Quasi-degenerate perturbation theory with general multiconfiguration self-consistent field reference functions

Vibrational Electronic-Thermofield Coupled Cluster (VE-TFCC) Theory for Quantum Simulations of Vibronic Coupling Systems at Thermal Equilibrium

A vibrational electronic-thermofield coupled cluster (VE-TFCC) approach is developed to calculate thermal properties of non-adiabatic vibronic coupling systems. The thermofield (TF) theory and a mixed linear exponential ansatz based on second-quantized Bosonic construction operators are introduced to propagate the thermal density operator as a "pure state" in the Bogoliubov representation. Through this compact representation of the thermal density operator, the approach is basis-set-free and scales classically (polynomial) as the number of degrees of freedoms (DoF) in the system increases. The VE-TFCC approach is benchmarked with small test models and a real molecular compound (CoF4- anion) against the conventional sum over states (SOS) method and applied to calculate thermochemistry properties of a gas-phase reaction: CoF3 + F- → CoF4-. Results shows that the VE-TFCC approach, in conjunction with vibronic models, provides an effective protocol for calculating thermodynamic properties of vibronic coupling systems.

Adiabat-to-Diabat Angle in Seam Space: Renner-Teller-Type and Pseudo-Jahn-Teller-Type Problems

In this study, we examine the adiabat-to-diabat (ATD) angles for trajectories in 2-dimensional vibrational subspace of the seam space of two degenerate states. In circulating around the tangential touching degeneracy center, the ATD angle is changed by2 π ${2\pi }$ or 0, similar to the Renner-Teller problem and the pseudo-Jahn-Teller problem, respectively. These ATD angle profiles may be indistinguishable from those of circulating multiple conical intersections or a pseudo-Jahn-Teller center. Methods to discern those seemingly indistinguishable cases are proposed. A sharp zigzag variation of the ATD angle is seen as a feature for trajectories that graze a pseudo-Jahn-Teller-type tangential touching center, in contrast to the monotonic steep variation for grazing a conical intersection or a Renner-Teller-type tangential touching center.

Time dependent vibrational electronic coupled cluster (VECC) theory for non-adiabatic nuclear dynamics

A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photo-electron/UV-VIS absorption spectra as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born-Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation for the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only a few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favorable computational cost. In benchmark applications to small models and molecules, the VECC method provides accurate results compared to multi-configurational time-dependent Hartree calculations when predicting short-time dynamical properties (i.e., photo-electron/UV-VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities, the VECC method is also successfully applied to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Aranda and Santoro [J. Chem. Theory Comput. 17, 1691, (2021)].

The Lack of Triplet Fusion for an Intramolecular Singlet Fission Chromophore: The Expected, the Unexpected, and a Reconciliation

Singlet fission (SF) has the potential to play a key role in photovoltaics since it generates a larger number of longer-lived triplet excitons after photoabsorption. Intramolecular SF (iSF) is of special interest since it enables tuning of SF efficiency by adjusting interchromophore configuration through covalent interaction. However, as elaborated in the present work, iSF chromophores are doomed to dissatisfy one general thermodynamic criterion for all SF chromophores, intramolecular or not: E(T2) ≥ 2E(T1), and therefore, the fusion of two triplet excitons to one triplet exciton is thermodynamically favorable. In our nonadiabatic quantum dynamics simulation for a model iSF chromophore, this expected fusion does not occur, because of the inefficient intersystem crossing hidden under the cover of internal conversion of the triplet fusion. A reconciliation is achieved between the dissatisfaction of E(T2) ≥ 2E(T1) and the large tetraradical character for general iSF chromophores.

Spin-orbit coupling in low-lying electronic states of CuH

Potential energy curves for the low-lying electronic states of CuH have been calculated using the MRCI method with a large active space containing the 3d, 4s, 4pz and 3d' orbitals of the copper atom. All electronic states of CuH correlating with the 3d10 4s1 (2S) and 3d9 4s2 (2D) states of Cu were included, and spin-orbit corrections were calculated using the MRCI wavefunctions. Potential energy curves were obtained for individual Ω states, and the Einstein A coefficients were computed for the spin-forbidden transitions from the low-lying electronic states to the X1Σ+ ground state. Diagonal and off-diagonal elements of the spin-orbit Hamiltonian matrix were calculated for the X1Σ+, A1Σ+, 13Σ+, 23Σ+, 11Π, 13Π, 11Δ and 13Δ states, and the mixing of vibronic wavefunctions was investigated using the eigenvectors. The available experimental data on vibrational levels of the A1Σ+ excited state of CuH and CuD were combined in a multi-isotopologue Birge-Sponer plot, and the ab initio data on the unobserved vibrational levels were used for a more accurate extrapolation, resulting in a new experimental value for the equilibrium dissociation energy (De) of the CuH molecule. The De value for the ground state of CuH was determined to be 22 630 ± 250 cm-1, resulting in D0 values of 2.686 and 2.720 eV for CuH and CuD, respectively. Therefore, new experimental values for the bond dissociation enthalpies of CuH and CuD are reported to be 262.9 ± 3 and 266.2 ± 3 kJ mol-1, respectively.

Triplet Separation after the Fastest Intramolecular Singlet Fission in the Smallest Chromophore

Singlet fission is of key importance in harvesting solar energy in solar cells, as it generates a pair of triplet excitons on the incidence of a photon. This phenomenon is not yet widely employed in the organic photovoltaics industry mostly because of the rarity of singlet fission chromophores. Pyrazino[2,3-g]quinoxaline-1,4,6,9-tetraoxide was recently designed as the smallest intramolecular singlet fission chromophore, and it undergoes the fastest singlet fission with a 16 fs time scale. The subsequent separation of the generated triplet-pair is of likewise importance as their efficient generation. Through quantum chemistry calculations and quantum dynamics simulations, we show that the triplet-pair separates to residing on two chromophores with an ∼80% probability on each collision between a chromophore with the triplet-pair and a ground state chromophore. Avoided crossing, instead of conical intersection, is involved in the efficient exciton separation.

Accurate Spin-Orbit Coupling by Relativistic Mixed-Reference Spin-Flip-TDDFT

Relativistic mixed-reference spin-flip (MRSF)-TDDFT is developed considering the spin-orbit coupling (SOC) within the mean-field approximation. The resulting SOC-MRSF faithfully reproduces the experiments with very high accuracy, which is also consistent with the values by four-component (4c) relativistic CASSCF and 4c-CASPT2 in the spin-orbit-energy splitting calculations of the C, Si, and Ge atoms. Even for the fifth-row element Sn, the SOC-MRSF yielded accurate splittings (∼ 3 % error). In the SOC calculations of the molecular 4-thiothymine with a third-row element, SOC-MRSF values are in excellent agreement with those of the SO-GMC-QDPT2 level, regardless of geometries and exchange-correlation functionals. The same SOC-MRSF predicted the anticipated chance of S₁ (nπ*) → T₁ (ππ*) intersystem crossing, even in thymine with only second-row elements. With its accuracy and practicality, thus, SOC-MRSF is a promising electronic structure protocol in challenging situations such as nonadiabatic molecular dynamics (NAMD) incorporating both internal conversions and intersystem crossings in large systems.

Design of the Smallest Intramolecular Singlet Fission Chromophore with the Fastest Singlet Fission

We designed an intramolecular singlet fission (iSF) chromophore, pyrazino[2,3-g]quinoxaline-1,4,6,9-tetraoxide. Appropriate substitutions into anthracene enhance the tetraradical character, so that the molecule accommodates a pair of triplet excitons in its lowest singlet excited state. Our simulation showed a 16 fs fast iSF of the design, which is a new record. The design also sets a new record of small size iSF chromophore and high exciton density. The design can be synthesized by oxidizing the tertiary N centers of the existent pyrazino[2,3-g]quinoxaline.

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

Theoretical analysis of the role of complex transition dipole phase in XUV transient-absorption probing of charge migration

We theoretically investigate the role of complex dipole phase in the attosecond probing of charge migration. The iodobromoacetylene ion (ICCBr⁺) is considered as an example, in which one can probe charge migration by accessing both the iodine and bromine ends of the molecule with different spectral windows of an extreme-ultraviolet (XUV) pulse. The analytical expression for transient absorption shows that the site-specific information of charge migration is encoded in the complex phase of cross dipole products for XUV transitions between the I-4d and Br-3d spectral windows. Ab-initio quantum chemistry calculations on ICCBr⁺ reveal that there is a constant π phase difference between the I-4d and Br-3d transient-absorption spectral windows, irrespective of the fine-structure energy splittings. Transient absorption spectra are simulated with a multistate model including the complex dipole phase, and the results correctly reconstruct the charge-migration dynamics via the quantum beats in the two element spectral windows, exhibiting out-of-phase oscillations.

Field-induced single-ion magnets exhibiting tri-axial anisotropy in a 1D Co(II) coordination polymer with a rigid ligand 4,4'-(buta-1,3-diyne-1,4-diyl)dibenzoate

Herein a 1D Co(II) coordination polymer of formula [Co(η¹-L1)(η²-L1)(py)₂(H₂O)]_n (CoCP) has been synthesised using the rigid H2L1 proligand, containing a long spacer bearing two triple bonds. Single-crystal X-ray diffraction showed that Co(II) adopts a distorted octahedral geometry. The state-averaged complete active self-consistent field (SA-CASSCF) calculation showed that the ground state of CoCP is a high spin quartet with a highly multiconfigurational character of its electronic structure. Due to the large intra- and intermolecular distances between the spin carriers, the magnetic interactions are negligible and the zero-field splitting (ZFS) effects of cobalt(II) ions are predominant. This behavior was confirmed by direct current (DC) magnetic measurements and theoretical calculations using the broken-symmetry approach. Quantum chemical calculations indicate that CoCP has a negative axial component possessing mixed tri-axial anisotropy. The DC magnetic susceptibility data were fitted with a Griffith-Figgis Hamiltonian and the obtained parameters are in good agreement with those simulated by the ab initio calculation. Alternating current (AC) magnetic measurements showed a field induced slow magnetic relaxation in CoCP, which is attributed to the hyperfine interaction effects.

Analytic gradients for restricted active space second-order perturbation theory (RASPT2)

The computational cost of analytic derivatives in multireference perturbation theory is strongly affected by the size of the active space employed in the reference self-consistent field calculation. To overcome previous limits on the active space size, the analytic gradients of single-state restricted active space second-order perturbation theory (RASPT2) and its complete active space second-order perturbation theory (CASPT2) have been developed and implemented in a local version of OpenMolcas. Similar to previous implementations of CASPT2, the RASPT2 implementation employs the Lagrangian or Z-vector method. The numerical results show that restricted active spaces with up to 20 electrons in 20 orbitals can now be employed for geometry optimizations.

Parameterization of a linear vibronic coupling model with multiconfigurational electronic structure methods to study the quantum dynamics of photoexcited pyrene

With this work, we present a protocol for the parameterization of a Linear Vibronic Coupling (LVC) Hamiltonian for quantum dynamics using highly accurate multiconfigurational electronic structure methods such as RASPT2/RASSCF, combined with a maximum-overlap diabatization technique. Our approach is fully portable and can be applied to many medium-size rigid molecules whose excited state dynamics requires a quantum description. We present our model and discuss the details of the electronic structure calculations needed for the parameterization, analyzing critical situations that could arise in the case of strongly interacting excited states. The protocol was applied to the simulation of the excited state dynamics of the pyrene molecule, starting from either the first or the second bright state (S₂ or S₅). The LVC model was benchmarked against state-of-the-art quantum mechanical calculations with optimizations and energy scans and turned out to be very accurate. The dynamics simulations, performed including all active normal coordinates with the multilayer multiconfigurational time-dependent Hartree method, show good agreement with the available experimental data, endorsing prediction of the excited state mechanism, especially for S₅, whose ultrafast deactivation mechanism was not yet clearly understood.

Diboron- and Diaza-Doped Anthracenes and Phenanthrenes: Their Electronic Structures for Being Singlet Fission Chromophores

We used quantum chemistry methods at the levels of mixed-reference spin-flip time-dependent density functional theory and multireference perturbation theory to study diboron- and diaza-doped anthracenes and phenanthrenes. This class of structures recently surged as potential singlet fission chromophores. We studied electronic structures of their excited states and clarified the reasons why they satisfy or fail to satisfy the energy criteria for singlet fission chromophores. Many studied structures have their S₁ states not dominated by HOMO → LUMO excitation, so they cannot be described using the conventional two site model. This is attributed to frontier orbital energy shifts induced by the doping and different charge-transfer energies in different one-electron singlet excitations or, in other words, different polarizations of hole and/or particle orbitals in their S₁ and T₁ states. There is a mirror relation between the orbital energy shifts induced by diboron- and diaza-dopings, which together with alternant hydrocarbon pairings of occupied and unoccupied orbitals, leads to more mirror relations between the excited states of the two types of doped structures.

Reduced scaling extended multi-state CASPT2 (XMS-CASPT2) using supporting subspaces and tensor hyper-contraction

We present a reduced scaling formulation of the extended multi-state CASPT2 (XMS-CASPT2) method, which is based on our recently developed state-specific CASPT2 (SS-CASPT2) formulation using supporting subspaces and tensor hyper-contraction. By using these two techniques, the off-diagonal elements of the effective Hamiltonian can be computed with only O(N³) operations and O(N²) memory, where N is the number of basis functions. This limits the overall computational scaling to O(N⁴) operations and O(N²) memory. Thus, excited states can now be obtained at the same reduced (relative to previous algorithms) scaling we achieved for SS-CASPT2. In addition, we also investigate how the energy denominators can be factorized with the Laplace quadrature when some of the denominators are negative, which is critical for excited state calculations. An efficient implementation of the method has been developed using graphical processing units while also exploiting spatial sparsity in tensor operations. We benchmark the accuracy of the new method by comparison to non-THC formulated XMS-CASPT2 for the excited states of various molecules. In our tests, the THC approximation introduces negligible errors (≈0.01 eV) compared to the non-THC reference method. Scaling behavior and computational timings are presented to demonstrate performance. The new method is also interfaced with quantum mechanics/molecular mechanics (QM/MM). In an example study of green fluorescent protein, we show how the XMS-CASPT2 potential energy surfaces and excitation energies are affected by increasing the size of the QM region up to 278 QM atoms with more than 2300 basis functions.

Ab initio study on the excited states of pyrene and its derivatives using multi-reference perturbation theory methods

Low-lying singlet excited states of pyrene derivatives originated from the 1La and 1Lb states of pyrene have decisive influences on their absorption and fluorescence emission behaviors. Calculation of these excited states with quantitative accuracy is required for the theoretical design of pyrene derivatives tailored to target applications; this has been a long-standing challenge for ab initio quantum chemical calculations. In this study, we explore an adequate computational scheme through calculations of pyrene and its phenyl-substituted derivatives using multi-reference perturbation theory (MRPT) methods. All valence π orbitals on the pyrene moiety were assigned to the active orbitals. Computational load was reduced by restricting the electron excitations within the active orbitals in the preparation of reference configuration space. A generalized multi-configuration quasi-degenerate perturbation theory (GMCQDPT) was adopted to treat the reference space other than the complete active space. The calculated 1La and 1Lb excitation energies of pyrene are in good agreement with the experimental values. Calculations of 1,3,6,8-tetraphenyl pyrene suggest that the energetic ordering of 1La and 1Lb is inverted through tetraphenyl substitution and its lowest singlet excited state is the 1La parentage of pyrene, which is consistent with the experimentally deduced scheme. These results are not readily obtained by MRPT calculations with a limited number of active orbitals and single-reference theory calculations. Diphenyl pyrenes (DPPy) were also calculated at the same level of theory to investigate the dependence on the substitution positions of phenyl groups.

Squeezing All Elements in the Periodic Table: Electron Configuration and Electronegativity of the Atoms under Compression

We present a quantum mechanical model capable of describing isotropic compression of single atoms in a non-reactive neon-like environment. Studies of 93 atoms predict drastic changes to ground-state electronic configurations and electronegativity in the pressure range of 0-300 GPa. This extension of atomic reference data assists in the working of chemical intuition at extreme pressure and can act as a guide to both experiments and computational efforts. For example, we can speculate on the existence of pressure-induced polarity (red-ox) inversions in various alloys. Our study confirms that the filling of energy levels in compressed atoms more closely follows the hydrogenic aufbau principle, where the ordering is determined by the principal quantum number. In contrast, the Madelung energy ordering rule is not predictive for atoms under compression. Magnetism may increase or decrease with pressure, depending on which atom is considered. However, Hund's rule is never violated for single atoms in the considered pressure range. Important (and understandable) electron shifts, s→p, s→d, s→f, and d→f are essential chemical and physical consequences of compression. Among the specific intriguing changes predicted are an increase in the range between the most and least electronegative elements with compression; a rearrangement of electronegativities of the alkali metals with pressure, with Na becoming the most electropositive s¹ element (while Li becomes a p group element and K and heavier become transition metals); phase transitions in Ca, Sr, and Ba correlating well with s→d transitions; spin-reduction in all d-block atoms for which the valence d-shell occupation is d ⁿ (4 ≤ n ≤ 8); d→f transitions in Ce, Dy, and Cm causing Ce to become the most electropositive element of the f-block; f→d transitions in Ho, Dy, and Tb and a s→f transition in Pu. At high pressure Sc and Ti become the most electropositive elements, while Ne, He, and F remain the most electronegative ones.

Slow-spin relaxation of a low-spin S = 1/2 FeIII carborane complex

In this communication, we report the first evidence of slow-spin relaxation of a low-spin FeIII carborane complex. Iron S = 1/2 complexes showing such behaviour are particularly appealing as qubit candidates because they fulfil some of the main requirements to reach long decoherence times, such as moderate magnetic anisotropy, small spin, metal element mainly with zero-nuclear spin and furthermore, large versatility to introduce chemical modifications.

Ab initio investigation of Br-3d core-excited states in HBr and HBr+ toward XUV probing of photochemical dynamics

Ultrafast X-ray/XUV transient absorption spectroscopy is a powerful tool for real-time probing of chemical dynamics. Interpretation of the transient absorption spectra requires knowledge of core-excited potentials, which necessitates assistance from high-level electronic-structure computations. In this study, we investigate Br-3d core-excited electronic structures of hydrogen bromide (HBr) using spin-orbit general multiconfigurational quasidegenerate perturbation theory (SO-GMC-QDPT). Potential energy curves and transition dipole moments are calculated from the Franck-Condon region to the asymptotic limit and used to construct core-to-valence absorption strengths for five electronic states of HBr (Σ 1 0 + ,   3 Π 1 ,   1 Π 1 ,   3 Π 0 + ,   3 Σ 1 ) and two electronic states of HBr+ (2Π3∕2, 2Σ1∕2). The results illustrate the capabilities of Br-3d edge probing to capture transitions of the electronic-state symmetry as well as nonadiabatic dissociation processes that evolve across avoided crossings. Furthermore, core-to-valence absorption spectra are simulated from the neutralΣ 1 0 + state and the ionicΠ 2 1 / 2 , 3 / 2 states by numerically solving the time-dependent Schrödinger equation and exhibit excellent agreement with the experimental spectrum. The comprehensive and quantitative picture of the core-excited states obtained in this work allows for transparent analysis of the core-to-valence absorption signals, filling gaps in the theoretical understanding of the Br-3d transient absorption spectra.

Vibronic interaction in CO3− photo-detachment: Jahn–Teller effects beyond structural distortion and general formalisms for vibronic Hamiltonians in trigonal symmetries

Expansion formalisms for trigonal Jahn–Teller and pseudo-Jahn–Teller vibronic Hamiltonians are developed and used to study and correctly interpret the photoelectron spectrum of CO₃⁻.

Electronegativity Seen as the Ground-State Average Valence Electron Binding Energy

We introduce a new electronegativity scale for atoms, based consistently on ground-state energies of valence electrons. The scale is closely related to (yet different from) L. C. Allen's, which is based on configuration energies. Using a combination of literature experimental values for ground-state energies and ab initio-calculated energies where experimental data are missing, we are able to provide electronegativities for elements 1-96. The values are slightly smaller than Allen's original scale, but correlate well with Allen's and others. Outliers in agreement with other scales are oxygen and fluorine, now somewhat less electronegative, but in better agreement with their chemistry with the noble gas elements. Group 11 and 12 electronegativities emerge as high, although Au less so than in other scales. Our scale also gives relatively high electronegativities for Mn, Co, Ni, Zn, Tc, Cd, Hg (affected by choice of valence state), and Gd. The new electronegativities provide hints for new alloy/compound design, and a framework is in place to analyze those energy changes in reactions in which electronegativity changes may not be controlling.

Exciton localization in excited-state dynamics of a tetracene trimer: a surface hopping LC-TDDFTB study

Excitons in the molecular aggregates of chromophores are key participants in important processes such as photosynthesis or the functioning of organic photovoltaic devices. Therefore, the exploration of exciton dynamics is crucial. Here we report on exciton localization during excited-state dynamics of the recently synthesized tetracene trimer [Liu et al., Org. Lett., 2017, 19, 580]. We employ the surface hopping approach to nonadiabatic molecular dynamics in conjunction with the long-range corrected time-dependent density functional tight binding (LC-TDDFTB) method [Humeniuk and Mitrić, Comput. Phys. Commun., 2017, 221, 174]. Utilizing a set of descriptors based on the transition density matrix, we perform comprehensive analysis of exciton dynamics. The obtained results reveal an ultrafast exciton localization to a single tetracene unit of the trimer during excited-state dynamics, along with exciton transfer between units.

Identifying (BN)2-pyrenes as a New Class of Singlet Fission Chromophores: Significance of Azaborine Substitution

Singlet fission converts one photoexcited singlet state to two triplet excited states and raises photoelectric conversion efficiency in photovoltaic devices. However, only a handful of chromophores have been known to undergo this process, which greatly limits the application of singlet fission in photovoltaics. We hereby identify a recently synthesized diazadiborine-pyrene ((BN)₂-pyrene) as a singlet fission chromophore. Theoretical calculations indicate that it satisfies the thermodynamics criteria for singlet fission. More importantly, the calculations provide a physical chemistry insight into how the BN substitution makes this happen. Both calculation and transient absorption spectroscopy experiments indicate that the chromophore has a better absorption than pentacene. The convenient synthesis pathway of the (BN)₂-pyrene suggests an in situ chromophore generation in photovoltaic devices. Two more (BN)₂-pyrene isomers are proposed as singlet fission chromophores. This study sets a step forward in the cross-link of singlet fission and azaborine chemistry.

Theoretical Modeling of Singlet Fission

Singlet fission is a photophysical reaction in which a singlet excited electronic state splits into two spin-triplet states. Singlet fission was discovered more than 50 years ago, but the interest in this process has gained a lot of momentum in the past decade due to its potential as a way to boost solar cell efficiencies. This review presents and discusses the most recent advances with respect to the theoretical and computational studies on the singlet fission phenomenon. The work revisits important aspects regarding electronic states involved in the process, the evaluation of fission rates and interstate couplings, the study of the excited state dynamics in singlet fission, and the advances in the design and characterization of singlet fission compounds and materials such as molecular dimers, polymers, or extended structures. Finally, the review tries to pinpoint some aspects that need further improvement and proposes future lines of research for theoretical and computational chemists and physicists in order to further push the understanding and applicability of singlet fission.

Computational investigations of click-derived 1,2,3-triazoles as keystone ligands for complexation with transition metals: a review

In recent years, metal complexes of organo 1,2,3-triazole click-derived ligands have attracted significant attention as catalysts in many chemical transformations and also as biological and pharmaceutical active agents. Regarding the important applications of these metal-organo 1,2,3-triazole-based complexes, in this review, we focused on the recently reported investigations of the structural, electronic, and spectroscopic aspects of the complexation process in transition metal complexes of 1,2,3-triazole-based click ligands. In line with this, the coordination properties of these triazole-based click ligands with transition metals were studied via several quantum chemistry calculations. Moreover, considering the complexation process, we have presented comparative discussions between the computational results and the available experimental data.

Quantum Chemical Study of the Water Exchange Mechanism of the Neptunyl(VI) and -(V) Aqua Ions

The water exchange reaction of the neptunyl(VI) and -(V) aqua ions was investigated with quantum chemical methods. Associative ( a) and dissociative ( d) exchange mechanisms were studied. The geometries and vibrational frequencies were computed with density functional theory (DFT) and multiconfiguration self-consistent field (MCSCF) methods. The Gibbs activation energies (Δ G^‡) for a and d pathways were calculated with DFT and wave function theory (WFT), extended general multiconfiguration quasi-degenerate second-order perturbation theory (XGMC-QDPT2) including spin-orbit (SO) coupling at the SO configuration interaction (CI) level. The DFT-WFT agreement for Δ G^‡ was poor for the investigated functionals except for LC-BOP-LRD. Due to ligand-field effects, Δ G^‡ for the associatively activated exchange reaction of NpO₂(OH₂)₅²⁺ with a f_δ¹ electron configuration is higher than for the actinyl(VI) aqua ions of U, Pu, and Am exhibiting f⁰, f_δ², and f_δ²f_ϕ¹ electron configurations.

Four-Component Relativistic State-Specific Multireference Perturbation Theory with a Simplified Treatment of Static Correlation

The relativistic multireference (MR) perturbative approach is one of the most successful tools for the description of computationally demanding molecular systems of heavy elements. We present here the ground state dissociation energy surfaces, equilibrium bond lengths, harmonic frequencies, and dissociation energies of Ag₂, Cu₂, Au₂, and I₂ computed using the four-component (4c) relativistic spinors based state-specific MR perturbation theory (SSMRPT) with improved virtual orbital complete active space configuration interaction (IVO-CASCI) functions. The IVO-CASCI method is a simple, robust, useful and lower cost alternative to the complete active space self-consistent field approach for treating quasidegenerate situations. The redeeming features of the resulting method, termed as 4c-IVO-SSMRPT, lies in (i) manifestly size-extensivity, (ii) exemption from intruder problems, (iii) the freedom of convenient multipartitionings of the Hamiltonian, (iv) flexibility of the relaxed and unrelaxed descriptions of the reference coefficients, and (v) manageable cost/accuracy ratio. The present method delivers accurate descriptions of dissociation processes of heavy element systems. Close agreement with reference values has been found for the calculated molecular constants indicating that our 4c-IVOSSMRPT provides a robust and economic protocol for determining the structural properties for the ground state of heavy element molecules with eloquent MR character as it treats correlation and relativity on equal footing.

Breaking the disulfide chemical bond using high energy photons: the dimethyl disulfide and methyl propyl disulfide molecules

In order to study the stability of the disulfide chemical bond in molecules subjected to a flux of high energy photons, the ionic fragmentation of DMDS and MPDS has been studied following excitation around the S 1s edge (∼2470 eV).

Theoretical study of one-electron-oxidized salen complexes of group 7 (Mn(iii), Tc(iii), and Re(iii)) and group 10 metals (Ni(ii), Pd(ii), and Pt(ii)) with the 3D-RISM-GMC-QDPT method: localized vs. delocalized ground and excited states in solution

Mixed-valence natures of one-electron oxidized salen complexes of group 7 and 10 metals are theoretically investigated by GMC-QDPT, incorporating solvation effects.

Through-Linker Intramolecular Singlet Fission: General Mechanism and Designing Small Chromophores

We perform quantum chemistry calculations and quantum dynamics simulations to investigate the covalent linker's through-bond effects in intramolecular singlet fission. A model molecule with two diazadiborine chromophore units and the para-phenylene linker is proposed. A general, step-by-step picture for the conversion from the single- to the multiexcitonic state through the linker is presented. On the basis of the picture, we discuss the triplet-pair delocalization into the linker and design two more chromophores with higher fission efficiency. All three designed chromophores have promising picosecond fission time scales and make good candidates for azaborine synthesis.

Design of Small Intramolecular Singlet Fission Chromophores: An Azaborine Candidate and General Small Size Effects

We report the first attempt to design small intramolecular singlet fission chromophores, with the aid of quantum chemistry and explicitly simulating the time evolution of state populations using quantum dynamics method. We start with three previously proposed azaborine-substituted intermolecular singlet fission chromophores. Through analyzing their frontier orbital amplitudes, we select a BN-substituted azulene as the building block. Covalently connecting two such monomers and tuning their relative configuration, we examine three dimers. One dimer is found to be an eminent candidate: the triplet-pair state is quickly formed within 1 ps, and the two triplets are ready to be disentangled. We elucidate the general small size effects in intramolecular singlet fission and focus on specific aspects which should be taken care of when manipulating the fission rate through steric hindrance.

Correct Quantum Chemistry in a Minimal Basis from Effective Hamiltonians

We describe how to create ab initio effective Hamiltonians that qualitatively describe correct chemistry even when used with a minimal basis. The Hamiltonians are obtained by folding correlation down from a large parent basis into a small, or minimal, target basis, using the machinery of canonical transformations. We demonstrate the quality of these effective Hamiltonians to correctly capture a wide range of excited states in water, nitrogen, and ethylene and to describe ground and excited state bond breaking in nitrogen and the chromium dimer, all in small or minimal basis sets.