Combined gradient projection/single component artificial force induced reaction (GP/SC-AFIR) method for an efficient search of minimum energy conical intersection (MECI) geometries

Minimum-Energy Conical Intersections by Compressed Multistate Pair-Density Functional Theory

Compressed multistate pair-density functional theory (CMS-PDFT) is a multistate version of multiconfiguration pair-density functional theory that can capture the correct topology of coupled potential energy surfaces (PESs) around conical intersections. In this work, we develop interstate coupling vectors (ISCs) for CMS-PDFT in the OpenMolcas and PySCF/mrh electronic structure packages. Yet, the main focus of this work is using ISCs to calculate minimum-energy conical intersections (MECIs) by CMS-PDFT. This is performed using the projected constrained optimization method in OpenMolcas, which uses ISCs to restrain the iterations to the conical intersection seam. We optimize the S1/S0 MECIs for ethylene, butadiene, and benzene and show that CMS-PDFT gives smooth PESs in the vicinities of the MECIs. Furthermore, the CMS-PDFT MECIs are in good agreement with the MECI calculated by the more expensive XMS-CASPT2 method.

Insights into the Luminescence Quantum Yields of Cyclometalated Iridium(III) Complexes: A Density Functional Theory and Machine Learning Approach

Cyclometalated iridium(III) complexes have been used in various optical materials, including organic light-emitting diodes (OLEDs) and photocatalysts, and a deeper understanding and prediction of their luminescence quantum yields (LQYs) greatly aid in accelerating material design. In this study, we integrated density functional theory (DFT) calculations with machine learning (ML) techniques to extract factors controlling LQY. Although a substantial data set of Ir(III) complexes and their LQYs is indispensable for constructing accurate ML models to predict LQYs, generating this type of data set is challenging due to the complexities associated with ab initio calculations of LQYs. To address this issue, we investigated the nonradiative decay process of nine Ir(III) complexes emitting blue to green, each exhibiting varying experimental LQYs, by using DFT calculations. For all nine complexes, the quenching process was induced by the rotation of the single bond in one of the ligands, which converted the six-coordinate structure to the five-coordinate structure. Since the decay mechanism was common for the nine Ir(III) complexes, parameters correlated with LQYs could be used as objective variables instead of LQYs. Based on this idea, we collected a data set featuring Ir(III) complexes and the energy differences between their six- and five-coordinate triplet structures, which correlated with LQYs. We also constructed ML models using the calculated LQYs as the objective variables with the parameters from the ground-state calculations as explanatory variables. The analyses of the constructed model revealed that the LUMO energy of the ligand made the most significant negative contribution to LQY. This suggests that the potential energy surface of the metal-to-ligand charge transfer (MLCT) excited state, which stabilizes the six-coordinate structure, is reduced by decreasing the energy of the unoccupied orbitals.

Oxidation and Reduction Pathways in the Knowles Hydroamination via a Photoredox-Catalyzed Radical Reaction

Systematic reaction path exploration revealed the entire mechanism of Knowles's light-promoted catalytic intramolecular hydroamination. Bond formation/cleavage competes with single electron transfer (SET) between the catalyst and substrate. These processes are described by adiabatic processes through transition states in an electronic state and non-radiative transitions through the seam of crossings (SX) between different electronic states. This study determined the energetically favorable SET path by introducing a practical computational model representing SET as non-adiabatic transitions via SXs between substrate's potential energy surfaces for different charge states adjusted based on the catalyst's redox potential. Calculations showed that the reduction and proton shuttle process proceeded concertedly. Also, the relative importance of SET paths (giving the product and leading back to the reactant) varies depending on the catalyst's redox potential, affecting the yield.

Substitution effect on the nonradiative decay and trans → cis photoisomerization route: a guideline to develop efficient cinnamate-based sunscreens

Cinnamate derivatives are very useful as UV protectors in nature and as sunscreen reagents in daily life. They convert harmful UV energy to thermal energy through effective nonradiative decay (NRD) including trans → cis photoisomerization. However, the mechanism is not simple because different photoisomeirzation routes have been observed for different substituted cinnamates. Here, we theoretically examined the substitution effects at the phenyl ring of methylcinnamate (MC), a non-substituted cinnamate, on the electronic structure and the NRD route involving trans → cis isomerization based on time-dependent density functional theory. A systematic reaction pathway search using the single-component artificial force-induced reaction method shows that the very efficient photoisomerization route of MC can be essentially described as "1ππ* (trans) → 1nπ* → T1 (3ππ*) → S0 (trans or cis)". We found that for efficient 1ππ* (trans) → 1nπ* internal conversion (IC), MC should have the substituent at the appropriate position of the phenyl ring to stabilize the highest occupied π orbital. Substitution at the para position of MC slightly lowers the 1ππ* state energy and photoisomerization occurs via a slightly less efficient "1ππ* (trans) → 3nπ* → T1 (3ππ*) → S0 (trans or cis)" pathway. Substitution at the meta or ortho positions of MC significantly lowers the 1ππ* state energy so that the energy barrier of IC (1ππ* → 1nπ*) becomes very high. This substitution leads to a much longer 1ππ* state lifetime than that of MC and para-substituted MC, and a change in the dominant photoisomerization route to "1ππ* (trans) → C[double bond, length as m-dash]C bond twisting on 1ππ* → S0 (trans or cis)". As a whole, the "1ππ* → 1nπ*" IC observed in MC is the most important initial step for the rapid change of UV energy to thermal energy. We also found that the stabilization of the π orbital (i) minimizes the energy gap between 1ππ* and 1nπ* at the 1ππ* minimum and (ii) makes the 0-0 level of 1ππ* higher than 1nπ* as observed in MC. These MC-like relationships between the 1ππ* and 1nπ* energies should be ideal to maximize the "1ππ* → 1nπ*" IC rate constant according to Marcus theory.

Analytical First-Order Derivatives of Second-Order Extended Multiconfiguration Quasi-Degenerate Perturbation Theory (XMCQDPT2): Implementation and Application

Analytical gradient theory for the second-order extended multiconfiguration quasi-degenerate perturbation theory (XMCQDPT2), which can be regarded as the multistate version of the multireference second-order Møller-Plesset perturbation theory (MRMP2), is formulated and implemented. The theory is similar to the previous analytical gradient theory for MCQDPT2, but we take into account the intruder state avoidance (ISA) technique and the "extension" of the MCQDPT2 theory by Granovsky. Although the (X)MCQDPT2 theory is not invariant with respect to rotations among the active orbitals, the resulting analytical gradients are accurate. We demonstrate the utility of the current algorithm in optimizing the minimum energy conical intersections (MECIs) of ethylene, butadiene, benzene, the retinal model chromophore PSB3, and the green fluorescent protein model chromophore pHBI. The XMCQDPT2 MECIs are very similar to the XMS-CASPT2 MECIs in terms of molecular conformation and the computed energies. We also discuss possible improvements of the current algorithm.

Different photoisomerization routes found in the structural isomers of hydroxy methylcinnamate

An experimental and theoretical study has been carried out to elucidate the nonradiative decay (NRD) and trans(E) → cis(Z) isomerization from the S1 (1ππ*) state of structural isomers of hydroxy methylcinnamate (HMC); ortho-, meta- and para-HMC (o-, m- and p-HMC). A low temperature matrix-isolation Fourier Transform Infrared (FTIR) spectroscopic study revealed that all the HMCs are cis-isomerized upon UV irradiation. A variety of laser spectroscopic methods have been utilized for jet-cooled gas phase molecules to investigate the vibronic structure and lifetimes of the S1 state, and to detect the transient state appearing in the NRD process. In p-HMC, the zero-point level of the S1 state decays as quickly as 9 ps. A transient electronic state reported by Tan et al. (Faraday Discuss. 2013, 163, 321-340) was reinvestigated by nanosecond UV-tunable deep UV pump-probe spectroscopy and was assigned to the T1 state. For m- and o-HMC, the lifetime at the zero-point energy level of S1 is 10 ns and 6 ns, respectively, but it becomes substantially shorter at an excess energy higher than 1000 cm-1 and 600 cm-1, respectively, indicating the onset of NRD. Different from p-HMC, no transient state (T1) was observed in m- nor o-HMC. These experimental results are interpreted with the aid of TDDFT calculations by considering the excited-state reaction pathways and the radiative/nonradiative rate constants. It is concluded that in p-HMC, the trans → cis isomerization proceeds via a [trans-S1 → 1nπ* → T1 → cis-S0] scheme. On the other hand, in o- and m-HMC, the isomerization proceeds via a [trans-S1 → twisting along the C[double bond, length as m-dash]C double bond by 90° on S1 → cis-S0] scheme. The calculated barrier height along the twisting coordinate agrees well with the observed onset of the NRD channel for both o- and m-HMC.

Exploring radiative and nonradiative decay paths in indole, isoindole, quinoline, and isoquinoline

Radiative and nonradiative decay paths from the first excited singlet electronic state (S₁) in four heteroaromatics, indole, isoindole, quinoline, and isoquinoline, were systematically explored.

Implementation and performance of the artificial force induced reaction method in the GRRM17 program

This article reports implementation and performance of the artificial force induced reaction (AFIR) method in the upcoming 2017 version of GRRM program (GRRM17). The AFIR method, which is one of automated reaction path search methods, induces geometrical deformations in a system by pushing or pulling fragments defined in the system by an artificial force. In GRRM17, three different algorithms, that is, multicomponent algorithm (MC-AFIR), single-component algorithm (SC-AFIR), and double-sphere algorithm (DS-AFIR), are available, where the MC-AFIR was the only algorithm which has been available in the previous 2014 version. The MC-AFIR does automated sampling of reaction pathways between two or more reactant molecules. The SC-AFIR performs automated generation of global or semiglobal reaction path network. The DS-AFIR finds a single path between given two structures. Exploration of minimum energy structures within the hypersurface in which two different electronic states degenerate, and an interface with the quantum mechanics/molecular mechanics method, are also described. A code termed SAFIRE will also be available, as a visualization software for complicated reaction path networks. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.