The advent of attosecond techniques opens up the possibility to observe experimentally electron dynamics following ionization of molecules. Theoretical studies of pure electron dynamics at single fixed nuclear geometries in molecules have demonstrated oscillatory charge migration at a well-defined frequency but often neglecting the natural width of the nuclear wave packet. The effect on electron dynamics of the spatial delocalization of the nuclei is an outstanding question. Here, we show how the inherent distribution of nuclear geometries leads to dephasing. Using a simple analytical model, we demonstrate that the conditions for a long-lived electronic coherence are a narrow nuclear wave packet and almost parallel potential-energy surfaces of the states involved. We demonstrate with numerical simulations the decoherence of electron dynamics for two real molecular systems (paraxylene and polycyclic norbornadiene), which exhibit different decoherence time scales. To represent the quantum distribution of geometries of the nuclear wave packet, the Wigner distribution function is used. The electron dynamics decoherence result has significant implications for the interpretation of attosecond spectroscopy experiments since one no longer expects long-lived oscillations. The generation of attosecond pulses in the extreme ultraviolet range (using high harmonic generation in gases) [1,2] has opened up the possibility to probe dynamics in atoms, molecules, and solids with attosecond resolution [3-5]-the natural time scale of electronic motion. Attosecond techniques have since been developed and applied successfully to a range of problems, including the real-time observation of electronic relaxation in krypton atoms [6], the measurement of delays in photoemission of electrons in condensed-matter [7] and atomic [8] systems using the streaking technique, and the observation of electron dynamics in krypton atoms upon valence ionization using transient absorption spectroscopy [9].One key target of attosecond experiments remains the real-time observation and control of electron dynamics upon ionization in molecules [10][11][12][13][14][15][16][17]. The interference between electronic eigenstates, populated coherently, alternates between constructive and destructive and leads to oscillating motion of the electronic density with a period inversely proportional to the energy gap. This is "pure" electron dynamics (i.e., takes place even if the nuclei are fixed) and is often called charge migration in the literature [18] or hole migration if it is induced by electron correlation [19,20].A fascinating and outstanding question in the theoretical description of electron dynamics in molecules is the effect of the nuclei since most studies are carried out at a single fixed nuclear geometry (usually the equilibrium geometry of the neutral species) [21][22][23][24][25][26]. (Some studies include several conformers [22,27] but again with a single geometry per conformer.) These simulations predict long-lived oscillating motion in the electron...

Topological data analysis is a family of recent mathematical techniques seeking to understand the ‘shape’ of data, and has been used to understand the structure of the descriptor space produced from a standard chemical informatics software from the point of view of solubility. We have used the mapper algorithm, a TDA method that creates low-dimensional representations of data, to create a network visualization of the solubility space. While descriptors with clear chemical implications are prominent features in this space, reflecting their importance to the chemical properties, an unexpected and interesting correlation between chlorine content and rings and their implication for solubility prediction is revealed. A parallel representation of the chemical space was generated using persistent homology applied to molecular graphs. Links between this chemical space and the descriptor space were shown to be in agreement with chemical heuristics. The use of persistent homology on molecular graphs, extended by the use of norms on the associated persistence landscapes allow the conversion of discrete shape descriptors to continuous ones, and a perspective of the application of these descriptors to quantitative structure property relations is presented.Electronic supplementary materialThe online version of this article (10.1186/s13321-018-0308-5) contains supplementary material, which is available to authorized users.

Bulk water molecular dynamics simulations based on a series of atomistic water potentials (TIP3P, TIP4P/Ew, SPC/E and OPC) are compared using new techniques from the field of topological data analysis. The topological invariants (the different degrees of homology) derived from each simulation frame are used to create a series of persistence diagrams from the atomic positions. These are averaged over the simulation time using the persistence image formalism, before being normalised by their total magnitude (the L1 norm) to ensure a size independent descriptor (L1NPI). We demonstrate that the L1NPI formalism is suitable for the analysis of systems where the number of molecules varies by at least a factor of 10. Using standard machine learning techniques, a basic linear SVM, it is shown that differences in water models are able to be isolated to different degrees of homology. In particular, whereas first degree homology is able to distinguish between all atomistic potentials studied, OPC is the only potential that differs in its second degree homology. The L1 normalised persistence images are then used in the comparison of a series of Stillinger–Weber potential simulations to the atomistic potentials and the effects of changing the strength of three-body interactions on the structures is easily evident in L1NPI space, with a reduction in variance of structures as interaction strength increases being the most obvious result. Furthermore, there is a clear tracking in L1NPI space of the λ parameter. The L1NPI formalism presents a useful new technique for the analysis of water and other materials. It is approximately size-independent, and has been shown to contain information as to real structures in the system. We finally present a perspective on the use of L1NPIs and other persistent homology techniques as a descriptor for water solubility. Electronic supplementary material The online version of this article (10.1186/s13321-019-0369-0) contains supplementary material, which is available to authorized users.

Understanding the geometry and topology of configuration or conformational spaces of molecules has relevant applications in chemistry and biology such as the proteins folding problem, drug design and the structure activity relationship problem. Despite their relevance, configuration spaces of molecules are only partially understood. In this paper we discuss both theoretical and computational approaches to the configuration spaces of molecules and their associated energy landscapes. Our mathematical approach shows that when symmetries of the molecules are taken into account, configuration spaces of molecules give rise to certain principal bundles and orbifolds. We also make use of a variety of geometric and topological tools for data analysis to study the topology and geometry of these spaces.

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