Minimum Energy Conical Intersections Research Articles

Study of the Energy Crossing Between Excited States Affected by the Electronegativity of Substituents for Three 4-Azido-1,8-naphthalimide Derivatives.

Rapid detection of H2S is crucial for human physiological health and natural ecosystems. In this study, the fluorescent sensing mechanisms of three 4-azido-1,8-naphthalimide-based fluorescent probes to monitor H2S were theoretically investigated by density functional theory and time-dependent density functional theory. The potential energy curve of the charge transfer (CT) state has a crossover with that of the locally excited (LE) state proved by the constructed linear interpolating internal coordinate pathway. Thus, the transform takes place from the LE state to the CT state causing the fluorescence quenching of the probes from a nonradiative transition process of the CT state. The distance between the Franck-Condon point and the minimal energy conical intersection becomes larger with the increase of the electronegativity of substituents on the 1,8-naphthalimide fluorophore. In addition, the degree of charge separation is closely related to the energy difference between the CT and the LE states which are also essentially affected by the electronegativity of the substituents. Since the electronegativity of the substituents has proved important for the probes, our work lays a certain theoretical foundation for the design and synthesis of more sensitive 4-azido-1,8-naphthalimide-based fluorescent probes.

Theoretical Investigation on the Reversible Photoswitch Mechanism of Benzylidene-Oxazolone System.

The design and application of molecular photoswitches have attracted much attention. Herein, we performed a detailed computational study on the photoswitch benzylidene-oxazolone system based on static electronic structure calculations and on-the-fly excited-state dynamic simulations. For the Z and E isomer, we located six and four minimum energy conical intersections (MECIs) between the first excited state (S1) and the ground state (S0), respectively. Among them, the relaxation pathway driven by ring-puckering motion is the most competitive channel with the photoisomeization process, leading to the low photoisomerization quantum yield. In the dynamic simulations, about 88 % and 66 % trajectories decay from S1 to S0 for Z and E isomer, respectively, within the total simulation time of ~2 ps. The photoisomeization quantum yields obtained in our study (0.20 for Z→E and 0.12 for E→Z) agree well with the experimental measured values (0.25 and 0.11), even though the number of trajectories is limited to 50. Our study sheds light on the complexity of the benzylidene-oxazolone system 's deactivation process and the competitive mechanisms among different reaction channels, which provides theoretical guidance for further design and development of benzylidene-oxazolone based molecular photoswitches.

"On-the-Fly" Nonadiabatic Dynamics Simulation on the Ultrafast Photoisomerization of a Molecular Photoswitch Iminothioindoxyl: An RMS-CASPT2 Investigation.

Iminothioindoxyl (ITI) is a new class of photoswitch that exhibits many excellent properties including well-separated absorption bands in the visible region for both conformers, ultrafast Z to E photoisomerization as well as the millisecond reisomerization at room temperature for the E isomer, and switchable ability in both solids and various solvents. However, the underlying ultrafast photoisomerization mechanism at the atomic level remains unclear. In this work, we have employed a combination of high-level RMS-CASPT2-based static electronic structure calculations and nonadiabatic dynamics simulations to investigate the ultrafast photoisomerization dynamics of ITI. Based on the minimum-energy structures, minimum-energy conical intersections, linear interpolation internal coordinate paths, and nonadiabatic dynamics simulations, the overall photoisomerization scenario of ITI upon excitation is established. Upon excitation around 416 nm, the molecule will be excited to the S2 state considering its close energy to the experimentally measured absorption maximum and larger oscillator strength, from which ultrafast decay of S2 to S1 state can take place efficiently with a time constant of 62 fs. However, the photoisomerization is not likely to complete in the S2 state since the dihedral associated with the Z to E isomerization changes little during the relaxation. Upon relaxing to the S1 state, the molecule will decay to the S0 state ultrafast with a time constant of 232 fs. In contrast, the decay of the S1 state is important for the isomerization considering that the dihedral related to the isomerization of the hopping structures is close to 90°. Therefore, the S1/S0 intersection region should be important for the isomerization of ITI. Arriving at the S0 state, the molecule can either go back to the original Z reactant or isomerize to the E products. At the end of the 500 fs simulation time, the E configuration accounts for nearly 37% of the final structures. Moreover, the photoisomerization mechanism is different from the isomerization mechanism in the ground state; i.e., instead of the inversion mechanism in the ground state, the photoisomerization prefers the rotation mechanism. Our results not only agree well with previous experimental studies but also provide some novel insights that could be helpful for future improvements in the performance of the ITI photoswitches.

Theoretical study of the substituent effects on the ESIPT mechanism of salicylideneaniline and the TICT photochemistry reactions.

The study of salicylideneaniline (SA) and its derivatives is critical due to their special photophysical properties and environmental sensitivity. In this work, the density time-dependent functional theory (TDDFT) and complete-active-space self-consistent-field (CASSCF) methods were carried out to calculate the substituent effect on excited-state properties and dynamics of SA derivatives. We found the para-substitution triggers the excited-state intramolecular proton transfer (ESIPT) reaction, exhibiting the dual-fluorescent phenomena. However, the meta- and ortho-substitutions impel the non-radiative transition process along the minimum energy conical intersection (MECI), forming the twisted intramolecular charge transfer (TICT) state to prevent ESIPT. This investigation of substituent effects on the photochemical processes and photophysical properties will provide the benchmarks for the design of fluorescent materials.

Efficient Spin-Adapted Implementation of Multireference Algebraic Diagrammatic Construction Theory. I. Core-Ionized States and X-ray Photoelectron Spectra.

We present an efficient implementation of multireference algebraic diagrammatic construction theory (MR-ADC) for simulating core-ionized states and X-ray photoelectron spectra (XPS). Taking advantage of spin adaptation, automatic code generation, and density fitting, our implementation can perform calculations for molecules with more than 1500 molecular orbitals, incorporating static and dynamic correlation in the ground and excited electronic states. We demonstrate the capabilities of MR-ADC methods by simulating the XPS spectra of substituted ferrocene complexes and azobenzene isomers. For the ground electronic states of these molecules, the XPS spectra computed using the extended second-order MR-ADC method (MR-ADC(2)-X) are in a very good agreement with available experimental results. We further show that MR-ADC can be used as a tool for interpreting or predicting the results of time-resolved XPS measurements by simulating the core ionization spectra of azobenzene along its photoisomerization, including the XPS signatures of excited states and the minimum energy conical intersection. This work is the first in a series of publications reporting the efficient implementations of MR-ADC methods.

Optimizing Conical Intersections without Explicit Use of Non-Adiabatic Couplings.

We present two alternative methods for optimizing minimum energy conical intersection (MECI) molecular geometries without knowledge of the derivative coupling (DC). These methods are based on the utilization of Lagrange multipliers: (i) one method uses an approximate calculation of the DC, while the other (ii) do not require the DC. Both methods use the fact that information on the DC is contained in the Hessian of the squared energy difference. Tests done on a set of small molecular systems, in comparison with other methods, show the ability of the proposed methods to optimize MECIs. Finally, we apply the methods to the furimamide molecule, to optimize and characterize its S1/S2 MECI, and to optimizing the S0/S1 MECI of the silver trimer.

Development of Parallel On-the-Fly Crystal Algorithm for Global Exploration of Conical Intersection Seam Space.

Conical intersection (CI) seams are configuration spaces of a molecular system where two or more (spin) adiabatic electronic states are degenerate in energy. They play essential roles in photochemistry because nonradiative decays often occur near the minima of the seam, i.e., the minimum energy CIs (MECIs). Thus, it is important to explore the CI seams and discover the MECIs. Although various approaches exist for CI seam exploration, most of them are local in nature, requiring reasonable initial guesses of geometries and nuclear gradients during the search. Global search algorithms, on the other hand, are powerful because they can fully sample the configurational space and locate important MECIs missed by local algorithms. However, global algorithms are often computationally expensive for large systems due to their poor scalability with respect to the number of degrees of freedom. To overcome this challenge, we develop the parallel on-the-fly Crystal algorithm to globally explore the CI seam space, taking advantage of its superior scaling behavior. Specifically, Crystal is coupled with on-the-fly evaluations of the excited and ground state energies using multireference electronic structure methods. Meanwhile, the algorithm is parallelized to further boost its computational efficiency. The effectiveness of this new algorithm is tested for three types of molecular photoswitches of significant importance in material and biomedical sciences: photostatin (PST), stilbene, and butadiene. A rudimentary implementation of the algorithm is applied to PST and stilbene, resulting in the discovery of all previously identified MECIs and several new ones. A refined version of the algorithm, combined with a systematic clustering technique, is applied to butadiene, resulting in the identification of an unprecedented number of energetically accessible MECIs. The results demonstrate that the parallel on-the-fly Crystal algorithm is a powerful tool for automated global CI seam exploration.

Nuclear Quantum Effects on Nonadiabatic Dynamics of a Green Fluorescent Protein Chromophore Analogue: Ring-Polymer Surface-Hopping Simulation.

Herein, we have used the "on-the-fly" ring-polymer surface-hopping simulation method with the centroid approximation (RPSH-CA), in combination with the multireference OM2/MRCI electronic structure calculations to study the photoinduced dynamics of a green fluorescent protein (GFP) chromophore analogue in the gas phase, i.e., o-HBI, at 50, 100, and 300 K with 1, 5, 10, and 15 beads (3600 1 ps trajectories). The electronic structure calculations identified five new minimum-energy conical intersection (MECI) structures, which, together with the previous one, play crucial roles in the excited-state decay dynamics of o-HBI. It is also found that the excited-state intramolecular proton transfer (ESIPT) occurs in an ultrafast manner and is completed within 20 fs in all the simulation conditions because there is no barrier associated with this ESIPT process in the S1 state. However, the other excited-state dynamical results are strongly related to the number of beads. At 50 and 100 K, the nuclear quantum effects (NQEs) are very important; therefore, the excited-state dynamical results change significantly with the bead number. For example, the S1 decay time deduced from time-dependent state populations becomes longer as the bead number increases. Nevertheless, an essentially convergent trend is observed when the bead number is close to 10. In contrast, at 300 K, the NQEs become weaker and the above dynamical results converge very quickly even with 1 bead. Most importantly, the NQEs seriously affect the excited-state decay mechanism of o-HBI. At 50 and 100 K, most trajectories decay to the S0 state via perpendicular keto MECIs, whereas, at 300 K, only twisted keto MECIs are responsible for the excited-state decay. The present work not only comprehensively explores the temperature-dependent photoinduced dynamics of o-HBI, but also demonstrates the importance and necessity of NQEs in nonadiabatic dynamics simulations, especially at relatively low temperatures.

A CASSCF/MRCI trajectory surface hopping simulation of the photochemical dynamics and the gas phase ultrafast electron diffraction patterns of cyclobutanone.

We present the simulation of the photochemical dynamics of cyclobutanone induced by the excitation of the 3s Rydberg state. For this purpose, we apply the complete active space self-consistent field method together with the spin-orbit multireference configuration interaction singles treatment, combined with the trajectory surface hopping for the inclusion of nonadiabatic effects. The simulations were performed in the spin-adiabatic representation, including nine electronic states derived from three singlet and two triplet spin-diabatic states. Our simulations reproduce the two previously observed primary dissociation channels: the C2 pathway yielding C2H4 + CH2CO and the C3 pathway producing c-C3H6 + CO. In addition, two secondary products, CH2 + CO from the C2 pathway and C3H6 from the C3 pathway, both of them previously reported, are also observed in our simulation. We determine the ratio of the C3:C2 products to be about 2.8. Our findings show that most of the trajectories reach their electronic ground state within 200fs, with dissociation events finished after 300fs. We also identify the minimum energy conical intersections that are responsible for the relaxation and provide an analysis of the photochemical reaction mechanism based on multidimensional scaling. Furthermore, we demonstrate a minimal impact of triplet states on the photodissociation mechanism within the observed timescale. In order to provide a direct link to experiments, we simulate the gas phase ultrafast electron diffraction patterns and connect their features to the underlying structural dynamics.

Minimum-Energy Conical Intersections by Compressed Multistate Pair-Density Functional Theory.

Compressed multistate pair-density functional theory (CMS-PDFT) is a multistate version of multiconfiguration pair-density functional theory that can capture the correct topology of coupled potential energy surfaces (PESs) around conical intersections. In this work, we develop interstate coupling vectors (ISCs) for CMS-PDFT in the OpenMolcas and PySCF/mrh electronic structure packages. Yet, the main focus of this work is using ISCs to calculate minimum-energy conical intersections (MECIs) by CMS-PDFT. This is performed using the projected constrained optimization method in OpenMolcas, which uses ISCs to restrain the iterations to the conical intersection seam. We optimize the S1/S0 MECIs for ethylene, butadiene, and benzene and show that CMS-PDFT gives smooth PESs in the vicinities of the MECIs. Furthermore, the CMS-PDFT MECIs are in good agreement with the MECI calculated by the more expensive XMS-CASPT2 method.

Mechanistic insights into the AIE properties of BF2 complexes of N-acetyl 2-aminobenzothiazoles as rotorless polyheteroaromatics

A series of four novel BF2 complexes of N-acetyl 2-aminobenzothiazoles featuring rigid rotorless polyheteroaromatic structures have been designed and synthesized. All of these compounds exhibited AIE properties with excellent solid-state fluorescence quantum yields up to 81.7%. Theoretical calculations revealed the characteristics of their ground-state structures and excitation processes. Their seemingly abnormal nonradiative decay in solutions was investigated from both direct vibrational relaxation and S0/S1 surface crossing perspectives by the two-channel model. The minimum energy conical intersection (MECI) located by SF-TDDFT method indicated that the CI is mainly induced by the deformation of the BF2 complex ring, leads to elevated energy level, and thus is not responsible for the fluorescence quenching. The potential energy curve (PEC) constructed along the distortion angle θ of BF2 complex ring showed that when θ reaches 50° (the dark-state region approaching MECI), the energy barrier is only 0.11 eV, suggesting that the deformed dark state could serve as an effective deactivation channel via ultrafast internal conversion (IC). Crystallographic analysis illustrated that the F atoms perpendicular to the polyheterocycle could effectively prohibit detrimental π-π stacking and enhance intermolecular interactions, thereby resulting in efficient solid-state emission.

Photoisomerization mechanism of iminoguanidinium receptors from spectroscopic methods and quantum chemical calculations.

The hydrazone functional group, when coupled with a pyridyl substituent, offers a unique class of widely tunable photoswitches, whose E-to-Z photoisomerization equilibria can be controlled through intramolecular hydrogen bonding between the N-H hydrazone donor and the pyridyl acceptor. However, little is known about the photoisomerization mechanism in this class of compounds. To address this issue, we report a pyridine-appended iminoguanidinium photoswitch that is functionally related to acylhydrazones and provides insight into the photoisomerization processes between the E and Z configurations. The E-to-Z photoisomerization of the E-2-pyridyl-iminoguanidinium cation (2PyMIG) in DMSO, prepared as the bromide salt, was quantified by 1H NMR, and probed in real time with ultrafast laser spectroscopy. The photoisomerization process occurs on a picosecond timescale, resulting in low fluorescence yields. The multiconfigurational reaction path found with the growing string method features a small barrier (4.3 or 6.5 kcal mol-1) that the E isomer in the π-π* state must overcome to reach the minimum energy conical intersection (MECI) connecting the E and Z isomers of 2PyMIG. While two possible pathways exist depending on the orientation of the pyridine ring, both exhibit the same qualitative features along the path and at their MECIs, involving simultaneous changes in the CCNN and CNNC dihedral angles. Furthermore, the ground state barrier for pyridine ring rotation is readily accessible, thus a low barrier pathway to the experimentally observed Z isomer exists for both MECIs leading to a transition from the E isomer to photoproduct. Combining multiconfigurational reaction path calculations using growing string method with time-resolved fluorescence spectroscopy provided crucial insights into the photoisomerization process of 2PyMIG, resulting in both the computational and experimental results pointing to rapid photoisomerization via a surface crossing between the singlet π-π* and the ground states.

Excited-state dynamics of 4-hydroxyisoindoline-1,3-dione and its derivative as fluorescent probes.

Fluorescent probes have become promising tools for monitoring the concentration of peroxynitrite, which is linked to many diseases. However, despite focusing on developing numerous peroxynitrite based fluorescent probes, limited emphasis is placed on their sensing mechanism. Here, we investigated the sensing mechanism of a peroxynitrite fluorescent probe, named BHID-Bpin, with a focus on the relevant excited state dynamics. The photoexcited BHID-Bpin relaxes to its ground state via an efficient nonradiative process (∼300 ps) due to the presence of a minimum energy conical intersection between its first excited state and ground state. However, upon reacting with peroxynitrite, the Bpin moiety is cleaved from BHID-Bpin and BHID is formed. The formed BHID exhibits strong dual band fluorescence which is caused by an ultrafast excited-state intramolecular proton transfer process (∼1 ps).

Auger-Meitner and X-ray Absorption Spectra of Ethylene Cation: Insight into Conical Intersection Dynamics.

We present a theoretical investigation of the near-edge X-ray absorption fine structure and the Auger-Meitner decay spectra of ethylene and its cation. Herein, we demonstrate that our method, coupled with the nuclear ensemble approach, successfully reproduces the natural bandwidth structure of the experimental resonant Auger-Meitner decay spectra of ethylene, which is not very well reproduced within the Franck-Condon approximation. Furthermore, we analyze the Auger-Meitner decay spectra of the ethylene cation in light of minimum energy conical intersection structures involving the two lowest cationic states (D1 and D0), providing valuable insights into the ultrafast D1/D0 relaxation dynamics. Our results suggest that Auger-Meitner electron spectroscopy can help elucidate the mechanism behind the initial 20 fs of the relaxation dynamics.

A different view on the deactivation process of 3-hydroxy-salicylidene-methylamine system

Schiff bases stand out as a highly significant class of photochromic materials with widespread applications. The exploration of their photochromic mechanisms has garnered substantial interest over the past decades. In this work, we investigated the photochromic mechanism of 3-hydroxy-salicylidene methylamine (3-OH-SMA) by high-level electronic structure calculations and on-the-fly excited state dynamics simulations. Our investigation revealed the identification of three minimum energy conical intersections between S1 and S0 states, while only the one characterized by the central C = N bond twisting motion was involved in the deactivation process. This finding contrasts with previous reports, suggesting that the excited state intramolecular proton transfer (ESIPT) process was the main reaction channel in 3-OH-SMA. The proposed new decay mechanism provides valuable theoretical insights, paving the way for the further enhancement or rational design of photochromic materials.

A-Band Absorption Spectrum of the ClSO Radical: Electronic Structure of the Sulfinyl Group.

Sulfur oxide species (RSOx) play a critical role in many fields, ranging from biology to atmospheric chemistry. Chlorine-containing sulfur oxides may play a key role in sulfate aerosol formation in Venus' cloud layer by catalyzing the oxidation of SO to SO2 via sulfinyl radicals (RSO). We present results from the gas-phase UV-vis transient absorption spectroscopy study of the simplest sulfinyl radical, ClSO, generated from the pulsed-laser photolysis of thionyl chloride at 248 nm (at 40 Torr of N2 and 292 K). A weak absorption spectrum from 350 to 480 nm with a peak at 385 nm was observed, with partially resolved vibronic bands (spacing = 226 cm-1), and a peak cross section σ(385 nm) = (7.6 ± 1.9) × 10-20 cm2. From ab initio calculations at the EOMEE-CCSD/ano-pVQZ level, we assigned this band to 12A' ← X2A″ and 22A' ← X2A″ transitions. The spectrum was modeled as a sum of a bound-to-free transition to the 12A' state and a bound-to-bound transition to the 22A' state with similar oscillator strengths; the prediction agreed well with the observed spectrum. We attributed the vibronic structure to a progression in the bending vibration of the 22A' state. Further calculations at the XDW-CASPT2 level predicted a conical intersection between the excited 12A' and 22A' potential energy surfaces near the Franck-Condon region. The geometry of the minimum-energy conical intersection was similar to that of the ground-state geometry. The lack of structure at shorter wavelengths could be evidence of a short excited-state lifetime arising from strong vibronic coupling. From simplified molecular orbital analysis, we attributed the ClSO spectrum to transitions involving the out-of-plane π/π* orbitals along the S-O bond and the in-plane orbital possessing a σ/σ* character along the S-Cl bond. We hypothesize that these orbitals are common to other sulfinyl radicals, RSO, which would share a combination of a strong and a weak transition in the UV (near 300 nm) and visible (400-600 nm) regions.

CASPT2//CASSCF studies on mechanistic photophysics of 3-hydroxyflavone

3-Hydroxyflavone (3-HF) as the backbone of flavonols has been extensively studied on the dual fluorescence and excited-state intramolecular proton transfer (ESIPT) after photoexcitation. However, its detailed excited-state relaxation mechanism is still unclear. Herein, the minimum-energy structures, conical intersections and singlet–triplet crossing points of 3-HF in the 1ππ∗, 1nπ∗, 3ππ∗, 3nπ∗, and S0 states in the gas phase were first optimized by the CASPT2//CASSCF method. Then, the minimum-energy proton transfer (MEPT) and excited-state decay (ESD) pathways were calculated as well. Based on the calculation results, we proposed several possible ESD pathways from the initially populated bright S2(ππ*) state. The major channel is singlet-involved and stretch-torsion coupled ESIPT pathway. 3-HF in normal (N) form first undergoes efficient 1ππ* ESIPT with a small barrier of 2.2 kcal/mol to yield the 1ππ* proton-transferred tautomer (T). Subsequently, the T tautomer approaches the nearby accessible S1/S0 conical intersection and then occurs internal conversion (IC) to fall back to the S0 state. Finally, the S0 species quickly transfers into the N conformer via the reverse ground state intramolecular proton transfer (GSIPT) to realize the ground-state recovery. In addition, the minor ESD pathways are involved less efficient intersystem crossing (ISC) processes. The present work could provide insights into understanding the photophysics of flavonols and their derivatives.

Turn on the luminescence channel by the suppression of conical intersection process for the sulfur-containing hydrogen-bonded molecules

The sulfur-containing hydrogen bonds exhibit notable potential in gene and protein engineering. As an important research direction of sulfur-containing hydrogen bonding dynamics, the excited-state intramolecular proton transfer (ESIPT) reaction of the thiol proton has garnered significant interest. Recently, Chou et al. synthesized a series of sulfur-containing H-bonded molecules, inclusive of 3-thiolflavone (3 TF), its trifluoromethyl derivative (3FTF), and its diethylamino derivative (3NTF), thereby inaugurating a new chapter in the ESIPT reaction of the thiol proton. Nevertheless, many open issues cannot be answered solely by experimental means and call for a detailed theoretical investigation, especially the relationship between the molecular excited-state properties and different luminescence properties of the three molecules. Herein, we validate that the molecules undergo the ESIPT reaction of the thiol proton and identify the time scale through the time-dependent density functional theory (TDDFT) calculation. Moreover, employing the spin-flip TDDFT approach, the analysis of the non-radiative transition process reveals that difference in Gibbs free energy of activation (ΔG⧧) for the transition from Frank-Condon point to minimum energy conical intersection (MECI) point primarily accounts for the different luminescence properties of the three molecules. Besides, we also reveal the reason for the abnormal blue-shifted fluorescence of the 3NTF in the aggregated state by the ONIOM (TDDFT: UFF) strategy. These findings are favorable to understanding the luminescence mechanism of sulfur-containing H-bonded molecules and provide a reference for the synthesis and design of the luminescent materials based on the molecules with thiol proton transfer properties.

Theoretical Investigation of the E/Z Photoisomerization Pathway in 1-(2-Pyrrolyl)-2-(2-thienyl)ethylene.

Molecular-level understanding of photochemistry in simple vinylene-linked systems such as ethylene and stilbene has been a major area of research. However, the effect of replacing the two benzene rings by five-membered heterocyclic rings, thiophene and pyrrole, is yet to be reported. In the present theoretical study, our aim is to illustrate photoinduced processes in a vinylene-linked thiophene-pyrrole system. Computational studies are carried out at the RI-MP2/RI-ADC(2)/cc-pVTZ level to explore different isomerization pathways. Minimum-energy conical intersection (MECI) structures are categorized into two types: closed-ring and twisted-pyramidalized structures. Relaxation through the former MECIs is accessible only from the cis isomers. However, the latter MECIs are inaccessible due to high energy barriers along the linear interpolation in internal coordinate paths.

Unveiling controlling factors of the S0/S1 minimum-energy conical intersection (3): Frozen orbital analysis based on the spin-flip theory.

Conical intersections (CIs), which indicate the crossing of two or more adiabatic electronic states, are crucial in the mechanisms of photophysical, photochemical, and photobiological processes. Although various geometries and energy levels have been reported using quantum chemical calculations, the systematic interpretation of the minimum energy CI (MECI) geometries is unclear. A previous study [Nakai et al., J. Phys. Chem. A 122, 8905 (2018)] performed frozen orbital analysis (FZOA) based on time-dependent density functional theory (TDDFT) at the MECI formed between the ground and first electronic excited states (S0/S1 MECI), thereby inductively clarifying two controlling factors. However, one of the factors that the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy gap became close to the HOMO-LUMO Coulomb integral was not valid in the case of spin-flip TDDFT (SF-TDDFT), which is frequently used as a means of the geometry optimization of MECI [Inamori et al., J. Chem. Phys. 152, 144108 (2020)]. This study revisited the controlling factors using FZOA for the SF-TDDFT method. Based on spin-adopted configurations within a minimum active space, the S0-S1 excitation energy is approximately represented by the HOMO and LUMO energy gap ΔεHL, a contribution from Coulomb integrals JHL″ and that from the HOMO-LUMO exchange integral KHL″. Furthermore, numerical applications of the revised formula at the SF-TDDFT method confirmed the control factors of S0/S1 MECI.