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Computational and Theoretical Insights on Molecular Structure, Solvation, Interactions and New Materials Design

A special issue of Molecules (ISSN 1420-3049). This special issue belongs to the section "Computational and Theoretical Chemistry".

Deadline for manuscript submissions: 31 March 2025 | Viewed by 11741

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Guest Editor
Department of Physical Chemistry, Pharmacy Faculty, Collegium Medicum of Bydgoszcz, Nicolaus Copernicus University in Toruń, Kurpińskiego 5, 85-950 Bydgoszcz, Poland
Interests: theoretical chemistry; in silico modeling; solution thermodynamics; new materials screening
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Special Issue Information

Dear Colleagues,

The exploration of molecular phenomena is a multidisciplinary inquiry that spans the domains of chemistry, physics, biology, and materials science. As the Guest Editor for the upcoming Special Issue, I invite colleagues to contribute to the following potential areas and topics that can enhance our understanding of molecular structure, solvation, solute-solvent interactions, stability, and dynamics of dissolution phenomena. All kinds of submissions, including reviews, original papers, and short essays, are welcome as contributions to the various aspects of the titled phenomena. The potential themes include deciphering molecular structures and quantifying intermolecular interactions using modern electronic structure analysis, emerging computational techniques such as quantum chemistry, density functional theory, molecular dynamics, and machine learning methodologies. In particular new fresh ideas related to solvation dynamics and equilibria as well as solvation effects and mechanism are welcome. The submission of novel and innovative concepts pertaining to the dynamics and equilibria of solvation, as well as the effects and mechanisms underlying solvation is encouraged. As computational methods have progressed to the extent that the prediction and elucidation of molecular geometries have attained a high degree of sophistication the studies of real physical phenomena are possible. Hence stands as valuable tools in the realm of materials science, computational design and characterization of novel materials. The role of solvation and molecular interactions in shaping the properties of materials provides a platform for groundbreaking research, offering opportunities to engineer materials with tailored functionalities. Furthermore the amalgamation of spectroscopic techniques with computational tools offers avenues for unraveling the intricacies of molecular architecture, thereby providing insights into the forces dictating their existence and such contributions are also expected.

Prof. Dr. Piotr Cysewski
Guest Editor

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Keywords

  • solvation effects
  • solvation dynamics
  • designed solvents
  • intermolecular interactions
  • molecular modeling
  • machine learning
  • materials science
  • saturated solutions
  • chemical reactivity
  • computational techniques

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Published Papers (10 papers)

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11 pages, 1330 KiB  
Article
Simulation Studies of the Dynamics and the Connectivity Patterns of Hydrogen Bonds in Water from Ambient to Supercritical Conditions
by Dorota Swiatla-Wojcik
Molecules 2024, 29(23), 5513; https://doi.org/10.3390/molecules29235513 - 21 Nov 2024
Viewed by 868
Abstract
Pressurized high-temperature water attracts attention as a promising medium for chemical synthesis, biomass processing or destruction of hazardous waste. Adjustment to the desired solvent properties requires knowledge on the behavior of populations of hydrogen-bonded molecules. In this work, the interconnection between the hydrogen [...] Read more.
Pressurized high-temperature water attracts attention as a promising medium for chemical synthesis, biomass processing or destruction of hazardous waste. Adjustment to the desired solvent properties requires knowledge on the behavior of populations of hydrogen-bonded molecules. In this work, the interconnection between the hydrogen bond (HB) dynamics and the structural rearrangements of HB networks have been studied by molecular dynamics simulation using the modified central force flexible potential and the HB definition controlling pair interaction energy, HB length and HB angle. Time autocorrelation functions for molecular pairs bonded continuously and intermittently and the corresponding mean lifetimes have been calculated for conditions ranging from ambient to supercritical. A significant reduction in the continuous and intermittent lifetimes has been found between (293 K, 0.1 MPa) and (373 K, 25 MPa) and attributed to the decreasing size of patches embedded in the continuous HB network. The loss of global HB connectivity at ca. (573 K, 10 MPa) and the investigated supercritical conditions do not noticeably affect the HB dynamics. Over the whole temperature range studied, the reciprocal intermittent lifetime follows the transition state theory dependence on temperature with the activation energy of 10.4 kJ/mol. Calculations of the lifetime of molecules that do not form hydrogen bonds indicate that at supercritical temperatures, the role of reactions involving an unbound H2O molecule as a reactant can be enhanced by lowering system density. Full article
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Selected normalized time correlation functions of continuous hydrogen bonding calculated for the thermodynamic conditions specified in <a href="#molecules-29-05513-t001" class="html-table">Table 1</a>.</p>
Full article ">Figure 2
<p>Selected normalized time correlation functions of intermittent hydrogen bonding calculated for the thermodynamic conditions specified in <a href="#molecules-29-05513-t001" class="html-table">Table 1</a>.</p>
Full article ">Figure 3
<p>Selected normalized time correlation functions of monomer persistence calculated for the thermodynamic conditions specified in <a href="#molecules-29-05513-t001" class="html-table">Table 1</a>.</p>
Full article ">Figure 4
<p>(<b>a</b>) The reciprocal intermittent lifetime &lt;τ<sub>int</sub>&gt; versus 1000/T (squares) and the non-linear fit to the TST dependence: <math display="inline"><semantics> <mrow> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mo>&lt;</mo> <msub> <mrow> <mi mathvariant="sans-serif">τ</mi> </mrow> <mrow> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> </mrow> </msub> <mo>&gt;</mo> </mrow> </mfrac> </mstyle> <mo>=</mo> <msup> <mrow> <mi mathvariant="normal">A</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msup> <mi mathvariant="normal">T</mi> <mo> </mo> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">x</mi> <mi mathvariant="normal">p</mi> <mfenced separators="|"> <mrow> <mo>−</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <msup> <mrow> <mi mathvariant="normal">E</mi> </mrow> <mrow> <mo>≠</mo> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">T</mi> </mrow> </mfrac> </mstyle> </mrow> </mfenced> </mrow> </semantics></math> [A′ = 0.032 ps<sup>−1</sup>; E<sup>≠</sup> = 10.4 kJ/mol; Adj. R-square = 0.998] (red curve). (<b>b</b>) Temperature dependence of the average continuous lifetime of HBs &lt;τ<sub>c</sub>&gt; (squares) and the average lifetime of monomers &lt;τ<sub>nb</sub>&gt; (triangles). Lifetimes calculated for sub- and super-critical conditions are shown by blue squares and green triangles.</p>
Full article ">Figure 5
<p>The calculated HB lifetimes versus the mean number of HBs per molecule (&lt;n<sub>HB</sub>&gt;): (black points and left axis)—intermittent; (red points and right scale)—continuous. Lifetimes calculated for sub- and super-critical conditions are shown by open squares. Inset: the dependence of a degree of connectivity (P<sub>g</sub>) defined as the total fraction of molecules engaged in the clusters of at least five hydrogen-bonded molecules [<a href="#B8-molecules-29-05513" class="html-bibr">8</a>]. The dashed line at &lt;n<sub>HB</sub>&gt; ~ 1.9 indicates breakage of the continuous HB network (right) into a variety of statistically independent clusters (left).</p>
Full article ">Figure 6
<p>Persistence of non-bonded molecules (monomers) as a function of the mean number of HBs per molecule (&lt;n<sub>HB</sub>&gt;). Open squares correspond to sub- and super-critical conditions. Inset: the dependence of a degree of connectivity P<sub>g</sub> on &lt;n<sub>HB</sub>&gt; as in <a href="#molecules-29-05513-f005" class="html-fig">Figure 5</a>.</p>
Full article ">
13 pages, 6092 KiB  
Article
Anchoring and Catalytic Performance of Co@C2N Monolayer for Rechargeable Li-SexSy Batteries: A First-Principles Calculations
by Xiaojing Li, Yingbo Zhang, Chenchen Liu and Shuwei Tang
Molecules 2024, 29(22), 5264; https://doi.org/10.3390/molecules29225264 - 7 Nov 2024
Viewed by 585
Abstract
SexSy composite cathode materials, which offer superior theoretical capacity compared to pure selenium and improved electrochemical properties relative to pure sulfur, have aroused considerable interest in recent decades on account of their applications in electric vehicles and energy storage grids. [...] Read more.
SexSy composite cathode materials, which offer superior theoretical capacity compared to pure selenium and improved electrochemical properties relative to pure sulfur, have aroused considerable interest in recent decades on account of their applications in electric vehicles and energy storage grids. In the current work, the feasibility of a Co@C2N monolayer as a promising host candidate for the cathode material of Li-SexSy batteries has been evaluated using first-principles calculations, and particular efforts have been devoted to underscoring the anchoring mechanism and catalytic performance of the Co@C2N monolayer. The pronounced synergistic effects of Co-S and Li-N bonds lead to increased anchoring performance for Li2SexSy/SexSy clusters on the surface of Co@C2N monolayer, which effectively inhibit the shuttle effect. The charge density difference and Mulliken charge analysis underscores a substantial charge transfer from the Li2SexSy and SexSy clusters to the Co@C2N monolayer, which indicates a noticeable chemical interaction between them. Further electronic property calculations show that the Co@C2N monolayer can improve the electrical conductivity of cathode materials for Li-SexSy batteries by maintaining semi-metallic characteristics after anchoring of Li2SexSy/SexSy clusters. Additionally, the catalytic performance of the Co@C2N monolayer is evaluated in terms of the reduction pathway of Se8 and the decomposition energy barrier of the Li2SeS cluster, which highlights the catalytic role of the Co@C2N monolayer in the formation and decomposition of the Li2SeS cluster during the cycle processes. Overall, the Co@C2N monolayer emerges as a promising host material and catalyst for Li-SexSy batteries with remarkable anchoring and catalytic performance. Full article
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Figure 1

Figure 1
<p>(<b>a</b>,<b>b</b>) The optimized structures of intrinsic C<sub>2</sub>N and Co@C<sub>2</sub>N monolayers. The magenta, blue, and purple circles denote the Co, N, and C atoms, respectively. (<b>c</b>–<b>e</b>) The electronic band structures of (<b>c</b>) intrinsic C<sub>2</sub>N and (<b>d</b>) spin-up and (<b>e</b>) spin-down states of Co@C<sub>2</sub>N monolayers along the high symmetrical Γ-Μ-Κ-Γ path. Reproduced with permission from the Journal “Nanoscale”/Royal Society of Chemistry, ref. [<a href="#B32-molecules-29-05264" class="html-bibr">32</a>].</p>
Full article ">Figure 2
<p>The most stable structures of Li<sub>2</sub>Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span> and Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span> (<span class="html-italic">x</span> + <span class="html-italic">y</span> = 2, 4, 6, 8) clusters.</p>
Full article ">Figure 3
<p>(<b>a</b>) Binding energies of Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span> and Li<sub>2</sub>Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span> (<span class="html-italic">x</span> + <span class="html-italic">y</span> = 2, 4, 6, 8) clusters anchored on the surface of the Co@C<sub>2</sub>N monolayer at different adsorption positions. (<b>b</b>) Binding energies of the most stable Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span> and Li<sub>2</sub>Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span> (<span class="html-italic">x</span> + <span class="html-italic">y</span> = 2, 4, 6, 8) clusters on the surface of the Co@C<sub>2</sub>N monolayer.</p>
Full article ">Figure 4
<p>The most stable configurations of Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span> and Li<sub>2</sub>Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span> clusters anchored on the Co@C<sub>2</sub>N monolayer. All considered structures are shown in <a href="#app1-molecules-29-05264" class="html-app">Table S2 of the Supporting Information</a>.</p>
Full article ">Figure 5
<p>Electron density difference of Li<sub>2</sub>Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span> and Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span> clusters anchored on the surface of the Co@C<sub>2</sub>N monolayer. The charge density for the isovalue contour is 0.03 e Å<sup>−3</sup>. The cyan and yellow colors refer to the charge accumulation and depletion, respectively.</p>
Full article ">Figure 6
<p>Mulliken charge transfer between Li<sub>2</sub>Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span>/Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span> clusters and the Co@C<sub>2</sub>N monolayer.</p>
Full article ">Figure 7
<p>Electron localization function (ELF) plots of Li<sub>2</sub>Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span>/Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span> clusters adsorbed on the Co@C<sub>2</sub>N monolayer.</p>
Full article ">Figure 8
<p>The calculated average open circuit voltages (V) of Li<sub>2</sub>Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span> clusters adsorbed on the Co@C<sub>2</sub>N monolayer.</p>
Full article ">Figure 9
<p>Energy profiles for the reduction of Li<sub>2</sub>Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span>/Se<span class="html-italic"><sub>x</sub></span>S<span class="html-italic"><sub>y</sub></span> clusters on the surface of the Co@C<sub>2</sub>N monolayer. The magenta, blue, purple, orange, and yellow circles denote the Co, N, C, Se and S atoms, respectively.</p>
Full article ">Figure 10
<p>Energy barriers of the decomposition of Li<sub>2</sub>SeS on intrinsic C<sub>2</sub>N and the Co@C<sub>2</sub>N monolayer. The IS, TS, and FS represent the initial state, transition state, and final state along the decomposition pathway of Li<sub>2</sub>SeS cluster.</p>
Full article ">
17 pages, 7834 KiB  
Article
Structural, Elastic, Electronic, Dynamic, and Thermal Properties of SrAl2O4 with an Orthorhombic Structure Under Pressure
by Hongli Guo, Huanyin Yang, Suihu Dang, Shunru Zhang and Haijun Hou
Molecules 2024, 29(21), 5192; https://doi.org/10.3390/molecules29215192 - 2 Nov 2024
Viewed by 607
Abstract
Its outstanding mechanical and thermodynamic characteristics make SrAl2O4 a highly desirable ceramic material for high-temperature applications. However, the effects of elevated pressure on the structural and other properties of SrAl2O4 are still poorly understood. This study encompassed [...] Read more.
Its outstanding mechanical and thermodynamic characteristics make SrAl2O4 a highly desirable ceramic material for high-temperature applications. However, the effects of elevated pressure on the structural and other properties of SrAl2O4 are still poorly understood. This study encompassed structural, elastic, electronic, dynamic, and thermal characteristics. Band structure calculations indicate that the direct band gap of SrAl2O4 is 4.54 eV. In addition, the Cauchy pressures provide evidence of the brittle characteristics of SrAl2O4. The mechanical and dynamic stability of SrAl2O4 is evident from the accurate determination of its elastic constants and phonon dispersion relations. In addition, a comprehensive analysis was conducted of the relationship between specific heat and entropy concerning temperature variations. Full article
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Figure 1

Figure 1
<p>Crystal structure of orthorhombic SrAl<sub>2</sub>O<sub>4</sub> (The green, purple, and red balls are Sr, Al, and O atoms, respectively).</p>
Full article ">Figure 2
<p>The surface contours of linear compressibility <span class="html-italic">β</span> (TPa<sup>−1</sup>) of SrAl<sub>2</sub>O<sub>4</sub>. (<b>a</b>) 0 GPa, (<b>b</b>) 30 GPa, (<b>c</b>) 50 GPa.</p>
Full article ">Figure 3
<p>The surface contours of shear modulus <span class="html-italic">G</span> (GPa) of SrAl<sub>2</sub>O<sub>4</sub>. (<b>a</b>) 0 GPa, (<b>b</b>) 30 GPa, (<b>c</b>) 50 GPa.</p>
Full article ">Figure 4
<p>The surface contours of Young’s modulus <span class="html-italic">E</span> (GPa) of SAl<sub>2</sub>O<sub>4</sub>. (<b>a</b>) 0 GPa, (<b>b</b>) 30 GPa, (<b>c</b>) 50 GPa.</p>
Full article ">Figure 5
<p>Projections of linear compressibility <span class="html-italic">β</span> (TPa<sup>−1</sup>) in xy, xz, and yz planes of SrAl<sub>2</sub>O<sub>4</sub>. (<b>a</b>) 0 GPa, (<b>b</b>) 30 GPa, (<b>c</b>) 50 GPa.</p>
Full article ">Figure 6
<p>Projections of shear modulus <span class="html-italic">G</span> (GPa) in xy, xz, and yz planes of SrAl<sub>2</sub>O<sub>4</sub>. (<b>a</b>) 0 GPa, (<b>b</b>) 30 GPa, (<b>c</b>) 50 GPa.</p>
Full article ">Figure 7
<p>Projections of Young’s modulus <span class="html-italic">G</span> (GPa) in xy, xz, and yz planes of SrAl<sub>2</sub>O<sub>4</sub>. (<b>a</b>) 0 GPa, (<b>b</b>) 30 GPa, (<b>c</b>) 50 GPa.</p>
Full article ">Figure 8
<p>Electronic band structures for SrAl<sub>2</sub>O<sub>4</sub>. (<b>a</b>) 0 GPa, (<b>b</b>) 30 GPa, and (<b>c</b>) 50 GPa.</p>
Full article ">Figure 9
<p>Total and partial density of states for SrAl<sub>2</sub>O<sub>4</sub>. (<b>a</b>) 0 GPa, (<b>b</b>) 30 GPa, and (<b>c</b>) 50 GPa.</p>
Full article ">Figure 10
<p>Phonon band structure for SrAl<sub>2</sub>O<sub>4</sub>. (<b>a</b>) 0 GPa, (<b>b</b>) 30 GPa, and (<b>c</b>) 50 GPa.</p>
Full article ">Figure 11
<p>Total and partial phonon density of states (PDOS) for SrAl<sub>2</sub>O<sub>4</sub>. (<b>a</b>) 0 GPa, (<b>b</b>) 30 GPa, and (<b>c</b>) 50 GPa.</p>
Full article ">Figure 12
<p>(<b>a</b>) Variation in the specific heat capacity <span class="html-italic">C</span><sub>V</sub> and (<b>b</b>) entropy <span class="html-italic">S</span> for orthorhombic SrAl<sub>2</sub>O<sub>4</sub>.</p>
Full article ">Figure 13
<p>The convergence curves.</p>
Full article ">
22 pages, 10758 KiB  
Article
Molecular Simulation of the Water Diffusion Behavior and Electronic Properties of Boron-Nitride-Composited Mineral Oil
by Yang Wang, Wenchao Yan, Kunqi Cui, Chuanhui Cheng, Yuanyang Ren and Kai Wu
Molecules 2024, 29(18), 4500; https://doi.org/10.3390/molecules29184500 - 22 Sep 2024
Cited by 1 | Viewed by 1451
Abstract
Despite the fact that doping nanoparticles into insulating transformer oil has proven to be an effective method of enhancing its dielectric and electrical properties, it remains unclear how different types and surface conditions of nanoparticles may affect their dielectric and electrical properties. Therefore, [...] Read more.
Despite the fact that doping nanoparticles into insulating transformer oil has proven to be an effective method of enhancing its dielectric and electrical properties, it remains unclear how different types and surface conditions of nanoparticles may affect their dielectric and electrical properties. Therefore, the effect of doping various types of BN nanoparticles (nanosphere, nanotube, and nanosheet) in insulating mineral oil (MO) on the diffusion properties of water molecules and electrical properties across the BN/MO interface was investigated using molecular dynamics (MD) and Density Functional Theory (DFT) simulations. Our results show that different surface morphology and grafted functional groups in different types of BN nanoparticles have a significant impact both on the water diffusion behavior and the interfacial potential barrier across the interface between BN and MO. In the MO system directly doped by BN nanospheres, water diffusion behavior is not significantly restricted. However, grafting -NH2 polar groups onto the BN nanoparticle surface may significantly limit the diffusion behavior of water due to the strong attraction between the -NH2 polar groups and water molecules; the most significant effect is with nanospheres, followed by nanotubes and nanosheets. In terms of electrical properties across the interface between BN and MO, the h-BN surface (derived from BN nanosheets and nanotubes) acts as a trap for electrons in MO (−0.59 eV), while the c-BN surface (derived from BN nanospheres) acts as a potential barrier for electrons in MO (1.45 eV), and it is noteworthy that the presence of water molecules near the interface between BN and MO has little impact on the potential barriers. Advancing a fundamental understanding of the electrical and water diffusion properties of MO in correlation with the surface morphology of different types of nanoparticles is key to improving the insulation properties of oil-impregnated power transformers. Full article
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Figure 1

Figure 1
<p><span class="html-italic">MSD</span> curves of water molecules in MO doped with BN materials of different types.</p>
Full article ">Figure 2
<p>Illustration of a hydrogen bond in the W model. O atoms are shown in red, H atoms in white.</p>
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<p>Illustration of hydrogen bonds in the A-BN_NSphere model: (<b>a</b>) O–H···O, (<b>b</b>) N–H···O, and (<b>c</b>) O–H···N hydrogen bonds. O atoms are shown in red, H atoms in white, N atoms in blue, B atoms in pink, and C atoms in grey.</p>
Full article ">Figure 4
<p>The interaction energy, hydrogen bond energy, and the average number of hydrogen bonds in different types of BN-doped MO models.</p>
Full article ">Figure 5
<p><span class="html-italic">MSD</span> curves of water molecules at different temperatures in the A-BN_NSphere model.</p>
Full article ">Figure 6
<p>RDFs of O–H and N–H pairs at different temperatures: (<b>a</b>) O–H RDF and (<b>b</b>) N–H RDF.</p>
Full article ">Figure 7
<p>The interaction energy, hydrogen bond energy, and average number of hydrogen bonds in the A-BN_NSphere model under different temperatures.</p>
Full article ">Figure 8
<p>Charge density differences of BN/MO interfacial models with or without the addition of water molecules: (<b>a</b>) h-BN/MO, (<b>b</b>) h-BN/H<sub>2</sub>O/MO, (<b>c</b>) c-BN/MO, and (<b>d</b>) c-BN/H<sub>2</sub>O/MO. The isosurface level was uniformly set to 0.0002 e bohr<sup>−3</sup>, with yellow and cyan areas indicating electron accumulation and depletion, respectively. O atoms are shown in red, H atoms in pink, N atoms in blue, B atoms in green, and C atoms in brown.</p>
Full article ">Figure 9
<p>Averaged charge density differences along the Z-direction: (<b>a</b>) h-BN/MO and (<b>b</b>) c-BN/MO interface models. In between the blue dotted lines is the interfacial area between the BN layer and the MO layer.</p>
Full article ">Figure 10
<p>Schematic illustration of the partitioning of the interface model in different regions to investigate LDOS.</p>
Full article ">Figure 11
<p>Local and projected DOS of BN/MO interfaces with or without water molecules: (<b>a</b>) h-BN/MO, (<b>b</b>) h-BN/H<sub>2</sub>O/MO, (<b>c</b>) c-BN/MO, and (<b>d</b>) c-BN/H<sub>2</sub>O/MO.</p>
Full article ">Figure 12
<p>Potential distribution along the Z-axis of four BN/MO interfacial models.</p>
Full article ">Figure 13
<p>Potential barriers at BN/MO interfaces.</p>
Full article ">Figure 14
<p>Models of BN nanoparticle with or without surface modification: (<b>a</b>) BN_NSphere, (<b>b</b>) BN_NTube, (<b>c</b>) BN_Nsheet, (<b>d</b>) A-BN_NSphere, (<b>e</b>) A-BN_NTube, and (<b>f</b>) A-BN_NSheet. H atoms in white, N atoms in blue, B atoms in pink.</p>
Full article ">Figure 15
<p>MO/BN interface models: (<b>a</b>) model of the h-BN/MO interface; (<b>b</b>) h-BN/MO interfacial model with two water molecules inserted at each surface (denoted as h-BN/H<sub>2</sub>O/MO); (<b>c</b>) model of the c-BN/MO interface; (<b>d</b>) c-BN/MO interfacial model with two water molecules inserted at each surface (denoted as c-BN/H<sub>2</sub>O/MO). O atoms are shown in red, H atoms in pink, N atoms in blue, B atoms in green, and C atoms in brown.</p>
Full article ">
12 pages, 402 KiB  
Article
Calculation of Some Low-Lying Electronic Excitations of Barium Monofluoride Using the Equation of Motion (EOM)-CC3 Method with an Effective Core Potential Approach
by Marko Horbatsch
Molecules 2024, 29(18), 4356; https://doi.org/10.3390/molecules29184356 - 13 Sep 2024
Viewed by 866
Abstract
Barium monofluoride (BaF) is a polar molecule of interest in measurements of the electron electric dipole moment. For this purpose, efforts are underway to investigate this molecule embedded within cryogenic matrices, e.g., in solid Ne. For a theoretical understanding of the electronic structure [...] Read more.
Barium monofluoride (BaF) is a polar molecule of interest in measurements of the electron electric dipole moment. For this purpose, efforts are underway to investigate this molecule embedded within cryogenic matrices, e.g., in solid Ne. For a theoretical understanding of the electronic structure of such an embedded molecule, the need arises for efficient methods which are accurate but also able to handle a number of atoms which surround the molecule. The calculation for gas-phase BaF can be reduced to involve only outer electrons by representing the inner core of Ba with a pseudopotential, while carrying out a non-relativistic calculation with an appropriate basis set. Thus, the method is effectively at a scalar-relativistic level. In this work, we demonstrate to which extent this can be achieved using coupled-cluster methods to deal with electron correlation. As a test case, the SrF(X2Σ+B2Σ+) transition is investigated, and excellent accuracy is obtained with the EOM-CC3 method. For the BaF(X2Σ+A2Δ, X2Σ+A2Π, X2Σ+B2Σ+) transitions, various coupled-cluster approaches are compared with very good agreement for EOM-CC3 with experimentally derived spectroscopic parameters, at the level of tens of cm1. An exception is the excitation to the A2Δ state, for which the energy is overestimated by 230cm1. The poor convergence behavior for this particular state is demonstrated by providing results from calculations with basis sets of n = 3, 4, 5)-zeta quality. The calculated excitation energy for the B2Σ+ state agrees better with a deperturbation analysis than with the effective spectroscopic value, with a difference of 120cm1. Full article
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<p>Vertical excitation energies <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>T</mi> </mrow> </semantics></math> in <math display="inline"><semantics> <msup> <mi>cm</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> as a function of <span class="html-italic">R</span> (in Å) for the electronic transition SrF<math display="inline"><semantics> <mrow> <mo>(</mo> <msup> <mi>X</mi> <mrow> <mspace width="0.166667em"/> <mn>2</mn> </mrow> </msup> <msup> <mo>Σ</mo> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>B</mi> <mrow> <mspace width="0.166667em"/> <mn>2</mn> </mrow> </msup> <msup> <mo>Σ</mo> <mo>+</mo> </msup> <mo>)</mo> </mrow> </semantics></math>. The blue, red, and green dots represent the EOM-CC3 results obtained with the aug-cc-pVnZ-PP family with n = 3, 4, 5, respectively. For <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>2.08</mn> </mrow> </semantics></math> Å and <math display="inline"><semantics> <mrow> <mi mathvariant="normal">n</mi> <mo>=</mo> <mn>4</mn> <mo>,</mo> <mn>5</mn> </mrow> </semantics></math>, the vertical excitation energies correspond to <math display="inline"><semantics> <msub> <mi>T</mi> <mi>e</mi> </msub> </semantics></math> according to the present work. Stars: experimental value extracted from the analysis of rotational and vibrational (<math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </semantics></math>) excitations [<a href="#B23-molecules-29-04356" class="html-bibr">23</a>]; the symbol location indicates the values of <math display="inline"><semantics> <msub> <mi>R</mi> <mi>e</mi> </msub> </semantics></math> for both states. Other theoretical values for <math display="inline"><semantics> <msub> <mi>T</mi> <mi>e</mi> </msub> </semantics></math>: squares are the CAS-SCF/MRCI values (Ref. [<a href="#B27-molecules-29-04356" class="html-bibr">27</a>]), and diamonds are X2C-FSCC (Ref. [<a href="#B3-molecules-29-04356" class="html-bibr">3</a>]).</p>
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<p>Morse potentials derived from the calculated data points (green circles) are shown as solid green curves for the states BaF(<math display="inline"><semantics> <mrow> <msup> <mi>X</mi> <mrow> <mspace width="0.166667em"/> <mn>2</mn> </mrow> </msup> <msup> <mo>Σ</mo> <mo>+</mo> </msup> </mrow> </semantics></math>) on the left, and BaF(<math display="inline"><semantics> <mrow> <msup> <mi>B</mi> <mrow> <mspace width="0.166667em"/> <mn>2</mn> </mrow> </msup> <msup> <mo>Σ</mo> <mo>+</mo> </msup> </mrow> </semantics></math>) on the right. The magenta dashed curves show experimentally determined Morse potentials using Equation (<a href="#FD3-molecules-29-04356" class="html-disp-formula">3</a>) and values from Ref. [<a href="#B31-molecules-29-04356" class="html-bibr">31</a>]. The black vertical lines indicate the calculated vibrational energy levels for <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </semantics></math>. The data points are for the aug-cc-pV5Z-PP/aug-cc-PV5Z basis set combination. The fits omit the data points for <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>2.01</mn> </mrow> </semantics></math> Å, (cf. text).</p>
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<p>EOM-CC3 vertical excitation energies <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>T</mi> </mrow> </semantics></math> in <math display="inline"><semantics> <msup> <mi>cm</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> as a function of <span class="html-italic">R</span> (in Å) for the electronic transitions <math display="inline"><semantics> <mrow> <msup> <mi>X</mi> <mrow> <mspace width="0.166667em"/> <mn>2</mn> </mrow> </msup> <msup> <mo>Σ</mo> <mo>+</mo> </msup> <mo>→</mo> <msup> <mrow> <msup> <mi>A</mi> <mo>′</mo> </msup> </mrow> <mrow> <mspace width="0.166667em"/> <mn>2</mn> </mrow> </msup> <mo>Δ</mo> </mrow> </semantics></math> (green), <math display="inline"><semantics> <mrow> <msup> <mi>X</mi> <mrow> <mspace width="0.166667em"/> <mn>2</mn> </mrow> </msup> <msup> <mo>Σ</mo> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>A</mi> <mrow> <mspace width="0.166667em"/> <mn>2</mn> </mrow> </msup> <mo>Π</mo> </mrow> </semantics></math> (blue), and <math display="inline"><semantics> <mrow> <msup> <mi>X</mi> <mrow> <mspace width="0.166667em"/> <mn>2</mn> </mrow> </msup> <msup> <mo>Σ</mo> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>B</mi> <mrow> <mspace width="0.166667em"/> <mn>2</mn> </mrow> </msup> <msup> <mo>Σ</mo> <mo>+</mo> </msup> </mrow> </semantics></math> (red). The curves represent spline fits to data obtained with the basis cc-pV5Z-PP for barium and aug-cc-pV5Z for fluorine. The crosses are data points obtained with both basis sets augmented, which lowers the values for the excitation energies by up to <math display="inline"><semantics> <mrow> <mn>30</mn> <mspace width="0.166667em"/> <msup> <mi>cm</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>.</p>
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14 pages, 2639 KiB  
Article
Theoretical Investigation of the Effects of Aldehyde Substitution with Pyran Groups in D-π-A Dye on Performance of DSSCs
by Suzan K. Alghamdi, Abdulaziz I. Aljameel, Rageh K. Hussein, Khalled Al-heuseen, Mamduh J. Aljaafreh and Dina Ezzat
Molecules 2024, 29(17), 4175; https://doi.org/10.3390/molecules29174175 - 3 Sep 2024
Cited by 2 | Viewed by 959
Abstract
This work investigated the substitution of the aldehyde with a pyran functional group in D-π-aldehyde dye to improve cell performance. This strategy was suggested by recent work that synthesized D-π-aldehyde dye, which achieved a maximum absorption wavelength that was only slightly off the [...] Read more.
This work investigated the substitution of the aldehyde with a pyran functional group in D-π-aldehyde dye to improve cell performance. This strategy was suggested by recent work that synthesized D-π-aldehyde dye, which achieved a maximum absorption wavelength that was only slightly off the threshold for an ideal sensitizer. Therefore, DFT and TD-DFT were used to investigate the effect of different pyran substituents to replace the aldehyde group. The pyran groups reduced the dye energy gap better than other known anchoring groups. The proposed dyes showed facile intermolecular charge transfer through the localization of HOMO and LUMO orbitals on the donor and acceptor parts, which promoted orbital overlap with the TiO2 surface. The studied dyes have HOMO and LOMO energy levels that could regenerate electrons from redox potential electrodes and inject electrons into the TiO2 conduction band. The lone pairs of oxygen atoms in pyran components act as nucleophile centers, facilitating adsorption on the TiO2 surface through their electrophile atoms. Pyrans increased the efficacy of dye sensitizers by extending their absorbance range and causing the maximum peak to redshift deeper into the visible region. The effects of the pyran groups on photovoltaic properties such as light harvesting efficiency (LHE), free energy change of electron injection, and dye regeneration were investigated and discussed. The adsorption behaviors of the proposed dyes on the TiO2 (1 1 0) surface were investigated by means of Monte Carlo simulations. The calculated adsorption energies indicates that pyran fragments, compared to the aldehyde in the main dye, had a greater ability to induce the adsorption onto the TiO2 substrate. Full article
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<p>The construction of proposed dyes by substituting the aldehyde group in the base compound with three different pyran moieties.</p>
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<p>FMO contours of the HOMOs and LUMOs of the studied dyes.</p>
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<p>The HOMO and LUMO energy levels for the base compound and the designed dyes.</p>
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<p>The 3D map of the molecular electrostatic potential of BC and the designed dyes.</p>
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<p>TD-DFT simulation of the absorption spectra of the studied dyes at the MPW1PW91/6-311G** level in dichloromethane.</p>
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<p>Side views that show stable adsorption configurations of the BC and BC-pyran dye/TiO<sub>2</sub> (110) systems.</p>
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10 pages, 1737 KiB  
Article
Reproducing the Solvatochromism of Merocyanines by PCM Calculations
by Andrés Aracena, Marcos Caroli Rezende and Sebastián Pizarro
Molecules 2024, 29(17), 4103; https://doi.org/10.3390/molecules29174103 - 29 Aug 2024
Viewed by 755
Abstract
Polarizable continuum methods (PCM) have been widely employed for simulating solvent effects, in spite of the fact that they either ignore specific interactions in solution or only partially reproduce non-specific contributions. Examples of three solvatochromic dyes with a negative, a positive and a [...] Read more.
Polarizable continuum methods (PCM) have been widely employed for simulating solvent effects, in spite of the fact that they either ignore specific interactions in solution or only partially reproduce non-specific contributions. Examples of three solvatochromic dyes with a negative, a positive and a reverse behavior illustrate the achievements and shortcomings of PCM calculations and the causes for their variable success. Even when qualitatively mimicking non-specific solvent effects, departures of calculated values from experimental data may be significant (20–30%). In addition, they can utterly fail to reproduce an inverted behavior that is caused by significant specific contributions by the solvent. As shown through a theoretical model that rationalizes and predicts the solvatochromism of phenolate merocyanines based on DFT (Density Functional Theory) descriptors in the gas phase, PCM shortcomings are to be held responsible for its eventual failure to reproduce experimental data in solution. Full article
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<p>Structures of merocyanine dyes exhibiting a negative (<b>1</b>) [<a href="#B14-molecules-29-04103" class="html-bibr">14</a>,<a href="#B15-molecules-29-04103" class="html-bibr">15</a>,<a href="#B16-molecules-29-04103" class="html-bibr">16</a>], reverse (<b>2</b>) [<a href="#B20-molecules-29-04103" class="html-bibr">20</a>] and positive (<b>3</b>) [<a href="#B21-molecules-29-04103" class="html-bibr">21</a>] solvatochromism.</p>
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<p>Plots of the calculated transition energies of dye <b>1</b>, <span class="html-italic">E</span><sub>T</sub>(calc.) against the solvent <span class="html-italic">E</span><sub>T</sub>(30) values, employing the standard PCM and the SMD option. Calculated values for both options are compared with the experimental straight line.</p>
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<p>Comparison of the experimental (black squares) [<a href="#B20-molecules-29-04103" class="html-bibr">20</a>] and calculated (red circles) solvatochromic plots of dye <b>2</b> in various solvents.</p>
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<p>Comparison of the experimental (black squares) [<a href="#B21-molecules-29-04103" class="html-bibr">21</a>] and calculated (red circles) solvatochromic plots of dye <b>3</b> in various solvents.</p>
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<p>Examples of solvatochromic phenolate betaines exhibiting a positive [<a href="#B30-molecules-29-04103" class="html-bibr">30</a>,<a href="#B31-molecules-29-04103" class="html-bibr">31</a>,<a href="#B32-molecules-29-04103" class="html-bibr">32</a>], reverse [<a href="#B33-molecules-29-04103" class="html-bibr">33</a>,<a href="#B34-molecules-29-04103" class="html-bibr">34</a>] or negative [<a href="#B35-molecules-29-04103" class="html-bibr">35</a>,<a href="#B36-molecules-29-04103" class="html-bibr">36</a>] behavior.</p>
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<p>Schematic representation of the solvatochromic behavior of phenolate betaines <b>1</b>–<b>12</b> as a function of the difference Δ<span class="html-italic">f</span><sub>G</sub><sup>+</sup> between the group Fukui electrophilic functions of their charge-transferring fragments A–B. Solvatochromic transition energies <span class="html-italic">E</span><sub>T</sub> vary with the relative electrophilicities of the two conjugated fragments, expressed in terms of their Fukui electrophilic functions. Dyes exhibiting negative solvatochromism (<b>1</b>,<b>10</b>–<b>12</b>) are shown in red, those exhibiting a positive behavior (<b>3</b>–<b>7</b>) are depicted in blue, those with an inverted behavior (<b>2</b>,<b>8</b>,<b>9</b>) in purple.</p>
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17 pages, 6851 KiB  
Article
Enhancing Sulfidization and Flotation of Smithsonite Using Eco-Friendly Triethanolamine: Insights from Experimental and Simulation Studies
by Song Zhang, Guanyu Liang, Yongjun Xian and Shuming Wen
Molecules 2024, 29(14), 3433; https://doi.org/10.3390/molecules29143433 - 22 Jul 2024
Viewed by 1090
Abstract
Triethanolamine (TEA) is a promising eco-friendly alternative to inorganic ammonia for enhancing surface sulfidization and flotation recovery of smithsonite. Micro-flotation experiments revealed an enhancement in smithsonite recovery to 95.21% with TEA modification, comparable to the results obtained using ammonia. The mechanisms behind the [...] Read more.
Triethanolamine (TEA) is a promising eco-friendly alternative to inorganic ammonia for enhancing surface sulfidization and flotation recovery of smithsonite. Micro-flotation experiments revealed an enhancement in smithsonite recovery to 95.21% with TEA modification, comparable to the results obtained using ammonia. The mechanisms behind the ability of TEA to enhance the sulfidization process were investigated through surface analysis and molecular dynamics simulations. TEA modification increased the content of sulfidization products, the proportion of crucial S22− in adsorbed products, and the thickness and size of the sulfidization product layer. The complexation of TEA with Zn sites formed positively charged Zn–TEA complexes that adsorb onto the smithsonite surface. These complexes promoted negatively charged HS adsorption, creating a multi-layered adsorption structure. Moreover, TEA modification reduced the total energy required for the sulfidization. These findings open up new possibilities for using eco-friendly reagents in mineral processing, highlighting the potential of TEA in green mineral processing practices. Full article
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<p>Smithsonite flotation recovery versus (<b>a</b>) pulp pH, (<b>b</b>) TEA concentration, (<b>c</b>) Na<sub>2</sub>S concentration, and (<b>d</b>) SIAX concentration under the following test conditions: (<b>a</b>) 5 × 10<sup>−4</sup> mol/L TEA, 3 × 10<sup>−4</sup> mol/L Na<sub>2</sub>S, 2 × 10<sup>−4</sup> mol/L CuSO<sub>4</sub>, and 50 mg/L SIAX; (<b>b</b>) at pH around 10 at 3 × 10<sup>−4</sup> mol/L Na<sub>2</sub>S, 2 × 10<sup>−4</sup> mol/L CuSO<sub>4</sub>, and 50 mg/L SIAX; (<b>c</b>) at pH around 10 at 7 × 10<sup>−4</sup> mol/L TEA, 2 × 10<sup>−4</sup> mol/L CuSO<sub>4</sub>, and 50 mg/L SIAX; (<b>d</b>) at pH around 10, 3 × 10<sup>−4</sup> mol/L Na<sub>2</sub>S, 2 × 10<sup>−4</sup> mol/L CuSO<sub>4</sub>, surface modifier: 7 × 10<sup>−4</sup> mol/L TEA or NH<sub>3</sub>·H<sub>2</sub>O.</p>
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<p>XPS: (<b>a</b>) full spectra and (<b>b</b>) relative atomic quantities of the surface of the smithsonite samples: without treatment, treated with Na<sub>2</sub>S, treated with TEA and Na<sub>2</sub>S.</p>
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<p>S 2p XP spectra on smithsonite sample surfaces: (<b>a</b>) without treatment, (<b>b</b>) treated with Na<sub>2</sub>S, and (<b>c</b>) treated with TEA and Na<sub>2</sub>S; and (<b>d</b>) PROP of different chemical states of S.</p>
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<p>Zn 2p XP spectra on smithsonite sample surfaces: (<b>a</b>) without treatment, (<b>b</b>) treated with Na<sub>2</sub>S, and (<b>c</b>) treated with TEA and Na<sub>2</sub>S; and (<b>d</b>) PROP of different chemical states S.</p>
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<p>XP spectra of S 2p with different etching times for samples (<b>a</b>) treated with Na<sub>2</sub>S and (<b>b</b>) treated with TEA and Na<sub>2</sub>S.</p>
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<p>FESEM micrographs and EDS mappings (<b>a-1</b>–<b>b-2</b>, blue square: magnified region), EDS analysis results (<b>c-1</b>,<b>c-2</b>), AFM 3D and height images (<b>d-1</b>–<b>e-2</b>, blue and red dotted lines: AFM section), and height profiles (<b>f</b>) of smithsonite samples treated with Na<sub>2</sub>S, with and without the presence of TEA.</p>
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<p>Effect of pH on zeta potential of smithsonite surface (<b>a</b>); electric double-layer models of smithsonite during TEA modification (<b>b-1</b>) and sulfidization (<b>b-2</b>).</p>
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<p>TEA molecules (<b>a</b>), adsorption models (<b>b-1</b>,<b>b-2</b>), temperature (<b>c</b>), kinetic energy (<b>d</b>), and potential energy (<b>e</b>) obtained from AIMD simulations.</p>
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<p>Initial (<b>a-1</b>,<b>b-1</b>) and equilibrium adsorption models (<b>a-2</b>,<b>b-2</b>) of the interactions between HS<sup>−</sup> and the smithsonite (101) crystal plane in the absence and presence of TEA, along with the relative concentration distribution curves (<b>c</b>,<b>d</b>) of TEA and HS<sup>−</sup> with respect to their vertical distances from the smithsonite (101) plane.</p>
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<p>Schematic of TEA modification to enhance surface sulfidization of smithsonite.</p>
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<p>XRD pattern of smithsonite sample and reference JCPDS card.</p>
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20 pages, 6371 KiB  
Article
Experimental and Theoretical Insights into the Intermolecular Interactions in Saturated Systems of Dapsone in Conventional and Deep Eutectic Solvents
by Piotr Cysewski, Tomasz Jeliński and Maciej Przybyłek
Molecules 2024, 29(8), 1743; https://doi.org/10.3390/molecules29081743 - 11 Apr 2024
Cited by 4 | Viewed by 1479
Abstract
Solubility is not only a crucial physicochemical property for laboratory practice but also provides valuable insight into the mechanism of saturated system organization, as a measure of the interplay between various intermolecular interactions. The importance of these data cannot be overstated, particularly when [...] Read more.
Solubility is not only a crucial physicochemical property for laboratory practice but also provides valuable insight into the mechanism of saturated system organization, as a measure of the interplay between various intermolecular interactions. The importance of these data cannot be overstated, particularly when dealing with active pharmaceutical ingredients (APIs), such as dapsone. It is a commonly used anti-inflammatory and antimicrobial agent. However, its low solubility hampers its efficient applications. In this project, deep eutectic solvents (DESs) were used as solubilizing agents for dapsone as an alternative to traditional solvents. DESs were composed of choline chloride and one of six polyols. Additionally, water–DES mixtures were studied as a type of ternary solvents. The solubility of dapsone in these systems was determined spectrophotometrically. This study also analyzed the intermolecular interactions, not only in the studied eutectic systems, but also in a wide range of systems found in the literature, determined using the COSMO-RS framework. The intermolecular interactions were quantified as affinity values, which correspond to the Gibbs free energy of pair formation of dapsone molecules with constituents of regular solvents and choline chloride-based deep eutectic solvents. The patterns of solute–solute, solute–solvent, and solvent–solvent interactions that affect solubility were recognized using Orange data mining software (version 3.36.2). Finally, the computed affinity values were used to provide useful descriptors for machine learning purposes. The impact of intermolecular interactions on dapsone solubility in neat solvents, binary organic solvent mixtures, and deep eutectic solvents was analyzed and highlighted, underscoring the crucial role of dapsone self-association and providing valuable insights into complex solubility phenomena. Also the importance of solvent–solvent diversity was highlighted as a factor determining dapsone solubility. The Non-Linear Support Vector Regression (NuSVR) model, in conjunction with unique molecular descriptors, revealed exceptional predictive accuracy. Overall, this study underscores the potency of computed molecular characteristics and machine learning models in unraveling complex molecular interactions, thereby advancing our understanding of solubility phenomena within the scientific community. Full article
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<p>The solubility profiles of dapsone at room temperature (T = 25 °C) expressed as solvent composition-related mole fractions. The following notation was adopted: (1:2) choline chloride DESs with propane-1,2-diol (P2D), butane-1,3-diol (B3D) glycerol (GLY), ethylene glycol (ETG), diethylene glycol (DEG), triethylene glycol (TEG), and acetone (ACE)-water [<a href="#B27-molecules-29-01743" class="html-bibr">27</a>], where x<sub>2</sub>* stands for mole fractions of solute-free DES or ACE in aqueous mixtures.</p>
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<p>The structure of dapsone represented together with its distribution of electron density (<b>a</b>) and the dataset of dapsone solubility (<b>b</b>) expressed in terms of the logarithm of mole fractions for three sets of saturates systems, namely neat solvents, (1)N, binary solvents mixtures, (2)B, and ternary deep eutectic solvents, (3)D, including quaternary water-diluted ones.</p>
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<p>Distributions of the experimental values of dapsone solubility in three studied subsets presented in the form of box (<b>top</b>) and violin (<b>bottom</b>) plots.</p>
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<p>The characteristics of the dapsone self-association affinity expressed in the form of a violin plot. The values of the Gibbs free energies are expressed in kcal/mol.</p>
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<p>The distributions of self-association affinity values and corresponding EECF values as a function of solubility expressed in the form of logarithmic values of dapsone mole fraction. The values of the Gibbs free energies, G(AA), are expressed in kcal/mol.</p>
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<p>The characteristics of the solute–solvent affinity expressed in the form of a violin plot. The values of the Gibbs free energies are expressed in kcal/mol.</p>
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<p>The distributions of solute–solvent affinity values and corresponding EECF values as a function of solubility expressed in the form of logarithmic values of dapsone mole fraction. The values of the Gibbs free energies, G(AB), are expressed in kcal/mol.</p>
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<p>The characteristics of the solvent–solvent affinity expressed in the form of a violin plot. The values of the Gibbs free energies are expressed in kcal/mol.</p>
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<p>The distributions of solvent–solvent affinity and corresponding EECF values as a function of solubility, expressed in logarithmic values of dapsone mole fraction. The Gibbs free energies, G(BB), are expressed in kcal/mol.</p>
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<p>The correlation between solvent–solvent interactions and corresponding EECT values.</p>
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<p>(<b>a</b>) The representation of the accuracy of the developed NuSV regression model characterizing the relationship between computed and measured logarithmic values of dapsone mole fraction in saturated conditions. The values of the optimized model parameters are the following C = 9.995195013432355, degree = 2, gamma = 0.6489637022275867, and nu = 0.13135730736919388. The importance of the descriptors was found to be as follows: G(AA) = 1.33, G(AB) = 0.46, G(BB) = 0.69, EECT(AA) = 0.42, EECT(AB) = 0.49, and EECT(BB) = 0.82. (<b>b</b>) The applicability domain analysis as a qualitative diagnostic metric is provided.</p>
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Review

Jump to: Research

30 pages, 1610 KiB  
Review
A Review of Machine Learning and QSAR/QSPR Predictions for Complexes of Organic Molecules with Cyclodextrins
by Dariusz Boczar and Katarzyna Michalska
Molecules 2024, 29(13), 3159; https://doi.org/10.3390/molecules29133159 - 2 Jul 2024
Cited by 3 | Viewed by 2315
Abstract
Cyclodextrins are macrocyclic rings composed of glucose residues. Due to their remarkable structural properties, they can form host–guest inclusion complexes, which is why they are frequently used in the pharmaceutical, cosmetic, and food industries, as well as in environmental and analytical chemistry. This [...] Read more.
Cyclodextrins are macrocyclic rings composed of glucose residues. Due to their remarkable structural properties, they can form host–guest inclusion complexes, which is why they are frequently used in the pharmaceutical, cosmetic, and food industries, as well as in environmental and analytical chemistry. This review presents the reports from 2011 to 2023 on the quantitative structure–activity/property relationship (QSAR/QSPR) approach, which is primarily employed to predict the thermodynamic stability of inclusion complexes. This article extensively discusses the significant developments related to the size of available experimental data, the available sets of descriptors, and the machine learning (ML) algorithms used, such as support vector machines, random forests, artificial neural networks, and gradient boosting. As QSAR/QPR analysis only requires molecular structures of guests and experimental values of stability constants, this approach may be particularly useful for predicting these values for complexes with randomly substituted cyclodextrins, as well as for estimating their dependence on pH. This work proposes solutions on how to effectively use this knowledge, which is especially important for researchers who will deal with this topic in the future. This review also presents other applications of ML in relation to CD complexes, including the prediction of physicochemical properties of CD complexes, the development of analytical methods based on complexation with CDs, and the optimisation of experimental conditions for the preparation of the complexes. Full article
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Graphical abstract
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<p>Structural formulas of (<b>a</b>) α-CD, (<b>b</b>) β-CD, (<b>c</b>) γ-CD, and (<b>d</b>) exemplary 3D structure of the β-CD–flurbiprofen inclusion complex based on crystallographic data [<a href="#B2-molecules-29-03159" class="html-bibr">2</a>]. The flurbiprofen molecule is shown in green.</p>
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<p>Structural formulas of HP-β-CD, SBE-β-CD, and RM-β-CD.</p>
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<p>(<b>a</b>) Biological neuron (adapted from [<a href="#B82-molecules-29-03159" class="html-bibr">82</a>]), (<b>b</b>) artificial neuron, and (<b>c</b>) artificial neural network.</p>
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<p>(<b>a</b>) Prediction error and (<b>b</b>) coefficient of determination, <span class="html-italic">R</span><sup>2</sup>, as a function of model complexity plotted for data from the training and test sets. Part (<b>a</b>) is adapted from [<a href="#B86-molecules-29-03159" class="html-bibr">86</a>].</p>
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