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

Abstract

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 spincrossing reactions (predissociation of N 2 O, singlet-triplet conversion in CH 2 , 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 (ie, 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. K E Y W O R D Schemical reactions, spin-adiabatic surface, spin-crossing reaction | INTRODUCTIONIn most chemical reactions, the total electron spin is conserved. However, if a reaction involves high-spin species, such as oxygen ( 3 P) and nitrogen ( 4 N) atoms, molecular oxygen ( 3 O 2 ), and transition metals, [1][2][3][4][5][6][7][8] a change in the electron spin might occur during the transition from the reactant to the product. Such spin-crossing reactions are known to be enabled by the spin-orbit coupling (SOC) between different spin states. [9,10] While usually slower than their spin-conserved counterparts (especially in cases with a weak SOC), spin-crossing reactions can play an important role in biochemical processes, homogeneous/heterogeneous catalysis, energy storage/conversion, etc.In the study of spin-crossing reactions, one can explore either the spin-diabatic or spin-adiabatic potential energy surfaces. In the spindiabatic approach, the central task is to reach the crossing seam of two spin-diabatic potential energy surfaces, and then locate the minimum energy crossing point (MECP) on the crossing seam. [11][12][13][14] This is illustrated in Figure 1A for a triplet-to-singlet reaction. Once the MECP is found, Yunwen Tao and Zheng Pei contributed equally to this study.

Probing the Kinetic Origin of Varying Oxidative Stability of Ethyl‐ vs. Propyl‐spaced Amines for Direct Air Capture

“…[35] To address this, we adopt the MECP formalism, which is a reliable way to approximate the transition states of spin-forbidden reactions for compounds containing only light elements. [36] We started by simulating the unimolecular ROOH decomposition reactions for the three amino-oligomers shown in Figure 2. MECP-estimated energy barriers (DE � MECP ) for ROOH decomposition for these compounds (Figure S5) are significantly higher than H-abstraction free energy barriers, ranging from 146 to 173 kJ mol À 1 .…”

Describing Polytopal Rearrangements of Fluxional Molecules with Curvilinear Coordinates Derived from Normal Vibrational Modes: A Conceptual Extension of Cremer–Pople Puckering Coordinates

“…The different pathways describing these two conformational changes originate in the different rotation axes leading to D 3 h and C 2 v TSs for the Bailar and the Ray–Dutt twists, respectively. Twists converting an octahedral structure to a trigonal prismatic one at the TS are often associated with spin-state changes of the central metal atom enabled by spin–orbit coupling between different spin states. , However, in this work, we focus on the aspect of geometrical changes during the twisting motion.…”

“…Twists converting an octahedral structure to a trigonal prismatic one at the TS are often associated with spin-state changes of the central metal atom enabled by spin−orbit coupling between different spin states. 141,142 However, in this work, we focus on the aspect of geometrical changes during the twisting motion.…”