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 Journal of Mathematical ChemistryJournal Prestige (SJR): 0.332 Citation Impact (citeScore): 1Number of Followers: 5      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1572-8897 - ISSN (Online) 0259-9791 Published by Springer-Verlag  [2469 journals]
• mad-GP: automatic differentiation of Gaussian processes for molecules and
materials

Abstract: Abstract In this paper, we introduce a Python library called mad-GP that enables users to more easily explore the design space of Gaussian process (GP) surrogate models for modeling potential energy surfaces (PESs). A user of mad-GP only needs to write down the functional form of the prior mean function (i.e., a prior guess for the PES) and kernel function (i.e., a constraint on the class of PESs), and the library handles all required derivative implementations via automatic differentiation (AD). We validate the design of mad-GP by applying it to perform geometry optimization of small molecules. In particular, we test the effectiveness of fitting GP surrogates to energies and/or forces, and perform a preliminary study on the use of non-constant priors and hierarchical kernels in GP PES surrogates. We find that GPs that fit forces perform comparably with GPs that fit both energies and forces, although force-only GPs are more robust for optimization because they do not require an additional step to be applied during optimization. We also confirm that constant mean functions and Matérn kernels work well as reported in the literature, although our tests also identify several other promising candidates (e.g., Coulomb matrices with three-times differentiable Matérn kernels). Our tests validate that AD is a viable method for performing geometry optimization with GP surrogate models on small molecules.
PubDate: 2022-06-01

• A multistep method with optimal phase and stability properties for
problems in quantum chemistry

Abstract: Abstract A new two-step method is introduced in the present paper. The new algorithm is conditionally P-Stable and an economical scheme. It has vanished phase-lag and it’s first to fourth derivatives. We use for the new scheme the symbol LOWPF5DECN2ST. We apply the newly introduced method to problems in Quantum Chemistry. The new scheme is defined as economical since it uses 4 function evaluations per step in order to achieve an algebraic order (AOR) of 10.
PubDate: 2022-06-01

• Dendrimer eigen-characteristics

Abstract: Abstract Local graph symmetry groups act in a non-identical fashion on just a proper (local) subset of a graph’s vertices, and consequent theorems for adjacency matrices simplify eigen-solutions. These theorems give a way to deal with a hierarchy of local sub-symmetries, such as are manifested by so-called “dendrimers”, which are (highly) branched polymers obtainable at a given generation number r from the polymer at the preceding generation number (r − 1) by connecting d copies of new branching monomer units to each end-unit of this preceding tree-like dendrimer, the initial generation number r = 1 consisting of a single monomer unit connected to d others. Our local symmetry methodology leads to an (essentially) analytic eigen-solution for the Bethe tree case, with the branching units just single sites—but further there result novel (qualitatively distinctive) features: eigenvector localization and eigenvalue clumping. Moreover, these novel characteristics persist for more general “dendrimers”, here considered and illustrated in the context of electronic structure of conjugated-carbon π-networks. The overall view here is of a systematic development and characterization for such dendrimer polymers paralleling some aspects of the standard development and characteristics for linear-chain benzenoid polymers—for instance, that of plotting eigen-energies as a function of symmetry. Clumping of eigen-spectra, and localization features in dendrimer eigenfunctions occur and are examined.
PubDate: 2022-05-16

• Convergence of the electronic density for a target region in cluster
models of a NH $$_3$$ 3 molecular crystal

Abstract: Abstract In this paper we illustrate the advantage of addressing size-intensive properties of target regions without first converging the ground-state energy of that region. We use local occupied and virtual orbitals to separate the orbital space of NH $$_3$$ clusters into an orbital space for the target region (a central NH $$_3$$ molecule) and for the remaining cluster. Convergence characteristics of the Hartree–Fock (HF) energy and, indirectly, the electronic density of the target region are shown. The calculations illustrate that although the energy of the target region will not converge with cluster size, the electronic density will. The convergence of the electronic density of the target region is subsequently exploited to obtain HF dipole moments and CC2-in-HF vertical excitation energies. For these properties convergence is seen upon the inclusion of approximately three shells beyond the target region. This shows that local size-intensive properties of a target region can be investigated without converging the energy. We further show that a minimal basis description of the outer shells are sufficient to capture the correct interaction with the target region. The possibility of computing size-intensive properties for a target region using a converged electronic density, without requiring convergence in the energy itself, is currently an underexploited feature.
PubDate: 2022-04-29

• A Rayleigh–Ritz Method for Numerical Solutions of Linear Fredholm
Integral Equations of the Second Kind

Abstract: Abstract A Rayleigh–Ritz Method is suggested for solving linear Fredholm integral equations of the second kind numerically in a desired accuracy. To test the performance of the present approach, the classical one-dimensional Schrödinger equation $$-y^{\prime \prime }(x)+v(x)y(x)=\lambda y(x),\ x\in (-\infty ,\infty )$$ has been converted into an integral equation. For a regular problem, the unbounded interval is truncated to $$x\in [-\ell ,\ell ]$$ , where $$\ell$$ is regarded as a boundary parameter. Then, the resulting integral equation has been solved and the results are compared with the very well known eigenvalues of the Schrödinger equation with several types of potential functions v(x). It is shown that the eigenvalues recorded to about 15 significant figures are in excellent agreement with the results that exist in the literature.
PubDate: 2022-04-27

• Laplace transform method in one dimensional quantum mechanics on the semi
infinite axis

Abstract: Abstract In this paper we discuss the Laplace transform method for solving one dimensional Schrödinger equation in a semi infinite axis. As examples we discuss the delta potential, quantum bouncer, Coulomb-like potential and half harmonic potential.
PubDate: 2022-04-23

• Analysis of solutions of time-dependent Schrödinger equation of a
particle trapped in a spherical box

Abstract: Abstract Three sets of exact solutions of the time-dependent Schrödinger equation of a particle that is trapped in a spherical box with a moving boundary wall have been calculated analytically. For these solutions, some physical quantities such as time-dependent average energy, average force, disequilibrium, quantum similarity measures as well as quantum similarity index have been investigated. Moreover, these solutions are compared concerning these physical quantities. The time-correlation functions among these solutions are investigated.
PubDate: 2022-04-23

• Phase-space Rényi entropy, complexity and thermodynamic picture of
density functional theory

Abstract: Abstract Phase-space Rényi entropy and complexity are defined within the thermodynamic picture of density functional theory. The structural entropy defined by Pipek, Varga and Nagy, the LMC statistical complexity introduced by López-Ruiz, Mancini and Calbet and generalized complexity proposed by López-Ruiz, Nagy, Romera and Sanudo are extended to the phase space. It is shown that in case of constant local temperature the logarithm of the phase-space LMC complexity reduces to the position-space structural entropy defined by Pipek et al.
PubDate: 2022-04-23

• Peripherality in networks: theory and applications

Abstract: Abstract We investigate several related measures of peripherality and centrality for vertices and edges in networks, including the Mostar index which was recently introduced as a measure of peripherality for both edges and networks. We refute a conjecture on the maximum possible Mostar index of bipartite graphs. We asymptotically answer another problem on the maximum difference between the Mostar index and the irregularity of trees. We also prove a number of extremal bounds and computational complexity results about the Mostar index, irregularity, and measures of peripherality and centrality. We discuss graphs where the Mostar index is not an accurate measure of peripherality. We construct a general family of graphs with the property that the Mostar index is strictly greater for edges that are closer to the center. We also investigate centrality and peripherality in two graphs which represent the SuperFast and MOZART-4 systems of atmospheric chemical reactions by computing various measures of peripherality and centrality for the vertices and edges in these graphs. For both of these graphs, we find that the Mostar index is closer to a measure of centrality than peripherality of the edges. We also introduce some new indices which perform well as measures of peripherality on the SuperFast and MOZART-4 graphs.
PubDate: 2022-04-18

• Persistence and stability of a class of kinetic compartmental models

Abstract: Abstract In this paper we show that the dynamics of a class of kinetic compartmental models with bounded capacities, monotone reaction rates and a strongly connected interconnection structure is persistent. The result is based on the chemical reaction network (CRN) and the corresponding Petri net representation of the system. For the persistence analysis, it is shown that all siphons in the Petri net of the studied model class can be characterized efficiently. Additionally, the existence and stability of equilibria are also analyzed building on the persistence and the theory of general compartmental systems. The obtained results can be applied in the analysis of general kinetic models based on the simple exclusion principle.
PubDate: 2022-04-09

• Sudden excitations of harmonic normal modes

Abstract: Abstract The N-harmonium boson system, i.e., a completely integrable model of N particles where both the external confinement and the two-particle interaction are harmonic, is investigated under the action of sudden time-dependent perturbation. This quench-like external perturbation of confinement has a quadrupolar space-character. The time-independent transition probabilities, which characterize the impact of quench as average occupation numbers, form a complete distribution in the sense of probability theory. The quench-generated energy shift $$\Delta E$$ in the correlated many-body system, and a purity-type Rényi entropy $$S_{\alpha =2}$$ are calculated. Challenging reinterpretations of such an energy change in terms of variables of a classical thermodynamical system of $$N(N-1)/2$$ pairs are given as well. As in the case of the ground-state correlated system, an entropy could characterize a global link to energetically optimized independent-particle models.
PubDate: 2022-04-04

• Molecular device design based on chemical reaction networks: state
feedback controller, static pre-filter, addition gate control system and
full-dimensional state observer

Abstract: Abstract For the modeling and operation of biological computing, chemical reaction networks (CRNs) constitute an ideal programming paradigm for the simulation of various digital and analog circuits. In this manuscript, an originally divergent linear time-invariant (LTI) CRNs system is made stable by constructing a state feedback controller. State feedback controllers control the internal characteristics of a linear system through the state matrix of the system. A static pre-filter based on CRNs is constructed in order to ensure the tracking effect of system response. Next, considering extraneous disturbances to the LTI system, an integration element is added in the first channel of the control system to stably suppress disturbance input. Moreover, the state feedback controller is utilized to build an addition gate control system. When a leak reaction occurs in the addition gate, the addition gate control system produces the correct calculation result, whereas the addition gate calculation is wrong. Finally, a full-dimensional state observer based on CRNs is implemented in this paper. In the case of external disturbance interference or incomplete modeling, the state trajectories of the system are observed by the full-dimensional state observer.
PubDate: 2022-03-21

• Sombor index: review of extremal results and bounds

Abstract: Abstract The Sombor index was introduced in 2020, and was soon followed by a remarkably large number of studies, both chemical and mathematical. In this review we collect the existing bounds and extremal results related to the Sombor index and its variants.
PubDate: 2022-03-19

• Investigation of chemical space networks using graph measures and random
matrix theory

Abstract: Abstract Large collections of molecules (chemical libraries) are nowadays routinely screened in the process of designing drugs for specific ailments. Chemical and structural similarities between these molecules can be quantified using molecular descriptors, and these similarities can in turn be used to represent any chemical library as an undirected network called a chemical space network (CSN). Here we study different CSNs using conventional graph measures as well as random matrix theory (RMT). For the conventional graph measures, we focus on the average degree, average path length, graph diameter, degree assortativity, transitivity, average clustering coefficient and modularity. For the RMT analyses, we examine the eigenvalue spectra of adjacency matrices constructed from the molecular similarities for different CSNs, and examine their local fluctuation properties, contrasting them with the predictions of RMT. Changes in the conventional graph measures and RMT statistics with the network structure are examined for three different chemical libraries by varying the edge density (fraction of the actual to the maximum possible number of edges) of the networks. It is found that the assortativity among the conventional graph measures, and long-range fluctuation statistics of RMT in eigenvalue space respond to the changes in global network structure as well as the chemical space. We expect that this investigation of the network characteristics of different kinds of chemical libraries will provide guidance in the design of high-throughput screening libraries for different drug design applications.
PubDate: 2022-03-17

• The total quasi-steady-state for multiple alternative substrate reactions

Abstract: Abstract The Michaelis–Menten–Briggs–Haldane approximation and its extension, the total quasi-steady-state approximation (tQSSA) are famous assumptions for simplification of mathematical modeling of enzyme-substrate reactions. These approximations and their validity conditions are well studied for a single substrate reaction system. However, the extension of these studies for the tQSSA of the general case of multiple substrate reactions is yet to be performed precisely due to the consequent non-linear expressions for tQSSA. In this paper, we introduce a linearization method for equations governing the tQSSA of multiple substrate reactions to obtain an analytical solution for the evolution of concentrations of reactants that is valid throughout the whole time period. In addition, we provide the validity conditions of the tQSSA for multiple substrate reaction systems using the singular perturbation analysis method.
PubDate: 2022-03-11
DOI: 10.1007/s10910-022-01339-6

• Locating a double vacancy or Stone–Wales point defect on a hexagonal
quantum grid

Abstract: Abstract A graphene nano-ribbon structure can be modelled by a 3-regular hexagonal grid. We convert this to a rectangular coordinate system in order to identify uniquely the position of either the $$\text {V}_2(5-8-5)$$ double vacancy (DV) defect or the Stone–Wales SW(55–77) defect. This is done by using the lengths of the closed paths along the edges of the underlying graph. By sending a signal from one of the vertices and detecting the returning impulses one can observe experimentally the spectrum of the structure. Using the trace formula it is possible to determine the lengths of all closed paths (periodic orbits) starting and ending at the given vertex where a detector is placed. We present an algorithm which enables one to pinpoint the precise coordinates of a DV defect by using at most three reference points. Similarly we provide an algorithm for finding an SW defect.
PubDate: 2022-03-11
DOI: 10.1007/s10910-022-01337-8

• On using Brandt groupoids in physicochemical research

Abstract: Abstract We are interested in the possibility of using Brandt groupoids in physical chemistry. They can, in particular, describe local symmetry and spatially limited motion of particles, in which the latter can move only a limited distance from their initial position. As an illustrative example, we consider the mutual exchange of the positions of the ligands in the coordination compounds.
PubDate: 2022-03-11
DOI: 10.1007/s10910-022-01335-w

• On the exact revival of Morse oscillator wave packets

Abstract: Abstract The exact analytic expressions of the autocorrelation function and Husimi distribution function for a Morse oscillator wave packet have been derived and we use them to see the evolution of the wave packet. The dynamics of Morse oscillator wave packets for the dimers ArXe, Be2 and Li2 have been discussed. Special emphasis has been given on the revival phenomenon of such wave packets. It is obtained that the exact revivals of wave packets for ArXe, Be2 and Li2 do not occur at the revival times (trev) but at the instances 3.5, 8.5 and 33.5 times and their simple multiple of trev respectively.
PubDate: 2022-03-05
DOI: 10.1007/s10910-022-01336-9

• Weakly reversible CF-decompositions of chemical kinetic systems

Abstract: Abstract This paper studies chemical kinetic systems which decompose into weakly reversible complex factorizable (CF) systems. Among power law kinetic systems, CF systems (denoted as PL-RDK systems) are those where branching reactions of a reactant complex have identical rows in the kinetic order matrix. Mass action and generalized mass action systems (GMAS) are well-known examples. Schmitz’s global carbon cycle model is a previously studied non-complex factorizable (NF) power law system (denoted as PL-NDK). We derive novel conditions for the existence of weakly reversible CF-decompositions and present an algorithm for verifying these conditions. We discuss methods for identifying independent decompositions, i.e., those where the stoichiometric subspaces of the subnetworks form a direct sum, as such decompositions relate positive equilibria sets of the subnetworks to that of the whole network. We then use the results to determine the positive equilibria sets of PL-NDK systems which admit an independent weakly reversible decomposition into PL-RDK systems of PLP type, i.e., the positive equilibria are log-parametrized, which is a broad generalization of a Deficiency Zero Theorem of Fortun et al. (MATCH Commun. Math. Comput. Chem. 81:621–638, 2019).
PubDate: 2022-03-05
DOI: 10.1007/s10910-022-01332-z

• Graph entropies, enumeration of circuits, walks and topological properties
of three classes of isoreticular metal organic frameworks

Abstract: Abstract One of the fundamental challenges in reticular chemistry is the characterization of the complexity of the underlying molecular network, in which high complexity signifies low symmetry and high diversity. The entropy of a network is one such topological descriptor that serves to characterize the order/disorder structural complexity. In this paper, we obtain the entropy measures by computing systematic expressions of the self-powered degree-based topological indices for three isoreticular metal organic frameworks with a zinc based central unit and stringed binding linkers with varying benzene molecule counts. We have also enumerated the self-returning and nonreturning walks for these isoreticular structures in order to provide potential pathways for charge and ion transport. We have considered other properties such as eccentricities, radius, diameter, vertex and edge equivalence classes that facilitate rapid computations of thermochemistry and hence relative stabilities of isoreticular networks.
PubDate: 2022-02-28
DOI: 10.1007/s10910-021-01321-8

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