Incorporating nuclear vibrational energies into the "atom in molecules" analysis: An analytical study.

The quantum theory of atoms in molecules (QTAIM) is based on the clamped nucleus paradigm and solely working with the electronic wavefunctions, so does not include nuclear vibrations in the AIM analysis. On the other hand, the recently extended version of the QTAIM, called the multi-component QTAIM (MC-QTAIM), incorporates both electrons and quantum nuclei, i.e., those nuclei treated as quantum waves instead of clamped point charges, into the AIM analysis using non-adiabatic wavefunctions. Thus, the MC-QTAIM is the natural framework to incorporate the role of nuclear vibrations into the AIM analysis. In this study, within the context of the MC-QTAIM, the formalism of including nuclear vibrational energy in the atomic basin energy is developed in detail and its contribution is derived analytically using the recently proposed non-adiabatic Hartree product nuclear wavefunction. It is demonstrated that within the context of this wavefunction, the quantum nuclei may be conceived pseudo-adiabatically as quantum oscillators and both isotropic harmonic and anisotropic anharmonic oscillator models are used to compute the zero-point nuclear vibrational energy contribution to the basin energies explicitly. Inspired by the results gained within the context of the MC-QTAIM analysis, a heuristic approach is proposed within the context of the QTAIM to include nuclear vibrational energy in the basin energy from the vibrational wavefunction derived adiabatically. The explicit calculation of the basin contribution of the zero-point vibrational energy using the uncoupled harmonic oscillator model leads to results consistent with those derived from the MC-QTAIM.

SH···N and SH···P blue-shifting H-bonds and N···P interactions in complexes pairing HSN with amines and phosphines.

Quantum calculations at the MP2/aug-cc-pVDZ level examine complexes pairing HSN with aliphatic amines and phosphines. Complexes are cyclic and contain two attractive interactions. The first is a SH···N/P H-bond in which the S-H covalent bond contracts and shifts its stretching frequency to the blue, more so for amines than for phosphines. The second interaction is different for the amines and phosphines. The amines engage in a NH···N H-bond comparable in strength to the aforementioned SH···N interaction. In contrast, the second interaction in the phosphine complexes is a direct N···P attraction without an intervening H. This interaction is due in part to opposite partial charges on the N and P atoms, as well as covalent forces generated by charge transfer effects.