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Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin–orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm–Dancoff approximation to TDDFT, spin–flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine–Ag20 complex), we emphasize that caution is needed to properly account for system–environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments. [ABSTRACT FROM AUTHOR]

Computational modeling of plasmon-mediated molecular photophysical and photochemical behaviors can help us better understand and tune the bound molecular properties and reactivity and make better decisions to design and control nanostructures. However, computational investigations of coupled plasmon–molecule systems are challenging due to the lack of accurate and efficient protocols to simulate these systems. Here, we present a hybrid scheme by combining the real-time time-dependent density functional theory (RT-TDDFT) approach with the time-domain frequency dependent fluctuating charge (TD-ωFQ) model. At first, we transform ωFQ in the frequency-domain, an atomistic electromagnetic model for the plasmonic response of plasmonic metal nanoparticles (PMNPs), into the time-domain and derive its equation-of-motion formulation. The TD-ωFQ introduces the nonequilibrium plasmonic response of PMNPs and atomistic interactions to the electronic excitation of the quantum mechanical (QM) region. Then, we combine TD-ωFQ with RT-TDDFT. The derived RT-TDDFT/TD-ωFQ scheme allows us to effectively simulate the plasmon-mediated "real-time" electronic dynamics and even the coupled electron–nuclear dynamics by combining them with the nuclear dynamics approaches. As a first application of the RT-TDDFT/TD-ωFQ method, we study the nonradiative decay rate and plasmon-enhanced absorption spectra of two small molecules in the proximity of sodium MNPs. Thanks to the atomistic nature of the ωFQ model, the edge effect of MNP on absorption enhancement has also been investigated and unveiled. [ABSTRACT FROM AUTHOR]

In order to understand the mechanism of the electrochemical reduction of CO* on Cu(111), which competitively generates two intermediates, CHO* and COH*, we performed a first principles calculation on these two electrocatalytic reactions, including the solvent effect and imposing a constant potential. The transition states of the two reactions under constant potential conditions were located by the electrochemical nudged elastic band (eNEB) method and the charge effect in the two reactions was elucidated by charge correction in the constant potential model and Bader charge analysis. It was found that the two reactions have different potential dependencies and involve different degrees of partial charge transfer. In addition, we confirmed that the COH* reaction pathway exists only in a certain potential range when using the implicit solvent model. [ABSTRACT FROM AUTHOR]

The complex interplay between molecules and plasmonic metal nanoparticles (MNPs) presents a set of particular characteristics in absorption/scattering spectra such as excitonic splitting, asymmetric line shapes, plasmon-induced absorption enhancement and transparencies, etc. Although the MNP-molecule systems have been intensively investigated experimentally and theoretically, the construction of a theoretical framework which can produce all the disparate experimental observations and account for the electron-phonon (e-p) coupling is still in progress. Here, we present a theoretical approach which can account for both the plasmon-exciton coupling and the e-p interaction and produce all the spectral line shapes ranging from Fano antiresonance to Rabi splitting by simply tuning the coupling strength or plasmon damping rate. Additionally, we demonstrate the evolution of vibronic spectra and exciton dynamics with the coupling strength, plasmon damping rate, and detuning energy. It is found that the vibronic structures appearing in Rabi-like spectra are worse resolved, wider, and more largely shifted than those appearing in the Fano regime, attributed to the more significant deformation of the molecular vibrational wavepacket in the Rabi-like regime than that in the Fano regime as the molecular e-p interaction increases. The positive/negative value of detuning energy can induce different degrees of the vibrational wavepacket deformation and subsequently a different effect on the spectra in different coupling regimes. [ABSTRACT FROM AUTHOR]

It is of great importance and worthy of efforts to give a clear structure–property relationship and microscopic mechanism of fluorescence emitters with high quantum yield. In this work, we perform a detailed computational investigation to give an explanation to the high efficiency of a fluorescence emitter XBTD‐NPh based TADF sensitized fluorescence (TSF) OLEDs, and construct a symmetry structure DSBNA‐BTD. Theoretical calculations show that XBTD‐NPh is a long‐time phosphorescent material at 77 K and TADF is attributed to the RISC of T1 to S1 state. For DSBNA‐BTD, excitons arrived at T1 state comes to a large rate of nonradiatively path to the ground state, meaning it is may not be an efficient TADF molecule. For both molecules, the fast IC between T2 and T1 state results in that the hot exciton channel T1‐Tn‐S1 makes no contribution to the TADF. [ABSTRACT FROM AUTHOR]

The nonadiabatic phenomena, which are characterized by a strong coupling between electronic and nuclear motions, are ubiquitous. The nonadiabatic effect of the studied system can be significantly affected by the surrounding environment, such as solvents, in which such nonadiabatic process takes place. It is essential to develop the theoretical models to simulate these processes while accurately modeling the solvent environment. The time-dependent density functional theory (TDDFT) is currently the most efficient approach to describe the electronic structures and dynamics of complex systems, while the polarizable continuum model (PCM) represents one of the most successful examples among continuum solvation models. Here, we formulate the first-order derivative couplings (DCs) between the ground and excited states as well as between two excited states by utilizing time-independent equation of motion formalism within the framework of both linear response and spin flip formulations of TDDFT/CPCM (the conductor-like PCM), and implement the analytical DCs into the Q-CHEM electronic structure software package. The analytic implementation is validated by the comparison of the analytical and finite-difference results, and reproducing geometric phase effect in the protonated formaldimine test case. Taking 4-(N,N-dimethylamino)benzonitrile and uracil in the gas phase and solution as an example, we demonstrate that the solvent effect is essential not only for the excitation energies of the low-lying excited-states but also for the DCs between these states. Finally, we calculate the internal conversion rate of benzophenone in a solvent with DC being used. The current implementation of analytical DCs together with the existing analytical gradient and Hessian of TDDFT/PCM excited states allows one to study the nonadiabatic effects of relatively large systems in solutions with low computational cost. [ABSTRACT FROM AUTHOR]

We performed a first-principles systematic study on the fitness of two tricyclic donors (acridine and benzazasiline) interacting with five acceptors (triazine or triphenylborane-based) within the donor-acceptor-donor (D-A-D) framework for the potential application in organic light-emitting diodes (OLEDs) as thermally activated delayed fluorescence (TADF) emitters. Three types of compounds (D1-A-D1 (I), D2-A-D2 (II), and D1-A-D2 (III) were thus constructed to investigate the substitution pattern which can exhibit good TADF performance. We found that: by incorporating into the D-A-D frameworks and adopting an appropriate donor/acceptor combination, the studied compounds can bear rather small singlet-triplet gaps of ∼ 0.02 eV, and the emission energy can span a large space in (deep-)blue region ( 2.62 ∼ 3.13 eV); the molecular symmetry, in addition to the character of donors, control the properties of excited states, and acridine is more easily to be excited compared to benzazasiline. The symmetric setup (types I and II) is more suitable than asymmetric counterpart (type III) for optimal optoelectric properties. Accompanied with estimation of emission energy and rate constant, this study suggests that benzazasiline donor can serve as a versatile structural unit to combine with triphenylborane-based acceptor cores for constructing deep-blue D-A-D TADF emitters. [ABSTRACT FROM AUTHOR]

In this review, we summarize the computationally efficient time-dependent approaches to calculating the vibronic spectra including one-photon/two-photon absorption (OPA/TPA), emission, circular dichroism (CD), and resonance Raman/hyper-Raman scattering (RRS/RHRS) spectra with inclusion of the mode-mixing, Frank-Condon (FC) and Herzberg-Teller (HT) effects. At first, a unified dependency of spectral differential cross sections (SDCSs) on a generalized linear polarizability is derived in view of the relationship between SDCSs and the linear or nonlinear polarizabilities. Then, the Green's function technique is adopted to calculate the polarizability to avoid the tedious summation over the large number of vibrational states. To demonstrate the computational accuracy and efficiency, we apply the generalized time-dependent approaches to calculate the OPA(E)/TPA, RRS, and RHRS spectra of a series of radicals and organic molecules. The computational accuracy is demonstrated by a close comparison between the simulated spectra and the available experimental data. In the spectral calculations, we apply our recently developed analytical energy-derivative approaches for the excited states within the framework of time-dependent density functional theory (TDDFT) to calculate the electronic-structure parameters which enter the expressions of SDCSs, such as the excited-state geometries, energy gradient, harmonic vibrational frequencies, the geometrical derivatives of transition dipole moments, and so forth. It is found that the integrated approach which combines the time-dependent approach to SDCSs with the analytical energy-derivative approaches for TDDFT excited-state structure parameters breaks the bottlenecks of vibronic spectroscopy calculation down. © 2014 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

It has been widely recognized that plasmonic metal nanoparticles (MNPs) can enhance the power convention efficiency (PCE) of dye-sensitized solar cells (DSSCs). This enhancement is ascribed to the combined effects of plasmon decay, scattering, near-field enhancement, and exciting charge carriers in semiconductors through plasmon-induced resonance energy transfer (PIRET) and hot electron injection (HEI). PIRET and HEI processes appeared between MNPs, and semiconductors have been intensively investigated; however, it is not clear how the collaborative effect of PIRET and photon-induced direct and indirect electron transfer (PICT) occurred between plasmonic metals and dyes, and the interference of different charge separation channels (CSCs) starting from PIRET and PICT affects the PCE of DSSCs. This work aims to address these issues. We apply a model Hamiltonian method, which obviously includes both PIRET and PICT processes from Au MNP to dye molecules and incorporates the dye's electron-phonon interaction, to investigate the carrier dynamics. It is found that PIRET deforms the wavepacket dynamics of the molecular excited state and results in ten-fold enhancement of dye absorption. MNPs augment light absorption and increase the electron density in empty molecular orbitals of the dye molecule. Consequently, this enhances the interfacial charge separation. Furthermore, we observed the interference behavior of two CSCs and gave a full-scale insight into the correlation between the constructive/destructive interference and the electronic-state properties as well as carrier-phonon interactions. This work provides a theoretical guidance to optimize DSSCs. [ABSTRACT FROM AUTHOR]

This work is devoted to deriving and implementing analytic second- and third-order energy derivatives with respect to the nuclear coordinates and external electric field within the framework of the hybrid quantum mechanics/molecular mechanics method with induced charges and dipoles (QM/DIM). Using these analytic energy derivatives, one can efficiently compute the harmonic vibrational frequencies, infrared (IR) and Raman scattering (RS) spectra of the molecule in the proximity of noble metal clusters/nanoparticles. The validity and accuracy of these analytic implementations are demonstrated by the comparison of results obtained by the finite-difference method and the analytic approaches and by the full QM and QM/DIM calculations. The complexes formed by pyridine and two sizes of gold clusters (Au18 and Au32) at varying intersystem distances of 3, 4, and 5 Å are used as the test systems, and Raman spectra of 4,4′-bipyridine in the proximity of Au2057 and Ag2057 metal nanoparticles (MNP) are calculated by the QM/DIM method and compared with experimental results as well. We find that the QM/DIM model can well reproduce the IR spectra obtained from full QM calculations for all the configurations, while although it properly enhances some of the vibrational modes, it artificially overestimates RS spectral intensities of several modes for the systems with very short intersystem distance. We show that this could be improved, however, by incorporating the hyperpolarizability of the gold metal cluster in the evaluation of RS intensities. Additionally, we address the potential impact of charge migration between the adsorbate and MNPs. [ABSTRACT FROM AUTHOR]

We comment on an excited‐state localization method recently proposed by Blanc et al. (J. Comput. Chem. 2023, 44, 105). Elaborate comparisons are made to demonstrate that their method is a less‐comprehensive version of the diabatization method proposed by us 2 years earlier (J. Phys. Chem. Lett. 2021, 12, 1032). [ABSTRACT FROM AUTHOR]

The donor‐acceptor interface plays a critically important role in determining the power conversion efficiency of organic solar cells via controlling charge separation (CS) and recombination (CR) processes. Here, we combine the electronic structure calculations with electron transfer rate theory to clarify the CS and CR processes in ThQs‐C60/PDIxCN2 donor‐acceptor complexes. The results reveal that in ThQs‐PDIxCN2 the CS comes from both the dissociations of photo‐induced singlet exciton and singlet fission‐induced triplet exciton with a high efficiency, whereas in ThQs‐C60 only the singlet exciton dissociation can take place because the triplet exciton lies below the charge‐transfer exciton. However, very high CR rates in ThQs‐PDIxCN2 obliterate the benefit of fast CS, inversely leading to the ThQ‐C60 complex with a better cell efficiency. The present results are consistent with experimental observation and may furnish a possible patten to improve the overall conversion efficiency. © 2018 Wiley Periodicals, Inc. The charge separation (CS) and recombination (CR) processes in the donor‐acceptor interface play a critically important role in the determination of power conversion efficiency of organic solar cells. This work performs a theoretical calculation on CS and CR rates of ThQs‐C60/PDIxCN2 complexes and offers a theoretical explanation to the experimental observation. [ABSTRACT FROM AUTHOR]

Both the vibrationally resolved and statistically averaged one-photon absorption (OPA) and two-photon absorption (TPA) spectra of the anionic form of chromophore (AC) in its micro-environment of yellow fluorescent protein (YFP) Citrine have been calculated. The result comparison has been made with those of the AC model compounds in vacuo and methanol solution, which allows us to allocate the individual contribution of the intramolecular electron-vibrational coupling, the electrostatic π-stacking interaction between Tyr203 and AC, and the interaction between AC and its micro-environment to the spectra. The results reveal that the non-Condon vibronic coupling effect is responsible for the blue shift of TPA absorption maximum compared with its OPA counterpart corresponding to S0 → S1, and that the π-stacking interaction between Tyr203 and AC alters the relative intensities of TPA maxima, which further enhances the higher-energy vibronic peaks and weakens the lowest-energy peak. The statically averaged OPA and TPA spectra calculated by quantum mechanics/molecular mechanics (QM/MM) methods based on Born-Oppenheimer molecular dynamics simulation largely deviate the experimental spectral lineshapes, which further verifies the significant contribution of non-Condon vibronic coupling effect on the spectra. The interaction of individual amino acid residue or water close to AC+Tyr203 has different effects on the spectra, which may increase/decrease the excitation energy depending on its position and electronic property. [ABSTRACT FROM AUTHOR]

The spectral densities of diagonal and nondiagonal exciton-phonon (e-p) coupling for tetracene crystal have been calculated by the harmonic oscillator (HO) model and ground-state MD-based approaches. We find that classical MD-based approaches overestimate the coupling of exciton with high-frequency vibrational modes and predict the strongest e-p coupling appeared above 1500 cm −1 whereas HO model and AIMD-based approach predict it appeared at ∼ 1400 cm −1 . Additionally, the calculated spectral densities of nondiagonal e-p coupling for three different dimers show that they are continuously distributed in the range of 0–150 cm −1 and are 2–3 order of magnitude smaller than the maxima of diagonal e-p coupling. [ABSTRACT FROM AUTHOR]

The vibrationally resolved absorption spectra of zinc phthalocyanine (ZnPc) aggregates (up to 70 monomers) are explored using the non-Markovian stochastic Schrödinger equation. Various types of local excitations, charge-transfer (CT) excitations, and exciton–phonon couplings are explicitly included in a comprehensive model Hamiltonian, which is parameterized by first-principles calculations. The absorption spectral simulations clarify that the two absorption bands in the Q-band region observed in experiments can be assigned to the contribution from the CT-mediated interactions, rather than the mixtures of different-type aggregates, as prevailingly assumed. Furthermore, the relative intensities of the two bands are found to be closely related to the intermolecular distance and molecular number in a ZnPc aggregate. From the investigation of the decoherence process after optical excitation, it is found that CT states can induce coherence regeneration as the time scale of charge separation is much faster than that of the vibration-induced decoherence. However, they would instead boost the decoherence process as the two time scales become comparable. The two different effects of CT states may suggest a novel way to regulate the decoherence process in excitation energy relaxation. [ABSTRACT FROM AUTHOR]

The nonlinear optical properties of hybrid systems composed of a silver nanosphere and an open-ended finite-sized armchair single-walled carbon nanotube (SWCNT) are systematically investigated by the hybrid time-dependent Hartree–Fock (TDHF)/finite difference time domain (FDTD) approach, which combines the real-time TDHF approach for the molecular electronic dynamics with the classical computational electrodynamics approach, the FDTD, for solving Maxwell's equations. The high order harmonic generation (HHG) spectra of SWCNTs are studied as a function of the intensity (I0) and frequency (ω0) of the incident field, and SWCNTs length as well. It is found that the near field generated by a Ag nanoparticle has an overall enhancement to the molecular HHG in all the energy range, and it extends the HHG spectra to high energy. The inhomogeneity of the near field results in the appearance of even-order harmonics, and their corresponding spectral intensities are sensitive to ω0, therefore the near field's gradient. When ω0 is far away from the frequency of plasmon resonance of the silver nanosphere (ωc), the interference between the incident and scattering light beams extends the spectral range and makes the HHG spectra more sensitive to I0, while at ω0 = ωc, the impact of the interference on the spectra is negligible. [ABSTRACT FROM AUTHOR]

Natural light‐harvesting (LH) systems can divide identical dyes into unequal aggregate states, thereby achieving intelligent "allocation of labor". From a synthetic point of view, the construction of such kinds of unequal and integrated systems without the help of proteinaceous scaffolding is challenging. Here, we show that four octatetrayne‐bridged ortho‐perylene diimide (PDI) dyads (POPs) self‐assemble into a quadruple assembly (POP)4 both in solution and in the solid state. The two identical PDI units in each POP are compartmentalized into weakly coupled PDIs (P520) and closely stacked PDIs (P550) in (POP)4. The two extreme pools of PDI chromophores were unambiguously confirmed by single‐crystal X‐ray crystallography and NMR spectroscopy. To interpret the formation of the discrete quadruple assembly, we also developed a two‐step cooperative model. Quantum‐chemical calculations indicate the existence of multiple couplings within and across P520 and P550, which can satisfactorily describe the photophysical properties of the unequal quadruple assembly. This finding is expected to help advance the rational design of dye stacks to emulate functions of natural LH systems. [ABSTRACT FROM AUTHOR]

Natural light‐harvesting (LH) systems can divide identical dyes into unequal aggregate states, thereby achieving intelligent "allocation of labor". From a synthetic point of view, the construction of such kinds of unequal and integrated systems without the help of proteinaceous scaffolding is challenging. Here, we show that four octatetrayne‐bridged ortho‐perylene diimide (PDI) dyads (POPs) self‐assemble into a quadruple assembly (POP)4 both in solution and in the solid state. The two identical PDI units in each POP are compartmentalized into weakly coupled PDIs (P520) and closely stacked PDIs (P550) in (POP)4. The two extreme pools of PDI chromophores were unambiguously confirmed by single‐crystal X‐ray crystallography and NMR spectroscopy. To interpret the formation of the discrete quadruple assembly, we also developed a two‐step cooperative model. Quantum‐chemical calculations indicate the existence of multiple couplings within and across P520 and P550, which can satisfactorily describe the photophysical properties of the unequal quadruple assembly. This finding is expected to help advance the rational design of dye stacks to emulate functions of natural LH systems. [ABSTRACT FROM AUTHOR]

Nowadays, it is an attractive strategy to promote the efficiency of photocatalytic reactions by introducing the heterojunctions. Bismuth vanadate (BiVO4), one of the promising non-titania-based visible light-driven semiconductor photocatalysts, possesses three different crystal phases which can transform from one phase to another under appropriate conditions. The heterophase junction built by the monoclinic scheelite (s-m) and tetragonal zircon (z-t) phase BiVO4 has been demonstrated to have high photocatalytic activity than the single-phase BiVO4. Here we presented a step-by-step protocol based on the first-principles density functional theory calculations to explore the origin of high photocatalytic activity existed in BiVO4 heterojunction. The mixed-phase geometrical structures, density of states, electrostatic potential, electron localization function and band offsets of optimal interface have been calculated. For the heterojunction, the calculated valence band maximum and conduction band minimum of z-t BiVO4 are 0.29 and 0.32 eV above those of s-m BiVO4, respectively, indicating that the presence of interface in monoclinic/tetragonal heterophase provides a spatial condition for charge carrier separation and promotes the separation of photoinduced electron–hole pairs. Further calculations reveal that the direction of electron migration across the phase boundary is from z-t to s-m, consistent with the experimental observation. [ABSTRACT FROM AUTHOR]

Stepwise ring closing processes of platinum(II) alkynyl arkynyl bridged DTEs (OO→OC→CC) were studied theoretically with density functional theory method in this work for better understanding the Pt(II) alkynyl coordination effect on the photophysical and photochemical properties of dithienylethene (DTE). It is observed that the absorption spectrum of OO complex is red-shifted compared with that of ring-opened DTE monomer because of the decreased HOMO-LUMO gap energy. The first S 0 →S 1 absorption of OC is red shifted than that of OO and is blue shifted than that of CC complex because of the increased conjugation of the ring-closed DTE moiety. In addition, potential energy surface (PSE) studies show that the energy barrier for the ring-closing process in the ground state of Pt(II) complex is smaller than that of the isolated DTE monomer and the isomerization process is changed from endothermic to exothermic reaction. Moreover, the energy barrier for the first ring-closing process is a little larger than the second ring-closing process involved in the DTE moieties. More important, similar with that in the DTE monomers, the ring closing processes in the ionic and triplet states of Pt(II) complexes is easier than that in the neutral case. [ABSTRACT FROM AUTHOR]

• An innovative aptamer SERS biosensor for highly sensitive protein biomarker detection was presented. • The biosensor contains SERS tags and novel magnetic capture substrates. • Aptamers against CRP were modified on both SERS tag and magnetic capture substrate for specific recognition. • This method exhibits excellent selectivity and specificity and displays high accuracy in actual human serum samples. • This strategy can be extended to the detection of other biomarkers and hold great promise in the clinical diagnosis. The design of a rapid, simple, and ultrasensitive detection platform of protein biomarkers has become an urgent need in early diagnosis and treatment. Surface-enhanced Raman scattering (SERS) technology, with the unique advantages of ultra-sensitivity and fingerprint recognition, has attracted much attention in biomarker detection. An innovative aptamer SERS biosensor for highly sensitive protein biomarker detection was presented. This biosensor contains a SERS tag (reporter-labeled Au nano-bridged nanogaps particles, Au NNPs) and novel magnetic capture substrate (Ag-coated Fe 3 O 4 -Au NPs, Ag MNPs). C-reactive protein (CRP), a representative biomarker for diagnosing, was used to assess the SERS performance of this biosensor. Aptamers against CRP were modified on both SERS tag and magnetic capture substrate for specific recognition by Au NNPs-CRP-Ag MNPs sandwich assay. This strategy achieved sensitive detection of CRP with a limit of detection (LOD) of 10 fM (1.14 pg/mL), and is much lower than reported analytical methods. Besides, this method exhibits excellent selectivity and specificity for CRP under the interference of other proteins and displays high accuracy in the detection of actual human serum samples. This proposed detection strategy can be extended to the sensitive detection of other biomarker proteins and hold great promise in the clinical diagnosis of diseases. [ABSTRACT FROM AUTHOR]

In the modeling of spin‐crossing reactions, it has become popular to directly explore the spin‐adiabatic surfaces. Specifically, through constructing spin‐adiabatic states from a two‐state Hamiltonian (with spin‐orbit coupling matrix elements) at each geometry, one can readily employ advanced geometry optimization algorithms to acquire a "transition state" structure, where the spin crossing occurs. In this work, we report the implementation of a fully‐variational spin‐adiabatic approach based on Kohn‐Sham density functional theory spin states (sharing the same set of molecular orbitals) and the Breit‐Pauli one‐electron spin‐orbit operator. For three model spin‐crossing reactions (predissociation of N2O, singlet‐triplet conversion in CH2, and CO addition to Fe(CO)4), the spin‐crossing points were obtained. Our results also indicated the Breit‐Pauli one‐electron spin‐orbit coupling can vary significantly along the reaction pathway on the spin‐adiabatic energy surface. On the other hand, due to the restriction that low‐spin and high‐spin states share the same set of molecular orbitals, the acquired spin‐adiabatic energy surface shows a cusp (ie, a first‐order discontinuity) at the crossing point, which prevents the use of standard geometry optimization algorithms to pinpoint the crossing point. An extension with this restriction removed is being developed to achieve the smoothness of spin‐adiabatic surfaces. [ABSTRACT FROM AUTHOR]