Spin-flip methods in quantum chemistry

Ultrafast Photoinduced Dynamics in 1,3-Cyclohexadiene: A Comparison of Trajectory Surface Hopping Schemes†

Photoinduced nonadiabatic processes play a crucial role in a wide range of disciplines, from fundamental steps in biology to modern applications in advanced materials science. A theoretical understanding of these processes is highly desirable, and trajectory surface hopping (TSH) has proven to be a well-suited framework for a wide range of systems. In this work, we present a comprehensive comparison between two TSH algorithms, the conventional Tully's fewest switches surface hopping (FSSH) scheme and the Landau-Zener surface hopping (LZSH), to study the photoinduced ring-opening of 1,3-cyclohexadiene (CHD) to 1,3,5-hexatriene at the spin-flip time-dependent density functional theory (SF-TDDFT) level of theory. Additionally, we compare our results with a literature study at the extended multistate complete active space second-order perturbation theory method (XMS-CASPT2) level of theory. Our results show that the average population and lifetimes estimated with LZSH using SF-TDDFT are closer to the literature (using multireference methods) than those estimated with FSSH using SF-TDDFT. The latter speaks in favor of applying LZSH in combination with the SF-TDDFT method to study larger and more complex systems such as molecular photoswitches where the CHD molecule acts as a backbone. In addition, we present an implementation of Tully's FSSH algorithm as an extension to the PySurf software package.

The photochemical trans → cis and thermal cis → trans isomerization pathways of azobenzo-13-crown ether: A computational study on a strained cyclic azobenzene system

The isomerization of azobenzo-13-crown ether can be expected to be hindered due to the polyoxyethylene linkage connecting the 2,2'-positions of azobenzene. The mixed reference spin-flip time-dependent density functional theory results reveal that the planar and rotational minima of the first photo-excited singlet state (S1) of the trans-isomer pass through a barrier (2.5-5.0 kcal/mol) as it goes toward the torsional conical intersection (S0/S1) geometry ( Collapse

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Affiliation(s)

Dilawar Singh Sisodiya Department of Chemistry, Birla Institute of Technology and Science (BITS), Pilani, K. K. Birla Goa Campus, Zuarinagar, India
Anjan Chattopadhyay Department of Chemistry, Birla Institute of Technology and Science (BITS), Pilani, K. K. Birla Goa Campus, Zuarinagar, India

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A Merger of the Spin-Flip ORMAS Approach and the MC-PDFT Method

The SF-ORMAS-PDFT (spin-flip occupation restricted multiple active space-pair density functional theory) approach combines the SF-ORMAS-CI method with the MC-PDFT method to treat both static and dynamic correlation in multiconfigurational systems. The static correlation description is generated via the spin-flip approach, which uses a high-spin single reference determinant to treat excited states with multiconfigurational characters. The on-top pair density functional theory uses a translation scheme applied to GGA density functionals. The SF-ORMAS-PDFT scheme has also been combined with virtual valence orbitals (VVO), a well-defined subspace of the virtual molecular orbitals, giving rise to significant speedups relative to the use of the full virtual space. The accuracy of the SF-ORMAS-PDFT method is tested by calculating 65 vertical excitation energies of 12 small- and medium-sized organic molecules. The SF-ORMAS-PDFT vertical excitation energies calculated with VVOs are comparable to those calculated with the full virtual space. The SF-ORMAS-PDFT/6-31G(d) level of theory predicts the rotational barrier of ethylene to be 65.5 and 65.9 kcal/mol, with full virtual space and VVOs, respectively. These predicted barrier heights compare well with the experimental value of 65 kcal/mol.

Coupled-cluster treatment of complex open-shell systems: the case of single-molecule magnets

We investigate the reliability of two cost-effective coupled-cluster methods for computing spin-state energetics and spin-related properties of a set of open-shell transition-metal complexes. Specifically, we employ the second-order approximate coupled-cluster singles and doubles (CC2) method and projection-based embedding that combines equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) with density functional theory (DFT). The performance of CC2 and EOM-CCSD-in-DFT is assessed against EOM-CCSD. The chosen test set includes two hexaaqua transition-metal complexes containing Fe(II) and Fe(III), and a large Co(II)-based single-molecule magnet with a non-aufbau ground state. We find that CC2 describes the excited states more accurately, reproducing EOM-CCSD excitation energies within 0.05 eV. However, EOM-CCSD-in-DFT excels in describing transition orbital angular momenta and spin-orbit couplings. Moreover, for the Co(II) molecular magnet, using EOM-CCSD-in-DFT eigenstates and spin-orbit couplings, we compute spin-reversal energy barriers, as well as temperature-dependent and field-dependent magnetizations and magnetic susceptibilities that closely match experimental values within spectroscopic accuracy. These results underscore the efficiency of CC2 in computing state energies of multi-configurational, open-shell systems and highlight the utility of the more cost-efficient EOM-CCSD-in-DFT for computing spin-orbit couplings and magnetic properties of complex and large molecular magnets.

Dual Optical Cycling Centers Mounted on an Organic Scaffold: New Insights from Quantum Chemistry Calculations and Symmetry Analysis

Molecules cooled to ultracold temperatures are desirable for applications in fundamental physics and quantum information science. However, cooling polyatomic molecules with more than six atoms has not yet been achieved. Building on the idea of an optical cycling center (OCC), a moiety supporting a set of localized and isolated electronic states within a polyatomic molecule, molecules with two OCCs (bi-OCCs) may afford better cooling efficiency by doubling the photon scattering rate. By using quantum chemistry calculations, we assess the extent of the coupling of the two OCCs with each other and the molecular scaffold. We show that promising coolable bi-OCC molecules can be proposed by following chemical design principles.

Benchmarking Ionization Potentials from pCCD Tailored Coupled Cluster Models

The ionization potential (IP) is an important parameter providing essential insights into the reactivity of chemical systems. IPs are also crucial for designing, optimizing, and understanding the functionality of modern technological devices. We recently showed that limiting the CC ansatz to the seniority-zero sector proves insufficient in predicting reliable and accurate ionization potentials within an IP equation-of-motion coupled-cluster formalism. Specifically, the absence of dynamical correlation in the seniority-zero pair coupled cluster doubles (pCCD) model led to unacceptably significant errors of approximately 1.5 eV. In this work, we aim to explore the impact of dynamical correlation and the choice of the molecular orbital basis (canonical vs localized) in CC-type methods targeting 230 ionized states in 70 molecules, comprising small organic molecules, medium-sized organic acceptors, and nucleobases. We focus on pCCD-based approaches as well as the conventional IP-EOM-CCD and IP-EOM-CCSD. Their performance is compared to the CCSD(T) or CCSDT equivalent and experimental reference data. Our statistical analysis reveals that all investigated frozen-pair coupled cluster methods exhibit similar performance, with differences in errors typically within chemical accuracy (1 kcal/mol or 0.05 eV). Notably, the effect of the molecular orbital basis, such as canonical Hartree-Fock or natural pCCD-optimized orbitals, on the IPs is marginal if dynamical correlation is accounted for. Our study suggests that triple excitations are crucial in achieving chemical accuracy in IPs when modeling electron detachment processes with pCCD-based methods.

Reverse intersystem crossing mechanisms in doped triangulenes

Thermally activated delayed fluorescence (TADF) has emerged as one of the most promising strategies in the quest for organic light emitting diodes with optimal performance. This computational study dissects the mechanistic intricacies of the central photophysical step, reverse intersystem crossing (rISC) in N and B doped triangulenes as potential multi-resonance TADF compounds. Optimal molecular patterns conducive to efficient rISC, encompassing dopant atom size, number, and distribution, are identified. Additionally, we assess various electronic structure methods for characterizing TADF-relevant molecular systems. The findings identify the distinct role of the direct and mediated mechanisms in rISC, and provide insights into the design of advanced TADF chromophores for next-generation OLED technology.

A Novel Abiotic Pathway for Phosphine Synthesis over Acidic Dust in Venus' Atmosphere

Recent ground-based observations of Venus have detected a single spectral feature consistent with phosphine (PH3) in the middle atmosphere, a gas which has been suggested as a biosignature on rocky planets. The presence of PH3 in the oxidized atmosphere of Venus has not yet been explained by any abiotic process. However, state-of-the-art experimental and theoretical research published in previous works demonstrated a photochemical origin of another potential biosignature-the hydride methane-from carbon dioxide over acidic mineral surfaces on Mars. The production of methane includes formation of the HC · O radical. Our density functional theory (DFT) calculations predict an energetically plausible reaction network leading to PH3, involving either HC · O or H· radicals. We suggest that, similarly to the photochemical formation of methane over acidic minerals already discussed for Mars, the origin of PH3 in Venus' atmosphere could be explained by radical chemistry starting with the reaction of ·PO with HC·O, the latter being produced by reduction of CO2 over acidic dust in upper atmospheric layers of Venus by ultraviolet radiation. HPO, H2P·O, and H3P·OH have been identified as key intermediate species in our model pathway for phosphine synthesis.

Two determinant distinguishable cluster

A two reference determinant version of the distinguishable cluster with singles and doubles (DCSD) has been developed. We have implemented the two determinant distinguishable cluster (2D-DCSD) and the corresponding traditional 2D-CCSD method in a new open-source package written in Julia called ElemCo.jl. The methods were benchmarked on singlet and triplet excited states of valence and Rydberg character, as well as for singlet-triplet gaps of diradicals. It is demonstrated that the distinguishable cluster approximation improves the accuracy of 2D-CCSD.

Dissociation of Hydrofluorocarbon Molecules after Electron Impact in Plasma

The process of dissociation for two hydrofluorocarbon molecules in low triplet states excited by electron impact in plasma is investigated by ab initio molecular dynamics (AIMD). The interest in the dissociation of hydrofluorocarbons in plasma is motivated by their role in plasma etching in microelectronic technologies. Dissociation of triplet states is very fast, and the reaction products can be predicted. In this work, it was found that higher triplet states relax into the lowest triplet state within a few femtoseconds due to nonadiabatic dynamics, such that the simplest ab initio MD on the lowest triplet state seems to give a reasonable estimate of the reaction channels branching ratios. We provide evidence of the existence of simple rules for the dissociation of hydrofluorocarbon molecules in triplet states. For molecules with a double bond, the bonds adjacent to the double bond dissociate faster than the other bonds.

Ensemble Ground State of a Many-Electron System with Fractional Electron Number and Spin: Piecewise-Linearity and Flat-Plane Condition Generalized

Description of many-electron systems with a fractional electron number (Ntot) and fractional spin (Mtot) is of great importance in physical chemistry, solid-state physics, and materials science. In this Letter, we provide an exact description of the zero-temperature ensemble ground state of a general, finite, many-electron system and characterize the dependence of the energy and the spin-densities on both Ntot and Mtot, when the total spin is at its equilibrium value. We generalize the piecewise-linearity principle and the flat-plane condition and determine which pure states contribute to the ground-state ensemble. We find a new derivative discontinuity, which manifests for spin variation at a constant Ntot, as a jump in the Kohn-Sham potential. We identify a previously unknown degeneracy of the ground state, such that the total energy and density are unique, but the spin-densities are not. Our findings serve as a basis for development of advanced approximations in density functional theory and other many-electron methods.

Reconciling TD-DFT and CASPT2 electronic structure methods for describing the photophysics of DNA

Time-dependent density functional theory (TD-DFT) and multiconfigurational second-order perturbation theory (CASPT2) are two of the most widely used methods to investigate photoinduced dynamics in DNA-based systems. These methods sometimes give diverse dynamics in physiological environments usually modeled by quantum mechanics/molecular mechanics (QM/MM) protocol. In this work, we demonstrate for the uridine test case that the underlying topology of the potential energy surfaces of electronic states involved in photoinduced relaxation is similar in both electronic structure methods. This is verified by analyzing surface-hopping dynamics performed at the QM/MM level on aqueous solvated uridine at TD-DFT and CASPT2 levels. By constraining the dynamics to remain onπ π * state we observe similar fluctuations in energy and relaxation lifetimes in surface-hopping dynamics in both TD-DFT and experimentally validated CASPT2 methods. This finding calls for a systematic comparison of the ES potential energy surfaces of DNA and RNA nucleosides at the single- and multi-reference levels of theory. The anomalous long excited state lifetime at the TD-DFT level is explained byn π * trapping due to the tendency of TD-DFT in QM/MM schemes with electrostatic embedding to underestimate the energy of theπ π * state leading to a wrongπ π * / n π * energetic order. A study of the FC energetics suggests that improving the description of the surrounding environment through polarizable embedding or by the expansion of QM layer with hydrogen-bonded waters helps restore the correct state order at TD-DFT level. Thus by combining TDDFT with an accurate modeling of the environment, TD-DFT is positioned as the standout protocol to model photoinduced dynamics in DNA-based aggregates and multimers.

Excited State Properties of Point Defects in Semiconductors and Insulators Investigated with Time-Dependent Density Functional Theory

We present a formulation of spin-conserving and spin-flip hybrid time-dependent density functional theory (TDDFT), including the calculation of analytical forces, which allows for efficient calculations of excited state properties of solid-state systems with hundreds to thousands of atoms. We discuss an implementation on both GPU- and CPU-based architectures along with several acceleration techniques. We then apply our formulation to the study of several point defects in semiconductors and insulators, specifically the negatively charged nitrogen-vacancy and neutral silicon-vacancy centers in diamond, the neutral divacancy center in 4H silicon carbide, and the neutral oxygen-vacancy center in magnesium oxide. Our results highlight the importance of taking into account structural relaxations in excited states in order to interpret and predict optical absorption and emission mechanisms in spin defects.

A Nonorthogonal Configuration Interaction Approach to Singlet Fission in Perylenediimide Compounds

Perylenediimide molecules constitute a family of chromophores that undergo singlet fission, a process in which an excited singlet state converts into lower energy triplets on two neighboring molecules, potentially increasing the efficiency of organic solar cells. Here, the nonorthogonal configuration interaction method is applied to study the effect of the different crystal packing of various perylenediimide derivatives on the relative energies of the singlet and triplet states, the intermolecular electronic couplings, and the relative rates for singlet fission. The analysis of the wave functions and electronic couplings reveals that charge transfer states play an important role in the singlet fission mechanism. Dimer conformations where the PDI molecules are at large displacements along the long axis and short on the short axis are posed as the most favorable for singlet fission. The role of the substituent at the imide group has been inspected concluding that, although it has no effect in the energies, for some conformations it significantly influences the electronic couplings, and therefore, replacing this substituent with hydrogen may introduce artifacts in the computational modeling of the PDI molecules.

Tailoring light-induced charge transfer and intersystem crossing in FeCO using time-dependent spin-orbit configuration interaction

Real-time (RT) electronic structure methods provide a natural framework for describing light-matter interactions in arbitrary time-dependent electromagnetic fields (EMF). Optically induced excited state transitions are of particular interest, which require tuned EMF to drive population transfer to and from the specific state(s) of interest. Intersystem crossing, or spin-flip, may be driven through shaped EMF or laser pulses. These transitions can result in long-lived "spin-trapped" excited states, which are especially useful for materials requiring charge separation or protracted excited state lifetimes. Time-dependent configuration interaction (TDCI) is unique among RT methods in that it may be implemented in a basis of eigenstates, allowing for rapid propagation of the time-dependent Schrödinger equation. The recent spin-orbit TDCI (TD-SOCI) enables a real-time description of spin-flip dynamics in an arbitrary EMF and, therefore, provides an ideal framework for rational pulse design. The present study explores the mechanism of multiple spin-flip pathways for a model transition metal complex, FeCO, using shaped pulses designed to drive controlled intersystem crossing and charge transfer. These results show that extremely tunable excited state dynamics can be achieved by considering the dipole transition matrix elements between the states of interest.

Machine Learning-Based Screening for Potential Singlet Fission Chromophores: The Challenge of Imbalanced Data Sets

Excitation with one photon of a singlet fission (SF) material generates two triplet excitons, thus doubling the solar cell efficiency. Therefore, the SF molecules are regarded as new generation organic photovoltaics, but it is hard to identify them. Recently, it was demonstrated that molecules of low-to-intermediate diradical character (DRC) are potential SF chromophores. This prompts a low-cost strategy for finding new SF candidates by computational high-throughput workflows. We propose a machine learning aided screening for SF entrants based on their DRC. Our data set comprises 469 784 compounds extracted from the PubChem database, structurally rich but inherently imbalanced regarding DRC values. We developed well performing classification models that can retrieve potential SF chromophores. The latter (∼4%) were analyzed by K-means clustering to reveal qualitative structure-property relationships and to extract strategies for molecular design. The developed screening procedure and data set can be easily adapted for applications of diradicaloids in photonics and spintronics.

Doubly Tuned Exchange-Correlation Functionals for Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory

It is demonstrated that significant accuracy improvements in MRSF-TDDFT can be achieved by introducing two different exchange-correlation (XC) functionals for the reference Kohn-Sham DFT and the response part of the calculations, respectively. Accordingly, two new XC functionals of doubly tuned Coulomb attenuated method-vertical excitation energy (DTCAM-VEE) and DTCAM-AEE were developed on the basis of the "adaptive exact exchange (AEE)" concept in the framework of the Coulomb-attenuating XC functionals. The values by DTCAM-VEE are in excellent agreement with those of Thiel's set [mean absolute errors (MAEs) and the interquartile range (IQR) values of 0.218 and 0.327 eV, respectively]. On the other hand, DTCAM-AEE faithfully reproduced the qualitative aspects of conical intersections (CIs) of trans-butadiene and thymine and the nonadiabatic molecular dynamics (NAMD) simulations on thymine. The latter functional also remarkably exhibited the exact 1/R asymptotic behavior of the charge-transfer state of an ethylene-tetrafluoroethylene dimer and the accurate potential energy surfaces (PESs) along the two torsional angles of retinal protonated Schiff base model with six double bonds (rPSB6). Overall, DTCAM-AEE generally performs well, as its MAE (0.237) and IQR (0.41 eV) are much improved as compared to BH&HLYP. The current idea can also be applied to other XC functionals as well as other variants of linear response theories, opening a new way of developing XC functionals.

A Perspective on Sustainable Computational Chemistry Software Development and Integration

The power of quantum chemistry to predict the ground and excited state properties of complex chemical systems has driven the development of computational quantum chemistry software, integrating advances in theory, applied mathematics, and computer science. The emergence of new computational paradigms associated with exascale technologies also poses significant challenges that require a flexible forward strategy to take full advantage of existing and forthcoming computational resources. In this context, the sustainability and interoperability of computational chemistry software development are among the most pressing issues. In this perspective, we discuss software infrastructure needs and investments with an eye to fully utilize exascale resources and provide unique computational tools for next-generation science problems and scientific discoveries.

State-Interaction Approach for Evaluating g-Tensors within EOM-CC and RAS-CI Frameworks: Theory and Benchmarks

Among various techniques designed for studying open-shell species, electron paramagnetic resonance (EPR) spectroscopy plays an important role. The key quantity measured by EPR is the g-tensor, describing the coupling between an external magnetic field and molecular electronic spin. One theoretical framework for quantum chemistry calculations of g-tensors is based on response theory, which involves substantial developments that are specific to the underlying electronic structure models. A simplified and easier-to-implement approach is based on the state-interaction scheme, in which perturbation is included by considering a small number of states. We describe and benchmark the state-interaction approach using equation-of-motion coupled-cluster and restricted-active-space configuration interaction wave functions. The analysis confirms that this approach can deliver accurate results and highlights caveats of applying it, such as a choice of the reference state, convergence with respect to the number of states used in calculations, etc. The analysis also contributes toward a better understanding of challenges in calculations of higher-order properties using approximate wave functions.

Correlation vs. exchange competition drives the singlet-triplet excited-state inversion in non-alternant hydrocarbons

In this work, we focus on the understanding of the driving force behind the S1-T1 excited-state energy inversion (which would thus violate Hund's rule, making the S1 state lower in energy than the T1 state) of two non-benzenoid non-alternant hydrocarbons, composed of odd-membered rings. The molecules considered here have identical chemical composition but different atomic configuration in space. The delicate interplay between structural and electronic factors that might induce inversion and its energy extension, only by a few meV, is systematically investigated here by state-of-the-art calculations. Qualitative and quantitative accurate predictions are obtained employing post-HF methods, thanks to the balanced and careful inclusion of electron correlation effects. The obtained results might guide and rationalize new searches for molecules violating Hund's rule, concomitantly demonstrating the importance of key contributions from the theoretical method of choice.

Mechanistic Basis for Red Light Switching of Azonium Ions

Azonium ions formed by the protonation of tetra-ortho-methoxy-substituted aminoazobenzenes photoisomerize with red light under physiological conditions. This property makes them attractive as molecular tools for the photocontrol of physiological processes, for example, in photopharmacology. However, a mechanistic understanding of the photoisomerization process and subsequent thermal relaxation is necessary for the rational application of these compounds as well as for guiding the design of derivatives with improved properties. Using a combination of sub-ps/ns transient absorption measurements and quantum chemical calculations, we show that the absorption of a photon by the protonated E-H+ form of the photoswitch causes rapid (ps) isomerization to the protonated Z-H+ form, which can also absorb red light. Proton transfer to solvent then occurs on a microsecond time scale, leading to an equilibrium between Z and Z-H+ species, the position of which depends on the solution pH. Whereas thermal isomerization of the neutral Z form to the neutral E form is slow (∼0.001 s-1), thermal isomerization of Z-H+ to E-H+ is rapid (∼100 s-1), so the solution pH also governs the rate at which E/E-H+ concentrations are restored after a light pulse. This analysis provides the first complete mechanistic picture that explains the observed intricate photoswitching behavior of azonium ions at a range of pH values. It further suggests features of azonium ions that could be targeted for improvement to enhance the applicability of these compounds for the photocontrol of biomolecules.

Spin-Flip Unitary Coupled Cluster Method: Toward Accurate Description of Strong Electron Correlation on Quantum Computers

Quantum computers have emerged as a promising platform to simulate strong electron correlation that is crucial to catalysis and photochemistry. However, owing to the choice of a trial wave function employed in the variational quantum eigensolver (VQE) algorithm, accurate simulation is restricted to certain classes of correlated phenomena. Herein, we combine the spin-flip (SF) formalism with the unitary coupled cluster with singles and doubles (UCCSD) method via the quantum equation-of-motion (qEOM) approach to allow for an efficient simulation of a large family of strongly correlated problems. We show that the developed qEOM-SF-UCCSD/VQE method outperforms its UCCSD/VQE counterpart for simulation of the cis-trans isomerization of ethylene, and the automerization of cyclobutadiene and the predicted qEOM-SF-UCCSD/VQE barrier heights are in a good agreement with the experimentally determined values. The developments presented herein will further stimulate the investigation of this approach for simulations of other types of correlated/entangled phenomena on quantum computers.

Natural orbitals and two-particle correlators as tools for the analysis of effective exchange couplings in solids

Using generalizations of spin-averaged natural orbitals and two-particle charge correlators for solids, we investigate the electronic structure of antiferromagnetic transition-metal oxides with a fully self-consistent, imaginary-time GW method. Our findings disagree with the Goodenough-Kanamori (GK) rules that are commonly used for the qualitative interpretation of such solids. First, we found a strong dependence of the natural orbital occupancies on momenta, contradicting GK assumptions. Second, along the momentum path, the character of natural orbitals changes. In particular, the contributions of oxygen 2s orbitals are important, which has not been considered in the GK rules. To analyze the influence of the electronic correlation on the values of effective exchange coupling constants, we use both natural orbitals and two-particle correlators and show that electronic screening modulates the degree of superexchange by stabilizing the charge-transfer contributions, which greatly affects these coupling constants. Finally, we give a set of predictions and recommendations regarding the use of density functional, Green's function, and wave-function methods for evaluating effective magnetic couplings in molecules and solids.

Organic compounds for solid state luminescence enhancement/aggregation induced emission: a theoretical perspective

Organic luminophores displaying one or more forms of luminescence enhancement in solid state are extremely promising for the development and performance optimization of functional materials essential to many modern key technologies. Yet, the effort to harness their huge potential is riddled with hurdles that ultimately come down to a limited understanding of the interactions that result in the diverse molecular environments responsible for the macroscopic response. In this context, the benefits of a theoretical framework able to provide mechanistic explanations to observations, supported by quantitative predictions of the phenomenon, are rather apparent. In this perspective, we review some of the established facts and recent developments about the current theoretical understanding of solid-state luminescence enhancement (SLE) with an accent on aggregation-induced emission (AIE). A description of the macroscopic phenomenon and the questions it raises is accompanied by a discussion of the approaches and quantum chemistry methods that are more apt to model these molecular systems with the inclusion of an accurate yet efficient simulation of the local environment. A sketch of a general framework, building from the current available knowledge, is then attempted via the analysis of a few varied SLE/AIE molecular systems from literature. A number of fundamental elements are identified offering the basis for outlining design rules for molecular architectures exhibiting SLE that involve specific structural features with the double role of modulating the optical response of the luminophores and defining the environment they experience in solid state.

Measuring Electron Correlation: The Impact of Symmetry and Orbital Transformations

In this perspective, the various measures of electron correlation used in wave function theory, density functional theory and quantum information theory are briefly reviewed. We then focus on a more traditional metric based on dominant weights in the full configuration solution and discuss its behavior with respect to the choice of the N-electron and the one-electron basis. The impact of symmetry is discussed, and we emphasize that the distinction among determinants, configuration state functions and configurations as reference functions is useful because the latter incorporate spin-coupling into the reference and should thus reduce the complexity of the wave function expansion. The corresponding notions of single determinant, single spin-coupling and single configuration wave functions are discussed and the effect of orbital rotations on the multireference character is reviewed by analyzing a simple model system. In molecular systems, the extent of correlation effects should be limited by finite system size and in most cases the appropriate choices of one-electron and N-electron bases should be able to incorporate these into a low-complexity reference function, often a single configurational one.

Spin-Orbit Couplings of Open-Shell Systems with Restricted Active Space Configuration Interaction

In this work we perform electronic structure calculations to unravel the origin of spin-orbit couplings (SOCs) in open-shell molecules. For that, we select systems displaying di or polyradical character, e.g., trimethylene, and analyze the changes in the magnitude of SOC constants along molecular distortions of ethylene and in the presence of intermolecular interactions between open and closed-shell moieties in the O₂-C₂H₄ system. Calculations were performed by using nonrelativistic wave functions obtained with the restricted active space configuration interaction (RASCI) method, in conjunction with a recent implementation for the calculation of SOC based on the spin-orbit mean field approximation. Our results demonstrate the suitability of RASCI in the calculation of SOCs of open-shell systems, while providing a deep understanding of the relationship between couplings and the nature of the electronic states. Moreover, we introduce a new definition of the SOC constant for the study of molecular aggregates.

Theory, implementation, and disappointing results for two-photon absorption cross sections within the doubly electron-attached equation-of-motion coupled-cluster framework

The equation-of-motion coupled-cluster singles and doubles method with double electron attachment (EOM-DEA-CCSD) is capable of computing reliable energies, wave functions, and first-order properties of excited states in diradicals and polyenes that have a significant doubly excited character with respect to the ground state, without the need for including the computationally expensive triple excitations. Here, we extend the capabilities of the EOM-DEA-CCSD method to the calculations of a multiphoton property, two-photon absorption (2PA) cross sections. Closed-form expressions for the 2PA cross sections are derived within the expectation-value approach using response wave functions. We analyze the performance of this new implementation by comparing the EOM-DEA-CCSD energies and 2PA cross sections with those computed using the CC3 quadratic response theory approach. As benchmark systems, we consider transitions to the states with doubly excited character in twisted ethene and in polyenes, for which EOM-EE-CCSD (EOM-CCSD for excitation energies) performs poorly. The EOM-DEA-CCSD 2PA cross sections are comparable with the CC3 results for twisted ethene; however, the discrepancies between the two methods are large for hexatriene. The observed trends are explained by configurational analysis of the 2PA channels.

Intermolecular-Type Conical Intersections in Benzene Dimer

The equilibrium and conical intersection geometries of the benzene dimer were computed in the framework of the conventional, linear-response time-dependent and spin-flipped time-dependent density functional theories (known as DFT, TDDFT and SF-TDDFT) as well as using the multiconfigurational complete active space self-consistent field (CASSCF) method considering the minimally augmented def2-TZVPP and the 6-31G(d,p) basis sets. It was found that the stacking distance between the benzene monomers decreases by about 0.5 Å in the first electronic excited state, due to the stronger intermolecular interaction energy, bringing the two monomers closer together. Intermolecular-type conical intersection (CI) geometries can be formed between the two benzene molecules, when (i) both monomer rings show planar deformation and (ii) weaker (approximately 1.6-1.8 Å long) C-C bonds are formed between the two monomers, with parallel and antiparallel orientation with respect to the monomer. These intermolecular-type CIs look energetically more favorable than dimeric CIs containing only one deformed monomer. The validity of the dimer-type CI geometries obtained by SF-TDDFT was confirmed by the CASSCF method. The nudged elastic band method used for finding the optimal relaxation path has confirmed both the accessibility of these intermolecular-type CIs and the possibility of the radiationless deactivation of the electronic excited states through these CI geometries. Although not as energetically favorable as the previous two CI geometries, there are other CI geometries characterized by the relative rotation of monomers at different angles around a vertical C-C axis.

Magnetic exchange interactions in binuclear and tetranuclear iron(III) complexes described by spin-flip DFT and Heisenberg effective Hamiltonians

Low-energy spectra of single-molecule magnets (SMMs) are often described by Heisenberg Hamiltonians. Within this formalism, exchange interactions between magnetic centers determine the ground-state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants (J) for a set of iron (III) binuclear and tetranuclear complexes from all-electron calculations using non-collinear spin-flip time-dependent density functional theory (NC-SF-TDDFT). For 12 binuclear complexes with J-values ranging from -6 to -132 cm^-1 , our benchmark calculations using the short-range hybrid ωPBEh functional and 6-31G(d,p) basis set agree well with the experimentally derived values (mean absolute error of 4.7 cm^-1 ). For the tetranuclear SMMs, the computed J constants are within 6 cm^-1 from the experimentally derived values. We explore the range of applicability of the Heisenberg model by analyzing bonding patterns in these Fe(III) complexes using natural orbitals (NO), their occupations, and the number of effectively unpaired electrons. The results illustrate the efficiency of the spin-flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Conical Intersection in Chemiluminescence of Cyclic Peroxides

Chemiluminescence (CL) utilizing chemiexcitation for energy transformation is one of the most highly sensitive and useful analytical techniques. The chemiexcitation is a chemical process of a ground-state reactant producing an excited-state product, in which a nonadiabatic event is facilitated by conical intersections (CIs), the specific molecular geometries where electronic states are degenerated. Cyclic peroxides, especially 1,2-dioxetane/dioxetanone derivatives, are the iconic chemiluminescent substances. In this Perspective, we concentrated on the CIs in the CL of cyclic peroxides. We first present a computational overview on the role of CIs between the ground (S₀) state and the lowest singlet excited (S₁) state in the thermolysis of cyclic peroxides. Subsequently, we discuss the role of the S₀/S₁ CI in the CL efficiency and point out misunderstandings in some theoretical studies on the singlet chemiexcitations of cyclic peroxides. Finally, we address the challenges and future prospects in theoretically calculating S₀/S₁ CIs and simulating the dynamics and chemiexcitation efficiency in the CL of cyclic peroxides.

Using diketopyrrolopyrroles to stabilize double excitation and control internal conversion

Diketopyrrolopyrrole (DPP) is a pivotal functional group to tune the physicochemical properties of novel organic photoelectronic materials. Among multiple uses, DPP-thiophene derivatives forming a dimer through a vinyl linker were recently shown to quench the fluorescence observed in their isolated monomers. Here, we explain this fluorescence quenching using computational chemistry. The DPP-thiophene dimer has a low-lying doubly excited state that is not energetically accessible for the monomer. This state delays the fluorescence allowing internal conversion to occur first. We characterize the doubly excited state wavefunction by systematically changing the derivatives to tune the π-scaffold size and the acceptor and donor characters. The origin of this state's stabilization is related to the increase in the π-system and not to the charge-transfer features. This analysis delivers core conceptual information on the electronic properties of organic chromophores arranged symmetrically around a vinyl linker, opening new ways to control the balance between luminescence and internal conversion.

Geminal-based electronic structure methods in quantum chemistry. Toward a geminal model chemistry

In this review, we discuss the recent progress in developing geminal-based theories for challenging problems in quantum chemistry. Specifically, we focus on the antisymmetrized geminal power, generalized valence bond, antisymmetrized product of strongly orthogonal geminals, singlet-type orthogonal geminals, the antisymmetric product of 1-reference orbital geminal, also known as the pair coupled cluster doubles ansatz, and geminals constructed from Richardson-Gaudin states. Furthermore, we review various corrections to account for the missing dynamical correlation effects in geminal models and possible extensions to target electronically excited states and open-shell species. Finally, we discuss some numerical examples and present-day challenges for geminal-based models, including a quantitative and qualitative analysis of wave functions, and software availability.

Efficient Implementation of Block-Correlated Coupled Cluster Theory Based on the Generalized Valence Bond Reference for Strongly Correlated Systems

An optimized implementation of block-correlated coupled cluster theory based on the generalized valence bond wave function (GVB-BCCC) for the singlet ground state of strongly correlated systems is presented. The GVB-BCCC method with two-pair correlation (GVB-BCCC2b) or up to three-pair correlation (GVB-BCCC3b) will be the focus of this work. Three major techniques have been adopted to dramatically accelerate GVB-BCCC2b and GVB-BCCC3b calculations. First, the GVB-BCCC2b and GVB-BCCC3b codes are noticeably optimized by removing redundant calculations. Second, independent amplitudes are identified by constraining excited configurations to be pure singlet states and only independent amplitudes need to be solved. Third, an incremental updating scheme for the amplitudes in solving the GVB-BCCC equations is adopted. With these techniques, accurate GVB-BCCC3b calculations are now accessible for systems with relatively large active spaces (50 electrons in 50 orbitals) and GVB-BCCC2b calculations are affordable for systems with much larger active spaces. We have applied GVB-BCCC methods to investigate three typical kinds of systems: polyacenes, pentaprismane, and [Cu₂O₂]²⁺ isomers. For polyacenes, we demonstrate that GVB-BCCC3b can capture more than 94% of the total correlation energy even for 12-acene with 50 π electrons. For the potential energy curve of simultaneously stretching 15 C-C bonds in pentaprismane, our calculations show that the GVB-BCCC3b results are quite close to the results from the density matrix renormalization group (DMRG) over the whole range. For two dinuclear copper oxide isomers, their relative energy predicted by GVB-BCCC3b is also in good accord with the DMRG result. All calculations show that the inclusion of three-pair correlation in GVB-BCCC is critical for accurate descriptions of strongly correlated systems.

Reference Energies for Cyclobutadiene: Automerization and Excited States

Cyclobutadiene is a well-known playground for theoretical chemists and is particularly suitable to test ground- and excited-state methods. Indeed, due to its high spatial symmetry, especially at the D_4h square geometry but also in the D_2h rectangular arrangement, the ground and excited states of cyclobutadiene exhibit multiconfigurational characters and single-reference methods, such as standard adiabatic time-dependent density-functional theory (TD-DFT) or standard equation-of-motion coupled cluster (EOM-CC), are notoriously known to struggle in such situations. In this work, using a large panel of methods and basis sets, we provide an extensive computational study of the automerization barrier (defined as the difference between the square and rectangular ground-state energies) and the vertical excitation energies at D_2h and D_4h equilibrium structures. In particular, selected configuration interaction (SCI), multireference perturbation theory (CASSCF, CASPT2, and NEVPT2), and coupled-cluster (CCSD, CC3, CCSDT, CC4, and CCSDTQ) calculations are performed. The spin-flip formalism, which is known to provide a qualitatively correct description of these diradical states, is also tested within TD-DFT (combined with numerous exchange-correlation functionals) and the algebraic diagrammatic construction [ADC(2)-s, ADC(2)-x, and ADC(3)]. A theoretical best estimate is defined for the automerization barrier and for each vertical transition energy.

Designing 3d metal oxides: selecting optimal density functionals for strongly correlated materials

Transition metal oxides (TMOs) have remarkable physicochemical properties, are non-toxic, and have low cost and high annual production, thus they are commonly studied for various technological applications. Density functional theory (DFT) can help to optimize TMO materials by providing insights into their electronic, optical and thermodynamic properties, and hence into their structure-performance relationships, over a wide range of solid-state structures and compositions. However, this is underpinned by the choice of the exchange-correlation (XC) functional, which is critical to accurately describe the highly localized and correlated 3d-electrons of the transition metals in TMOs. This tutorial review presents a benchmark study of density functionals (DFs), ranging from generalized gradient approximation (GGA) to range-separated hybrids (RSH), with the all-electron def2-TZVP basis set, comparing magneto-electro-optical properties of 3d TMOs against experimental observations. The performance of the DFs is assessed by analyzing the band structure, density of states, magnetic moment, structural static and dynamic parameters, optical properties, spin contamination and computational cost. The results disclose the strengths and weaknesses of the XC functionals, in terms of accuracy, and computational efficiency, suggesting the unprecedented PBE0-1/5 as the best candidate. The findings of this work contribute to necessary developments of XC functionals for periodic systems, and materials science modelling studies, particularly informing how to select the optimal XC functional to obtain the most trustworthy description of the ground-state electron structure of 3d TMOs.

State-specific solvation for restricted active space spin-flip (RAS-SF) wave functions based on the polarizable continuum formalism

The restricted active space spin-flip (RAS-SF) formalism is a particular form of single-reference configuration interaction that can describe some forms of strong correlation at a relatively low cost and which has recently been formulated for the description of charge-transfer excited states. Here, we introduce both equilibrium and nonequilibrium versions of a state-specific solvation correction for vertical transition energies computed using RAS-SF wave functions, based on the framework of a polarizable continuum model (PCM). Ground-state polarization is described using the solvent's static dielectric constant and in the nonequilibrium solvation approach that polarization is modified upon vertical excitation using the solvent's optical dielectric constant. Benchmark calculations are reported for well-studied models of photo-induced charge transfer, including naphthalene dimer, C₂H₄⋯C₂F₄, pentacene dimer, and perylene diimide (PDI) dimer, several of which are important in organic photovoltaic applications. For the PDI dimer, we demonstrate that the charge-transfer character of the excited states is enhanced in the presence of a low-dielectric medium (static dielectric constant ɛ₀ = 3) as compared to a gas-phase calculation (ɛ₀ = 1). This stabilizes mechanistic traps for singlet fission and helps to explain experimental singlet fission rates. We also examine the effects of nonequilibrium solvation on charge-separated states in an intramolecular singlet fission chromophore, where we demonstrate that the energetic ordering of the states changes as a function of solvent polarity. The RAS-SF + PCM methodology that is reported here provides a framework to study charge-separated states in solution and in photovoltaic materials.

Providing theoretical insight into the role of symmetry in the photoisomerization mechanism of a non-symmetric dithienylethene photoswitch

Dithienylethene (DTE) molecular photoswitches have shown to be excellent candidates in the design of efficient optoelectronic devices, due to their high photoisomerization quantum yield (QY), for which symmetry is suggested to play a crucial role. Here, we present a theoretical study on the photochemistry of a non-symmetric dithienylethene photoswitch, with a special emphasis on the effect of asymmetric substitution on the photocyclization and photoreversion mechanisms. We used the Spin-Flip Time Dependent Density Functional Theory (SF-TDDFT) method to locate and characterize the main structures (conical intersections and minima) of the ground state and the first two excited states, S₁ and S₂, along the ring-opening/closure reaction coordinate of the photocyclization and photoreversion processes, and to identify the important coordinates governing the radiationless decay pathways. Our results suggest that while the main features that characterize the photoisomerization of symmetric DTEs are also present for the photoisomerization of the non-symmetric DTE, the lower energy barrier on S₁ along the cycloreversion reaction speaks in favor of a more efficient and therefore a higher cycloreversion QY for the non-symmetric DTEs, making them a better candidate for molecular optoelectronic devices than their symmetric counterparts.

Single Excitation Energies Obtained from the Ensemble "HOMO-LUMO Gap": Exact Results and Approximations

In calculations based on density functional theory, the "HOMO-LUMO gap" (difference between the highest occupied and lowest unoccupied molecular orbital energies) is often used as a low-cost, ad hoc approximation for the lowest excitation energy. Here we show that a simple correction based on rigorous ensemble density functional theory makes the HOMO-LUMO gap exact in principle and significantly more accurate in practice. The introduced perturbative ensemble density functional theory approach predicts different and useful values for singlet-singlet and singlet-triplet excitations, using semilocal and hybrid approximations. Excitation energies are similar in quality to time-dependent density functional theory, especially at high fractions of exact exchange. The approach therefore offers an easy-to-implement and low-cost route to robust prediction of molecular excitation energies.

Theoretical Study of Light-Induced Crosslinking Reaction Between Pyrimidine DNA Bases and Aromatic Amino Acids

Low-lying electronic excited states and their relaxation pathways as well as energetics of the crosslinking reaction between uracil as a model system for pyrimidine-type building blocks of DNA and RNA and benzene as a model system for aromatic groups of tyrosine (Tyr) and phenylalanine (Phe) amino acids have been studied in the framework of density functional theory. The equilibrium geometries of the ground and electronic excited states as well as the crossing points between the potential energy surfaces of the uracil–benzene complex were computed. Based on these results, different relaxation pathways of the electronic excited states that lead to either back to the initial geometry configuration or the dimerization between the six-membered rings of the uracil–benzene complex have been identified, and the energetic conditions for their occurrence are discussed. It can be concluded that the DNA–protein crosslinking reaction can be induced by the external electromagnetic field via the dimerization reaction between the six-membered rings of the uracil–benzene pair at the electronic excited-state level of the complex. In the case of the uracil–phenol complex, the configuration of the cyclic adduct (dimerized) conformation is less likely to be formed.

Open-shell extensions to closed-shell pCCD

The pair coupled cluster doubles (pCCD) ansatz represents an inexpensive but accurate single-reference method to describe multi-reference problems. By construction, pCCD remains, however, applicable to closed-shell systems. For the first time, we present extensions to pCCD that allow us to target open-shell molecules with up to 4 unpaired electrons. Although requiring only modest computational cost, our methods approach chemical accuracy for some challenging cases, while their performance is comparable to more expensive models like DMRG or CCSD(T).

Revealing the Contest between Triplet-Triplet Exchange and Triplet-Triplet Energy Transfer Coupling in Correlated Triplet Pair States in Singlet Fission

Understanding the separation of the correlated triplet pair state ¹(TT) intermediate is critical for leveraging singlet fission to improve solar cell efficiency. This separation mechanism is dominated by two key interactions: (i) the exchange interaction (K) between the triplets which leads to the spin splitting of the biexciton state into ¹(TT),³(TT) and ⁵(TT) states, and (ii) the triplet-triplet energy transfer integral (t) which enables the formation of the spatially separated (but still spin entangled) state ¹(T···T). We develop a simple ab initio technique to compute both the biexciton exchange (K) and biexciton transfer coupling. Our key findings reveal new conditions for successful correlated triplet pair state dissociation. The biexciton exchange interaction needs to be ferromagnetic or negligible to the triplet energy transfer for favorable dissociation. We also explore the effect of chromophore packing to reveal geometries where these conditions are achieved for tetracene.

Origins of the photoinitiation capacity of aromatic thiols as photoinitiatiors: a computational study

In this work, we report the photophysical properties of three thiol derivatives, commonly used as photoinitiators in thiol-ene free radical polymerization, the ultimate goal being to rationalize the main reason behind the photoinitiation efficiency. For this aim, time dependent density functional theory is used to simulate the absorption spectra of alkyl thiol (R-SH), thiophenol (PhSH) and p-(trifluoromethyl) thiophenol (p-CF₃PhSH), describe their excited state topologies, and explore their potential energy surfaces along the S-H dissociation. Excited state calculations have shown that the S-H photolysis is achieved through the triplet excited states following intersystem crossing from the originally populated singlet manifolds. More specifically, while in aromatic thiol derivatives dissociation is mainly triplet-state mediated, the first excited singlet state and first triplet state of alkyl thiol are both dissociative and hence potentially capable of generating the photoinduced radical species. We have also justified the experimental findings concerning the photoinitiator efficiency considering both their potential energy surface topologies and the absorption intensity, in the lowest energy region.

peri-Acenoacene molecules: tuning of the singlet and triplet excitation energies by modifying their radical character

The energy difference between singlet and triplet excitons, or ΔE_ST, is a key parameter for novel light-emission mechanisms (i.e., TADF or thermally activated delayed fluorescence) or other photoactivated processes. We have studied a set of conjugated molecules (peri-acenoacenes and their heteroatom-doped analogues) to observe the evolution of their excited-state properties upon increasing the system size with and without substitution with a pair of N atoms. Since these molecules exhibit a (ground-state) diradicaloid character, together with marked correlation effects influencing the excited-states formed, we have applied a variety of theoretical methods (FT-DFT, TD-DFT, SF-TD-DFT, CIS, CIS(D), SCS-CC2, SA-CASSCF, and SC-NEVPT2) to bracket the accuracy of the results while concomitantly providing insights into electronic structure. The results show how this chemical strategy (N-doping) largely modifies not only the excited-state energies but also the oscillator strengths and the ΔE_ST values, constituting versatile platforms for fine-tuned photophysical applications.