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Keywords = quantum-like correlations

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12 pages, 354 KB  
Article
The Dirac Equation in a Linear Potential and Quantized Electromagnetic Field: Spin–Rest Entanglement
by Yassine Chargui and Sultan Al-Harbi
Quantum Rep. 2025, 7(4), 63; https://doi.org/10.3390/quantum7040063 - 12 Dec 2025
Viewed by 158
Abstract
We derive the exact eigenfunctions and energy equation for a Dirac particle in a monochromatic quantized electromagnetic plane wave and a confining scalar linear potential. It is shown that the system’s energy spectrum exhibits a forbidden region that vanishes when the particle–field interaction [...] Read more.
We derive the exact eigenfunctions and energy equation for a Dirac particle in a monochromatic quantized electromagnetic plane wave and a confining scalar linear potential. It is shown that the system’s energy spectrum exhibits a forbidden region that vanishes when the particle–field interaction is switched off. We then analyze the effect of particle–field coupling on quantum entanglement between the particle’s spin and the remaining degrees of freedom. Our results show that the profile of the spin–rest entanglement, measured by negativity and Von Neumann entropy, follows the energy profile of the state: it is monotonic when the energy is monotonic, and non-monotonic otherwise. These results may provide insights into quantum correlations in Dirac-like systems describing low-energy excitations of graphene and trapped ions. Full article
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13 pages, 2756 KB  
Article
Acid Versus Amide—Facts and Fallacies: A Case Study in Glycomimetic Ligand Design
by Martin Smieško, Roman P. Jakob, Tobias Mühlethaler, Roland C. Preston, Timm Maier and Beat Ernst
Molecules 2025, 30(24), 4751; https://doi.org/10.3390/molecules30244751 - 12 Dec 2025
Viewed by 182
Abstract
The replacement of ionizable functional groups that are predominantly charged at physiological pH with neutral bioisosteres is a common strategy in medicinal chemistry; however, its impact on binding affinity is often context-dependent. Here, we investigated a series of amide derivatives of a glycomimetic [...] Read more.
The replacement of ionizable functional groups that are predominantly charged at physiological pH with neutral bioisosteres is a common strategy in medicinal chemistry; however, its impact on binding affinity is often context-dependent. Here, we investigated a series of amide derivatives of a glycomimetic E-selectin ligand, in which the carboxylate group of the lead compound is substituted with a range of amide and isosteric analogs. Despite the expected loss of the salt-bridge interaction with Arg97, several amides retained or even improved the binding affinity. Co-crystal structures revealed conserved binding poses across the series, with consistent interactions involving the carbonyl oxygen of the amide and the key residues Tyr48 and Arg97. High-level quantum chemical calculations ruled out a direct correlation between carbonyl partial charges and affinity. Instead, a moderate correlation was observed between ligand binding and the out-of-plane pyramidality of the amide nitrogen, suggesting a favorable steric adaptation within the binding site. Molecular dynamics (MD) simulations revealed that high-affinity ligands exhibit enhanced solution-phase pre-organization toward the bioactive conformation, likely reducing the entropic penalty upon binding. Further analysis of protein–ligand complexes using Molecular mechanics/Generalized born surface area (MM-GB/SA) decomposition suggested minor lipophilic contributions from amide substituents. Taken together, this work underscores the importance of geometric and conformational descriptors, beyond classical electrostatics, in driving affinity in glycomimetic ligand design and provides new insights into the nuanced role of amides as carboxylate isosteres in protein–ligand recognition. Full article
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16 pages, 5751 KB  
Article
Tunable Superconductivity in BSCCO via GaP Quantum Dots
by Qingyu Hai, Duo Chen, Ruiyuan Bi, Yao Qi, Lifeng Xun, Xiaoyan Li and Xiaopeng Zhao
Materials 2025, 18(23), 5458; https://doi.org/10.3390/ma18235458 - 3 Dec 2025
Viewed by 382
Abstract
The enhancement of superconducting properties of high-temperature copper-oxide superconductors like B(P)SCCO remains a hot research topic in the field of superconducting materials. This study introduces GaP quantum dots (QDs) as a heterophase, leveraging their electroluminescent properties to enhance the superconductivity of B(P)SCCO. Experimental [...] Read more.
The enhancement of superconducting properties of high-temperature copper-oxide superconductors like B(P)SCCO remains a hot research topic in the field of superconducting materials. This study introduces GaP quantum dots (QDs) as a heterophase, leveraging their electroluminescent properties to enhance the superconductivity of B(P)SCCO. Experimental results demonstrate that the electroluminescence generated by GaP quantum dots (QDs) under an applied electric field induces tunable superconducting enhancement of B(P)SCCO. A reproducible trend of enhancement in the critical transition temperature (Tc) and depairing current density (Jd) is observed with increasing QD electroluminescent intensity, suggesting a positive correlation. This electroluminescence-induced enhancement dominates over the inherent impurity effects at optimal QD content. Full article
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14 pages, 2527 KB  
Article
A HF-Free Synthesis Method for High-Luminescent Efficiency Narrow-Bandgap Red Phosphor K3AlF6: Mn4+ with NH4HF2 as the Molten Salt
by Chenxing Liao, Feng Zhou, Wei Xie and Liaolin Zhang
Solids 2025, 6(4), 66; https://doi.org/10.3390/solids6040066 - 1 Dec 2025
Viewed by 215
Abstract
Mn4+-doped fluoride red phosphors are widely used in white LED lighting and display applications due to their excellent luminescent properties. However, their synthesis relies heavily on highly toxic aqueous hydrofluoric acid, which not only causes severe environmental and soil/water pollution but [...] Read more.
Mn4+-doped fluoride red phosphors are widely used in white LED lighting and display applications due to their excellent luminescent properties. However, their synthesis relies heavily on highly toxic aqueous hydrofluoric acid, which not only causes severe environmental and soil/water pollution but also makes it difficult to control the microstructure of the products due to the rapid reaction rate. In this study, low-melting-point NH4HF2 was used as the molten salt, with KMnO4 and MnF2 as manganese sources, to synthesize the red phosphor K3AlF6: Mn4+ via the molten salt method. After the reaction, impurities such as NH4HF2 were removed by washing with a dilute H2O2 solution. The microstructure, photoluminescence properties, thermal quenching behavior, and application in warm white light-emitting diodes (W-LEDs) of the K3AlF6: Mn4+ phosphors were investigated. The results indicate that the phosphors prepared by this method consist of a single pure phase. By adjusting the molten salt content, the morphology of the product can be transformed from nanoparticle-like to nanorod-like structures. All products exhibit the characteristic red emission of Mn4+ under blue and violet light excitation, with the optimally doped sample achieving an internal quantum efficiency (IQE) of 69% under blue light excitation. The combination of the obtained K3AlF6: Mn4+ with the yellow phosphor YAG enabled the fabrication of W-LEDs. These W-LEDs achieved a color rendering index (Ra) of 86.8, a luminous efficacy (LE) of 77 lm/W, and a correlated color temperature (CCT) of 3690 K, along with excellent color stability under operating conditions. Full article
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18 pages, 2390 KB  
Article
Thermal BCS-BEC Crossovers in Finite Systems
by Angelo Plastino, Flavia Pennini and Victor Apel
Entropy 2025, 27(11), 1116; https://doi.org/10.3390/e27111116 - 30 Oct 2025
Viewed by 429
Abstract
We investigate the thermal evolution of fermionic pairings in a finite-size SU(2) × SU(2) complex model, drawing an analogy to the BCS-BEC crossover in interacting quantum gases. Unlike the conventional crossover, which is driven by tuning the interaction strength, our study [...] Read more.
We investigate the thermal evolution of fermionic pairings in a finite-size SU(2) × SU(2) complex model, drawing an analogy to the BCS-BEC crossover in interacting quantum gases. Unlike the conventional crossover, which is driven by tuning the interaction strength, our study suggests that temperature alone can induce a smooth transition from weakly bound Cooper pairs (BCS-like state) to tightly bound dimers (BEC-like state). Using an exactly solvable model with a finite number of fermions, we analyze the structure of eigenstates, pairing correlations, and thermodynamic response functions. We demonstrate that different multiplet structures, characterized by distinct quasi-spin quantum numbers, become thermally accessible, effectively mimicking the crossover behavior seen in ultracold Fermi gases. Our results provide new insights into the role of thermal fluctuations in quantum pairing phenomena and suggest alternative routes for exploring crossover physics in mesoscopic and strongly correlated systems. Full article
(This article belongs to the Section Statistical Physics)
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10 pages, 1153 KB  
Article
Entanglement Islands in 1D and 2D Lattices with Defects
by Ivan P. Christov
Entropy 2025, 27(11), 1093; https://doi.org/10.3390/e27111093 - 23 Oct 2025
Viewed by 422
Abstract
We investigate the spatial structure of quantum entanglement in one- and two-dimensional lattice systems containing structural defects, using the Time-Dependent Quantum Monte Carlo (TDQMC) method. By constructing reduced density matrices from ensembles of guide waves, we resolve spatial variations in both Coulomb-mediated entanglement [...] Read more.
We investigate the spatial structure of quantum entanglement in one- and two-dimensional lattice systems containing structural defects, using the Time-Dependent Quantum Monte Carlo (TDQMC) method. By constructing reduced density matrices from ensembles of guide waves, we resolve spatial variations in both Coulomb-mediated entanglement and coherence without requiring full many-body wavefunctions. This approach reveals localized regions, entanglement islands, where quantum correlations are enhanced or suppressed due to the presence of vacancies or interaction inhomogeneities. In 1D systems, entanglement tends to concentrate near defects, while in 2D systems, we observe bridge-like and radially symmetric domains. Our results demonstrate that TDQMC offers a scalable and physically transparent framework for real-space quantum information analysis, with implications for information transfer in atomic-size structures, quantum materials, entanglement-based sensing, and coherent state engineering. Full article
(This article belongs to the Special Issue Editorial Board Members' Collection Series on Quantum Entanglement)
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14 pages, 2575 KB  
Article
Synthesis and Characterization of 4-Indolylcyanamide: A Potential IR Probe for Local Environment
by Min You, Qingxue Li, Zilin Gao, Changyuan Guo and Liang Zhou
Molecules 2025, 30(20), 4063; https://doi.org/10.3390/molecules30204063 - 12 Oct 2025
Viewed by 536
Abstract
This study reports the synthesis and comprehensive spectroscopic characterization of 4-indolylcyanamide (4ICA), a novel indole-derived infrared (IR) probe designed for assessing local microenvironments in biological systems. 4ICA was synthesized via a two-step procedure with an overall yield of 43%, and its structure was [...] Read more.
This study reports the synthesis and comprehensive spectroscopic characterization of 4-indolylcyanamide (4ICA), a novel indole-derived infrared (IR) probe designed for assessing local microenvironments in biological systems. 4ICA was synthesized via a two-step procedure with an overall yield of 43%, and its structure was confirmed using high-resolution mass spectrometry and 1HNMR. Fourier Transform Infrared (FTIR) spectroscopy revealed that the cyanamide group stretching vibration of 4ICA exhibits exceptional solvent-dependent frequency shifts, significantly greater than those of conventional cyanoindole probes. A strong linear correlation was observed between the vibrational frequency and the combined Kamlet–Taft parameter, underscoring the dominant role of solvent polarizability and hydrogen bond acceptance in modulating its spectroscopic behavior. Quantum chemical calculations employing density functional theory (DFT) with a conductor-like polarizable continuum model (CPCM) provided further insight into the solvatochromic shifts and suppression of Fermi resonance in high-polarity solvents such as DMSO. Additionally, IR pump–probe measurements revealed short vibrational lifetimes (~1.35 ps in DMSO and ~1.13 ps in ethanol), indicative of efficient energy relaxation. With a transition dipole moment nearly twice that of traditional nitrile-based probes, 4ICA demonstrates enhanced sensitivity and signal intensity, establishing its potential as a powerful tool for site-specific environmental mapping in proteins and complex biological assemblies using nonlinear IR techniques. Full article
(This article belongs to the Special Issue Indole Derivatives: Synthesis and Application 3rd edition)
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34 pages, 5443 KB  
Article
Quantum and Topological Dynamics of GKSL Equation in Camel-like Framework
by Sergio Manzetti and Andrei Khrennikov
Entropy 2025, 27(10), 1022; https://doi.org/10.3390/e27101022 - 28 Sep 2025
Viewed by 520
Abstract
We study the dynamics of von Neumann entropy driven by the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation, focusing on its camel-like behavior—a hump-like entropy evolution reflecting the system’s adaptation to its environment. Within this framework, we analyze quantum correlations under decoherence and environmental interaction for three [...] Read more.
We study the dynamics of von Neumann entropy driven by the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation, focusing on its camel-like behavior—a hump-like entropy evolution reflecting the system’s adaptation to its environment. Within this framework, we analyze quantum correlations under decoherence and environmental interaction for three sets of quantum states. Our results show that the sign of the entanglement entropy’s derivative serves as an indicator of the system’s drift toward either classical or quantum information exchange—an insight relevant to quantum error correction and dissipation in quantum thermal machines. We parameterize quantum states using both single-parameter and Bloch-sphere representations, where the angle θ on the Bloch sphere corresponds to the state’s position. On this sphere, we construct gradient and basin maps that partition the dynamics of quantum states into stable and unstable regions under decoherence. Notably, we identify a Braiding ring of decoherence-unstable states located at θ=3π4; these states act as attractors under a constructed Lyapunov function, illustrating the topological and dynamical complexity of quantum evolution. Finally, we propose a testable experimental setup based on camel-like entropy and discuss its connection to the theoretical framework of this entropy behavior. Full article
(This article belongs to the Special Issue Entanglement Entropy in Quantum Field Theory)
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18 pages, 4003 KB  
Article
Understanding the Paradigm of Molecular-Network Conformations in Nanostructured Se-Rich Arsenoselenides AsxSe100−x (x < 10)
by Oleh Shpotyuk, Zdenka Lukáčová Bujňáková, Yaroslav Shpotyuk and Andriy Kovalskiy
Molecules 2025, 30(16), 3380; https://doi.org/10.3390/molecules30163380 - 14 Aug 2025
Viewed by 656
Abstract
The paradigm of molecular-network conformations in Se-rich glassy arsenoselenides AsxSe100−x compositionally approaching pure Se (x < 10) is considered, employing comprehensive XRD analysis of diffuse peak-halos and nanocrystalline reflections from the known Se polymorphs in their XRD patterns. Within a [...] Read more.
The paradigm of molecular-network conformations in Se-rich glassy arsenoselenides AsxSe100−x compositionally approaching pure Se (x < 10) is considered, employing comprehensive XRD analysis of diffuse peak-halos and nanocrystalline reflections from the known Se polymorphs in their XRD patterns. Within a modified microcrystalline model, the changes with growing Se content in these alloys are interpreted in terms of suppression in intermediate range ordering due to shifting to high diffraction angles and a narrowed FSDP (first sharp diffraction peak)-related diffuse peak-halo, accompanied by enhancement in extended range ordering due to a shift to low diffraction angles and a broadened SSDP (second sharp diffraction peak)-related peak-halo. Overlapping of these peak-halos is enhanced in Se-rich alloys, tending towards unified FSDP-SSDP-related halos with characteristic doublet asymmetry due to the remnants of nanocrystalline trigonal t-Se. Drastic enhancement of the crystallization processes related to the trigonal t-Se phase is a principal feature of nanostructurization effects in Se-rich glassy arsenoselenides driven by nanomilling. The nanostructurization response in these alloys is revealed as a fragmentation impact on the correlation length of the FSDP-responsible entities, accompanied by an agglomeration impact on the correlation length of the SSDP-responsible entities. The FSDP- and SSDP-related diffuse peak-halos become more distinguishable in the XRD patterning of nanostructured arsenoselenides, being associated with other contributions from crystalline remnants, such as those expected in transition to glassy arsenoselenides with higher Se content. An irregular sequence of randomly distributed cis- and trans-configurated multiatomic Se linkages is visualized by ab initio quantum-chemical modeling of Sen chain- and ring-like conformations. The most critical point of molecular-network disproportionality analysis in the examined arsenoselenide AsxSe100−x glassy alloys obeying the chain-crossing model corresponds to x = 7 (equivalent to 93 at. % of Se in the binary As-Se system), as an equilibrium point between mixed cis-trans-configurated Se7 chains and exceptionally cis-configurated molecular Se8 rings. At the basis of developed models, the paradigm of thermodynamically stable molecular-network conformations in the nanostructured Se-rich arsenoselenides AsxSe100−x (x < 10) is surely resolved in favor of chain-like network-forming conformations composed of mixed cis-trans-configurated network-forming multiatomic Se fragments. Full article
(This article belongs to the Special Issue Exclusive Feature Papers in Physical Chemistry, 3rd Edition)
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32 pages, 642 KB  
Review
Exotic Heavy Hadrons
by Humberto Garcilazo and Alfredo Valcarce
Symmetry 2025, 17(8), 1324; https://doi.org/10.3390/sym17081324 - 14 Aug 2025
Cited by 1 | Viewed by 927
Abstract
We review our recent findings on the structure and properties of exotic heavy hadrons, focusing on two main topics. First, we examine the role of correlations driven by the short-range Coulomb-like color interaction in hidden heavy-flavor pentaquarks. We show how this framework consistently [...] Read more.
We review our recent findings on the structure and properties of exotic heavy hadrons, focusing on two main topics. First, we examine the role of correlations driven by the short-range Coulomb-like color interaction in hidden heavy-flavor pentaquarks. We show how this framework consistently accounts for the observed pattern of Pc and Pcs states in the hidden-charm sector and enables predictions for the hidden-bottom sector, where experimental data are still lacking. The second topic explores the possibility of forming stable multihadron molecules from deeply bound two-hadron exotic states. In this context, a bound state of three B mesons, denoted as Tbbb, with quantum numbers (I)JP=(1/2)2, is presented. We find that the binding energy generally decreases as the number of hadrons increases, primarily due to effects of the Pauli principle and the appearance of new decay thresholds. Nonetheless, resonances may still arise in specific cases, depending on the internal thresholds of the system. Finally, we discuss how the decay width of an exotic multihadron resonance can offer valuable insights into its internal structure and underlying dynamics. Full article
(This article belongs to the Special Issue Symmetry in Hadron Physics)
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15 pages, 628 KB  
Article
Accurate Nonrelativistic Energy Calculations for Helium 1snp1,3P (n = 2 to 27) States via Correlated B-Spline Basis Functions
by Jing Chi, Hao Fang, Yong-Hui Zhang, Xiao-Qiu Qi, Li-Yan Tang and Ting-Yun Shi
Atoms 2025, 13(8), 72; https://doi.org/10.3390/atoms13080072 - 4 Aug 2025
Viewed by 1215
Abstract
Rydberg atoms play a crucial role in testing atomic structure theory, quantum computing and simulation. Measurements of transition frequencies from the 21,3S states to Rydberg P1,3 states have reached a precision of several kHz, which poses [...] Read more.
Rydberg atoms play a crucial role in testing atomic structure theory, quantum computing and simulation. Measurements of transition frequencies from the 21,3S states to Rydberg P1,3 states have reached a precision of several kHz, which poses significant challenges for theoretical calculations, since the accuracy of variational energy calculations decreases rapidly with increasing principal quantum number n. Recently the complex “triple” Hylleraas basis was employed to attain the ionization energy of helium 24P1 state with high accuracy. Different from it, we extended the correlated B-spline basis functions (C-BSBFs) to calculate the Rydberg states of helium. The nonrelativistic energies of 1snpP1,3 states up to n=27 achieve at least 14 significant digits using a unified basis set, thereby greatly reducing the complexity of the optimization process. Results of geometric structure parameters and cusp conditions were presented as well. Both the global operator and direct calculation methods are employed and cross-checked for contact potentials. This C-BSBF method not only obtains high-accuracy energies across all studied levels but also confirms the effectiveness of the C-BSBFs in depicting long-range and short-range correlation effects, laying a solid foundation for future high-accuracy Rydberg-state calculations with relativistic and QED corrections included in helium atom and low-Z helium-like ions. Full article
(This article belongs to the Special Issue Atom and Plasma Spectroscopy)
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13 pages, 1031 KB  
Article
MITS: A Quantum Sorcerer’s Stone for Designing Surface Codes
by Avimita Chatterjee, Debarshi Kundu and Swaroop Ghosh
Entropy 2025, 27(8), 812; https://doi.org/10.3390/e27080812 - 29 Jul 2025
Viewed by 889
Abstract
In the evolving field of quantum computing, optimizing Quantum Error Correction (QEC) parameters is crucial due to the varying types and amounts of physical noise across quantum computers. Traditional simulators use a forward paradigm to derive logical error rates from inputs like code [...] Read more.
In the evolving field of quantum computing, optimizing Quantum Error Correction (QEC) parameters is crucial due to the varying types and amounts of physical noise across quantum computers. Traditional simulators use a forward paradigm to derive logical error rates from inputs like code distance and rounds, but this can lead to resource wastage. Adjusting QEC parameters manually with tools like STIM is often inefficient, especially given the daily fluctuations in quantum error rates. To address this, we introduce MITS, a reverse engineering tool for STIM that automatically determines optimal QEC settings based on a given quantum computer’s noise model and a target logical error rate. This approach minimizes qubit and gate usage by precisely matching the necessary logical error rate with the constraints of qubit numbers and gate fidelity. Our investigations into various heuristics and machine learning models for MITS show that XGBoost and Random Forest regressions, with Pearson correlation coefficients of 0.98 and 0.96, respectively, are highly effective in this context. Full article
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21 pages, 2880 KB  
Article
Valorization of a Natural Compound Library in Exploring Potential Marburg Virus VP35 Cofactor Inhibitors via an In Silico Drug Discovery Strategy
by Mohamed Mouadh Messaoui, Mebarka Ouassaf, Nada Anede, Kannan R. R. Rengasamy, Shafi Ullah Khan and Bader Y. Alhatlani
Curr. Issues Mol. Biol. 2025, 47(7), 506; https://doi.org/10.3390/cimb47070506 - 2 Jul 2025
Cited by 1 | Viewed by 1123
Abstract
This study focuses on exploring potential inhibitors of the Marburg virus interferon inhibitory domain protein (MARV-VP35), which is responsible for immune evasion and immunosuppression during viral manifestation. A combination of in silico techniques was applied, including structure-based pharmacophore virtual screening, molecular docking, absorption, [...] Read more.
This study focuses on exploring potential inhibitors of the Marburg virus interferon inhibitory domain protein (MARV-VP35), which is responsible for immune evasion and immunosuppression during viral manifestation. A combination of in silico techniques was applied, including structure-based pharmacophore virtual screening, molecular docking, absorption, distribution, metabolism, excretion, and toxicity (ADMET) analysis, molecular dynamics (MD), and molecular stability assessment of the identified hits. The docking scores of the 14 selected ligands ranged between −6.88 kcal/mol and −5.28 kcal/mol, the latter being comparable to the control ligand. ADMET and drug likeness evaluation identified Mol_01 and Mol_09 as the most promising candidates, both demonstrating good predicted antiviral activity against viral targets. Density functional theory (DFT) calculations, along with relevant quantum chemical descriptors, correlated well with the docking score hierarchy, and molecular electrostatic potential (MEP) mapping confirmed favorable electronic distributions supporting the docking orientation. Molecular dynamics simulations further validated complex stability, with consistent root mean square deviation (RMSD), root mean square fluctuation (RMSF), and secondary structure element (SSE) profiles. These findings support Mol_01 and Mol_09 as viable candidates for experimental validation. Full article
(This article belongs to the Special Issue Molecular Research in Bioactivity of Natural Products, 2nd Edition)
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28 pages, 13728 KB  
Article
Molecular Recognition of SARS-CoV-2 Mpro Inhibitors: Insights from Cheminformatics and Quantum Chemistry
by Adedapo Olosunde and Xiche Hu
Molecules 2025, 30(10), 2174; https://doi.org/10.3390/molecules30102174 - 15 May 2025
Cited by 1 | Viewed by 1249
Abstract
The SARS-CoV-2 main protease (Mpro), essential for viral replication, remains a prime target for antiviral drug design against COVID-19 and related coronaviruses. In this study, we present a systematic investigation into the molecular determinants of Mpro inhibition using an integrated approach combining large-scale [...] Read more.
The SARS-CoV-2 main protease (Mpro), essential for viral replication, remains a prime target for antiviral drug design against COVID-19 and related coronaviruses. In this study, we present a systematic investigation into the molecular determinants of Mpro inhibition using an integrated approach combining large-scale data mining, cheminformatics, and quantum chemical calculations. A curated dataset comprising 963 high-resolution structures of Mpro–ligand complexes—348 covalent and 615 non-covalent inhibitors—was mined from the Protein Data Bank. Cheminformatics analysis revealed distinct physicochemical profiles for each inhibitor class: covalent inhibitors tend to exhibit higher hydrogen bonding capacity and sp3 character, while non-covalent inhibitors are enriched in aromatic rings and exhibit greater aromaticity and lipophilicity. A novel descriptor, Weighted Hydrogen Bond Count (WHBC), normalized for molecular size, revealed a notable inverse correlation with aromatic ring count, suggesting a compensatory relationship between hydrogen bonding and π-mediated interactions. To elucidate the energetic underpinnings of molecular recognition, 40 representative inhibitors (20 covalent, 20 non-covalent) were selected based on principal component analysis and aromatic ring content. Quantum mechanical calculations at the double-hybrid B2PLYP/def2-QZVP level quantified non-bonded interaction energies, revealing that covalent inhibitors derive binding strength primarily through hydrogen bonding (~63.8%), whereas non-covalent inhibitors depend predominantly on π–π stacking and CH–π interactions (~62.8%). Representative binding pocket analyses further substantiate these findings: the covalent inhibitor F2F-2020198-00X exhibited strong hydrogen bonds with residues such as Glu166 and His163, while the non-covalent inhibitor EDG-MED-10fcb19e-1 engaged in extensive π-mediated interactions with residues like His41, Met49, and Met165. The distinct interaction patterns led to the establishment of pharmacophore models, highlighting key recognition motifs for both covalent and non-covalent inhibitors. Our findings underscore the critical role of aromaticity and non-bonded π interactions in driving binding affinity, complementing or, in some cases, substituting for hydrogen bonding, and offer a robust framework for the rational design of next-generation Mpro inhibitors with improved selectivity and resistance profiles. Full article
(This article belongs to the Special Issue Fundamental Aspects of Chemical Bonding—2nd Edition)
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21 pages, 350 KB  
Article
Time-like Extra Dimensions: Quantum Nonlocality, Spin, and Tsirelson Bound
by Mohammad Furquan, Tejinder P. Singh and P Samuel Wesley
Universe 2025, 11(5), 137; https://doi.org/10.3390/universe11050137 - 27 Apr 2025
Viewed by 2680
Abstract
The E8E8 octonionic theory of unification suggests that our universe is six-dimensional and that the two extra dimensions are time-like. These time-like extra dimensions, in principle, offer an explanation of the quantum nonlocality puzzle, also known as the EPR [...] Read more.
The E8E8 octonionic theory of unification suggests that our universe is six-dimensional and that the two extra dimensions are time-like. These time-like extra dimensions, in principle, offer an explanation of the quantum nonlocality puzzle, also known as the EPR paradox. Quantum systems access all six dimensions, whereas classical systems such as detectors experience only four dimensions. Therefore, correlated quantum events that are time-like separated in 6D can appear to be space-like separated and, hence, nonlocal, when projected to 4D. Our lack of awareness of the extra time-like dimensions creates the illusion of nonlocality, whereas, in reality, the communication obeys special relativity and is local. Bell inequalities continue to be violated because quantum correlations continue to hold. In principle, this idea can be tested experimentally. We develop our analysis after first constructing the Dirac equation in 6D using quaternions and using the equation to derive spin matrices in 6D and then in 4D. We also show that the Tsirelson bound of the CHSH inequality can in principle be violated in 6D. Full article
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