Constrained Nuclear-Electronic Orbital Transition State Theory Using Energy Surfaces with Nuclear Quantum Effects

Hydrogen-atom transfer is crucial in a myriad of chemical and biological processes, yet the accurate and efficient description of hydrogen-atom transfer reactions and kinetic isotope effects remains challenging due to significant quantum effects on hydrogenic motion, especially tunneling and zero-point energy. In this paper, we combine transition state theory (TST) with the recently developed constrained nuclear-electronic orbital (CNEO) theory to propose a new transition state theory denoted CNEO-TST. We use CNEO-TST with CNEO density functional theory (CNEO-DFT) to predict reaction rate constants for two prototypical gas-phase hydrogen-atom transfer reactions and their deuterated isotopologic reactions. The CNEO-TST is similar to conventional TST except that it employs constrained minimized energy surfaces to include zero-point energy and shallow tunneling effects in the effective potential. We find that the new theory predicts reaction rates quite accurately at room temperature. The effective potential surface must be generated by CNEO theory rather than by ordinary electronic structure theory, but because of the favorable computational scaling of CNEO-DFT, the cost will remain economical even for large systems. Our results show that dynamics calculations with this approach achieve accuracy comparable to variational TST with a semiclassical multidimensional tunneling transmission coefficient at and above room temperature. Therefore, CNEO-TST can be a useful tool for rate prediction, even for reactions involving highly quantal motion, such as many chemical and biochemical reactions involving transfers of hydrogen atoms, protons, or hydride ions.