Aiming at the aqueous chemistry of the cadmium ion (Cd2+), this study systematically investigated the aqueous configurations and thermodynamic stabilities of Cd2+ and its hydrolyzed species with different coordination numbers, by using various combinations of quantum chemical calculation methods and implicit solvation models. The results reveal that the implicit solvent model exerts a notable influence on the structures and energies of Cd2+ ion and its hydrolyzed species, as well as the predicted pK a values. The combination of PBE0-D3(BJ), M06-2X, and wB97XD functionals with the IEF-PCM model (employing UA0 radii) effectively simulates the aqueous configurations of Cd2+ hydrates and hydrolyzed species. Meanwhile, the MP2 method, the double-hybrid functionals B2PLYPD3 and mPW2PLYPD, coupled with either the IEF-PCM model (utilizing Pauling or Bondi radii) or the SMD model, yields Cd2+ hydrolysis pK a values that closely matching experimental data. The results indicate that the aqueous Cd2+ ion primarily exists in the form of hexahydrate Cd(H2O)6 2+, and its hydrolyzed species, Cd(OH)m (2-m)+ (m = 1-4), mainly exist as tetracoordinate Cd(OH)(H2O)3 + and Cd(OH)2(H2O)2 0, tricoordinate Cd(OH)3 -, and tetracoordinate Cd(OH)4 2 -, respectively. The study is expected to provide valuable references for systematically studying the interactions between Cd2+ and other inorganic ligands in aqueous systems.

This study investigates the coordination structures and formation constants of cadmium halide complexes (CdXn(H2O)(CN-n)(2-n)+, X = F, Cl, Br, and I; n = 1, 2, 3, and 4; and CN = 3, 4, 5, and 6) using a quantum-chemical cluster-continuum model. By comparing the relative energies of 24 different coordination structures for each category of CdXn(H2O)(CN-n)(2-n)+ (X = F, Cl, Br, and I), it is found that all four types of complexes prefer low-coordination structures, primarily existing in tri- or tetra-coordination. In calculating the solvation energy of halide ions using different thermodynamic cycle methods, it is found that the cluster cycle yields results closer to experimental values than the monomer cycle. Halide ions with high electronegativity and small radii require more water molecules to form stable solvation structures. In complex formation constant (log K) calculations, the log K values from monomer cycles are generally larger than those from the cluster cycles. The accuracy of log K estimation is jointly affected by the thermodynamic cycle type, the solvation characteristics of the halide ion, and the entropy change of the reaction. Accurate log K determination for cadmium halide complexes is enabled by the "cluster-size-matching" approach. This work aids in predicting the coordination structures of heavy metal-halide complexes, especially offering a feasibility reference for thermodynamic cycle methods in calculating their thermodynamic parameters.

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The dissociative (D) mechanistic water-exchange kinetics of aquated Al3+ in aqueous solution is systematically studied using the density functional theory–quantum chemical cluster model (DFT–CM) method. The modeled pathways include dehydration of hexacoordinated Al(H2O)63+ and successive hydration of pentacoordinated Al(H2O)53+. For the hydration of Al(H2O)53+, the attacking pathways corresponding to the second-shell solvent water molecules at different sites are investigated. The gas phase-supermolecule-polarizable continuum model (GP-SM-PCM) is used to simulate the explicit and bulk solvation effects. The reactant, transition state, and product geometries of the modeled reaction pathways are optimized at the B3LYP/6-311+G(d,p) level of theory. The real and apparent water-exchange reaction mechanisms of Al3+ are analyzed on the basis of Gibbs free energy changes for the dehydration and hydration pathways. The possible ligand competition with the solvent water molecules in the formation of aqueous Al3+–li...

The rattling and rotation behaviours of the hydrated excess proton (H+) in water are investigated using the density functional theory–quantum chemical cluster model (DFT-CM) method. The rattling pathways for the target proton *H+ between two adjacent O atoms in the form of Zundel configurations with symmetrical solvation environments are obtained. The zero-point contribution reduces the reaction energy barrier and enables the rattling to occur spontaneously at room temperature. The rotational behaviour of *H+ in the form of *H+·H2O* is found. Upon *H+·H2O* rotation, *H+ changes its position accompanied by concerted displacement of surrounding solvent water molecules and the breaking and formation of hydrogen bonds. The “*H+·H2O* rotating migration mechanism” is proposed for the proton transfer mechanism in water — the same *H+ migrates via *H+·H2O* rotation through void in solvent water, rather than different protons hopping along water hydrogen bond chains as known as the Grotthuss mechanism.

In this study, the Al-27 NMR chemical shifts and relative stabilities of monomeric Al3+ hydrolytic species with different coordination structures in aqueous solution are systematically investigated by using the density functional theory quantum chemical cluster model (DFT-CM) at the B3LYP/6-311+G(d,p) level. The main work includes: the static configurations of 20 possible existing monomeric Al3+ hydrolytic species from Al3+ to Al(OH)(4)(-) are optimized, and their Al-27 NMR shieldings are calculated; the dehydration reaction pathways for typical monomeric Al3+ hydrolytic species are modeled, and the dominant forms of the intermediate hydrolytic species of Al(OH)(2+), Al(OH)(2)(+), and Al(OH)(3)(0) are analyzed based on the Gibbs free energy changes of the dehydration reactions. The important role of the tetracoordinated Al(H2O)-(OH)(3)(0) in the formation mechanism of the polynuclear Keggin-Al-13 further studying the formation and transformation mechanisms of the is discussed. This work provides valuable references for aqueous monomeric and polymeric Al species.

The stable geometries of a series of mononuclear bidentate chelating Al(III)-carboxylate complexes in aqueous solution are optimized and their transition-states for water-exchange reactions are modeled with the density functional theory - quantum chemical cluster model (DFT-CM) method. The studied carboxylates include oxalate, malonate, succinate, phthalate, salicylate and benzoate. Thermodynamic stability constants K-aq and water-exchange reaction rate constants k(ex) of the tested Al (III)- carboxylate complexes are estimated from calculated Gibbs free energy changes. The estimated k(ex) values suggest that the coordination of dicarboxylate and salicylate ligands to Al3+ leads to the labilization of inner-shell coordinated waters and that the cis waters of chelate rings are more labile than trans waters. From estimated log K-aq and log k(ex) values of aqueous mononuclear Al(III)- carboxylate complexes, linear correlations between log K-aq, log k(ex) values and experimental apparent rate constants k(L) of carboxylate ligand-promoted delta-Al2O3 mineral dissolution are established. Based on the calculation results, cis labilizing effects of the carboxylate ligands, strong "log k(L) similar to log K-aq" correlations, and weak "log k(L) similar to log k(ex)" correlations are discussed. This work offers further insight into intrinsic relationships between mineral surface and aqueous metal complexes and furthers understanding of mineral dissolution kinetics at the molecular level. (C) 2018 Elsevier Ltd. All rights reserved.

The formation mechanisms, thermodynamic stabilities, and water-exchange reactivities of 1:1 monomer aluminum-salicylate (Al-salicylate) complexes in acidic aqueous solution are investigated using the density functional theory-quantum chemical cluster model (DFT-CM) method. (1) The formation pathways for possible monodentate and bidentate Al-salicylate configurations are modeled with the gas phase-supermolecule-polarizable continuum model (GP-SM-PCM). It shows that the formation pathways for the Al-salicylate complexes follow the Eigen-Wilkins mechanism, where the dissociation of an inner-shell coordinated water of Al3+ is the rate-determining step. (2) The formation constants K-aq for different Al-salicylate configurations are estimated based on the total Gibbs free energy changes Delta G degrees for their overall formation pathways. It is indicated that in the acidic aqueous solution at pH similar to 3, the main existence form of the 1:1 monomer Al-salicylate complex is the phenol-deprotonated bidentate Al(Sal)(H2O)(4)(+) with six-membered ring. Its log K-aq is calculated as 13.8, in good agreement with the literature values of 12.9-14.5. (3) The water-exchange reactions are modeled for different Al-salicylate configurations. The water-exchange rate constant for Al(Sal)(H2O)(4)(+) is estimated as log k(H2O) = 3.9 s(-1), close to the experimental value of 3.7 s(-1). It proves again that this configuration is the dominant form under experimental conditions.

Chiral substances widely exist in the environment and organisms. It is of great scientific significance to investigate the characteristics of chiral metal-organic in environment. In this work, density functional theory (DFT) calculations combined with cluster model (CM) were performed at B3LYP/6-311+G(d,p) level to investigate the chiral aluminium-organic complexes. Using both aluminium-oxalate and aluminium-maltolate as examples, systematic studies on the static and dynamic properties of chiral aluminium-organic complexes were conducted. Static configurations for one pair of aluminium-oxalate and three pairs of aluminium-maltolate chiral were optimized to obtain their static structure parameters and energetic parameters, as well as spectroscopic properties. Ten possible water-exchange reaction pathways were obtained and the water-exchange rate constants are predicted. Chirality inversion pathway for aluminium-oxalate was simulated using Berny algorithm, and the activation barrier was obtained. The results show that the static structure parameters and energetic parameters of the enantiomers are basically same, but there are obvious differences in the dipole moment. The static structure parameters, dipole moment and the water-exchange rate constants are affected by the solvent effect. The inversion of enantiomers will happen in the environment, leading to the change in the proportion of chiral enantiomers.

Density functional theory (DFT) calculations combined with cluster models are performed at the B3LYP/6-311+G(d,p) level for investigating the solvent effects in Al(H2O)63+ water-exchange reactions. A "One-by-one" method is proposed to obtain the most representative number and arrangement of explicit H2Os in the second hydration sphere. First, all the possible ways to locate one explicit H2O in second sphere (Nm' = 1) based on the gas phase structure (Nm' = 0) are examined, and the optimal pathway (with the lowest energy barrier) for Nm' = 1 is determined. Next, more explicit H2Os are added one by one until the inner-sphere is fully hydrogen bonded. Finally, the optimal pathways with Nm' = 0-7 are obtained. The structural and energetic parameters as well as the lifetimes of the transition states are compared with the results obtained with the "Independent-minimum" method and the "Independent-average" method, and all three methods show that the pathway with Nm' = 6 may be representative. Our results give a new idea for finding the representative pathway for water-exchange reactions in other hydrated metal ion systems.

The forced hydrolysis reaction of aqueous aluminum ion (Al3+) is of critical importance in Al chemistry, but its microscopic mechanism has long been neglected. Herein, density functional calculations reveal an external OH−‐induced barrierless proton dissociation mechanism for the forced hydrolysis of Al3+(aq). Dynamic reaction pathway modeling results show that the barrierless deprotonations induced by the second‐ or third‐shell external OH− proceed via the concerted proton transfer through H‐bond wires connected to the coordinated waters, and the inducing ability of the external OH− decreases with increasing hydration layers between Al(H2O)63+ and the external OH−. The OH−‐induced forced hydrolysis mechanism of Al3+(aq) is quite different from its self‐hydrolysis mechanism without OH−. The inducing ability is a unique characteristic of OH−, rather than other anions such as F− or Cl−.

The kinetic mechanism of spontaneous aluminum ion (Al3+) hydrolysis reaction in aqueous solution is investigated using the density functional theory-quantum chemical cluster model method. Three typical reaction pathways for the spontaneous Al3+ hydrolysis reaction are modeled, including (1) the traditional spontaneous proton dissociation on the Al3+ inner-shell coordinated waters; (2) the conventional bulk water-assisted proton dissociation; and (3) the second-shell water-assisted synergistic dissociation of the protons on the Al3+ inner-shell waters. The results show that the electrostatic effects between Al3+ and its coordinated waters alone cannot fully account for the proton loss on an inner-shell coordinated water. It is suggested that the main reaction pathway for natural hydrolysis of aqueous Al3+ is the second-shell water-assisted synergistic proton dissociation, in which the participation of the second hydration shell is crucially important. The calculated synergistic proton dissociation rate constant, k(H)(+) = 1.14 X 10(5) s(-1), is in close agreement with the experimental results (1.09 X 10(5) s(-1) and 7.9 X 10(4) s(-1)). The first hydrolysis equilibrium constant pK(a1) of Al3+ is calculated as 5.82, also consistent with the literature value of 5.00. This work elucidates the molecular mechanism of the spontaneous Al3+ hydrolysis reaction in natural waters and has important environmental implications.

采用密度泛函理论(DFT)对不同温度、压力和溶剂条件下的Al(H2O)63+水交换反应进行了研究,系统地开展了以下工作:(1)采用超分子-极化连续模型在B3LYP/6-311+G(d,p)基组水平下优化得到Al(H2O)63+水交换反应的路径,在优化构型的基础上计算得到5组温度(278-358 K)条件下相应的水交换反应速率常数kex结果表明温度升高促进了Al(H2O)63+水交换反应的进行;(2)计算得到5组压力(0.4-1.2 atm)条件下Al(H2O)63+水交换反应的kex,研究表明在该地表水中常压范围内的压力变化对kex没有影响;(3)在极化连续模型下进行单点能计算时分别选择水、乙腈、乙醇、苯和四氯化碳等5种不同的主体溶剂,计算不同溶剂中Al(H2O)63+水交换反应的kex结果表明非极性溶剂中反应的活化Gibbs自由能较低,水交换速率加快.本文为不同环境条件下Al(H2O)63+水交换反应的研究提供了有用参考.

The following studies were carried out at B3LYP/6-31 l+G(d,p) level by density functional theory:(1)Ten possible configurations of 1∶1/1∶2/1∶3 Al-maltolate complexes were optimized and their static structural properties,NPA charges and energies were obtained.The 27Al NMR/1H NMR chemical shifts,ultraviolet spectral data and infrared absorptions of four isomers of Al(ma)3 were calculated and found to be corresponding with experimental results reported by literatures,which proved the applicability of the density functional theory.(2) Nine possible pathways of water-exchange reactions of 1∶1/1∶2 Al-maltolate complexes were simulated.The logarithm values of waterexchange rate constants log kex(S-1) of three sites were 2.4 (Al(ma)(H2O)24+(cis to ma)),2.6 (cis-Al(ma)2(H2O)2+(I))and 3.0 (trans-Al(ma)2(H2O)2+(I)) respectively,which were in good agreement with the experimental values of 2.5 (Al(ma)2+) and 3.3 (Al(ma)2+),and the corresponding sites were regarded as the active sites.(3) The mechanism of the relationship between toxicity of Al-maltolate complexes and their different speciation was discussed.

Based on the four models (gas phase (GP),polarizable continuum model (GP-PCM),supermolecule model(GP-SM) and supermolecule-polarizable continuum model (GP-SM-PCM)),we systematically conducted the following investigations using quantum chemical cluster models-density functional theory method.The water-exchange reaction of Al(H2O)63+ was simulated at the level of B3LYP/6-311+-G(d,p),and the single-point energies were calculated using MP2 method.Taking zero-point energies,thermal corrections and entropies into consideration,the activation Gibbs energy barries and water-exchange rate constant(kex) were calculated.The logkex values for water-exchange reactions of Al(H2O)63+ with GP-SM//MP2-PCM and GP-SM-PCM//MP2-PCM models were similar and consistent with available literature values.This indicates that the GP-SM//MP2-PCM model could simulate the water-exchange reaction of Al(H2O)63+ satisfactorily.

采用密度泛函理论(DFT)量子化学计算方法对铝-8-羟基喹啉配合物(Al-8-Hq)的静态结构以及水交换反应进行了研究,系统地开展了以下工作:(1)采用GP-PCM(气相模型并考虑本体溶剂效应)在B3LYP6-311+G(d,p)水平优化了Al-8-Hq溶液中可能存在的8种构型,获得了相应的静态结构参数、NPA电荷和能量;(2)采用GIAO方法在HF 6-311+G(d,p)水平下计算了1∶3配合物的27Al NMR化学位移,结果表明采用HF的GP-PCM模型化学位移计算值与实验值一致;(3)通过模拟1∶1/1∶2配合物8个不同位点的动态水交换反应,探讨了水交换反应机制并预测了水交换反应速率.本研究有助于从原子层面加深对Al-8-Hq配合物形态结构以及水交换反应动力学过程的理解和认识.

针对水溶液中铝离子第三水化层(hydration shell)对Al(H2O)3+6动态水交换反应特性的影响,本文采用密度泛函理论(Density functional theory,DFT)在B3LYP/6-311 +G(d,p)基组水平上进行了研究.探讨了第三水化层对第一到第二水化层水交换反应速率常数k1-2ex以及第二到三水化层水交换反应速率常数2-3ex的影响.研究结果表明,在第三水化层添加不同数目水分子时相应于k1-2ex和k2-3ex的活化能垒变化均不大,表明第三水化层对水交换反应速率常数k1-2ex和k2-3ex影响不大,采用第二水化层就可以较好处理Al(H2O)3+6的真实溶剂效应.

用密度泛函理论(DFT)量子化学计算方法对水溶液中Al3+第三水化层的静态结构特征进行了系统研究.在Bock构建的含有第一、第二水化层Al(H2O)63+·12H2O的基础上添加了第三水化层,系统考察了第三和第二水化层对第一水化层Al(H2O)63+的键长、键角等结构参数,以及自然布居分析(NPA)电荷特性的影响,同时探讨了Al3+(aq)配合物含有不同水化层时氢键网络结构,以及27Al-/17O-/1H-NMR的特性.

Density functional theory (DFT) calculations were performed on the structures and water-exchange reactions of aqueous Al(III)–salicylate complexes. Based on the four models (gas phase (GP); polarizable continuum model (PCM), which estimates the bulk solvent effect; supermolecule model (SM), which considers the explicit solvent effect, and supermolecule–polarizable continuum model (SM–PCM), which accounts for both types of solvent effects), we systematically conducted this study by examining three different properties of the complexes. (1) The microscopic properties of the aqueous Al(III)–salicylate complexes were studied by optimizing their various structures (including the possible 1:1 mono- and bidentate complexes, cis and trans isomers of the 1:2 bidentate complexes and 1:3 bidentate complexes) at the B3LYP/6-311+G(d, p) level. (2) The 27Al and 13C NMR chemical shifts were calculated using the GIAO method at the HF/6-311+G(d, p) level. The calculation results show that the values obtained with the SM–PCM models are in good agreement with the experimental data available in the literature, indicating that the models we employed are appropriate for Al(III)–salicylate complexes. (3) The water-exchange reactions of 1:1 mono- and bidentate Al(III)–salicylate complexes were simulated using supermolecule models at the B3LYP/6-311+G(d, p) level. The logarithm of the water-exchange rate constant (logkex) of the 1:1 bidentate complex predicted using the “logkex–dAl–OH2” correlation is 4.0, which is in good agreement with the experimental value of 3.7, whereas the calculated range of logkex of the 1:1 monodentate complexes is 1.3–1.9. By effectively combining the results for the thermodynamic static structures with the simulations of the kinetic water-exchange reactions, this work promotes further understanding of the configurations and formation mechanism of Al(III)–salicylate complexes.