In the study of materials and macromolecules by first-principle methods, the bond order is a useful tool to represent molecules, bulk materials and interfaces in terms of simple chemical concepts. Despite the availability of several methods to compute the bond order, most applications have been limited to small systems because a high spatial resolution of the wave function and an all-electron representation of the electron density are typically required. Both limitations are critical for large-scale atomistic calculations, even within approximate density-functional theory (DFT) approaches. In this work we describe our methodology to quickly compute delocalization indices for all atomic pairs, while keeping the same representation of the wave function used in most compute-intensive DFT calculations on high-performance computing equipments. We describe our implementation into a post-processing tool, designed to work with Quantum ESPRESSO, a popular open-source DFT package. In this way we recover a description in terms of covalent bonds from a representation of wave function containing no explicit information about atomic types and positions.

Rotational microwave jet spectroscopy studies of the monoterpenol α-fenchol have so far failed to identify its second expected torsional conformer, despite computational predictions that it is only very slightly higher in energy than the most stable conformer. Vibrational FTIR and Raman jet spectroscopy investigations reveal unusually complex OH and OD stretching spectra compared to other alcohols. Via modelling of the torsional states, observed spectral splittings are explained by delocalization of the hydroxy hydrogen atom through quantum tunneling between the two non-equivalent but accidentally near-degenerate conformers separated by a low and narrow barrier. The energy differences between the torsional states are determined to be only 16(1) and 7(1) cm$^{−1}hc$ for the protiated and deuterated alcohol, respectively, which further shrink to 9(1) and 3(1) cm$^{−1}hc$ upon OH or OD stretch excitation. Comparisons are made with the more strongly asymmetric monoterpenols borneol and isopinocampheol as well as with the symmetric, rapidly tunneling propargyl alcohol. Assigned are also for α-fenchol the third – in contrast localized – torsional conformer and the most stable dimer, as well as for propargyl alcohol the two most stable dimers.

The energy loss of photons due to the cosmological red shift is interpreted, here, as a periodical process of transferring electromagnetic field energy into the space. The transferred energy portions are independent on photon energy if this transfer occurs with their frequency. The amounts of periodically released energy are so small that the related ultra-long wave length photons have to be understood as perfectly delocalized. Thus, the described point of view bridges the quantum micro cosmos with the macro cosmos. It is proposed to regard this energy exchange as a typical property of universal time arrow and to interpret the “large numbers”, in particular the dimensionless reciprocal of product of Hubbles constant and Planck time as the fundamental parameter describing cosmic evolution.

The minimum energy structures of the Si3C5 and Si4C8 clusters are planar and contain planar tetracoordinate carbons (ptCs). These species have been classified, qualitatively, as global () and local () aromatics according to the adaptive natural density partitioning (AdNDP) method, which is an orbital localization method. This work evaluates these species' aromaticity, focusing on confirming and quantifying their global and local aromatic character. For this purpose, we use an orbital localization method based on the partitioning of the molecular space according to the topology of the electronic localization function (LOC-ELF). In addition, the magnetically induced current density is analyzed. The LOC-ELF-based analysis coincides with the AdNDP study (double aromaticity, global and local). Besides, the current density analysis detects global and local ring currents. The strength of the global and local current circuit is significant, involving 4n+2 - and -electrons, respectively. The latter implicates the Si-ptC-Si fragment, which would be related to the 3c-2e -bond detected by the orbital localization methods in this fragment.