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Within the nuclear-electronic orbital (NEO) framework, the real-time NEO time-dependent density functional theory (RT-NEO-TDDFT) approach enables the simulation of coupled electronic-nuclear dynamics. In this approach, the electrons and quantum nuclei are propagated in time on the same footing. A relatively small time step is required to propagate the much faster electronic dynamics, thereby prohibiting the simulation of long-time nuclear quantum dynamics. Herein, the electronic Born–Oppenheimer (BO) approximation within the NEO framework is presented. In this approach, the electronic density is quenched to the ground state at each time step, and the real-time nuclear quantum dynamics is propagated on an instantaneous electronic ground state defined by both the classical nuclear geometry and the nonequilibrium quantum nuclear density. Because the electronic dynamics is no longer propagated, this approximation enables the use of an order-of-magnitude larger time step, thus greatly reducing the computational cost. Moreover, invoking the electronic BO approximation also fixes the unphysical asymmetric Rabi splitting observed in previous semiclassical RT-NEO-TDDFT simulations of vibrational polaritons even for small Rabi splitting, instead yielding a stable, symmetric Rabi splitting. For the intramolecular proton transfer in malonaldehyde, both RT-NEO-Ehrenfest dynamics and its BO counterpart can describe proton delocalization during the real-time nuclear quantum dynamics. Thus, the BO RT-NEO approach provides the foundation for a wide range of chemical and biological applications.

 

Cryogenic infrared vibrational spectroscopy of D2-tagged cyanobenzoate (CBA) derivatives are obtained and analyzed to characterize the intrinsic spectroscopic responses of the -CO2‾ head group to its location on the ring in both the isolated anions and the cationic complexes with divalent metal ions, M2+ (M=Mg, Ca, Sr). The benzonitrile functionality establishes the different ring isomers (para, meta, ortho) according to the location of the carboxylate and provides an additional reporter on the molecular response to the proximal charge center. The aromatic carboxylates display slightly smaller shifts than those observed for a related aliphatic system upon metal ion complexation. Although the CBA anions display very similar band patterns for all three ring positions, upon complexation with metal ions, the ortho isomer yields dramatically different spectral responses in both the -CO2‾ moiety and the CN group. This behavior is traced to the emergence of a tridentate binding motif unique to the ortho isomer in which the metal ions bind to both the oxygen atoms of the carboxylate group and the N atom of the cyano group. In that configuration, the -CO2‾ moiety is oriented perpendicular to the phenyl ring, and the CN stretching fundamental is both strong and red-shifted relative to its behavior in the isolated neutral. The behaviors of the metal-bound ortho complexes occur in contrast to the usual blue shifts associated with “Lewis” type binding of metal ions end-on to -CN. The origins of these spectroscopic features are analyzed with the aid of electronic structure calculations, which also explore differences expected for complexation of monovalent cations to the ortho carboxylate. The resulting insights have implications for understanding the balance between electrostatic and steric interactions at metal binding sites in chemical and biological systems.