOR PEER REVIEW 3 of 15 surface,Energies reflecting2020, 13, 3027 large dipole, 10.68 debye and 3.81 debye, respectively. It is worth noting3 ofthat 14 the volumes of I2 and KI are much larger than that of AN. Van der Waals aggregation occurs between electrophilicKI are much electron larger surface than that and of AN. nucleophilic Van der Waals one. aggregation occurs between electrophilic electron surface and nucleophilic one. 2.2. Verification of KI3 Formation by Van der Waals Aggregation of I2 and KI in Electrolytes. 2.2. Verification of KI3 Formation by Van der Waals Aggregation of I2 and KI in Electrolytes We speculate that the minimum number of molecules which may form vdW aggregates in AN We speculate that the minimum number of molecules which may form vdW aggregates in AN should be three, and one of them is AN. Figure 2 shows ESPM of equilibrium geometry of vdW should be three, and one of them is AN. Figure2 shows ESPM of equilibrium geometry of vdW aggregates of (I2)2AN, (KI)2AN, and acetonitrile (AN)3. When compared to ESPM of I2, and KI and aggregates of (I2)2AN, (KI)2AN, and acetonitrile (AN)3. When compared to ESPM of I2, and KI and AN ANin Figure in Figure 1, 1all, all of of trimeric trimeric aggregates aggregates resultresult from from vdW vdW aggregation aggregation between between the electron-poorthe electron-poor electrophilicelectrophilic surface surface and and the the electro electro-rich-rich nucleophilic nucleophilic surface. surface.

(a) (b) (c)

FigureFigure 2. Electrostatic 2. Electrostatic potential potential map map (ESPM) (ESPM) with with the heat the of heat formation, of formation, dipole as measure dipole of as solubility measure of solubilityand energy and energygap of energy gap of of energy lowest unoccupied of lowest unoccupied molecular orbital molecular (ELUMO) orbital+ 1 and (ELUMO ELUMO) + as1 and measure of conductivity: (a) (I2)2AN; (b) (KI)2AN; (c) acetonitrile (AN)3. ELUMO as measure of conductivity: (a) (I2)2AN; (b) (KI)2AN; (c) acetonitrile (AN)3. All vdW aggregates form exothermically, suggesting stability in AN. The most stable vdW aggregateAll vdW of aggregates (KI) AN (heat form of formation exothermically, is 49.6 kcalsuggesting/mol) gives stability a colorful in ESPM, AN. The predicting most stable further vdW 2 − aggregatevdW aggregation of (KI)2AN with (heat KI of and formation I2 in AN. is −49.6 kcal/mol) gives a colorful ESPM, predicting further vdW aggregationFigure3 shows with ESPMKI and of I2 I in2 and AN. KI and AN, KI3 and I2 and KI, and KI3 and (AN)2. All vdW aggregatesFigure 3 shows give large ESPM heat of of I formation2 and KI and,and interestingly,AN, KI3 and I 2I2aggregates and KI, and with KI KI3 inand aggregate (AN)2. of All I2 vdW aggregatesand KI andgive AN. large Geometry heat of formation of I3− gives and, angle interestingly, of 172◦ comparable I2 aggregates to that ofwith geometry KI in aggregate I3− in KI3 andof I2 and (AN) . DFT/MM-determined− UV-Vis spectrum comparison (λmax: 447 nm and 414 nm)− veriﬁes in situ KI and AN.2 Geometry of I3 gives angle of 172° comparable to that of geometry I3 in KI3 and (AN)2. DFT/MMformation-determined of KI3 from UV I2-Visand KIspectrum in AN. In comparison situ formation (max of KI: 3 447from nm I2 andand KI 414 is also nm) conﬁrmed verifies in situ vdW aggregate of KI3 and I2 and KI. formation of KI3 from I2 and KI in AN. In situ formation of KI3 from I2 and KI is also confirmed in vdW aggregate of KI3 and I2 and KI. Energies 20202020, 1313, 3027x FOR PEER REVIEW 4 of 15 14

(a) (b) (c) Figure 3. Equilibrium geometry of van der Waals aggregates and their heat of formation and Electrostatic

Figurepotential 3. map Equilibrium (ESPM) of geometryenergy structures: of van (a der)I2 and Waals KI and aggregates AN; (b) KIand3 and their I2 and heat KI; of (c ) formation KI3 and (AN) and2. Electrostatic potential map (ESPM) of energy structures: (a) I2 and KI and AN; (b) KI3 and I2 and KI; 2.3. Van der Waals Aggregation of Potassium Triiodide (KI3) and 4-Tertbyutylpyridine (TB) Eﬀect on (c) KI3 and (AN)2. DSSC Electrolytes

2.3. VanInterestingly, der Waals Aggregation DFT/MM of of vdWPotassium aggregate Triiodide of KI(KI33)and and I42-andTertbyutylpyridine KI reveals that (TB) the Effect energy on DSSC gap of Electrolytes.ELUMO + 1 and ELUMO is 0.19 eV, predicting that the aggregate is semiconducting once it is formed. With this prediction in mind, DFT/MM is extended to vdW aggregates of (KI3)2 and AN, and of (KI3)2 Interestingly, DFT/MM of vdW aggregate of KI3 and I2 and KI reveals that the energy gap of and (AN) to clarify the reason why the electrolyte of KI /I /AN become semiconducting. In addition, ELUMO +2 1 and ELUMO is 0.19 eV, predicting that the aggregate2 is semiconducting once it is formed. since it is well-known that presence of 4-tert-butylpyridine (TBP) in the electrolytes improves open With this prediction in mind, DFT/MM is extended to vdW aggregates of (KI3)2 and AN, and of (KI3)2 circuit voltage (Voc) of DSSC. Open circuit voltage depends on electron leak-free unidirectional and (AN)2 to clarify the reason why the electrolyte of KI /I2 /AN become semiconducting. In addition, photocurrent [8,10]. DFT/MM is also extended to vdW aggregate of (KI ) and TBP. since it is well-known that presence of 4-tert-butylpyridine (TBP) in the3 2electrolytes improves open Figure4 shows the EPSM of equilibrium geometry of vdW aggregates of (KI ) and AN, (KI ) and circuit voltage (Voc) of DSSC. Open circuit voltage depends on electron leak3 2-free unidirectional3 2 (AN)2, (KI3)2 and TBP. The heat of formation values verify exclusive formation of vdW dimer of KI3 in photocurrent [8,10]. DFT/MM is also extended to vdW aggregate of (KI3)2 and TBP. wet type DSSC electrolytes. UV-Vis spectra support the orange color of the electrolytes. Energy gaps of Figure 4 shows the EPSM of equilibrium geometry of vdW aggregates of (KI3)2 and AN, (KI3)2 LUMO + 1 and LUMO are all less than 0.2 eV, and their conﬁgurations explain unidirectional electron and (AN)2, (KI3)2 and TBP. The heat of formation values verify exclusive formation of vdW dimer of ﬂow from LUMO + 1 to LUMO. Interestingly, the vdW aggregate of (KI3)2 and TBP gives the smallest KI3 in wet type DSSC electrolytes. UV-Vis spectra support the orange color of the electrolytes. Energy energy gap of 0.05 eV. gaps of LUMO + 1 and LUMO are all less than 0.2 eV, and their configurations explain unidirectional In order to validate conductivity of electron-running state of the vdW aggregates of KI3 -based electron flow from LUMO + 1 to LUMO. Interestingly, the vdW aggregate of (KI3)2 and TBP gives the electrolytes, EPM and energy structures of electron injected [(KI ) and AN]. and [(KI ) and TBP]. smallest energy gap of 0.05 eV. 3 2 − 3 2 − are examined (Figure5). Reddish ESPM indicates nucleophilic surface state, both negative values In order to validate conductivity of electron-running state of the vdW aggregates of KI3 -based of heat of their electron acceptance verify their electron acceptability, and hopping between them is electrolytes, EPM and energy structures of electron injected [(KI3)2 and AN].− and [(KI3)2 and TBP].− favorable in the electrolytes. As for surface energy structures, Ea (HOMO) is identical with electron are examined (Figure 5). Reddish ESPM indicates nucleophilic surface state, both negative values of singly occupied molecular orbital (SOMO). Accepted electron (spin density) is located in bLUMO. heat of their electron acceptance verify their electron acceptability, and hopping between them is We understand that spin may run on bLUMO at electron running process. The energy gap of bLUMO favorable in the electrolytes. As for surface energy structures, Ea (HOMO) is identical with electron and SOMO (0.46 eV and 0.35 eV, respectively), is small enough for spin (unpaired electron) to run singly occupied molecular orbital (SOMO). Accepted electron (spin density) is located in bLUMO. under irradiance of solar energy (hν). We understand that spin may run on bLUMO at electron running process. The energy gap of bLUMO and SOMO (0.46 eV and 0.35 eV, respectively), is small enough for spin (unpaired electron) to run under irradiance of solar energy (h). Energies 2020, 13, x FOR PEER REVIEW 5 of 14 Energies 2020, 13, 3027 5 of 14 Energies 2020, 13, x FOR PEER REVIEW 5 of 15

Figure 4. Equilibrium geometry of van der Waals aggregates, heat of formation and energy gap of Figure 4. Equilibrium geometry of van der Waals aggregates, heat of formation and energy gap of ELUMO + 1 and ELUMO: (a) (KI3)2 and AN; ∆E = −64.1 kcal/mol (b) (KI3)2 and (AN)2; (c) (KI3)2 and 4- FigureELUMO 4. Equilibrium+ 1 and ELUMO: geometry (a) (KI of3) 2vanand der AN; Waals∆E = aggregates64.1 kcal/,mol heat (b of) (KIformation3)2 and (AN)and 2e;(nergyc) (KI gap3)2 andof tert-butylpyridine (TBP); (d) LUMO configuration of− (KI3)2 and AN; (e) LUMO configuration of (KI3)2 4-tert-butylpyridine (TBP); (d) LUMO configuration of (KI ) and AN; (e) LUMO configuration of ELUMO + 1 and ELUMO: (a) (KI3)2 and AN; ∆E = −64.1 kcal/mol3 2 (b) (KI3)2 and (AN)2; (c) (KI3)2 and 4- and (AN)2; (f) LUMO configuration of (KI3)2 and 4-tert-butylpyridine (TBP). (KI ) and (AN) ;(f) LUMO configuration of (KI ) and 4-tert-butylpyridine (TBP). tert-3butylpyridine2 2 (TBP); (d) LUMO configuration3 of2 (KI3)2 and AN; (e) LUMO configuration of (KI3)2

and (AN)2; (f) LUMO configuration of (KI3)2 and 4-tert-butylpyridine (TBP).

(a) (b)

Figure 5. Cont. Energies 2020, 13, x FOR PEER REVIEW 6 of 14

Energies 2020, 13, 3027 6 of 14 Energies 2020, 13, x FOR PEER REVIEW 6 of 14

(e) (f)

Figure 5. Equilibrium geometry of electron running-state with heat of electron acceptance and energy structures: (a) ESPM of [(KI3)2 and AN].−; (b) ESPM of [(KI3)2 and TBP].−; (c) SOMO configuration of

[(KI3)2 and AN].−; (d) EbLUMO configuration of [(KI3)2 and TBP].−; (e) EbLUMO configuration of [(KI3)2

and AN].−; (f) [(KI3)2 and TBP].−.

2.4. Electrostatic Potential(e) Map (ESPM) of TiO2 Anatase Nanoparticle and Conductivity.(f) Figure 5. Equilibrium geometry of electron running-state with heat of electron acceptance and energy FigureFigure 5. Equilibrium 6 shows the geometry ESPM of of electron anatase running TiO2 model-state with of heat Ti9O of18H electron and OHacceptance proposed and energy by Jono and . . structures: (a) ESPM of [(KI3)2 and AN].− −; (b) ESPM of [(KI3)2 and TBP].− −;(c) SOMO configuration of Yamashitastructures (Jono: (a) ESPM-Yamashita of [(KI3 )2model) and AN] [11].; (b) ESPM The validityof [(KI3) 2 ofand the TBP] Jono; (c)- YamashitaSOMO configuration model forof TiO2 . . [(KI[(KI3)32 )and2 and AN] AN].−; (d−); EbLUMO(d) EbLUMO configuration configuration of [(KI of3 [(KI)2 and3) 2TBP]and.− TBP]; (e) EbLUMO−;(e) EbLUMO configuration configuration of [(KI3) of2 nanoparticle (NP) has. been confirmed elsewhere. [12]. Colorful ESPM verifies that three-dimensional and[(KI AN]3)2 and.−; (f) AN] [(KI−3);2 (andf) [(KI TBP]3)2 .−and. TBP] −. vdW aggregates may form TiO2 thin films and result in giving porous structures when sintered at

2.4.high Electrostatic temperature. Potential Map (ESPM) of TiO2 Anatase Nanoparticle and Conductivity 2.4. Electrostatic Potential Map (ESPM) of TiO2 Anatase Nanoparticle and Conductivity. To understand the nature of electron acceptability and electron-transfer in TiO2, electron running Figure6 shows the ESPM of anatase TiO 2 model of Ti9O18H and OH proposed by Jono and molecularFigure 6orbital shows configurations the ESPM of of anatase LUMO TiO and2 model LUMO of + Ti 19 Oare18H shown and OHas the proposed side vie byw ( Jonoa) and and the Yamashita (Jono-Yamashita model) [11]. The validity of the Jono-Yamashita model for TiO2 nanoparticle Yamashitaview from (Jono the top-Yamashita (b) of the model)TiO2 model. [11]. The The e nergy validity gap ofof LUMO the Jono + -1Yamashita and LUMO model is 0.43 foreV, TiOwhich2 (NP) has been confirmed elsewhere [12]. Colorful ESPM verifies that three-dimensional vdW aggregates nanoparticleverifies and (NP) predicts has been that confirmed TiO2 model elsewhere and their [12]. vdW Colorful aggregates ESPM verifies become that semiconducting three-dimensional when may form TiO2 thin films and result in giving porous structures when sintered at high temperature. vdWLUMO aggregates and LUMO may + form 1 accept TiO photoelectron.2 thin films and result in giving porous structures when sintered at high temperature. To understand the nature of electron acceptability and electron-transfer in TiO2, electron running molecular orbital configurations of LUMO and LUMO + 1 are shown as the side view (a) and the view from the top (b) of the TiO2 model. The energy gap of LUMO + 1 and LUMO is 0.43 eV, which verifies and predicts that TiO2 model and their vdW aggregates become semiconducting when LUMO and LUMO + 1 accept photoelectron.

(a)

Figure 6. Cont.

(a) Energies 2020, 13, 3027 7 of 14 Energies 2020, 13, x FOR PEER REVIEW 7 of 14

(b)

FigureFigure 6.6. ElectrostaticElectrostatic potentialpotential mapmap andand electron electron energy energy structure structure of of TiO TiO2 2anatase anatase model model of of Ti Ti9O9O1818HH andand OH:OH:( (aa)) side side view;view; ( b(b)) view view from from top. top.

2.5. ElectrostaticTo understand Potential the nature Map (ESPM) of electron of Sensitizing acceptability N3 andDyes electron-transfer and Perspective of in V TiOan 2d,er electron Waals running molecularAggregation. orbital conﬁgurations of LUMO and LUMO + 1 are shown as the side view (a) and the view from the top (b) of the TiO2 model. The energy gap of LUMO + 1 and LUMO is 0.43 eV, which veriﬁes Figure 7 shows ESPM of two kinds of N3 (tetramethylammonium) (a homolog of N719) and N3 and predicts that TiO2 model and their vdW aggregates become semiconducting when LUMO and LUMO(proton)+ with1 accept UV photoelectron.-Vis spectra and electron energy structures. Colorful ESPM suggests that they are likely not to aggregate each other, but orange-colored SCN group sites may be vdW-aggregated by 2.5.electrophilic Electrostatic potassium Potential Maptriiodide (ESPM) (K+I of3−). Sensitizing Each energy N3 Dyesgap of and LUMO Perspective + 1 and of Van LUMO, der Waals 0.36 AggregationeV and 0.10 eV predicts that both N3 dyes are conductive. Figure7 shows ESPM of two kinds of N3 (tetramethylammonium) (a homolog of N719) and N3 Recently we reported that DFT/MM predict that DFT/MM-determined UV-Vis absorption (proton) with UV-Vis spectra and electron energy structures. Colorful ESPM suggests that they are spectra are strongly affected by vdW aggregation with other molecules, which was exemplified by likely not to aggregate each other, but orange-colored SCN group sites may be vdW-aggregated by UV-Vis spectrum of benzene solution [3]. Figure 7 reveals that DFT/MM-based UV-Vis spectrum of electrophilic potassium triiodide (K+I ). Each energy gap of LUMO + 1 and LUMO, 0.36 eV and N3 (tetramethylammonium) is quite comparable3− to the incident photocurrent efficiency (IPCE) action Energies0.10 eV 20 predicts20, 13, x FOR that PEER both REVIEW N3 dyes are conductive. 8 of 15 spectra of N3-sensitized DSSC [13]. However, UV-Vis spectrum of N3 (proton) gives 380 nm red shifted one with decreased strength of absorption. DFT/MM-determined three-dimensional molecular structures verify that the difference comes from a change of coordination structure of ligands, bipyridyl and SCN ligands around Ru(II) ion (see Section 3).

FigureFigure 7. 7.Electrostatic Electrostatic potential potential map and map energy and structures energy of N3 structures dyes: (a) N3 of (tetramethylammonium); N3 dyes: (a) N3 (tetramethylammonium);(b) N3 (proton). (b) N3 (proton).

Recently we reported that DFT/MM predict that DFT/MM-determined UV-Vis absorption spectra are stronglyFigure a 7.ﬀ ectedElectrostatic by vdW aggregation potential map with and other energy molecules, structures which was of N3 exempliﬁed dyes: (a by) UV-Vis N3 spectrum(tetramethylammonium); of benzene solution (b) [N33]. (proton). Figure7 reveals that DFT /MM-based UV-Vis spectrum of N3 Energies 2020, 13, 3027 8 of 14

(tetramethylammonium) is quite comparable to the incident photocurrent eﬃciency (IPCE) action spectra of N3-sensitized DSSC [13]. However, UV-Vis spectrum of N3 (proton) gives 380 nm red Energiesshifted 20 one20, 1 with3, x FOR decreased PEER REVIEW strength of absorption. DFT/MM-determined three-dimensional molecular9 of 15 structures verify that the diﬀerence comes from a change of coordination structure of ligands, bipyridyl and SCN ligands around Ru(II) ion (see Section3). 2.6. Verification of Van der Waals Aggregation of N3 Dye with Anatase TiO2 Model

2.6. VerificationHere, let us of consider Van der WaalsvdW aggregation Aggregation ofof N3anatase Dye with TiO Anatase2 and N3 TiO dye2 Model molecule, which may allow us to gain insights into the electronic natures of the TiO2 /N3 (proton) dye interface in DSSC. The Here, let us consider vdW aggregation of anatase TiO2 and N3 dye molecule, which may allow us problem of dye-anchoring on anatase TiO2 had been argued several times in the past, e.g., ester to gain insights into the electronic natures of the TiO2 /N3 (proton) dye interface in DSSC. The problem formation with bipyridyl carboxylic acid ligand (bpy-dca), coordination of the bipyridyl ligand to of dye-anchoring on anatase TiO2 had been argued several times in the past, e.g., ester formation with Tbipyridyli(IV), and carboxylic hydrogen acid bonding ligand with (bpy-dca), the bipyridyl coordination ligand of [14 the–16]. bipyridyl DFT/MM ligand now to verifies Ti(IV), and that hydrogen N3 dye canbonding be anchored with the by bipyridyl van der Waals ligand force [14– 16of]. hydrogen DFT/MM bonding now verifies between that the N3 hydroxyl dye can begroup anchored on TiO by2 and the carboxyl group of N3 dye (Figure 8). Heat of formation of −13.1 kcal/mol is not large enough van der Waals force of hydrogen bonding between the hydroxyl group on TiO2 and the carboxyl group toof form N3 dye strong (Figure vdW8). aggregation. Heat of formation We failed of to13.1 obtain kcal /UVmol-Vis is notabsorption large enough spectra to of form the strongaggregate. vdW − However,aggregation. surface We failed electron to obtain energy UV-Vis structures, absorption EHOMO spectra and of ELUMO the aggregate. and their However, configurations surface electron verify thatenergy photoexcitation structures, EHOMO of N3 dye and induces ELUMO electron and their injection configurations from HOMO’s verify on that SCN photoexcitation ligands to LUMO’s of N3 on anatase TiO2. dye induces electron injection from HOMO’s on SCN ligands to LUMO’s on anatase TiO2.

Figure 8. Electrostatic potential map (ESPM) of N3 (proton), adsorbed TiO anatase model of Ti O H Figure 8. Electrostatic potential map (ESPM) of N3 (proton), adsorbed TiO2 anatase model of Ti9O1818H andand OH OH and and N3 N3 (proton) (proton) and and electron electron energy energy structures structures with with HOMO/LUMO HOMO/LUMO config conﬁgurationuration for ( fora): ( (aa)): view(a) view from from top; top;(b) side (b) side view. view. 2.7. Van der Waals Aggregation of N3 Dye with Potassium Triiodide 2.7. Van der Waals Aggregation of N3 Dye with Potassium Triiodide. Remarkable vdW aggregation power of in situ formed potassium triiodide works on N3 (proton) Remarkable vdW aggregation power of in situ formed potassium triiodide works on N3 (proton) dye molecules (Figure9). Formation of vdW-aggregate of N3 (proton) and (KI 3)2 and of N3(proton) dye molecules+ (Figure 9). Formation of vdW-aggregate of N3 (proton) and (KI3)2 and of N3(proton) and K I3− are both exothermic (∆E = 79.7 kcal/mol and ∆E = 142 kcal/mol respectively) and UV-Vis and K+I3− are both exothermic (E = −79.7− kcal/mol and ∆E = −142− kcal/mol respectively) and UV-Vis absorption maxima shift from near IR region to visible region. Interestingly, the UV-Vis spectra of the absorption maxima shift from near IR region to visible region. Interestingly, the UV-Vis spectra of KI aggregates are consistent with reported IPCE action spectra (λ = 600–700 nm) of N3-sensitized the KI aggregates are consistent with reported IPCE action spectra (= 600–700 nm) of N3-sensitized DSSC [13]. DSSC [13]. The most stabilized vdW aggregate of N3 (proton) and K+I3− can be regarded as a new type of triiodide aggregated ruthenium dye. DFT/MM assigns the absorption maximum to molecular orbital components. All of them are regarded as results of photoexcitation from HOMO’s on SCN ligands to LUMO’s on bipyridyl ligands (Figure 10). Energies 2020, 13, 3027 9 of 14 Energies 2020, 13, x FOR PEER REVIEW 10 of 15

Energies 2020, 13, x FOR PEER REVIEW 10 of 15

Figure 9. Van der Waals Aggregation of N3 with potassium triiodide to respective N3 and (KI3)2 and Figure 9. V+an der Waals Aggregation of N3 with potassium triiodide to respective N3 and (KI3)2 and N3 and K I3−. N3 and K+I3−. + The most stabilized vdW aggregate of N3 (proton) and K I3− can be regarded as a new type of triiodide aggregated ruthenium dye. DFT/MM assigns the absorption maximum to molecular orbital

components.Figure 9. All Van of der them Waals are Aggregation regarded as of results N3 with of potassium photoexcitation triiodide from to respective HOMO’s N3 on and SCN (KI ligands3)2 and to

LUMO’sN3 and on bipyridyl K+I3−. ligands (Figure 10).

Figure 10. Energy structure of van der Waals (vdW)-aggregate of N3 (proton) with potassium

triiodide of N3 (proton) and K+I3−. UV-Vis spectrum and surface electron energy structure.

. 3. Discussion Figure 10. Energy structure of van der Waals (vdW)-aggregate of N3 (proton) with potassium triiodide + PhotoconversionofFigure N3 (proton) 10. Energy and efficiency K structureI3−. UV-Vis (  of) of spectrumvan solar der cells Waals and of surface (DSSCvdW electron)- aggregateis determined energy of N3structure. by (proton) the following with potassium Equation: triiodide of N3 (proton) and K+I3−. UV-Vis spectrum and surface electron energy structure. 3. Discussion = Jsc × Voc × ff / E (1) where3. DiscussionPhotoconversion Jsc is the short circuit efficiency photocurrent, (η) of solar V cellsoc is the of DSSCopen circuit is determined voltage, by ff is the fill following factor and Equation: E is solar energy 100 mW/cm2 Photoconversion efficiency () of solar cells of DSSC is determined by the following Equation: Nazeeruddin, who invented a seriesη of= JN3sc dyes,Voc reportedff / E that N3-dye-sensitized DSSC give (1)Jsc × × = 16.8–19.0 mA/cm2, Voc = 600–770 mV, and ff 0.65= Jsc –×0.72, Voc × and ff / Ep hotoconversion efficiency () at AM 1.5,(1) 7.4where–9.3%.Jsc Inis theaddition, short circuithe successfully photocurrent, measuredVoc is excellent the open IPCE circuit spectra voltage, ( ff= 500is fill–630 factor nm and(70– E80%)) is solar of where Jsc is the short circuit photocurrent, Voc is the open circuit voltage, ff is fill factor and E is solar energy 100 mW/cm2. DSSCenergy sensitized 100 mW/cm by respective2 N3 (proton) and N3 (tetrabutylammonium) (N719) [13]. Nazeeruddin, who invented a series of N3 dyes, reported that N3-dye-sensitized DSSC give In Figure 11, DSSC key components, anatase TiO2 model, in situ-formed I3− -aggregated N3 dye Nazeeruddin, who2 invented a series of N3 dyes, reported that N3-dye-sensitized DSSC give Jsc J = 16.8–19.0+ − mA/cm , V = 600–770 mV, and ff 0.65–0.72, and photoconversion efficiency (η) at ofsc N3 and K I3 , KI3-dimer2 aggregates,oc (KI3)2 and AN, and (KI3)2 and TBP, are aligned referring to the = 16.8–19.0 mA/cm , Voc = 600–770 mV, and ff 0.65–0.72, and photoconversion efficiency () at AM 1.5, electrostatic7.4–9.3%. In potential addition, map he successfully (ESPM). The measured pale green excellent colored IPCE ESPM spectra of (KI (3) 2= and 500 –AN630, nmand (70 (KI–80%))3)2 and of DSSC sensitized by respective N3 (proton) and N3 (tetrabutylammonium) (N719) [13]. In Figure 11, DSSC key components, anatase TiO2 model, in situ-formed I3− -aggregated N3 dye of N3 and K+I3−, KI3-dimer aggregates, (KI3)2 and AN, and (KI3)2 and TBP, are aligned referring to the electrostatic potential map (ESPM). The pale green colored ESPM of (KI3)2 and AN, and (KI3)2 and Energies 2020, 13, x FOR PEER REVIEW 11 of 15

TBP predict further vdW aggregation. Especially, vdW aggregation between N3 and K+I3−, and (KI3)2 and AN or (KI3)2 and TBP is apparent in view of ESPM. The above-mentioned high Voc = 0.6–0.77 mV and the fill factors 0.65–0.72 of DSSC are validated as follows: Photo-formed electron runs through degenerate LUMO and LUMO + 1. Each LUMO + 1 and LUMO configuration visualize effective electron transfer in DSSC devices by following Energies 2020, 13, 3027 10 of 14 comparable potential energy of the KI3-assisted aggregates (Figure 11). Photoelectron on irradiated Ti9O18H and OH and N3 (proton) has a potential from −3.22 eV to −3.53AM 1.5,eV and 7.4–9.3%. transfer In to addition, LUMO + he1 and successfully LUMO with measured potential excellent from −4.20 IPCE eV to spectra −4.63 eV. (λ =Photoelectron500–630 nm may(70–80%)) have of potential DSSC sensitized energy of by 0.98 respective–1.1 eV N3on (proton)anode to and cathode. N3 (tetrabutylammonium) In general, clear-cut (N719)Voc becomes [13]. measurableIn Figure by 11effective, DSSC electron key components, transfer via anatase electrolytes TiO2 model, of (KI3 in)2 and situ-formed AN, and I 3of− -aggregated(KI3)2 and TBP. N3 The dye + measuredof N3 and V Koc I=3 −0.6, KI–0.773-dimer mV is aggregates, less than theoretical (KI3)2 and AN,ones and of 0.98 (KI–3)1.12 and eV,TBP, and aremeans aligned that referringphotoelectron to the leakageelectrostatic is not potential suppressed map enough (ESPM). on The N3 pale-anchored green coloredTiO2 NP ESPM electrodes. of (KI3 Improved)2 and AN, conductivity and (KI3)2 and of + (KITBP3)2 predict and TBP further (energy vdW gap: aggregation. 0.05 eV) is Especially,consistent vdWwith aggregationenhancement between of conversion N3 and efficiency K I3−, and of (KIsolar3)2 cells.andAN or (KI3)2 and TBP is apparent in view of ESPM.

Figure 11. Visualization of unidirectional electron diﬀusion via vdW aggregation in DSSC composed Figure 11. Visualization of unidirectional electron diffusion via vdW aggregation in DSSC composed of Ti9O18H and OH/N3 (proton) /KI3 in acetonitrile (AN). of Ti9O18H and OH/N3 (proton) /KI3 in acetonitrile (AN).

The above-mentioned high Voc = 0.6–0.77 mV and the fill factors 0.65–0.72 of DSSC are validated The IPCE action spectrum ranges are 350–800 nm; at 350 nm (about 50%), at 500–630 nm (70– as follows: Photo-formed electron runs through degenerate LUMO and LUMO + 1. Each LUMO + 1 80%) and at 800 nm (about 5%) [13]. The excellent IPCE action spectra for N3-sensitized DSSC is now and LUMO configuration visualize effective electron transfer in DSSC devices by following comparable validated theoretically due to effective visible light-absorption of N3 and K+I− dyes on porous TiO2 potential energy of the KI3-assisted aggregates (Figure 11). films. Photoelectron on irradiated Ti9O18H and OH and N3 (proton) has a potential from 3.22 eV to Figure 12 shows a comparison of the UV-Vis spectra of N3 (proton), N3 and K+I−3−, and N3 3.53 eV and transfer to LUMO + 1 and LUMO with potential from 4.20 eV to 4.63 eV. Photoelectron (tetramethylammonium− ) as a homologue of N719. UV-Vis allowed− transition occurs− between highest may have potential energy of 0.98–1.1 eV on anode to cathode. In general, clear-cut Voc becomes occupied molecular orbital (HOMO), HOMO − 1, and HOMO − 2 on SCN ligands to lowest measurable by effective electron transfer via electrolytes of (KI3)2 and AN, and of (KI3)2 and TBP. unoccupied molecular orbital (LUMO), LUMO + 1, and LUMO + 2 on bpy-dca ligands. In addition, The measured Voc = 0.6–0.77 mV is less than theoretical ones of 0.98–1.1 eV,and means that photoelectron when the molecular structures are compared, the coordination structures of N3 and K+I3− and N3 leakage is not suppressed enough on N3-anchored TiO2 NP electrodes. Improved conductivity of (KI3)2 (tetramethylammonium) are quite comparable, explaining that the respective 280 nm and 380 nm and TBP (energy gap: 0.05 eV) is consistent with enhancement of conversion efficiency of solar cells. blue shift (bathochromic shift) comes from ligand-coordination change induced by vdW and The IPCE action spectrum ranges are 350–800 nm; at 350 nm (about 50%), at 500–630 nm (70–80%) and at 800 nm (about 5%) [13]. The excellent IPCE action spectra for N3-sensitized DSSC is now + validated theoretically due to effective visible light-absorption of N3 and K I− dyes on porous TiO2 films. Energies 2020, 13, 3027 11 of 14

+ Figure 12 shows a comparison of the UV-Vis spectra of N3 (proton), N3 and K I3−, and N3 (tetramethylammonium) as a homologue of N719. UV-Vis allowed transition occurs between highest occupied molecular orbital (HOMO), HOMO 1, and HOMO 2 on SCN ligands to lowest − − unoccupied molecular orbital (LUMO), LUMO + 1, and LUMO + 2 on bpy-dca ligands. In addition, + when the molecular structures are compared, the coordination structures of N3 and K I3− and N3

(tetramethylammonium)Energies 2020, 13, x FOR PEER areREVIEW quite comparable, explaining that the respective 280 nm and 380 nm12 of blue 15 shift (bathochromic shift) comes from ligand-coordination change induced by vdW and Coulomb interactionCoulomb interaction of N3 with of I3− N3and with tetramethylammonium. I3− and tetramethylammonium. The hyperchromic The hyperchromic eﬀect of increase effect of of increase strength (εof) and strength the bathochromic (ε) and the eﬀ ect bathochromic (the red shift) effect in absorption (the red spectrum shift) in of absorption N3 (tetramethylammonium) spectrum of N3 validates(tetramethylammonium) that N719 is a respectable validates sensitizerthat N719 ofis a DSSC. respectable sensitizer of DSSC.

Figure 12. Comparison of DFT/MM-predicted UV-Vis spectra and energy structures of TiO2 sensitizing + dyes of N3 (proton), N3 (proton) and K I3− and N3 (tetramethylammonium). Figure 12. Comparison of DFT/MM-predicted UV-Vis spectra and energy structures of TiO2 4. Conclusions sensitizing dyes of N3 (proton), N3 (proton) and K+I3− and N3 (tetramethylammonium).

Experimental and theoretical UV-Vis spectral analyses of sensitizing dyes on TiO2 NPs were not4. Conclusion successful enough so far [17–20]. As we reported [3,5], Spartan (Q-Chem) (Wavefunction, Inc.

Irvin.Experimental CA, USA) is a and comprehensive theoretical UVab-initio-Vis spectralquantum-chemistry analyses of sensitizing software dyes for accurateon TiO2 NPs predictions were not of molecularsuccessful structures, enough so reactivities,far [17–20]. As and we vibrational, reported [3,5], electronic Spartan and (Q NMR-Chem) spectra. (Wavefunction, We are very Inc. proudIrvin. ofCA, the USA) verification is a comprehensive power of density ab-initio functional quantum theory-based-chemistry molecular software for modeling accurate (DFT predictions/MM) using of Spartanmolecular (involving structures, Q-Chem), reactivities, and and now vibrational, demonstrate electronic that vdW and aggregationNMR spectra. power We are of very triiodide proud ionof contributesthe verification to solar power light of harvesting density functional of N3 and etheoryffective-based electron molecular diffusion modeling in in situ (DFT/MM) formed triiodide using ion-basedSpartan (involving electrolytes. Q- TheChem), strong and tendency now demonstrate of vdW aggregation that vdW via aggregation I3− at interfaces power of of DSSC triiodide facilitates ion DSSCcontributes fabrication to solar with light high harvesting performance of N3 of and fill factoreffective (ff )electron and respectable diffusion open in in circuitsitu formed voltage triiodide (Voc). ion-Asbased a perspective electrolytes. conclusion, The strong DFT tendency/MM is of a vdW useful aggregation tool for verifying via I3− at and interfaces predicting of DSSC conductivity facilitates of electronicDSSC fabrication molecular with aggregates, high performance IPCE action of fill spectra factor and (ff)theoretical and respectableVoc of open solar circuit cells, asvoltage mentioned (Voc). in the DFTAs/ MMa perspective of perovskite conclusion, solar cells DFT/MM [3]. is a useful tool for verifying and predicting conductivity of electronic molecular aggregates, IPCE action spectra and theoretical Voc of solar cells, as mentioned in the DFT/MM of perovskite solar cells [3]. During editing period of the article, we succeeded to obtain DFT/MM-based UV-Vis spectrum of van der Waals aggregate of N3(proton) with two acetonitrile (AN) molecules (see Supplementary). It is now verified that the aggregation of N3 with AN, i.e. solvation of AN to N3, also affect energy structures of N3, giving four max: 692 nm (0.0008), 823 nm (0.0242), 875 nm (0.0164), 875 nm (0.0164). Compared to max of N3 (proton)K+I3−, we conclude that the K+I3− aggregation to N3 is much more dramatic, causing favorable energy structure change of N3 (proton) followed by coordination geometry change. Energies 2020, 13, 3027 12 of 14

During editing period of the article, we succeeded to obtain DFT/MM-based UV-Vis spectrum of van der Waals aggregate of N3(proton) with two acetonitrile (AN) molecules (see Supplementary). It is now veriﬁed that the aggregation of N3 with AN, i.e. solvation of AN to N3, also aﬀect energy structures of N3, giving four λmax: 692 nm (0.0008), 823 nm (0.0242), 875 nm (0.0164), 875 nm (0.0164). + Compared to λmax of N3 (proton)K+I3−, we conclude that the K I3− aggregation to N3 is much more dramatic, causing favorable energy structure change of N3 (proton) followed by coordination geometry change.

5. Materials and Methods The DFT-based MM with the SPARTAN’18 (Wavefunction, Inc. Irving, CA, USA) program code can be conducted by using high-end personal computers, deriving equilibrium geometries of van der Waals (vdW) aggregates such as I2 and KI, and their aggregates with a Ru complex (N3 dye) and TiO2 NP, along with the isosurface of the electrostatic potential based on the electronic charge distribution, thus helping us to gain insights into the nature of the iodine-based vdW bonds. Similar to the previous works [1–6], the DFT-based MM with B3LYP/6-31G(d) was employed to obtain the equilibrium geometry and electronic structure of vdW aggregates. Prior to the DFT calculation, the geometries of the molecular aggregates were determined by the molecular mechanics with the Merck molecular force ﬁeld (MMFF) [21], so that the intermolecular vdW interaction and the electrostatic interaction was taken into account. The following calculation at the B3LYP/6-31G(d) level results in equilibrium geometry, van der Waals bonding is correctly described. To simulate UV-Vis spectra revealing allowed electronic transitions with wavelength and intensity, we used the time-dependent DFT within the linear response regime [22,23]. The surface electron density and electrostatic potential map were used to elucidate molecular aggregation with vdW and electrostatic Coulomb interaction without covalent bonding. For a review of the quantum mechanical methods used in SPARTAN, see reference [24–27].

Supplementary Materials: The following are available online at http://www.mdpi.com/1996-1073/13/11/3027/s1, Figure S1: Energy structure of vdW-aggregate of N3 with acetonitrile (AN) of N3 and (AN)2: UV/Vis spectrum and surface electron energy structure. Author Contributions: Conceptualization, S.Y. (Susumu Yanagisawa) and S.Y. (Shozo Yanagida); methodology, software, validation and formal analysis, S.Y. (Shozo Yanagida); investigation, S.Y. (Susumu Yanagisawa) and S.Y. (Shozo Yanagida); resources, S.Y. (Shozo Yanagida); writing—original draft preparation, S.Y. (Susumu Yanagisawa); supervision, S.Y. (Shozo Yanagida); project administration, S.Y. (Shozo Yanagida); funding acquisition, S.Y. (Shozo Yanagida). All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors thank W. J. Hehre (Wavefunction, Inc. Irvine, CA, USA), and N. Uchida and Y. Watanabe (Wavefunction, Inc. Japan Branch Office, Kouji-machi, Chiyoda-ku, Tokyo Japan) for discussion on DFT-based molecular modeling using ‘Spartan 19’. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations The following abbreviations are used in this manuscript:

vdW van der Waals MM Molecular modelling LUMO Lowest-unoccupied molecular orbital ESPM Electrostatic potential map MMFF Merck molecular force ﬁeld DFT Density functional theory HOMO Highest-occupied molecular orbital DSSC Dye-sensitized solar cell NP Nanoparticle Energies 2020, 13, 3027 13 of 14

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