Investigating proton tunneling dynamics in the time-dependent Schrödinger equation

Understanding the temporal evolution of the wave function in the proton tunneling reactions allows us to make theoretical predictions on the possible femtosecond spectroscopy patterns. However, the analytical solution of the time-dependent Schrödinger equation of complex molecules is challenging and requires a high computational cost. In this study, we solve the time-dependent Schrödinger equation using the Fourier grid Hamiltonian method, highlighting its simplicity of calculation, even for multidimensional tunneling reactions. The obtained model is applied to studying malonaldehyde's two-dimensional intramolecular proton tunneling, comparing the results with those obtained using other computational methods.

Density Functional Theory and Atoms-in-Molecules Investigation of Intramolecular Hydrogen Bonding in Derivatives of Malonaldehyde and Implications for Resonance-Assisted Hydrogen Bonding

A density functional theory (DFT) and atoms-in-molecules (AIM) analysis has been applied to the intramolecular hydrogen bonding in the enol conformers of malonaldehyde and its fluoro-, chloro-, cyano-, and nitro-substituted derivatives. With the B3LYP/6-311++G(2d,p) method, good agreement between the DFT geometries and published experimental structures has been found. The donor-acceptor distance was also varied in a series of constrained optimizations in order to determine if energetic, structural, and topological trends associated with intermolecular hydrogen bonding remain valid in the intramolecular case. At very short donor-acceptor distances (<2.24 A), the hydrogen is symmetrically located between donor and acceptor; at distances longer than this, the hydrogen bonding is no longer symmetric. The AIM methodology has been applied to explore the topology of the electron density in the intramolecular hydrogen bonds of the chosen model systems. Most AIM properties for intramolecular hydrogen bond distances longer than 2.24 A show smooth trends, consistent with intermolecular hydrogen bonds. Integrated AIM properties have also been used to explore the phenomenon of resonance-assisted hydrogen bonding (RAHB). It is shown that as the donor-acceptor distance is varied, pi-electron density is redistributed among the carbon atoms in the intramolecular hydrogen bond ring; however, contrary to prior studies, the integrated atomic charges on the donor-acceptor atoms were found to be insensitive to variation of hydrogen-bonding distance.

The nature of solid-state N-H triplebondO/O-H triplebond N tautomeric competition in resonant systems. Intramolecular proton transfer in low-barrier hydrogen bonds formed by the triplebond O=C-C=N-NH triple bond --> <-- triplebond HO-C=C-N=N triplebond Ketohydrazone-Azoenol system. A variable-temperature X-ray crystallographic and DFT computational study

The tautomeric.O=C-C=N-NH triplebond --> <-- HO-C=C-N=N triplebond ketohydrazone-azoenol system may form strong N-H triplebond O/O-H triplebond N intramolecular resonance-assisted H-bonds (RAHBs) which are sometimes of the low-barrier H-bond type (LBHB) with dynamic exchange of the proton in the solid state. The problem of the N-H triplebond O/O-H triplebond N competition in these compounds is studied here through variable-temperature (100, 150, 200, and 295 K) crystal-structure determination of pF = 1-(4-F-phenylazo)2-naphthol and oF = 1-(2-F-phenylazo)2-naphthol, two molecules that, on the ground of previous studies (Gilli, P; Bertolasi, V.; Ferretti, V.; Gilli, G. J. Am. Chem. Soc. 2000, 122, 10405), were expected to represent an almost perfect balance of the two tautomers. According to predictions, the two molecules form remarkably strong bonds (d(N triplebond O) = 2.53-2.55 A) of double-minimum or LBHB type with dynamic N-H triplebond O/ O-H triplebond N exchange in the solid state. The enthalpy differences between the two minima, as measured by van't Hoff methods from the X-ray-determined proton populations, are very small and amount to DeltaH degrees = -0.120 and DeltaH degrees = -0.156 kcal mol(-)(1) in favor of the N-H triplebond O form for pF and oF, respectively. Successive emulation of pF by DFT methods at the B3LYP/6-31+G(d,p)//B3LYP/6-31+G(d,p) level has shown that both energetic and geometric experimental aspects can be almost perfectly reproduced. Generalization of these results was sought by performing DFT calculations at the same level of theory along the complete proton-transfer (PT) pathway for five test molecules designed in such a way that the RAHB formed changes smoothly from weak N-H triplebond O to strong O-H.N through very strong N-H triplebond O/O-H triplebond N bond of LBHB type. A systematic correlation analysis of H-bond energies, H-bond and pi-conjugated fragment geometries, and H-bond Bader's AIM topological properties performed along the PT-pathways leads to the following conclusions: (a) any X-H triplebond Y H-bonded system is fully characterized by its intrinsic PT-barrier, that is, the symmetric barrier occurring when the proton affinities of X and Y are identical; (b) the intrinsic X-H triplebond Y bond associated with the symmetric barrier is the strongest possible bond in that system and will be single-minimum (single-well, no-barrier) or double-minimum (double-well, low-barrier) according to whether the intrinsic PT-barrier is lower or slightly higher than the zero-point vibrational level of the proton; (c) with reference to the intrinsic H-bond, the effect of chemical substitution can only be that of making more and more dissymmetric the PT-barrier, while the two H-bonds split in a higher-energy bond which is stronger because closer to the transition-state structure and in a lower-energy one (the stable form) which is weaker because farther from it; (d) complete dissymmetrization of the PT-barrier will increasingly weaken the more stable H-bond until the formation of an extreme dissymmetric single-minimum or dissymmetric single-well H-bond.