Automated reaction path searches for spin‐forbidden reactions

Abstract

Many catalytic and biomolecular reactions containing transition metals involve changes in the electronic spin state. These processes are referred to as "spin-forbidden" reactions within nonrelativistic quantum mechanics framework. To understand detailed reaction mechanisms of spin-forbidden reactions, one must characterize reaction pathways on potential energy surfaces with different spin states and then identify crossing points. Here we propose a practical computational scheme, where only the lowest mixed-spin eigenstate obtained from the diagonalization of the spin-coupled Hamiltonian matrix is used in reaction path search calculations. We applied this method to the FeO + H → Fe + H O, FeO + CH → Fe + CH OH, and Mn + OCS → MnS + CO reactions, for which crossings between the different spin states are known to play essential roles in the overall reaction kinetics. © 2018 Wiley Periodicals, Inc.

Constructing spin‐adiabatic states for the modeling of spin‐crossing reactions. I. A shared‐orbital implementation

“…In general, our work reinforces the attractiveness of building spin-adiabatic energy surfaces for studying spin-crossing reactions [15,[22][23][24][25][26] as well as the feasibility of computing SOC on the fly within the Breit-Pauli one-electron operator framework. [46,47] However, in order to build more smooth spin-adiabatic potential energy surfaces using the Breit-Pauli one-electron operator so that standard TS search and reaction pathway optimization algorithms can be utilized, more general methods to construct the spin-diabatic states need to be developed.…”

“…[4] Over the years, the MECP approach has been successfully applied to numerous spin-crossing reactions. [15,[22][23][24][25][26] As illustrated in Figure 1B, within this approach, one computes SOC at each geometry to construct the lowest-energy spin-adiabatic state, and then search for a TS and the minimum energy pathway on the spin-adiabatic surface. [17,19,20] The spin-adiabatic approach, [3,21] on the other hand, has gained a lot of momentum in the last couple of years.…”

“…[1,3,4,7,16] One can further study the transition rate between different spin-diabatic states by including SOC in nonadiabatic transition state (TS) theory simulations [17,18] or surface hopping dynamics. Such a so-called TS-SOC approach has been applied to a number of systems: O 2 addition to gold hydride complexes and predissociation of N 2 O and N 2 Se, [15,22,23] CO addition to Fe(CO) 4 and hydrogen elimination from a tungsten complex, [24] FeO + reacting with H 2 or CH 4 and Mn + reacting with OCS, [25] and several first-row transition metal cations (Sc + to Cu + ) reacting with OCS molecule. [15,[22][23][24][25][26] As illustrated in Figure 1B, within this approach, one computes SOC at each geometry to construct the lowest-energy spin-adiabatic state, and then search for a TS and the minimum energy pathway on the spin-adiabatic surface.…”

“…[37,38] In the first TS-SOC implementation by Harvey and coworkers, [15] ZORA coupling was computed on the fly (ie, for each geometry) during the TS search. [25] Such an approximation removes the orbital-dependence of SOC values and thus greatly simplifies the evaluation of analytical nuclear gradients and Hessian matrices. [25] Such an approximation removes the orbital-dependence of SOC values and thus greatly simplifies the evaluation of analytical nuclear gradients and Hessian matrices.…”

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

“…This spin–orbit coupling value was used to optimize spin‐inversion structures efficiently. The coupling parameter used in this work was sufficiently small and did not significantly affect the original potential energy surface shape at the molecular structure deviating from the spin‐inversion point . First, we used the upper eigen state of the (2 × 2) Hamiltonian matrix, and then, we performed standard geometry optimization to find a potential energy minimum on the upper mixed‐spin potential energy surface.…”