BDF: A relativistic electronic structure program package

Harnessing synergistic effects in GQD@Pt(II) nanocomposites for enhanced photovoltaic performance: a computational study

CONTEXT

The development of efficient solar energy conversion technologies is crucial for addressing global energy challenges and reducing reliance on fossil fuels. Platinum(II) complexes are promising materials for photovoltaic applications due to their strong light absorption and long-lived excited states. However, their narrow absorption in the visible spectrum and stability issues limit their performance. Combining platinum(II) complexes with graphene quantum dots (GQDs) can enhance photovoltaic performance by leveraging the complementary light harvesting and charge transfer characteristics of the two components. This study utilizes density functional theory (DFT) calculations to explore their electronic structures, charge transfer dynamics, and photoelectric performance. Specifically, it investigates the effects of incorporating different substituents, either electron-donating or electron-withdrawing, onto the fluorene motif of the Pt(II) complex. The findings reveal that combining GQDs with Pt(II) complexes extends light absorption into the UV range, enabling comprehensive solar utilization. Upon photoexcitation, electrons migrate between the GQD conduction band and the Pt(II) complex, stabilizing charges and enhancing extraction. Substituents significantly influence charge transfer dynamics: electron-withdrawing groups promote transfer to the GQD, while electron-donating groups encourage charge separation and delocalization. Nanocomposites featuring electron-donating substituents achieve the highest energy conversion efficiencies, with GQD@Pt(II)-NPh2 reaching 24.6%. This is attributed to improved light harvesting, efficient charge injection, and reduced recombination. These insights guide the rational design of GQD-Pt(II) nanocomposites, optimizing charge separation and transfer processes for enhanced photovoltaic performance. The computational approach employed here provides a robust tool for developing advanced materials in renewable energy technologies.

METHODS

The computational studies reported in this work were performed using the DFT approach, specifically employing the hybrid functional PBE0. The PBE0 functional's accuracy in describing electronic structures and excited-state properties is essential for understanding charge transfer processes, photoabsorption, and emission characteristics in metal-organic complexes. Geometry optimizations and time-dependent DFT (TD-DFT) calculations were carried out to investigate the properties of the nanocomposites. The effects of solvents were replicated using the conductor-like polarizable continuum model (CPCM). The charge transfer length (ΔL) and interfragment charge transfer (ΔQ) were calculated using the Multiwfn software package, and all calculations were performed using the BDF software package.

Global Potential Energy Surfaces by Compressed-State Multistate Pair-Density Functional Theory for Hyperthermal Collisions in the O2+O2 System

Interactions between oxygen molecules play an important role in atmospheric chemistry and hypersonic flow chemistry in atmospheric entries. Recently, high-quality ab initio potential energy surface (PES) of the quintet O4 was reported by Paukku et al. [J. Chem. Phys. 147, 034301 (2017)]. 10543 configurations were sampled and calculated at the level of MS-CASPT2/maug-cc-pVTZ with scaled external correlation. The PES was fitted to a many-body (MB) form with the many-body part described by the permutationally invariant polynomial approach (MB-PIP). In this work, the PIP-Neural Network (PIP-NN) and MB-PIP-NN methods were used to refit the PES based on the same data by Paukku et al. Three PESs were compared. It was found that the performances differ significantly in the O+O3 region as well as in the long-range region. Therefore, additional 1300 points were sampled, and the efficient compressed-state multistate pair-density functional theory (CMS-PDFT) was used to calculate the electronic structure of these 1300 points and 10543 points by Paukku et al. Then, a completely new quintet PES was fitted using the MB-PIP-NN method. Based on this PES, the quasi-classical trajectory (QCT) approach was used to reveal all possible reaction channels for hyperthermal O2-O2 collisions.

Combining Functional Units to Design Organic Materials with Dynamic Room-Temperature Phosphorescence under Continuous Ultraviolet Irradiation

Developing materials with dynamic room-temperature phosphorescence (RTP) properties is crucial for expanding the applications of organic light-emitting materials. In this study, we designed and synthesized two novel RTP molecules by combining functional units, incorporating the folded unit thianthrene into the classic luminescent cores thioxanthone or anthraquinone to construct TASO and TA2O. In this combination, the TA unit contributes to the enhancement of spin-orbit coupling (SOC), while the luminescent core governs the triplet energy level. After the strategic manipulation of SOC using the thianthrene unit, the target molecules exhibited a remarkable enhancement in RTP performance. This strategy led to the successful development of TASO and TA2O molecules with outstanding dynamic RTP properties when exposed to continuous ultraviolet irradiation, a result that can be ascribed to their efficient RTP, improved absorption ability, and oxygen-sensitive RTP properties. Leveraging the oxygen-mediated ultraviolet-radiation-induced RTP enhancement in TASO-doped polymer films, we developed a novel time-resolved detection technique for identifying phase separation in polymers with varying oxygen permeability. This research offers a promising approach for constructing materials with dynamic RTP properties.

Pushing the Limit of Photo-Controlled Polymerization: Hyperchromic and Bathochromic Effects

The photocatalyst (PC) zinc tetraphenylporphyrin (ZnTPP) is highly efficient for photoinduced electron/energy transfer reversible addition-fragmentation chain transfer (PET-RAFT) polymerization. However, ZnTPP suffers from poor absorbance of orange light by the so-called Q-band of the absorption spectrum (maximum absorption wavelength λmax = 600 nm, at which molar extinction coefficient εmax = 1.0×104 L/(mol·cm)), hindering photo-curing applications that entail long light penetration paths. Over the past decade, there has not been any competing candidate in terms of efficiency, despite a myriad of efforts in PC design. By theoretical evaluation, here we rationally introduce a peripheral benzo moiety on each of the pyrrole rings of ZnTPP, giving zinc tetraphenyl tetrabenzoporphyrin (ZnTPTBP). This modification not only enlarges the conjugation length of the system, but also alters the a1u occupied π molecular orbital energy level and breaks the accidental degeneracy between the a1u and a2u orbitals, which is responsible for the low absorption intensity of the Q-band. As a consequence, not only is there a pronounced hyperchromic and bathochromic effect (λmax = 655 nm and εmax = 5.2×104 L/(mol·cm)) of the Q-band, but the hyperchromic effect is achieved without increasing the intensity of the less useful, low wavelength absorption peaks of the PC. Remarkably, this strong 655 nm absorption takes advantage of deep-red (650-700 nm) light, a major component of solar light exhibiting good atmosphere penetration, exploited by the natural PC chlorophyll a as well. Compared with ZnTPP, ZnTPTBP displayed a 49% increase in PET-RAFT polymerization rate with good control, marking a significant leap in the area of photo-controlled polymerization.

Promoting Catalytic Performance Involving Hydrogen Spillover by Ion Exchange of Pt@A Catalysts to Regulate Reactant Adsorption

Zeolite-encapsulated metal nanoparticle systems have exhibited interesting catalytic performances via the hydrogen spillover process, yet how to further utilize the function of zeolite supports to promote catalytic properties in such a process is still challenging and has rarely been investigated. Herein, to address this issue, the strategy to strengthen the adsorption energy of reactant onto the zeolite surface via a simple ion exchange method has been implemented. Ion-exchanged linde type A (LTA) zeolite-encapsulated platinum nanoclusters (Pt@NaA, Pt@HA, Pt@KA, and Pt@CaA) were prepared to study the influence of ion exchange on the catalytic performance in the model reaction of hydrogenation of acetophenone to 1-phenylethanol. The reaction results showed that the Pt@CaA catalyst exhibited the best catalytic activity in the series of encapsulated catalysts, and the selectivity of 1-phenylethanol approached 100%. As revealed by density functional theory (DFT) calculations and acetophenone temperature-programmed desorption (acetophenone-TPD) experiments, in comparison with introduced cations of Na+, H+, and K+, ion-exchanged Ca2+ on the zeolite maximumly enhanced the adsorption of carbonyl groups in acetophenone, playing a critical role in achieving the highest activity and excellent catalytic selectivity among the Pt@A catalysts.

Renormalized-Residue-Based Multireference Configuration Interaction Method for Strongly Correlated Systems

The implementation of multireference configuration interaction (MRCI) methods in quantum systems with large active spaces is hindered by the expansion of configuration bases or the intricate handling of reduced density matrices (RDMs). In this work, we present a spin-adapted renormalized-residue-based MRCI (RR-MRCI) approach that leverages renormalized residues to effectively capture the entanglement between active and inactive orbitals. This approach is reinforced by a novel efficient algorithm, which also facilitates an efficient deployment of spin-adapted matrix product state MRCI (MPS-MRCI). The RR-MRCI framework possesses several advantages: (1) It considers the orbital entanglement and utilizes highly compressed MPS structure, improving computational accuracy and efficiency compared with internally contracted (ic) MRCI. (2) Utilizing small-sized buffer environments of a few external orbitals as probes based on quantum information theory, it enhances computational efficiency over MPS-MRCI and offers potential application to large molecular systems. (3) The RR framework can be implemented in conjunction with ic-MRCI, eliminating the need for high-rank RDMs, by using distinct renormalized residues. We evaluated this method across nine diverse molecular systems, including Cu2O22+ with an active space of (24e,24o) and two complexes of lanthanide and actinide with active space (38e,36o), demonstrating the method's versatility and efficacy.

GUGA-based MRCI approach with core-valence separation approximation (CVS) for the calculation of the core-excited states of molecules

We develop and demonstrate how to use the Graphical Unitary Group Approach (GUGA)-based MRCISD with Core-Valence Separation (CVS) approximation to compute the core-excited states. First, perform a normal Self-Consistent-Field (SCF) or valence MCSCF calculation to optimize the molecular orbitals. Second, rotate the optimized target core orbitals and append to the active space, form an extended CVS active space, and perform a CVS-MCSCF calculation for core-excited states. Finally, construct the CVS-MRCISD expansion space and perform a CVS-MRCISD calculation to optimize the CI coefficients based on the variational method. The CVS approximation with GUGA-based methods can be implemented by flexible truncation of the Distinct Row Table. Eliminating the valence-excited configurations from the CVS-MRCISD expansion space can prevent variational collapse in the Davidson iteration diagonalization. The accuracy of the CVS-MRCISD scheme was investigated for excitation energies and compared with that of the CVS-MCSCF and CVS-CASPT2 methods using the same active space. The results show that CVS-MRCISD is capable of reproducing well-matched vertical core excitation energies that are consistent with experiments by combining large basis sets and a rational reference space. The calculation results also highlight the fact that the dynamic correlation between electrons makes an undeniable contribution in core-excited states.

Unified construction of relativistic Hamiltonians

It is shown that the four-component (4C), quasi-four-component (Q4C), and exact two-component (X2C) relativistic Hartree-Fock equations can be implemented in a unified manner by making use of the atomic nature of the small components of molecular 4-spinors. A model density matrix approximation can first be invoked for the small-component charge/current density functions, which gives rise to a static, pre-molecular mean field to be combined with the one-electron term. As a result, only the nonrelativistic-like two-electron term of the 4C/Q4C/X2C Fock matrix needs to be updated during the iterations. A "one-center small-component" approximation can then be invoked in the evaluation of relativistic integrals, that is, all atom-centered small-component basis functions are regarded as extremely localized near the position of the atom to which they belong such that they have vanishing overlaps with all small- or large-component functions centered at other nuclei. Under these approximations, the 4C, Q4C, and X2C mean-field and many-electron Hamiltonians share precisely the same structure and accuracy. Beyond these is the effective quantum electrodynamics Hamiltonian that can be constructed in the same way. Such approximations lead to errors that are orders of magnitude smaller than other sources of errors (e.g., truncation errors in the one- and many-particle bases as well as uncertainties of experimental measurements) and are, hence, safe to use for whatever purposes. The quaternion forms of the 4C, Q4C, and X2C equations are also presented in the most general way, based on which the corresponding Kramers-restricted open-shell variants are formulated for "high-spin" open-shell systems.

Spin-Adapted Externally Contracted Multireference Configuration Interaction Method Based on Selected Reference Configurations

As one kind of approximation of the full configuration interaction solution, the selected configuration interaction (sCI) methods have been shown to be valuable for large active spaces. However, the inclusion of dynamic correlation beyond large active spaces is necessary for more quantitative results. Since the sCI wave function can provide a compact reference for multireference methods, previously, we proposed an externally contracted multireference configuration interaction method using the sCI reference reconstructed from the density matrix renormalization group wave function [J. Chem. Theory Comput. 2018, 14, 4747-4755]. The DMRG2sCI-EC-MRCI method is promising for dealing with more than 30 active orbitals and large basis sets. However, it suffers from two drawbacks: spin contamination and low efficiency when using Slater determinant bases. To solve these problems, in this work, we adopt configuration state function bases and introduce a new algorithm based on the hybrid of tree structure for convenient configuration space management and the graphical unitary group approach for efficient matrix element calculation. The test calculation of naphthalene shows that the spin-adapted version could achieve a speed-up of 6.0 compared with the previous version based on the Slater determinant. Examples of dinuclear copper(II) compound as well as Ln(III) and An(III) complexes show that the sCI-EC-MRCI can give quantitatively accurate results by including dynamic correlation over sCI for systems with large active spaces and basis sets.

Toward the Rational Design of Organic Catalysts for Organocatalysed Atom Transfer Radical Polymerisation

Thanks to their diversity, organic photocatalysts (PCs) have been widely used in manufacturing polymeric products with well-defined molecular weights, block sequences, and architectures. Still, however, more universal property-performance relationships are needed to enable the rational design of such PCs. That is, a set of unique descriptors ought to be identified to represent key properties of the PCs relevant for polymerisation. Previously, the redox potentials of excited PCs (PC*) were used as a good descriptor for characterising very structurally similar PCs. However, it fails to elucidate PCs with diverse chromophore cores and ligands, among which those used for polymerisation are a good representative. As showcased by model systems of organocatalysed atom transfer radical polymerisation (O-ATRP), new universal descriptors accounting for additional factors, such as the binding and density overlap between the PC* and initiator, are proposed and proved to be successful in elucidating the experimental performances of PCs in polymerisation. While O-ATRP is exemplified here, the approach adopted is general for studying other photocatalytic systems.

Scalar Relativistic Effects with Multiwavelets: Implementation and Benchmark

The importance of relativistic effects in quantum chemistry is widely recognized, not only for heavier elements but throughout the periodic table. At the same time, relativistic effects are strongest in the nuclear region, where the description of electrons through a linear combination of atomic orbitals becomes more challenging. Furthermore, the choice of basis sets for heavier elements is limited compared with lighter elements where precise basis sets are available. Thanks to the framework of multiresolution analysis, multiwavelets provide an appealing alternative to overcoming this challenge: they lead to robust error control and adaptive algorithms that automatically refine the basis set description until the desired precision is reached. This allows one to achieve a proper description of the nuclear region. In this work, we extended the multiwavelet-based code MRChem to the scalar zero-order regular approximation framework. We validated our implementation by comparing the total energies for a small set of elements and molecules. To confirm the validity of our implementation, we compared both against a radial numerical code for atoms and the plane-wave-based code EXCITING.

Error of relativistic effective core potentials for closed-shell diatomic molecules of p-block heavy and superheavy elements in DFT and TDDFT calculations

Pseudopotentials (PP) are extensively used in electronic structure calculations, particularly for molecules containing heavy elements. Parameters in PPs are mainly determined from ab initio results, and errors of such PPs in density functional theory (DFT) calculations have been studied previously. However, PP errors on results with spin-orbit coupling and those in time-dependent DFT (TDDFT) calculations have not been reported previously. In this work, we investigate the error of the small-core energy-consistent Stuttgart/Koln pseudopotentials in DFT and TDDFT calculations with and without spin-orbit coupling. Ground state bond lengths, harmonic frequencies, dissociation energies, and vertical excitation energies for a series of closed-shell diatomic heavy and superheavy p-block molecules are calculated using several popular exchange-correlation functionals. PP errors are estimated by comparing with results using the all-electron Dirac-Coulomb (-Gaunt) Hamiltonian. Our results show that the difference between ground state properties and most excitation energies in scalar-relativistic calculations with the PP and those of all-electron calculations is quite small. This difference becomes somewhat larger when spin-orbit coupling (SOC) is present, especially for properties that are affected by SOC to some extent. In addition, the errors of the PPs are insensitive to the employed exchange-correlation functionals in most cases. Our results indicate that reasonable DFT and TDDFT results can be obtained using the small-core energy-consistent Stuttgart/Koln pseudopotentials for heavy and super-heavy p-block molecules.

New pyrrolo[3,2-b]pyrroles with AIE characteristics for detection of dichloromethane and chloroform

Three new pyrrolo[3,2-b]pyrrole derivatives containing methoxyphenyl, pyrene or tetraphenylethylene (TPE) units (compounds 1-3) have been designed, synthesized and fully characterized. The aggregation-induced emission (AIE) properties of compounds 1-3 were tested in different water fraction (fw ) of tetrahydrofuran (THF). The pyrrolo[3,2-b]pyrrole derivative 3 containing TPE units exhibited typical AIE features with an enhanced emission (∼32-fold) in the solid state versus in solution; compounds 1 and 2 exhibited an aggregation-caused quenching effect. In addition, the steric and electronic effects of the peripheral moieties on the emission behavior, both in solution and in the solid state, have been investigated. Moreover, pyrrolo[3,2-b]pyrrole 1 exhibits high sensitivity and selectivity for dichloromethane and chloroform solvents, with the system displaying a new emission peak and fast response time under ultraviolet irradiation.

Nonadiabatic molecular dynamics simulations for ultrafast photo-induced ring-opening and isomerization reactions of 2,2-diphenyl-2H-chromene

Nonadiabatic molecular dynamics simulations with a global switching algorithm have been performed at the TD-CAM-B3LYP-D3/def2-SVP level of theory for ultrafast photo-induced ring-opening and isomerization reactions upon S1 excitation for 2,2-diphenyl-2H-chromene (DPC). Both DPC-T and DPC-C conformers undergo ring-opening relaxation and isomerization pathways accompanied with pyran conformation conserved and converted on the S1 or S0 states via competition and cooperation between C-O bond dissociation and pyran inversion motions. Upon S1 excitation, the DPC-T mainly relaxes to the T-type conical intersection region and thus yields a higher ring-opening efficiency with a faster S1 decay and intermediate formation than those of the DPC-C mainly relaxing to C-type conical intersection. The simulated ring-opening quantum yield for DPC-T (DPC-C) is 0.91 (0.76), which is in good agreement with the experimental value of 0.7-0.9, and the thermal weight averaged lifetimes are estimated as 182.0 fs, 228.6 fs, and 1262.4 fs for the excited-state decay, intermediate formation, and ring-opening product, respectively. These time constants are in good agreement with the experimentally measured τ1 time constant of 190-450 fs and τ2 time constant of 1000-1800 fs. The present work could be a valuable reference for understanding the nature of the photorelaxation mechanisms of DPC, and could help to develop DPC-based photoresponsive materials.

When do tripdoublet states fluoresce? A theoretical study of copper(II) porphyrin

Open-shell molecules rarely fluoresce, due to their typically faster non-radiative relaxation rates compared to closed-shell ones. Even rarer is the fluorescence from states that have two more unpaired electrons than the open-shell ground state, since they involve excitations from closed-shell orbitals to vacant-shell orbitals, which are typically higher in energy compared to excitations from or out of open-shell orbitals. States that are dominated by the former type of excitations are known as tripdoublet states when they can be described as a triplet excitation antiferromagnetically coupled to a doublet state, and their description by unrestricted single-reference methods (e.g., U-TDDFT) is notoriously inaccurate due to large spin contamination. In this work, we applied our spin-adapted TDDFT method, X-TDDFT, and the efficient and accurate static-dynamic-static second order perturbation theory (SDSPT2), to the study of the excited states as well as their relaxation pathways of copper(II) porphyrin; previous experimental works suggested that the photoluminescence of some substituted copper(II) porphyrins originate from a tripdoublet state, formed by a triplet ligand π → π* excitation antiferromagnetically coupled with the unpaired d electron. Our results demonstrated favorable agreement between the X-TDDFT, SDSPT2 and experimental excitation energies, and revealed noticeable improvements of X-TDDFT compared to U-TDDFT, not only for vertical excitation energies but also for adiabatic energy differences. These suggest that X-TDDFT is a reliable tool for the study of tripdoublet state fluorescence. Intriguingly, we showed that the aforementioned tripdoublet state is only slightly above the lowest doublet excited state and lies only slightly higher than the lowest quartet state, which suggests that the tripdoublet of copper(II) porphyrin is long-lived enough to fluoresce due to a lack of efficient non-radiative relaxation pathways; an explanation for this unusual state ordering is given. Indeed, thermal vibration correlation function (TVCF)-based calculations of internal conversion, intersystem crossing, and radiative transition rates confirm that copper(II) porphyrin emits thermally activated delayed fluorescence (TADF) and a small amount of phosphorescence at low temperature (83 K), in accordance with experiment. The present contribution is concluded by a few possible approaches of designing new molecules that fluoresce from tripdoublet states.

Benchmark computational investigations for the basic model of the salt-water complex: NaCl(H2O) and its anion NaCl(H2O). Phys Chem Chem Phys 2023;25:27215-27229. [PMID: 37791409 DOI: 10.1039/d3cp03421f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

The microsolvation of salts in water is a fundamental physicochemical process. In this work, the aqueous salt complex NaCl(H2O) and its anion NaCl(H2O)- were investigated using comprehensive calculations, including the costly and accurate CCSD(T)-F12a and focal point analysis (FPA) methods. For the neutral NaCl(H2O), three isomers exist, two of which are mirror-symmetric with almost identical structures and their corresponding anions are also mirror-symmetric. For the NaCl(H2O)- anion, there are four isomers. Several transition states are found for the first time. The structural rearrangements of neutral NaCl(H2O) and NaCl(H2O)- anions are mainly caused by breaking and forming of the hydrogen bonds and the enhancement and weakening of interactions between Na and O atoms. The distributions of the anion complexes from 15-300 K are computed and compared to recent experimental results. The analysis of the intermolecular weak interactions shows the weak van der Waals interactions between Na and O atoms, as well as hydrogen bonding between H and Cl. Moreover, the theoretically predicted anion photoelectron spectra are assigned and analyzed in detail, and they agree with experimental spectra satisfactorily. The Na-Cl stretching vibrational mode dominates the vibrational structure in both anion spectra with some minor contributions from the intermolecular motions between H2O and NaCl.

SOiCISCF: Combining SOiCI and iCISCF for Variational Treatment of Spin-Orbit Coupling

It has recently been shown that the SOiCI approach [Zhang, N.; J. Phys.: Condens. Matter 2022, 34, 224007], in conjunction with the spin-separated exact two-component relativistic Hamiltonian, can provide very accurate fine structures of systems containing heavy elements by treating electron correlation and spin-orbit coupling (SOC) on an equal footing. Nonetheless, orbital relaxations/polarizations induced by SOC are not yet fully accounted for due to the use of scalar relativistic orbitals. This issue can be resolved by further optimizing the still real-valued orbitals self-consistently in the presence of SOC, as done in the spin-orbit coupled CASSCF approach [Ganyushin, D.; et al. J. Chem. Phys. 2013, 138, 104113] but with the iCISCF algorithm [Guo, Y.; J. Chem. Theory Comput. 2021, 17, 7545-7561] for large active spaces. The resulting SOiCISCF employs both double group and time reversal symmetries for computational efficiency and the assignment of target states. The fine structures of p-block elements are taken as showcases to reveal the efficacy of SOiCISCF.

Noncovalent interactions of aromatic heterocycles: rotational spectroscopy and theoretical calculations of the thiazole-CF4 and thiazole-SF6 complexes

The complexes of thiazole with CF4 and SF6 have been investigated by Fourier transform microwave spectroscopy and quantum chemical calculations. One rotational spectrum was observed for the thiazole-CF4 complex. Experiments and theoretical computations confirmed that the observed structure of thiazole-CF4 is primarily formed due to N⋯CCF4 interaction with the C atom of CF4 located in the plane of the thiazole ring. The rotational transitions of thiazole-CF4 exhibit A/E torsional splitting induced by the internal rotation of the -CF3 top. The potential barrier of the -CF3 internal rotation is 0.2411(1) kJ mol-1, consistent with the calculated value (∼0.3 kJ mol-1). For the thiazole-SF6 complex, one conformer with SF6 located above the thiazole ring is detected. The observed structure of thiazole-SF6 is mainly stabilized by van der Waals interactions. The energy decomposition analysis reveals that the electrostatics and dispersion are the dominant attractive contributions to the formation of thiazole-CF4 and thiazole-SF6 dimers, whereas the weight of the dispersion term becomes more significant in the thiazole-SF6 complex compared to that of the thiazole-CF4 complex.

Ultrafast Photocontrolled Rotation in a Molecular Motor Investigated by Machine Learning-Based Nonadiabatic Dynamics Simulations

The thermal helix inversion (THI) of the overcrowded alkene-based molecular motors determines the speed of the unidirectional rotation due to the high reaction barrier in the ground state, in comparison with the ultrafast photoreaction process. Recently, a phosphine-based motor has achieved all-photochemical rotation experimentally, promising to be controlled without a thermal step. However, the mechanism of this photochemical reaction has not yet been fully revealed. The comprehensive computational studies on photoisomerization still resort to nonadiabatic molecular dynamics (NAMD) simulations based on electronic structure calculations, which remains a high computational cost for large systems such as molecular motors. Machine learning (ML) has become an accelerating tool in NAMD simulations recently, where excited-state potential energy surfaces (PESs) are constructed analytically with high accuracy, providing an efficient approach for simulations in photochemistry. Herein the reaction pathway is explored by a spin-flip time-dependent density functional theory (SF-TDDFT) approach in combination with ML-based NAMD simulations. According to our computational simulations, we notice that one of the key factors of fulfilling all-photochemical rotation in the phosphine-based motor is that the excitation energies of four isomers are similar. Additionally, a shortcut photoinduced transformation between unstable isomers replaces the THI step, which shares the conical intersection (CI) with photoisomerization. In this study, we provide a practical approach to speed up the NAMD simulations in photochemical reactions for a large system that could be extended to other complex systems.

Unraveling the Spin-State Energetics of FeN4 Complexes with Ab Initio Methods

A systematic analysis was conducted to explore the spin-state energetics of a series of 19 FeN4 complexes. The performance of a large number of multireference methods was assessed, highlighting the significant challenges associated with accurately describing the spin-state energetics of FeN4 complexes. Most multireference methods were found to be susceptible to errors originating from the reference CASSCF wavefunction, leading to an overstabilization of high-spin states. Nonetheless, a few multireference methods, namely, CASPT2/CC, DSRG-MRPT3, and LDSRG(2), demonstrated promising performance compared to the benchmark CCSD(T) method. Furthermore, our study revealed that FeN4 complexes having a quintet ground state are exceedingly rare. Accordingly, only one specific model (Fe(L2)) and one synthesized complex (Fe(OTBP)) have the quintet ground state among the studied complexes. This scarcity of quintet FeN4 complexes highlights the unique nature of these systems and raises intriguing questions regarding the factors influencing spin states, such as the size of the macrocycle cavity, the introduction of substituents, or the induction of out-of-plane deformation.

A Heavy-atom-free Molecular Motif Based on Symmetric Bird-like Structured Tetraphenylenes with Room-Temperature Phosphorescence (RTP) Afterglow over 8 s

In recent years, pure organic room-temperature phosphorescence (RTP) with highly efficient and long-persistent afterglow has drawn substantial awareness. Commonly, spin-orbit coupling can be improved by introducing heavy atoms into pure-organic molecules. However, this strategy will simultaneously increase the radiative and non-radiative transition rate, further resulting in dramatic decreases in the excited state lifetime and afterglow duration. Here in this work, a highly symmetric bird-like structure tetraphenylene (TeP), and its three symmetrical halogenated derivatives (TeP-F, TeP-Cl and TeP-Br) are synthesized, while their RTP properties and mechanisms are systematically investigated by both theoretical and experimental approaches. As the results, the rigid, highly twisted conformation of TeP restricts the non-radiative processes of RTP and gives rise to the enhancement of electron-exchange, which can contribute to the RTP radiation process. Despite the faint RTP of the bromine and chlorine-substituted ones (TeP-Br, TeP-Cl), the fluoro-substituted TeP-F exhibited a long phosphorescent lifetime up to 890 ms, corresponding to an extremely long RTP afterglow over 8 s, which could be incorporated into the best series of non-heavy-atom RTP materials reported in previous literature.

A general method for locating stationary points on the mixed-spin surface of spin-forbidden reaction with multiple spin states

Some chemical reactions proceed on multiple potential energy surfaces and are often accompanied by a change in spin multiplicity, being called spin-forbidden reactions, where the spin-orbit coupling (SOC) effects play a crucial role. In order to efficiently investigate spin-forbidden reactions with two spin states, Yang et al. [Phys. Chem. Chem. Phys. 20, 4129-4136 (2018)] proposed a two-state spin-mixing (TSSM) model, where the SOC effects between the two spin states are simulated by a geometry-independent constant. Inspired by the TSSM model, we suggest a multiple-state spin-mixing (MSSM) model in this paper for the general case with any number of spin states, and its analytic first and second derivatives have been developed for locating stationary points on the mixed-spin potential energy surface and estimating thermochemical energies. To demonstrate the performance of the MSSM model, some spin-forbidden reactions involving 5d transition elements are calculated using the density functional theory (DFT), and the results are compared with the two-component relativistic ones. It is found that MSSM DFT and two-component DFT calculations may provide very similar stationary-point information on the lowest mixed-spin/spinor energy surface, including structures, vibrational frequencies, and zero-point energies. For the reactions containing saturated 5d elements, the reaction energies by MSSM DFT and two-component DFT agree very well within 3 kcal/mol. As for the two reactions OsO+ + CH4 → OOs(CH2)+ + H2 and W + CH4 → WCH2 + H2 involving unsaturated 5d elements, MSSM DFT may also yield good reaction energies of similar accuracy but with some counterexamples. Nevertheless, the energies may be remarkably improved by a posteriori single point energy calculations using two-component DFT at the MSSM DFT optimized geometries, and the maximum error of about 1 kcal/mol is almost independent of the SOC constant used. The MSSM method as well as the developed computer program provides an effective utility for studying spin-forbidden reactions.

Pressure-induced room-temperature phosphorescence enhancement based on purely organic molecules with a folded geometry

The pressure-dependent luminescence behavior of purely organic compounds is an important topic in the field of stimulus-responsive smart materials. However, the relevant studies are mainly limited to the investigation of fluorescence properties, while room-temperature phosphorescence (RTP) of purely organic compounds has not been investigated. Here, we filled in this gap regarding pressure-dependent RTP by using a model molecule selenanthrene (SeAN) with a folded geometry. For the first time to the best of our knowledge, a unique phenomenon involving pressure-induced RTP enhancement was discovered in an SeAN crystal, and an underlying mechanism involving folding-induced spin-orbit coupling enhancement was revealed. Pressure-induced RTP enhancement was also observed in an analog of SeAN also showing a folded geometry, but in this case yielded a white-light emission that is very rare in purely organic RTP-displaying materials.

Theoretically Revealing the Response of Intermolecular Vibration Energy Transfer and Decomposition Process of the DNTF System to Electric Fields Using Two-Dimensional Infrared Spectra

The external electric field (E-field), which is an important stimulus, can change the decomposition mechanism and sensitivity of energetic materials. As a result, understanding the response of energetic materials to external E-fields is critical for their safe use. Motivated by recent experiments and theories, the two-dimensional infrared (2D IR) spectra of 3,4-bis (3-nitrofurazan-4-yl) furoxan (DNTF), which has a high energy, a low melting point, and comprehensive properties, were theoretically investigated. Cross-peaks were observed in 2D IR spectra under different E-fields, which demonstrated an intermolecular vibration energy transfer; the furazan ring vibration was found to play an important role in the analysis of vibration energy distribution and was extended over several DNTF molecules. Measurements of the non-covalent interactions, with the support of the 2D IR spectra, indicated that there were obvious non-covalent interactions among different DNTF molecules, which resulted from the conjugation of the furoxan ring and the furazan ring; the direction of the E-field also had a significant influence on the strength of the weak interactions. Furthermore, the calculation of the Laplacian bond order, which characterized the C-NO₂ bonds as trigger bonds, predicted that the E-fields could change the thermal decomposition process of DNTF while the positive E-field facilitates the breakdown of the C-NO₂ in DNTFⅣ molecules. Our work provides new insights into the relationship between the E-field and the intermolecular vibration energy transfer and decomposition mechanism of the DNTF system.

Kylin 1.0: An ab-initio density matrix renormalization group quantum chemistry program

The accurate evaluation of electron correlations is highly necessary for the proper descriptions of the electronic structures in strongly correlated molecules, ranging from bond-dissociating molecules, polyradicals, to large conjugated molecules and transition metal complexes. For this purpose, in this paper, a new ab-initio quantum chemistry program Kylin 1.0 for electron correlation calculations at various quantum many-body levels, including configuration interaction (CI), perturbation theory (PT), and density matrix renormalization group (DMRG), is presented. Furthermore, fundamental quantum chemistry methods such as Hartree-Fock self-consistent field (HF-SCF) and the complete active space SCF (CASSCF) are also implemented. The Kylin 1.0 program possesses the following features: (1) a matrix product operator (MPO) formulation-based efficient DMRG implementation for describing static electron correlation within a large active space composed of more than 100 orbitals, supporting both U 1 n × U 1 S z $$ \mathrm{U}{(1)}_{\mathrm{n}}\times \mathrm{U}{(1)}_{{\mathrm{S}}_{\mathrm{z}}} $$ and U 1 n × SU 2 S $$ \mathrm{U}{(1)}_{\mathrm{n}}\times \mathrm{SU}{(2)}_{\mathrm{S}} $$ symmetries; (2) an efficient second-order DMRG-self-consistent field (SCF) implementation; (3) an externally contracted multi-reference CI (MRCI) and Epstein-Nesbet PT with DMRG reference wave functions for including the remaining dynamic electron correlation outside the large active spaces. In this paper, we introduce the capabilities and numerical benchmark examples of the Kylin 1.0 program.

Relativistic Semistochastic Heat-Bath Configuration Interaction

In this work we present the extension of semistochastic heat-bath configuration interaction (SHCI) to work with any two-component and four-component Hamiltonian. The vertical detachment energy (VDE) of AuH₂^- and zero-field splitting (ZFS) of NpO₂²⁺ is calculated by correlating more than 100 spinors in both cases. This work demonstrates the capability of SHCI to treat problems where both relativistic effect and electron correlation are important.

A Biomimetic Emitter Inspired from Green Fluorescent Protein

The unique tripeptide structure of green fluorescent protein (GFP), a Ser-Tyr-Gly motif, generates the mature chromophore in situ to define the emission profiles of GFP. Here, we describe the rational design and discovery of a biomimetic fluorescent emitter, MBP, by mimicking the key structure of the Ser-Tyr-Gly motif. Through systematically tailoring the tripeptide, a family of four chromophores were engineered, while only MBP exhibited bright fluorescence in different fluid solvents with highly enhanced quantum yields. Distinct to previous hydrogen-bonding-induced fluorescence quenching of GFP chromophore analogues, the emission of MBP was only slightly decreased in protic solvents. Heteronuclear multiple bond correlation techniques demonstrated the fundamental mechanism for enhanced fluorescence emission owing to the synergy of the formation of the intramolecular hydrogen-bonding-ring structure and the self-restricted effect, which was further illustrated via theoretical calculations. This work puts forward an extraordinary approach toward highly emissive biomimicking fluorophores, which gives new insights into the emission mechanisms and photophysics of GFP-like chromophores.

Frozen-Density Embedding for Including Environmental Effects in the Dirac-Kohn-Sham Theory: An Implementation Based on Density Fitting and Prototyping Techniques

Frozen density embedding (FDE) represents an embedding scheme in which environmental effects are included from first-principles calculations by considering the surrounding system explicitly by means of its electron density. In the present paper, we extend the full four-component relativistic Dirac-Kohn-Sham (DKS) method, as implemented in the BERTHA code, to include environmental and confinement effects with the FDE scheme (DKS-in-DFT FDE). The implementation, based on the auxiliary density fitting techniques, has been enormously facilitated by BERTHA's python API (PyBERTHA), which facilitates the interoperability with other FDE implementations available through the PyADF framework. The accuracy and numerical stability of this new implementation, also using different auxiliary fitting basis sets, has been demonstrated on the simple NH₃-H₂O system, in comparison with a reference nonrelativistic implementation. The computational performance has been evaluated on a series of gold clusters (Au_n, with n = 2, 4, 8) embedded into an increasing number of water molecules (5, 10, 20, 40, and 80 water molecules). We found that the procedure scales approximately linearly both with the size of the frozen surrounding environment (consistent with the underpinnings of the FDE approach) and with the size of the active system (in line with the use of density fitting). Finally, we applied the code to a series of heavy (Rn) and super-heavy elements (Cn, Fl, Og) embedded in a C₆₀ cage to explore the confinement effect induced by C₆₀ on their electronic structure. We compare the results from our simulations, with respect to more-approximate models employed in the atomic physics literature. Our results indicate that the specific interactions described by FDE are able to improve upon the cruder approximations currently employed, and, thus, they provide a basis from which to generate more-realistic radial potentials for confined atoms.

Exact two-component Hamiltonians for relativistic quantum chemistry: Two-electron picture-change corrections made simple

Based on self-consistent field (SCF) atomic mean-field (amf) quantities, we present two simple yet computationally efficient and numerically accurate matrix-algebraic approaches to correct both scalar-relativistic and spin-orbit two-electron picture-change effects (PCEs) arising within an exact two-component (X2C) Hamiltonian framework. Both approaches, dubbed amfX2C and e(xtended)amfX2C, allow us to uniquely tailor PCE corrections to mean-field models, viz. Hartree-Fock or Kohn-Sham DFT, in the latter case also avoiding the need for a point-wise calculation of exchange-correlation PCE corrections. We assess the numerical performance of these PCE correction models on spinor energies of group 18 (closed-shell) and group 16 (open-shell) diatomic molecules, achieving a consistent ≈10^-5 Hartree accuracy compared to reference four-component data. Additional tests include SCF calculations of molecular properties such as absolute contact density and contact density shifts in copernicium fluoride compounds (CnF_n, n = 2,4,6), as well as equation-of-motion coupled-cluster calculations of x-ray core-ionization energies of 5d- and 6d-containing molecules, where we observe an excellent agreement with reference data. To conclude, we are confident that our (e)amfX2C PCE correction models constitute a fundamental milestone toward a universal and reliable relativistic two-component quantum-chemical approach, maintaining the accuracy of the parent four-component one at a fraction of its computational cost.

A platform for blue-luminescent carbon-centered radicals

Organic radicals, which have unique doublet spin-configuration, provide an alternative method to overcome the efficiency limitation of organic light-emitting diodes (OLEDs) based on conventional fluorescent organic molecules. Further, they have made great breakthroughs in deep-red and near-infrared OLEDs. However, it is difficult to extend their fluorescence into a short-wavelength region because of the natural narrow bandgap of the organic radicals. Herein, we significantly expand the scope of luminescent radicals by showing a new platform of carbon-centered radicals derived from N-heterocyclic carbenes that produce blue to green emissions (444–529 nm). Time-dependent density functional theory calculations and experimental investigations disclose that the fluorescence originates from the high-energy excited states to the ground state, demonstrating an anti-Kasha behavior. The present work provides an efficient and modular approach toward a library of carbon-centered radicals that feature anti-Kasha’s rule emission, rendering them as potential new emitters in the short-wavelength region.

Organic radicals, which have unique doublet spin-configuration, provide an alternative method to overcome the efficiency limitation of organic light-emitting diodes (OLEDs) but extending their fluorescence into a short-wavelength region remains challenging. Here, the authors significantly expand the scope of luminescent radicals by showing a new platform of carbon-centered radicals that produce blue to green emission.

Self-Adaptive Real-Time Time-Dependent Density Functional Theory for X-ray Absorptions

Real-time time-dependent density functional theory (RT-TDDFT) can in principle access the whole absorption spectrum of a many-electron system exposed to a narrow pulse. However, this requires an accurate and efficient propagator for the numerical integration of the time-dependent Kohn-Sham equation. While a low-order time propagator is already sufficient for the low-lying valence absorption spectra, it is no longer the case for the X-ray absorption spectra (XAS) of systems composed even only of light elements, for which the use of a high-order propagator is indispensable. It is then crucial to choose a largest possible time step and a shortest possible simulation time, so as to minimize the computational cost. To this end, we propose here a robust AutoPST approach to determine automatically (Auto) the propagator (P), step (S), and time (T) for relativistic RT-TDDFT simulations of XAS.

Tuning Catalyst-Free Photocontrolled Polymerization by Substitution: A Quantitative and Qualitative Interpretation

Catalyst-free photocontrolled reversible addition-fragmentation chain transfer (RAFT) polymerization avoids the side effects of photocatalysts but has the accompanying slow kinetics, thereby warranting more efficient photolysis and faster chain transfer. To understand the underlying mechanisms, both quantitative and qualitative interpretations are needed. Such a goal can be achieved by the iCAS (imposed automatic selection and localization of complete active spaces) approach [J. Chem. Theory Comput. 2021, 17, 4846], which maintains the same CAS and meanwhile provides localized orbitals along the whole reaction. Taking dithiobenzoate as a representative of RAFT agents, it is found here that electron-donating substitution (by methoxy) clearly outperforms both electron-standing (by methyl) and electron-withdrawing (by cyano) substitutions in facilitating photo-RAFT polymerization, by narrowing the gap between the π* and σ* orbitals, so as to facilitate the π* → σ* charge transfer dominating both the photolysis and chain transfer processes. Such findings are of general values.

SOiCI and iCISO: combining iterative configuration interaction with spin-orbit coupling in two ways

The near-exact iCIPT2 approach for strongly correlated systems of electrons, which stems from the combination of iterative configuration interaction (iCI, an exact solver of full CI) with configuration selection for static correlation and second-order perturbation theory (PT2) for dynamic correlation, is extended to the relativistic domain. In the spirit of spin separation, relativistic effects are treated in two steps: scalar relativity is treated by the infinite-order, spin-free part of the exact two-component (X2C) relativistic Hamiltonian, whereas spin-orbit coupling (SOC) is treated by the first-order, Douglas-Kroll-Hess-like SOC operator derived from the same X2C Hamiltonian. Two possible combinations of iCIPT2 with SOC are considered, i.e., SOiCI and iCISO. The former treats SOC and electron correlation on an equal footing, whereas the latter treats SOC in the spirit of state interaction, by constructing and diagonalizing an effective spin-orbit Hamiltonian matrix in a small number of correlated scalar states. Both double group and time reversal symmetries are incorporated to simplify the computation. Pilot applications reveal that SOiCI is very accurate for the spin-orbit splitting (SOS) of heavy atoms, whereas the computationally very cheap iCISO can safely be applied to the SOS of light atoms and even of systems containing heavy atoms when SOC is largely quenched by ligand fields.

Quasi-Relativistic Calculation of EPR g Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance

We present an exact two-component (X2C) ansatz for the EPR g tensor using gauge-including atomic orbitals (GIAOs) and a magnetically balanced basis set expansion. In contrast to previous X2C and four-component relativistic ansätze for the g tensor, this implementation results in a gauge-origin-invariant formalism. Furthermore, the derivatives of the relativistic decoupling matrix are incorporated to form the complete analytical derivative of the X2C Hamiltonian. To reduce the associated computational costs, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The quasi-relativistic X2C and DLU-X2C Hamiltonians accurately reproduce the results of the parent four-component relativistic theory when accounting for two-electron picture-change effects with the modified screened nuclear spin-orbit approximation in the respective one-electron integrals and integral derivatives. According to our benchmark studies, the uncontracted Dyall and segmented-contracted Karlsruhe x2c-type basis sets perform well when compared to large even-tempered basis sets. Moreover, (range-separated) hybrid density functional approximations such as LC-ωPBE and ωB97X-D are needed to match the experimental findings. The impact of the GIAOs depends on the distribution of the spin density, and their use may change the Δg shifts by 10-50% as shown for [(C₅Me₅)₂Y(μ-S)₂Mo(μ-S)₂Y(C₅Me₅)₂]^-. Routine calculations of large molecules are possible with widely available and comparably low-cost hardware as demonstrated for [Pt(C₆Cl₅)₄]^- with 3003 basis functions and three spin-(1/2) La(II) and Lu(II) compounds, for which we observe good agreement with the experimental findings.

New Light on an Old Story: Breaking Kasha's Rule in Phosphorescence Mechanism of Organic Boron Compounds and Molecule Design

In this work, the phosphorescence mechanism of (E)-3-(((4-nitrophenyl)imino)methyl)-2H-thiochroman-4-olate-BF2 compound (S-BF2) is investigated theoretically. The phosphorescence of S-BF2 has been reassigned to the second triplet state (T2) by the density matrix renormalization group (DMRG) method combined with the multi-configurational pair density functional theory (MCPDFT) to approach the limit of theoretical accuracy. The calculated radiative and non-radiative rate constants support the breakdown of Kasha's rule further. Our conclusion contradicts previous reports that phosphorescence comes from the first triplet state (T1). Based on the revised phosphorescence mechanism, we have purposefully designed some novel compounds in theory to enhance the phosphorescence efficiency from T2 by replacing substitute groups in S-BF2. Overall, both S-BF2 and newly designed high-efficiency molecules exhibit anti-Kasha T2 phosphorescence instead of the conventional T1 emission. This work provides a useful guidance for future design of high-efficiency green-emitting phosphors.

Stable copernicium hexafluoride (CnF6) with an oxidation state of VI

As the heaviest group 12 element known currently, copernicium (Cn) often presents the oxidation states of I+, II+, and rarely IV+ as in its homologue mercury. In this work we systematically studied the stability of some oxides, fluorides, and oxyfluorides of Cn by two-component relativistic calculations and found that the CnF₆ molecule with an oxidation state of VI+ has an extraordinary stability. CnF₆ may decompose into CnF₄ by conquering an energy barrier of about 34 kcal mol^-1 without markedly releasing heat. Our results indicate that CnF₆ may exist under some special conditions.

iCISCF: An Iterative Configuration Interaction-Based Multiconfigurational Self-Consistent Field Theory for Large Active Spaces

An iterative configuration interaction (iCI)-based multiconfigurational self-consistent field (SCF) theory, iCISCF, is proposed to handle systems that require large active spaces. The success of iCISCF stems from three ingredients: (1) efficient selection of individual configuration state functions spanning the active space while maintaining full spin symmetry; (2) the use of Jacobi rotation for optimization of the active orbitals in conjunction with a quasi-Newton algorithm for the core/active-virtual and core-active orbital rotations; (3) a second-order perturbative treatment of the residual space left over by the selection procedure (i.e., iCISCF(2)). Several examples that go beyond the capability of CASSCF are taken as showcases to reveal the efficacy of iCISCF and iCISCF(2), facilitated by iCAS for imposed automatic selection and localization of active orbitals.

The Static-Dynamic-Static Family of Methods for Strongly Correlated Electrons: Methodology and Benchmarking

A series of methods (SDSCI, SDSPT2, iCI, iCIPT2, iCISCF(2), iVI, and iCAS) is introduced to accurately describe strongly correlated systems of electrons. Born from the (restricted) static-dynamic-static (SDS) framework for designing many-electron wave functions, SDSCI is a minimal multireference (MR) configuration interaction (CI) approach that constructs and diagonalizes a [Formula: see text] matrix for [Formula: see text] states, regardless of the numbers of orbitals and electrons to be correlated. If the full molecular Hamiltonian H in the QHQ block (which describes couplings between functions of the first-order interaction space Q) of the SDSCI CI matrix is replaced with a zeroth-order Hamiltonian [Formula: see text] before the diagonalization is taken, we obtain SDSPT2, a CI-like second-order perturbation theory (PT2). Unlike most variants of MRPT2, SDSPT2 treats single and multiple states in the same way and is particularly advantageous in the presence of near degeneracy. On the other hand, if the SDSCI procedure is repeated until convergence, we will have iterative CI (iCI), which can converge quickly from the above to the exact solutions (full CI) even when starting with a poor guess. When further combined with the selection of important configurations followed by a PT2 treatment of dynamic correlation, iCI becomes iCIPT2, which is a near-exact theory for medium-sized systems. The microiterations of iCI for relaxing the coefficients of contracted many-electron functions can be generalized to an iterative vector interaction (iVI) approach for finding exterior or interior roots of a given matrix, in which the dimension of the search subspace is fixed by either the number of target roots or the user-specified energy window. Naturally, iCIPT2 can be employed as the active space solver of the complete active space (CAS) self-consistent field, leading to iCISCF(2), which can further be combined with iCAS for automated selection of active orbitals and assurance of the same CAS for all states and all geometries. The methods are calibrated by taking the Thiel set of benchmark systems as examples. Results for the corresponding cations, a new set of benchmark systems, are also reported.

Bridging Carotenoid-to-Bacteriochlorophyll Energy Transfer of Purple Bacteria LH2 With Temperature Variations: Insights From Conformational Changes

Photosynthesis is a key process for converting light energy into chemical energy and providing food for lives on Earth. Understanding the mechanism for the energy transfers could provide insights into regulating energy transfers in photosynthesis and designing artificial photosynthesis systems. Many efforts have been devoted to exploring the mechanism of temperature variations affecting the excitonic properties of LH2. In this study, we performed all-atom molecular dynamics (MD) simulations and quantum mechanics calculations for LH2 complex from purple bacteria along with its membrane environment under three typical temperatures: 270, 300, and 330 K. The structural analysis from validated MD simulations showed that the higher temperature impaired interactions at N-terminus of both α and β polypeptide helices and led to the dissociation of this hetero polypeptide dimer. Rhodopin-β-D-glucosides (RG1) moved centripetally with α polypeptide helices when temperature increased and enlarged their distances with bacteriochlorophylls molecules that have the absorption peak at 850 nm (B850), which resulted in reducing the coupling strengths between RG1 and B850 molecules. The present study reported a cascading mechanism for temperature regulating the energy transfers in LH2 of purple bacteria.

NAC-TDDFT: Time-Dependent Density Functional Theory for Nonadiabatic Couplings

First-order nonadiabatic coupling (NAC) matrix elements (fo-NACMEs) are the basic quantities in theoretical descriptions of electronically nonadiabatic processes that are ubiquitous in molecular physics and chemistry. Given the large size of systems of chemical interests, time-dependent density functional theory (TDDFT) is usually the first choice of methods. However, the lack of many-electron wave functions in TDDFT renders the formulation of NAC-TDDFT for fo-NACMEs conceptually difficult. Because of this, various variants of NAC-TDDFT have been proposed in the literature from different standing points, including the Hellmann-Feynman-like expression and auxiliary/pseudo-wave function (AWF)-, equation-of-motion (EOM)-, and time-dependent perturbation theory (TDPT)-based formulations. Based on critical analyses, the following conclusions are made here: (1) The Hellmann-Feynman-like expression, which is rooted in exact wave function theory, is hardly useful due to huge demand on basis sets. (2) Although most popular, the AWF variants of NAC-TDDFT are not theoretically founded and become ambiguous particularly for the fo-NACMEs between two excited states, although they do agree with the EOM and TDPT variants under the Tamm-Dancoff approximation. (3) The TDPT variant of NAC-TDDFT is theoretically most rigorous but suffers from numerical instabilities on the one hand and does not differ to a significant extent from the EOM variant on the other hand. (4) As such, the EOM variant of NAC-TDDFT for the fo-NACMEs between the ground and excited states and between two excited states is solely the right choice in practice. These formal analyses are fully supported by numerical experimentations, taking azulene as a showcase. The proper implementation of the EOM variant of NAC-TDDFT is also highlighted, showing that the fo-NACMEs between the ground and excited states and between two excited states are computationally very much the same as the analytic energy gradients of DFT and TDDFT, respectively. Possible future developments of the EOM variant of NAC-TDDFT are also highlighted. Its extensions to spin-adapted open-shell TDDFT and proper treatment of spin-orbit couplings (which are another source of force for electronically nonadiabatic processes) are particularly warranted in the near future.

Dynamic-then-Static Approach for Core Excitations of Open-Shell Molecules

Delta self-consistent-field methods are widely used in studies of electronically excited states. However, the nonaufbau determinants are generally spin-contaminated. Here, we describe a general approach for spin-coupling interactions of open-shell molecules, making use of multistate density functional theory (MSDFT). In particular, the effective exchange integrals that determine spin coupling are obtained by enforcing the multiplet degeneracy of the S+1 state in the M_S = S manifold. Consequently, they are consistent with the energy of the high-spin state that is adequately treated by Kohn-Sham density functional theory (DFT) and, thereby, free of double counting of correlation. The method was applied to core excitations of open-shell molecules and compared with those by spin-adapted time-dependent DFT. An excellent agreement with experiment was found employing the BLYP functional and aug-cc-pCVQZ basis set. Overall, MSDFT provides an effective combination of the strengths of DFT and wave function theory to achieve efficiency and accuracy.

iCAS: Imposed Automatic Selection and Localization of Complete Active Spaces

It is shown that in the spirit of "from fragments to molecule" for localizing molecular orbitals [J. Chem. Theory Comput. 2011, 7, 3643], a prechosen set of occupied/virtual valence/core atomic/fragmental orbitals can be transformed to an equivalent set of localized occupied/virtual pre-localized molecular orbitals (pre-LMO), which can then be taken as probes to select the same number of maximally matching localized occupied/virtual Hartree-Fock (HF) or restricted open-shell HF (ROHF) molecular orbitals as the initial local orbitals spanning the desired complete active space (CAS). In each cycle of the self-consistent field (SCF) calculation, the CASSCF orbitals can be localized by means of the noniterative "top-down least-change" algorithm for localizing ROHF orbitals [J. Chem. Phys. 2017, 146, 104104] such that the maximum matching between the orbitals of two adjacent iterations can readily be monitored, leading finally to converged localized CASSCF orbitals that overlap most the guess orbitals. Such an approach is to be dubbed as "imposed CASSCF" (iCASSCF or simply iCAS in short) for good reasons: (1) it has been assumed that only those electronic states that have largest projections onto the active space defined by the prechosen atomic/fragmental orbitals are to be targeted. This is certainly an imposed constraint but has wide applications in organic and transition metal chemistry where valence (or core) atomic/fragmental orbitals can readily be identified. (2) The selection of both initial and optimized local active orbitals is imposed from the very beginning by the pre-LMOs (which span the same space as the prechosen atomic/fragmental orbitals). Apart from the (imposed) automation and localization, iCAS has two additional merits: (a) the guess orbitals are guaranteed to be the same for all geometries, for the pre-LMOs do not change in character with geometry and (b) the use of localized orbitals facilitates the SCF convergence, particularly for large active spaces. Both organic molecules and transition-metal complexes are taken as showcases to reveal the efficacy of iCAS.

iOI: An Iterative Orbital Interaction Approach for Solving the Self-Consistent Field Problem

An iterative orbital interaction (iOI) approach is proposed to solve, in a bottom-up fashion, the self-consistent field problem in quantum chemistry. While it belongs grossly to the family of fragment-based quantum chemical methods, iOI is distinctive in that (1) it divides and conquers not only the energy but also the wave function and that (2) the subsystem sizes are automatically determined by successively merging neighboring small subsystems until they are just enough for converging the wave function to a given accuracy. Orthonormal occupied and virtual localized molecular orbitals are obtained in a natural manner, which can be used for all post-SCF purposes.

NMR Indirect Spin-Spin Coupling Constants in a Modern Quasi-Relativistic Density Functional Framework

A quasi-relativistic implementation of NMR indirect spin-spin coupling constants is presented. The exact two-component (X2C) Hamiltonian and its diagonal local approximation to the unitary decoupling transformation (DLU) are utilized together with the (modified) screened nuclear spin-orbit approach. In a restricted kinetic balance, the finite nucleus model is available for both the scalar and vector potentials. The implementation supports density functionals up to the fourth rung of Jacob's ladder, i.e., (range-separated) hybrid and local hybrid functionals based on a seminumerical ansatz. We assess the quality of our quasi-relativistic X2C approach by comparison with "fully" relativistic four-component results for small main-group molecules and alkynyl compounds. The mean absolute error introduced by the DLU scheme is less than 0.05 × 10¹⁹ T J^-2 of the reduced coupling constant for the small main-group molecules and 0.5 Hz for the alkynyl compounds. Thus, the error is significantly smaller than finite nucleus size effects for heavy elements. The basis set convergence and the impact of different density functional approximations are further studied. We propose a simple scheme to develop segmented-contracted relativistic all-electron basis sets for NMR spin-spin couplings. Our implementation allows us to perform calculations of extended molecules with reasonable computational effort, which is illustrated for the ¹J(¹¹⁹Sn, ³¹P) coupling constant of a low-valent tin phosphinidenide complex. The corresponding results are in good agreement with the experimental findings.

Relativistic EOM-CCSD for Core-Excited and Core-Ionized State Energies Based on the Four-Component Dirac-Coulomb(-Gaunt) Hamiltonian

We report an implementation of the core-valence separation approach to the four-component relativistic Hamiltonian-based equation-of-motion coupled-cluster with singles and doubles theory (CVS-EOM-CCSD) for the calculation of relativistic core-ionization potentials and core-excitation energies. With this implementation, which is capable of exploiting double group symmetry, we investigate the effects of the different CVS-EOM-CCSD variants and the use of different Hamiltonians based on the exact two-component (X2C) framework on the energies of different core-ionized and -excited states in halogen- (CH₃I, HX, and X^-, X = Cl-At) and xenon-containing (Xe, XeF₂) species. Our results show that the X2C molecular mean-field approach [Sikkema, J.; J. Chem. Phys. 2009, 131, 124116], based on four-component Dirac-Coulomb mean-field calculations (²DC^M), is capable of providing core excitations and ionization energies that are nearly indistinguishable from the reference four-component energies for up to and including fifth-row elements. We observe that two-electron integrals over the small-component basis sets lead to non-negligible contributions to core binding energies for the K and L edges for atoms such as iodine or astatine and that the approach based on Dirac-Coulomb-Gaunt mean-field calculations (²DCG^M) are significantly more accurate than X2C calculations for which screened two-electron spin-orbit interactions are included via atomic mean-field integrals.

Theory of Long-Lived Room-Temperature Phosphorescence in Organic Aggregates

ConspectusRoom-temperature phosphorescence (RTP) with a long afterglow from purely organic molecular aggregates has recently attracted many investigations because traditionally only inorganic and transition-metal complexes can emit phosphorescence at room temperature. Purely organic molecules can exhibit phosphorescence only at cryogenic temperatures and under inert conditions in solution. However, recently, a number of organic compounds have been found to demonstrate bright RTP upon aggregation, sometimes with a remarkable morphology dependence. We intended to rationalize such aggregation-induced organic RTP through theoretical investigation and quantum chemistry calculations by invoking intermolecular interaction effects. And we have identified the molecular descriptors for the molecular design of RTP materials.In this Account, we started with the proposition of the mechanism of intermolecular electrostatic-interaction-induced RTP at the molecular level by using molecular dynamics simulations, hybrid quantum mechanics, and molecular mechanics (QM/MM) coupled with the thermal vibration correlation function (TVCF) formalism we developed earlier. The effective intermolecular electrostatic interactions could stem from a variety of interactions in different organic RTP crystals, such as hydrogen bonding, π-halogen bonding, anion-π⁺ interaction, and d-pπ bonds and so forth. We find that these interactions can change the molecular orbital compositions involved in the lowest-lying singlet and triplet excited states that are responsible for phosphorescence, either through facilitating intersystem crossing from the excited-state singlet to the triplet and/or suppressing the nonradiative decay process from the lowest triplet to the ground state. This underlying RTP mechanism is believed to be very helpful in systematically and comprehensively understanding the aggregation/crystal-induced persistent organic RTP, which has been applied to explain a number of experiments.We then propose the molecular descriptors to characterize the phosphorescence efficiency and lifetime, respectively, derived from fundamental photophysical processes and requirements to obey the El-Sayed rule and generate phosphorescence. For a prototypical RTP system consisting of a carbonyl group and π-conjugated segments, the excited states can be regarded as an admixture of n → π* (with portion α) and π → π* (with portion β). The intersystem crossing (ISC) rate of S₁ → T_n is mostly governed by the modification of the product of α and β, and the nonradiative rate of T₁ → S₀ is determined by the β value of T₁. Thus, we employ γ = α × β and β to describe the phosphorescence efficiency and lifetime, respectively, which have been successfully applied in the molecular design of efficient and long-lived RTP systems in experiments. The molecular descriptors outlined in this Account, which are easily obtained from simple quantum chemistry calculations, are expected to play important roles in the machine-learning-based molecular screening in the future.