Spectroscopic Behaviour of Copper(II) Complexes Containing 2-Hydroxyphenones

Theoretical investigations by density functional theory (DFT) and time-dependent DFT (TD-DFT) methods shed light on how the type of ligand or attached groups influence the electronic structure, absorption spectrum, electron excitation, and intramolecular and interfacial electron transfer of the Cu(II) complexes under study. The findings provide new insight into the designing and screening of high-performance dyes for dye-sensitized solar cells (DSSCs).


Introduction
Copper(II/I) redox shuttles and copper dyes have received much interest as redox couples and dye sensitizers, respectively, for dye-sensitized solar cells (DSSCs) applications in recent years [1]. These first examples of full-copper solar cells, using copper(I) dyes with a copper(II/I) redox shuttle [2,3], create a new path for cheap and environmentally friendly DSSCs. Especially 4-coordinated copper(I) complexes, containing polypyridyl ligands, showed promising properties as dyes in DSSC [4][5][6][7].
Theoretical calculations using density functional theory are a handy tool to predict the UV-vis properties of both organic (for example LEG4 [8] and phenothiazine based dyes [9]) and metal-containing dyes. DFT calculations are reported for different transition metal complexes suitable to be used as dyes in DSSC, for example the well-known experimentally efficient Zn-porphyrin based sensitizer YD2-o-C8 [10], the well-known N3 ruthenium(II) sensitizer [5], and copper(II) complexes containing bipyridine-and phenanthroline-based ligands [1]. During such theoretical studies, UV/vis spectra are computed [11,12], absorbance maxima in the solar range are identified, and the molecular orbitals (MOs) involved in excitations relating to the absorbance maxima identified. Knowledge of the MOs involved in excitations can identify the type of excitation such as metal-to-ligand chargetransfer (MLCT) [11,13,14], ligand-to-metal charge-transfer (LMCT), ILCT (intra-ligand charge transfer) [12], and ligand-to-ligand charge transfer (LLCT) bands [9]. DFT calculated properties to evaluate the dye performance in DSSCs, such as charge transfer characteristics, light harvesting efficiency (LHE), the excited-state lifetime (τ), driving force of electron injection (∆G inject ) and dye regeneration (∆G regenerate ), are often reported [5,11,[13][14][15][16][17]. DFT calculations can assist in the design of complexes with improved photo conversion. We recently reported on the experimental synthesis and electrochemical properties of a series of 4-coordinated copper(II) complexes containing 2-hydroxyphenones. Since 4-coordinated copper(I) complexes, containing polypyridyl ligands, showed promising properties as dye, in this contribution we focus on the UV-vis spectroscopic properties of 4-coordinated copper(II) complexes containing 2-hydroxyphenones (see Scheme 1). Results obtained by density functional theory (DFT) and time-dependent DFT (TD-DFT) methods are theoretically evaluated to provide a new insight into the designing and screening of high-performance dyes for DSSCs.

Results and Discussion
The Cu(II) complexes of this study are d 9 complexes of d-electron occupation ; see Figure 1 for a molecular orbital (MO) energy level diagram of Cu(HBP)2 (5) with the mainly d-based and ligand-based MO energy levels identified, showing the mainly d-based MOs. Since the HOMO is ligand-based and the LUMO copper-based, the maximum wavelength UV-vis excitation peak of Cu(HBP)2, (5), will be of ligand-to-metal charge-transfer (LMCT) character. Low energy UV-vis excitation peaks of Cu(HBP)2, (5), that do not involve the LUMO, will be ligand-to-ligand charge transfer (LLCT) character.

Experimental and Calculated UV-vis
Complexes (1)-(9) exhibit experimentally a large absorbance peak in the region 340-450 nm and a small peak in the range of 550-800 nm (see Figure 2a-c with data in Table  1). Since complexes (1)- (9) showed experimental absorption in the visible wavelength range, they could be considered as dyes in DSSC. Different DFT functionals and basis set combinations were used to identify the DFT method that best reproduced the experimental UV/vis absorbance maximum 401.0 nm of Cu(HBP)2 (5), the results are shown in Figure 3. The selected long range-corrected (LC) pure functionals, as well as some hybrid functionals overestimated the excitation energy (wavelength too low), while pure functionals (PW91, BP86, PBE) and asymptotically correct XC potentials (SAOP and LB94) overestimated the excitation energy. The B3LYP functional performed best, followed by PW6B95D3 and PBEh1PB. The B3LYP optimized ground state geometry were in good agreement with an available experimental crystal structure of (5) [18].

Results and Discussion
The Cu(II) complexes of this study are d 9 complexes of d-electron occupation Figure 1 for a molecular orbital (MO) energy level diagram of Cu(HBP) 2 (5) with the mainly d-based and ligand-based MO energy levels identified, showing the mainly d-based MOs. Since the HOMO is ligand-based and the LUMO copper-based, the maximum wavelength UV-vis excitation peak of Cu(HBP) 2 , (5), will be of ligand-to-metal charge-transfer (LMCT) character. Low energy UV-vis excitation peaks of Cu(HBP) 2 , (5), that do not involve the LUMO, will be ligand-to-ligand charge transfer (LLCT) character.

Experimental and Calculated UV-Vis
Complexes (1)-(9) exhibit experimentally a large absorbance peak in the region 340-450 nm and a small peak in the range of 550-800 nm (see Figure 2a-c with data in Table 1). Since complexes (1)- (9) showed experimental absorption in the visible wavelength range, they could be considered as dyes in DSSC. Different DFT functionals and basis set combinations were used to identify the DFT method that best reproduced the experimental UV/vis absorbance maximum 401.0 nm of Cu(HBP) 2 (5), the results are shown in Figure 3. The selected long range-corrected (LC) pure functionals, as well as some hybrid functionals overestimated the excitation energy (wavelength too low), while pure functionals (PW91, BP86, PBE) and asymptotically correct XC potentials (SAOP and LB94) overestimated the excitation energy. The B3LYP functional performed best, followed by PW6B95D3 and PBEh1PB. The B3LYP optimized ground state geometry were in good agreement with an available experimental crystal structure of (5) [18]. cillator strengths (f), as well as the experimental maximum wavelength (λmax) and maximum absorbance (λA,max) peaks.     The TDDFT simulated UV/vis spectra, obtained by selected computational methods (details of the DFT methods are provided in Section 3.1), are shown in Figure 2, with more detail of the B3LYP/6-311G(d,p)/def2-TZVPP method in Figure 4. There are 3 main bands in each of the calculated spectra, of which the indicated band 1 and band 2 correspond to the experimentally observed absorbance peaks in the regions 340-450 nm (band 2) and 550-800 nm (band 1). In the 340-450 nm (band 2) region, the calculated absorbance peaks generally consist of 2 closely overlapping peaks. The wavelength of the lowest energy oscillator in this region was used to be compared with the experimental wavelengths (Figure 3 and Table 1). The large experimental peaks of complexes (1)-(9) in the region 340-450 nm (band 2), are best reproduced by band 2 of the B3LYP/6-311G(d,p)/def2-TZVPP method with an average deviation (AD) from experiment of 2.4 nm. The PW6B95D3/CEP-121G and PBEh1PB/CEP-121G methods gave AD of band 2 values of complexes (1)-(9), from experiment values, of 6.3 and 9.1 nm, respectively. The M06/CEP-121G and M06/SDD TD-DFT methods, using the B3LYP/6-311G(d,p)/def2-TZVPP optimized geometry gave AD of band 2 values from experiment values of 9.2 and 9.8 nm, respectively. The PW6B95D3/CEP-121G and PBEh1PB/CEP-121G methods did not show any absorbance peak above 450 nm (band 1), while the B3LYP/6-311G(d,p)/def2-TZVPP method, as well as the M06/CEP-121G and M06/SDD TD-DFT methods, using the B3LYP/6-311G(d,p)/def2-TZVPP optimized geometries, did show the small experimentally observed band 1 peaks, though at a wavelength 150-200 nm lower than experimentally observed (see Figure 2). The B3LYP/6-311G(d,p)/def2-TZVPP results, the best agreement with the experiment, will thus be discussed in more detail. The B3LYP/6-311G(d,p)/def2-TZVPP calculated maximum absorption wavelengths (λA,max), oscillator strength (f), and energy are summarized in Table 1 for the main absorbance peaks calculated for (1)-(9).  Figure 3. Calculated absorbance maxima (nm on y-axis) in the region 320-620 nm using the indicated DFT method (x-axis), compared to the experimental absorbance maxima 401.0 nm of Cu(HBP) 2 (5), indicated in red. DFT methods in best agreement with experiment are shown in dark blue. The DFT methods used are indicated as functional/basis1/basis2 where functional is the DFT functional used, basis2 is the basis set used for Cu, and basis1 is the basis set used for C, H and O. If no basis2 is indicated, basis1 is also used for Cu. The five methods showing "B3LYP go" in brackets used the optimized B3LYP geometry in the TD-DFT calculation with the indicated method. For all the other methods, geometry optimization as well as TD-DFT calculations were done with the indicated method.
The main MOs involved the transition of the maximum absorbance peak, λA,max, of (5), are visualized is Figure 5 and summarized in Table 2 for molecules (1)- (9). The natural transition orbitals (NTOs) involved the main transitions of the λA,max peak of (5), are visualized in Figure 6. The NTO method provides a compact orbital representation of the orbitals involved in a transition from the electronic ground to the electronic excited state [19]. The NTO transition occurs from a small set of particle (occupied)-hole (unoccupied) pairs [20]. Both the MOs evaluation and the NTOs show than the large experimental peaks observed in the region 340-450 nm (Figure 2(aii)) that correspond to the calculated band 2 peaks (Figure 2, Table 1) in the same 340-450 nm range, are LLCT bands.

DSSC Application
The absorption ranges of the dyes (1)-(9) fall in the visible region, thus ensuring effective solar energy usage (see Figure 2). We therefore present and discuss theoretical calculated properties of (1)-(9), as needed for dyes in DSSC containing the (I 3 − /I − ) redox mediator and TiO 2 semiconductor. The B3LYP/6-311G(d,p)/def2-TZVPP calculated light harvesting efficiency (LHE), excited state lifetime (τ in ns), HOMO energies (E HOMO ), LUMO energies (E LUMO ), ∆G inject (eV) and ∆G regenerate (eV) values are tabulated in Table 3, with the HOMO and LUMO energies visualized in Figure 7. Table 4 gives the same calculated properties for dyes theoretically investigated as photochromic dyes for DSSC in literature [21][22][23][24] (see Figure 8 for the structures of the dyes).       Figure 8).  [17] sitizers for a next-generation dye-sensitized solar cell. However, since Kohn−Sham MOs involved in the main excitations are all symmetrical round copper ( Figure 5), the distance between the centroid of the hole and the electron after excitation will be small. Excitation would thus mainly lead to intramolecular electron recombination with low efficiency electron injection into the semiconductor [17]. Structural modifications (e.g., mixed ligand complexes) are needed before these complexes could qualify as dyes in the framework of DSSCs.

Relationships Involving Experimental UV-vis Peaks
From the experimental optic UV-vis data, the experimental optical energy gap (ΔEexp, optical) related to an experimental UV-vis peak can be calculated, using different approaches such as using λA,max, λonset or energy obtained from a Tauc plot, as illustrated in Figure 9a,b for molecule (5). The high intensity experimental peak (peak identified as band 2 in Figure  2a at 401 nm for (5)) was used to obtain ΔEexp, optical, A-max = 3.1 eV, ΔEexp, optical, onset = 2.6 eV and ΔEexp, optical, Tauc = 2.8 eV for (5). The results are different and depend on the selected approach. Similarly, the theoretically calculated energy gap depends on the DFT method used. When calculating the theoretical energy gap, the specific MOs involved in the theoretical transition (e.g., at 401.2 nm for (5)), which agree with the experimental UV-Vis peak (401 nm for (5)), need to be used [30]; namely 37.7% HOMO-1 to LUMO + 3 (Egap = 3.68 eV) and 36.4% HOMO to LUMO + 4 (Egap = 3.67 eV) transitions for (5) (see Figure 4). The average of the Egap of the main transitions involved in theoretically calculated peak (ΔEcalc,, A-max), relates to the experimentally calculated Egap of the same peak (ΔEexp, A-max) for molecules (1)- (7), as well as to the excitation energy of the λA,max peak (see Figure 10, data in Table 5). The obtained experimentally determined Egap and the DFT calculated Egap do not coincide with each other, but they show similar tendencies. HOMO and LUMO energies are of interest since they generally are involved in the lowest energy electronic transitions. The photo-induced electron transfer from the dye to the excited state of dye is followed by electron injection into the semiconductor surface. By comparing the computed E HOMO and E LUMO of the dyes with the potential of the CB of the TiO 2 semi-conductor, and with the potential of the most widely used electrolyte redox couple I − /I 3 − [25], respectively, the propelling force of electron injection (∆G inject ) and dye regeneration (∆G regenerate ) in DSSCs is evaluated [9]. More negative HOMO energies than the I − /I 3 − redox couple imply a fast regeneration of the oxidized dyes. More positive LUMO energies than the E CB of TiO 2 could ensure an effective injection of excited electrons [26]. The HOMO and LUMO energies of (1)-(9) are compared to the energy of the CB of TiO 2 and the redox potential of the (I 3 − /I − ) redox couple in Figure 7. The B3LYP/6-311G(d,p)/def2-TZVPP calculated HOMO-LUMO gaps of complexes (1)-(9) fluctuate in the range of 2.95-3.19 eV, as shown in Figure 7. The changes in the LUMO levels (within 0.46 eV) rather than the HOMO levels (within 0.25 eV) mainly cause the differences in energy gap. Specifically, complexes (6) and (7) have the maximal HOMO-LUMO gap of 3.19 eV, while complex (1) has the minimum value of 2.95 eV. Comparing the unsubstituted hydroxybenzophenone Cu complex (5) (gap = 3.09 eV), the largest difference in the gap of 0.10 eV is observed with (6) and (7), indicating that the addition of an electron donating ester substituent, increases the LUMO level and thus leads to a larger HOMO-LUMO gap for (6) and (7). The HOMO-LUMO gap decreases significantly (up to 0.14 eV for (1)) with addition of electron withdrawing halide substituent groups. With the solar energy maximum occurring near 500 nm, a lower energy gap is likely to result in high photocurrents in the DSSC. This suggests that lower energy gaps are more suitable as photosensitizers in the DSSCs [27,28]. The HOMO and LUMO levels of the Cu(II) complexes fit well with the CB of TiO 2 and the redox potential of the (I 3 − /I − ) electrolyte. Figure 7 shows the HOMOs are suitably lower than the redox potential of I − /I 3 − electrolyte (−4.8 eV) [5], which would be useful for the regeneration of the excited dyes; while the LUMOs are aptly higher than CB of TiO 2 (4.0 eV) [29], enabling the efficient electron injection into the semiconductor.
The visible and near UV regions are the most essential region for photon-to-current conversion to obtain information about the electronic transitions and its corresponding molecular orbital properties. The LHE of the dye sensitizer should be as high as possible to maximize the photocurrent response [21,28]. The oscillator strength of the dye associated with the wavelength corresponds to the peak absorbance through intramolecular charge transfer (ICT). A high f generally results in a higher LHE, while a small HOMO-LUMO energy gap increases the light-capturing capacity and improves the efficiency of the DSSCs. The f value of the dye with alkoxy groups ((7), Table 1) was higher than that reported for some other dyes (Table 4), which suggested that the LHE of complex (7) would also be greater compared to other dyes. The LHE should be as high as possible to maximize the short-circuit current density (J SC ) [22].
The Gibbs energy change for electron injection ∆G inject affects the electron injection rate and therefore the current density J SC in DSSCs. The ∆G inject values of all the dyes were favourable for injection into the TiO 2 (conduction band) CB edge. On the other hand, the redox levels of the electrolyte are higher than the ground state of the dye, leading to favourable ∆G reg for regeneration of dyes. The larger the absolute values of ∆G inject and ∆G reg , the greater will be the ease with which the charge transfers between the conduction band of the dye and the electrolyte [21].
These results indicate that the copper-based complexes (1)-(9) might be effective sensitizers for a next-generation dye-sensitized solar cell. However, since Kohn−Sham Mos involved in the main excitations are all symmetrical round copper ( Figure 5), the distance between the centroid of the hole and the electron after excitation will be small. Excitation would thus mainly lead to intramolecular electron recombination with low efficiency electron injection into the semiconductor [17]. Structural modifications (e.g., mixed ligand complexes) are needed before these complexes could qualify as dyes in the framework of DSSCs.

Relationships Involving Experimental UV-Vis Peaks
From the experimental optic UV-vis data, the experimental optical energy gap (∆E exp, optical ) related to an experimental UV-vis peak can be calculated, using different approaches such as using λ A,max , λ onset or energy obtained from a Tauc plot, as illustrated in Figure 9a,b for molecule (5). The high intensity experimental peak (peak identified as band 2 in Figure 2a at 401 nm for (5)) was used to obtain ∆E exp, optical, A-max = 3.1 eV, ∆E exp, optical, onset = 2.6 eV and ∆E exp, optical, Tauc = 2.8 eV for (5). The results are different and depend on the selected approach. Similarly, the theoretically calculated energy gap depends on the DFT method used. When calculating the theoretical energy gap, the specific Mos involved in the theoretical transition (e.g., at 401.2 nm for (5)), which agree with the experimental UV-Vis peak (401 nm for (5)), need to be used [30]; namely 37.7% HOMO-1 to LUMO + 3 (E gap = 3.68 eV) and 36.4% HOMO to LUMO + 4 (E gap = 3.67 eV) transitions for (5) (see Figure 4). The average of the E gap of the main transitions involved in theoretically calculated peak (∆E calc, A-max ), relates to the experimentally calculated E gap of the same peak (∆E exp, A-max ) for molecules (1)-(7), as well as to the excitation energy of the λ A,max peak (see Figure 10, data in Table 5). The obtained experimentally determined E gap and the DFT calculated E gap do not coincide with each other, but they show similar tendencies.      Figure 4 for (5)), (b) the excitation energy of the λA,max peak. (Data in Table 5)  Figure 4 for (5)), (b) the excitation energy of the λ A,max peak (Data in Table 5).

DFT Calculations
The molecules (1)-(9) were optimized using the density functional theory (DFT) program Gaussian 16 [32] and different DFT functionals and basis set combinations. The DFT methods used are indicated as functional/basis1/basis2 where functional is the DFT functional used, basis2 is the basis set used for Cu, and basis1 is the basis set used for C, H and O. If no basis2 is indicated, basis1 is also used for Cu. The five methods showing "B3LYP go" in brackets in Figure 3 used the optimized B3LYP geometry in the TD-DFT calculation with the indicated method. For all the other methods, geometry optimization as well as TD-DFT calculations were done with the indicated method. For example, the B3LYP/6-311G(d,p)/def2-TZVPP method uses the hybrid B3LYP functional [33,34], the triple-ζ 6-311G(d,p) basis set for the lighter atoms (C, H, Cl, F, O) and the def2-TZVPP basis set [35] for the core and valence electrons of Cu. The PW6B95D3/CEP-121G and PBEh1PB/CEP-121G methods use PW6B95D3 [36] and PBEh1PBE [37] functionals, re-spectively, both with the CEP-121G basis set [38][39][40] for all atoms. TD-DFT calculations were performed on molecules (1)-(9) [41][42][43], using the same level of theory as for the optimization, except when indicated that the B3LYP optimized geometries were used.
All calculations were performed in DMSO as implicit solvent, the experimental solvent used for the UV-vis spectra. The improved IEF-PCM solvation model, the integral equation formalism (IEF) version of the Polarizable Continuum Model (PCM), was used to model solvation effects [44,45]. The input coordinates for the compounds were constructed using Chemcraft [46].
From the TD-DFT results, the following properties related to DSSC were obtained or calculated: 1.
λ max with the corresponding calculated transition energy E (cm −1 ) and the calculated oscillator strength (f ) of the excited state; 2.
Using the equation below: τ (in s) = 1.499/(f E 2 ) (1) where E * dye is the oxidation potential of the excited dye (approximated by energy difference E dye − E λ max ), E dye is the oxidation potential of the dye (approximated by HOMO energy), E CB is the reduction potential of the conduction band edge (TiO 2 with E CB = −4.0 eV vs. vacuum or −0.5 eV vs. NHE [29] is used in this study), E λ max is the electronic vertical transition energy corresponding to λ max potential, and E electrolyte is the redox potential of the electrolyte (the I − /I 3 − redox couple is used in this study, with E I − /I − 3 = −4.8 eV vs. vacuum or 0.3 eV vs. NHE) [25].

Calculations Involving Experimental Data
From the experimental UV-vis, the experimental band gap energy can be calculated from the formula ∆E opt = hc/λ = 1240/λ, where the wavelength λ is obtained from (i) the maximum absorbance wavelength λ max , (ii) the λ onset or (iii) from a Tauc plot denoting the onset of absorption [49] (see Section 2.3). The Tauc plot of (αE p ) 2 versus E p is according to the following equation [50][51][52][53]: where α represents the absorption coefficient, K is a constant, E p is photon energy and E g is the band-gap energy. Values for α and E p are determined by: E p = hc/λ where A is the absorption (arbitrary units) and d is the sample thickness, which for a cuvette is 1 cm, h Planck's constant with hc = 1240 eV and λ representing the wavelength in nm. The band-gap energy, E g , was determined by linear extrapolation of absorption edges on the graph of (αE p ) 2 versus E p to the x-axis where y = 0.

Conclusions
The lowest energy excitation of the Cu(HBP) 2 complexes, involving a ligand-based MO and a metal based LUMO, are of LMCT character, while all other low energy excitations that do not involve the LUMO, will be LLCT bands. TDDFT results and properties related to DSSC (λ A,max , τ, LHE, ∆G inject and ∆G regenerate ) indicated that these Cu(HBP) 2 complexes show promising performance, and with structural modifications can be made suitable for applications in the next-generation DSSCs.