Exhaustive enumeration of molecular substructures

This article addresses the systematic and complete enumeration of all the substructures of any size present in a given molecule. The study is not restricted to features which could be defined a priori such as rings or chains. Contrary to prior expectation the exhaustive enumeration is tractable with current computational tools. Results are presented for several families of skeletons which are widespread in chemistry. It is shown that the numbers of constituent substructures of each size are related to the molecular topology, in particular the degree of branching. The number substructures which are distinct depends additionally on the number of different atom and bond types present. The overall shapes of the distribution of substructure counts as a function of substructure size are found to be similar within particular classes of molecules. These distributions are compared and found to be characteristic of certain topologies. For several simple classes of molecule, analytic expressions are provided for the numbers of substructures as a function of fragment and molecule size. These results hold promise for identifying potentially useful scaffolds for use in combinatorial chemistry. © 1997 by John Wiley & Sons, Inc.     

The role of isomorphism in synthetic analysis. Pruning the search tree by finding disjoint isomorphic substructures

Isomorphism is an equivalence relation that is less stringent than identity (equality), and it is useful for synthetic analysis, since it allows one to find reflexive routes for targets even when they do not have an element of symmetry.     

Computer-based system for correlating molecular structures with mass spectral data Methods for generating molecular substructures and for incorporating fragmentation rules

The masses of ions observed in the mass spectrum of a pure compound are correlated with the masses of the molecular substructures of the compound. Three methods are described for generating molecular substructures. Each method is evaluated to establish how effectively it generates the molecular substructures and correlates the masses of the molecular substructures with the masses of the observed fragment ions. Rules for mass-spectral fragmentation processes are incorporated into the mass spectral analysis software and illustrated for retro-aldol and lactone-ester reactions occurring in the thermospray mass spectra of oligomycin antibiotics.     

Newton trajectories for finding stationary points on molecular potential energy surfaces

We present a new algorithm for computing Newton trajectories based on the Quadratic String Method (QSM) and explain how this can be used to find key stationary points on the molecular potential energy surface (PES). This method starts by using the intersections of Newton trajectories to locate stationary points on the PES. These points could then be used to determine the minimum energy path. The new method, called QSM-NT, is shown to be efficient and reliable for both analytical potential energy surfaces and potential energy surfaces computed from quantum chemistry calculations. The advantages and pitfalls of this method for exploring PES are discussed. In particular, the problem of discontinuous Newton trajectories is elucidated.     

On the validity and applicability of the connected moments expansion

The theoretical justification, and typical convergence properties, of Cioslowski's connected moments expansion for the ground-state energy of a quantum-mechanical system are considered. This size extensive expansion is an alternative to Rayleigh-Schrodinger perturbation theory, and is expected to be useful in electronic structure calculations based on many-determinant reference functions, where perturbation theory is not applicable. It is found from example molecular electronic structure calculations that, in some cases, the expansion does not converge correctly to the true energy. An im- proved expansion derived from a padé approximant, and an analysis of its validity, is presented here.     

Learning size-adaptive molecular substructures for explainable drug–drug interaction prediction by substructure-aware graph neural network

Drug–drug interactions (DDIs) can trigger unexpected pharmacological effects on the body, and the causal mechanisms are often unknown. Graph neural networks (GNNs) have been developed to better understand DDIs. However, identifying key substructures that contribute most to the DDI prediction is a challenge for GNNs. In this study, we presented a substructure-aware graph neural network, a message passing neural network equipped with a novel substructure attention mechanism and a substructure–substructure interaction module (SSIM) for DDI prediction (SA-DDI). Specifically, the substructure attention was designed to capture size- and shape-adaptive substructures based on the chemical intuition that the sizes and shapes are often irregular for functional groups in molecules. DDIs are fundamentally caused by chemical substructure interactions. Thus, the SSIM was used to model the substructure–substructure interactions by highlighting important substructures while de-emphasizing the minor ones for DDI prediction. We evaluated our approach in two real-world datasets and compared the proposed method with the state-of-the-art DDI prediction models. The SA-DDI surpassed other approaches on the two datasets. Moreover, the visual interpretation results showed that the SA-DDI was sensitive to the structure information of drugs and was able to detect the key substructures for DDIs. These advantages demonstrated that the proposed method improved the generalization and interpretation capability of DDI prediction modeling.

SA-DDI is designed to learn size-adaptive molecular substructures for drug–drug interaction prediction and can provide explanations that are consistent with pharmacologists.     

High effectiveness of oligothienylenevinylene as molecular wires in Zn-porphyrin and C60 connected systems

Photoinduced energy transfer and electron transfer processes have been found between the excited singlet state of Zn-porphyrin and C(60) via an oligothienylenevinylene bridge depending on the length of the oligothiophene and solvent polarity.     

On finding the rate constants of linear and nonlinear systems

In lowest approximation, a certain chemical reaction is described by a system of first-order linear differential equations with unknown constant coefficients. One can therefore write down an expression for the state of the system at time t, and from this find the endpoint of the reaction in terms of the initial state and the rate constants. The relative values of some rate constants can then be estimated from experimental data. A better approximation in which the differential equations are nonlinear is also considered, and it turns out that because of symmetry in the reaction, the relationship between the final state and the ratios of the rate constants is unchanged. Although the differential equations now appear much less tractable, the problem of relating the rate constants to the endpoint of the reaction can be formulated and solved in terms of probabilities. The results illustrate an important property of reaction schemes in which some of the steps are reversible. More generally, this is a property of differential equations: provided that they continue to satisfy certain linear constraints, the parameters of a linear system of ordinary differential equations can vary without affecting the asymptotic solution.     

Conjugating polymer superlattice and porphyrin arrays connected with molecular wire: approaching ultimate functional materials

Approaches to conjugating polymer superlattice and one- and two-dimensional porphyrin arrays connected with molecular wire are shown, demonstrated using preparative methods and functions of the resulting materials. The conjugating polymer superlattice composed of copoly(pyrrole and bithiophene)s showed a high energy shift in photoluminescence when the well layer thickness was smaller than ca. 100 Å, which presents a quantum size effect. The P(V) tetraphenylporphyrin arrays connected with oligothiophene showed photoconductivity via a hole carrier mechanism. On the contrary, the P(V) tetraphenylporphyrin arrays connected with ethylene glycol showed that photoexcitation was localized, which implies a photo-information storage at a certain porphyrin moiety. This leads to an idea of a photoactive neuron model.     

Decomposition of unitary matrices for finding quantum circuits: application to molecular Hamiltonians

Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Evolution of quantum circuits faces two major challenges: complex and huge search space and the high costs of simulating quantum circuits on classical computers. Here, we use the group leaders optimization algorithm to decompose a given unitary matrix into a proper-minimum cost quantum gate sequence. We test the method on the known decompositions of Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, and the sender part of the quantum teleportation. Using this procedure, we present the circuit designs for the simulation of the unitary propagators of the Hamiltonians for the hydrogen and the water molecules. The approach is general and can be applied to generate the sequence of quantum gates for larger molecular systems.     

On an inconsistency connected with koopman's theorem

On the basis of Koopmans' theorem two methodically different ways to estimate the effect of a spin-orbit perturbation on the ionization potentials of I₂ have been proposed. In the present paper a model system is constructed to show the equivalence of both methods.     

Three-state molecular shuttles operated using acid/base stimuli with distinct outputs

This paper describes the acid/base-mediated three-state translational isomerization of two [2]rotaxanes, each containing N-alkylaniline and N,N-dialkylamine centers as binding sites for threaded dibenzo[24]crown-8 units. Under neutral conditions, the dialkylamine unit predominantly recognized the crown ether component through cooperative binding of a proton; when both amino units were protonated under acidic conditions, both translational isomers were generated; the addition of a strong base caused aniline-crown ether interactions to dominate. The three states of the [2]rotaxane featuring the 3,5-diphenylaniline terminus in its dumbbell-shaped component were accompanied by distinct absorptive outputs that were detectable using UV spectroscopy.     

On the existence of multiply connected monolayered cyclofusenes with given parameters

For a given bipartite graph G its skewness is defined as the difference between the sizes of its classes of bipartition. We show that a multiply connected monolayered cyclofusene with m ≥ 2 internal holes and skewness k exists if and only if 0 ≤ k ≤ 2m − 2, thus settling in affirmative two conjectures raised in a recent paper by Karimi et al.     

On the ABC index of connected graphs with given degree sequences

The atom-bond connectivity (ABC) index of a graph G is defined to be \(ABC(G)=\sum _{uv\in E(G)}\sqrt{\frac{d(u)+d(v)-2}{d(u)d(v)}}\) where d(u) is the degree of a vertex u. The ABC index plays a key role in correlating the physical–chemical properties and the molecular structures of some families of compounds. In this paper, we describe the structural properties of graphs which have the minimum ABC index among all connected graphs with a given degree sequence. Moreover, these results are used to characterize the extremal graphs which have the minimum ABC index among all unicyclic and bicyclic graphs with a given degree sequence.     

Exploiting distinct molecular architectures of ultrathin films made with iron phthalocyanine for sensing

The possibility of generating distinct film properties from the same material is crucial for a number of applications, which can only be achieved by controlling the molecular architecture. In this paper we demonstrate as a proof-of-principle that ultrathin films produced from iron phthalocyanine (FePc) may be used to detect trace amounts of copper ions in water, where advantage was taken of the cross sensitivity of the sensing units that displayed distinct electrical properties. The ultrathin films were fabricated with three methods, namely physical vapor deposition (PVD), Langmuir-Blodgett (LB), and electrostatic layer-by-layer (LbL) techniques, where for the latter tetrasulfonated phthalocyanine was used (FeTsPc). PVD and LB films were more homogeneous than the LbL films at both microscopic and nanoscopic scales, according to results from micro-Raman spectroscopy and atomic force microscopy (AFM), respectively. From FTIR spectroscopy data, these more homogeneous films were found to have FePc molecules oriented preferentially, tilted in relation to the substrate surface, while FeTsPc molecules were isotropically distributed in the LbL films. Impedance spectroscopy measurements with films adsorbed onto interdigitated gold electrodes indicated that the electrical response depends on the type of film-forming method and varies with incorporation of copper ions in aqueous solutions. Using principal component analysis (PCA), we were able to exploit the cross sensitivity of the sensing units and detect copper ions (Cu(2+)) down to 0.2 mg/L, not only in ultrapure water but also in distilled and tap water. This level of sensitivity is sufficient for quality control of water for human consumption, with a fast, low-cost method.     

QSAR models based on isomorphic and nonisomorphic data fusion for predicting the blood brain barrier permeability

A QSAR model for predicting the blood brain barrier permeability (BBBP) in a large and heterogeneous variety of compounds (136 compounds) has been developed using approximate similarity (AS) matrices as predictors and PLS as multivariate regression technique. AS values fuse information of both the isomorphic similarity and nonisomorphic dissimilarity with the purpose of achieving an accurate predictive space. In addition to the fact of applying AS values to heterogeneous data sets, a new concept on graph isomorphism based on the extended maximum common subgraph (EMCS) is defined for the building of AS spaces considering the atoms and bonds, which are bridges between the isomorphic and nonisomorphic substructures. This new isomorphism detection has as objective to take into account the position and nature of the nucleus substituents, thus allowing the development of accurate models for large and diverse sets of compounds. After an outliers study, the training and test stages were made and the results obtained using several AS approaches were compared. Several validation processes were carried out by means of employing several test sets, and high predictive ability was obtained for all the cases (Q(2) = 0.81 and standard error in prediction, SEP = 0.29).     

On subspectral acyclic molecular graphs

Based on the contraction and expansion of graphs, the subspectrality of acyclic molecular graphs is treated in a systematic way. The graphs containing eigenvalues 0, t 1 and ± 2 are discussed in detail, with emphasis on how to detect and construct the concealed species which can neither be recognized by symmetry considerations nor by the Heilbronner procedure. As a consequence, graphs and their counts have been given for species with numbers of vertices less than 16.Also known as Yuan-sun Kiang.     

On reciprocal molecular topological index

We report some properties of the reciprocal molecular topological index RMTI of a connected graph, and, in particular, its relationship with the first Zagreb index M₁. We also derive the upper bounds for RMTI in terms of the number of vertices and the number of edges for various classes of graphs, including K _r+1 -free graphs with r ≥ 2, quadrangle-free graphs, and cacti. Additionally, we consider a Nordhaus-Gaddum-type result for RMTI.