Quantum theory of atoms in molecules for photovoltaics

Solar Energy 190 (2019) 475–487

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Solar Energy journal homepage: www.elsevier.com/locate/solener

Quantum theory of atoms in molecules for photovoltaics Vladimir Potemkin, Nadezhda Palko, Maria Grishina

⁎

T

South Ural State University, 76, pr. Lenina, Chelyabinsk 454080, Russia

ARTICLE INFO

ABSTRACT

Keywords: Benzothiadiazole unit Dye-sensitized solar cells Photovoltaic performances Quantum theory of atoms in molecules

Electronic properties of benzothiadiazole (BTD) unit containing dyes adsorbed on TiO2 nano-particles have been estimated using Quantum Theory of Atoms in Molecules (QTAIM). We found that short circuit photocurrent density Jsc and open circuit photovoltage Voc of the studied DSSCs are well related to the electronic properties of dyes, namely charges of BTD atomic basins of nitrogens, summary isodensity surface area and summary volume of hydrogen basins. Analysis of deviations of predicted and observed photovoltaic properties allowed to reveal device fabrication details influencing positively and negatively on device efficiency. Found relationships have been used for design of new promising dyes and recommendation of the better fabrication details of DSSCs with significantly higher photovoltaic properties as compared to the studied and published. For newly designed metal-free BTD-unit containing dyes, Jsc is expected to reach 20.7–25.8 mA/cm2, Voc – 0.858–1.029 V and power conversion efficiency η – 10.6–16.3%.

1. Introduction Solar energy is the plum, gratis and pollution-free energy resource. Researches intensively develop technologies converting solar light to commonly used forms. One of them is electric energy based on photovoltaic effect. Now there are a lot of types of photovoltaic devices (crystalline silicon cells, thin-film solar cells, multi-junction cells) which are based on different materials performing energy conversion from light to electricity (Edoff, 2012; O'Regan and Grätzel, 1991; Xu and Schoonen, 2000). These are perovskite, liquid inks, organic polymer solar cells, light-absorbing dyes, quantum dots (CdS, Sb2S3, CdSe, etc.), etc. Among them, the dye-sensitized solar cells using lightabsorbing metal-free dyes can be low cost and low ecotoxic devices (Park et al., 2016; McEvoy et al., 2013). Many recent publications touch low cost metal-free organic dyes combined with iodide/triiodide (I-/I3-) redox pair containing electrolyte demonstrating good photovoltaic efficiency (Xu et al., 2015; Selopal et al., 2016). These are carbazoles including the oligothiophene backbone (MK-2, MK-14) (Hara and Koumura, 2009.), indolines (Wang et al., 2014a), oligo-phenylene vinylene dyes (Hwang et al., 2007), coumarine dyes (Wang et al., 2007), benzooxadiazoles (WS-55) (Xie et al., 2016), benzoselenadiazoles, cyclopentadithiophene linker dyes

(Tsao et al., 2011; Grisorio et al., 2014; Mao et al., 2015), etc. Among metal-free organic sensitizers BTD derivatives showed very good perspectives in the current DSSC technologies (Chai et al., 2015). To date, a few promising BTD unit containing sensitizers demonstrated high efficiency, more than 10% (Hwang et al., 2007; Selopal et al., 2016; Joly et al., 2015). Most articles include detailed experimental study of new BTD dyes, their properties, the dyes-based DSSCs fabrication methods, photovoltaic performances and IPCE action spectra. The following performances are used to evaluate the quality of DSSCs: (1) short circuit photocurrent density (Jsc), (2) open circuit photovoltage (Voc), (3) fill factor (FF) and (4) power conversion efficiency (η) which is related to Jsc, Voc and FF as follows (Nelson, 2003):

= Jsc Voc FF / Ps where Ps is incident light power density. In Standard Test Condition, Ps equals 1000 W m−2 or 100 mW cm−2, temperature is 25 °C, the Air Mass (AM) 1.5 spectrum. The recent data show that both a dye structure and a device fabrication method determine device performances. For example, Wu et al., 2012a; Kang et al., 2014; Wu et al., 2012b; Chai et al., 2015; Zhu et al., 2011 demonstrate that the efficiency of the devices based on the BTD dye WS-2 varies from 3.86% (low efficiency) and up to 8.90% (good

Abbreviations: DSSC, dye-sensitized solar cells; BTD, benzothiadiazole; IPCE, incident photon-to-electron conversion efficiency; TBP, tert-butyl pyridine; DMPII, 1,2dimethyl-3-N-propylimidazolium iodide; DMII, 1,3-dimethylimidazolium iodide; PMII, 1-methyl-3-propylimidazolium iodide; BMII, 1-butyl-3-methylimidiazolium iodide; GuNCS, guanidine thiocyanate; DCA, deoxycholic acid; CDCA, chenodeoxycholic acid; QTAIM, quantum theory of atoms in molecules; AM, air mass; R, correlation coefficient; St.Err, standard error of estimate ⁎ Corresponding author. E-mail addresses: [email protected] (V. Potemkin), [email protected] (N. Palko), [email protected] (M. Grishina). https://doi.org/10.1016/j.solener.2019.08.048 Received 1 June 2019; Received in revised form 25 July 2019; Accepted 17 August 2019 Available online 23 August 2019 0038-092X/ © 2019 International Solar Energy Society. Published by Elsevier Ltd. All rights reserved.

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Table 1 (continued)

Table 1 Names of dyes given in refs (see substituents Scheme 1, Electronic Annex (Tables S1–S4)) and photovoltaic performances of the dyes based DSSCs with the maximal efficiency found in literature. Reference

Name

Jsc(best), mA/cm2

Voc(best), V

FF(best)

η(best), %

Velusamy et al. (2005), Zhu et al. (2011) Velusamy et al. (2005) Zhu et al. (2011) Wu et al. (2012a); Kang et al. (2014); Wu et al. (2012b); Chai et al. (2015); Zhu et al. (2011) Zhu et al. (2011) Wu et al. (2012a); Wu et al. (2012a); Lee et al. (2011) Lee et al. (2011) Lee et al. (2011) Lee et al. (2011) Kim et al. (2008) Kim et al. (2008) Wu and Zhu (2013) Tang et al. (2010) Tang et al. (2010) Kim et al. (2010) Kim et al. (2010) Haid et al. (2012) Haid et al. (2012) Wu et al. (2012b) Zhu et al. (2014) Huang et al. (2015) Wang et al. (2014a) Wang et al. (2014a) Liu et al. (2015) Liu et al. (2015) Seo et al. (2012) Seo et al. (2012) Lee et al. (2013) Lee et al. (2013) Lee et al. (2013) Lu et al. (2015) Roiati et al. (2015); Grisorio et al. (2014) Roiati et al. (2015); Grisorio et al. (2014) Eom et al. (2015) Mao et al. (2015) Huang et al. (2015) Chen et al. (2013) Chen et al. (2013) Chen et al. (2013) Zhang et al. (2014) Zhang et al. (2014) Zhang et al. (2014) Kang et al. (2014) Kang et al. (2014) Kang et al. (2014) Wang et al. (2014b) Katono et al. (2014) Katono et al. (2014) Chai et al. (2015) Chai et al. (2015) Chai et al. (2015) Han et al. (2014) Han et al. (2014)

WS-4 (S-1)

11.2

0.6

0.75

5

S-3

3.21

0.517

0.69

1.15

WS-1 WS-2

11.9 17.93

0.65 0.661

0.68 0.74

5.3 8.9

WS-3 WS-6 WS-11 HKK-BTZ1 HKK-BTZ2 HKK-BTZ3 HKK-BTZ4 JK-68 JK-69 WS-13 BzTCA BzTMCA K-2 K-3 1 2 WS-9 WS-23 DQ-5 XS-46 XS-45 DX2 DX3 HKK-CM4 HKK-CM5 H11 H12 H13 OD-9 G1

9.5 15 10.4 15 10.6 13 17.9 17.1 14.98 12.2 16.46 11.94 8.13 12.24 6.04 18.47 18 16.91 17.61 15.2 17.8 8.01 10.28 14.3 13.3 9.14 10.01 12.07 9.69 12.2

0.69 0.672 0.629 0.58 0.54 0.56 0.62 0.61 0.77 0.705 0.545 0.555 0.47 0.549 0.423 0.64 0.696 0.672 0.685 0.631 0.635 0.62 0.61 0.58 0.56 0.54 0.55 0.72 0.818 0.69

0.75 0.77 0.71 0.65 0.59 0.63 0.66 0.72 0.77 0.75 0.67 0.71 0.651 0.566 0.7 0.69 0.72 0.717 0.59 0.69 0.68 0.7 0.7 0.72 0.68 0.67 0.68 0.72 0.642 0.71

4.9 7.76 4.64 5.72 3.37 4.55 7.3 4.66 6.61 6.45 6.04 4.68 2.49 3.8 1.78 8.21 9.04 8.15 7.12 6.62 7.69 2.6 4.41 5.97 5.03 3.32 3.7 6.19 5.09 6

G2

15.9

0.71

0.72

8.1

SGT-130 CA-III DQ-4 DOBT-I DOBT-II DOBT-III DOBT-IV DOBT-V DOBT-VI AR-II-13 JZ-117 JZ-145 D-2

16.77 13.62 14.51 7.86 12.1 12.74 15.05 16.88 15.37 12.7 17.1 18.8 15.24

0.851 0.62 0.721 0.829 0.818 0.784 0.686 0.662 0.629 0.73 0.642 0.717 0.786

0.7334 0.67 0.65 0.74 0.73 0.73 0.6453 0.6403 0.6402 0.712 0.675 0.673 0.67

10.47 5.67 6.78 4.82 7.19 7.29 6.66 7.16 6.19 6.6 7.4 9.1 7.99

KM-10

14.5

0.653

0.742

7.1

KM-11

16

0.678

0.732

8

WS-37 WS-38 WS-51 ZXY-1 ZXY-3

16.23 12.32 19.69 12.08 10.99

0.692 0.699 0.7 0.61 0.71

0.716 0.727 0.731 0.69 0.69

8.04 6.27 10.08 5.07 5.4

Reference

Name

Jsc(best), mA/cm2

Voc(best), V

FF(best)

η(best), %

Joly et al. (2015) Joly et al. (2015) Joly et al. (2015) Joly et al. (2015) Grisorio et al. (2015) Hu et al. (2013) Hu et al. (2013) Du et al. (2015) Joly et al. (2015) Yang et al. (2014) Seo et al. (2012)

RK1 RK2 6RK1 6ORK1 G3

18.26 14.92 16.76 17.81 18.11

0.76 0.75 0.76 0.76 0.663

0.74 0.78 0.76 0.75 0.72

10.2 8.71 9.67 10.11 8.64

DIA-9 DIA-10 C-321 RKF JH307 C311

9.71 11.82 16.78 18.82 14.71 2.32

0.712 0.682 0.686 0.71 0.645 0.572

0.75 0.72 0.711 0.72 0.673 0.706

5.2 5.82 8.2 9.69 6.4 0.9

efficiency) dependently on the method of the device fabrication. Refs are presented in Table 1 show that varying a BTD unit containing dye at the constant DSSCs fabrication method, the devices performances also change significantly, e.g. the efficiency changes within 3.81–10.08% range. At that, a dye and the dye-based DSSC fabrication methods are chosen intuitively, by guess usually based on recent experience. The accumulated experimental data published in different sources can be used for unified theoretical analysis to recover the influence of both dye molecular structure and fabrication method on the DSSCs performances. This will help to predict the most promising sensitizers and choose scientifically grounded fabrication methods of the dye-based DSSCs. One of the possible scientifically grounded variants of investigation includes the use of electronic properties derived from QTAIM computations of dyes and their complexes with TiO2 nanoparticles. Thus, in the current work, a theoretical study of BTD unit containing sensitizers whose generalized structure is shown in Scheme 1 and its substituents are given in Electronic Annex (Tables S1–S4) has been performed. In refs (Table 1) we found UV/vis absorption spectra of dyes, IPCE action spectra and DSSCs photovoltaic performances measured under Standard Test Condition (namely, Ps = 100 mW cm−2, temperature is 25 °C, AM 1.5 light). Since some sensitizers (e.g. WS-2, WS-9, DOBT-I, DOBT-II, DOBT-III, etc.) were used for fabrication of various DSSCs differing in fabrication details, then among the devices based on one dye, we selected a device with the maximal efficiency and considered its photovoltaic performances given in Table 1 and designated as Jsc(best), Voc(best), FF(best), η(best), fabrication details of the devices are given in Electronic Annex (Table S5). Fabrication details of the studied devices are the following: electrolyte composed of 0.02–0.07 M I2, 0.05–0.1 M LiI, 0.5–0.75 M TBP (tert-butyl pyridine) in different solvents. The following conditions vary: (1) electrolyte solvent can be either dehydrated acetonitrile, or acetonitrile/valeronitrile (v/v, 85:15) solvents mixture, or 3-methoxypropionitrile; (2) in most cases either DMPII (0.25–0.6 M), or PMII (0.6 M), or (0.6–1 M), or BMII are used as additives in the electrolyte; (3) TiO2 photoelectrode immersion in (0.2–0.5 mM) dye bath either in CH2Cl2, or CHCl3, or CH2Cl2/EtOH, or THF/EtOH (v/v, 2:1), or t-butanol/CHCl3 (v:v, 1:1), or CH3CH2OH-CHCl3 (v/v, 7:3); (4) immersion time is 8–24 h; (5) co-adsorbents either can be absent or can be 0.5–80 mM CDCA, or 1–80 mM DCA; (6) in some cases 0.1 M GuNCS is present in the electrolyte (this is a component of Z960 electrolyte); (7) the thickness of TiO2 scattering (0–13 μm) and transparent nano-layers (4–8 μm) as well as the size of TiO2 nano-particles of the layers vary. 2. Materials and methods 2.1. Modelling of dyes adsorbed on TiO2 nano-particles Spherical anatase nanoparticles of TiO2 of various sizes from 20 to 40 nm were modeled by packing anatase unit cells (Howard et al, 1991) 476

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R are given in the Table S1 and S2; R’ – = – π – A’ are given in Table S3, Y1, Y2= H, F, OC8H17 Scheme 1. General structure of the BTD-unit based dyes considered in the work. R are given in the Tables S1 and S2; R′ – = – π – A′ are given in Tables S3, Y1, Y2 = H, F, OC8H17.

along a, b, c axes and determining the inscribed sphere in the resulting nano-rode. Then complexes of dyes with nano-particles have been modelled using algorithm MOPS (Grishina et al., 2002; Shchelokov et al., 2018) with implicit accounting of the solvent used in the procedure of the photoelectrode immersion in dye bath (see Electronic Annex, Table S5). MOPS is based on the assumption that any structural changes mainly arise as a result of molecular motion. Then the directions of molecular motion can be determined from the equation Potemkin et al. (2002):

approach estimating the energy (Eij) of intermolecular atom-atomic interactions including electrostatic and van der Waals energies (Potemkin et al, 2009) with the estimation of the probabilities (pij) of contacts.

GFL = L

where Uij is the depth of the potential, Rije is the equilibrium distance equal to the sum of van der Waals radii; qi and qj are the charges of the atoms i and j computed with the modified Full Equalization of Orbital Electronegativities, ε0 is the vacuum permittivity, pij is the probability of the intermolecular atom-atomic interaction, nij is a coordination number of ith atom with respect to the jth atom and Si is the solventaccessible area of the ith atom. “TiO2 nanoparticle – dye” complexes simulation accounting a solvent used for the dye bath (Electronic Annex, Table S5) showed that two types of structures are possible, the first of which has a carboxyl group oriented to the TiO2 surface (Fig. 1a), and the second is characterized by a dye aromatic system lying on the TiO2 nanoparticle (Fig. 1b). However, complexes shown in Fig. 1b are more stable. Their energy is 15–43 kJ/mol lower than the energy of complexes shown in Fig. 1a for the considered dataset. Moreover, complex shown in Fig. 1b explains the role of alkyl radicals of efficient dyes: they fill TiO2 cavities. Most carbons, nirtogens and hydrogens of the molecules interact with TiO2 surface. This should affect both IPCE action spectra and UV/ vis spectra of dye-adsorbed TiO2 thin films as compared to dye solution spectra.

N 1 N

EMERA =

Eij i=1 j> i

=

F - matrix of force constants (Hessian) which are defined as the E2 second derivative of the energy by the coordinate, e.g., 1xNy = x y 1 N element of the F-matrix showing the change in the energy of the system with the change in × coordinate of the 1st atom and change of y coordinate of the Nth atom, G - an inverse mass matrix, Λ and L - eigenvalues and eigenvectors of the matrix A = GF. Elements of diagonal Λ-matrix are squares of vibrational, rotational and translational frequencies. Each L-vector shows the direction of atomic motion during vibration/rotation/translation: To find the geometry of the most stable complex, MOPS includes the following steps: 1. Presupposes a geometry of the starting complex and minimizes its energy. 2. Calculates Hessian of potential energy for the complex, finds Λ and L of the matrix A = GF. 3. Moves the atoms of the complex along each of the modes, both in the positive and in the negative directions to reach the nearest maximum of the potential energy. 4. After overcoming the maximum, the potential energy of the complex is minimized in Cartesian coordinates. In this case, both the geometry of the complex and minimum of potential energy change.

Eij = pij

nij Si exp( Eij/ kT ) 1+

N exp( l =1

Eil/ kT )

2Uij

Rije Rij

6

+ Uij

Rije Rij

12

+

qi qj 4

0 Rij

pij

,

2.2. QTAIM electronic properties Electronic properties of dyes adsorbed on TiO2 thin film has been estimated using QTAIM suggested by Richard F. W. Bader (Bader, 1994). Electronic structure of molecular systems has been estimated using free-orbital quantum chemistry method AlteQ. Recently, it has been shown that AlteQ reproduces experimental 3D maps of the electron density of organic and inorganic compounds with good quality (Potemkin and Grishina, 2008, 2018a, 2018b; Salmina et al., 2013; Slepukhin et al., 2013; Grishina et al., 2016). This has been demonstrated by comparing experimental electron densities derived from low temperature, high resolution X-ray diffraction data with the calculated values. Along with the three-dimensional and two-dimensional electronic integral characteristics of molecules and atoms proposed by other authors, the new characteristics proposed in the current paper and given below have been implemented in “Electron properties calculation: Integration over atomic basins” software, available for online calculations at www.ChemoSophia.com web page (Potemkin and Grishina, 2008, 2018a, 2018b; Salmina et al., 2013; Slepukhin et al., 2013; Grishina et al., 2016).

If there is a minimum with less energy than the previously obtained at step 2, then the newly found complex is saved and used as the starting point. In this case, steps 2–4 are performed again for the newly found complex. If all newly discovered potential energy minima are higher than the minimum found at the previous cycle (number (n − 1)), then the last complex (namely, (n − 1)) is considered as the final search result. Only those vibrational modes which change dye conformation and orientation about a nano-particle have been accounted. Potential energy and Hessian of complexes have been computed using combined MM3-MERA force field with implicit solvent accounting (Grishina et al., 2002). MM3-MERA force field total energy of complexes equals the sum of MM3 total energy (EMM3) and MERA energy (EMERA):

Etotal = EMM 3 + EMERA MERA reproduces experimental heats of evaporation, enthalpy and entropy of formation, etc. (Grishina et al., 2002). It is a non-parametric 477

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Fig. 1. Possible complexes of 6ORK1 dye with a TiO2 anatase nano-particle in the conditions of the dye bath (acetonitrile/tert-butanol): (a) orientation of the carboxyl group to the TiO2 surface (Etotal = 250 939.44 kJ/mol); (b) dye aromatic system lying on the TiO2 nanoparticle (Etotal = 250 909.14 kJ/mol).

The following molecular characteristics have been computed: molecular volume (Vm), molecular isodensity surface area (Sm), the number of electrons of all considered atomic shells (Ne), the number of own electrons of atoms in their basins (Rom1), the number of electrons of the second-, third, forth-, fifth-, sixth-order overlaps in the atomic basins (correspondingly, Rom2, Rom3, Rom4, Rom5, Rom6), the positive and negative external surface areas (Spm, Snm), the sum of the isodensity surface areas of positively charged atoms multiplied by their charge, the sum of the isodensity surface areas of negatively charged atoms multiplied by their charge (SQpm and SQnm, respectively): N

N

Vm =

Vj; Sm = j =1

j =1

Sj (ext ) =

Nj (own) =

N 2 3 4);

= Nj (1

2); Rom3 =

Nj (1

Nj (1

2

2)

3);

= =

j=1

Rom5 =

Nj (1

Qj = Nj

2 3 4 5);

j=1 2 3 4 5 6);

Spm =

j=1

Snm =

Sj (ext ); jwithQj > 0

Sj (ext ); SQpA = jwithQj < 0

SQnA =

j

j

j

1 2 dV

2)

i dV

+ Nj (1 Nj (1

1 2 3 4 dV .

2 3)

2 3)

=

+ Nj (1 j

2 3 4)

1 2 3 dV

+ Nj (1 Nj (1

2 3 4 5)

+ ...

2 3 4)

..

Nj (total)

where dV is the instantaneous change in the volume, dS is the instantaneous change in the surface, j is electron density function of the jth atom, 1 2 , 1 2 3 , 1 2 3 4 , 1 2 3 4 5 , 1 2 3 4 5 6 are the electron density functions of the second, third, forth, fifth, sixth orders overlaps. The atomic electronic characteristics were taken to evaluate summary characteristics for each major atomic type observed in organic compounds. These are atoms-organogens (H, C, N, O, P, S) and halogens (F, Cl, Br, I). The set of electronic descriptors has been estimated:

N

Nj (1

j dV

j

i j

N

j=1

dS

Nj (neighbors ) =

N

Nj (1 j=1

Nj (1

Ej

Nj (total) = Nj (own) + Nj (neighbors )

j=1

j =1

Rom6 =

dV

Nj (total);

N

Nj (own); Rom2 =

Rom 4 =

j

N

Sj (ext ); Ne =

N

Rom1 =

Vj =

Sj (ext )·Qj ; jwithQj > 0

Sj (ext )· Qj ji withQj < 0

where N is the total number of atoms in the molecule, Vj is the volume of the jth atomic basin ( j ), Sj (ext ) is the isodensity surface area of the jth atom (Ej is the isodensity surface of the jth atom with electron density equal 0.001 a.u), Nj (total) is the total number of electrons of jth atom, Nj (own) is the number of own electrons of the jth atom in its basin, Nj (1 2) , Nj (1 2 3) , Nj (1 2 3 4) , Nj (1 2 3 4 5) , Nj (1 2 3 4 5 6) are the numbers of electrons of the second, third, forth, fifth, sixth orders overlaps in the jth atomic basin, Qj is the charge of the jth atomic basin, Nj – is atomic number of jth atom.

1) VA is the summary volume of atomic basins of A element (e.g. VH, VC, VN, VS, etc. are the summary volumes of H atoms, C atoms, N atoms, S atoms, etc. respectively in a molecule): NA

VA =

VAi, Ai = 1

where VAi is the volume of ith atom of A element (H, C, N, O, P, S, F, Cl, Br, I), NA is the total number of atoms of A element in the brutto478

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V. Potemkin, et al.

formulae of the molecule; NH, NC, NN, NS are the total numbers of H atoms, C atoms, N atoms, S atoms, etc. respectively);

SQnA =

2) SA is the summary isodensity surface area of atoms of A element (e.g. SH, SC, SN, SS, etc, are the summary isodensity surface areas of H atoms, C atoms, N atoms, S atoms, etc. respectively in a molecule):

10) SQpA is the sum of positively charged isodensity surface area multiplied by the charge of ith atomic basin of A element (e.g. SQpH, SQpC, SQpN, SQpS, etc.):

NA

SA =

S Ai (ext )· Q Ai . Ai andQ Ai < 0

SQpA =

SAi (ext ),

S Ai (ext )· Q Ai. Ai andQAi 0

Ai = 1

where S Ai (ext ) is the isodensity surface area of the ith atom of A element;

In addition, the ratios of the above descriptors to molecular descriptors and atomic type descriptors were calculated. E.g.:

3) RoA is the summary number of electrons of atomic basins of A element (e.g. RoH, RoC, RoN, RoS):

Ro6H _Vm =

Ro6S _SS =

NA

RoA =

NAi (total) Ai = 1

3.1. Spectral properties Absorption spectral properties determine dye applicability as a sensitizer in DSSCs. The properties of dyes in solution and on TiO2 photoelectrode differ (Zhu et al., 2011). To investigate the changes, the theoretical study of spectral characteristics of dye solutions, dye-adsorbed TiO2 thin films and IPCE action spectra has been performed. We found that surface mostly determines changes of spectral properties of dye-adsorbed TiO2 thin films and IPCE action spectra as compared to dye solutions. In other words, maximal peak wavelength of dye-adsorbed TiO2 thin film λ1(TiO2) is related to the λ1(Sol.) of dye solution and to the nitrogen isodensity surface area – SN (SN = SnN) (Fig. 2a), while the second peak wavelength of dye-adsorbed TiO2 thin film λ2(TiO2) is well related to the λ2(Sol.) of dye solution and external surface area of negatively charged carbon atoms – SnC (Fig. 2b). The following equations were found:

4) Ro1A is the summary number of own electrons in the atomic basins of atoms of A element (e.g. Ro1H, Ro1C, Ro1N, Ro1S, etc.): NA

NAi (own) Ai = 1

5) Ro2A is the summary numbers of electrons of the second order overlaps in the atomic basins of A element (e.g. Ro2H, Ro2C, Ro2N, Ro2S, etc.): NA

Ro2A =

N Ai (1

2)

Ai = 1

Analogously, Ro3A, Ro4A, Ro5A, Ro6A are the summary numbers of electrons of the third-, forth-, fifth-, sixth-orders overlaps of atoms of A element. 6) RoneiA is the summary number of electrons of neighbors in the atomic basins of A element (e.g. RoneiH, RoneiC, RoneiN, RoneiS, etc.):

N Ai (neighbors ) Ai = 1

7) RoonA is the summary number of electrons of atoms of A element in the basins of neighbors (e.g. RoonH, RoonC, RoonN, RoonS, etc.) NA

RoonA =

N Ai (in the basins of neighbors ) Ai = 1

where N Ai (in the basins of neighbors ) is the number of electrons of the ith atom of A element in the basins of neighbors. 8) SpA and SnA are the summary positively and negatively charged isodensity surface areas (e.g. SpH, SpC, SpN, SpS, etc are positively charged areas, SnH, SnC, SnN, SnS are negatively charged areas of H, C, N, S, etc. atoms respectively).

SpA =

S Ai (ext ) SnA = Ai andQ Ai > 0

1 (TiO2 )

=

18 + 0.874 1 (Sol. ) + 1.70SN

2 (TiO2)

= 151 + 0.568 1 (Sol. ) + 0.136SnC

Correlation coefficients (R), R square (R2), standard errors of estimate (St.Err) are given in Fig. 2 captions. Both equations are quite explicable: the first peak wavelength is most likely associated with n → π* electron transitions peaks which are determined by presence of nitrogens, while the second peak wavelength is most likely π → π* electron transitions which are determined by aromatic carbons. Consequently, TiO2 thin film affects the dye nitrogen and carbon electron excitation and flowing. The electrons of negatively charged nitrogens and carbons of a dye adsorbed on TiO2 nano-layer become less associated with nuclei and consequently they are simply removable under light photon harvesting. It contributes the electron flowing in nanoporous TiO2 and explain the increasing of λ1(TiO2) and λ2(TiO2) wavelengths with the increase of the dye negatively charged surface areas (SN = SnN and SnC). Therefore, the higher negatively charged isodensity surfaces of the dye nitrogens and carbons, the easier excitation of a dye on TiO2 nano-film, the greater red shifts of the λ1 and λ2 peaks in the dye-adsorbed TiO2 film spectrum as compared to the dye solution spectrum. Considering IPCE action spectra, we found that minimal onset wavelength of the spectra appears in 300–350 nm region and weakly related to the minimal absorption peak wavelengths determined for dye solution and for dye adsorbed on TiO2 thin film – λ2(Sol.) and λ2(TiO2). It can be explained by the fact that DSSCs are comprised of various components absorbing light in near ultra-violet region, e.g. I2 and I3(Afrooz and Dehghani, 2015), which determine DSSCs action in the region. However, the maximal onset wavelength of the IPCE action spectra (λonset(IPCE)) depends on dye absorption properties. The

NA

RoneiA =

Ro6S SH , SH _VH = . SS VH

3. Results and discussion

where N Ai (total) is the number of electrons of the ith atomic basin of A element including own electrons N Ai (own) of the atom and electrons of its neighbors N Ai (neighbors ) ;

Ro1A =

SQpH Ro6H , SQpH _Sm = , Vm Sm

S Ai (ext ) Ai andQ Ai < 0

where QAi is the charge of the ith atomic basin of A element. 9) SQnA is the sum of negatively charged isodensity surface area multiplied by the charge of ith atomic basin of A element (e.g. SQnH, SQnC, SQnN, SQnS, etc.): 479

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Fig. 2. Observed and predicted first (a) and second (b) peak wavelengths of dye-adsorbed TiO2 thin film. (a) 53 points, R = 0.89, R2 = 0.79, St.Err. = 19 nm, (b) 38 points, R = 0.92, R2 = 0.85, St.Err. = 11 nm.

Fig. 3. The relation of the maximal onset wavelength of the IPCE action spectra to dye-adsorbed TiO2 thin film maximal peak wavelength and to the rate of the hydrogen surface in the total molecular surface (SQpH_Sm) of the dyes (47 points, R = 0.83, R2 = 0.69, St.err. = 31 nm).

relation of the λonset(IPCE) value to λ1(TiO2) value and to the hydrogens isodensity surface area fraction in the total molecular isodensity surface area (SQpH_Sm) of dyes was found (Fig. 3): onset (IPCE )

= 338 + 1.3 1 (TiO2)

on the device performances, the representative set of dyes with the photovoltaic characteristics measured using absolutely the same DSSCs fabrication details is needed. We collected the set of 17 BTD derivatives whose DSSCs were fabricated using almost the same scheme and ingredients shown in Table 2. The selected data are designated as Jsc(Sel.), Voc(Sel.), FF(Sel.), η(Sel.). Briefly, all the devices named standard DSSCs are comprised of 0.1 M LiI, 0.05 M I2, 0.6 M DMPII, and 0.5 M TBP in dehydrated acetonitrile, the TiO2 photoelectrode was soaked in the 0.3 mM dye solutions. We found Jsc(Sel.) is related to the difference in the charges of the nitrogens N2 and N5 of the BTD system (Fig. 4a) of dyes adsorbed on TiO2 nano-particle:

1.30·10 4SQpH _Sm

The higher λ1(TiO2) and the smaller SQpH_Sm, the broader IPCE action spectra of the dye-based DSSC fabricated using details described in the item 2.1. Spectral properties and computed properties are given in Electronic Annex (Table S5). 3.2. Photovoltaic performances obtained for the DSSCs fabricated using the same details and named standard DSSCs

Jsc (Sel. ) = 13.87 + 410·(QN 2

To evaluate the influence of details of the dye electronic structure

QN 5).

(1)

We can suppose that R-radicals and π-block compete with each 480

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Table 2 Selected DSSCs fabricated using the same fabrication details, their performances and computed QTAIM properties influencing photovoltaics (charges of the N2 and N5 basins (QN2 and QN5) of the BTD system, the ratio of sulfur sixth-order electron overlaps to the sulfur isodensity surface area (Ro6S_SS). Reference

Name

Jsc(Sel.), mA/ cm2

Voc(Sel.) , V

FF(Sel.)

η(Sel.), %

QN2-QN5, a.u.(e)

1/Ro6S_SS, a.u. (bohr2/e)

Jsc(Sel. and Pred.Eq. (2)) mA/cm2

Wu et al. (2012a); Kang et al. (2014); Wu et al. (2012b); Chai et al. (2015); Zhu et al. (2011) Wu et al. (2012a); Wu et al. (2012a); Lee et al. (2011) Seo et al. (2012) Seo et al. (2012) Mao et al. (2015) Chen et al. (2013) Chen et al. (2013) Chen et al. (2013) Zhang et al. (2014) Zhang et al. (2014) Zhang et al. (2014) Chai et al. (2015) Chai et al. (2015) Chai et al. (2015) Yang et al. (2014)

WS-2

11.8

0.589

0.73

5.07

−0.006291

17241.3793

12.0

WS-6 WS-11 HKK-BTZ1 HKK-CM4 HKK-CM5 CA-III DOBT-I DOBT-II DOBT-III DOBT-IV DOBT-V DOBT-VI WS-37 WS-38 WS-51 JH-307

14.3 10.4 11.9 12.2 10.8 13.62 6.54 9.14 10.2 15.05 16.88 15.37 16.23 12.32 19.69 14.71

0.639 0.629 0.54 0.58 0.55 0.62 0.829 0.818 0.784 0.686 0.662 0.629 0.692 0.699 0.7 0.645

0.75 0.71 0.59 0.68 0.66 0.67 0.74 0.73 0.73 0.6453 0.6403 0.6402 0.716 0.727 0.731 0.673

6.85 4.64 3.81 4.82 3.93 5.67 4.44 5.31 6.89 6.66 7.16 6.19 8.04 6.27 10.08 6.4

−0.00058 −0.004234 −0.00241 −0.005819 −0.004247 −0.006318 −0.001695 −0.007731 −0.014227 0.006858 0.004897 0.002511 0.001288 −0.001831 0.005001 −0.000597

17543.8596 11494.2529 11363.6364 18518.5185 19230.7692 16129.0323 142857.143 142857.143 15873.0159 14492.7536 10416.6667 10416.6667 14925.3731 13333.3333 11764.7059 11235.9551

14.0 12.9 13.6 12.1 12.6 12.0 8.9 6.8 9.3 16.7 16.2 15.3 14.7 13.7 16.1 14.2

other. This criterion shows how simple the delocalization of electrons in the system is. In this case, the symmetric BTD system plays the role of an indicator: the larger the charge of N2 with respect to the charge of N5, the easier the transfer of electrons from the R-radical to the π-block, the carboxyl group and, therefore, to a TiO2 thin film. It influences positively on the Jsc(Sel.) value. Since all considered dyes contain at least 1 sulfur atom in BTD, many dyes contain sulfur atoms in pi-block and in R-radical as well, it is logical that sulfur atoms of the dyes play important role in the work of the DSSCs influencing mostly Jsc. The ratio of sulfur sixth-order electron overlaps to the sulfur isodensity surface area (Ro6S_SS) improves the quality of the Jsc(Sel.) prognosis. The linear relationship Jsc(Sel.) to both factors is shown in Fig. 4b. The role of the sulfur can be explained by the fact that sulfur possesses 3d empty level and exciting electrons can occupy the level. The most excitable electrons are electrons which are less attracted to the nuclei. Consequently, they can be observed in the high order overlaps. Therefore, it is logical that electrons of the sixth-order overlaps in the basins of sulfur atoms provide greater Jsc(Sel.). We found that Jsc(Sel.) is

related both to the Ro6S_SS and to the difference of the basin charges of the N2 and N5 nitrogen atoms (Scheme 1) of the BTD system:

Jsc (Sel. ) = 14.84 + 349·(QN 2

QN 5)

3.8·10 5 . Ro6S _SS

(2)

The consideration of Voc(Sel.) value showed that it is well related to the ratio of the summary isodensity surface area of hydrogens to the summary volume of hydrogens (SH_VH):

Voc (Sel. ) = 2.33

1.37· SH _VH .

(3)

The smaller SH_VH values are typical of compounds with long alkylic chains which are very important for dye adsorption on TiO2. FF(Sel.) was shown to be weakly related to the dye electronic properties. 3.3. The influence of device fabrication details on DSSCs photovoltaic performances We used (2) and (3) eqs to predict Jsc(Sel.) and Voc(Sel.) properties

Fig. 4. The relation of short circuit photocurrent density of standard DSSCs to electronic properties of dyes: (a) the difference in the charges of the nitrogens N2 and N5 of the BTD system (17 points, R = 0.69, R2 = 0.48, St.err. = 2.4); (b) the ratio of sulfur sixth-order electron overlaps to the sulfur isodensity surface area as well (17 points, R = 0.844, R2 = 0.71, St. err. = 1.8). 481

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Fig. 5. The influence of device fabrication details on short circuit photocurrent density: * – DSSCs whose fabrication details influence negatively on Jsc, ● – standard DSSCs (DSSCs are comprised of 0.1 M LiI, 0.05 M I2, 0.6 M DMPII, and 0.5 M TBP in dehydrated acetonitrile, the TiO2 photoelectrode was soaked in the 0.3 mM dye solutions), ○ – DSSCs whose fabrication details are slightly different from standard DSSCs (e.g. the time of the electrode soaking in the dye bath differs from 24 h; DCA presence in electrolyte, the use of acetonitrile or acetonitrile:valeronitrile solvent for the dye bath), Δ – DSSCs whose fabrication details influence positively on Jsc.

that one would expect if the DSSCs were made similarly to standard DSSCs described in the previous item 3.2. Computed properties are given in Electronic Annex (Table S5). Consideration of the predicted Jsc(Sel. and Pred.) and its relation to the observed Jsc(best) value showed the dependency demonstrated in Fig. 5. Thus, the device fabrication details influence too seriously on Jsc. We analyzed which fabrication details influence positively on the Jsc and which of them decrease it when compared to the standard DSSCs. All dyes whose devices were made using the following fabrication details demonstrate much smaller Jsc than predicted value for standard DSSCs including standard error of estimate ΔJsc (see Electronic Annex Table S5): Jsc (best) < Jsc(Sel. and Pred.) ± Δ Jsc(Sel. and Pred.)

S5): Jsc (best) > Jsc(Sel. and Pred.) ± Δ Jsc(Sel. and Pred.) 1) Inclusion of CDCA as the coadsorbent increases Jsc, at that the CDCA concentration should be at least 10 mM and higher. 20 mM, 30 mM, 40 mM are very good in all considered cases – DOBT-I, DOBT-II, DOBT-III, JK-68. Smaller concentration (2 mM, 0.5 mM applied for 1, DX2, DX3 dyes) almost does not increase Jsc of the dye-based devices. 2) Binary alcohols containing solvents (CHCl3:C2H5OH, acetonitrile:CH3OH, acetonitrile:tBuOH) which are used for the photoelectrode immersion in the dye solution influence positively. But recommending the solvent for practical aims, a researcher should take into account a dye solubility in the binary solvents. 3) GuNCS has a positive effect on the performances.

1) No additives DMPII, DMII, BMII, PMII (S3, K-2, K-3, DX2, DX3); 2) The time of TiO2-covered photoelectrode immersion in the dye solution is much less than 24 h (H11, H12, H13 – 8 h, 1 dye – 5 h, C321 – 6 h, DX2, DX3- overnight). For most compounds, 12 h is enough to achieve sufficient adhesion providing the computed Jsc(Sel. and Pred.) value, but in some cases compounds need longer time for thermodynamically stable adhesion on the photoelectrode. 3) 3-Methoxypropionitrile (DX2, DX3 dyes), chlorobenzene (1 dye) and THF (G1, G2 dyes) used as solvents for the dye bath of the photoelectrode. The solvents do not provide sufficient adhesion of the dyes on the photoelectrode. 4) Insufficient concentration of I2 – 0.03 M and smaller (G1, G2, H11, H12, H13) 5) Insufficient dye concentration equal to 0.2 mM or smaller (G1, G2) in alcohols free THF or acetonitrile solvents. Mostly the 0.3 mM dye solution should be used for the better Jsc in the case of use of the alcohols free baths. Though, some devices made using immersion of the photoelectrode in the 0.2 mM dye solution in alcoholic solvents (EtOH, MeOH, acetonitrile-tBuOH) gave Jsc(best) comparable to the predicted Jsc(Sel.) (RK1, RK2, 6RK1, 6ORK1, RKF)

Not sufficient influence or not established (see Electronic Annex Table S5): Jsc (best) ≈ Jsc(Sel. and Pred.) ± Δ Jsc(Sel. and Pred.) 1) At least, DCA even in high concentration (80 mM) either dissonantly influence on the Jsc (in some cases, increasing its value and in other decreasing it) or does not provide significant Jsc increase to overcome the influence of other negative factors. In the case of HKKBTZ1, HKK-BTZ3, HKK-CM5 dyes, Jsc(best) almost equals Jsc(Sel. and Pred.). In the case of HKK-BTZ2, HKK-CM4, BzTMCA (DCA – 1 mM) Jsc(Sel. and Pred.) > Jsc (best), while in the case of HKK-BTZ4, WS9, WS-23, BzTCA (DCA – 1 mM) dyes, Jsc(Sel. and Pred.) < Jsc (best). Probably, DCA provides dye adhesion on TiO2 film but it does not seriously affects Jsc when compared to the CDCA. 2) Use of acetonitrile or binary acetonitrile:valeronitrile solvent (different rates 1:1 or 85:15, v/v) for the dye bath of the photoelectrode. The consideration of the predicted Voc(Sel.) for the whole dataset of compounds showed that fabrication details less seriously influence on the Voc as compared to the Jsc and much significantly determined by structural features of the dyes. We found that observed Voc of the compound 1 is seriously deviated from the predicted Voc value. As it

Therefore, these device fabrication features can decrease Jsc as compared to the expected Jsc value for the standard DSSCs. The following details influence positively on Jsc as compared to the fabrication details of the standard DSSCs (see Electronic Annex Table 482

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Fig. 6. Open circuit photovoltage Voc and the ratio of the summary isodensity surface area to the summary volume of hydrogens (66 points, R = 0.67, R2 = 0.45, St.Err. = 0.064 V).

was shown above in the Jsc study, the photoelectrode was kept in chlorobenzene dye bath of compound 1 for 4 h. The time is not enough for good dye adsorption on TiO2-nano layer and chlorobenzene is not the best solvent for adhesion because this compound is well soluble in chlorobenzene which prevents its efficient adhesion on TiO2 surface. We obtained that the observed Voc(best) is well related to the Voc(Sel.) predicted using Eq. (3). The Fig. 6 shows that computed Voc values are observed within St.Err. of Voc(best) and SH_VH of dyes is good electronic property to predict Voc of devices. Analysis of the SH_VH of the whole considered dataset of 66 compounds showed that it is strictly determined by presence of alkylic chains. The greater SH_VH and consequently the smaller Voc are observed either for compounds without long alkylic chains or for compounds with unfolded and straight alkylic chains (Fig. 7a,b). The smaller SH_VH (1.00–1.19 Å−1) and consequently the greater Voc are typical of compounds with long folded and curved alkylic radicals forming hydrophobic intramolecular interactions with neighboring alkylic or aromatic radicals Fig. 7(c,d). Such geometry implies cavities Fig. 7d which could be filled with the DSSCs electrolyte components. This feature induces the better stability of the TiO2-dye complex system enhancing Voc value. Since SH_VH varies mostly due to the change in the isodensity surface area of hydrogens, then it should be as smaller as it is possible to provide higher Voc.

substituted BTD unit (3 variants), 3) basis of R-radical (37 variants); 4) and 5) two substituents in R-radical (each including 8 variants). Genetic code is shown in Fig. 8, variants of structural fragments encoded by each gene are given in Electronic Annex (Tables S7-S10). Figs. 9 and 10 show examples of concrete structures with their genetic codes. Moreover, they demonstrate crossover and mutation procedures producing new children and their mutants from selected parents. Goodness of structures was estimated using product of desirability functions each depending on Voc and Jsc predicted values:

g = g1·g2 = exp( exp(a1 + b1 Voc ))·exp( exp(a2 + b2 Jsc )) where a1, b1, a2, b2 are coefficients found using boundary conditions, namely g1 = 0.9 at Voc = 0.9 V and g2 = 0.9 at Jsc = 25 mA/cm2. The method permitted to design promising dyes in real time. Designed compounds are given in Electronic Annex Table S6. We found that all predicted dyes are expected to absorb light at 410–700 nm and to be active on 300–800 nm wave length range in IPCE action spectra. Jsc for predicted compounds is expected to be within 14–25.8 mA/cm2 range, Voc within 0.858–1.029 V and device efficiency η at FF = 70% is expected to be within 8.6–16.3% (Table 3). To simplify synthesis procedure we also suggested modified structures (homologues of the predicted compounds) with good photovoltaics (Table 3). In some cases, such high values of Jsc equal 20.7–25.8 mA/cm2 have never been observed for tested BTD unit based dyes (observed maximal value Jsc = 19.69 mA/cm2). The same applies expected values of Voc equal 0.858–1.029 V which in all cases exceed maximal value Voc = 0.851 V observed for the considered dataset of DSSCs.

3.4. Design of new promising BTD unit containing dyes. Based on QTAIM electronic properties and found relationships we designed new promising BTD-unit containing dyes whose DSSCs fabricated using positively influencing details described in item 3.3 are expected to be much better than the dataset of considered DSSCs. The combinatorial set of radicals and substituents given in Electronic Annex (Tables S1–S4) permits to create 106 560 variants of molecules whose QTAIM computations could take years. Therefore, we applied DesPot method (Potemkin and Grishina, 2018b) based on genetic algorithm optimizing molecular goodness in the space of substituents. Genetic code of structures included 5 genes: 1) π-block (15 variants), 2)

4. Conclusion We highlight that aromatic system of BTD unit containing dyes lies on TiO2 nano-layer surface covering photoelectrode. This has been found using MOPS algorithm modelling dyes complexed to commonly used 20 nm TiO2 nano-particles. Furthermore, it helped to explain the change of optical properties of dyes in TiO2 thin films (namely, UV/vis absorption and IPCE spectra) as compared to dye solutions. Using AlteQ method for electron structure evaluation and QTAIM theory, we found 483

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Fig. 7. 3D common features of dyes whose DSSCs have low Voc (a,b) and good Voc (c,d): (a) DX-3 (Voc = 0.61 V, SH_VH = 1.27 Å−1); (b) HKK-BTZ2 (Voc = 0.54 V, SH_VH = 1.29 Å−1); (c) DOBT-I (Voc = 0.829 V, SH_VH = 1.10 Å−1) (d) WS-51 Voc = (0.700 V, SH_VH = 1.19 Å−1).

Fig. 8. 5 genes encoding structural fragments in a dye structure.

electronic properties of dyes determining the relation of UV/vis absorption and IPCE spectra observed for TiO2 thin films to absorption spectra of dye solutions. We found relations of Jsc and Voc photovoltaic performances to the charges of BTD atomic basins of nitrogens and to the ratio of hydrogen summary isodensity surface area and volume. Analysis of deviations of predicted and observed photovoltaic properties allowed to reveal device fabrication details influencing positively

and negatively on device efficiency. Found relationships have been used for design of new more promising dyes and better fabrication details of DSSCs with significantly higher photovoltaic properties as compared to the studied and published.

484

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Fig. 9. Crossover of two parents producing two children and genetic codes of dyes (structural fragments encoded by each gene are given in Electronic Annex (Tables S7–S10)).

Fig. 10. Mutation of children producing two mutants and genetic codes of dyes (structural fragments encoded by each gene are given in Electronic Annex (Tables S7–S10)).

485

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Table 3 New dyes (structures are given in Electronic Annex Table S6) with a BTD-unit, whose solar cells are predicted to be better than those found in the literature. Recommended fabrication details: 0.1 M LiI, 0.05 M I2, 0.6 M BMII (or DMII, DMPII, PMII), and 0.5 M TBP in dehydrated acetonitrile, the TiO2 photoelectrode soaked in the 0.3 mM dye solutions, at least 10 mM CDCA; the use of alcohols or binary alcohols containing solvents (CHCl3:C2H5OH, acetonitrile:CH3OH, acetonitrile:tBuOH) for the photoelectrode immersion (better 24 h) in the dye solution.

parent67 parent1 parent14 parent16 parent27 parent3 parent33 parent36 parent38 parent48 parent55 parent56 parent58 parent60 parent77 parent89 parent9 parent94 modified33 modified36 modified38 modified58 modified60 modified9 modified77 modified89

QN5 a.u. (e)

QN2 a.u.(e)

Ro6S_SS a.u. (e/ borh2)

SH_VH Å−1

Jsc(pred. Eq. (1)) mA/ cm2

Jsc(pred. Eq. (2)) mA/ cm2

Voc(pred. Eq. (3)) V

η(expected at FF = 70%), %

−0.0922 −0.0962 −0.0907 −0.0938 −0.0962 −0.0890 −0.0893 −0.0765 −0.0931 −0.0940 −0.0922 −0.0833 −0.0956 −0.0789 −0.0948 −0.0822 −0.0881 −0.0925 −0.0942 −0.0778 −0.0943 −0.0953 −0.0799 −0.0932 −0.0903 −0.0806

−0.0831 −0.0831 −0.0736 −0.0647 −0.0680 −0.0822 −0.0816 −0.0720 −0.0864 −0.0756 −0.0753 −0.0770 −0.0696 −0.0716 −0.0842 −0.0782 −0.0833 −0.0921 −0.0832 −0.0641 −0.0877 −0.0643 −0.0730 −0.0820 −0.0876 −0.0778

0.000181 0.000202 0.000271 0.000205 0.000198 0.000204 0.000213 0.000071 0.000155 0.000216 0.000258 0.000143 0.000216 0.000080 0.000222 0.000139 0.000244 0.000384 0.000210 0.000071 0.000117 0.000223 0.000080 0.000211 0.000213 0.000139

1.071 1.008 1.015 1.060 1.005 0.950 1.074 1.010 1.070 1.059 1.038 1.060 1.035 1.061 1.050 1.009 1.034 1.061 1.066 1.037 1.082 1.024 1.075 1.061 0.988 0.987

17.6 19.3 20.9 25.8 25.4 16.7 17.0 15.7 16.6 21.4 20.8 16.4 24.5 16.9 18.2 15.5 15.8 14.0 18.4 19.3 16.5 26.6 16.7 18.4 15.0 15.1

17.8 19.2 20.7 24.8 24.5 17.0 17.4 15.9 16.9 21.1 20.6 16.8 23.7 16.9 18.4 16.0 16.3 14.9 18.5 19.0 16.8 25.5 16.8 18.6 15.6 15.6

0.863 0.948 0.939 0.877 0.953 1.029 0.858 0.946 0.864 0.880 0.908 0.878 0.912 0.877 0.891 0.947 0.914 0.876 0.870 0.909 0.848 0.927 0.858 0.876 0.976 0.978

10.6 12.7 13.6 15.2 16.3 12.0 10.2 10.4 10.0 13.0 13.1 10.1 15.1 10.4 11.4 10.3 10.1 8.6 11.2 12.3 9.8 17.2 10.0 11.3 10.2 10.3

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