Spin-Forbidden Channels in Reactions of Unsaturated Hydrocarbons with O(3P)

Magnetic exchange interactions in binuclear and tetranuclear iron(III) complexes described by spin-flip DFT and Heisenberg effective Hamiltonians

Low-energy spectra of single-molecule magnets (SMMs) are often described by Heisenberg Hamiltonians. Within this formalism, exchange interactions between magnetic centers determine the ground-state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants (J) for a set of iron (III) binuclear and tetranuclear complexes from all-electron calculations using non-collinear spin-flip time-dependent density functional theory (NC-SF-TDDFT). For 12 binuclear complexes with J-values ranging from -6 to -132 cm^-1 , our benchmark calculations using the short-range hybrid ωPBEh functional and 6-31G(d,p) basis set agree well with the experimentally derived values (mean absolute error of 4.7 cm^-1 ). For the tetranuclear SMMs, the computed J constants are within 6 cm^-1 from the experimentally derived values. We explore the range of applicability of the Heisenberg model by analyzing bonding patterns in these Fe(III) complexes using natural orbitals (NO), their occupations, and the number of effectively unpaired electrons. The results illustrate the efficiency of the spin-flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.

Nitrene formation is the first step of the thermal and photochemical decomposition reactions of organic azides

In this work, the decomposition of a prototypical azide, isopropyl azide, both in the ground and excited states, has been investigated through the use of multiconfigurational CASSCF and MS-CASPT2 electronic structure approaches. Particular emphasis has been placed on the thermal reaction starting at the S₀ ground state surface. It has been found that the azide thermally decomposes via a stepwise mechanism, whose rate-determining step is the formation of isopropyl nitrene, which is, in turn, the first step of the global mechanism. After that, the nitrene isomerizes to the corresponding imine derivative. Two routes are possible for such a decomposition: (i) a spin-allowed path involving a transition state; and (ii) a spin-forbidden one via a S₀/T₀ intersystem crossing. Both intermediates have been determined and characterised. Their associated relative energies have been found to be quite similar, 45.75 and 45.52 kcal mol^-1, respectively. To complete this study, the kinetics of the singlet and triplet channels are modeled with the MESMER (Master Equation Solver for Multi-Energy Well Reactions) code by applying the RRKM and Landau-Zener (with WKB tunnelling correction) theories, respectively. It is found that the canonical rate-coefficients of the singlet path are 2-orders of magnitude higher than the rate-coefficients of the forbidden reaction. In addition, the concerted mechanism has been investigated that would lead to the formation of the imine derivative and nitrogen extrusion in the first step of the decomposition. After a careful analysis of CASSCF calculations with different active spaces and their comparison with single electronic configuration methods (MP2 and B3LYP), the concerted mechanism is discarded.

Spin Crossover of Thiophosgene via Multidimensional Heavy-Atom Quantum Tunneling

The spin-crossover reaction of thiophosgene has drawn broad attention from both experimenters and theoreticians as a prime example of radiationless intramolecular decay via intersystem crossing. Despite multiple attempts over 20 years, theoretical predictions have typically been orders of magnitude in error relative to the experimentally measured triplet lifetime. We address the T₁ → S₀ transition by the first application of semiclassical golden-rule instanton theory in conjunction with on-the-fly electronic-structure calculations based on multireference perturbation theory. Our first-principles approach provides excellent agreement with the experimental rates. This was only possible because instanton theory goes beyond previous methods by locating the optimal tunneling pathway in full dimensionality and thus captures "corner cutting" effects. Since the reaction is situated in the Marcus inverted regime, the tunneling mechanism can be interpreted in terms of two classical trajectories, one traveling forward and one backward in imaginary time, which are connected by particle-antiparticle creation and annihilation events. The calculated mechanism indicates that the spin crossover is sped up by many orders of magnitude due to multidimensional quantum tunneling of the carbon atom even at room temperature.

A New Pathway for Intersystem Crossing: Unexpected Products in the O(3P) + Cyclopentene Reaction

We investigated the reaction of O(³P) with cyclopentene at 4 Torr and 298 K using time-resolved multiplexed photoionization mass spectrometry, where O(³P) radicals were generated by 351 nm photolysis of NO₂ and reacted with excess cyclopentene in He under pseudo-first-order conditions. The resulting products were sampled, ionized, and detected by tunable synchrotron vacuum ultraviolet radiation and an orthogonal acceleration time-of-flight mass spectrometer. This technique enabled measurement of both mass spectra and photoionization spectra as functions of time following the initiation of the reaction. We observe propylketene (41%), acrolein + ethene (37%), 1-butene + CO (19%), and cyclopentene oxide (3%), of which the propylketene pathway was previously unidentified experimentally and theoretically. The automatically explored reactive potential energy landscape at the CCSD(T)-F12a/cc-pVTZ//ωB97X-D/6-311++G(d,p) level and the related master equation calculations predict that cyclopentene oxide is formed on the singlet potential energy surface, whereas propylketene is first formed on the triplet surface. These calculations provide evidence that significant intersystem crossing can happen in this reaction not only around the geometry of the initial triplet adduct but also around that of triplet propylketene. The formation of 1-butene + CO is initiated on the triplet surface, with bond cleavage and hydrogen transfer occurring during intersystem crossing to the singlet surface. At present, we are unable to explain the mechanistic origins of the acrolein + ethene channel, and we thus refrain from assigning singlet or triplet reactivity to this channel. Overall, at least 60% of the products result from triplet reactivity. We propose that the reactivity of cyclic alkenes with O(³P) is influenced by their greater effective degree of unsaturation compared with acyclic alkenes. This work also suggests that searches for minimum-energy crossing points that connect triplet surfaces to singlet surfaces should extend beyond the initial adducts.

Crossed-Beam and Theoretical Studies of the O(3P, 1D) + Benzene Reactions: Primary Products, Branching Fractions, and Role of Intersystem Crossing

Reliable modeling of hydrocarbon oxidation relies critically on knowledge of the branching fractions (BFs) as a function of temperature (T) and pressure (p) for the products of the reaction of the hydrocarbon with atomic oxygen in its ground state, O(³P). During the past decade, we have performed in-depth investigations of the reactions of O(³P) with a variety of small unsaturated hydrocarbons using the crossed molecular beam (CMB) technique with universal mass spectrometric (MS) detection and time-of-flight (TOF) analysis, combined with synergistic theoretical calculations of the relevant potential energy surfaces (PESs) and statistical computations of product BFs, including intersystem crossing (ISC). This has allowed us to determine the primary products, their BFs, and extent of ISC to ultimately provide theoretical channel-specific rate constants as a function of T and p. In this work, we have extended this approach to the oxidation of one of the most important species involved in the combustion of aromatics: the benzene (C₆H₆) molecule. Despite extensive experimental and theoretical studies on the kinetics and dynamics of the O(³P) + C₆H₆ reaction, the relative importance of the C₆H₅O (phenoxy) + H open-shell products and of the spin-forbidden C₅H₆ (cyclopentadiene) + CO and phenol adduct closed-shell products are still open issues, which have hampered the development of reliable benzene combustion models. With the CMB technique, we have investigated the reaction dynamics of O(³P) + benzene at a collision energy (E_c) of 8.2 kcal/mol, focusing on the occurrence of the phenoxy + H and spin-forbidden C₅H₆ + CO and phenol channels in order to shed further light on the dynamics of this complex and important reaction, including the role of ISC. Concurrently, we have also investigated the reaction dynamics of O(¹D) + benzene at the same E_c. Synergistic high-level electronic structure calculations of the underlying triplet/singlet PESs, including nonadiabatic couplings, have been performed to complement and assist the interpretation of the experimental results. Statistical (RRKM)/master equation (ME) computations of the product distribution and BFs on these PESs, with inclusion of ISC, have been performed and compared to experiment. In light of the reasonable agreement between the CMB experiment, literature kinetic experimental results, and theoretical predictions for the O(³P) + benzene reaction, the so-validated computational methodology has been used to predict (i) the BF between the C₆H₅O + H and C₅H₆ + CO channels as a function of collision energy and temperature (at 0.1 and 1 bar), showing that their increase progressively favors radical (phenoxy + H)-forming over molecule (C₅H₆ + CO and phenol stabilization)-forming channels, and (ii) channel-specific rate constants as a function of T and p, which are expected to be useful for improved combustion models.

Equation-of-Motion Coupled-Cluster Protocol for Calculating Magnetic Properties: Theory and Applications to Single-Molecule Magnets

We present a new computational protocol for computing macroscopic magnetic properties of transition-metal complexes using the equation-of-motion coupled-cluster (EOM-CC) framework. The approach follows a two-step state-interaction scheme: we first compute zero-order states using nonrelativistic EOM-CC and then use these states to evaluate matrix elements of the spin-orbit and Zeeman operators. Diagonalization of the resulting Hamiltonian yields spin-orbit- and field-perturbed eigenstates. Temperature- and field-dependent magnetization and susceptibility are computed by numerical differentiation of the partition function. To compare with powder-sample experiments, these quantities are numerically averaged over field orientations. We applied this protocol to several single-molecule magnets (SMMs) with Fe(II) and Fe(III) in trigonal pyramidal, linear, and trigonal bipyramidal coordination environments. We described the underlying electronic structure by the electron-attachment (EOM-EA) and spin-flip (EOM-SF) variants of EOM-CC. The computed energy barriers for spin inversion, and macroscopic magnetization and susceptibility agree well with experimental data. Trends in magnetic anisotropy and spin-reversal energy barriers are explained in terms of a molecular orbital picture rigorously distilled from spinless transition density matrices between many-body states. The results illustrate excellent performances of EOM-CC in describing magnetic behavior of mononuclear transition-metal SMMs.

Modeling Spin-Crossover Dynamics

In this article, we review nonadiabatic molecular dynamics (NAMD) methods for modeling spin-crossover transitions. First, we discuss different representations of electronic states employed in the grid-based and direct NAMD simulations. The nature of interstate couplings in different representations is highlighted, with the main focus on nonadiabatic and spin-orbit couplings. Second, we describe three NAMD methods that have been used to simulate spin-crossover dynamics, including trajectory surface hopping, ab initio multiple spawning, and multiconfiguration time-dependent Hartree. Some aspects of employing different electronic structure methods to obtain information about potential energy surfaces and interstate couplings for NAMD simulations are also discussed. Third, representative applications of NAMD to spin crossovers in molecular systems of different sizes and complexities are highlighted. Finally, we pose several fundamental questions related to spin-dependent processes. These questions should be possible to address with future methodological developments in NAMD.

Theoretical Study of the Extent of Intersystem Crossing in the O(3P) + C6H6 Reaction with Experimental Validation

The extent of intersystem crossing in the O(³P) + C₆H₆ reaction, a prototypical system for spin-forbidden reactions in oxygenated aromatic molecules, is theoretically evaluated for the first time. Calculations are performed using nonadiabatic transition-state theory coupled with stochastic master equation simulations and Landau-Zener theory. It is found that the dominant intersystem crossing pathways connect the T2 and S0 potential energy surfaces through at least two distinct minimum-energy crossing points. The calculated channel-specific rate constants and intersystem crossing branching fractions differ from previous literature estimates and provide valuable kinetic data for the investigation of benzene and polycyclic aromatic hydrocarbons oxidation in interstellar, atmospheric, and combustion conditions. The theoretical results are supported by crossed molecular beam experiments with electron ionization mass-spectrometric detection and time-of-flight analysis at 8.2 kcal/mol collision energy. This system is a suitable benchmark for theoretical and experimental studies of intersystem crossing in aromatic species.

The reaction of O(3P) with alkynes: a dynamic and computational study focusing on formyl radical production

Production of formyl radical, HCO, from reactions of O(³P) with alkynes (acetylene, propyne, 1-butyne, and 1-pentyne) has been investigated using cavity ringdown laser absorption spectroscopy (CRDLAS) and computational methods. No HCO was detected from reaction with acetylene, while the amount of HCO increased for propyne and 1-butyne, dropping off somewhat for 1-pentyne. These results differ from trends previously observed for reactions of O(³P) with alkenes, which exhibit the largest HCO production for the smallest alkene and drop off as the alkene size increases. Computational studies employing density functional and coupled cluster methods have been employed to investigate the triplet and singlet state pathways for HCO production. Because intersystem crossing (ISC) has been shown to be important in these processes, the minimum energy crossing point (MECP) between the triplet and singlet surfaces has been studied. We find the MECP for propyne to possess C₁ symmetry and to lie lower in energy than previous studies have found. Natural Bond Orbital and Natural Resonance Theory analyses have been performed to investigate the changes in spin density and bond order along the reaction pathways for formation of HCO. Explanations are suggested for the trend in HCO formation observed for the alkynes. The trend in alkyne HCO yield also is compared and contrasted with the trend previously observed for the alkenes.

Constructing Spin-Adiabatic States for the Modeling of Spin-Crossing Reactions. I. A Shared-Orbital Implementation

In the modeling of spin-crossing reactions, it has become popular to directly explore the spin-adiabatic surfaces. Specifically, through constructing spin-adiabatic states from a two-state Hamiltonian (with spin-orbit coupling matrix elements) at each geometry, one can readily employ advanced geometry optimization algorithms to acquire a "transition state" structure, where the spin crossing occurs. In this work, we report the implementation of a fully-variational spin-adiabatic approach based on Kohn-Sham density functional theory spin states (sharing the same set of molecular orbitals) and the Breit-Pauli one-electron spin-orbit operator. For three model spin-crossing reactions [predissociation of N₂O, singlet-triplet conversion in CH₂, and CO addition to Fe(CO)₄], the spin-crossing points were obtained. Our results also indicated the Breit-Pauli one-electron spin-orbit coupling can vary significantly along the reaction pathway on the spin-adiabatic energy surface. On the other hand, due to the restriction that low-spin and high-spin states share the same set of molecular orbitals, the acquired spin-adiabatic energy surface shows a cusp (i.e. a first-order discontinuity) at the crossing point, which prevents the use of standard geometry optimization algorithms to pinpoint the crossing point. An extension with this restriction removed is being developed to achieve the smoothness of spin-adiabatic surfaces.

Spin-flip methods in quantum chemistry

This Perspective discusses salient features of the spin-flip approach to strong correlation and describes different methods that sprung from this idea. The spin-flip treatment exploits the different physics of low-spin and high-spin states and is based on the observation that correlation is small for same-spin electrons. By using a well-behaved high-spin state as a reference, one can access problematic low-spin states by deploying the same formal tools as in the excited-state treatments (i.e., linear response, propagator, or equation-of-motion theories). The Perspective reviews applications of this strategy within wave function and density functional theory frameworks as well as the extensions for molecular properties and spectroscopy. The utility of spin-flip methods is illustrated by examples. Limitations and proposed future directions are also discussed.

Quantitative El-Sayed Rules for Many-Body Wave Functions from Spinless Transition Density Matrices

One-particle transition density matrices and natural transition orbitals enable quantitative description of electronic transitions and interstate properties involving correlated many-body wave functions within the molecular orbital framework. Here we extend the formalism to the analysis of tensor properties, such as spin-orbit couplings (SOCs), which involve states of different spin projection. By using spinless density matrices and Wigner-Eckart's theorem, the approach allows one to treat the transitions between states with arbitrary spin projections in a uniform way. In addition to a pictorial representation of the transition, the analysis also yields quantitative contributions of hole-particle pairs into the overall many-body matrix elements. In particular, it helps to rationalize the magnitude of computed SOCs in terms of El-Sayed's rules. The capabilities of the new tool are illustrated by the analysis of the equation-of-motion coupled-cluster calculations of two transition metal complexes.

General framework for calculating spin-orbit couplings using spinless one-particle density matrices: Theory and application to the equation-of-motion coupled-cluster wave functions

Standard implementations of nonrelativistic excited-state calculations compute only one component of spin multiplets (i.e., M_s = 0 triplets); however, matrix elements for all components are necessary for deriving spin-dependent experimental observables. Wigner-Eckart's theorem allows one to circumvent explicit calculations of all multiplet components. We generate all other spin-orbit matrix elements by applying Wigner-Eckart's theorem to a reduced one-particle transition density matrix computed for a single multiplet component. In addition to computational efficiency, this approach also resolves the phase issue arising within Born-Oppenheimer's separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculation of spin-orbit couplings using equation-of-motion coupled-cluster wave functions are presented. The two-electron contributions are included via the mean-field spin-orbit treatment. Intrinsic issues of constructing spin-orbit mean-field operators for open-shell references are discussed, and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.

Enhancing Spin-Orbit Coupling by Introducing a Lone Pair Electron with p Orbital Character in a Thermally Activated Delayed Fluorescence Emitter: Photophysics and Devices

Reverse intersystem crossing (RISC) is the rate-limited step for the radiative process of thermally activated delayed fluorescence (TADF) materials, which is important to achieve ideal photoluminescence and electroluminescence efficiency. Herein, we propose a new strategy of introducing a lone pair (n) electron with p orbital character to enhance spin-orbit coupling (SOC) for promoting the RISC process. A proof-of-concept TADF molecule with p orbital lone pairs, namely, MoCz-PCN, was developed, and three counterparts without any p lone pairs, namely, DMAc-PCN, DPAc-PCN, and SpiroAc-PCN, were constructed for comparison. The experimental data revealed that MoCz-PCN exhibits a ca. 1.9 times higher RISC rate than the counterparts, which can be ascribed to enhanced SOC. Moreover, a significant increase in external quantum efficiency is observed in the MoCz-PCN-based OLED device. These findings provide a feasible strategy to develop highly efficient TADF emitters by introducing a lone pair (n) electron with p orbital character.

EOM-CC guide to Fock-space travel: the C2 edition

Electronic structure calculations for C₂, C₂⁻, and C₂²⁻ using the CC/EOM-CC family of methods. Results illustrate that EOM-CCSD provides an attractive alternative to MR approaches.