3.2. Electronic Structure
Electronic structure analysis gives the charge transfer characteristics. The energy level of HOMO, LUMO, and energy gaps (
) and electron density of the frontier MOs are the important parameter reflecting the electronic excitation and transition characteristics of the dyes, shown in
Table S1 and
Figure 2 and
Figure 3. As shown in
Figure 2, HOMO and LUMO belong to the π and
, respectively [
35]. For LS-385 and LS-386, the electron density of HOMO is distributed on the D-π-
-π part; the electron density of LUMO resides in the π-
-π-
part; and for LUMO+1, the electron density is the distribution on the
-π-
part; most of the electrons are in the acceptor; and for the HOMO-1, the electron is distributed throughout the molecule. LS-385 and LS-386 exhibit a similar electron density distribution. For LS-387, the LUMO distribution is not significantly different from the other two molecules, but HOMO energies have a good aggregation on the donor, indicating that LS-387 has a better push-pull effect.
The driving force for electron injection and oxidation dye regeneration can be evaluated by the energy levels. As shown in
Figure 3, the LUMO energy levels of three molecules are higher than the conduction band (CB) of TiO
2 [
] of −4.0 eV, which facilitates electron injection from the excited dyes to the TiO
2 electrode. The LUMO energy levels of LS-385, LS-386, and LS-387 are lower than that of the redox potential
/
(−4.60 eV [
36,
37]), which means that the electrolyte can release electrons into the oxidative dye. From
Table S1, the HOMO energies of the three molecules in vacuum can be arranged as LS-387 (−5.125 eV) > LS-386 (−5.564 eV) > LS-385 (−5.595 eV), it is probably because the N atom in LS-387 donor is effective in reducing the HOMO level. The LUMO energies are in following order: LS-387 (−2.789 eV) > LS-385 (−2.918 eV) > LS-386 (−2.962 eV), it can be concluded that both HOMO and LUMO of LS-387 are greater than for other molecules. Higher HOMO energy can result in higher electron donation capabilities, meaning that LS-387 has strong electronic donation capabilities. In solvent, the HOMO and LUMO of LS-385 and LS-386 do not show obvious changes compared with vacuum (see in
Figure 3). While for LS-387 in solvent, the HOMO is greater than that in vacuum, and the LUMO is less than that in vacuum.
The HOMO and LUMO energy levels after adsorption on titanium dioxide are shown in
Figure 3. The HOMO energy of LS-387/s and LS-387/s +
are −5.085 eV and −5.100 eV (see
Table S1), respectively. It is obvious that the HOMO has changed slightly before and after adsorption onto
. For LUMO, LS-387/s +
(−3.286 eV) is significantly higher than LS-387/s (−2.912 eV). A similar trend also occurs in the other two molecules. In addition, the energy gap also shows a downward trend compared with isolated molecules; their values are: LS-385/s +
(2.287 eV), LS-386/s +
(2.291 eV), and LS-387/s +
(1.814 eV).
The charge difference density (CDD) of the three molecules was used to study the charge transfer characteristics (see
Figure S1). The CDD map clearly shows the change of charge density between the ground state and the excited state during photo-excitation, [
38,
39], indicating the ICT direction. As shown in
Figure S1, the electron density is mainly distributed in BTZ units and acceptor, and the hole density is mainly distributed in donor, π-bridge, and BTZ, therefore, CI is from donor to acceptor.
Figure 4 shows the CDD of the dye and
complex model, which has a more obvious charge separation compared with the isolated dye molecules. As shown in
Figure 4, for LS-385/
and LS-386/
, the electron density is gradually transferred into
clusters with the increase of energy levels, and the hole density is gathered in the site of the donor. For LS-387/
, with the increase of the energy levels, the separation of electrons and holes become gradually obvious; for
it seems that the electrons tend to be distributed in
clusters on one site, while the hole distribution is on the molecule near the site of the donor, thus enhancing the ICT characteristics of LS-387.
3.3. Electronic Absorption Spectra
Based on the geometry optimization of the ground-state, the excited states of the three dyes and dyes/
were calculated based on TD-DFT/cam-B3lyp/6–31G(d) in vacuum and DMF solvent. As compared, a diffused basis set 6–31+G(d,p) was used to calculate
on the basis of optimization with the same basis set, and the values of
for LS-385, LS-386, LS-387, are 543.27 nm, 564.42 nm and 671.80 nm, respectively, which are greatly red-shifted in comparison with experiment (425 nm, 425 nm, and 475 nm). Therefore, the basis set 6–31G(d) was used in the following calculations due to the wide application and certain accuracy. As shown in
Table 2, the maximum wavelength (
) of the three molecules in vacuum can be arranged as follows: LS-387 (449.11 nm) > LS-386 (426.65 nm) > LS-385 (421.57 nm), and LS-387 has about 25 nm red-shift. In solvent, the
is in order: LS-387 (470.40 nm) > LS-386 (428.83 nm) ≈ LS-385 (428.47 nm), and LS-387 also has about 40 nm red-shift compared with LS-385 and LS-386, which is due to the fact that LS-387 has a smaller energy gap to exhibit a high molar extinction coefficient and produce more electrons under visible light. Meanwhile, the LS-387 also showed higher
in the experiment [
16].
As shown in
Figure 5a, the UV-Vis absorption spectra of the three dye molecules in vacuum and solvent cover the near-ultraviolet and visible regions, and they all have distinct double absorption peaks. The highest absorption peak is due to the first excited state (
), and its electronic transition is from HOMO to LUMO, showing better ICT characteristics. For LS-385 in vacuum and solvent, the lower absorption peak (located near 325 nm) is mainly attributed to the second excited state (
), and the corresponding electronic transition is from HOMO to LUMO + 1 (
f = 0.5094 and 0.4518 in vacuum and solvent, respectively). It can be seen from the similar charge distribution of LUMO and LUMO + 1 that the electron transfer pathway is similar to that of
. For LS-386 in solvent, the main absorption peak at 330 nm corresponds to the second excited state (
), it shows an electron transition from HOMO to LUMO + 1 (
f = 0.4001); and for LS-387 in vacuum and solvent, the second absorption peak (near 340 nm) corresponds to a transition from HOMO→LUMO + 1 in the S2 (
f = 0.4445 and 0.4431 in vacuum and solvent, respectively); similarly, the transition of this state is the same as
. In summary,
is mainly ICT derived from the
excited state.
Figure 5b shows the UV-Vis absorption spectra of three dyes after adsorbing on
cluster, and the absorption spectra of three dyes having red-shifted compared to isolated dyes. Moreover, the molar extinction coefficients of LS-386 and LS-387 have a marked increase of 7.64 ×
and 7.14 ×
, respectively. Therefore, the absorption spectrum of dyes after adsorption has obviously changed, which can increase the ICT and the electron transfers into
CB.
The analysis of natural bond orbitals (NBO) provides a deeper understanding of the optical excitation properties of dyes. As shown in
Table 3, the difference in charge (∆q, from
to
) of the three molecules at the donor group indicates that LS-387 and LS-386 have a strong electron-providing ability compared with LS-385. This is probably because oxygen atoms on the LS-385 donor have poor electron capacity. Compared with LS-385 and LS-386, the BTZ group of LS-387 sneaked into the electron collection of the receptor. Besides, ∆q on the acetylene bridge of LS-385 (−0.09), LS-386 (−0.08), and LS-387 (−0.086), provide an ICT channel. Also, the acceptor of ∆q shows the following: LS-387 (0.09) > LS-386 (0.08) ≈ LS-385 (0.08), which illustrates that LS-387 has a strong ability to accept electrons. As a result, LS-387 should stimulate more electron transfer in the optical excitation mechanism.
3.5. Analysis of Chemical Reaction Parameters
Another method for evaluating the charge transfer properties of sensitizers is the recombination energy [
35], and the Marcus theory gives the rate formula [
45]:
where
λ is the recombination energy,
T is the temperature, A is the electron coupling, and
is the Boltzmann constant.
Quantitative methods provide a feasible method for studying charge transport in organic material systems [
46] and for calculating hole and electron recombination energy (
and
), which can be calculated [
46]:
The above parameters can be obtained by optimizing the neutral molecular structure and the anion (cation) structure. As shown in
Table 4,
of the three molecules in vacuum can be arranged: LS-385 (0.25 eV) > LS-386 (0.20 eV) > LS-387 (0.18 eV); and
can be arranged in the order: LS-386 (0.42 eV) > LS-385 (0.37 eV) > LS-387 (0.33 eV).
Table 4 also shows the
and
in DMF solvent has a noticeable decrease, and LS-387 has a lower recombination energy in vacuum and solvent, which will produce better molecular charge transfer and thus better photoelectric performance.
Electrochemical parameters (such as chemical hardness h, electrophilic index
ω, electron accepting power
, and electron donating ability
) are important factors affecting the efficiency of photovoltaic cells. The relevant calculated data are in
Table 4. The parameter h represents the impedance for ICT [
47]. Low chemical hardness is characterized by low ICT resistance, which in turn increases the acceptability of electrons [
40]. Therefore, good dyes should have low h and higher
. As shown in
Table 4, LS-387 (h = 2.22 eV) has a lower chemical hardness compared with that of LS-385 (h = 2.37 eV) and LS-386 (h = 2.32 eV), and the h of three molecules is: vacuum > solvent, indicating that LS-387 has a smaller ICT resistance in solvent. Moreover, LS-387 in solvent has a higher electron accepting power (
= 7.36) than LS-385 (
= 6.41) and LS-386 (
= 6.56), which implies that LS-387 exhibits a higher electron withdrawing capacity through its receptor moiety. Taken the two parameters into account, it can be inferred that LS-387 will have higher ICT and PCE. The higher the electrophilic index (
ω), the higher the stability of the dye becomes. In solvent, LS-387 has a higher electrophilicity index (
ω = 9.27 eV) compared with that of LS-385 (
ω = 8.41 eV) and LS-386 (
ω = 8.57 eV), and the
ω of three dyes is solvent > vacuum, which indicate LS-387 has a higher energetic stability. In order to obtain a large electron supply capacity, the hope is that the molecule has a lower electron donating energy.
Table 4 shows that LS-387 in vacuum has a lower electron donating power (
= 5.93 eV) compared with that of LS-385 (
= 6.35 eV) and LS-386 (
= 6.46 eV); however, in solvent, the three dyes have a higher
compared with that in vacuum. Never the less, comprehensive consideration on the chemical reactivity parameters indicates that LS-387 in solvent has a better chemical reactivity parameter, resulting in a better photoelectric performance of LS-387 among the three dyes.
3.6. Performance of DSSCs Based on Dyes
The LHE is an important parameter to measure the performance of sensitizer and to evaluate
.
Table 5 shows LS-387 (0.9485) in vacuum has a higher LHE compared with LS-385 (0.9315) and LS-386 (0.8220). Moreover, in DMF solvent the LHE of them increases to different degrees. The higher LHE will lead to higher
, therefore, LS-387 will have better photoelectric conversion performance due to its higher LHE.
In addition, the influence of the electron injection efficiency of the excited state (
) on the
was evaluated. The
is closely related to the driving force of electron injection (
). The Marcus theory determines the electron transfer ability of an excited state dye into a semiconductor [
48,
49]:
where
is the rate constant (in
) of the electron injection from dye to
, h is the Planck constant,
is the Boltzmann constant,
is the electron injection free energy,
λ is the reorganization energy. |
| is the coupling constant between the reagent and the product potential curves. It can be concluded from the above equation that a larger |
| will increase
and result in faster electron injection. Hsu et al. have given the equation for
[
50]:
According to Koopmans approximation, the
is derived from [
51,
52]:
Preat’s theoretical method shows the calculation method of
[
53]:
Here
represents the oxidation potential of the dye in the excited state,
represents the reduction potential of
semiconductor [
54] (
= 4.0 eV) Thereunto
can also be expressed as:
where
represents the oxidation reduction potential of the ground state,
represents the energy of the ICT. Higher oxidation potentials can result in greater driving force for the injection.
As show in
Table 5, the
, the
, and |
| of LS-385, LS-386 and LS-387 were calculated. The oxidation potential (
) of the three dyes in vacuum is as follows: LS-387 (2.364 eV) < LS-386 (2.658 eV) ≈ LS-385 (2.654 eV), and in solvent is as follows: LS-387 (2.449 eV) < LS-386 (2.677 eV) < LS-385 (2.681 eV); so LS-387 has a lower value of
in vacuum and solvent. Lower
will result in easier photooxidation.
The value of
is negative, which means that dye excited states can easily inject electrons into
CB. As shown in
Table 5, the absolute value of the
of the three dyes in vacuum can be arranged in sequence: LS-387 (1.636 eV) > LS-385 (1.346 eV) > LS-386 (1.342 eV), and the
of the three molecules is higher than 0.2 eV, which also shows that the molecular excited states can smoothly inject electrons into the
CB. Moreover, the absolute value of
for LS-387 is much larger than LS-385 and LS-386. Therefore, LS-387 has the higher
;
Table 5 also lists the coupling constant (
) in vacuum and solvent, in which LS-387 has the higher
compared with LS-385 and LS-386. Therefore, LS-387 will produce a higher
and further improve efficiency.
The dye regeneration free energy (
) can be used to characterize the regeneration ability of dye molecules from
/
electrolyte; the higher the
drive, the better the regenerative capacity and electron transport capacity of the dye become.
can be calculated as the difference between the redox potential of
/
(
= −4.60 eV) [
55,
56] and
.
Table 5 shows the
of the three dyes can be arranged: LS−385 (0.995 eV) > LS−386 (0.964 eV) > LS−387 (0.525 eV); and dyes in the solvent follow the same sequence. The values of
of the three dyes in vacuum and solvent are higher than 0.5 eV, which means that the three dyes can finalize the regenerative process.
An important parameter to study charge transfer efficiency is the excited state lifetime (τ), which can be evaluated via the following equation:
where
E represents the excitation energy of the different electronic states (
) and f is the oscillator strength. Relevant data are in
Table 6. The τ of the three dyes are arranged in sequence: LS 386 (1.82 ns) < LS-385 (2.02 ns) < LS-387 (2.29 ns). Intuitive data shows that LS-387 maintains long-term stability in the cationic state.
The
represents the difference between the quasi-Fermi level (electrons in the titanium dioxide conduction band) and the redox potential (electrolyte) [
57]. Movement of the
after the dye adsorption on the semiconductor substrate directly affects the
, and the relationship between the movement of the
and adsorbed molecular characteristics can be written as [
31,
58]:
where
is the dipole moment component of the dye molecules perpendicular to the surface of
,
is the absorption concentration of the semiconductor surface, and
and
represent the dielectric constant and the organic monolayer in vacuum, respectively. The dyes with larger
and
will generate a larger
.
Figure 6a shows that for isolated dyes, the
(in Debye) of LS-387 (12.9878D) is the largest compared with LS-385 and LS-386; for dye/
9, the value of
should follow the sequence of LS-387 > LS-385 > LS-386 (see
Figure 6b). Therefore, the high
of LS-387 can be contributed to the larger
of LS-387, which is in good agreement with the experimental results [
16].
3.9. Molecular Design
By analyzing the photoelectric properties of the original dyes, we can obtain the conclusion that the parameters of LS-387 are superior to the others; as a result, LS-387 produces better PCE(
η = 5.61% [
16]). DFT provides a design strategy for controlling performance from the viewpoint of theory [
60,
61,
62]. Based on LS-387, we theoretically designed fifteen new dye molecules to improve the electro-optical performance. On the donor group, we symmetrically introduced to the electron donating substituents (–OH, –NH
2 and –OCH
3); on the molecule’s acceptor group, the electron-acceptors (–CF
3, –F and –CN). By introducing different groups, we reduced the molecular energy gap, which is conducive to a red-shift of the absorption spectrum; at the same time, the introduction of individual groups can improve the dye regeneration free energy to some extent, thus improving the regeneration efficiency (
) and
of the dyes. On LS-387, we defined five positions (
) to introduce electron groups (see
Figure 8). Also, in
and
, three donor groups were introduced, where the molecules are named: LS-387-X (X = 1A, 1B, 1C, 12A, 12B and 12C); and in the acceptor group(
,
, and
), we introduced three electron-acceptors, where the molecules are named: LS-387-Y (Y = 3D, 3E, 3F, 4D, 4E, 4F, 5D, 5E and 5F).
The molecules (LS-387-X and LS-387-Y) ground state were optimized in DMF solvent, and bond length and dihedral angle are listed in
Tables S4 and S5. As shown in
Table S4, the bond length (
to
) of LS-387-1A (1B and 1C) is not obviously changed compared with LS-387; However, the
of LS-387-12A (12B and 12C) is higher than LS-387. It seems that introducing into two of the same electron groups leads to larger bond length that can affect the stability of the molecules. In addition, in the acceptor group, the
and
of LS-387-3D (3E, 3F, 4D, 4E, 4F, 5D, 5E and 5F) is greater than LS-387, but the
is not obviously changed compared with LS-387. Therefore, the electronic groups introduced by the acceptors are also not conducive to improving the stability of the molecules. As shown in
Table S5, the dihedral angle (∠1) of LS-387-X (X = 1A, 1B, 1C, 12A, 12B and 12C) is not obviously changed compared to LS-387; for the dihedral angle ∠2, the LS-387-12C (−0.062) has a smaller value than LS-387, and the molecule is more planar in the acceptor site, which is beneficial to ICT. For LS-387-Y, due to the interatomic repulsive effect of the group, the increases of ∠1 and ∠2 will be different, and the ICT will have a negative effect.
Figure 9 shows the HOMO, LUMO energy level and the energy gap (∆G = |H − L|), and data are listed in
Table S6. The energy gap of LS-387-1B and LS-387-12B is 2.072 eV and 1.921 eV, and the higher HOMO energy level of LS-387-1B and LS-387-12B will result in a small gap (see
Figure 9a). Because a narrow energy gap is favorable to red-shift absorption, the smaller energy gap for LS-387-1B and LS-387-12B by introducing
will lead to a larger absorption peak. For acceptor designed molecules LS-387-Y, the LS-387-3D (1.676 eV), LS-387-4D (2.115 eV), and LS-387-5D (2.128 eV) have a lower gap (see
Figure 9b), which is due to lower LUMO level for LS-387-Y (3D, 4D and 5D). To sum up, the introduction of the
group at the donor site and the introduction of
at the acceptor site can reduce the gap, thus leading to a red-shift in the maximum absorption peak and improvement of the light trapping efficiency.
The excited state characteristics of the design molecules were calculated, and the results are listed in
Table S7. As shown in
Table S7, the LS-387-1B and the LS-387-12B have the
of 496.16 nm and 490.19 nm, which is larger than LS-387 (470.40 nm). So dye LS-387-1B and LS-387-12B have a red-shift of 20–25 nm. The first excited states of LS-387-1B and LS-387-12B show an electron transition of HOMO→LUMO (see
Figure S2). While for the LS-387-3D, its
(an electron transition is HOMO→LUMO) is found to be 485.58 nm, which configuration will produce a larger red-shift relative to the original molecule.
Figure S3 shows absorption spectra of 15 designed molecules, which show that LS-387-1B and LS-387-12B have obvious red-shifted absorption (LS-387-3D has an obvious absorption peak red-shifted relative to the original molecules). In summary, it was found that the design by introducing the
group individually or in pairs on the donor site should reduce the energy gap and make the spectrum red-shifted, and then improve the ICT; introducing on the acceptor site
position
groups has a similar trend.
From
Section 3.4, IP and EA are important injection parameters, and
can be used to characterize the electronic contribution of dye molecules [
62,
63,
64]. The LS-387-1B (12A, 12B and 12C) has a lower value of IP compared with LS-387 (see
Table S8), and the EA of LS-387-3D has a large value relative to LS-387 and other designed molecules. Therefore, LS-387-1B (12A, 12B and 12C) will produce a higher outcome of extracting electrons, and LS-387-3D will have a better absorbing ability of electrons. The
of LS-387-3D produced a lower value relative to the original molecule and other designed molecules, therefore, LS-387-3D will show better electronic ability.
On the basis of the ground state optimizations of fifteen designed molecules, four electrochemical activity parameters are also listed in
Table S8. The h of LS-387-1B (12A, 12B and 12C) has a significant decrease compared with LS-387 (0.88). Among the above three designed dyes, for LS-387-1B (12B) the introduction of
in the donor terminal reduces the chemical hardness of the dyes more effectively than other introductions of
and –OH. The LS-387-3D (4D and 5D) and the LS-387-3E also has a lower h compared with LS-387. In summary, introduction of two electron groups (
) in the donor site or the introduction of
(
and –CN) in the acceptor are more beneficial to reducing the h of the dye molecules. Moreover, the dyes of LS-387-12A (12B and 12C) have a higher
compared to LS-387 and LS-387-1A (1B and 1C). LS-387-3D (13.17) and LS-387-3F (9.76) also has a maximum value of
. So, introduction of electron-donating groups (
) in pairs on the donor site and introduction of
and ‒CN in the acceptor site
were beneficial to increase the
dye molecules. Therefore, the above two parameters indicated that LS-387-12B and LS-387-3D (3F) would have a higher
. The higher absolute value of
can lead spontaneously to inject electrons to TiO
2.
Table 7 shows that LS-387-1B (12B) has a higher absolute value of
compared with dye LS-387. The higher HOMO levels of LS-387-1B (12B) lead to greater
(see
Figure 9a). The introduction of the
group is helpful to increase the electron injection, and introduction of two
groups can still further increase the electron injection compared with single introduction of
. Also, the coupling constant (
) is listed in
Table 7. For serials LS-387-X, LS-387-1B (12B) has the higher
compared with LS-387 and the other five dyes, which means that faster electron injection can occur for LS-387-1B (12B). The dye regeneration free energy (
) has important effects on the PCE. As shown in
Table 7, for LS-387-X, LS-387-12A (12C) has a higher value of
compared with other dyes, indicating that two groups
and
are beneficial to improve the free energy of the dye regeneration. In addition, for LS-387-3D (4D and 5D), the
is large than LS-387, showing that the –CN radical group is helpful to improve the free energy of the dye regeneration. The larger
is beneficial to improve
and increase
. Considering the above three properties (
,
and LHE), the
of LS-387-1B (12B) and LS-387-3D (4D and 5D) will be better than LS-387.
Table 7 shows the
of fifteen designed molecules, and for LS-387-X, the LS-387-1B has a higher
compared with LS-387; for LS-387-Y, the dyes of LS-387-4D (4E and 4F) have higher
compared with LS-387. In summary, introduction of electron-donating groups (
) on the donor site and introduction of electron-acceptor groups (
,
and
) on the acceptor site
are beneficial for the improvement of
, which then improves the
.