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

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

Divide-and-Conquer Linear-Scaling Quantum Chemical Computations.

Fragmentation and embedding schemes are of great importance when applying quantum-chemical calculations to more complex and attractive targets. The divide-and-conquer (DC)-based quantum-chemical model is a fragmentation scheme that can be connected to embedding schemes. This feature article explains several DC-based schemes developed by the authors over the last two decades, which was inspired by the pioneering study of DC self-consistent field (SCF) method by Yang and Lee (J. Chem. Phys. 1995, 103, 5674-5678). First, the theoretical aspects of the DC-based SCF, electron correlation, excited-state, and nuclear orbital methods are described, followed by the two-component relativistic theory, quantum-mechanical molecular dynamics simulation, and the introduction of three programs, including DC-based schemes. Illustrative applications confirmed the accuracy and feasibility of the DC-based schemes.

Experimental and Theoretical Evidence for Relativistic Catalytic Activity in C-H Activation of N-Phenylbenzamide Using a Cationic Iridium Complex.

This study elucidates that relativistic effect plays a key role in catalytic C-H activation using a cationic Ir complex. Experiments show that the cationic Ir(I)-diphosphine catalyst can be used for the deuterium substitution of N-phenylbenzamide, whereas a cationic Rh(I)-diphosphine catalyst is scarcely effective. Density functional theory calculations, including the relativistic effect, demonstrate a large difference in the reaction energy diagrams for the C-H activation of N-phenylbenzamide between the cationic Ir and Rh catalysts. In particular, the relatively low reaction barrier and considerably stabilized product obtained for the Ir catalysts are rationalized by strong Ir-C and Ir-H interactions, which originate from the relativistic self-consistent d-orbital expansion of Ir.

Tetraaryldiborane(4) Can Emit Dual Fluorescence Responding to the Structural Change around the B-B Bond.

We report the successful synthesis of tetramesityldiborane(4) (Mes4 B2 ) through the reductive coupling of a dimesitylborinium ion. Owing to the steric protection conferred by the mesityl groups, Mes4 B2 shows exceptional chemical stability and remains intact in water. Single-crystal X-ray analysis revealed that Mes4 B2 has an orthogonal geometry, where the B-B center is completely hidden by the mesityl groups. Remarkably, Mes4 B2 emits dual fluorescence at 460 and 620 nm, both in solution and in the solid state. Theoretical calculations showed that Mes4 B2 in the excited S1 state adopts a twisted or planar geometry, which is responsible for the shorter- or longer-wavelength fluorescence, respectively. The intensity ratio of the dual fluorescence is sensitive to the viscosity of the medium, which suggests that Mes4 B2 has potential as a ratiometric viscosity sensor.

Direct Near Infrared Light-Activatable Phthalocyanine Catalysts.

The high penetration of near-infrared (NIR) light makes it effective for use in selective reactions under light-shielded conditions, such as in sealed reactors and deep tissues. Herein, we report the development of phthalocyanine catalysts directly activated by NIR light to transform small organic molecules. The desired photocatalytic properties were achieved in the phthalocyanines by introducing the appropriate peripheral substituents and central metal. These phthalocyanine photocatalysts promote cross-dehydrogenative-coupling (CDC) under irradiation with 810 nm NIR light. The choice of solvent is important, and a mixture of a reaction-accelerating (pyridine) and -decelerating (methanol) solvents was particularly effective. Moreover, we demonstrate photoreactions under visible-light-shielded conditions through the transmission of NIR light. A combined experimental and computational mechanistic analysis revealed that this NIR reaction does not involve a photoredox-type mechanism with electron transfer, but instead a singlet-oxygen-mediated mechanism with energy transfer.

An Air- and Water-Stable B4 N4 -Heteropentalene Serving as a Host Material for a Phosphorescent OLED.

Replacement of the carbon-carbon bonds of antiaromatic compounds with polar boron-nitrogen bonds often provides isoelectronic BN compounds with excellent thermodynamic stability and interesting photophysical properties. By this element-substitution strategy, we synthesized a new B4 N4 -heteropentalene derivative, 1, which is fully substituted with mesityl groups. Owing to kinetic protection by the sterically bulky substituents, 1 is remarkably stable toward air and even water. Single-crystal X-ray analysis of 1 revealed the bonding characteristics of the B4 N4 -heteropentalene structure. In a glassy matrix, 1 emitted short-wavelength phosphorescence with an onset at 350 nm, indicating that the triplet energy is substantially high. DFT calculations reasonably explained the ground- and excited-state electronic structures of 1 as well as its emission properties. Motivated by the high-energy triplet state of 1, we used it as a host material to fabricate a phosphorescent organic light-emitting diode with an external quantum efficiency of 15 %.

Assessing locally range-separated hybrid functionals from a gradient expansion of the exchange energy density.

Locally range-separated hybrid (LRSH) functionals feature a real-space-dependent range separation function (RSF) instead of a system-independent range-separation parameter, which thus enables a more flexible admixture of exact exchange than conventional range-separated hybrid functionals. In particular, the development of suitable RSF models and exploring the capabilities of the LRSH approach, in general, are tasks that require further investigations and will be addressed in this work. We propose a non-empirical scheme based on a detailed scaling analysis with respect to a uniform coordinate scaling and on a short-range expansion of the range-separated exchange energy density to derive new RSF models from a gradient expansion of the exchange energy density. After optimizing a small set of empirical parameters introduced to enhance their flexibility, the resulting second- and fourth-order RSFs are evaluated with respect to atomic exchange energies, atomization energies, and transition barrier heights.

Picture-change correction in relativistic density functional theory.

Relativistic quantum chemical calculations are performed based on one of two physical pictures, namely the Dirac picture and the Schrödinger picture. With regard to the latter, the so-called picture-change effect (PCE) and picture-change correction (PCC) have been studied. The PCE, which is the change in the expectation value associated with the transformation, is not commonly a minor effect. The electron density, which is given by the expectation value of the density operator, is a fundamental variable in relativistic density functional theory (RDFT). Thus, performing the PCC in RDFT calculations is essential not only in terms of numerical agreement with the Dirac picture, but also from the viewpoint of fundamental theory. This paper explains theories and numerical studies of PCE and PCC in RDFT after overviewing those in properties, which involves the authors' works on the development of RDFT in the Schrödinger picture and relativistic exchange-correlation functionals based on picture-change-corrected variables.

An Element-Substituted Cyclobutadiene Exhibiting High-Energy Blue Phosphorescence.

1,3,2,4-Diazadiboretidine, an isoelectronic heteroanalogue of cyclobutadiene, is an interesting chemical species in terms of comparison with the carbon system, whereas its properties have never been investigated experimentally. According to Baird's rule, Hückel antiaromatic cyclobutadiene acquires aromaticity in the lowest triplet state. Here we report experimental and theoretical studies on the ground- and excited-state antiaromaticity/aromaticity as well as the photophysical properties of an isolable 1,3,2,4-diazadiboretidine derivative. The crystal structure of the diazadiboretidine derivative revealed that the B2 N2 ring adopts a planar rhombic geometry in the ground state. Yet, theoretical calculations showed that the B2 N2 ring turns to a square geometry with a nonaromatic character in the lowest triplet state. Notably, the diazadiboretidine derivative has the lowest singlet and triplet states lying at close energy levels and displays blue phosphorescence.

Machine-learned electron correlation model based on frozen core approximation.

The machine-learned electron correlation (ML-EC) model is a regression model in the form of a density functional that reproduces the correlation energy density based on wavefunction theory. In a previous study [T. Nudejima et al., J. Chem. Phys. 151, 024104 (2019)], the ML-EC model was constructed using the correlation energy density from all-electron calculations with basis sets including core polarization functions. In this study, we applied the frozen core approximation (FCA) to the correlation energy density to reduce the computational cost of the response variable used in machine learning. The coupled cluster singles, doubles, and perturbative triples [CCSD(T)] correlation energy density obtained from a grid-based energy density analysis was analyzed within FCA and correlation-consistent basis sets without core polarization functions. The complete basis set (CBS) limit of the correlation energy density was obtained using the extrapolation and composite schemes. The CCSD(T)/CBS correlation energy densities based on these schemes showed reasonable behavior, indicating its appropriateness as a response variable. As expected, the computational time was significantly reduced, especially for systems containing elements with a large number of inner-shell electrons. Based on the density-to-density relationship, a large number of data (5 662 500 points), which were accumulated from 30 molecules, were sufficient to construct the ML-EC model. The valence-electron correlation energies and reaction energies calculated using the constructed model were in good agreement with the reference values, the latter of which were superior in accuracy to density functional calculations using 71 exchange-correlation functionals. The numerical results indicate that the FCA is useful for constructing a versatile model.

Relativistic local hybrid functionals and their impact on 1s core orbital energies.

In this work, we report the first relativistic density functional theory calculations using relativistic local hybrid functionals. Besides outlining the construction of relativistic local hybrid exchange within a two-component-relativistic framework based on the picture-change transformation of the density matrix and a recently developed relativistic iso-orbital indicator, we investigate the influence of two-electron-relativistic effects, using relativistic functional ingredients in local hybrid functionals, and the choice of the exchange-correlation functional on atomic 1s core orbital energies of light and heavier elements. Finally, we discuss the applicability of relativistic 1s core orbital shifts for the relativistic correction of non-relativistic 1s core excitation energies.

Unveiling controlling factors of the S0/S1 minimum energy conical intersection (2): Application to penalty function method.

Minimum-energy conical intersection (MECI) geometries play an important role in photophysics, photochemistry, and photobiology. In a previous study [Nakai et al., J. Phys. Chem. A 122, 8905 (2018)], frozen orbital analysis at the MECI geometries between the ground and first electronic excited states (S0/S1 MECI), which considers the main configurations contributing to the excitation, inductively clarified two controlling factors. First, the exchange integral between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) approximately becomes zero. Second, the HOMO-LUMO gap becomes close to the HOMO-LUMO Coulomb integral. This study applies the controlling factors to the penalty function method, which is the standard MECI optimization technique, and minimizes the energy average of the two states with the constraint that the energy gap between the states vanishes. Numerical assessments clarified that the present method could obtain the S0/S1 MECI geometries more efficiently than the conventional one.

Spin-flip approach within time-dependent density functional tight-binding method: Theory and applications.

A spin-flip time-dependent density functional tight-binding (SF-TDDFTB) method is developed that describes target states as spin-flipping excitation from a high-spin reference state obtained by the spin-restricted open shell treatment. Furthermore, the SF-TDDFTB formulation is extended to long-range correction (LC), denoted as SF-TDLCDFTB. The LC technique corrects the overdelocalization of electron density in systems such as charge-transfer systems, which is typically found in conventional DFTB calculations as well as density functional theory calculations using pure functionals. The numerical assessment of the SF-TDDFTB method shows smooth potential curves for the bond dissociation of hydrogen fluoride and the double-bond rotation of ethylene and the double-cone shape of H3 as the simplest degenerate systems. In addition, numerical assessments of SF-TDDFTB and SF-TDLCDFTB for 39 S0 /S1 minimum energy conical intersection (MECI) structures are performed. The SF-TDDFTB and SF-TDLCDFTB methods drastically reduce the computational cost with accuracy for MECI structures compared with SF-TDDFT.

Restoring the iso-orbital limit of the kinetic energy density in relativistic density functional theory.

In contrast to nonrelativistic density functional theory, the ratio between the von Weizsäcker and the Kohn-Sham kinetic energy density, commonly used as iso-orbital indicator t within exchange-correlation functionals beyond the generalized-gradient level, violates the exact iso-orbital limit and the appropriate parameter range, 0 ≤ t ≤ 1, in relativistic density functional theory. Based on the exact decoupling procedure within the infinite-order two-component method and the Cauchy-Schwarz inequality, we present corrections to the relativistic and the picture-change-transformed nonrelativistic kinetic energy density that restores these exact constraints. We discuss the origin of the new correction terms and illustrate the effectiveness of the current approach for several representative cases. The proposed generalized iso-orbital indicator tλ is expected to be a useful ingredient for the development of relativistic exchange-correlation functionals.

Efficient Semi-Numerical Implementation of Relativistic Exact Exchange within the Infinite-Order Two-Component Method Using a Modified Chain-of-Spheres Method.

We present an efficient implementation of relativistic exact exchange within the infinite-order two-component method (IOTC) by employing a state-of-the-art seminumerical integration technique. For accurate consideration of the picture change, inherent to two-component methods, we propose a new scheme based on a relativistic or picture-change transformation of the density matrix, which provides a simple and efficient formulation of relativistically transformed quantities such as the electron density or exact exchange and thus avoids expensive integral transformations. We show that the new scheme does not introduce additional numerical or theoretical errors beyond the approximations of the IOTC method. For the efficient implementation of exact-exchange integrals, we build upon a modified version of the chain-of-spheres exact-exchange (COSX) method. In addition to the conventional overlap and density matrix screening by S- and P-junctions, respectively, we introduce a new simple screening technique in the sense of the original COSX method by additionally considering the asymptotic decay of the integrals over the Coulomb operator within the new F-junctions. Together with the picture-change transformation of the density matrix, this modified COSX method is shown to provide superior efficiency for the calculation of relativistic exact exchange compared to a conventional analytical direct self-consistent-field implementation of exact exchange.

Machine-learned electron correlation model based on correlation energy density at complete basis set limit.

We propose a machine-learned correlation model that is built using the regression between density variables such as electron density and correlation energy density. The correlation energy density of coupled cluster singles, doubles, and perturbative triples [CCSD(T)] is derived based on grid-based energy density analysis. The complete basis set (CBS) limit is estimated using the composite method, which has been reported to calculate the total correlation energy. The numerical examination revealed that the correlation energy density of the CCSD(T)/CBS level is appropriate for the response variable of machine learning. In addition to the density variables used in the exchange-correlation functionals of the density functional theory, the Hartree-Fock (HF) exchange energy density and electron density based on the fractional occupation number of molecular orbitals were employed as explanatory variables. Numerical assessments confirmed the accuracy and efficiency of the present correlation model. Consequently, the present protocol, namely, learning the CCSD(T)/CBS correlation energy density using density variables obtained by the HF calculation with a small basis set, yields an efficient correlation model.

Extension and acceleration of relativistic density functional theory based on transformed density operator.

We report an extension of relativistic density functional theory (RDFT) within one-component or two-component expressions that relies on a unitary-transformed density operator as well as a unitary-transformed Hamiltonian [Oyama et al., Chem. Phys. Lett. 680, 37 (2017)]. The transformed density operator is introduced to avoid the picture-change effect in the electron density, density gradient, kinetic energy density, and exchange-correlation potential. We confirmed that the implementation based on the spin-free infinite-order Douglas-Kroll-Hess method gives total, orbital, and excitation energies close to the reference values given by four-component RDFT calculations. To reduce the computational cost due to the transformed density operator, the local unitary transformation was also implemented. Numerical assessments revealed that the present scheme enabled the RDFT calculation of polyatomic systems with negligibly small picture-change effect.

RAQET: Large-scale two-component relativistic quantum chemistry program package.

The Relativistic And Quantum Electronic Theory (RAQET) program is a new software package, which is designed for large-scale two-component relativistic quantum chemical (QC) calculations. The package includes several efficient schemes and algorithms for calculations involving large molecules which contain heavy elements in accurate relativistic formalisms. These calculations can be carried out in terms of the two-component relativistic Hamiltonian, wavefunction theory, density functional theory, core potential scheme, and evaluation of electron repulsion integrals. Furthermore, several techniques, which have frequently been used in non-relativistic QC calculations, have been customized for relativistic calculations. This article introduces the brief theories and capabilities of RAQET with several calculation examples. © 2018 Wiley Periodicals, Inc.

Unveiling Controlling Factors of the S0/S1 Minimum Energy Conical Intersection: A Theoretical Study.

The minimum energy conical intersection (MECI) geometries play an important role in photophysics and photochemistry. Although a number of MECI geometries can be identified using quantum chemical methods, their chemical interpretation remains unclear. In this study, a systematic analysis was performed on the MECIs between the singlet (S0) and lowest singlet excited (S1) states of organic molecules. The frozen orbital analysis (FZOA), which approximates the excited states with minimal main configurations, was adopted to analyze the excitation energy components at the S0/S1 MECI geometries as well as the S0 and S1 equilibrium geometries. At the S0/S1 MECI geometries, the HOMO-LUMO gaps decreased as expected but did not disappear. The remaining gaps were balanced with the HOMO-LUMO Coulomb integrals. Furthermore, we discovered that the HOMO-LUMO exchange integrals became approximately zero. On the basis of this fact, a systematic interpretation of the S0/S1 MECI geometries has been described.