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The performance of various hybrid density functionals is assessed for 105 singlet and 105 corresponding triplet vertical excitation energies from the QUEST database. The overall lowest mean absolute error is obtained with the local hybrid (LH) functional LH12ct-SsirPW92 with individual errors of 0.11 eV (0.11 eV) for singlet (triplet) n → π* excitations and 0.29 eV (0.17 eV) for π → π* excitations. This is slightly better than with the overall best performing global hybrid M06-2X [n → π*: 0.13 eV (0.17 eV), π → π*: 0.30 eV (0.20 eV)], while most other global and range-separated hybrids and some LHs suffer from the “triplet problem” of time-dependent density functional theory. This is exemplified by correlating the errors for singlet and triplet excitations on a state-by-state basis. The excellent performance of LHs based on a common local mixing function, i.e., an LMF constructed from the spin-summed rather than the spin-resolved semilocal quantities, is systematically investigated by the introduction of a spin-channel interpolation scheme that allows us to continuously modulate the fraction of opposite-spin terms used in the LMF. The correlation of triplet and singlet errors is systematically improved for the n → π* excitations when larger fractions of the opposite-spin-channel are used in the LMF, whereas this effect is limited for the π → π* excitations. This strongly supports a previously made hypothesis that attributes the excellent performance of LHs based on a common LMF to cross-spin-channel nondynamical correlation terms.

We present an efficient implementation of nonadiabatic coupling matrix elements (NACMEs) for density functional theory/multireference configuration interaction (DFT/MRCI) wave functions of singlet and triplet multiplicity and an extension of the Vibes program that allows us to determine rate constants for internal conversion (IC) in addition to intersystem crossing (ISC) nonradiative transitions. Following the suggestion of Plasser et al. [J. Chem. Theory Comput. 12, 1207 (2016)], the derivative couplings are computed as finite differences of wave function overlaps. Several measures have been taken to speed up the calculation of the NACMEs. Schur’s determinant complement is employed to build up the determinant of the full matrix of spin-blocked orbital overlaps from precomputed spin factors with fixed orbital occupation. Test calculations on formaldehyde, pyrazine, and xanthone show that the mutual excitation level of the configurations at the reference and displaced geometries can be restricted to 1. In combination with a cutoff parameter of tnorm = 10−8 for the DFT/MRCI wave function expansion, this approximation leads to substantial savings of cpu time without essential loss of precision. With regard to applications, the photoexcitation decay kinetics of xanthone in apolar media and in aqueous solution is in the focus of the present work. The results of our computational study substantiate the conjecture that S1 T2 reverse ISC outcompetes the T2 ↝ T1 IC in aqueous solution, thus explaining the occurrence of delayed fluorescence in addition to prompt fluorescence.

The Infrared (IR) and Raman spectra of various defects in silicon, containing both oxygen atoms (in the interstitial position, Oi) and a vacancy, are computed at the quantum mechanical level by using a periodic supercell approach based on a hybrid functional (B3LYP), an all-electron Gaussian-type basis set, and the Crystal code. The first of these defects is VO: the oxygen atom, twofold coordinated, saturates the unpaired electrons of two of the four carbon atoms on first neighbors of the vacancy. The two remaining unpaired electrons on the first neighbors of the vacancy can combine to give a triplet (Sz = 1) or a singlet (Sz = 0) state; both states are investigated for the neutral form of the defect, together with the doublet solution, the ground state of the negatively charged defect. Defects containing two, three, and four oxygen atoms, in conjunction with the vacancy V, are also investigated as reported in many experimental papers: VO2 and VOOi (two oxygen atoms inside the vacancy, or one in the vacancy and one in interstitial position between two Si atoms) and VO2Oi and VO22Oi (containing three and four oxygen atoms). This study integrates and complements a recent investigation referring to Oi defects [Gentile et al., J. Chem. Phys. 152, 054502 (2020)]. A general good agreement is observed between the simulated IR spectra and experimental observations referring to VOx (x = 1–4) defects.

Photoswitchable diarylethenes (DAEs), over years of intense fundamental and applied research, have been established among the most commonly chosen molecular photoswitches, often employed as controlling units in molecular devices and smart materials. At the same time, providing reliable explanation for their photophysical behavior, especially the mechanism of the photo-cycloreversion transformation, turned out to be a highly challenging task. Herein, we investigate this mechanism in detail by means of multireference semi-empirical quantum chemistry calculations, allowing, for the first time, for a balanced treatment of the static and dynamic correlation effects, both playing a crucial role in DAE photochemistry. In the course of our study, we find the second singlet excited state of double electronic-excitation character to be the key to understanding the nature of the photo-cycloreversion transformation in DAE molecular photoswitches.

Photoionization dynamics of N,N-dimethylaniline (DMA) from highly electronically excited states in ethanol solution was investigated by means of femtosecond two-pulse two-photon excitation transient absorption (2PE-TA) spectroscopy. The first pump pulse prepares the lowest singlet excited state (S1 state) of DMA, and the second one excites the S1 state into higher excited states. In the case with the second pulse at 500 nm, the ionization took place via a rapid channel (

We have studied two regioisomeric terrylenediimide (TDI) dimers in which the 1-positions of two TDIs are linked via 1,3- or 1,4-phenylene spacers, mTDI2 and pTDI, respectively. The nature and the dynamics of the multiexciton state are tuned by altering the through-bond electronic couplings in the ground and excited states and by changing the solvent environment. Our results show that controlling the electronic coupling between the two chromophores by an appropriate choice of linker can result in independent triplet state formation, even though the initial correlated triplet pair state is confined to a dimer. Moreover, even in polar solvents, if the electronic coupling is strong, the correlated triplet pair state is observed prior to symmetry-breaking charge separation. These results point out the close relationship between the singlet, correlated triplet pair, and charge transfer states in molecular dimers.

Stabilizing mechanisms of three possible isomers (phenolate-keto, phenolate-enol, and phenol-enolate) of the oxyluciferin anion hydrated with quantum explicit water molecules in the first singlet excited state were investigated using first-principles Born–Oppenheimer molecular dynamics simulations for up to 1.8 ns (or 3.7 × 106 MD steps), revealing that the surrounding water molecules were distributed to form clear single-layered structures for phenolate-keto and multi-layered structures for phenolate-enol and phenol-enolate isomers. The isomers employed different stabilizing mechanisms compared to the ground state. Only the phenolate-keto isomer became attracted to the water molecules in its excited state and was stabilized by increasing the number of hydrogen bonds with nearby water molecules. The most stable isomer in the excited state was the phenolate-keto, and the phenolate-enol and phenol-enolate isomers were higher in energy by ∼0.38 eV and 0.57 eV, respectively, than the phenolate-keto. This was in contrast to the case of ground state in which the phenolate-enol was the most stable isomer.

We present an ab initio exciton model that extends the Frenkel exciton model and includes valence, charge-transfer, and multiexcitonic excited states. It serves as a general, parameter-free, yet computationally efficient and scalable approach for simulation of singlet fission processes in multichromophoric systems. A comparison with multiconfigurational methods confirms that our exciton model predicts consistent energies and couplings for the pentacene dimer and captures the correct physics. Calculations of larger pentacene clusters demonstrate the computational scalability of the exciton model and suggest that the mixing between local and charge-transfer excitations narrows the gap between singlet and multiexcitonic states. Local vibrations of pentacene molecules are found to facilitate singlet–multiexcitonic state-crossing and hence are important for understanding singlet fission. The exciton model developed in this work also sets the stage for further implementation of the nuclear gradients and nonadiabatic couplings needed for first principles nonadiabatic quantum molecular dynamics simulations of singlet fission.

The molecular dissociation energy has often been explained and discussed in terms of singlet bonds, formed by bounded pairs of valence electrons. In this work we use a highly correlated resonating valence bond ansatz, providing a consistent paradigm for the chemical bond, where spin fluctuations are shown to play a crucial role. Spin fluctuations are known to be important in magnetic systems and correspond to the zero point motion of the spin waves emerging from a magnetic broken symmetry state. Recently, in order to explain the excitation spectrum of the carbon dimer, an unusual quadruple bond has been proposed. Within our ansatz, a satisfactory description of the carbon dimer is determined by the magnetic interaction of two Carbon atoms with antiferromagnetically ordered S = 1 magnetic moments. This is a first step that, thanks to the highly scalable and efficient quantum Monte Carlo technique, may open the way for understanding challenging complex systems containing atoms with large spins (e.g. transition metals).

In this paper, we introduce a new strategy for improving the efficiency of upconversion emissions based on triplet–triplet exciton annihilation (TTA-UC) in the solid state. We designed a ternary blend system consisting of a triplet sensitizer (TS), an exciton-transporting host polymer, and a small amount of an annihilator in which the triplet-state energies of the TS, host, and annihilator decrease in this order. The key idea underpinning this concept involves first transferring the triplet excitons generated by the TS to the host and then to the annihilator, driven by the cascaded triplet energy landscape. Because of the small annihilator blend ratio, the local density of triplet excitons in the annihilator domain is higher than those in conventional binary TS/annihilator systems, which is advantageous for TTA-UC because TTA is a density-dependent bimolecular reaction. We tracked the triplet exciton dynamics in the ternary blend film by transient absorption spectroscopy. Host triplet excitons are generated through triplet energy transfer from the TS following intersystem crossing in the TS. These triplet excitons then diffuse in the host domain and accumulate in the annihilator domain. The accumulated triplet excitons undergo TTA to generate singlet excitons that are higher in energy than the excitation source, resulting in UC emission. Based on the excitation-intensity and blend-ratio dependences of TTA-UC, we found that our concept has a positive impact on accelerating TTA.

The performance of organic light-emitting diodes based on thermally activated delayed fluorescence emitters depends on the efficiency of reverse intersystem crossing (RISC) processes, which are promoted by a small energy gap between the lowest singlet (S1) and triplet (T1) excited states and large spin–orbit couplings. Recently, it was proposed that the introduction of secondary donor units into 2,3,4,5,6-penta(9H-carbazol-9-yl)benzonitrile (5CzBN) can significantly increase the mixing between triplet states with charge-transfer (CT) and local-excitation characteristics and consequently increase the spin–orbit couplings. Here, the results of long-range corrected density functional theory calculations show that the main impact on the RISC rates of substituting 5CzBN with secondary donors is due to a decrease in adiabatic singlet–triplet energy gaps and intramolecular reorganization energies rather than to a change in spin–orbit couplings. Our calculations underline that at least two singlet and three triplet excited states contribute to the ISC/RISC processes in 5CzBN and its derivatives. In addition, we find that in all emitters, the lowest singlet excited-state potential energy surface has a double-minimum shape.

Internal conversion decay dynamics associated with the potential energy surfaces of three low-lying singlet excited electronic states, S1 (ππ*, A′), S2 (ππ*, A′), and S3 (nπ*, A″), of tropolone are investigated theoretically. Energetic and spatial aspects of conical intersections of these electronic states are explored with the aid of the linear vibronic coupling approach. Symmetry selection rules suggest that non-totally symmetric modes would act as coupling modes between S1 and S3 as well as between S2 and S3. We found that the S1–S2 interstate coupling via totally symmetric modes is very weak. A diabatic vibronic Hamiltonian consisting of 32 vibrational degrees of freedom is constructed to simulate the photoinduced dynamics of S0 → S1 and S0 → S2 transitions. We observe a direct nonadiabatic population transfer from S1 to S3, bypassing S2, during the initial wavepacket propagation on S1. On the other hand, the initial wavepacket evolving on S2 would pass through the S2–S3 and S1–S3 conical intersections before reaching S1. The presence of multiple proton transfer channels on the S1–S2–S3 coupled potential energy surfaces of tropolone is analyzed. Our findings necessitate the treatment of proton tunneling dynamics of tropolone beyond the adiabatic symmetric double well potentials.

The vacuum ultraviolet (VUV) spectrum for cyclohepta-1,3,5-triene up to 10.8 eV shows several broad bands, which are compared with electron impact spectra. Local curve fitting exposed groups of sharp vibrational peaks, which are assigned to Rydberg states. The vertical excitation profile of the VUV spectrum, reproduced by time dependent density functional theory (TDDFT), gives a good interpretation of the principal regions of absorption. Fourth order Möller–Plessett perturbation theory, including single, double, and quadruple excitations, showed that the lowest singlet and triplet states retain CS symmetry. This contrasts with TDDFT where several low-lying excited states are planar. Detailed vibrational analysis of the first UV band was performed by Franck–Condon, Herzberg–Teller, and their combined methods. These show the dominance of mid-range frequencies, while the lowest frequency (75 cm−1) has negligible importance. In contrast, the second excited (Rydberg) state shows a major progression with separations of 115 (6) cm−1. This is interpreted by re-analysis of the X2A′ ionic state at the anharmonic level. Extremely low exponent Gaussian functions enabled several low-lying Rydberg state energies to be determined theoretically; extrapolation of the 3s-, 4s-, and 5s-Rydberg state calculated energies gives the adiabatic ionization energy as 7.837 eV (4) with δ 0.964 (2). Similarly, extrapolation of the centroids of the observed Rydberg states gave the vertical ionization energy (VIE) as VIE1 = 8.675 ± 0.077, close to the photoelectron spectroscopy VIE value [8.55 (1) eV]. Postprint

A series of triads consisting of a triarylamine donor, a naphthalenediimide acceptor, and a palladium photosensitizer bridge was investigated for the photoinduced electron transfer processes and the spin chemistry involved. In this series, the ligand in the palladium photosensitizer was varied from bis-dipyrrinato to porphodimethenato and to a porphyrin. With the porphyrin photosensitizer, no charge separated state could be reached. This is caused by the direct relaxation of the excited photosensitizer to the ground state by intersystem crossing. The bis-dipyrrinato-palladium photosensitizer gave only a little yield (7%) of the charge separated state, which is due to the population of a metal centered triplet state and a concomitant geometrical rearrangement to a disphenoidal coordination sphere. This state relaxes rapidly to the ground state. In contrast, in the porphodimethenato-palladium triads, a long lived (μs to ms) charge separated state could be generated in high quantum yields (66%-74%) because, here, the population of a triplet metal centered state is inhibited by geometrical constraints. The magnetic field dependent transient absorption measurement of one of the porphodimethenato triads revealed a giant magnetic field effect by a factor of 26 on the signal amplitude of the charge separated state. This is the consequence of a magnetic field dependent triplet-singlet interconversion that inhibits the fast decay of the charge separated triplet state through the singlet recombination channel. A systematic comparative analysis of the spin-dependent kinetics in terms of three classical and one fully quantum theoretical methods is provided, shedding light on the pros and cons of each of them.

Quantum dot (QD) sensitized triplet exciton generation has demonstrated promising applications in various fields such as photon up-conversion through triplet–triplet annihilation. However, how direct triplet energy transfer from the QD to the acceptor through Dexter energy transfer (DET) competes with other processes, including Forster resonance energy transfer (FRET) and charge transfer, remains poorly understood. Herein, the competition of these pathways for QD-sensitized triplet excited state generation in CdSe QD-modified boron dipyrromethene (BODIPY) complexes is studied using transient absorption spectroscopy. After excitation of the CdSe QD with 500 nm pulses, the BODIPY triplet excited state is generated through charge recombination in a charge separated intermediate state (QD−·–BODIPY+·). This intermediate state is populated either through FRET from the excited QD to BODIPY followed by electron transfer from the singlet excited state of BODIPY to the QD or through hole transfer from the excited QD to BODIPY. The triplet excited state generation efficiencies from the FRET and hole transfer pathways are estimated to be (6.18 ± 1.39)% and (13.5 ± 3.1)%, respectively. Compared to these indirect pathways, direct DET from the QD to the BODIPY triplet state is kinetically not competitive. These results demonstrate that sequential charge transfer can be an efficient pathway for triplet excited state generation in QD–acceptor complexes.

The excited state photodynamics of isolated benzene have been studied in the nanosecond range by two-step photoionization through various vibrations of the lowest singlet state, with imaging photoelectron spectroscopy detection. Photoelectron spectra are measured as a function of pump–probe delay time, and their time evolution is successfully compared to a biexponential decay function without regard to a particular kinetic model. The only reasonable kinetic model with only two exponentials is the one that involves an intersystem crossing from S1 to T1, although that model has previously been called into question by high-resolution studies that failed to find any singlet–triplet perturbations in Zeeman studies of the S1 spectrum. That contradiction remains unresolved.

The all-electron first-principles GW+Bethe-Salpeter method was applied to six carbazole benzonitrile (CzBN) derivatives, which were recently reported to be both thermally activated delayed fluorescence (TADF) active and inactive despite their singlet-triplet splittings being commonly around 0.2 eV. The present method successfully reproduced very similar photoabsorption spectra as experiments from the viewpoint of the peak positions and relative peak heights. We also performed exciton analysis with the exciton wave functions for several lowest singlet and triplet exciton states to reveal the details of the optical properties. We applied this to not only the present six CzBN derivatives but also 18 other TADF molecules and proposed a new exciton map to classify the molecules as the TADF active/inactive by using the exciton binding energy in the vertical axis and the ratio of electron and hole delocalization in the horizontal axis. Our results suggest two possible TADF mechanisms: spatially less localized hole states than the electron states where the exciton binding energy is proportional to the ratio of hole and electron delocalization and spatially more localized hole states than the electron states where the exciton binding energy should be large.

Excited states relaxation in complex molecules often involves two types of nonradiative transitions, internal conversion (IC) and intersystem crossing (ISC). In the situations when the timescales of IC and ISC are comparable, an interplay between these two types of transitions can lead to complex nonadiabatic dynamics on multiple electronic states of different characters and spin multiplicities. We demonstrate that the generalized ab initio multiple spawning (GAIMS) method interfaced with the fast graphics processing unit-based TeraChem electronic structure code can be used to model such nonadiabatic dynamics involving both the IC and ISC transitions in molecules of moderate size. We carried out 1500 fs GAIMS simulations leading to the creation of up to 2500 trajectory basis functions to study the excited states relaxation in 2-cyclopentenone. After a vertical excitation from the ground state to the bright S2 state, the molecule quickly relaxes to the S1 state via conical intersection. The following relaxation proceeds along two competing pathways: one involves IC to the ground state, and the other is dominated by ISC to the low-lying triplet states. The time constants describing the population transfer between the six lowest singlet and triplet states predicted by the GAIMS dynamics are in good agreement with the characteristic times of IC and ISC obtained from the analysis of the time-resolved photoelectron spectrum.

In this work, we consider the existence and topography of seams of conical intersections (CIs) for two key singlet–triplet systems, including a uniformly scaled spin–orbit interaction. The basic one triplet and one singlet state system denoted as (S0,T1) and the two singlets and one triplet system denoted as (S0,S1,T1) are treated. Essential to this analysis are realistic electronic structure data taken from a recently reported neural network fit for the 1,21A and 13A states of NH3, including Hsf (spin-free) and Hso (spin–orbit) surfaces derived from high quality ab initio wavefunctions. Three types of seams for the (S0,S1,T1) system are reported, which depend on the choice of the electronic Hamiltonian, He. The nonrelativistic CI seam [He = Hsf, (S0,S1)], the energy minimized nonrelativistic singlet–triplet intersection seam [He = Hsf, (S0,T1)], and the fully relativistic seam in the spin-diabatic representation (He = Htot = Hsf + Hso) are reported as functions of R(N–H). The derivative couplings are computed using He = Htot and Hsf from the fit data. The line integral of the derivative coupling is employed to juxtapose the geometric phase in the relativistic, He = Htot, and nonrelativistic, He = Hsf, cases. It is found for the (S0,T1) system that there is no CI in the spin-adiabatic representation, while for the (S0,S1,T1) system, CI can only be formed for two pairs of spin-adiabatic electronic states. The geometric phase effect thus needs to be handled with care when it comes to spin-nonconserving dynamics simulations.

Coupled pairs of nuclear spin-1/2 support one singlet state and three triplet states. Transitions between the singlet state and one of the triplet states may be driven by an oscillating low-frequency magnetic field, in the presence of couplings to a third nuclear spin, and a weak bias magnetic field. The oscillating field is in the same direction as the bias field and is called a WOLF (Weak Oscillating Low Field) pulse. Application of a WOLF pulse allows for the generation of strong nuclear hyperpolarization of 13C nuclei, starting from the nuclear singlet polarization of a 1H spin pair, associated with the enriched para-spin isomer of hydrogen gas. Hyperpolarization is demonstrated for two molecular systems.

Nonadiabatic trajectory surface hopping simulations are reported for trans-C5H6NH2+, a model of the rhodopsin chromophore, using the augmented fewest-switches algorithm. Electronic structure calculations were performed using time-dependent density functional theory (TDDFT) in both its conventional linear-response (LR) and its spin-flip (SF) formulations. In the SF-TDDFT case, spin contamination in the low-lying singlet states is removed by projecting out the lowest triplet component during iterative solution of the TDDFT eigenvalue problem. The results show that SF-TDDFT qualitatively describes the photoisomerization of trans-C5H6NH2+, with favorable comparison to previous studies using multireference electronic structure methods. In contrast, conventional LR-TDDFT affords qualitatively different photodynamics due to an incorrect excited-state potential surface near the Franck–Condon region. In addition, the photochemistry (involving pre-twisting of the central double bond) appears to be different for SF- and LR-TDDFT, which may be a consequence of different conical intersection topographies afforded by these two methods. The present results contrast with previous surface-hopping studies suggesting that the LR-TDDFT method’s incorrect topology around S1/S0 conical intersections is immaterial to the photodynamics.

We have studied the magneto-electroluminescence (MEL) response in light emitting diodes based on 2D-(PEA)2PbI4 and 3D-MAPbI3 hybrid organic-inorganic perovskites at cryogenic temperatures. We found that the MEL is negative, i.e., the EL decreases with the applied field strength, B. In addition, the MEL(B) response has a Lorentzian line shape whose width depends on the perovskite used. We interpret the MEL(B) response using the "Δg mechanism" in which the spin of the injected electron-hole (e-h) pairs oscillates between singlet and triplet configurations due to different precession frequencies of the electron and hole constituents that originate from the difference, Δg, in the electron and hole gyromagnetic constants, g. In this model, the MEL(B) linewidth is inversely proportional to the spin lifetime and Δg. The model used is validated by directly measuring the spin lifetime of photogenerated e-h pairs using the circularly polarized pump-probe transmission technique with 100 fs resolution.

We report the magnetic field dependence of the magneto-photocurrent (MPC) in organic light emitting diodes made of homo-polymer organic layers and compare it to the measured magneto-conductance (MC) in the same diodes. We find that the response MPC(B) is very different from MC(B) in at least two respects. (a) The low field (B50 mT) response of MPC(B) is narrower by a factor of ∼5 from that of MC(B). (b) At high fields (B4 T), MPC(B) has a stronger dependence on B, d(MPC)/dB ∼ 5d(MC)/dB. We attribute these differences to a unique feature of charge transfer excimers that are responsible for MPC: sub-ns fast fusion back to singlet excitons and slow (ns to μs) dissociation to free charges. In contrast, MC(B) is determined by long lived (10 ns) polaron pairs having singlet and triplet dissociation rates of the same order.

Generation of triplet excited states through radical pair intermediates has been extensively studied in molecular complexes. Similar schemes remain rare in hybrid structures of quantum dot-organic molecules, despite intense recent interest of quantum dot sensitized triplet excited state generation. Herein, we demonstrate that the efficiency of the intersystem crossing from the singlet to the triplet state in boron dipyrromethene (BODIPY) can be enhanced in CdSe quantum dot-BODIPY complexes through a radical pair intermediate state consisting of an unpaired electron in the quantum dot conduction band and that in oxidized BODIPY. By transient absorption spectroscopy, we show that the excitation of BODIPY with 650 nm light leads to the formation of a charge separated state by electron transfer from BODIPY to CdSe (with a time constant of 6.33 ± 1.13 ns), competing with internal conversion to the ground state within BODIPY, and the radical pair state decays subsequently by back charge recombination to generate a triplet excited state (with a time constant of 158 ± 28 ns) or the ground state of BODIPY. The overall quantum efficiency of BODIPY triplet excited state generation was determined to be (27.2 ± 3.0)%. The findings of efficient triplet state formation and intermediate radical pair states in this hybrid system suggest that quantum dot-molecule complexes may be a promising platform for spintronics applications.

In this paper, the generalized Kohn-Sham energy decomposition analysis (GKS-EDA) scheme is extended to molecular interactions in open shell singlet states, which is a challenge for many popular EDA methods due to the multireference character. Based on broken symmetry (BS) unrestricted density functional theory with a spin projection approximation, the extension scheme, named GKS-EDA(BS) in this paper, divides the total interaction energy into electrostatic, exchange-repulsion, polarization, correlation, and dispersion terms. Test examples include the pancake bond in the phenalenyl dimer, the ligand interactions in the Fe(ii)-porphyrin complexes, and the radical interactions in dehydrogenated guanine-cytosine base pairs and show that GKS-EDA(BS) is a practical EDA tool for open shell singlet systems.

Generation of electron spin polarization (ESP) during the bimolecular quenching of an excited chromophore by a free radical is generally explained by the radical-triplet pair mechanism, which is capable of giving the magnitudes of ESP arising from the quenching of the singlet or the triplet excited chromophore. When the chromophore and the free radical are covalently linked, although there are several mechanisms to explain the observed spin-polarized electron paramagnetic resonance signals under a variety of experimental conditions and in different chromophore-radical systems, there are no schemes that allow quantitative determination of the magnitude of ESP. In this work, we present a phenomenological scheme with this objective. In this scheme, we have incorporated several concepts of the reversed quartet mechanism of Rozenshtein et al. [J. Phys. Chem. A 109, 11144 (2005)] to our phenomenological sequential quenching scheme [V. Rane and R. Das, J. Phys. Chem. A 119, 5515 (2015)] of ESP in covalently linked chromophore-radical systems. This phenomenological reversed quartet scheme is able to explain the observed inversion of ESP with time and can also give a quantitative measure of the absorptive and emissive ESP in such systems. We have applied this scheme to the photophysical quenching of a series of newly synthesized pyrene-TEMPO molecules, where a spacer group of different lengths covalently links the pyrene chromophore and the TEMPO free radical. Given the simplicity of our scheme, reasonable estimates of the magnitudes of the ESP have been obtained in all cases.

CdSe quantum dots are functionalized with the organic dye iron β-tetraaminophthalocyanine to reward a solution-processable hybrid material with two individually addressable optical resonances. We exploit this dual functionality during optical write/optical read patterning experiments and show that it is possible to simultaneously write complex optical patterns with positive and negative fluorescence contrast. This is enabled by a fluorescence enhancement under near-resonant excitation of the quantum dots in combination with a fluorescence bleaching during excitation of the singlet transition of the phthalocyanine. The presence of the organic dye not only enables negative optical patterning but also enhances the contrast during positive patterning. Furthermore, the patterning result is strongly dependent on the excitation wavelength during readout. Our results highlight the new possibilities that arise from combining inorganic quantum dots and organic π-systems into hybrid nanocomposites.

Analytic energy gradients of individual singlet and triplet states with respect to nuclear coordinates are derived and implemented for the collinear mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT), which eliminates the problematic spin-contamination of SF-TDDFT. Dimensional-transformation matrices for the singlet and triplet response spaces are introduced, simplifying the subsequent derivations. These matrices enable the general forms of MRSF-TDDFT equations to be similar to those of SF-TDDFT, suggesting that the computational overhead of singlet or triplet states for MRSF-TDDFT is nearly identical to that of SF-TDDFT. In test calculations, the new MRSF-TDDFT yields quite different optimized structures and energies as compared to SF-TDDFT. These differences turned out to mainly come from the spin-contamination of SF-TDDFT, which are largely cured by MRSF-TDDFT. In addition, it was demonstrated that the clear separation of singlet states from triplets dramatically simplifies the location of minimum energy conical intersection. As a result, it is clear that the MRSF-TDDFT has advantages over SF-TDDFT in terms of both accuracy and practicality. Therefore, it can be a preferred method, which is readily applied to other "black-box" type applications, such as the minimum-energy optimization, reaction path following, and molecular dynamics simulations.

We report the extended explicitly correlated approximate coupled-cluster singles and doubles CC2(F12*)-XSP method suitable for response properties. Equations are derived using an automated approach and have subsequently been hand-coded into the computer program KOALA, in which for all two-electron integrals, density fitting is employed. Numerical results are presented for the lowest two vertical singlet excitation energies of a set of selected molecules. The results show that the CC2(F12*)-XSP method provides the correct basis-set limit with no bias to the ground state, and an excellent agreement with reference CC2 values using large basis sets is found. Using Dunning's aug-cc-pVTZ basis, the CC2(F12*)-XSP method yields excitation energies which are converged within 1 mEh to the basis-set limit for valence excitations.

We show that in a spin system of two magnetically inequivalent protons coupled to a heteronucleus such as 13C, an adiabatic magnetic field sweep, passing through zero field, transfers proton singlet order into magnetization of the coupled heteronucleus. This effect is potentially useful in parahydrogen-enhanced nuclear magnetic resonance, and is demonstrated on singlet-hyperpolarized [1-13C]maleic acid, which is prepared via the reaction between [1-13C]acetylene dicarboxylic acid and para-enriched hydrogen gas. The magnetic field sweeps are of microtesla amplitudes, and have durations on the order of seconds. We show a polarization enhancement by a factor of 104 in the 13C spectra of [1-13C]maleic acid in a 1.4 T magnetic field.

We analyze the energetics and internal conversion dynamics of singlet and triplet manifolds to identify the possible intersystem crossing pathways in odd-numbered [n]cycloparaphenylenes ([n]CPPs, n = 5, 7, and 9). Quantum wavepacket propagation calculations within the linear vibronic coupling framework suggest that both [5]- and [7]CPPs rapidly relax to S2 upon populating “bright” higher singlet excited states. The S2–S1 energy decreases with the increase in CPP size, and hence, [9]CPP exhibits a faster S2 → S1 internal conversion decay. Higher triplet states act as receiver states for the intersystem crossing happening either via S1 or S2. The wavepacket evolving on the receiver triplet state would decay to lower states via multiple conical intersections and reach T1. The estimated size-dependent fluorescence and emission energies are in good accord with the experiment.

A synchrotron-based vacuum ultraviolet (VUV) absorption spectrum of norbornadiene (NBD) is reported, and the extensive vibrational structure obtained has been analyzed. The previously known 5b 13s-Rydberg state has been reinterpreted by comparison with our recent high-resolution photoelectron spectral analysis of the X 2B 1 ionic state. Additional vibrational details in the region of this Rydberg state are observed in its VUV spectrum when compared with the photoelectron 2B 1 ionic state; this is attributed to the underlying valence state structure in the VUV. Valence and Rydberg state energies have been obtained by configuration interaction and time-dependent density functional theoretical methods. Several low-lying singlet valence states, especially those that arise from ππ* excitations, conventionally termed NV 1 to NV 4, have been examined in detail. Their Franck-Condon (FC) and Herzberg-Teller (HT) profiles have been investigated and fitted to the VUV spectrum. Estimates of the experimental 0 0 band positions have been made from these fits. The anomaly of the observed UV absorption by the 1A 2 state of NBD is attributed to HT effects. Generally, the HT components are less than 10% of the FC terms. The calculated 5b 13s lowest Rydberg state also shows a low level of HT components. The observed electron impact spectra of NBD have been analyzed in detail in terms of triplet states.

Recent studies have indicated that nitramide (NH2NO2) may be formed more plentifully in the atmosphere than previously thought, while also being a missing source of the greenhouse gas nitrous oxide (N2O) via catalyzed isomerization. To validate the importance of NH2NO2 in the Earth’s atmosphere, the ground and first electronic excited states of NH2NO2 were characterized and its photochemistry was investigated using multireference and coupled cluster methods. NH2NO2 is non-planar and of singlet multiplicity in the ground state while exhibiting large out-of-plane rotation in the triplet first excited state. One-dimensional cuts of the adiabatic potential energy surface calculated using the MRCI+Q method show low-lying singlet electronic states with minima in their potential along the N–N and N–O bond coordinates. Due to vertical excitation energies in the 225–180 nm region, photochemical processes will not compete in the troposphere, causing N2O production to be the predicted major removal process of NH2NO2. In the upper atmosphere, photodissociation to form NH2NO + O (3P) is suggested to be a major photochemical removal pathway.

Emissive layers in phosphorescent organic light-emitting diodes commonly make use of guest–host blends such as Ir(ppy)3:CBP to achieve high external quantum efficiencies. However, while the Ir(ppy)3:CBP blend has been studied experimentally, crucial questions remain regarding how exciton diffusion is dependent on the distribution of the guest in the host, which can currently only be addressed at the atomic level via computational modeling. In this work, kinetic Monte Carlo simulations are utilized to gain insight into exciton diffusion in Ir(ppy)3:CBP blend films. The effects of both guest concentration and exciton density on various system properties are analyzed, including the probability of singlet excitons being converted to triplets, and the probability of those triplets decaying radiatively. Significantly, these simulations suggest that triplet diffusion occurs almost exclusively via guest–guest Dexter transfer and that concentration quenching of triplets induced by guest–guest intermolecular dipole-dipole interactions has a negligible effect at high exciton densities due to the prevalence of triplet–triplet annihilation. Furthermore, results for vacuum deposited morphologies derived from molecular dynamics simulations are compared to the results obtained using a simple cubic lattice approximation with randomly distributed guest molecules. We show that while differences in host-based processes such as singlet diffusion are observed, overall, the results on the fate of the excitons are in good agreement for the two morphology types, particularly for guest-based processes at low guest concentrations where guest clustering is limited.

The accurate description of biradical systems, and in particular the resolution of their singlet-triplet gaps, has long posed a major challenge to the development of electronic structure theories. Biradicaloid singlet ground states are often marked by strong correlation and, hence, may not be accurately treated by mainstream, single-reference methods such as density functional theory or coupled cluster theory. The anti-Hermitian contracted Schr\"odinger equation (ACSE), whose fundamental quantity is the two-electron reduced density matrix rather than the N-electron wave function, has previously been shown to account for both dynamic and strong correlations when seeded with a strongly correlated guess from a complete active space (CAS) calculation. Here, we develop a spin-averaged implementation of the ACSE, allowing it to treat higher multiplicity states from the CAS input without additional state preparation. We apply the spin-averaged ACSE to calculate the singlet-triplet gaps in a set of small main group biradicaloids, as well as the organic four-electron biradicals trimethylenemethane and cyclobutadiene, and naphthalene, benchmarking the results against other state-of-the-art methods reported in the literature.

In the present work, we performed a computational investigation of the photoisomerization of spiro[1,3-dihydroindole-2,2′-chromene] [spiropyran (SP)] to merocyanine. The electronic energies and wavefunctions were obtained from configuration interaction calculations, using the floating occupation molecular orbital method, in a semiempirical framework. The parameters of the semiempirical Hamiltonian were re-optimized to reproduce ab initio literature data for SP. In our dynamics simulations, we considered, besides S0, the excited states S1, S2, and S3, which are very close in energy in the Franck–Condon region. We obtained a singlet lifetime of 0.67 ps, in line with the experimental results. We found the photoisomerization quantum yield to depend on the electronic state initially populated.

Nonadiabatic coupling is absent between the electronic ground X and first excited (singlet) A states of formaldehyde. As laser fields can induce conical intersections between these two electronic states, formaldehyde is particularly suitable for investigating light-induced nonadiabaticity in a polyatomic molecule. The present work reports on the spectrum induced by light-the so-called field-dressed spectrum-probed by a weak laser pulse. A full-dimensional ab initio approach in the framework of Floquet-state representation is applied. The low-energy spectrum, which without the dressing field would correspond to an infrared vibrational spectrum in the X-state, and the high-energy spectrum, which without the dressing field would correspond to the X → A spectrum, are computed and analyzed. The spectra are shown to be highly sensitive to the frequency of the dressing light allowing one to isolate different nonadiabatic phenomena.

Polymers are desirable optoelectronic materials, stemming from their solution processability, tunable electronic properties, and large absorption coefficients. An exciting development is the recent discovery that singlet fission (SF), the conversion of a singlet exciton to a pair of triplet states, can occur along the backbone of an individual conjugated polymer chain. Compared to other intramolecular SF compounds, the nature of the triplet pair state in SF polymers remains poorly understood, hampering the development of new materials with optimized excited state dynamics. Here, we investigate the effect of solvent polarity on the triplet pair dynamics in the SF polymer polybenzodithiophene-thiophene-1,1-dioxide. We use transient emission measurements to study isolated polymer chains in solution and use the change in the solvent polarity to investigate the role of charge transfer character in both the singlet exciton and the triplet pair multiexciton. We identify both singlet fluorescence and direct triplet pair emission, indicating significant symmetry breaking. Surprisingly, the singlet emission peak is relatively insensitive to solvent polarity despite its nominal "charge-transfer" nature. In contrast, the redshift of the triplet pair energy with increasing solvent polarity indicates significant charge transfer character. While the energy separation between singlet and triplet pair states increases with solvent polarity, the overall SF rate constant depends on both the energetic driving force and additional environmental factors. The triplet pair lifetime is directly determined by the solvent effect on its overall energy. The dominant recombination channel is a concerted, radiationless decay process that scales as predicted by a simple energy gap law.

Thermally activated triplet-to-singlet upconversion is attractive from both fundamental science and exciton engineering, but controlling the process from molecular configuration is still unrevealed. In particular, the flexibility of the freedom of molecular geometry is of major importance to understand the kinetics of the phonon-induced upconversion. Here, we focus on two linearly connected donor-acceptor molecules, 9,9-dimethyl-9,10-dihydroacridine-2,4,6-triphenyl-1,3,5-triazine (DMAC-TRZ) and hexamethylazatriangulene-2,4,6-triphenyl-1,3,5-triazine (HMAT-TRZ), as the model system. While DMAC-TRZ possesses a rotational degree of freedom in the dihedral angle between the donor and acceptor moieties, i.e., C-N bond in tertiary amine, the rotation is structurally restricted in HMAT-TRZ. The rotationally flexible DMAC-TRZ showed significant triplet-to-singlet upconversion caused by thermal activation. On the other hand, the rotation-restricted HMAT-TRZ showed negligible thermal upconversion efficiency. We elaborate on the origin of the photophysical properties from the viewpoint of the geometries in the excited states using time-resolved infrared spectroscopy and quantum chemical calculations. We uncovered that the structural restriction of the intramolecular flexibility significantly affects the optimized geometry and phonon modes coupled to the spin conversion. As a result of the rotation restriction, the spin flipping in HMAT-TRZ was coupled to bending motion instead of the rotation. In contrast, the free rotation fluctuation in the DMAC-TRZ mixes local-excitation and charge-transfer characters, leading to successful activation of the delayed fluorescence as well as the reverse intersystem crossing. Our discovery sheds light on the mechanism of the triplet-to-singlet upconversion, providing a microscopic strategy to control the optoelectronic properties from a molecular viewpoint.

A full-dimensional rigorous quantum mechanical treatment of non-reactive inelastic scattering of an open-shell diatom [e.g., NO(2Π)] with a structureless and spinless atom is presented within the time-independent close-coupling framework. The inclusion of the diatomic vibrational degree of freedom allows the investigation of transitions between different vibrational manifolds, in addition to those between different rotational, spin–orbit, and Λ-doublet states. This method is applied to the scattering of vibrationally excited NO(2Π) with Ar and H (with its spin ignored). The former has negligible vibrational inelasticity, thanks to the weak interaction between the two collisional partners. This conclusion justifies the commonly used two-dimensional approximation in treating NO scattering with rare gas atoms. The latter, on the other hand, is shown to undergo significant vibrational relaxation, even in the ultra-cold regime, owing to a chemically bonded (HNO) complex on the lowest-lying singlet potential energy surfaces.

Mechanistic details of the excited triplet state formation upon photoexcitation to the low-lying singlet manifold in naphthalene diimide and perylene diimide derivatives are explored theoretically. Static and dynamic aspects of two singlets (S1 and S2) and six triplets (T1-T6) of these molecules are investigated. Suitable vibronic Hamiltonians are constructed to investigate the internal conversion dynamics in both the singlet and triplet manifolds. Computed singlet-triplet energetics, spin-orbit coupling matrix elements, and intersystem crossing rates strongly suggest an efficient intersystem crossing process involving higher triplet states (T6, T5, and T4). Separate full dimensional quantum wavepacket simulations of singlet and triplet manifolds in the approximate linear vibronic model by assuming initial Franck-Condon conditions are carried out to unravel the internal conversion decay dynamics in the respective manifolds. The obtained diabatic electronic populations and nuclear densities are analyzed to illustrate the triplet generation pathways involving higher triplet states in these molecules.

This work proposes to describe open-shell molecules or radicals using the framework of the doubly occupied configuration interaction (DOCI) treatments, so far limited to closed-shell system studies. The proposal is based on considering molecular systems in singlet states generated by adding extra hydrogen atoms located at infinite distance from the target radical system. The energy of this radical is obtained by subtracting the energies of the dissociated hydrogen atoms from that provided by the two-electron reduced density matrix corresponding to the singlet state system in the DOCI space, which is variationally calculated by imposing a set of N-representability conditions. This method is numerically assessed by describing potential energy curves and reduced density matrices in selected ionic and neutral open-shell systems in the doublet spin symmetry ground state. Fil: Oña, Ofelia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina Fil: Torre, Alicia. Universidad del País Vasco; España Fil: Lain, Luis. Universidad del País Vasco; España Fil: Alcoba, Diego Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina Fil: Ríos, Elías Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina Fil: Massaccesi, Gustavo Ernesto. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

The time-dependent density functional theory (TDDFT) has been broadly used to investigate the excited-state properties of various molecular systems. However, the current TDDFT heavily relies on outcomes from the corresponding ground-state density functional theory (DFT) calculations which may be prone to errors due to the lack of proper treatment in the non-dynamical correlation effects. Recently, thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, \textit{J. Chem. Phys.} \textbf{136}, 154104 (2012)], a DFT with fractional orbital occupations, was proposed, explicitly incorporating the non-dynamical correlation effects in the ground-state calculations with low computational complexity. In this work, we develop time-dependent (TD) TAO-DFT, which is a time-dependent, linear-response theory for excited states within the framework of TAO-DFT. With tests on the excited states of H$_{2}$, the first triplet excited state ($1^3\Sigma_u^+$) was described well, with non-imaginary excitation energies. TDTAO-DFT also yields zero singlet-triplet gap in the dissociation limit, for the ground singlet ($1^1\Sigma_g^+$) and the first triplet state ($1^3\Sigma_u^+$). In addition, as compared to traditional TDDFT, the overall excited-state potential energy surfaces obtained from TDTAO-DFT are generally improved and better agree with results from the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD).

A Feshbach optimized photoassociation (FOPA) process for preparing ultracold excited-state 39K133Cs molecules is studied theoretically. Under the joint action of the magnetic field and short laser pulse, the colliding atoms in a superposition state composed of eight hyperfine components are converted into a molecule in the vibrational level of the excited state via two transition processes, the transition between singlet states and the transition between triplet states. The association efficiency can be significantly enhanced by taking advantage of Feshbach resonance. At different resonance positions, different hyperfine components of the superposition state dominate over the FOPA process, and the quantum interference displays different behaviors. Compared with the FOPA process only including a single hyperfine component, the quantum interference in the FOPA process containing all hyperfine components has a visible effect on the association efficiency.

Molecular cations of HO4+ and DO4+ are produced in a supersonic expansion. They are mass-selected, and infrared photodissociation spectra of these species are measured with the aid of argon-tagging. Although previous theoretical studies have modeled these systems as proton-bound dimers of molecular oxygen, infrared spectra have free OH stretching bands, suggesting other isomeric structures. As a consequence, we undertook extensive computational studies. Our conformer search used a composite method based on an economical combination of single- and multi-reference theories. Several conformers were located on the quintet, triplet, and singlet surfaces, spanning in energy of only a few thousand wavenumbers. Most of the singlet and triplet conformers have pronounced multiconfigurational character. Previously unidentified covalent-like structures (H—O—O—O—O) on the singlet and triplet surfaces likely represent the global minima. In our experiments, HO4+ is formed in a relatively hot environment, and similar experiments have been shown capable of producing multiple conformers in low-lying electronic states. None of the predicted HO4+ isomers can be ruled out a priori based on energetic arguments. We interpret our argon-tagged spectra with Second-Order Vibrational Perturbation Theory with Resonances (VPT2+K). The presence of one or more covalent-like isomers is the only reasonable explanation for the spectral features observed.

Algorithmic cooling methods manipulate an open quantum system in order to lower its temperature below that of the environment. We achieve significant cooling of an ensemble of nuclear spin-pair systems by exploiting the long-lived nuclear singlet state, which is an antisymmetric quantum superposition of the "up" and "down" Zeeman states. The effect is demonstrated by nuclear magnetic resonance (NMR) experiments on a molecular system containing a coupled pair of near-equivalent 13C nuclei. The populations of the system are subjected to a repeating sequence of cyclic permutations separated by relaxation intervals. The long-lived nuclear singlet order is pumped well beyond the unitary limit. The pumped singlet order is converted into nuclear magnetization which is enhanced by 21% relative to its thermal equilibrium value.

Using configuration interaction ab initio methods, the evolution of the lowest electronic states of singlet and triplet spin multiplicities of HOSO+ along the stretching and bending coordinates of is investigated. Equilibrium geometries, rotational constants, and harmonic vibrational frequencies of the lowest electronic states are calculated, i.e., X1A', 11A″, 13A', and 13A″. The global minimum of the 11A″ state is located below the first dissociation limit and its calculated lifetime is predicted to be 0.40 µs, making it suitable for detection by laser-induced fluorescence. According to the potential energy surfaces, HOSO+ should produce SO2+ and H after ultraviolet photon absorption to the 21A' state. This work opens the door to investigate the branching ratio and the production rates of SO2+, SO+, and OH from HOSO+. These insights can help understand the SO2 cycle in the earth's atmosphere and its effect on cooling our planet.

Singlet fission is one of the most promising routes to overcome the single-junction efficiency limit for solar cells. Singlet fission-enhanced silicon solar cells are the most desirable implementation, but transfer of triplet excitons, the product of singlet fission, into silicon solar cells has proved to be very challenging. Here, we report on an all optical measurement technique for the detection of triplet exciton quenching at semiconductor interfaces, a necessary requirement for triplet exciton or charge transfer. The method relies on the growth of individual, single-crystal islands of the singlet fission material on the silicon surface. The islands have different heights, and we correlate these heights to the quenching efficiency of triplet excitons. The quenching efficiency is measured by spatially resolved delayed fluorescence and compared to a diffusion-quenching model. Using silicon capped with a blocking thermal oxide and aromatic monolayers, we demonstrate that this technique can quickly screen different silicon surface treatments for triplet exciton quenching.

First singlet (S1) excitations are of primary importance in the photoluminescence spectra of organic chromophores. However, due to the multi-determinantal nature of the singlet excited states, standard Kohn-Sham density-functional theory (DFT) is not applicable. While linear-response time-dependent DFT is the method of choice for the computation of excitation energies, it fails severely for excitations with charge-transfer character. Becke’s recent virial exciton model [A. D. Becke, J. Chem. Phys. 148, 044112 (2018)] offers a promising solution to employ standard DFT for calculation of the S1 excitation energy in molecular systems. Here, it is shown that the virial exciton model is free of charge-transfer error. It is equally reliable for S1 excitations with significant charge-transfer character as for other classes of transitions.First singlet (S1) excitations are of primary importance in the photoluminescence spectra of organic chromophores. However, due to the multi-determinantal nature of the singlet excited states, standard Kohn-Sham density-functional theory (DFT) is not applicable. While linear-response time-dependent DFT is the method of choice for the computation of excitation energies, it fails severely for excitations with charge-transfer character. Becke’s recent virial exciton model [A. D. Becke, J. Chem. Phys. 148, 044112 (2018)] offers a promising solution to employ standard DFT for calculation of the S1 excitation energy in molecular systems. Here, it is shown that the virial exciton model is free of charge-transfer error. It is equally reliable for S1 excitations with significant charge-transfer character as for other classes of transitions.

The intersystem crossing (ISC) pathways of triplet benzene molecules in a benzene crystal were investigated theoretically. A combination of the gradient projection (GP) method, which is a standard method for optimizing the crossing seam of two potential energy surfaces, and the single-component artificial-force-induced reaction (SC-AFIR) method (GP/SC-AFIR) was used. This is the first reported use of a GP/SC-AFIR calculation using a density functional theory calculation with periodic boundary conditions. A systematic search for the minimum-energy structures in the seams of crossing of the singlet (S0) and triplet (T1) potential energy surfaces (S0/T1-MESX structures) found 39 independent S0/T1-MESX structures. Energy barriers between the S0/T1-MESX and the stationary structure of the triplet state (T1-MIN) were computed, and then two competing ISC pathways were extracted; the calculated overall energy barrier to the intermolecular C-C-bonded type (SX3) and the out-of-plane bent C-H type (SX15) S0/T1-MESX structures from T1-MIN were 0.26 and 0.27 eV, respectively. The rate constants for SX3 and SX15 formation were estimated to be 5.07 × 108 and 2.17 × 108 s-1 (at 273 K), respectively, or 9.73 × 10-5 and 4.78 × 10-6 s-1 (at 77 K), respectively. At 273 K, which is close to the melting point of the benzene crystal (278.5 K), SX3 and SX15 are easily accessible from T1-MIN, and ISC could occur through the S0/T1-MESX points. By contrast, at 77 K, T1-MIN survives long enough for phosphorescence to compete with ISC.