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Title: Analytical gradients for nuclear–electronic orbital multistate density functional theory: Geometry optimizations and reaction paths

Hydrogen tunneling plays a critical role in many biologically and chemically important processes. The nuclear–electronic orbital multistate density functional theory (NEO-MSDFT) method was developed to describe hydrogen transfer systems. In this approach, the transferring proton is treated quantum mechanically on the same level as the electrons within multicomponent DFT, and a nonorthogonal configuration interaction scheme is used to produce delocalized vibronic states from localized vibronic states. The NEO-MSDFT method has been shown to provide accurate hydrogen tunneling splittings for fixed molecular systems. Herein, the NEO-MSDFT analytical gradients for both ground and excited vibronic states are derived and implemented. The analytical gradients and semi-numerical Hessians are used to optimize and characterize equilibrium and transition state geometries and to generate minimum energy paths (MEPs), for proton transfer in the deprotonated acetylene dimer and malonaldehyde. The barriers along the resulting MEPs are lower when the transferring proton is quantized because the NEO-MSDFT method inherently includes the zero-point energy of the transferring proton. Analysis of the proton densities along the MEPs illustrates that the proton density can exhibit symmetric or asymmetric bilobal character associated with symmetric or slightly asymmetric double-well potential energy surfaces and hydrogen tunneling. Analysis of the contributions to the intrinsic reaction more » coordinate reveals that changes in the C–O bond lengths drive proton transfer in malonaldehyde. This work provides the foundation for future reaction path studies and direct nonadiabatic dynamics simulations of a wide range of hydrogen transfer reactions.

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The Journal of Chemical Physics
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Article No. 114115
American Institute of Physics
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National Science Foundation
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  1. Abstract

    The Hohenberg-Kohn theorem of density-functional theory establishes the existence of a bijection between the ground-state electron density and the external potential of a many-body system. This guarantees a one-to-one map from the electron density to all observables of interest including electronic excited-state energies. Time-Dependent Density-Functional Theory (TDDFT) provides one framework to resolve this map; however, the approximations inherent in practical TDDFT calculations, together with their computational expense, motivate finding a cheaper, more direct map for electronic excitations. Here, we show that determining density and energy functionals via machine learning allows the equations of TDDFT to be bypassed. The framework we introduce is used to perform the first excited-state molecular dynamics simulations with a machine-learned functional on malonaldehyde and correctly capture the kinetics of its excited-state intramolecular proton transfer, allowing insight into how mechanical constraints can be used to control the proton transfer reaction in this molecule. This development opens the door to using machine-learned functionals for highly efficient excited-state dynamics simulations.

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