Computational Analysis of Chemical Reactions Using a Variational Quantum Eigensolver Algorithm without Specifying Spin Multiplicity

The analysis of a chemical reaction along the ground-state potential energy surface in conjunction with an unknown spin state is challenging because electronic states must be separately computed several times using different spin multiplicities to find the lowest energy state. However, in principle, the ground state could be obtained with just a single calculation using a quantum computer without specifying the spin multiplicity in advance. In the present work, ground-state potential energy curves for PtCO were calculated as a proof-of-concept using a variational quantum eigensolver (VQE) algorithm. This system exhibits a singlet-triplet crossover as a consequence of the interaction between Pt and CO. VQE calculations using a statevector simulator were found to converge to a singlet state in the bonding region, while a triplet state was obtained at the dissociation limit. Calculations performed using an actual quantum device provided potential energies within ±2 kcal/mol of the simulated energies after error mitigation techniques were adopted. The spin multiplicities in the bonding and dissociation regions could be clearly distinguished even in the case of a small number of shots. The results of this study suggest that quantum computing can be a powerful tool for the analysis of the chemical reactions of systems for which the spin multiplicity of the ground state and variations in this parameter are not known in advance.

Heavy‐Atom Quantum Tunnelling in Spin Crossovers of Nitrenes**

We simulate two recent matrix‐isolation experiments at cryogenic temperatures, in which a nitrene undergoes spin crossover from its triplet state to a singlet state via quantum tunnelling. We detail the failure of the commonly applied weak‐coupling method (based on a linear approximation of the potentials) in describing these deep‐tunnelling reactions. The more rigorous approach of semiclassical golden‐rule instanton theory in conjunction with double‐hybrid density‐functional theory and multireference perturbation theory does, however, provide rate constants and kinetic isotope effects in good agreement with experiment. In addition, these calculations locate the optimal tunnelling pathways, which provide a molecular picture of the reaction mechanism. The reactions involve substantial heavy‐atom quantum tunnelling of carbon, nitrogen and oxygen atoms, which unexpectedly even continues to play a role at room temperature.

Dioxygen Activation and Pyrrole α-Cleavage with Calix[4]pyrrolato Aluminates: Enzyme Model by Structural Constraint

The present work describes the reaction of triplet dioxygen with the porphyrinogenic calix[4]pyrrolato aluminates to alkylperoxido aluminates in high selectivity. Multiconfigurational quantum chemical computations disclose the mechanism for this spin‐forbidden process. Despite a negligible spin–orbit coupling constant, the intersystem crossing (ISC) is facilitated by singlet and triplet state degeneracy and spin–vibronic coupling. The formed peroxides are stable toward external substrates but undergo an unprecedented oxidative pyrrole α‐cleavage by ligand aromatization/dearomatization‐initiated O−O σ‐bond scission. A detailed comparison of the calix[4]pyrrolato aluminates with dioxygen‐related enzymology provides insights into the ISC of metal‐ or cofactor‐free enzymes. It substantiates the importance of structural constraint and element–ligand cooperativity for the functions of aerobic life.

Extending nudged elastic band method to reaction pathways involving multiple spin states

There are diverse reactions including spin-state crossing, especially the reactions catalyzed by transition metal compounds. To figure out the mechanisms of such reactions, the discussion of minimum energy intersystem crossing (MEISC) points cannot be avoided. These points may be the bottleneck of the reaction or inversely accelerate the reactions by providing a better pathway. It is of great importance to reveal their role in the reactions by computationally locating the position of the MEISC points together with the reaction pathway. However, providing a proper initial guess for the structure of the MEISC point is not as easy as that of the transition state. In this work, we extended the nudged elastic band (NEB) method for multiple spin systems, which is named the multiple spin-state NEB method, and it is successfully applied to find the MEISC points while optimizing the reaction pathway. For more precisely locating the MEISC point, a revised approach was adopted. Meanwhile, our examples also suggest that special attention should be paid to the criterion to define an image optimized as the MEISC point.

Spin-inversion mechanisms in O2 binding to a model heme compound: A perspective from nonadiabatic wave packet calculations

Spin-inversion dynamics in O₂ binding to a model heme complex, which consisted of Fe(II)-porphyrin and imidazole, were studied using nonadiabatic wave packet dynamics calculations. We considered three active nuclear degrees of freedom in the dynamics, including the motions along the Fe-O distance, Fe-O-O angle, and Fe out-of-plane distance. Spin-free potential energy surfaces for the singlet, triplet, quintet, and septet states were developed using density functional theory calculations, and spin-orbit coupling elements were obtained from CASSCF-level electronic structure calculations. The spin-inversion mainly occurred between the singlet state and one of the triplet states due to large spin-orbit couplings and the contributions of other states were extremely small. The present quantum dynamics calculations suggested that the narrow crossing region model plays a dominant role in the O₂ binding dynamics. In addition, the one-dimensional Landau-Zener model underestimated the nonadiabatic transition probability.

Spin-inversion mechanisms in O2 binding to a model heme complex revisited by density function theory calculations

Spin-inversion mechanisms in O₂ binding to a model heme complex, consisting of Fe(II)-porphyrin and imidazole, were investigated using density-functional theory calculations. First, we applied the recently proposed mixed-spin Hamiltonian method to locate spin-inversion structures between different total spin multiplicities. Nine spin-inversion structures were successfully optimized for the singlet-triplet, singlet-quintet, triplet-quintet, and quintet-septet spin-inversion processes. We found that the singlet-triplet spin-inversion points are located around the potential energy surface region at short Fe-O distances, whereas the singlet-quintet and quintet-septet spin-inversion points are located at longer Fe-O distances. This suggests that both narrow and broad crossing models play roles in O₂ binding to the Fe-porphyrin complex. To further understand spin-inversion mechanisms, we performed on-the-fly Born-Oppenheimer molecular dynamics calculations. The reaction coordinates, which are correlated to the spin-inversion dynamics between different spin multiplicities, are also discussed.

A detailed analysis of the spin-crossover reaction of H2S binding to heme and the six-coordinated FeP(Im)-HS- porphyrin complex

The potential energy surfaces of the H₂S binding to iron-porphyrin (FeP) with the imidazole (Im) ligand via intersystem crossings are investigated by using density functional theory. The minimum energy intersystem crossing point (MEISCP) between the quintet and triplet states (MEISCP_TQ) for the Fe(II)P(Im)-H₂S complex is located at a Fe-S distance of 3.39 Å with only 1.1 kcal/mol above the quintet state minimum. The second spin-crossover point, where a change from the triplet to the singlet state occurs, comes at a much shorter Fe-S distance of 2.79 Å, and the MEISCP_ST is located at 3.7 kcal/mol above the triplet state minimum. The nature of the chemical bonding along the Fe-S reaction coordinate from the ground state singlet to the quintet state along the path to the separated species is analyzed. An inspection of the vibrational modes reveals that the largest contribution to the triplet-quintet transition around the quintet and triplet state minimum comes from the symmetric shrinking of the pyrrole units of the porphyrin ring, indicating that the related reaction coordinate plays a main role in the intersystem crossing. The fully optimized structures of the Fe(II)P(Im)-HS^- complex corresponding to three different spin multiplicities (M = 1, 3, 5) are characterized by a bent Fe-H-S conformation. The binding of the hydrosulfide anion to Fe(II)P(Im) in the quintet state induces a 0.2 Å displacement of the Fe atom out of the nitrogen porphyrin (N_pyr) plane. The fully optimized structure of the ground state of Fe(II)P(Im)-HS^- agrees well with experimental data for the corresponding heme models.

Intersystem crossing in tunneling regime: T1 → S0 relaxation in thiophosgene

The T1 excited state relaxation in thiophosgene has attracted much attention as a relatively simple model for the intersystem crossing (ISC) transitions in polyatomic molecules. The very short (20-40 ps) T1 lifetime predicted in several theoretical studies strongly disagrees with the experimental values (∼20 ns) indicating that the kinetics of T1 → S0 ISC is not well understood. We use the nonadiabatic transition state theory (NA-TST) with the Zhu-Nakamura transition probability and the multireference perturbation theory (CASPT2) to show that the T1 → S0 ISC occurs in the quantum tunneling regime. We also introduce a new zero-point vibrational energy correction scheme that improves the accuracy of the predicted ISC rate constants at low internal energies. The predicted lifetimes of the T1 vibrational states are between one and two orders of magnitude larger than the experimental values. This overestimation is attributed to the multidimensional nature of quantum tunneling that facilitates ISC transitions along the non-minimum energy path and is not accounted for in the one-dimensional NA-TST.

Substitution effects on olefin epoxidation catalyzed by Oxoiron(IV) porphyrin π-cation radical complexes: A dft study

The effects of peripheral fluorine atoms on epoxidation reactions of ethylene by oxoiron(IV) porphyrin cation radical complex in the quartet and sextet spin multiplicities are systematically investigated using the DFT method. The overall reaction routes are determined using a model system of ethylene and Fe(IV)OCl-porphyrin with substituted fluorine atoms. By obtaining the energy diagrams and electron- and spin-density difference contour maps of the transition states and intermediate compounds, we confirm that the electron-withdrawing by peripheral fluorine atoms enhances the reactivity as the number of fluorine atoms increases, as is observed experimentally. The intersystem crossing between the quartet and sextet spin multiplicities is discussed by means of the intrinsic reaction coordinate method. We conclude that the rate-determining step is located at the first transition state (TS1) for the activation of CC and FeO bonds, and the ground electronic state changes from quartet to sextet around the TS1. © 2019 Wiley Periodicals, Inc.

The dramatic effect of N-methylimidazole on trans axial ligand binding to ferric heme: experiment and theory

The binding energy of CO, O2 and NO to isolated ferric heme, [FeIIIP]+, was studied in the presence and absence of a σ donor (N-methylimidazole and histidine) as the trans axial ligand. This study combines the experimental determination of binding enthalpies by equilibrium measurements in a low temperature ion trap using the van't Hoff equation and high level DFT calculations. It was found that the presence of N-methylimidazole as the axial ligand on the [FeIIIP]+ porphyrin dramatically weakens the [FeIIIP-ligand]+ bond with an up to sevenfold decrease in binding energy owing to the σ donation by N-methylimidazole to the FeIII(3d) orbitals. This trans σ donor effect is characteristic of ligation to iron in hemes in both ferrous and ferric redox forms; however, to date, this has not been observed for ferric heme.

Constraint structure optimization to a specific minimum using ionization energy

A structure optimization method with ionization energy constraint is developed to explore structures with specific ionization energy. The Levine-Coe-Martínez penalty function (J Phys Chem B 2008, 112, 405) was adopted, and the penalty function includes a predefined core-ionization energy and inner-shell ionization energy. For an S_N 2 reaction, isomerization of a platinum complex, a proton transfer reaction, and carbon monoxide adsorption on a palladium cluster, the present method was tested, and the targeted energy minima were obtained as designated by the input ionization energy. The shape of the objective function, the parameters in the penalty function, and structural changes during the optimization process were discussed. An automated parameter setting and possible problems are discussed for future direction. © 2018 Wiley Periodicals, Inc.