The quantum interference in singlet fission (SF) among the multiple pathways from singlet excited states to correlated triplet pair states is comprehensively investigated. The analytical analysis reveals that this interference is strongly affected by the exciton–exciton coupling and is closely related to the property of J- and H-type of aggregates. Different from the interference in the spectra of aggregates, which depends only on the sign of exciton–exciton coupling, the interference in SF is additionally related to the signs of couplings between singlet excited states and triplet pair states. The interference dynamics is further demonstrated numerically by a time-dependent wavepacket diffusion method with electron–phonon interactions incorporated. Finally, we take a pentacene dimer as a concrete example to show how to adjust the constructive and destructive interferences in SF dynamics in terms of J-/H-aggregate behaviors. The results presented here may provide guiding principles for designing efficient SF materials through directly tuning quantum interference via morphology engineering.

Although the triplet states of fullerenes have prosperous applications, it remains unclear how the structural parameters of singlet and triplet states control the intersystem crossing (ISC) rates. Here, electronic structure calculations (reorganization energy, driving force, and spin–orbit coupling) and a rate theory (Marcus formula) are employed to quantitatively predict the ISC rates of isolated fullerenes Cn (n = 60–110). The results demonstrate that the driving force is not the only factor to predict the ISC rates. For instance, although C80, C82, and C110 have the favorable driving force, the ISC rates are close to zero because of small spin obit couplings, whereas small ISC rates of C96 and C100 result from quite small reorganization energies. Meanwhile, in addition to well-known C60 and C70, C92 possesses good ISC property with obviously large ISC rate. C92 also has a higher triplet-state energy than singlet-state oxygen energy; it may thus have a good photoactive property.

It has been experimentally demonstrated that the stereometric packings of two new bisPC71BM isomers have an important impact on the power conversion efficiency of organic solar cells. Here, a theoretical investigation is made to reveal the mechanism behind from detailed photophysical processes in performed cells. The results show that the crystal packings of isomers affect the electron mobilities dominantly from the electronic coupling for electron transfer, and the trends of calculated mobilities are consistent with experimental measurements although the magnitudes are obviously larger. For the performed cells from two isomers with poly(3-hexylthiophene) as a donor, it is found that the exciton dissociation yields are also different, manifesting that stereometric packings essentially control the cell efficiency via both electron mobilities and exciton dissociation. Furthermore, the reasons for low cell efficiencies are analyzed, and possible improvements are suggested.

A time-dependent wavepacket diffusion method is used to investigate the effects of charge transfer (CT) states, singlet exciton, and multiexciton migrations on singlet fission (SF) dynamics in organic aggregates. The results reveal that the incorporation of CT states can result in SF dynamics different from the direct interaction between singlet exciton and multiexciton, and an obvious SF interference is also observed between the direct channel and the indirect channel mediated by CT states. In the case of direct interaction, although the fast population transfer of singlet exciton in monomers, caused by the increase of exciton–exciton interaction, can accelerate the SF process, the spatial coherence alternatively has a counter-productive effect, and their competition leads to an optimal exciton–exciton interaction at which SF has a maximal rate. This trade-off relationship in SF dynamics is further analyzed from different perspectives, specifically in spatial and energy representations, and is also confirmed through the indication that static energy disorders can speed up SF process by destructing the coherence. Meanwhile, it is found that the couplings among multiexciton states decrease SF rates by the multiexciton coherence and backward conversion from multiexciton to singlet exciton states.

The experimental carrier mobility value of organic semiconductors has been increasing rapidly in recent years to well exceed the theoretical limit based on the hopping model calculated using the semi-classical Marcus theory, calling for better understanding and evaluation of carrier mobility. On the other hand, bandlike transport behavior has been observed for some ultra-pure and closely-packed organic single crystals. In this work, we identify the roles of quantum nuclear tunnelling and the charge delocalization effects, leading to a comprehensive computational approach to assess the carrier mobility of organic semiconductors. We present the first-principles evaluated mobility results for some representative organic transport materials at four levels ranging from semiclassical hopping to quantum nuclear enabled hopping and to quantum wavepacket diffusion, and eventually to complete bandlike descriptions. We provide a comprehensive tool to assess the carrier mobility in organic semiconductors based on such improved understanding.

Molecular dynamics simulations and combined quantum mechanics and molecular mechanics calculations are employed to investigate dimethoxy-tetraphenylethylene (DMO-TPE) molecules in water solution for their detailed aggregation process and the mechanism of aggregation-induced emission. The molecular dynamics simulations show that the aggregates start to appear in the nanosecond time scale, and small molecular aggregates appear at low concentration; whereas the large aggregates with a chain-type structure appear at high concentration, and the intramolecular rotation is largely restricted by a molecular aggregated environment. The average radical distribution demonstrates that the waters join the aggregation process and that two types of hydrogen bonds between DMO-TPE and water molecules are built with the peaks at about 0.5 and 0.7 nm, respectively. The spectral features further reveal that the aggregates dominantly present J-type aggregation although they fluctuate between J-type and H-type at a given temperature. The statistical absorption, emission spectra, and the aggregation-induced emission enhancement with respect to the solution concentration agree well with the experimental measurements, indicating the significant effect of molecular environments on the molecular properties.

It is well known that interfacial structures and charge transfer in dye-sensitized solar cells are extremely important for the enhancement of cell efficiency. Here, the normal Raman spectra (NRS) and resonance Raman spectra (RRS) of a C343-sensitized TiO2 cluster (Ti9O18) are theoretically predicted from combined electronic structure calculations and a vibrationally-resolved spectral method to reveal the relationship between interfacial geometries and excited-state dynamics. The results show that although the NRS of free C343 and the C343–TiO2 cluster correspond to the vibrational motions of C343 in a high frequency domain, their mode frequencies show obvious differences due to the interaction of the TiO2 cluster on C343, and several new Raman active fingerprint modes, such as bidentate chelating bonding modes, can be used to determine interfacial geometries. However, the resonance Raman activities of low-frequency modes are significantly enhanced and several modes from the TiO2 cluster can be observed, consistent with experimental measurements. Furthermore, the RRS from a locally excited state and a charge transfer state of C343–TiO2 are dramatically different, for instance, new Raman active modes with 1212 cm−1, 1560 cm−1 and 1602 cm−1, corresponding to the motions of CH2 rocking, CC/C–N/CO stretching and CO/CC stretching, appear from the charge transfer state. The obtained information on mode-specific reorganization energies from these excited states is greatly helpful to understand and control interfacial electron transfer.

The unified coherent-to-diffusive energy relaxation of hot exciton in organic aggregates or polymers, which still remains largely unclear and is also a great challenge theoretically, is investigated from a time-dependent wavepacket diffusive approach. The results demonstrate that in the multiple time scale energy relaxation dynamics, the fast relaxation time essentially corresponds to the dephasing time of excitonic coherence motion, whereas the slow time is related to a hopping migration, and a suggested kinetic model successfully connects these two processes. The dependencies of those times on the initial energy and delocalization of exciton wavepacket as well as exciton–phonon interactions are further analyzed. The proposed method together with quantum chemistry calculations has explained an experimental observation of hot exciton energy relaxation in the low-bandgap copolymer PBDTTPD.

Redox-stimulated intramolecular isomerization of the DMSO ligand in [Os(bpy)2(DMSO)2]2+ (bpy = 2,2′-bipyridine; DMSO = dimethyl sulfoxide) was explored theoretically for better understanding the electrochromic properties of osmium sulfoxide complexes. It is found that the HOMO–LUMO gap is decreased because the electron transfer amount from DMSO1 ligand to Os center using Os–S1 linkage is larger than that using Os–O1 linkage, which makes the absorption of such electrochromic Os(II) sulfoxide complexes red-shifted. Moreover, it is observed that Os–O linkage is preferred by the “hard” Os(III) metal and the “soft” Os(I) metal prefers Os–S linkage, compared with Os(II). Intrinsic reaction pathway calculation results demonstrate that Os–S1 → Os–O1 isomerization is favored by Os(II) oxidation, while Os–O1 → Os–S1 isomerization is much easier to be triggered by reduction of Os(III) or Os(II). In addition, DMSO2 linkage isomerization becomes much harder to proceed attributed to the increased bond-strength between DMSO2 and Os center upon Os(II)–O1 → Os(II)–S1 rearrangement, which makes only one DMSO ligand isomerized observed experimentally.

The rational design and fabrication of mixed-phase oxide junctions is an attractive strategy for photocatalytic applications. A new tuneable α–β mixed-phase Ga2O3 has recently been discovered to have high activity for photocatalytic water splitting. Here we perform a first-principles study to reveal the nature of the efficient separation of photogenerated carriers achieved by the mixed-phase Ga2O3. It is found that the strain and lattice misfit at the interface junctions significantly tune their energy bands. As the interior angles between two components change, the characteristics of the valence band-edge states can be significantly different. Through analysis of the bonding strength of the bonds near the interfaces, and the comparison of calculated and experimentally-observed carrier migration directions, we suggest a favorable junction for the efficient separation of photogenerated carriers. This junction has a type-II band alignment with a valance band of α-Ga2O3 that is 0.35 eV higher than that of β-Ga2O3, and a conduction band offset of only 0.07 eV. It seems that electron migration across the phase boundary from α- to β-Ga2O3 mainly follows an adiabatic electron-transfer mechanism, due to strong orbital coupling between the conduction bands of the two phase materials.

The exciton dissociations and charge recombinations to a triplet state in the donor–acceptor heterojunction solar cells of [2,6-(4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b]dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)] (PCPDTBT) blended with ten different fullerene derivatives are theoretically investigated by using electronic structure calculations together with a Marcus formula. The detailed discussions of available accuracy in the evaluation of all quantities entering the rate expression (driving force, electronic coupling, and internal and external reorganization energies) are provided. The results reveal that the exciton dissociations in most blends are barrierless reactions because the corresponding values of driving forces and reorganization energies are very close; however, the recombinations from the charge transfer states to the triplet state of PCPDTBT occur in the Marcus normal regime. The predicted rates for both the exciton dissociation and charge recombination are in quite good agreement with experimental measurements. In addition, as the triplet charge transfer states are formed, their recombination rates become two orders larger than those for the singlet ones and have orders similar to the exciton dissociations. It is thus expected that the triplet charge recombinations are dominant channels, whereas the singlet charge recombinations can be safely neglected because of quite small rates compared to exciton dissociation ones.

This tutorial review primarily illustrates rate theories for charge transfer and separation in organic molecules for solar cells. Starting from the Fermi's golden rule for weak electronic coupling, we display the microcanonical and canonical rates, as well as the relationship with the Marcus formula. The fluctuation effect of bridges on the rate is further emphasized. Then, several rate approaches beyond the perturbation limit are revealed. Finally, we discuss the electronic structure theory for calculations of the electronic coupling and reorganization energy that are two key parameters in charge transfer, and show several applications.

Photo-physical properties of bromo-indolylmaleimide (IM-Br), indole-succinimide (IS), and their anions were theoretically investigated compared with the previous theoretical result for indolylmaleimide (IM) [Phys. Chem. Chem. Phys., 2010, 12, 9783]. The energies for the electronic excited states as well as the ground states were computed for these molecules using the multi-reference perturbation calculations based on the second order Rayleigh–Schrödinger perturbation theory (CASPT2) at the cc-pVDZ basis set level. The electron-accepting or electron-donating effect caused by bromine-substitution was discussed in the intra-molecular charge transfer (ICT) mechanism. The order of natural orbitals of the bromine-substituted monovalent anion with a deprotonated indole NH group (I(−)(−)M-Br) was found to be rearranged by the effect of electron-donation, which leads to pseudo-crossing of the potential energy cures of the S1 and S2 states. The large stokes shift observed for I(−)(−)M-Br was due to pseudo-crossing. Meanwhile, IM and IM-Br show abnormal deprotonation, which is explained by the charge distribution on the indole and maleimide moieties. Finally, the monovalent anions I(−)(−)M-Br and I(−)(−)M by a deprotonation of the indole NH end and the neutral IS were proposed to be the most feasible candidates corresponding to the experimental spectra in solution.

The intramolecular electronic couplings in organic mixed-valence systems [D-(ph)n-D]•+ (D = 2,5-dimethoxy-4-methylphenyl, n = 0, 1, and 2) are calculated by dominantly using density functional theory to investigate their dependence of functionals. Since these systems have the property that the charge is from localization to delocalization, the optimized structures are sensitive to the functionals. The geometric optimizations show that CAM-B3LYP and ωB97X-D functionals are good choices for delocalized systems and LC-ωPBE and M06HF are suitable for the systems from charge almost localization to localization. The calculations of electronic couplings demonstrate that the pure functional generally underestimates the electronic couplings whereas the pure HF overestimates them. Furthermore, the electronic couplings from the conventional generalized Mulliken-Hush method are very sensitive to the HF component in functionals, which makes it a challenge to accurately estimate the values. A new reduced two-state method is thus proposed to overcome the deficiency, and the obtained electronic couplings are less sensitive to the ω value in LC-ω PBE functional and they are also consistent with the experimental data.

The hydrogen-transfer reaction of W + NH3 incorporates four possible diabatic reaction pathways along with septet, quintet, triplet, and singlet states. The intersystem crossings thus play an important role in the reaction mechanisms. In this work, ab initio and DFT methods are used to determine all possible intermediates, transition states, products, and intersystem crossing points as well as the spin–orbit couplings. The mechanism of hydrogen elimination is further revealed by the natural bond orbital analysis. From the rate constants yielded by a nonadiabatic transition state theory, we find that two intersystem crossings significantly change the reaction pathways. Finally, we suggest a feasible reaction pathway with exothermicity 72.8 kcal/mol, which is consistent with the experimental measurements.

The electron mobilities of two n-type pentacenequinone derivative organic semiconductors, 5,7,12,14-tetraaza-6,13-pentacenequinone (TAPQ5) and 1,4,8,11-tetraaza-6,13-pentacenequinone (TAPQ7), are investigated with use of the methods of electronic structure and quantum dynamics. The electronic structure calculations reveal that the two key parameters for the control of electron transfer, reorganization energy and electronic coupling, are similar for these two isomerization systems, and the charge carriers essentially display one-dimensional transport properties. The mobilities are then calculated by using the time-dependent wavepacket diffusion approach in which the dynamic fluctuations of the electronic couplings are incorporated via their correlation functions obtained from molecular dynamics simulations. The predicted mobility of TAPQ7 crystal is about six times larger than that of TAPQ5 crystal. Most interestingly, Fermi’s golden rule predicts the mobilities very close to those from the time-dependent wavepacket diffusion method, even though the electronic couplings are explicitly large enough to make the perturbation theory invalid. The possible reason is analyzed from the dynamic fluctuations.

Triplet–triplet energy transfer in benzophenone–fluorene and benzophenone–fluorene–naphthalene molecules is theoretically investigated by using the rate theories and electronic structure calculations established for electron transfer. From the calculated electronic couplings for the single-step tunneling and multistep hopping pathways of the energy transfer from the donor benzophenone to the acceptor naphthalene, it is found that the tunneling comes from the direct electronic couplings between the donor and acceptor states, other than the coupling via the virtual bridge state in the conventional superexchange mechanism. The mode-specific reorganization energy calculations reveal that only the several high-frequency modes dominate the energy transfer, leading to an important nuclear tunneling effect. Succeedingly, with use of the obtained parameters, Fermi’s golden rule predicts the consistent energy transfer rates with experimental ones.

Thermal rate constants and kinetic isotope effects for the title reaction are calculated by using the quantum instanton approximation within the full dimensional Cartesian coordinates. The obtained results are in good agreement with experimental measurements at high temperatures. The detailed investigation reveals that the anharmonicity of the hindered internal rotation motion does not influence the rate too much compared to its harmonic oscillator approximation. However, the motion of the nonreactive methyl group in C2H6 significantly enhances the rates compared to its rigid case, which makes conventional reduced-dimensionality calculations a challenge. In addition, the temperature dependence of kinetic isotope effects is also revealed.

The radical cation of 4,10-ditert-butyl-5,9-diisopropyl-4,5,9,10-tetraazatetracyclo[6.2.2.2]-tetradecane (sBI4T+), as well as its substituted bis(hydrazine) radical cations, is chosen for the investigation of the electronegativity dependence of its intramolecular electron transfer. To do so, two parameters, reorganization energy and electronic coupling, are calculated with several ab initio approaches. It is found that the electronic couplings decrease with the increase of the group electronegativity while the reorganization energies do not show an explicit dependency. Furthermore, Marcus formula is employed to reveal those effect on the electron transfer rates. The predicted rates of electron transfer generally decrease with increasing group electronegativity, although not monotonically.

The non-Condon effect plays an important role in the process of electron transfer (ET). Several theoretical models have been proposed to investigate its effect on ET rates. In this paper, we overview a theoretical method for the calculations of the non-Condon ET rate constants proposed by us, and its applications to organic semiconductors. First, full quantum expressions of the non-Condon ET rates are presented with the electronic couplings having exponential, Gaussian and linear dependences in terms of the nuclear coordinates, respectively. The proposed formulas have closed forms in time domain and they thus can be easily applied in multi-mode systems. Then, the driving force dependences of the ET rates involving the non-Condon effect are calculated with the use of full quantum mechanical formulas. It is found that these dependences show very different properties from the Marcus one. As an example of applications, the approaches are used to investigate the non-Condon effect on the mobility of the organic semiconductor dithiophene-tetrathiafulvalene (DT-TTF). The results manifest that the non-Condon effect enhances ET rates compared with the Condon approximation, and static fluctuations of electronic coupling dominate the ET rate in the DT-TTF, which has been confirmed by the molecular dynamics simulation.

Electron transfer (ET) rate is a fundamental parameter to characterize ET processes in physical, chemical, material and biologic sciences. It is affected by a number of quantum phenomena, such as nuclear tunneling, curve crossing, quantum interference, and the coupling to the environment. It is thus a challenge to accurately evaluate the ET rate since one has to incorporate both quantum effects and dissipation. In this review article, we present several semiclassical theories proposed in our group to cover the regime from weak to strong electronic coupling. Their applications to some concrete systems are also shown.

Rate constants for the intramolecular electron-transfer reaction in the 2,7-dinitronaphthalene (2−), 4,4′-dinitrotolane (3−), and 2,2′-dimethyl-4,4′-dinitrobiphenyl (4−) radical anions in several polar aprotic solvents were estimated by simulating their ESR spectra at different temperatures. At 298 K, the rate constants are in the 2.0−8.0 × 109 s−1 range for 2− and 3− and in the 0.4−2.6 × 109 s−1 range for 4−. The rate constants of 3− and 4−, when corrected for changes in the activation energy (taken as the changes in λ, the transition energy of the mixed valence band), correlate with the inverse of the solvent relaxation time, showing that the reaction is controlled by solvent dynamics. Solvent effects are only found for 2− in benzonitrile (PhCN), the most viscous solvent studied. Calculations of the rate constants using the Kramers-based theory adapted to the adiabatic limit fit the Eyring plots of 2− in PhCN and of 3− and 4− both in MeCN and PhCN rather well.

We present a time-dependent density functional theory (TDDFT) study on the electron dynamics of small carbon clusters Cn (n = 9, 10) exposed to a linearly polarized (LP) or circularly polarized (CP) oscillating electric field of ultrafast laser with moderate laser intensity. The multielectron dynamics is described by propagating the reduced one-electron density matrix in real-time domain. The high harmonic generation (HHG) spectra of emission as well as the time evolution of atomic charges, dipole moments and dipole accelerations during harmonic generation are calculated. The microscopic structure−property correlation of carbon chains is characterized. It is found that the electron responses of Cn to the laser field oscillation become nonadiabatic as the field intensity is larger than 1.4 × 1013 W/cm2. The nonadiabatic multielectron effect is displayed by an explicit fluctuation on the induced atomic charges and the instantaneous dipole acceleration and by observing the additional peaks other than those predicted from the spectral selection rule in HHG spectra of Cn as well. The origin of these additional peaks is elucidated. The atomic charges of Cn in LP and CP laser pulses experience different type of oscillations as expected. In the linear structure C9, the atomic charges at the two ends experience larger amplitude oscillations than those near the chain center whereas the induced charges on each atom of C10 experience the equal amplitude oscillations in the CP laser pulse.

The ultrafast electron-transfer (ET) processes in three dye-sensitized TiO2 systems (pycooh−, catechol−, and alizarin−) are studied by using the real-time time-dependent density functional theory (RT-TDDFT). TiO2 cluster models are used to substitute TiO2 nanocrystals in order to check the quantum size effect on ET. The initial-state geometrical optimization for the individual constituents and coupled systems and the subsequent calculations for IR spectra and the density of states (DOS) are performed at the B3LYP/Lanl2dz theory level. The calculated IR spectra, the DOS, and the low-lying excited states reveal that the couplings between three dyes and TiO2 clusters are very strong so that an ultrafast electron injection from the excited dyes to TiO2 clusters is favored. By following the electronic motion of coupled systems after the photoexcitation of adsorbates in real time without allowing the nuclei to move, we predict an electronic injection time of a few femtoseconds for the present finite systems, which is slightly longer than the experimental measurements and other theoretical predications for the ET time on the same dye-sensitized bulk TiO2 systems due to the small clusters used in our simulation. We find that the ET time is appreciably dependent on the cluster size when the cluster is quite small. However, the size effects on ET time reduce dramatically as the cluster size reaches to a moderate middle size, for example, (TiO2)14. The electron−nuclear coupled movement does not play a significant role in the initial ET process in these three systems. The effects of different initial excited states on electronic dynamics are also discussed.

It has been experimentally demonstrated that the stereometric packings of two new bisPC71BM isomers have an important impact on the power conversion efficiency of organic solar cells. Here, a theoretical investigation is made to reveal the mechanism behind from detailed photophysical processes in performed cells. The results show that the crystal packings of isomers affect the electron mobilities dominantly from the electronic coupling for electron transfer, and the trends of calculated mobilities are consistent with experimental measurements although the magnitudes are obviously larger. For the performed cells from two isomers with poly(3-hexylthiophene) as a donor, it is found that the exciton dissociation yields are also different, manifesting that stereometric packings essentially control the cell efficiency via both electron mobilities and exciton dissociation. Furthermore, the reasons for low cell efficiencies are analyzed, and possible improvements are suggested.

The rational design and fabrication of mixed-phase oxide junctions is an attractive strategy for photocatalytic applications. A new tuneable α–β mixed-phase Ga2O3 has recently been discovered to have high activity for photocatalytic water splitting. Here we perform a first-principles study to reveal the nature of the efficient separation of photogenerated carriers achieved by the mixed-phase Ga2O3. It is found that the strain and lattice misfit at the interface junctions significantly tune their energy bands. As the interior angles between two components change, the characteristics of the valence band-edge states can be significantly different. Through analysis of the bonding strength of the bonds near the interfaces, and the comparison of calculated and experimentally-observed carrier migration directions, we suggest a favorable junction for the efficient separation of photogenerated carriers. This junction has a type-II band alignment with a valance band of α-Ga2O3 that is 0.35 eV higher than that of β-Ga2O3, and a conduction band offset of only 0.07 eV. It seems that electron migration across the phase boundary from α- to β-Ga2O3 mainly follows an adiabatic electron-transfer mechanism, due to strong orbital coupling between the conduction bands of the two phase materials.

Electron transfer (ET) rates of a charge localized (Class II) intervalence radical cation of a bis(hydrazine) are investigated theoretically. First, the intramolecular ET parameters, i.e., reorganization energy, electronic coupling, and effective frequency, are calculated using several ab initio approaches. And then, the extended Sumi−Marcus theory is employed to predict ET rates by using the parameters obtained. The results reveal that the rates of three isomers of [22/hex/22]+, oo+[22/hex/22]+, io+[22/hex/22]+, and oi+[22/hex/22]+, are agreement with the experiment quite well while the rate of isomer ii+[22/hex/22]+ is about 1000 times larger than those of the others. The validity of different ab initio approaches for this system is discussed.

Thermal rate constants and kinetic isotope effects for the title reaction are calculated by using the quantum instanton approximation within the full dimensional Cartesian coordinates. The obtained results are in good agreement with experimental measurements at high temperatures. The detailed investigation reveals that the anharmonicity of the hindered internal rotation motion does not influence the rate too much compared to its harmonic oscillator approximation. However, the motion of the nonreactive methyl group in C2H6 significantly enhances the rates compared to its rigid case, which makes conventional reduced-dimensionality calculations a challenge. In addition, the temperature dependence of kinetic isotope effects is also revealed.

It is well known that interfacial structures and charge transfer in dye-sensitized solar cells are extremely important for the enhancement of cell efficiency. Here, the normal Raman spectra (NRS) and resonance Raman spectra (RRS) of a C343-sensitized TiO2 cluster (Ti9O18) are theoretically predicted from combined electronic structure calculations and a vibrationally-resolved spectral method to reveal the relationship between interfacial geometries and excited-state dynamics. The results show that although the NRS of free C343 and the C343–TiO2 cluster correspond to the vibrational motions of C343 in a high frequency domain, their mode frequencies show obvious differences due to the interaction of the TiO2 cluster on C343, and several new Raman active fingerprint modes, such as bidentate chelating bonding modes, can be used to determine interfacial geometries. However, the resonance Raman activities of low-frequency modes are significantly enhanced and several modes from the TiO2 cluster can be observed, consistent with experimental measurements. Furthermore, the RRS from a locally excited state and a charge transfer state of C343–TiO2 are dramatically different, for instance, new Raman active modes with 1212 cm−1, 1560 cm−1 and 1602 cm−1, corresponding to the motions of CH2 rocking, CC/C–N/CO stretching and CO/CC stretching, appear from the charge transfer state. The obtained information on mode-specific reorganization energies from these excited states is greatly helpful to understand and control interfacial electron transfer.

This tutorial review primarily illustrates rate theories for charge transfer and separation in organic molecules for solar cells. Starting from the Fermi's golden rule for weak electronic coupling, we display the microcanonical and canonical rates, as well as the relationship with the Marcus formula. The fluctuation effect of bridges on the rate is further emphasized. Then, several rate approaches beyond the perturbation limit are revealed. Finally, we discuss the electronic structure theory for calculations of the electronic coupling and reorganization energy that are two key parameters in charge transfer, and show several applications.

Photo-physical properties of bromo-indolylmaleimide (IM-Br), indole-succinimide (IS), and their anions were theoretically investigated compared with the previous theoretical result for indolylmaleimide (IM) [Phys. Chem. Chem. Phys., 2010, 12, 9783]. The energies for the electronic excited states as well as the ground states were computed for these molecules using the multi-reference perturbation calculations based on the second order Rayleigh–Schrödinger perturbation theory (CASPT2) at the cc-pVDZ basis set level. The electron-accepting or electron-donating effect caused by bromine-substitution was discussed in the intra-molecular charge transfer (ICT) mechanism. The order of natural orbitals of the bromine-substituted monovalent anion with a deprotonated indole NH group (I(−)(−)M-Br) was found to be rearranged by the effect of electron-donation, which leads to pseudo-crossing of the potential energy cures of the S1 and S2 states. The large stokes shift observed for I(−)(−)M-Br was due to pseudo-crossing. Meanwhile, IM and IM-Br show abnormal deprotonation, which is explained by the charge distribution on the indole and maleimide moieties. Finally, the monovalent anions I(−)(−)M-Br and I(−)(−)M by a deprotonation of the indole NH end and the neutral IS were proposed to be the most feasible candidates corresponding to the experimental spectra in solution.