Ben-Chao Zhu

A systematic density functional theory (DFT) investigation was conducted to explore the geometric evolution, electronic properties, and relative stability of tin-doped gold clusters SnAun (n = 2–20). The lowest-energy structures were identified using the CALYPSO structure prediction method and refined at the B3PW91/LANL2DZ level of theory. Our results reveal a distinct size-dependent structural transition: small clusters (n ≤ 8) adopt simple polyhedral geometries (some nearly planar, others three-dimensional) with Sn at peripheral sites, while larger clusters (n ≥ 9) evolve into three-dimensional structures with the Sn atom progressively encapsulated within the Au framework, achieving high coordination in tetrahedral or polyhedral cages for n ≥ 15. Analysis of the average binding energy, second-order difference energy, and HOMO–LUMO gaps identifies SnAu4, SnAu8, and SnAu16 as magic-number clusters with enhanced stability. Natural bond orbital (NBO) analysis suggests significant charge transfer from the electropositive Sn atom to the Au matrix. Theoretical infrared and Raman spectra were simulated, providing distinct vibrational fingerprints that evolve from sharp peaks in small clusters to broad, complex bands in larger systems. Quantum theory of atoms in molecules (QTAIM) analysis suggests that the bonding is predominantly closed-shell (ionic/metallic), with Sn–Au bonds showing enhanced polarization compared with Au–Au bonds. A possible weak localized character in the smallest clusters cannot be excluded, but the overall framework remains closed-shell dominated.

The distinct roles of Mg2+ and Ca2+ ions in biomolecular assembly can be understood through their different hydration dynamics, but a quantitative, causal link between the water-exchange kinetics of cations and assembly pathways has been lacking. Here, we establish this relationship using multi-force-field all-atom molecular dynamics simulations combined with enhanced sampling and Markov state model analysis. By systematically comparing force fields that inherently encode different hydration exchange rates, we show that the Mg2+ ion, with its kinetically inert hydration shell (microsecond water exchange), must undergo stepwise dehydration to coordinate aspartate residues. This kinetic barrier limits its ability to induce microphase separation on microsecond timescales, positioning the Mg2+ ion as a slow “structural reorganizer” that gradually disrupts preexisting Arg–Asp salt bridges. In contrast, the Ca2+ ion, with its rapidly exchanging hydration shell (picosecond-to-nanosecond water exchange), directly bridges multiple aspartate side-chains and acts as a fast “microphase separation trigger.” Quantitative comparison of water-exchange rates across force fields, validated against experimental NMR data, establishes a causal chain from hydration kinetics to coordination modes to assembly timescales. Based on these results, we propose a “hydration clock” model in which the intrinsic water-exchange kinetics of cations dictates the fundamental timescales of biomolecular assembly. This work provides a kinetic framework, grounded in explicit-solvent molecular dynamics and multi-force-field validation, for understanding cation-specific effects and the rational design of time-programmable self-assembling systems.

The initial geometric configurations of gas-phase doped magnesium clusters incorporating rare-earth elements (La₂Mg_n and Lu₂Mg_n, n = 1-20) were systematically explored using the CALYPSO structure prediction software. Subsequent density functional theory (DFT) calculations were performed to conduct a comparative analysis of their structural evolution, stability, electronic properties, vibrational spectra, and chemical bonding characteristics. Key findings reveal that both La₂Mg_n and Lu₂Mg_n clusters adopt cage-like architectures for medium sizes (n ≥ 10), with rare-earth atoms encapsulated within the magnesium framework. Stability analyses identified La₂Mg₁₀, La₂Mg₁₅, Lu₂Mg₁₀, and Lu₂Mg₁₅ as potential ″magic-number″ clusters exhibiting enhanced relative stability. Electronic structure investigations through natural population analysis (NPA) demonstrate consistent electron transfer from Mg to rare-earth atoms, with lutetium exhibiting greater electron affinity than lanthanum. Notably, valence orbital distributions reveal distinct hybridization patterns between 5d/6s (Lu) and 5d/6s/4f (La) atomic orbitals. Theoretical infrared and Raman spectra predictions provide characteristic vibrational fingerprints to guide future experimental identification. Bonding critical point (BCP) analysis via atoms-in-molecules (AIM) theory further elucidates the nature of interatomic interactions in these heterometallic systems.

The molecular basis for the liquid-liquid phase separation (LLPS) behavior of various biomolecular components in the cell is the formation of multivalent and low-affinity interactions. When the content of these components exceeds a certain critical concentration, the molecules will spontaneously coalesce to form a new liquid phase; i.e., LLPS occurs. Intrinsically disordered proteins (IDPs) are usually rich in amino acids with charged side-chains, and thus, LLPS-involving interactions between their side-chains are of great interest. However, the molecular details of the coalescence of such charged IDPs in a salt solution are still lacking. Here, we focus on two types of peptide-chains with oppositely charged amino acids in extreme arrangements and investigate their aggregation patterns in various ionic environments. The results show that the interaction patterns between peptide-chains with nonuniform charge arrangement sequences are more sensitive to the surrounding cationic environment, and Na⁺ ions are more likely to cause aggregation of ASP residues compared to Mg²⁺ ions. As the ionic concentration increases, the electrostatic interactions between oppositely charged residues are gradually converted into a negative-negative amino acid interaction network bridged by Na⁺ ions, while the positive charge-rich regions are more strongly inclined to be exposed to the solvent environment and gain greater freedom of movement. Simultaneously, this effect will reach saturation with a further increase of salt concentration. The present study enriches insights into the electrostatic dominant factors in phase separation phenomena at the atomic level, which will hopefully inspire the design and application of targeted LLPS in the future.

Gas-phase PbMg _{n ⁻} ( n = 2–12) cluster structures were globally searched on their potential energy surfaces by means of the CALYPSO prediction software. Structural optimization and calculations of properties such as relative energy and electronic structure were then carried out by density functional theory for each size of low energy isomer. The structural, relative stability, natural charge population, natural electronic configuration and distribution of the strongest peaks of the infrared and Raman spectra of the low energy isomers of PbMg _{n ⁻} ( n = 2–12) clusters were systematically investigated in the present work. It was shown that the PbMg _{7 ⁻} cluster ground state isomer exhibits the highest stability, for which special electronic excitation and chemical bonding analyses were performed. It is reasonable to believe that this work enriches the structural, spectroscopic and other data of magnesium-based clusters and provides some theoretical basis for possible future experimental syntheses.

Gas-phase NbMg_n (n = 2-12) clusters were fully searched by CALYPSO software, and then the low-energy isomers were further optimized and calculated under DFT. It is shown that the three lowest energy isomers of NbMg_n (n = 3-12) at each size are grown from two seed structures, i.e., tetrahedral and pentahedral structures, and the transition size occurs at the NbMg₈ cluster. Interestingly, the relative stability calculations of the NbMg₈ cluster ground-state isomer stand out under the examination of several parameters' calculations. The charge-transfer properties of the clusters of the ground-state isomers of various sizes had been comprehensively investigated. In order to be able to provide data guidance for future experimental probing of these ground-state clusters, this work also predicted infrared and Raman spectra at the same level of theoretical calculations. The results show that the multipeak nature of the IR and Raman spectra predicts that it is difficult to distinguish them directly. Finally, the optical properties of these clusters were investigated by calculating the static linear, second-order nonlinear, and third-order nonlinear coefficients. Importantly and interestingly, the NbMg₈ cluster was shown to have superior nonlinear optical characteristics to all other clusters; thus, it is a powerful candidate for a potentially ultrasensitive nonlinear optical response device for some special purpose.

Stronger hydrophobic interactions result in more compact single-chain structures, elevating the tendency as well as the critical temperature of phase separation.