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Graph theory algorithms have been proposed in order to identify, follow in time, and statistically analyze the changes in conformations that occur along molecular dynamics (MD) simulations. The atomistic granularity level of the MD simulations is maintained within the graph theoric algorithms proposed here, isomorphism is a key component together with keeping the chemical nature of the atoms. Isomorphism is used to recognize conformations and construct the graphs of transitions, and the reduction in complexity of the isomorphism has been achieved by the introduction of "orbits" and "reference snapshots." The proposed algorithms are applied to MD trajectories of gas phase molecules and clusters as well as condensed matter. The changes in conformations followed over time are hydrogen bond(s), proton transfer(s), coordination number(s), covalent bond(s), multiple fragmentation(s), and H-bonded membered rings. The algorithms provide an automatic analysis of multiple trajectories in parallel, and can be applied to ab initio and classical MD trajectories alike, and to more coarse grain representations. [ABSTRACT FROM AUTHOR]

Some of our recent developments and applications of algorithmic graph theory for extracting the physical and chemical properties of materials from molecular dynamics simulations are presented. From the chemical viewpoint, the power of graph theory is illustrated in the search for a catalyst's active sites at a silica solid surface. From the physical viewpoint, we present graph algorithms that recognize the structural motifs that exist at the silica/liquid water interface. Statistical analyses of the instances of these surface-water motifs provide a detailed understanding of the structures and dynamics at the aqueous interface.

A novel approach based on a coarse-grained representation of topological graphs is proposed for the automatic analysis of molecular dynamics (MD) trajectories of hydrogen-bonded (H-Bonded) flexible biomolecules. Herein, our approach models an H-Bonded biomolecule by its H-Bonded cycles and its graph of cycles in which the vertices and links represent the intersections between these cycles. We propose a methodology in which each identified conformer/isomer from the MD is represented by a well-chosen set of H-Bonded cycles called a minimum cycle basis. The key component is the "polycycles" that distinguish the cycles that play the same polymorphic role in the molecule from the ones that lead to an actual conformational change of the molecule. The relevance of our proposed method is evaluated on MD trajectories of gas-phase biomolecules, for which the covalent bonds are unchanged over time and only the hydrogen bonds change over time. The polygraphs and their time evolution are shown to reveal the dynamicity of the metastructure(s) of the H-Bonded biomolecules while providing polymorphic information on the cycles. Such information on the dynamics and changes in the H-bond network, as some cycles change identity while retaining the same role in the overall structure, is not easily captured at the atomic level of representation. Such information can instead be captured by polymorphic cycles.

A method is introduced for the automated analysis of reactivity exploration for extended in silico databases of transition-metal catalysts. The proposed workflow is designed to tackle two key challenges for bias-free mechanistic explorations on large databases of catalysts: (1) automated exploration of the chemical space around each catalyst with unique structural and chemical features and (2) automated analysis of the resulting large chemical data sets. To address these challenges, we have extended the application of our previously developed ReNeGate method for bias-free reactivity exploration and implemented an automated analysis procedure to identify the classes of reactivity patterns within specific catalyst groups. Our procedure applied to an extended series of representative Mn(I) pincer complexes revealed correlations between structural and reactive features, pointing to new channels for catalyst transformation under the reaction conditions. Such an automated high-throughput virtual screening of systematically generated hypothetical catalyst data sets opens new opportunities for the design of high-performance catalysts as well as an accelerated method for expert bias-free high-throughput in silico reactivity exploration.

This paper reviews graph-theory-based methods that were recently developed in our group for post-processing molecular dynamics trajectories. We show that the use of algorithmic graph theory not only provides a direct and fast methodology to identify conformers sampled over time but also allows to follow the interconversions between the conformers through graphs of transitions in time. Examples of gas phase molecules and inhomogeneous aqueous solid interfaces are presented to demonstrate the power of topological 2D graphs and their versatility for post-processing molecular dynamics trajectories. An even more complex challenge is to predict 3D structures from topological 2D graphs. Our first attempts to tackle such a challenge are presented with the development of game theory and reinforcement learning methods for predicting the 3D structure of a gas-phase peptide.

Exploration of the chemical reaction space of chemical transformations in multicomponent mixtures is one of the main challenges in contemporary computational chemistry. To remove expert bias from mechanistic studies and to discover new chemistries, an automated graph-theoretical methodology is proposed, which puts forward a network formalism of homogeneous catalysis reactions and utilizes a network analysis tool for mechanistic studies. The method can be used for analyzing trajectories with single and multiple catalytic species and can provide unique conformers of catalysts including multinuclear catalyst clusters along with other catalytic mixture components. The presented three-step approach has the integrated ability to handle multicomponent catalytic systems of arbitrary complexity (mixtures of reactants, catalyst precursors, ligands, additives, and solvents). It is not limited to predefined chemical rules, does not require prealignment of reaction mixture components consistent with a reaction coordinate, and is not agnostic to the chemical nature of transformations. Conformer exploration, reactive event identification, and reaction network analysis are the main steps taken for identifying the pathways in catalytic systems given the starting precatalytic reaction mixture as the input. Such a methodology allows us to efficiently explore catalytic systems in realistic conditions for either previously observed or completely unknown reactive events in the context of a network representing different intermediates. Our workflow for the catalytic reaction space exploration exclusively focuses on the identification of thermodynamically feasible conversion channels, representative of the (secondary) catalyst deactivation or inhibition paths, which are usually most difficult to anticipate based solely on expert chemical knowledge. Thus, the expert bias is sought to be removed at all steps, and the chemical intuition is limited to the choice of the thermodynamic constraint imposed by the applicable experimental conditions in terms of threshold energy values for allowed transformations. The capabilities of the proposed methodology have been tested by exploring the reactivity of Mn complexes relevant for catalytic hydrogenation chemistry to verify previously postulated activation mechanisms and unravel unexpected reaction channels relevant to rare deactivation events.

DFT-based molecular dynamics simulations of the electrified air-liquid water interface are presented, where a homogeneous field is applied parallel to the surface plane. We unveil the field intensity for the onset of proton transfer and molecular dissociation; the protonic current/proton conductivity is measured as a function of the field intensity/voltage. The air-water interface is shown to exhibit a proton conductivity twice the one in the liquid water for field intensities below 0.40 V Å -1 . We show that this difference arises from the very specific organization of water in the binding interfacial layer (BIL, i.e. the air-water interface region) into a 2D-HBond-network that is maintained and enforced at the electrified interface. Beyond fields of 0.40 V Å -1 , water in the BIL and in the bulk liquid are aligned in the same way by the rather intense fields, hence leading to the same proton conductivity in both BIL and bulk water.

The combined approach of gas phase IR-UV ion dip spectroscopy experiments and DFT-based molecular dynamics simulations for theoretical spectroscopy reveals the 3D structures of (Ac-Phe-OMe)1,2 peptides using their far-IR/THz signatures. Both experimental and simulated IR spectra are well-resolved in the 100-800 cm-1 domain, allowing an unambiguous assignment of the conformers, that could not be achieved in other more congested spectral domains. We also present and make proofs-of-principles for our newly developed theoretical method for the assignment of (anharmonic) vibrational modes from MD simulations based on graph theory coupled to APT-weighted internal coordinates velocities DOS spectra. The principles of the method are reviewed, applications to the simple gas phase water and NMA (N-methyl-acetamide) molecules are presented, and application to the more complex (Ac-Phe-OMe)1,2 peptidic systems shows that the complexity in assigning vibrational modes from MD simulations is reduced with the graphs. Our newly developed graph-based methodology is furthermore shown to allow an easy comparison between the vibrational modes of isolated monomer(s) and their complexes, as illustrated by the (Ac-Phe-OMe)1,2 peptides.