Multireference Electronic Structure Research Articles

Computational Modeling of the Conformation-Dependent Atmospheric Reactivity of Criegee Intermediates.

The impacts of Criegee intermediates (CIs) on atmospheric chemistry depend significantly on the CI conformation. In this Perspective, I highlight examples of how electronic structure and statistical rate theory calculations, in conjunction with experiment, have revealed conformation-dependent details of both CI ground-state reactivity and electronic excitation. Calculations using single-reference electronic structure methods and conventional transition state theory have predicted that CIs with syn-alkyl or syn-vinyl substituents isomerize rapidly to vinyl hydroperoxides (VHPs) or dioxoles, both of which can decompose rapidly under atmospheric conditions. Ongoing computational research on hydroxyl radical (OH) roaming initiated by VHP dissociation requires the application of multireference electronic structure methods and variational transition state theory. CIs that lack both syn-alkyl and syn-vinyl substituents undergo either bimolecular reaction or π* ← π electronic excitation in the atmosphere. Accurate predictions of CI ultraviolet-visible spectra require multireference calculations with large active spaces and at least a second-order perturbative treatment of dynamic electron correlation. The extent to which electronic spectra can be diagnostic of the presence of specific CI conformers varies significantly with CI chemical identity.

Forte: A suite of advanced multireference quantum chemistry methods.

Forte is an open-source library specialized in multireference electronic structure theories for molecular systems and the rapid prototyping of new methods. This paper gives an overview of the capabilities of Forte, its software architecture, and examples of applications enabled by the methods it implements.

Toward Accurate Spin-Orbit Splittings from Relativistic Multireference Electronic Structure Theory.

Most nonrelativistic electron correlation methods can be adapted to account for relativistic effects, as long as the relativistic molecular spinor integrals are available, from either a four-, two-, or one-component mean-field calculation. However, relativistic multireference correlation methods remain a relatively unexplored area, with mixed evidence regarding the improvements brought by perturbative treatments. We report, for the first time, the implementation of state-averaged four-component relativistic multireference perturbation theories to second and third order based on the driven similarity renormalization group (DSRG). With our methods, named 4c-SA-DSRG-MRPT2 and 3, we find that the dynamical correlation included on top of 4c-CASSCF references can significantly improve the spin-orbit splittings in p-block elements and potential energy surfaces when compared to 4c-CASSCF and 4c-CASPT2 results. We further show that 4c-DSRG-MRPT2 and 3 are applicable to these systems over a wide range of the flow parameter, with systematic improvement from second to third order in terms of both improved error statistics and reduced sensitivity with respect to the flow parameter.

WFOT: A Wave Function Overlap Tool between Single- and Multi-Reference Electronic Structure Methods for Spectroscopy Simulation.

We report the development of a novel diagnostic tool, named wave function overlap tool (WFOT), designed to evaluate the overlap between wave functions computed at single-reference [i.e., time-dependent density functional theory or configuration interaction singles (CIS)] and multireference (i.e., CASSCF/CASPT2) electronic structure levels of theory. It relies on truncating the single- and multireference WFs to CIS-like expansions spanning the same configurational space and maximizing the molecular orbital overlap by means of a unitary transformation. To demonstrate the functionality of the tool, we calculate the transient spectrum of acetylacetone by evaluating excited state absorption signals with multireference quality on top of single-reference on-the-fly dynamics simulations. Semiautomatic spectra generation is facilitated by interfacing the tool with the COBRAMM package, which also allows one to use WFOT with several quantum chemistry codes such as Gaussian, NWChem, and OpenMolcas. Other exciting possibilities for the utilization of the code beyond the simulation of transient absorption spectroscopy are eventually discussed.

Development of Parallel On-the-Fly Crystal Algorithm for Global Exploration of Conical Intersection Seam Space.

Conical intersection (CI) seams are configuration spaces of a molecular system where two or more (spin) adiabatic electronic states are degenerate in energy. They play essential roles in photochemistry because nonradiative decays often occur near the minima of the seam, i.e., the minimum energy CIs (MECIs). Thus, it is important to explore the CI seams and discover the MECIs. Although various approaches exist for CI seam exploration, most of them are local in nature, requiring reasonable initial guesses of geometries and nuclear gradients during the search. Global search algorithms, on the other hand, are powerful because they can fully sample the configurational space and locate important MECIs missed by local algorithms. However, global algorithms are often computationally expensive for large systems due to their poor scalability with respect to the number of degrees of freedom. To overcome this challenge, we develop the parallel on-the-fly Crystal algorithm to globally explore the CI seam space, taking advantage of its superior scaling behavior. Specifically, Crystal is coupled with on-the-fly evaluations of the excited and ground state energies using multireference electronic structure methods. Meanwhile, the algorithm is parallelized to further boost its computational efficiency. The effectiveness of this new algorithm is tested for three types of molecular photoswitches of significant importance in material and biomedical sciences: photostatin (PST), stilbene, and butadiene. A rudimentary implementation of the algorithm is applied to PST and stilbene, resulting in the discovery of all previously identified MECIs and several new ones. A refined version of the algorithm, combined with a systematic clustering technique, is applied to butadiene, resulting in the identification of an unprecedented number of energetically accessible MECIs. The results demonstrate that the parallel on-the-fly Crystal algorithm is a powerful tool for automated global CI seam exploration.

Which Electronic Structure Method to Choose in Trajectory Surface Hopping Dynamics Simulations? Azomethane as a Case Study.

Nonadiabatic dynamics simulations have become a standard approach to explore photochemical reactions. Such simulations require underlying potential energy surfaces and couplings between them, calculated at a chosen level of theory, yet this aspect is rarely assessed. Here, in combination with the popular trajectory surface hopping dynamics method, we use a high-accuracy XMS-CASPT2 electronic structure level as a benchmark for assessing the performances of various post-Hartree-Fock methods (namely, CIS, ADC(2), CC2, and CASSCF) and exchange-correlation functionals (PBE, PBE0, and CAM-B3LYP) in a TD-DFT/TDA context, using the isomerization around a double bond as test case. Different relaxation pathways are identified, and the ability of the different methods to reproduce their relative importance and time scale is discussed. The results show that multireference electronic structure methods should be preferred, when studying nonadiabatic decay between excited and ground states. If not affordable, TD-DFT with TDA and hybrid functionals and ADC(2) are efficient alternatives but overestimate the nonradiative decay yield and thus may miss deexcitation pathways.

Insights into dioxygen binding on metal centers: an ab initio multireference electronic structure analysis.

Why does binding of dioxygen (O2) to metal centers, the initial step of O2 storage, transportation, and activation, almost inevitably induce metal-to-O2 single-electron transfer and generate superoxo (O2-˙) species, instead of genuine O02 adducts? To address this question, this study describes highly correlated wavefunction-based ab initio calculations using CASSCF/NEVPT2 (CASSCF = complete active space self-consistent field, and NEVPT2 = N-electron valence state second-order perturbation theory) approaches to explore the electronic-structure evolution of O2 association on Fe(II)(BDPP) (H2BDPP = 2,6-bis((2-(S)-diphenylhydroxylmethyl-1-pyrrolidinyl)methyl)pyridine) and Co(II)(BDPP) to produce S = 3 Fe(III)(BDPP)(O2-˙) (1) and Co(III)(BDPP)(O2-˙) (2). CASSCF/NEVPT2 calculations suggest that the processes furnishing 1 and 2 feature an avoided crossing resulting from interactions of two diabatic curves, of which one is characterized as Co(II) and Fe(II) centers interacting with a triplet O2 ligand and the other as Co(III) and Fe(III) centers bound to a superoxo ligand. In both cases, the avoided crossing induces a one-electron transfer from the divalent metal center to the incoming O2 ligand and leads to formation of trivalent metal-O2-˙ complexes. To facilitate the interpretation of complicated multireference wavefunctions, we formulated two-fragment spin eigenfunctions utilizing Clebsch-Gordan coefficients (CGCs) to rationalize computed spin populations on the metal centers and the O2 ligand and compared these results with usual valence bonding (VB) analyses. It turns out that both methods give the same results and are complementary to each other. Finally, the limitation of DFT approaches in describing complex electronic structures involving metal-ligand magnetic couplings is delineated.

Vibrational spectroscopy and dissociation dynamics of cyclohexyl hydroperoxide.

Organic hydroperoxides (ROOH) are ubiquitous in the atmospheric oxidation of volatile organic compounds (VOCs) as well as in low-temperature oxidation of hydrocarbon fuels. The present work focuses on a prototypical cyclic hydroperoxide, cyclohexyl hydroperoxide (CHHP). The overtone OH stretch (2νOH) spectrum of jet-cooled CHHP is recorded by IR multiphoton excitation with UV laser-induced fluorescence detection of the resulting OH products. A distinctive IR feature is observed at 7012.5 cm-1. Two conformers of CHHP are predicted to have similar stabilities (within 0.2 kcal mol-1) and overtone OH stretch transitions (2νOH), yet are separated by a significant interconversion barrier. The IR power dependence indicates that absorption of three or more IR photons is required for dissociation of CHHP to cyclohexoxy (RO) and OH radical products. Accompanying high-level single- and multi-reference electronic structure calculations quantitatively support the experimental results. Calculations are extended to a range of organic hydroperoxides to examine trends in bond dissociation energies associated with RO + OH formation and compared with prior theoretical results.

OH Roaming during the Ozonolysis of α-Pinene: A New Route to Highly Oxygenated Molecules?

The formation of low-volatility organic compounds in the ozonolysis of α-pinene, the dominant atmospheric monoterpene, provides an important route to aerosol formation. In this work, we consider a previously unexplored set of pathways for the formation of highly oxygenated molecules in α-pinene ozonolysis. Pioneering, direct experimental observations of Lester and co-workers have demonstrated a significant production of hydroxycarbonyl products in the dissociation of Criegee intermediates. Theoretical analyses indicate that this production arises from OH roaming-induced pathways during the OO fission of the vinylhydroperoxides (VHPs), which in turn come from internal H transfers in the Criegee intermediates. Ab initio kinetics computations are used here to explore the OH roaming-induced channels that arise from the ozonolysis of α-pinene. For computational reasons, the calculations consider a surrogate for α-pinene, where two spectator methyl groups are replaced with H atoms. Multireference electronic structure calculations are used to illustrate a variety of energetically accessible OH roaming pathways for the four VHPs arising from the ozonolysis of this α-pinene surrogate. Ab initio transition-state theory-based master equation calculations indicate that for the dissociation of stabilized VHPs, these OH roaming pathways are kinetically significant with a branching that generally increases from ∼20% at room temperature up to ∼70% at lower temperatures representative of the troposphere. For one of the VHPs, this branching already exceeds 60% at room temperature. For the overall ozonolysis process, these branching ratios would be greatly reduced by a limited branching to the stabilized VHP, although there would also be some modest roaming fraction for the nonthermal VHP dissociation process. The strong exothermicities of the roaming-induced isomerizations/additions and abstractions suggest new routes to fission of the cyclobutane rings. Such ring fissions would facilitate further autoxidation reactions, thereby providing a new route for producing highly oxygenated nonvolatile precursors to aerosol formation.

Core-level spectroscopy of the photodissociation process of BrCN molecule

Fewest-switches surfacing hopping (FSSH) simulations have been performed with the high-level multi-reference electronic structure method to explore the coupled electronic and nuclear dynamics upon photoexcitation of cyanogen bromide (BrCN). The potential energy surfaces (PES) of BrCN are charted as functions of the Jacobi coordinates (R, θ). An in-depth examination of the FSSH trajectories reveals the temporal dynamics of the molecule and the population changes of the lowest twelve states during BrCN’s photodissociation process, which presents a rich tapestry of dynamical information. Furthermore, the carbon K-edge x-ray absorption spectroscopy (XAS) is calculated with multi-reference inner-shell spectral simulations. The rotation of the CN fragment and the elongation of the C–Br bond are found to be the reason for the peak shifting in the XAS. Our findings offer a nuanced interpretation for inner-shell probe investigations of BrCN, setting the stage for a deeper understanding of the photodissociation process of cyanogen halides molecules.

Understanding Antiferromagnetic and Ligand Field Effects on Spin Crossover in a Triple-Decker Dimeric Cr(II) Complex.

Two possible explanations for the temperature dependence of spin-crossover (SCO) behavior in the dimeric triple-decker Cr(II) complex ([(η5-C5Me5)Cr(μ2:η5-P5)Cr(η5-C5Me5)]+) have been offered. One invokes variations in antiferromagnetic interactions between the two Cr(II) ions, whereas the other posits the development of a strong ligand-field effect favoring the low-spin ground state. We perform multireference electronic structure calculations based on the multiconfiguration pair-density functional theory to resolve these effects. We find quintet, triplet, and singlet electronic ground states, respectively, for the experimental geometries at high, intermediate, and low temperatures. The ground-state transition from quintet to triplet at an intermediate temperature derives from increased antiferromagnetic interactions between the two Cr(II) ions. By contrast, the ground-state transition from triplet to singlet at low temperature can be attributed to increased ligand-field effects, which dominate with continued variations in antiferromagnetic coupling. This study provides quantitative detail for the degree to which these two effects can act in concert for the observed SCO behavior in this complex and others subject to temperature-dependent variations in geometry.

Intruder-free cumulant-truncated driven similarity renormalization group second-order multireference perturbation theory.

Accurate multireference electronic structure calculations are important for constructing potential energy surfaces. Still, even in the case of low-scaling methods, their routine use is limited by the steep growth of the computational and storage costs as the active space grows. This is primarily due to the occurrence of three- and higher-body density matrices or, equivalently, their cumulants. This work examines the effect of various cumulant truncation schemes on the accuracy of the driven similarity renormalization group second-order multireference perturbation theory. We test four different levels of three-body reduced density cumulant truncations that set different classes of cumulant elements to zero. Our test cases include the singlet-triplet gap of CH2, the potential energy curves of the XΣg+1 and AΣu+3 states of N2, and the singlet-triplet splittings of oligoacenes. Our results show that both relative and absolute errors introduced by these cumulant truncations can be as small as 0.5kcal mol-1 or less. At the same time, the amount of memory required is reduced from O(NA6) to O(NA5), where NA is the number of active orbitals. No additional regularization is needed to prevent the intruder state problem in the cumulant-truncated second-order driven similarity renormalization group multireference perturbation theory methods.

OH Roaming and Beyond in the Unimolecular Decay of the Methyl-Ethyl-Substituted Criegee Intermediate: Observations and Predictions.

Alkene ozonolysis generates short-lived Criegee intermediates that are a significant source of hydroxyl (OH) radicals. This study demonstrates that roaming of the separating OH radicals can yield alternate hydroxycarbonyl products, thereby reducing the OH yield. Specifically, hydroxybutanone has been detected as a stable product arising from roaming in the unimolecular decay of the methyl-ethyl-substituted Criegee intermediate (MECI) under thermal flow cell conditions. The dynamical features of this novel multistage dissociation plus a roaming unimolecular decay process have also been examined with ab initio kinetics calculations. Experimentally, hydroxybutanone isomers are distinguished from the isomeric MECI by their higher ionization threshold and distinctive photoionization spectra. Moreover, the exponential rise of the hydroxybutanone kinetic time profile matches that for the unimolecular decay of MECI. A weaker methyl vinyl ketone (MVK) photoionization signal is also attributed to OH roaming. Complementary multireference electronic structure calculations have been utilized to map the unimolecular decay pathways for MECI, starting with 1,4 H atom transfer from a methyl or methylene group to the terminal oxygen, followed by roaming of the separating OH and butanonyl radicals in the long-range region of the potential. Roaming via reorientation and the addition of OH to the vinyl group of butanonyl is shown to yield hydroxybutanone, and subsequent C-O elongation and H-transfer can lead to MVK. A comprehensive theoretical kinetic analysis has been conducted to evaluate rate constants and branching yields (ca. 10-11%) for thermal unimolecular decay of MECI to conventional and roaming products under laboratory and atmospheric conditions, consistent with the estimated experimental yield (ca. 7%).

On the Simulation of Thermal Isomerization of Molecular Photoswitches in Biological Systems.

Molecular photoswitches offer precise, reversible photocontrol over biomolecular functions and are promising light-regulated drug candidates with minimal side effects. Quantifying thermal isomerization rates of photoswitches in their target biomolecules is essential for fine-tuning their light-controlled drug activity. However, the effects of protein binding on isomerization kinetics remain poorly understood, and simulations are crucial for filling this gap. Challenges in the simulation include describing multireference electronic structures near transition states, disentangling competing reaction pathways, and sampling protein-ligand interactions. To overcome these challenges, we used multiscale simulations to characterize the thermal isomerization of photostatins (PSTs), which are light-regulated microtubule inhibitors for potential cancer phototherapy. We employed a new ab initio multireference electronic structure method in a quantum mechanics/molecular mechanics setting and combined it with enhanced sampling techniques to characterize the cis to trans free-energy profiles of three PSTs in a vacuum, aqueous solution, and tubulin dimer. The significant advantage of our novel approach is the efficient treatment of the multireference character in PSTs' electronic wavefunction throughout the conformational sampling of protein-ligand interactions along their isomerization pathways. We also benchmarked our calculations using high-level ab initio multireference electronic structure methods and explored the competing isomerization pathways. Notably, calculations in a vacuum and implicit solvent models cannot predict the order of the PSTs' thermal half-lives in the aqueous solution observed in the experiment. Only by explicitly treating the solvent molecules can the correct order of isomerization kinetics be reproduced. Protein binding perturbs free-energy barriers due to hydrogen bonding between PSTs and nearby polar residues. Our work generates comprehensive, high-quality benchmark data and offers guidance for selecting computational methods to study the thermal isomerization of photoswitches. Ab initio multireference free-energy calculations in explicit molecular environments are crucial for predicting the effects of substituents on the thermal half-lives of photoswitches in biological systems.

A configuration-based heatbath-CI for spin-adapted multireference electronic structure calculations with large active spaces.

This work reports on a spin-pure configuration-based implementation of the heatbath configuration interaction (HCI) algorithm for selective configuration interaction. Besides the obvious advantage of being spin-pure, the presented method combines the compactness of the configurational ansatz with the known efficiency of the HCI algorithm and a variety of algorithmic and conceptual ideas to achieve a high level of performance. In particular, through pruning of the selected configurational space after HCI selection by means of a more strict criterion, a more compact wavefunction representation is obtained. Moreover, the underlying logic of the method allows us to minimize the number of redundant matrix-matrix multiplications while making use of just-in-time compilation to achieve fast diagonalization of the Hamiltonian. The critical search for 2-electron connections within the configurational space is facilitated by a tree-based representation thereof as suggested previously by Gopal et al. Usage of a prefix-based parallelization and batching during the calculation of the PT2-correction leads to a good load balancing and significantly reduced memory requirements for these critical steps of the calculation. In this way, the need for a semistochastic approach to the PT2 correction is avoided even for large configurational spaces. Finally, several test-cases are discussed to demonstrate the strengths and weaknesses of the presented method.

Spin-Forbidden Addition of Molecular Oxygen to Stable Enol Intermediates-Decarboxylation of 2-Methyl-1-tetralone-2-carboxylic Acid.

The deprotonation of an organic substrate is a common preactivation step for the enzymatic cofactorless addition of O2 to this substrate, as it promotes charge-transfer between the two partners, inducing intersystem crossing between the triplet and singlet states involved in the process. Nevertheless, the spin-forbidden addition of O2 to uncharged ligands has also been observed in the laboratory, and the detailed mechanism of how the system circumvents the spin-forbiddenness of the reaction is still unknown. One of these examples is the cofactorless peroxidation of 2-methyl-3,4-dihydro-1-naphthol, which will be studied computationally using single and multi-reference electronic structure calculations. Our results show that the preferred mechanism is that in which O2 picks a proton from the substrate in the triplet state, and subsequently hops to the singlet state in which the product is stable. For this reaction, the formation of the radical pair is associated with a higher barrier than that associated with the intersystem crossing, even though the absence of the negative charge leads to relatively small values of the spin-orbit coupling.

Four-body singlet potential-energy surface for reactions of calcium monofluoride

A full six-dimensional Born-Oppenheimer singlet potential-energy surface is constructed for the reaction CaF $+$ CaF $\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}{\mathrm{CaF}}_{2} +$ Ca using a multireference configuration-interaction electronic structure calculation. The ab initio data thus calculated are interpolated by Gaussian process regression. The four-body potential-energy surface features one ${D}_{2h}$ global minimum and one ${C}_{s}$ local minimum, connected by a barrierless transition state that lends insight to the reaction mechanism. This surface is intended to be of use in understanding ultracold chemistry of CaF molecules.

Excited states of ortho-nitrobenzaldehyde as a challenging case for single- and multi-reference electronic structure theory.

We present a large set of vertical excitation calculations for the ortho-nitrobenzaldehyde (oNBA) molecule, which exhibits a very challenging excited-state electronic structure like other nitroaromatic compounds. The single-reference methods produce mostly consistent results up to about 5.5eV. By contrast, the CAS second-order perturbation theory (CASPT2) results depend sensitively on the employed parameters. At the CAS self-consistent field level, the energies of the bright states are strongly overestimated while doubly excited states appear too low and mix with these states. This mixing hampers the CASPT2 step, leading to inconsistent results. Only by increasing the number of states in the state-averaging step to about 40-to cover all bright states embedded in the double excitations-and employing extended multistate CASPT2 couldCASPT2 results consistent with experimentbeobtained. We assign the four bands in the molecule's spectrum: The weakest band at 3.7eV arises from the states, the second one at 4.4eV from the ( ) state, the shoulder at 5.2eV from the ( ) state, and the maximum at 5.7eV from the ( ) states. We also highlight the importance of modern wave function analysis techniques in elucidating the absorption spectrum of challenging molecules.

Localized Active Space-State Interaction: a Multireference Method for Chemical Insight.

Multireference electronic structure methods, like the complete active space (CAS) self-consistent field model, have long been used to characterize chemically interesting processes. Important work has been done in recent years to develop modifications having a lower computational cost than CAS, but typically these methods offer no more chemical insight than that from the CAS solution being approximated. In this paper, we present the localized active space-state interaction (LASSI) method that can be used not only to lower the intrinsic cost of the multireference calculation but also to improve interpretability. The localized active space (LAS) approach utilizes the local nature of the electron-electron correlation to express a composite wave function as an antisymmetrized product of unentangled wave functions in local active subspaces. LASSI then uses these LAS states as a basis from which to express complete molecular wave functions. This not only makes the molecular wave function more compact but also permits flexibility in choosing those states to be included in the basis. Such selective inclusion of states translates to the selective inclusion of specific types of interactions, thereby allowing a quantitative analysis of these interactions. We demonstrate the use of LASSI to study charge migration and spin-flip excitations in multireference organic molecules. We also compute the J coupling parameter for a bimetallic compound using various LAS bases to construct the Hamiltonian to provide insights into the coupling mechanism.

Triplet-triplet Annihilation Dynamics of Naphthalene.

Triplet‐triplet annihilation (TTA) is a spin‐allowed conversion of two triplet states into one singlet excited state, which provides an efficient route to generate a photon of higher frequency than the incident light. Multiple energy transfer steps between absorbing (sensitizer) and emitting (annihilator) molecular species are involved in the TTA based photon upconversion process. TTA compounds have recently been studied for solar energy applications, even though the maximum upconversion efficiency of 50 % is yet to be achieved. With the aid of quantum calculations and based on a few key requirements, several design principles have been established to develop the well‐functioning annihilators. However, a complete molecular level understanding of triplet fusion dynamics is still missing. In this work, we have employed multi‐reference electronic structure methods along with quantum dynamics to obtain a detailed and fundamental understanding of TTA mechanism in naphthalene. Our results suggest that the TTA process in naphthalene is mediated by conical intersections. In addition, we have explored the triplet fusion dynamics under the influence of strong light‐matter coupling and found an increase of the TTA based upconversion efficiency.