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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 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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This content will become publicly available on March 14, 2026
Numerically stable resonating Hartree–Fock
The simulation of excited states at low computational cost remains an open challenge for electronic structure (ES) methods. While much attention has been given to orthogonal ES methods, relatively little work has been done to develop nonorthogonal ES methods for excited states, particularly those involving nonorthogonal orbital optimization. We present here a numerically stable formulation of the Resonating Hartree–Fock (ResHF) method that uses the matrix adjugate to remove numerical instabilities arising from nearly orthogonal orbitals, and as a result, we demonstrate improvements to ResHF wavefunction optimization. We then benchmark the performance of ResHF against complete active space self-consistent field in the avoided crossing of LiF, the torsional rotation of ethene, and the singlet–triplet energy gaps of a selection of small molecules. ResHF is a promising excited state method because it incorporates the orbital relaxation of state-specific methods, while retaining the correct state crossings of state-averaged approaches. Our open-source ResHF implementation, yucca, is available on GitLab.
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- Award ID(s):
- 2236959
- PAR ID:
- 10595267
- Publisher / Repository:
- AIP Publishing
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 162
- Issue:
- 10
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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