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.

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.

Simulation Reveals the Chameleonic Behavior of Macrocycles.

Conformational analysis is central to the design of bioactive molecules. It is particularly challenging for macrocycles due to noncovalent transannular interactions, steric interactions, and ring strain that are often coupled. Herein, we simulated the conformations of five macrocycles designed to express a progression of increasing complexity in environment-dependent intramolecular interactions and verified the results against NMR measurements in chloroform and dimethyl sulfoxide. Molecular dynamics using an explicit solvent model, but not the Monte Carlo method with implicit solvation, handled both solvents correctly. Refinement of conformations at the ab initio level was fundamental to reproducing the experimental observations─standard state-of-the-art molecular mechanics force fields were insufficient. Our simulations correctly predicted the intramolecular interactions between side chains and the macrocycle and revealed an unprecedented solvent-induced conformational switch of the macrocyclic ring. Our results provide a platform for the rational, prospective design of molecular chameleons that adapt to the properties of the environment.

P,N-Chelated Gold(III) Complexes: Structure and Reactivity.

Gold(III) complexes are versatile catalysts offering a growing number of new synthetic transformations. Our current understanding of the mechanism of homogeneous gold(III) catalysis is, however, limited, with that of phosphorus-containing complexes being hitherto underexplored. The ease of phosphorus oxidation by gold(III) has so far hindered the use of phosphorus ligands in the context of gold(III) catalysis. We present a method for the generation of P,N-chelated gold(III) complexes that circumvents ligand oxidation and offers full counterion control, avoiding the unwanted formation of AuCl4-. On the basis of NMR spectroscopic, X-ray crystallographic, and density functional theory analyses, we assess the mechanism of formation of the active catalyst and of gold(III)-mediated styrene cyclopropanation with propargyl ester and intramolecular alkoxycyclization of 1,6-enyne. P,N-chelated gold(III) complexes are demonstrated to be straightforward to generate and be catalytically active in synthetically useful transformations of complex molecules.

On the role of symmetry in XDW-CASPT2.

Herewith, we propose two new exponents for the recently introduced XDW-CASPT2 method [S. Battaglia and R. Lindh, J. Chem. Theory Comput. 16, 1555-1567 (2020)], which fix one of the largest issues hindering this approach. By using the first-order effective Hamiltonian coupling elements, the weighting scheme implicitly takes into account the symmetry of the states, thereby averaging Fock operators only if the zeroth-order wave functions interact with each other. The use of Hamiltonian couplings also provides a physically sounder approach to quantitate the relative weights; however, it introduces new difficulties when these rapidly die off to zero. The improved XDW-CASPT2 method is critically tested on several systems of photochemical relevance, and it is shown that it succeeds in its original intent of maintaining MS-CASPT2 accuracy for the evaluation of transition energies and at the same time providing smooth potential energy surfaces around near-degenerate points akin to XMS-CASPT2.

Analytic gradients for multiconfiguration pair-density functional theory with density fitting: Development and application to geometry optimization in the ground and excited states.

Density fitting reduces the computational cost of both energy and gradient calculations by avoiding the computation and manipulation of four-index electron repulsion integrals. With this algorithm, one can efficiently optimize the geometries of large systems with an accurate multireference treatment. Here, we present the derivation of multiconfiguration pair-density functional theory for energies and analytic gradients with density fitting. Six systems are studied, and the results are compared to those obtained with no approximation to the electron repulsion integrals and to the results obtained by complete active space second-order perturbation theory. With the new approach, there is an increase in the speed of computation with a negligible loss in accuracy. Smaller grid sizes have also been used to reduce the computational cost of multiconfiguration pair-density functional theory with little effect on the optimized geometries and gradient values.

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.

Simulations of valence excited states in coordination complexes reached through hard X-ray scattering.

Hard X-ray spectroscopy selectively probes metal sites in complex environments. Resonant inelastic X-ray scattering (RIXS) makes it is possible to directly study metal-ligand interactions through local valence excitations. Here multiconfigurational wavefunction simulations are used to model valence K pre-edge RIXS for three metal-hexacyanide complexes by coupling the electric dipole-forbidden excitations with dipole-allowed valence-to-core emission. Comparisons between experimental and simulated spectra makes it possible to evaluate the simulation accuracy and establish a best-modeling practice. The calculations give correct descriptions of all LMCT excitations in the spectra, although energies and intensities are sensitive to the description of dynamical electron correlation. The consistent treatment of all complexes shows that simulations can rationalize spectral features. The dispersion in the manganese(iii) spectrum comes from unresolved multiple resonances rather than fluorescence, and the splitting is mainly caused by differences in spatial orientation between holes and electrons. The simulations predict spectral features that cannot be resolved in current experimental data sets and the potential for observing d-d excitations is also explored. The latter can be of relevance for non-centrosymmetric systems with more intense K pre-edges. These ab initio simulations can be used to both design and interpret high-resolution X-ray scattering experiments.

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.

Non-radiative decay and fragmentation in water molecules after 1a1 -14a1 excitation and core ionization studied by electron-energy-resolved electron-ion coincidence spectroscopy.

In this paper, we examine decay and fragmentation of core-excited and core-ionized water molecules combining quantum chemical calculations and electron-energy-resolved electron-ion coincidence spectroscopy. The experimental technique allows us to connect electronic decay from core-excited states, electronic transitions between ionic states, and dissociation of the molecular ion. To this end, we calculate the minimum energy dissociation path of the core-excited molecule and the potential energy surfaces of the molecular ion. Our measurements highlight the role of ultra-fast nuclear motion in the 1a1 -14a1 core-excited molecule in the production of fragment ions. OH+ fragments dominate for spectator Auger decay. Complete atomization after sequential fragmentation is also evident through detection of slow H+ fragments. Additional measurements of the non-resonant Auger decay of the core-ionized molecule (1a1 -1) to the lower-energy dication states show that the formation of the OH+ + H+ ion pair dominates, whereas sequential fragmentation OH+ + H+ → O + H+ + H+ is observed for transitions to higher dication states, supporting previous theoretical investigations.

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.

Molecular Basis of the Chemiluminescence Mechanism of Luminol.

Light emission from luminol is probably one of the most popular chemiluminescence reactions due to its use in forensic science, and has recently displayed promising applications for the treatment of cancer in deep tissues. The mechanism is, however, very complex and distinct possibilities have been proposed. By efficiently combining DFT and CASPT2 methodologies, the chemiluminescence mechanism has been studied in three steps: 1) luminol oxygenation to generate the chemiluminophore, 2) a chemiexcitation step, and 3) generation of the light emitter. The findings demonstrate that the luminol double-deprotonated dianion activates molecular oxygen, diazaquinone is not formed, and the chemiluminophore is formed through the concerted addition of oxygen and concerted elimination of nitrogen. The peroxide bond, in comparison to other isoelectronic chemical functionalities (-NH-NH-, -N- -N- -, and -S-S-), is found to have the best chemiexcitation efficiency, which allows the oxygenation requirement to be rationalized and establishes general design principles for the chemiluminescence efficiency. Electron transfer from the aniline ring to the OO bond promotes the excitation process to create an excited state that is not the chemiluminescent species. To produce the light emitter, proton transfer between the amino and carbonyl groups must occur; this requires highly localized vibrational energy during chemiexcitation.

Dynamically weighted multireference perturbation theory: Combining the advantages of multi-state and state-averaged methods.

We introduce two new approaches to compute near-degenerate electronic states based on the driven similarity renormalization group (DSRG) framework. The first approach is a unitary multi-state formalism based on the DSRG (MS-DSRG), whereby an effective Hamiltonian is built from a set of state-specific solutions. The second approach employs a dynamic weighting parameter to smoothly interpolate between the multi-state and the state-averaged DSRG schemes. The resulting dynamically weighted DSRG (DW-DSRG) theory incorporates the most desirable features of both multi-state approaches (ability to accurately treat many states) and state-averaged methods (correct description of avoided crossings and conical intersections). We formulate second-order perturbation theories (PT2) based on the MS- and DW-DSRG and study the potential energy curves of LiF, the conical intersection of the two lowest singlet states of NH3, and several low-lying excited states of benzene, naphthalene, and anthracene. The DW-DSRG-PT2 predicts the correct avoided crossing of LiF and avoids artifacts produced by the corresponding state-specific and multi-state theories. Excitation energies of the acenes computed with the DW-DSRG-PT2 are found to be more accurate than the corresponding state-averaged values, showing a small dependence on the number of states computed.

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.

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.

Analysis of a Compound Class with Triplet States Stabilized by Potentially Baird Aromatic [10]Annulenyl Dicationic Rings.

The low-lying triplet state of a recently published compound (TMTQ) was analyzed quantum chemically in light of suggestions that it is influenced by Baird aromaticity. Two mesomeric structures describe this state: 1) a zwitterionic Baird aromatic structure with a triplet diradical 8π-electron methano[10]annulene (M10A) dicationic ring and 2) a Hückel aromatic with a neutral closed-shell 10π-electron ring. According to charge and spin density distributions, the Hückel aromatic structure dominates the triplet state (the Baird aromatic contributes at most 12 %), and separation of the aromatic fluctuation index (FLU) into α and ß electron contributions emphasizes this finding. The small singlet-triplet energy gap is due to Hückel aromaticity of the M10A ring, clarified by comparison to the smaller analogues of TMTQ. Yet, TMTQ and its analogues are Hückel-Baird hybrids allowing for tuning between closed-shell 4n+2 Hückel aromaticity and open-shell 4n Baird aromaticity.

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.

A surface hopping algorithm for nonadiabatic minimum energy path calculations.

The article introduces a robust algorithm for the computation of minimum energy paths transiting along regions of near-to or degeneracy of adiabatic states. The method facilitates studies of excited state reactivity involving weakly avoided crossings and conical intersections. Based on the analysis of the change in the multiconfigurational wave function the algorithm takes the decision whether the optimization should continue following the same electronic state or switch to a different state. This algorithm helps to overcome convergence difficulties near degeneracies. The implementation in the MOLCAS quantum chemistry package is discussed. To demonstrate the utility of the proposed procedure four examples of application are provided: thymine, asulam, 1,2-dioxetane, and a three-double-bond model of the 11-cis-retinal protonated Schiff base.