Development of an efficient geometry optimization method for water clusters

A geometry optimization method for water clusters (H(2)O)(n) was developed in the present study. The method was applied to the TIP3P and TIP4P water clusters in the range of n < or = 30, and the resulting structures were compared with the global-minimum structures in the literature (n < or = 25 for the TIP3P potential and n < or = 30 for the TIP4P potential). The method failed to reproduce the previously reported global minimum of the n = 24 TIP4P cluster. However, it was possible to find new global minima for the n = 24, 26-30 TIP3P cluster and the TIP4P clusters of 25, 28, 29, and 30 molecules.     

H·(H2O)n clusters: microsolvation of the hydrogen atom via molecular ab initio gradient embedded genetic algorithm (GEGA)

A new version of the ab initio gradient embedded genetic algorithm (GEGA) program for finding the global minima on the potential energy surface (PES) of mixed clusters formed by molecules and atoms is reported. The performance of the algorithm is demonstrated on the neutral H·(H(2)O)(n) (n = 1-4) clusters, that is, a radical H atom solvated in 1-4 water molecules. These clusters are of a fundamental interest. The solvated hydrogen atom forms during photochemical events in water, or during scavenging of solvated electrons by acids, and transiently exists in biological systems and possibly in inclusion complexes in the deep ocean and in the ice shield of earth. The processes associated with its existence are intriguingly complex, however, and have been the subject of decades-long debates. Using GEGA, we explicate the apparently extreme structural diversity in the H·(H(2)O)(n) (n = 1-4) clusters. All considered clusters have four basic structural types: type I, where the H radical is weakly coordinated to the oxygen atom of one of the water molecules; type II, where H is weakly coordinated to a H atom of one of the water molecules; type III, consisting of H(2), the OH radical, and n - 1 H(2)O molecules; and type IV, consisting of H(3)O and n - 1 H(2)O. There are myriads of isomers of all four types. The lowest energy species of types I and II are the isoenergetic global minima. H·(H(2)O)(n) clusters appear to be a challenging case for GEGA because they have many shallow minima close in energy some of which are significantly less stable than the global minimum. Additionally, the global minima themselves have high structural degeneracy, they are only weakly bound, and they are prone to dissociation. GEGA performed exceptionally well in finding both the global and the low-energy local minima that were subsequently confirmed at higher levels of theory.     

Protonated water clusters described by an empirical valence bond potential

The properties of low-lying stationary points on the potential energy surfaces of singly protonated water clusters (H(2)O)(n)H(+), are investigated using an empirical valence bond potential. Candidate global minima are reported for n=2-4, 8, and 20-22. For n=8, the variation in the energies and structures of low-lying minima with the number of valence bond states included in the model is studied. For n=4 and 8, disconnectivity graphs are also reported and are compared to results for the equivalent neutral water clusters as described by the rigid TIP3P potential. For the larger clusters, n=20-22, the structural properties of the low energy minima are compared with recently published spectroscopic data on these systems. The observed differences between the n=20 and n=21 systems are qualitatively reproduced by the model potential, but the similarities between the n=21 and n=22 systems are not.     

杂合型全局优化法优化水分子团簇结构

基于遗传算法、快速模拟退火及共轭梯度方法提出了一种快速的杂合型全局优化方法(fast hybrid global optimization algorithm, FHGOA),并将这一方法应用于TIP3P和TIPS2模型水分子团簇(H2O)n结构的优化.在进行TIP3P模型水分子团簇结构的优化过程中,发现了能量比文献值更低的团簇结构,且执行效率有较大提高.把该方法应用到优化TIPS2模型的水分子团簇,发现最优结构和采用TTM2-F模型优化的水分子团簇结构在n < 17时完全相同,为全表面结构;而在n=17、19、22时为单中心水分子笼状结构;在n=25、27时为双中心水分子笼状结构.说明随着团簇中水分子个数的增加,采用TIPS2和TTM2-F势能函数优化的团簇最优结构有相同的变化趋势.     

An evolutionary algorithm for the global optimization of molecular clusters: application to water, benzene, and benzene cation

We have developed an evolutionary algorithm (EA) for the global minimum search of molecular clusters. The EA is able to discover all the putative global minima of water clusters up to (H(2)O)(20) and benzene clusters up to (C(6)H(6))(30). Then, the EA was applied to search for the global minima structures of (C(6)H(6))(n)(+) with n = 2-20, some of which were theoretically studied for the first time. Our results for n = 2-6 are consistent with previous theoretical work that uses a similar interaction potential. Excluding the very symmetric global minimum structure for n = 9, the growth pattern of (C(6)H(6))(n)(+) with n ≥ 7 involves the (C(6)H(6))(2)(+) dimer motif, which is placed off-center in the cluster. Such observation indicates that potentials commonly used in the literature for (C(6)H(6))(n)(+) cannot reproduce the icosahedral-type packing suggested by the available experimental data.     

Physical properties of small water clusters in low and moderate electric fields

Likely candidates for the lowest minima of water clusters (H(2)O)(N) for N ≤ 20 interacting with a uniform electric field strength in the range E ≤ 0.6 V/? have been identified using basin-hopping global optimization. Two water-water model potentials were considered, namely TIP4P and the polarizable Dang-Chang potential. The two models produce some consistent results but also exhibit significant differences. The cluster internal energy and dipole moment indicate two varieties of topological transition in the structure of the global minimum as the field strength is increased. The first takes place at low field strengths (0.1 V/? 10) usually forming helical structures.     

A theoretical investigation on optimal structures of ethane clusters (C2H6)n with n ≤ 25 and their building-up principle

Geometry optimization of ethane clusters (C(2)H(6))(n) in the range of n ≤ 25 is carried out with a Morse potential. A heuristic method based on perturbations of geometries is used to locate global minima of the clusters. The following perturbations are carried out: (1) the molecule or group with the highest energy is moved to the interior of a cluster, (2) it is moved to stable positions on the surface of a cluster, and (3) orientations of one and two molecules are randomly modified. The geometry obtained after each perturbation is optimized by a quasi-Newton method. The global minimum of the dimer is consistent with that previously reported. The putative global minima of the clusters with 3 ≤ n ≤ 25 are first proposed and their building-up principle is discussed.     

Monte Carlo temperature basin paving with effective fragment potential: an efficient and fast method for finding low-energy structures of water clusters (H2O)20 and (H2O)25

Determining low-energy structures of large water clusters is a challenge for any optimization algorithm. In this work, we have developed a new Monte Carlo (MC)-based method, temperature basin paving (TBP), which is related to the well-known basin hopping method. In the TBP method, the Boltzmann weight factor used in MC methods is dynamically modified based on the history of the simulation. The states that are visited more are given a lower probability by increasing their temperatures and vice versa. This allows faster escapes from the states frequently visited in the simulation. We have used the TBP method to find a large number of low-energy minima of water clusters of size 20 and 25. We have found structures energetically same to the global minimum structures known for these two clusters. We have compared the efficiency of this method to the basin-hopping method and found that it can locate the minima faster. Statistical efficiency of the new method has been investigated by running a large number of trajectories. The new method can locate low-energy structures of both the clusters faster than some of the reported algorithms for water clusters and can switch between high energy and low-energy structures multiple times in a simulation illustrating its efficiency. The large number of minima obtained from the simulations is used to get both general and specific features of the minima. The distribution of minima for these two clusters based on the similarity of their oxygen frames shows that the (H(2)O)(20) can have different variety of structures, but for (H(2)O)(25), low-energy structures are mostly cagelike. Several (H(2)O)(25) structures are found with similar energy but with different cage architectures. Noncage structures of (H(2)O)(25) are also found but they are 6-7 kcal/mol higher in energy from the global minimum. The TBP method is likely to play an important role for exploring the complex energy landscape of large molecules.     

Geometry Optimization of Ba2+(H2O)n Clusters Using a Fast Hybrid Global Optimization Algorithm

A global optimization called fast hybrid global optimization algorithm was proposed based on genetic algorithm, fast simulated algorithm and conjugated gradient algorithm. We employ it to search the global minimum energy structures of Ba²⁺(H₂O)_n clusters for n = 1–30 within the TIP4P model. The results show that Ba²⁺(H₂O)_n clusters have the n+0 structure while n = 1–8. When n is in the range 9 ≤ n ≤ 18, the number of water molecules in the first shell around the barium ion is 8 and the other water molecules arrange in the outer shell. In the global minimum structure of Ba²⁺(H₂O)₁₉, the number of the first shell water molecules adds up to 9, and the value is kept until n = 30. According to the computational results, a conclusion that hydration numbers for Ba²⁺ is 9 can be drawn, which is in agreement with the result by a Monte Carlo simulation.     

Clusters of glycolic acid with three to six water molecules

Semiempirical, ab initio, and density functional theory calculations are used to locate many low-energy minima on the potential energy surfaces of the CH2OHCOOH-(H2O)n complexes with n = 3,4,5,6. In the clusters with three, four, and five water molecules, the lowest-energy structure consists of a (H2O)n complex, not necessarily of lowest energy, hydrogen bonded to the carboxylic group of the glycolic acid. The lowest-energy structure for n = 6 is similar except that the water hexamer is hydrogen bonded to both the carboxylic and alpha-hydroxyl groups of the acid. In all the lowest-energy clusters, the intramolecular hydrogen bond remains intact in the glycolic acid.     

s-四嗪-水簇复合物的理论研究

用量子化学B3LYP方法和6-31＋＋G**基函数研究了s-四嗪-水簇复合物基态分子间相互作用, 并进行了构型优化和频率计算, 分别得到无虚频稳定的s-四嗪-(水)₂复合物、s-四嗪-(水)₃复合物和s-四嗪-(水)₄复合物6个、9个和12个. 复合物存在较强的氢键作用, 复合物结构中形成一个N…H—O氢键并终止于O…H—C氢键的氢键水链构型最稳定. 经基组重叠误差和零点振动能校正后, 最稳定的1∶2, 1∶3和1∶4(摩尔比)复合物的结合能分别是41.35, 70.9和 94.61 kJ/mol. 振动分析显示氢键的形成使复合物中水分子H—O键对称伸缩振动频率减小(红移). 研究表明N…H键越短, N…H—O键角越接近直线, 稳定化能越大, 氢键作用越强. 同时, 用含时密度泛函理论方法在TD-B3LYP/6-31＋＋G**水平计算了s-四嗪单体及其氢键复合物的第一¹(n, p*)激发态的垂直激发能.     

Methanol-water mixtures: a microsolvation study using the effective fragment potential method

The formation process of methanol-water mixtures, (MeOH/H2O)n, n = 2, 3,..., 8 is studied at the molecular level using the general effective fragment potential (EFP2) method and second-order perturbation theory (MP2). Extensive Monte Carlo/simulated annealing global optimizations were used to locate global minimum structures for each n, for both homo and hetero clusters. Mixing at the microscopic level was investigated, and some general conclusions about the microsolvation behavior of these mixtures are presented. For all of these clusters, incomplete mixing is observed at the molecular level. Low-energy (MeOH/H2O)n clusters retain much of their initial structure in the global minima of the mixed clusters.     

Novel method for geometry optimization of molecular clusters: application to benzene clusters

A heuristic and unbiased method for searching optimal geometries of clusters of nonspherical molecules was constructed from the algorithm recently proposed for Lennard-Jones atomic clusters. In the method, global minima are searched by using three operators, interior, surface, and orientation operators. The first operator gives a perturbation on a cluster configuration by moving molecules near the center of mass of a cluster, and the second one modifies a cluster configuration by moving molecules to the most stable positions on the surface of a cluster. The moved molecules are selected by employing a contribution of the molecules to the potential energy of a cluster. The third operator randomly changes the orientations of all molecules. The proposed method was applied to benzene clusters. It was possible to find new global minima for (C6H6)11, (C6H6)14, and (C6H6)15. Global minima for (C6H6)16 to (C6H6)30 are first reported in this article.     

Intermolecular complexes of HXeOH with water: stabilization and destabilization effects

Theoretical and matrix-isolation studies of intermolecular complexes of HXeOH with water molecules are presented. The structures and possible decomposition routes of the HXeOH-(H(2)O)(n)(n = 0, 1, 2, 3) complexes are analyzed theoretically. It is concluded that the decay of these metastable species may proceed through the bent transition states (TSs), leading to the global minima on the respective potential energy surfaces, Xe + (H(2)O)(n+1). The respective barrier heights are 39.6, 26.6, 11.2, and 0.4 kcal/mol for n = 0, 1, 2, and 3. HXeOH in larger water clusters is computationally unstable with respect to the bending coordinate, representing the destabilization effect. Another decomposition channel of HXeOH-(H(2)O)(n), via a linear TS, leads to a direct break of the H-Xe bond of HXeOH. In this case, the attached water molecules stabilize HXeOH by strengthening the H-Xe bond. Due to the stabilization, a large blue shift of the H-Xe stretching mode upon complexation of HXeOH with water molecules is featured in calculations. On the basis of this computational result, the IR absorption bands at 1681 and 1742 cm(-1) observed after UV photolysis and annealing of multimeric H(2)O/Xe matrixes are assigned to the HXeOH-H(2)O and HXeOH-(H(2)O)(2) complexes. These bands are blue-shifted by 103 and 164 cm(-1) from the known monomeric HXeOH absorption.     

Lowest-energy structures of (C60)nX (X=Li+,Na+,K+,Cl-) and (C60)nYCl (Y=Li,Na,K) clusters for n</=13

Basin-hopping global optimization is used to find likely candidates for the lowest minima on the potential energy surface of (C(60))(n)X (X=Li(+),Na(+),K(+),Cl(-)) and (C(60))(n)YCl (Y=Li,Na,K) clusters with n相似文献   

Optimal covering of C(60) fullerene by rare gases

Putative global energy minima of clusters formed by the adsorption of rare gases on a C(60) fullerene molecule, C(60)X(N) (X=Ne, Ar, Kr, Xe; N ≤ 70), are found using basin-hopping global optimization in an empirical potential energy surface. The association energies per rare gas atom as a function of N present two noticeable minima for Ne and Ar and just one for Kr and Xe. The minimum with the smallest N is the deepest one and corresponds to an optimal packing monolayer structure; the other one gives a monolayer with maximum packing. For Kr and Xe, optimal and maximum packing structures coincide. By using an isotropic average form of the X-C(60) interaction, we have established the relevance of the C(60) surface corrugation on the cluster structures. Quantum effects are relevant for Ne clusters. The adsorption of these rare gases on C(60) follows patterns that differ significantly from the ones found recently for He by means of experimental and theoretical methods.     

Proton transfer and autoionization in HNO3·HCl·(H2O)n particles

The structure and spectroscopic properties of clusters of HNO(3)·HCl·(H(2)O)(n), with n = 1 to 6, have been calculated at the MP2/aug-cc-pVDZ level of theory. Altogether 22 different clusters have been found as stable structures, with minima in their potential energy surfaces. The clusters can be grouped in families with the same number of water molecules, and with close aggregation energies within each family. The addition of each new water molecule increments the aggregation energy of the clusters by a nearly constant value of 76.2 ± 0.1 Hartree. The proton transfer parameter and the coordination number of HNO(3) and HCl in each cluster have been evaluated, and the wavenumber shifts for the X(-)-H(+) vibration from the corresponding mode in the isolated molecules have also been predicted. These values allow classification of the acidic species in the clusters into three types, characterized by the strength of the hydrogen bond and the degree of ionization. A correspondence is found between the coordination number of HNO(3) and the magnitude of the X(-)-H(+) vibrational shift.     

Lowest-energy structures of water clusters (H2O)11 and (H2O)13

We employed a four-step searching/screening approach to determine best candidates for the global minima of (H2O)11 and (H2O)13. This approach can be useful when there exist a large number of low-lying and near-isoenergetic isomers, many of which have the same oxygen-skeleton structure. On the two new candidates for the global minimum of (H2O)11, one isomer can be viewed as placing the 11th molecule onto the side of the global minimum of (H2O)10 and the other can be viewed as removing the 12th molecule from the middle layer of the global minimum of (H2O)12. The three leading lowest-energy clusters of (H2O)13 can all be built starting from the global minimum of (H2O)12, with the difference being in the location of the 13th water molecule.     

Microsolvation of hydrogen sulfide: exploration of H2S.(H2O)n and SH-.H3O+.(H2O)n-1 (n = 5-7) cluster structures on ab initio potential energy surfaces by the scaled hypersphere search method

The scaled hypersphere search method was applied to ab initio potential energy surfaces of the H2S.(H2O)n/SH-.H3O+.(H2O)n-1 system with n = 5-7. Local minima databases including 121, 326, and 553 structures for n = 5-7, respectively, were obtained based on calculations at the MP2/6-311++G(3df,2p)//B3LYP/6-31+G** level. In these small cluster sizes, the SH-.H3O+.(H2O)n-1 type is still unstable relative to the H2S.(H2O)n type, and the global minima for H2S.(H2O)n are very similar to those of pure water clusters of (H2O)n+1. Thermodynamic simulations based on the present databases showed a structure transition from the well-mixed (H2O)n+1-like global minimum at low temperatures to unmixed complexes between H2S and (H2O)n at high temperatures.     

Potential energy surface and second virial coefficient of methane-water from ab initio calculations

Six-dimensional intermolecular potential energy surfaces (PESs) for the interaction of CH4 with H2O are presented, obtained from ab initio calculations using symmetry-adapted perturbation theory (SAPT) at two different levels of intramonomer correlation and the supermolecular approach at three different levels of electron correlation. Both CH4 and H2O are assumed to be rigid molecules with interatomic distances and angles fixed at the average values in the ground-state vibration. A physically motivated analytical expression for each PES has been developed as a sum of site-site functions. The PES of the CH4-H2O dimer has only two symmetry-distinct minima. From the SAPT calculations, the global minimum has an energy of -1.03 kcal/mol at a geometry where H2O is the proton donor, HO-H...CH4, with the O-H-C angle of 165 degrees, while the secondary minimum, with an energy of -0.72 kcal/mol, has CH4 in the role of the proton donor (H3C-H...OH2). We estimated the complete basis set limit of the SAPT interaction energy at the global minimum to be -1.06 kcal/mol. The classical cross second virial coefficient B12(T) has been calculated for the temperature range 298-653 K. Our best results agree well with some experiments, allowing an evaluation of the quality of experimental results.