Super-Exchange Charge Transfer in One-Photon and Two-Photon Absorption of Multibranched Compounds.

In this work, density functional theory is used to study organic molecules in a donor-acceptor (D-A) system centered on phenothiazine with strip and trigonal structures. The transition modes of the one-photon absorption (OPA) and two-photon absorption (TPA) processes of the two molecules are studied. The calculations show that the molar absorption coefficient of OPA for trigonal molecule TPPO and the cross section of TPA are both larger than those for strip molecule M1 due to the increase in the number of branches of the system. A special local excitation-enhanced charge-transfer excitation appears in strip-type molecule M1. In the charge-transfer process of trigonal D-A structure molecule TPPO, there are not only local excitation-enhanced charge-transfer excitation but also super-exchange charge transfer between the three branches that occurs due to the increase in the planarity of the system.

Introduction

Two-photon absorption (TPA) induces the transformation of molecules into excited electronic states by simultaneously absorbing and combining two low-energy photons (the energies of the two photons can be the same or different), which is a third-order nonlinear process.[1] However, under a high-power beam, using a light source approaching twice the linear absorption wavelength of the molecule to excite the molecule can also excite the same transition. Göppert–Mayer[2] first proposed the TPA theory in 1931. Kaiser and Garret[3] first verified the existence of TPA from a two-photon excitation experiment in 1962. TPA is characterized by its absorption intensity, which is proportional to the square of the incident light intensity. The long-wavelength absorption and short-wavelength emission of two-photon absorption allow the high penetration rate of light waves, which greatly reduces the dissipation and destruction of excitation light by the medium. The excellent optical properties of these organic nonlinear optical materials in the TPA process make them promising for applications, including dye-sensitized solar cells,[4−7] two-photon fluorescence microscopes,[8−12] optical data storage,[13−15] and photodynamic therapy.[12,16−20]

Many researchers have proposed methods of constructing TPA molecules in terms of molecular configuration and TPA characteristics to enhance the charge transfer within the molecule. It is common to construct a donor–acceptor (D–A) structure and increase the push–pull electron strength between substituents,[1,21−23] connect the two through conjugated linkers,[24−27] and construct molecules of different chiralities[28] and organic multibranched two-photon absorbing molecules with cores and branches.[29] Qiao, Mu, and co-workers reported that the triangular axial type of 1,3,5-triazine derivatives has a larger 2PA cross section compared to the striped and V-type.[30] In recent years, due to its nonplanar “butterfly” structure, phenothiazine can effectively inhibit the self-stacking of dye molecules to obtain higher photovoltage. Therefore, it is often used to design and synthesize various dye photosensitizers,[31,32] solar cells,[33,34] fluorescent probes,[35,36] and stimulus-responsive materials.[37] Meanwhile, the presence of nitrogen and sulfur heteroatoms in the molecule makes it more electron-donating, and multibranched molecules containing heteroatoms have larger π-domains and more pronounced multipolar features. Therefore, in this work, the TPA properties of strip and trigonal structures were studied with phenothiazine as an electron donor, and the effect of increasing the number of branches on the TPA properties was investigated.

In this work, we theoretically studied the TPA process of two phenothiazine derivatives with phenothiazine as a donor and oxadiazole end groups as an acceptor. With the central donor of phenothiazine, the oxadiazole end group is branched to form D–A strip structure molecule 1 and trigonal structure molecule 2, following the previous work of Wu et al.[38] The first molecule is 2-(4-(10-phenothiazinyl)benzene)-5-phenyl-1,3,4-oxadiazole (M1), and its branch is connected to the bond at position 10 of phenothiazine. The second molecule is 3,7,10-triplet(4-(2-phenyl-1,3,4-oxadiazole phenyl)) (TPPO), and its branches are connected to positions 3, 7, and 10 of phenothiazine, forming a trigonal structure. The optimized geometric configurations of M1 and TPPO are shown in Figure . First, by simulating the UV–vis and TPA spectra of one-photon absorption (OPA), the influence on the increase in the number of branches on the one-photon and TPA characteristics are analyzed. The TPA spectrum and the search for the intermediate state were achieved using the program developed by Mu and Sun based on the sum-of-states (SOS) model.[39] In this process, the influence of the increase in the number of branches on the one-photon and TPA characteristics are discussed for the emergence of super-exchange charge transfer different from the conventional ones, and the relationship between the structure and properties of charge transfer is understood in theory. Our study provides a theoretical basis for the design and synthesis of TPA materials and has good application prospects.

Figure 1

Two-dimensional structure diagrams (left) and the optimized geometric configuration diagrams (right) of molecules 1 and 2.

Method

Calculation Details

All quantum chemistry calculations were performed with the Gaussian 09 D.01 software package.[40] Using the B3LYP functional and the 6-31G(d) basis sets, with the density functional theory (DFT) method,[41−43] the molecular geometry of the ground state was optimized. The time-dependent DFT (TD-DFT)/B3LYP method is poor in the charge-transfer (CT) excitation calculation. Therefore, to calculate the electronic transitions of the two molecules, TD-DFT was used, on the theoretical level of CAM-B3LYP/TZVP.[44−46] According to the TPA spectrum and absorption cross section obtained by the program developed by Mu and Sun,[39] the two-dimensional (2D) charge-transfer matrix (CTM) and transition-density matrix (TDM) and three-dimensional (3D) charge-density difference (CDD) of each excited state and each path are obtained through the Multiwfn 3.7 program.[47] The 3D isosurface of the CDD map drawn using VMD software[48] can intuitively display the direction of charge transfer.

Two-Photon Absorption

Microscopically, the ratio of the molecular transition probability per unit time to the square of the photon flux is the cross section of the TPA to measure the size of the TPA. Based on the sum-of-states (SOS) model, TPA involves two absorption processes; the first process is to induce the molecule to transform into an excited state, and then to transition to a higher excited state. So, in the two-photon transition process, there will be different paths to the final state, and the absorption probability (δtp) is calculated by the sum-of-states (SOS) model that is the sum of the processes through all intermediate states.[49−51]where g is the ground state, j is the intermediate state, f is the final state, |g⟩, |j⟩, and |f⟩ are the wave functions of the three states, and w is the energy; the transition dipole moments of the two processes are expressed as ⟨f|u|j⟩ and ⟨j|u|g⟩, respectively. Here, ⟨g|u|g⟩ and ⟨f|u|f⟩ are the permanent dipole moments of the g and f states, respectively, and Δufg is the difference between the two. θ is the angle between ⟨j|u|g⟩ and ⟨f|u|j⟩, ϕ is the angle between Δufg and ⟨f|u|g⟩, and Γf is the TPA spectral line width. The first term of the formula is called the “three-state” term, and the second term is called the “two-state” term, which, respectively, represent the contribution of two-step transition and one-step transition to the absorption probability.

The cross section measuring the size of TPA[52,53] iswhere w is the energy of the incident light, a0 is the Bohr radius, α is the fine structure constant, c0 is the speed of light, and g(w) is the contour of the spectral line.

Transition-Density Matrix, Charge-Transfer Matrix, and Charge-Density Difference

The TDM can be used to calculate the transition density to analyze the coherence of atoms in the molecule to determine the excitation mode.

In real space, under a specific set of basis functions, the TDM can be constructed as[39]

Assuming that the system only has u and v, the charge-transfer process is expressed as the transition of i (unoccupied orbital) → j (occupied orbital) using these two basis functions, and the TDM at this time

If the absolute value of the diagonal element is large, the same basis function makes a large contribution to holes and electrons. In other words, holes and electrons have a significant overlap in this basis function, so the excitation is local excitation. If the off-diagonal elements are relatively large, it means that basis functions are strongly coupled during this process, which means that charge-transfer excitation has occurred.

The CTM is an effective 2D tool. The number of electrons transferred from R to S is calculated using the IFCT method.[46]where ΘR,hole is the amount of R occupied by the excited electrons, ΘS,ele is the amount occupied by S where the election is going, and the product of the two is defined as the number of electrons transferred from R to S. The more holes R occupies and the more electrons S occupies, the more electrons are transferred from R to S. The diagonal element of the CTM is in the form of “the number of electrons transferred by the fragment to itself,” and each nondiagonal element strictly shows the amount of electron transfer between atoms.

Because the TPA process will experience different intermediate states, the CDD can intuitively show where the electrons have gone and how much has been transferred, so this is a good way to observe the charge-transfer process in 3D space. First, a density matrix of excited states is generated as follows[39]

Among them, Pground and Pexcited are the density matrices of the wave functions of the unexcited state and the excited state, respectively, and P and P are the density matrices contributed by i and j, respectively. Then, the density matrix is diagonalized to generate a natural orbital, and finally, the CDD is obtained by difference.

Results and Discussion

Absorption Spectrum of OPA and TPA

The OPA UV–vis and TPA spectra for molecules 1 and 2 are shown in Figure a–d. Figure a,c shows the OPA spectra of M1 and TPPO, respectively. The left axis of the one-photon absorption spectrum represents the molar absorption intensity of the OPA process, and the right axis represents the oscillator intensity. As shown in Figure a, the OPA (UV–vis) spectrum of M1 consists of the strongest absorption peak, and many weak absorption peaks in the lower wavelength range, with its strongest absorption peak contributed by the S3 excited state. In contrast, TPPO has two other weak absorption peaks in the 315–370 nm range, consisting of S1 and S2, and its strongest absorption peak is mainly contributed by S3 and S4 together. Comparing the UV–vis spectrum of the two molecules, it can be seen that the absorption wavelength to the third excited state of M1 is 280.07 nm and the wavelength of TPPO is 305.91 nm. Therefore, it can be concluded that an increase in the number of branches leads to a red shift of the spectrum of the molecule. It can be seen that the molar absorption coefficient of TPPO is larger than that of M1, that is, as the number of branches increases, the absorption intensity of the molecule increases. For the excited state with intermediate energy, the OPA characteristic is not obvious but it may undergo the second process of TPA, be induced to a higher excited state, and finally undergo the TPA transition process.

Figure 2

OPA UV–vis and TPA spectrum of M1 (a, b) and TPPO (c, d). The black, blue, and green lines in (c, d) represent the sum, “three-state”, and “two-state” terms, respectively.

Figure b,d shows the TPA spectrum of the two molecules obtained using the three-state model. The left axis represents the absorption intensity (molar absorption coefficient) of the TPA process and the right axis represents the absorption cross section (the sum of the first and second terms in eq ). The complete TPA process is represented by a black solid line. The blue dotted line represents the “three-state” term, which is divided into two steps: the ground-state molecule transitions to the excited state by absorbing photons and then is induced to the final state, which can be expressed as Sg → Sj → Sf. The green dotted line represents the “two-state” term, which is a one-step transition without an intermediate state: a direct transition to the final state, which can be expressed as Sg → Sf. According to the TPA spectra of the two molecules, the first term accounts for the main part. As shown in Figure b,d, the TPA spectrum of M1 is mainly composed of main peaks and side peaks, and its strongest absorption peak is mainly contributed by S20 and S17. However, the TPA spectrum of TPPO is much more complicated than that of M1, and the TPA cross-sectional value of TPPO at 530 nm is 3149 GM, while that of M1 at 418 nm is 1427 GM. This shows that the planarity of the multibranched molecule may enhance the TPA cross-sectional values. It can be seen that the TPA spectrum of TPPO is the same as OPA and that the TPA peak has a significant red shift.

One-Photon Absorption

The increase in the number of branches of the two molecules centered on phenothiazine caused significant changes in the spectra of OPA and TPA. To fully understand the impact of the increase in the number of branches on charge transfer and to understand the relationship between the structure and properties of charge transfer, one-photon excitation is first analyzed. So, by drawing the CTM and CDD, the charge-transfer characteristics of the two molecules during the OPA process can be analyzed. The CTM diagram can clearly show where and how many electrons are transferred during the electron-excitation process. For M1, the OPA state S3, which constitutes the lowest energy absorption peak, as well as S15 and S34 are analyzed, as shown in Figure . It can be seen from Figure a that only the branched chain has charge transfer. In the CDD of the one-photon excited state of S3, the pink part in the picture represents electrons (increased electrons) and the blue part represents holes (decreased electrons). The branch is blue-pink, which means that only the branch has increased and decreased electrons, that is, charge transfer. Therefore, combined with the CTM and the CDD, S3 is locally excited. The CTM and CDD of S15 in Figure b show the charge transfer within the phenothiazine, but there is also charge transfer from phenothiazine to the benzene ring of the branch. This shows that the S15 excited state is locally excited and supplemented by charge-transfer excitation. For S34, it is mainly charge-transfer excitation, as shown in Figure c.

Figure 3

CTM and CDD for the S3 (a), S15 (b), and S34 (c) excited states of M1; in CDD, pink represents electrons and blue represents holes.

For the TPPO molecule, the analyzed excited states S3 and S4 constitute the lowest energy peak and S1 constitutes the shoulder of the lowest energy peak. Figure shows their CTM and CDD. As seen from the CDD of the S1 excited state, this is a local excitation on phenothiazine accompanied by a charge-transfer excitation of phenothiazine to the three branches. This can be confirmed from the CTM. Although this excited state has undergone charge transfer, it is only transferred to a part of the acceptor, so local excitation still plays a major role.

Figure 4

CTM and CDD for the S1 (a), S3 (b), and S4 (c) excited states of TPPO.

We have also analyzed the S3 excited state of TPPO. The CTM in Figure b shows the charge transfer from phenothiazine to the second and third branches. In addition to this, a super-exchange charge-transfer excitation between the second and third branches independent of phenothiazine emerged. It can be seen from the CDD that the branched chain is mainly electrons and the phenothiazines are mainly holes. That shows these excitation characteristics are dominated by the charge transfer, accompanied by weak local excitation. Comparing the S3 excited states of the two molecules, M1 is equivalent to the complete local excitation on the first branch, whereas TPPO is accompanied by a super-exchange charge-transfer excitation between the second and third branches independent of the phenothiazine. So, as the number of branches increases, the charge transfer becomes more intense. Comparing the excited states of S3 and S4, it can be seen from Figure c of CTM and CDD that, unlike S3, phenothiazine exhibits strong local excitation and a comparably strong charge transfer to the first branch.

According to the TPA spectra of the two phenothiazine derivatives, “three-state” term dominates, indicating that the two-step leap is the major part. This means that TPA will go through an intermediate virtual state and through two transition processes. If the transition probability (transition dipole moment) of these two processes is larger, the TPA excited state with a larger absorption cross section will be observed; so, we can determine the TPA excited state with a larger absorption cross section using the transition dipole moment. For the same two-photon excited state, there will be multiple choices of intermediate states. Therefore, we calculated the transition dipole moments of different paths in the TPA processes of the two molecules to find the intermediate state with the highest probability of appearing in the TPA transition, as shown in Table . Using the CDD and TDM of different intermediate states, we visualize the charge-transfer process and intuitively analyze the two-photon transition process.

Table 1

Elements of the TPA Transition Dipole Moment Matrix of M1

molecule	TPA states	process	integral value
M1	S17	⟨φS0|μ|φS3⟩ → ⟨φS3|μ|φS17⟩	9.849–2.7384
	S20	⟨φS0|μ|φS3⟩ → ⟨φS3|μ|φS20⟩	10.185–5.2888
		⟨φS0|μ|φS16⟩ → ⟨φS16|μ|φS20⟩	1.181–0.596
TPPO	S8	⟨φS0|μ|φS1⟩ → ⟨φS1|μ|φS8⟩	8.981–19.575
		⟨φS0|μ|φS3⟩ → ⟨φS3|μ|φS8⟩	9.849–2.738
	S25	⟨φS0|μ|φS3⟩ → ⟨φS3|μ|φS25⟩	9.849–2.371
		⟨φS0|μ|φS4⟩ → ⟨φ4|μ|φ25⟩	14.249–5.682
	S28	⟨φS0|μ|φS2⟩ → ⟨φS2|μ|φS28⟩	2.957–4.735
		⟨φS0|μ|φS7⟩ → ⟨φS7|μ|φ28⟩	5.724–1.334

According to the TPA spectrum, we analyzed the S17 and S20 excited states that constitute the strongest absorption peak in the TPA spectrum of M1. According to the transition dipole moment, the intermediate state of the S17 excited state of M1 is S3. According to the previous analysis, the first step, S0 → S3, of this two-photon transition is the complete local excitation in the branch. It can be seen from the TDM in Figure a that the second step, S3 → S17, is mainly the local excitation of the branched chain, accompanied by the excitation of the charge transfer between phenothiazine and the branched chain. It can be seen from the CDD that electrons are transferred from phenothiazine to the branched chain.

Figure 5

CTM, TDM, and CDD of the two-step process for the S17 and S20 excited states of M1. The TDM and CDD of (a) S3 → S17 and (b) S3 → S20. The CTM and CDD of (c) S0 → S16 and the TDM and CDD of (d) S16 → S20.

S3 is also an intermediate state of the S20 excited state. Comparing the two transition processes of S3 → S17 and S3 → S20, it is found that the transition mode is the same, as shown in Figure a,b. It can thus be inferred that the two-photon excited state with S3 as an intermediate state has the same excitation mode. As shown in Figure c,d, for S0 → S16, only electrons and holes exist on phenothiazine. CTM shows that only phenothiazine undergoes charge transfer, so this process is a local excitation. In the second step, both are locally excited and there is a charge transfer between the two; it can be seen from the CDD that the electron transfers from the center to the branch chain. Looking at the whole process at a macrolevel, the local excitation in the first step lays the foundation for the charge transfer in the second step. Therefore, it can be considered that the transition is local excitation-enhanced charge-transfer excitation. Therefore, it can be speculated that the TPA charge-transfer mode with different intermediate paths may be quite different.

The TPA spectrum of the molecule TPPO is much more complicated than that of M1, according to the TPA spectrum of TPPO; the S8 excited state with strong absorption cross sections and S25 and S28, which constitute the strongest absorption peaks are analyzed. For the S8 excited state, we analyzed the excitation characteristics of S1 and S3 as the intermediate states. When S1 is the intermediate state, in the first step, as we analyzed before, the S0 → S1 excitation is characterized by a clear local excitation accompanied by charge transfer from the central molecule to the benzene ring in the first half of the branch, as can be seen in Figure a. In the second step, the transition from S1 to S8 is also dominated by local excitation, but unlike the first step, the electrons are transferred from the branch to the central molecule, and there is also charge transfer between the branches, as shown in Figure a.

Figure 6

TDM and CDD of the two-step process for the S8 excited state of TPPO. The TDM and CDD of (a) S1 → S8 and (b) S3 → S8.

The other intermediate state of the S8 excited state is S3. As we have analyzed before, S0 → S3 is the charge-transfer excitation, which occurs between the central molecule and the second and third branches. S3 → S8 is the obvious charge-transfer excitation; electrons are transferred from the second and third branches to the central molecule and the first branch. As we can see from Figure b, we can get confirmation from the TDM. The charge transfer of the second, third, and first branches proves that the charge transfer between them, which is a kind of super-exchange charge transfer, does not go through the central molecule. In this three-prong D–A structure system, due to the increased versatility of the charge-transfer path, super-exchange charge transfer occurs between the three branches.

The strongest absorption peak of TPPO is contributed by several excited states. We analyzed the S25 and S28 excited states with relatively large cross sections. First, we analyzed the S25 excited state. The intermediate states we chose are S3 and S4, and the transition from S0 to S3 and S4 has been discussed, as shown in Figure . The TDM and CDD from the intermediate states S3 and S4 to S25 are shown in Figure . The CDD indicates that the electrons of these two paths are transferred from the branch to the central molecule. According to TDM, it can be seen that both have local charge excitation, but in the first path, there is a charge transfer between the first, second, and third branches, that is, super-exchange charge transfer. Therefore, in the excitation process from S3 to S25, the holes on the single chain are not obvious on CDD.

Figure 7

TDM and CDD of the two-step process for the S25 excited state of TPPO. The TDM and CDD of (a) S3 → S25 and (b) S4 → S25.

For the S28 excited state, it has two intermediate states, S2 and S7. The first and second steps of S2 as the intermediate excited state are both charge-transfer excitations, as shown in Figure . The first step is the transfer of electrons from the central molecule to the three branch chains. It can be seen from the CTM that electrons are transferred from the second and third branched chains to the first branched chain, which explains that the isosurface of electrons on the first branched chain in the CDD is relatively large. The second process is the transfer of electrons from the branched chain to phenothiazine. The charge-movement behavior of these two processes is exactly opposite, that is, the direction of charge transfer is opposite. Therefore, S28 with S2 as an intermediate state is a local excitation in the whole process. When the S7 state is the intermediate state, it can be seen from the CDD and CTM that the first process, S0 → S7, is obvious local excitation at the first branch. The second process is S7 → S28. It can be inferred from CDD shown in Figure c that there is not only the charge-transfer excitation from the central molecule to the first branch but also super-exchange charge transfer from the second and third branches to the first branch. However, the local excitation on the first branch cannot be ignored, which can be determined from the TDM. Therefore, for the same excited state, it involves different intermediate states, and its charge-transfer mode is very different. In conclusion, the increase in the number of branches of multibranched compounds during the TPA transition improves the planarity of the system, and the increase in charge-transfer paths allows the molecules to undergo super-exchange charge transfer, resulting in an increase in the TPA cross section.

Figure 8

CTM, TDM, and CDD of the two-step process for the S28 excited states of TPPO. The TDM and CDD of (a) S2 → S28 and (b) S0 → S2. The TDM and CDD of (c) S7 → S28 and the CTM and CDD of (d) S0 → S7.

Conclusions

DFT was used to calculate the OPA and TPA characteristics of organic molecules in the D–A system centered on phenothiazine with strip and trident structures. 2D and 3D visualization methods were used to analyze and discuss two molecules. First, increasing the number of branches significantly promotes the red shift of OPA and TPA peaks. Second, many special charge-transfer modes occur, and local excitation-enhanced charge-transfer excitation occurs in the TPA transition of the strip molecule. In addition, the trident structure shows a super-exchange charge transfer independent of the central molecule, which results in an increase in the absorption cross section. This model has new applications in photocatalysis, organic electronic devices, etc. Our research will further an understanding of the molecular design of multibranched compounds with large cross-sectional TPA.