Coupled electronic and nuclear interactions beyond the Born-Oppenheimer approximation

Abstract

Conventional quantum chemical methods have been developed within the adiabatic Born-Oppenheimer framework, where the nuclear and electronic degrees of freedom are assumed separable. Despite considerable successes in predicting thermodynamic and kinetic properties, adiabatic approaches fail to simulate the chemistry in non-Born-Oppenheimer regimes, such as proton transfer in vibrationally excited levels, light-initiated dynamics of luminescent materials, and nonadiabatic electron transfer between singlet and triplet manifolds. A novel theoretical method beyond the Born-Oppenheimer approximation is necessary for understanding the impact of nonclassical electron-nucleus couplings, which are usually treated as empirical posteriori correction to adiabatic calculations. Meanwhile, computational studies on nonadiabatic electron transfer in literature often estimate solute motion with an averaged or selected single molecular vibration and neglect the spin-vibrational interactions. An efficient implementation of the multi-mode rate law for nonadiabatic electron transfer, which accurately accounts for electronic interactions perturbed by molecular vibrations, is crucial to designing tunable light emitters capable of harvesting vibrational energy with reduced thermal dissipations.

As for the intrastate non-Born-Oppenheimer interactions, we have computed the electron-nucleus coupling by formulating an exact self-consistent nucleus-electron embedding potential from the factorization of total molecular wavefunction. A mean-field conditional electron density clamped to a quantal anharmonic vibration of selected nuclei has been shown to capture most of the non-Born-Oppenheimer corrections. The systematic improvement by including post-Hartree-Fock electron correlation is convenient based on nucleus-electron coupled molecular orbitals and determinants. We have applied our method to characterize vibrationally averaged molecular bonding properties of binding energy, the interatomic distance, and protonic and dynamic electron density. The non-Born-Oppenheimer correction to a proton shuttle mode in FHF− has been computed to validate our approach. The kinetic isotope effects can be calculated because our algorithm distinguishes isotopomers with different atomic masses.

In the absence of the first-order Herzberg-Teller couplings, the theoretically predicted rate constant of the singlet-to-triplet electron transfer deviates from experimental value by several orders of magnitude for many planar molecules, e.g., pyrromethene, hetero[8]circulene, and porphyrin. A general rate formula has been implemented to include Herzberg-Teller effects, whereby an accurate description of nonadiabatic electron transfer is feasible for a broad range of temperatures. Individual contribution from every single mode is considered using the accurate potential energy curve from high-level local coupled-cluster calculations. As an application to the dual emissive system, our results indicate that the coexistence of sluggish and rapid intersystem crossing channels is the photophysical origin of the room-temperature dual emission in a series of Pt(II) complexes with sizable bis-N-heterocyclic carbene ligands. For the fast channel, the spin-vibrational couplings not only enhance the singlet-to-triplet electron transfer rate by over an order of magnitude compared to Marcus theory prediction but also demonstrate significance in determining the optimum temperature for nonadiabatic electron transfer.