## What is/are First Singlet?

First Singlet - In a detailed case analysis of the first singlet and triplet excited states of formaldehyde the conceptional (dis-)advantages of the local hybrid scheme for excited-state gradients are exposed.^{[1]}Intramolecular hydrogen bond (IHB) of N-formylformamide derivatives in the both ground (GS) and first singlet excited state (S1) have been investigated by DFT and TD-DFT methods with the standard basis set 6-311++G (d,p), respectively.

^{[2]}TDDFT calculations point to facile reverse intersystem crossing (RISC) processes in 2EHO-CNPE from high-lying triplet states to the first singlet excited state (T2/T3 → S1) (hot-exciton channels) that enables a high radiative exciton yield (ηr ~ 69%) breaking the theoretical limit of 25% in conventional fluorescent OLEDs.

^{[3]}The experimental UV-vis and fluorescence spectra are well reproduced by the calculated vertical excitation energies in the ground state and the first singlet excited state.

^{[4]}The primary ring-opening of the pyran unit was found to occur in 300 fs yielding a non-planar intermediate in the first singlet excited state (S1).

^{[5]}Utilizing density functional theory (DFT) and time-dependent DFT, we calculate the first singlet (S1) and triplet (T1) excitation energy in the ground-state geometry and the first triplet excitation energy in the excited triplet state relaxed geometry (T1*).

^{[6]}It is confirmed that the doubly degenerate triplet level Т2 and the level Т1 are located below the first singlet excited level S1.

^{[7]}Systematic evaluations of excited-state potential energies of anionic 3NY were performed by density functional theory (DFT) and time-dependent DFT calculations, showing that intersystem crossing (ISC) from the first singlet state (S1) to the first or second triplet state (T1 or T2) is unlikely.

^{[8]}ESPT of 7‐HF is promoted by a significant shift of charge away from the OH group in the first singlet excited state, leading smoothly to the excited conjugate base and a protonated water cluster.

^{[9]}We obtain the energies of the first singlet (S1) and first triplet (T1) excited states of TADF materials by performing density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations on the ground state using the dependence on charge transfer amounts for the optimal Hartree-Fock percentage in the exchange-correlation of TD-DFT.

^{[10]}The results show that geometrical changes between the ground state (S0) and the first singlet excited state (S1) are restricted in film.

^{[11]}Results show that geometric changes between the first singlet excited state (S1) and ground state (S0) are restricted in solid phase with decreased root-mean squared displacement (RMSD).

^{[12]}MethodsThis is a single-centre prospective observational cohort study on healthy women in their first singleton pregnancy.

^{[13]}Comparing the optimized cluster amplitudes between $\textit{k}$-UpCCGSD and UCCGSD, the lack of generalized double excitations in $\textit{k}$-UpCCGSD accounts for the increased energy of the first singlet state.

^{[14]}The study of the geometry of the first singlet (S1) and triplet (T1) excited states of Q4 and Q5 demonstrate that the energy of the excited state in Q5 may be mostly spread as a result of the oscillations within the aliphatic hydrocarbons and in Q4 the intersystem crossing processes amplify the deactivation in the radiative path.

^{[15]}Herein, the complete active space self-consistent field (CASSCF) and its second-order perturbation (CASPT2) methods combined with time-dependent density functional theory (TD-DFT) calculations were employed to investigate the isomerization reaction mechanisms of an asymmetric N,C-chelate organoboron compound, B(ppy)MesPh, in the ground (S0) state and the first singlet excited (S1) state.

^{[16]}There exists a competition between the photoinduced electron transfer and energy transfer processes from the first singlet excited state of porphyrin core to fullerene moiety.

^{[17]}Specifically, (i) the ground state (S0) structure consists of a planar geometry in which three units can be identified, the central cyclohexene ring, the glycine- and the threonine-branch, reflecting the π conjugation of the system, (ii) the first singlet excited state (S1) shows a large oscillator strength and a typical ππ* excitation character and (iii) upon relaxation at S1 the originally ground-state planar structure undergoes a relaxation to a non-planar one, S1, especially at the carbon-nitrogen (CN) groups linking the cyclohexene ring to the glycine- or threonine-arm.

^{[18]}The ME generation in TPP is a slower process and occurs through an excimer-mediated path with a large coupling between the first singlet excited state and ME state.

^{[19]}In particular the vibronic excitations of the first singlet state of the CO spectrum, A 1?, are derived in the framework of the similarity approach, characterizing also the radiative properties to the ground electronic state.

^{[20]}Our results show that geometry changes between the ground state (S0) and the first singlet excited state (S1) are limited due to the intermolecular π-π and CH-π interactions.

^{[21]}The electron donor groups (EDG) and electron withdraw groups (EWG) effects on geometry, frontier orbital energies, reactivity indices and aromaticity in the first singlet excited state of platinabenzene were investigated and compared to ground state.

^{[22]}The solvent polarity has slight influence on the molecular geometries and orbitals, while it can decrease the energy gap between the first singlet excited state (S1) and first triplet excited state (T1) significantly.

^{[23]}The scanned potential energy curves reveal that the energy barriers of the first singlet excited state of the four compounds along the ESIPT reactions are predicted at 8.

^{[24]}In the preset work, in order to clarify whether ESIPT would take place in 10-HHBF, we have optimized the four-state geometrical structures (ground state S0, first singlet excited state S1, transition state S1-TS and after proton transfer S1-PT), carried out the Natural Population Analysis and scanned the ground-state and excited-state potential energy curves of 1-HHBF and 10-HHBF at TD-CAM-B3LYP/6-311 + g(2d,2p)/IEFPCM (cyclohexane) theory level.

^{[25]}On the ultrafast (fs) timescale, we could detect the decay of the first singlet excited state of PNO, and the formation of a short-lived transient species, that, based on its time-resolved resonance Raman (TR3) spectrum, we assign to the oxaziridine 1,2-diaza-7-oxa-bicyclo[4.

^{[26]}In these models, the excitation pulse populates the first excited state (the first singlet level) of the primary molecular form.

^{[27]}We obtained the energies of the first singlet (S1) and the first triplet (T1) excited states of the TADF materials by performing density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations to the ground state using dependence on charge transfer amounts for the optimal Hartree-Fock percentage in the exchange-correlation of TD-DFT.

^{[28]}A stepwise single electron transfer from the aminophthaloyl to the O-O bond initiates the decomposition of CP2-, and the light emitter is produced via the two crossings of the potential energy surfaces of the ground state (S0) and the first singlet excited state (S1).

^{[29]}Both dimers exhibited two independent radiative decay pathways, which are equilibrated thermally at room temperature: one is thermally activated delay fluorescence (TADF) via the first singlet excited state (S1) decay and the other is phosphorescence via the first triplet excited state (T1) decay.

^{[30]}Based on the comparison of the photophysical properties of PTZ-TTR in toluene and the aggregation state, we find that aggregation could induce a smaller energy gap between the first singlet excited state and the first triplet excited state.

^{[31]}We obtain the energies of the first singlet (S1) and first triplet (T1) excited states of TADF materials by performing DFT and time-dependent DFT (TD-DFT) calculations on the ground state using dependence on charge transfer amounts for the optimal Hartree-Fock percentage in the exchange-correlation of TD-DFT.

^{[32]}

## density functional theory

Utilizing density functional theory (DFT) and time-dependent DFT, we calculate the first singlet (S1) and triplet (T1) excitation energy in the ground-state geometry and the first triplet excitation energy in the excited triplet state relaxed geometry (T1*).^{[1]}Systematic evaluations of excited-state potential energies of anionic 3NY were performed by density functional theory (DFT) and time-dependent DFT calculations, showing that intersystem crossing (ISC) from the first singlet state (S1) to the first or second triplet state (T1 or T2) is unlikely.

^{[2]}We obtain the energies of the first singlet (S1) and first triplet (T1) excited states of TADF materials by performing density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations on the ground state using the dependence on charge transfer amounts for the optimal Hartree-Fock percentage in the exchange-correlation of TD-DFT.

^{[3]}Herein, the complete active space self-consistent field (CASSCF) and its second-order perturbation (CASPT2) methods combined with time-dependent density functional theory (TD-DFT) calculations were employed to investigate the isomerization reaction mechanisms of an asymmetric N,C-chelate organoboron compound, B(ppy)MesPh, in the ground (S0) state and the first singlet excited (S1) state.

^{[4]}We obtained the energies of the first singlet (S1) and the first triplet (T1) excited states of the TADF materials by performing density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations to the ground state using dependence on charge transfer amounts for the optimal Hartree-Fock percentage in the exchange-correlation of TD-DFT.

^{[5]}

## first triplet excited

The solvent polarity has slight influence on the molecular geometries and orbitals, while it can decrease the energy gap between the first singlet excited state (S1) and first triplet excited state (T1) significantly.^{[1]}Both dimers exhibited two independent radiative decay pathways, which are equilibrated thermally at room temperature: one is thermally activated delay fluorescence (TADF) via the first singlet excited state (S1) decay and the other is phosphorescence via the first triplet excited state (T1) decay.

^{[2]}Based on the comparison of the photophysical properties of PTZ-TTR in toluene and the aggregation state, we find that aggregation could induce a smaller energy gap between the first singlet excited state and the first triplet excited state.

^{[3]}

## triplet excited state

In a detailed case analysis of the first singlet and triplet excited states of formaldehyde the conceptional (dis-)advantages of the local hybrid scheme for excited-state gradients are exposed.^{[1]}

## first singlet excited

Intramolecular hydrogen bond (IHB) of N-formylformamide derivatives in the both ground (GS) and first singlet excited state (S1) have been investigated by DFT and TD-DFT methods with the standard basis set 6-311++G (d,p), respectively.^{[1]}TDDFT calculations point to facile reverse intersystem crossing (RISC) processes in 2EHO-CNPE from high-lying triplet states to the first singlet excited state (T2/T3 → S1) (hot-exciton channels) that enables a high radiative exciton yield (ηr ~ 69%) breaking the theoretical limit of 25% in conventional fluorescent OLEDs.

^{[2]}The experimental UV-vis and fluorescence spectra are well reproduced by the calculated vertical excitation energies in the ground state and the first singlet excited state.

^{[3]}The primary ring-opening of the pyran unit was found to occur in 300 fs yielding a non-planar intermediate in the first singlet excited state (S1).

^{[4]}It is confirmed that the doubly degenerate triplet level Т2 and the level Т1 are located below the first singlet excited level S1.

^{[5]}ESPT of 7‐HF is promoted by a significant shift of charge away from the OH group in the first singlet excited state, leading smoothly to the excited conjugate base and a protonated water cluster.

^{[6]}The results show that geometrical changes between the ground state (S0) and the first singlet excited state (S1) are restricted in film.

^{[7]}Results show that geometric changes between the first singlet excited state (S1) and ground state (S0) are restricted in solid phase with decreased root-mean squared displacement (RMSD).

^{[8]}Herein, the complete active space self-consistent field (CASSCF) and its second-order perturbation (CASPT2) methods combined with time-dependent density functional theory (TD-DFT) calculations were employed to investigate the isomerization reaction mechanisms of an asymmetric N,C-chelate organoboron compound, B(ppy)MesPh, in the ground (S0) state and the first singlet excited (S1) state.

^{[9]}There exists a competition between the photoinduced electron transfer and energy transfer processes from the first singlet excited state of porphyrin core to fullerene moiety.

^{[10]}Specifically, (i) the ground state (S0) structure consists of a planar geometry in which three units can be identified, the central cyclohexene ring, the glycine- and the threonine-branch, reflecting the π conjugation of the system, (ii) the first singlet excited state (S1) shows a large oscillator strength and a typical ππ* excitation character and (iii) upon relaxation at S1 the originally ground-state planar structure undergoes a relaxation to a non-planar one, S1, especially at the carbon-nitrogen (CN) groups linking the cyclohexene ring to the glycine- or threonine-arm.

^{[11]}The ME generation in TPP is a slower process and occurs through an excimer-mediated path with a large coupling between the first singlet excited state and ME state.

^{[12]}Our results show that geometry changes between the ground state (S0) and the first singlet excited state (S1) are limited due to the intermolecular π-π and CH-π interactions.

^{[13]}The electron donor groups (EDG) and electron withdraw groups (EWG) effects on geometry, frontier orbital energies, reactivity indices and aromaticity in the first singlet excited state of platinabenzene were investigated and compared to ground state.

^{[14]}The solvent polarity has slight influence on the molecular geometries and orbitals, while it can decrease the energy gap between the first singlet excited state (S1) and first triplet excited state (T1) significantly.

^{[15]}The scanned potential energy curves reveal that the energy barriers of the first singlet excited state of the four compounds along the ESIPT reactions are predicted at 8.

^{[16]}In the preset work, in order to clarify whether ESIPT would take place in 10-HHBF, we have optimized the four-state geometrical structures (ground state S0, first singlet excited state S1, transition state S1-TS and after proton transfer S1-PT), carried out the Natural Population Analysis and scanned the ground-state and excited-state potential energy curves of 1-HHBF and 10-HHBF at TD-CAM-B3LYP/6-311 + g(2d,2p)/IEFPCM (cyclohexane) theory level.

^{[17]}On the ultrafast (fs) timescale, we could detect the decay of the first singlet excited state of PNO, and the formation of a short-lived transient species, that, based on its time-resolved resonance Raman (TR3) spectrum, we assign to the oxaziridine 1,2-diaza-7-oxa-bicyclo[4.

^{[18]}A stepwise single electron transfer from the aminophthaloyl to the O-O bond initiates the decomposition of CP2-, and the light emitter is produced via the two crossings of the potential energy surfaces of the ground state (S0) and the first singlet excited state (S1).

^{[19]}Both dimers exhibited two independent radiative decay pathways, which are equilibrated thermally at room temperature: one is thermally activated delay fluorescence (TADF) via the first singlet excited state (S1) decay and the other is phosphorescence via the first triplet excited state (T1) decay.

^{[20]}Based on the comparison of the photophysical properties of PTZ-TTR in toluene and the aggregation state, we find that aggregation could induce a smaller energy gap between the first singlet excited state and the first triplet excited state.

^{[21]}

## first singlet state

Systematic evaluations of excited-state potential energies of anionic 3NY were performed by density functional theory (DFT) and time-dependent DFT calculations, showing that intersystem crossing (ISC) from the first singlet state (S1) to the first or second triplet state (T1 or T2) is unlikely.^{[1]}Comparing the optimized cluster amplitudes between $\textit{k}$-UpCCGSD and UCCGSD, the lack of generalized double excitations in $\textit{k}$-UpCCGSD accounts for the increased energy of the first singlet state.

^{[2]}In particular the vibronic excitations of the first singlet state of the CO spectrum, A 1?, are derived in the framework of the similarity approach, characterizing also the radiative properties to the ground electronic state.

^{[3]}