A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures.

In this work, three versions of self-consistent field/Kohn-Sham density functional theory (SCF/KS-DFT) orbital optimization are described and benchmarked. The methods are a modified version of the geometry version of the direct inversion in the iterative subspace approach (which we call r-GDIIS), the modified restricted step rational function optimization method (RS-RFO), and the novel subspace gradient-enhanced Kriging method combined with restricted variance optimization (S-GEK/RVO). The modifications introduced are aimed at improving the robustness and computational scaling of the procedures. In particular, the subspace approach in S-GEK/RVO allows the application to SCF/KS-DFT optimization of a machine learning technique that has proven to be successful in geometry optimizations. The performance of the three methods is benchmarked for a large number of small- to medium-sized organic molecules, at equilibrium structures and close to a transition state, and a second set of molecules containing closed- and open-shell transition metals. The results indicate the importance of the resetting technique in boosting the performance of the r-GDIIS procedure. Moreover, it is demonstrated that already at the inception of the subspace version of GEK to optimize SCF wave functions, it displays superior and robust convergence properties as compared to those of the standard state-of-the-art SCF/KS-DFT optimization methods.

Role of conical intersection seam topography in the chemiexcitation of 1,2-dioxetanes.

Chemiexcitation, the generation of electronic excited states by a thermal reaction initiated on the ground state, is an essential step in chemiluminescence, and it is mediated by the presence of a conical intersection that allows a nonadiabatic transition from ground state to excited state. Conical intersections classified as sloped favor chemiexcitation over ground state relaxation. The chemiexcitation yield of 1,2-dioxetanes is known to increase upon methylation. In this work we explore to which extent this trend can be attributed to changes in the conical intersection topography or accessibility. Since conical intersections are not isolated points, but continuous seams, we locate regions of the conical intersection seams that are close to the configuration space traversed by the molecules as they react on the ground state. We find that conical intersections are energetically and geometrically accessible from the reaction trajectory, and that topographies favorable to chemiexcitation are found in all three molecules studied. Nevertheless, the results suggest that dynamic effects are more important for explaining the different yields than the static features of the potential energy surfaces.

Impact of Excited-State Antiaromaticity Relief in a Fundamental Benzene Photoreaction Leading to Substituted Bicyclo[3.1.0]hexenes.

Benzene exhibits a rich photochemistry which can provide access to complex molecular scaffolds that are difficult to access with reactions in the electronic ground state. While benzene is aromatic in its ground state, it is antiaromatic in its lowest ππ* excited states. Herein, we clarify to what extent relief of excited-state antiaromaticity (ESAA) triggers a fundamental benzene photoreaction: the photoinitiated nucleophilic addition of solvent to benzene in acidic media leading to substituted bicyclo[3.1.0]hex-2-enes. The reaction scope was probed experimentally, and it was found that silyl-substituted benzenes provide the most rapid access to bicyclo[3.1.0]hexene derivatives, formed as single isomers with three stereogenic centers in yields up to 75% in one step. Two major mechanism hypotheses, both involving ESAA relief, were explored through quantum chemical calculations and experiments. The first mechanism involves protonation of excited-state benzene and subsequent rearrangement to bicyclo[3.1.0]hexenium cation, trapped by a nucleophile, while the second involves photorearrangement of benzene to benzvalene followed by protonation and nucleophilic addition. Our studies reveal that the second mechanism is operative. We also clarify that similar ESAA relief leads to puckering of S1-state silabenzene and pyridinium ion, where the photorearrangement of the latter is of established synthetic utility. Finally, we identified causes for the limitations of the reaction, information that should be valuable in explorations of similar photoreactions. Taken together, we reveal how the ESAA in benzene and 6π-electron heterocycles trigger photochemical distortions that provide access to complex three-dimensional molecular scaffolds from simple reactants.

Chemi- and Bioluminescence of Cyclic Peroxides.

Bioluminescence is a phenomenon that has fascinated mankind for centuries. Today the phenomenon and its sibling, chemiluminescence, have impacted society with a number of useful applications in fields like analytical chemistry and medicine, just to mention two. In this review, a molecular-orbital perspective is adopted to explain the chemistry behind chemiexcitation in both chemi- and bioluminescence. First, the uncatalyzed thermal dissociation of 1,2-dioxetane is presented and analyzed to explain, for example, the preference for triplet excited product states and increased yield with larger nonreactive substituents. The catalyzed fragmentation reaction and related details are then exemplified with substituted 1,2-dioxetanone species. In particular, the preference for singlet excited product states in that case is explained. The review also examines the diversity of specific solutions both in Nature and in artificial systems and the difficulties in identifying the emitting species and unraveling the color modulation process. The related subject of excited-state chemistry without light absorption is finally discussed. The content of this review should be an inspiration to human design of new molecular systems expressing unique light-emitting properties. An appendix describing the state-of-the-art experimental and theoretical methods used to study the phenomena serves as a complement.

Exact semi-classical light-matter interaction operator applied to two-photon processes with strong relativistic effects.

X-ray processes involve interactions with high-energy photons. For these short wavelengths, the perturbing field cannot be treated as constant, and there is a need to go beyond the electric-dipole approximation. The exact semi-classical light-matter interaction operator offers several advantages compared to the multipole expansion such as improved stability and ease of implementation. Here, the exact operator is used to model x-ray scattering in metal K pre-edges. This is a relativistic two-photon process where absorption is dominated by electric-dipole forbidden transitions. With the restricted active space state-interaction approach, spectra can be calculated even for the multiconfigurational wavefunctions including second-order perturbation. However, as the operator itself depends on the transition energy, the cost for evaluating integrals for hundreds of thousands unique transitions becomes a bottleneck. Here, this is solved by calculating the integrals in a molecular-orbital basis that only runs over the active space, combined with a grouping scheme where the operator is the same for close-lying transitions. This speeds up the calculations of single-photon processes and is critical for the modeling of two-photon scattering processes. The new scheme is used to model Kα resonant inelastic x-ray scattering of iron-porphyrin complexes with relevance to studies of heme enzymes, for which the total computational time is reduced by several orders of magnitude with an effect on transition intensities of 0.1% or less.

Competition between ring-puckering and ring-opening excited state reactions exemplified on 5H-furan-2-one and derivatives.

The influence of ring-puckering on the light-induced ring-opening dynamics of heterocyclic compounds was studied on the sample 5-membered ring molecules γ-valerolactone and 5H-furan-2-one using time-resolved photoelectron spectroscopy and ab initio molecular dynamics simulations. In γ-valerolactone, ring-puckering is not a viable relaxation channel and the only available reaction pathway is ring-opening, which occurs within one vibrational period along the C-O bond. In 5H-furan-2-one, the C=C double bond in the ring allows for ring-puckering which slows down the ring-opening process by about 150 fs while only marginally reducing its quantum yield. This demonstrates that ring-puckering is an ultrafast process, which is directly accessible upon excitation and which spreads the excited state wave packet quickly enough to influence even the outcome of an otherwise expectedly direct ring-opening reaction.

Modern quantum chemistry with [Open]Molcas.

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions.

Mechanism of activated chemiluminescence of cyclic peroxides: 1,2-dioxetanes and 1,2-dioxetanones.

Almost all chemiluminescent and bioluminescent reactions involve cyclic peroxides. The structure of the peroxide and reaction conditions determine the quantum efficiency of light emission. Oxidizable fluorophores, the so-called activators, react with 1,2-dioxetanones promoting the former to their first singlet excited state. This transformation is inefficient and does not occur with 1,2-dioxetanes; however, they have been used as models for the efficient firefly bioluminescence. In this work, we use the SA-CASSCF/CASPT2 method to investigate the activated chemiexcitation of the parent 1,2-dioxetane and 1,2-dioxetanone. Our findings suggest that ground state decomposition of the peroxide competes efficiently with the chemiexcitation pathway, in agreement with the available experimental data. The formation of non-emissive triplet excited species is proposed to explain the low emission efficiency of the activated decomposition of 1,2-dioxetanone. Chemiexcitation is rationalized considering a peroxide/activator supermolecule undergoing an electron-transfer reaction followed by internal conversion.

Optomechanical Control of Quantum Yield in Trans-Cis Ultrafast Photoisomerization of a Retinal Chromophore Model.

The quantum yield of a photochemical reaction is one of the most fundamental quantities in photochemistry, as it measures the efficiency of the transduction of light energy into chemical energy. Nature has evolved photoreceptors in which the reactivity of a chromophore is enhanced by its molecular environment to achieve high quantum yields. The retinal chromophore sterically constrained inside rhodopsin proteins represents an outstanding example of such a control. In a more general framework, mechanical forces acting on a molecular system can strongly modify its reactivity. Herein, we show that the exertion of tensile forces on a simplified retinal chromophore model provokes a substantial and regular increase in the trans-to-cis photoisomerization quantum yield in a counterintuitive way, as these extension forces facilitate the formation of the more compressed cis photoisomer. A rationale for the mechanochemical effect on this photoisomerization mechanism is also proposed.

Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table.

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization.

Molecular and Electronic Structure of Re2Br4(PMe3)4.

The dinuclear rhenium(II) complex Re2Br4(PMe3)4 was prepared from the reduction of [Re2Br8](2-) with (n-Bu4N)BH4 in the presence of PMe3 in propanol. The complex was characterized by single-crystal X-ray diffraction (SCXRD) and UV-visible spectroscopy. It crystallizes in the monoclinic C2/c space group and is isostructural with its molybdenum and technetium analogues. The Re-Re distance (2.2521(3) Å) is slightly longer than the one in Re2Cl4(PMe3)4 (2.247(1) Å). The molecular and electronic structure of Re2X4(PMe3)4 (X = Cl, Br) were studied by multiconfigurational quantum chemical methods. The computed ground-state geometry is in excellent agreement with the experimental structure determined by SCXRD. The calculated total bond order (2.75) is consistent with the presence of an electron-rich triple bond and is similar to the one found for Re2Cl4(PMe3)4. The electronic absorption spectrum of Re2Br4(PMe3)4 was recorded in benzene and shows a series of low-intensity bands in the range 10 000-26 000 cm(-1). The absorption bands were assigned based on calculations of the excitation energies with the multireference wave functions followed by second-order perturbation theory using the CASSCF/CASPT2 method. Calculations predict that the lowest energy band corresponds to the δ* → σ* transition, while the next higher energy bands were attributed to the δ* → π*, δ → σ*, and δ → π* transitions.

Constrained numerical gradients and composite gradients: Practical tools for geometry optimization and potential energy surface navigation.

A method is proposed to easily reduce the number of energy evaluations required to compute numerical gradients when constraints are imposed on the system, especially in connection with rigid fragment optimization. The method is based on the separation of the coordinate space into a constrained and an unconstrained space, and the numerical differentiation is done exclusively in the unconstrained space. The decrease in the number of energy calculations can be very important if the system is significantly constrained. The performance of the method is tested on systems that can be considered as composed of several rigid groups or molecules, and the results show that the error with respect to conventional optimizations is of the order of the convergence criteria. Comparison with another method designed for rigid fragment optimization proves the present method to be competitive. The proposed method can also be applied to combine numerical and analytical gradients computed at different theory levels, allowing an unconstrained optimization with numerical differentiation restricted to the most significant degrees of freedom. This approach can be a practical alternative when analytical gradients are not available at the desired computational level and full numerical differentiation is not affordable.

Smooth Things Come in Threes: A Diabatic Surrogate Model for Conical Intersection Optimization.

The optimization of conical intersection structures is complicated by the nondifferentiability of the adiabatic potential energy surfaces. In this work, we build a pseudodiabatic surrogate model, based on Gaussian process regression, formed by three smooth and differentiable surfaces that can adequately reproduce the adiabatic surfaces. Using this model with the restricted variance optimization method results in a notable decrease of the overall computational effort required to obtain minimum energy crossing points.

Characterizing Conical Intersections in DNA/RNA Nucleobases with Multiconfigurational Wave Functions of Varying Active Space Size.

We characterize the photochemically relevant conical intersections between the lowest-lying accessible electronic excited states of the different DNA/RNA nucleobases using Cholesky decomposition-based complete active space self-consistent field (CASSCF) algorithms. We benchmark two different basis set contractions and several active spaces for each nucleobase and conical intersection type, measuring for the first time how active space size affects conical intersection topographies in these systems and the potential implications these may have toward their description of photoinduced phenomena. Our results show that conical intersection topographies are highly sensitive to the electron correlation included in the model: by changing the amount (and type) of correlated orbitals, conical intersection topographies vastly change, and the changes observed do not follow any converging pattern toward the topographies obtained with the largest and most correlated active spaces. Comparison across systems shows analogous topographies for almost all intersections mediating population transfer to the dark 1nO/Nπ* states, while no similarities are observed for the "ethylene-like" conical intersection ascribed to mediate the ultrafast decay component to the ground state in all DNA/RNA nucleobases. Basis set size seems to have a minor effect, appearing to be relevant only for purine-based derivatives. We rule out structural changes as a key factor in classifying the different conical intersections, which display almost identical geometries across active space and basis set change, and we highlight instead the importance of correctly describing the electronic states involved at these crossing points. Our work shows that careful active space selection is essential to accurately describe conical intersection topographies and therefore to adequately account for their active role in molecular photochemistry.

The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry.

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

Regularized CASPT2: an Intruder-State-Free Approach.

In this work we present a new approach to fix the intruder-state problem (ISP) in CASPT2 based on σp regularization. The resulting σp-CASPT2 method is compared to previous techniques, namely, the real and imaginary level shifts, on a theoretical basis and by performing a series of systematic calculations. The analysis is focused on two aspects, the effectiveness of σp-CASPT2 in removing the ISP and the sensitivity of the approach with respect to the input parameter. We found that σp-CASPT2 compares favorably with respect to previous approaches and that different versions, σ1-CASPT2 and σ2-CASPT2, have different potential application domains. This analysis also reveals the unsuitability of the real level shift technique as a general way to avoid the intruder-state problem.

Photophysical characterization and fluorescence cell imaging applications of 4-N-substituted benzothiadiazoles.

In this work, a series of fluorescent 2,1,3-benzothiadiazole derivatives with various N-substituents in the 4-position was synthesized and photophysically characterized in various solvents. Three compounds emerged as excellent fluorescent probes for imaging lipid droplets in cancer cells. A correlation between their high lipophilicity and lipid droplet specificity could be found, with log P ≥ 4 being characteristic for lipid droplet accumulation.

Study on the conformational equilibrium of the alanine dipeptide in water solution by using the averaged solvent electrostatic potential from molecular dynamics methodology.

The ASEP/MD method has been employed for studying the solvent effect on the conformational equilibrium of the alanine dipeptide in water solution. MP2 and density functional theory (DFT) levels of theory were used and results were compared. While in gas phase cyclic structures showing intramolecular hydrogen bonds were found to be the most stable, the stability order is reversed in water solution. Intermolecular interaction with the solvent causes the predominance of extended structures as the stabilizing contacts dipeptide-water are favoured. Free-energy differences in solution were calculated and PPII, α(R), and C5 conformers were identified as the most stable at MP2 level. Experimental data from Raman and IR techniques show discrepancies about the relative abundance of α(R) y C5, our results support the Raman data. The DFT level of theory agrees with MP2 in the location and stability of PPII and α(R) forms but fails in the location of C5. MP2 results suggest the possibility of finding traces of C7eq conformer in water solution, in agreement with recent experiments.

Restricted-Variance Constrained, Reaction Path, and Transition State Molecular Optimizations Using Gradient-Enhanced Kriging.

Gaussian process regression has recently been explored as an alternative to standard surrogate models in molecular equilibrium geometry optimization. In particular, the gradient-enhanced Kriging approach in association with internal coordinates, restricted-variance optimization, and an efficient and fast estimate of hyperparameters has demonstrated performance on par or better than standard methods. In this report, we extend the approach to constrained optimizations and transition states and benchmark it for a set of reactions. We compare the performance of the newly developed method with the standard techniques in the location of transition states and in constrained optimizations, both isolated and in the context of reaction path computation. The results show that the method outperforms the current standard in efficiency as well as in robustness.

How machine learning can assist the interpretation of ab initio molecular dynamics simulations and conceptual understanding of chemistry.

Molecular dynamics simulations are often key to the understanding of the mechanism, rate and yield of chemical reactions. One current challenge is the in-depth analysis of the large amount of data produced by the simulations, in order to produce valuable insight and general trends. In the present study, we propose to employ recent machine learning analysis tools to extract relevant information from simulation data without a priori knowledge on chemical reactions. This is demonstrated by training machine learning models to predict directly a specific outcome quantity of ab initio molecular dynamics simulations - the timescale of the decomposition of 1,2-dioxetane. The machine learning models accurately reproduce the dissociation time of the compound. Keeping the aim of gaining physical insight, it is demonstrated that, in order to make accurate predictions, the models evidence empirical rules that are, today, part of the common chemical knowledge. This opens the way for conceptual breakthroughs in chemistry where machine analysis would provide a source of inspiration to humans.