Pb(m)-Phenyl (m = 1-5) complexes: an anion photoelectron spectroscopy and density functional study

The phenyl-lead metal complexes ([Pb(m)C6H5]-) produced from the reactions between benzene and lead clusters formed by laser ablation on a lead solid sample are studied by photoelectron spectroscopy (PES) and density functional theory (DFT). The adiabatic electron affinities (EAs) of [Pb(m)C6H5]- are obtained from PES at 308 nm, and the differences between the PES of [Pb(m)C6H5]- and the PES of Pbm- are discussed in detail. The results reveal that the phenyl group binds perpendicularly on lead clusters through the Pb-C sigma bond and the complexes have a closed shell structure. Calculations with DFT are carried out on the structural and electronic properties of [Pb(m)C6H5]-, and the adiabatic detachment energy for the optimized structures of anion are in agreement with the experimental PES results. The density of states (DOS) calculated is compared with experimental PES and is discussed. The most possible structures for each species are concluded, and the bonding between Pb and phenyl is analyzed, which also proves that the phenyl group binds perpendicularly on lead clusters through the Pb-C sigma bond.     

Can we understand the different coordinations and structures of closed‐shell metal cation‐water clusters?

We present a model potential for studying M(q+)(H(2)O)(n=1,9) clusters where M stands for either Na(+), Cs(+), Ca(2+), Ba(2+), or La(3+). The potential energy surfaces (PES) are explored by the Monte Carlo growth method. The results for the most significant equilibrium structures of the PES as well as for energetics are favorably compared to the best ab initio calculations found in the literature and to experimental results. Most of these complexes have a different coordination number in cluster compared to experimental results in solution or solid phase. An interpretation of the coordination number in clusters is given. In order to well describe the transition between the first hydration sphere and the second one we show that an autocoherent treatment of the electric field is necessary to correctly deal with polarization effects. We also explore the influence of the cation properties (charge, size, and polarizability) on both structures and coordination number in clusters, as well as the meaning of the second hydration sphere. Such an approach shows that the leading term in the interaction energy for a molecule in the second hydration sphere is an electrostatic attraction to the cation and not a hydrogen bond with the water molecules in the first hydration sphere.     

Flexible, ab initio potential, and dipole moment surfaces for water. I. Tests and applications for clusters up to the 22-mer

We report full-dimensional, ab initio potential energy and dipole moment surfaces, denoted PES and DMS, respectively, for arbitrary numbers of water monomers. The PES is a sum of 1-, 2-, and 3-body potentials which can also be augmented by semiempirical long-range higher-body interactions. The 1-body potential is a spectroscopically accurate monomer potential, and the 2- and 3-body potentials are permutationally invariant fits to tens of thousands of CCSD(T)/aug-cc-pVTZ and MP2/aug-cc-pVTZ electronic energies, respectively. The DMS is a sum of 1- and 2-body DMS, which are covariant fits to tens of thousands MP2/aug-cc-pVTZ dipole moment data. We present the details of these new 2- and 3-body potentials and then extensive applications and tests of this PES are made to the structures, classical binding energies, and harmonic frequencies of water clusters up to the 22-mer. In addition, we report the dipole moment for these clusters at various minima and compare the results against available and new ab initio calculations.     

A Fukui function‐guided genetic algorithm. Assessment on structural prediction of Sin (n = 12–20) clusters

Theoretical studies are essential for the structural characterization of clusters, when it comes to rationalize their unique size‐dependent properties and composition. However, the rapid growth of local minima on the potential energy surface (PES), with respect to cluster size, makes the candidate identification a challenging undertaking. In this article, we introduce a hybrid strategy to explore the PES of clusters. This proposal involves the use of a biased initial population of a genetic algorithm procedure. Each individual in this population is built by assembling small fragments, according to the best matching of the Fukui function. The performance of a genetic algorithm procedure. The performance of the method is assessed on the PES exploration of medium‐sized Si_n clusters (n = 12–20). The most relevant results are: (a) the method converges at almost half of the time used by the canonical version of the GA and, (b) in all the studied cases, with the exception of Si₁₃ and Si₁₆, the method allowed to identify the global minimum (GM) and other important low‐lying structures. Additionally, the apparent deficiency of the proposal to identify the GM was corrected when a Si atom, or other low‐lying isomers, were considered to build the clusters. © 2017 Wiley Periodicals, Inc.     

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.     

Ab initio quantum dynamics with very weak van der Waals interactions: Structure and stability of small Li2(1Sigmag+)-(He)n clusters

The potential energy surface (PES) for the interaction between Li2(1Sigmag+) and 4He has been computed using an accurate, post-Hartree-Fock quantum calculation for its ground electronic state. The orientational anisotropy of the forces and the interplay between repulsive and attractive effects within the PES are analyzed to extract information on the possible existence of bound states in the triatomic system. The structures of a few of the Li2(He)n small clusters are examined by comparing a classical approach with a full quantum one to generate bound configurations and to extract information on the possible spatial arrangements of the smaller clusters via à vis the location of the Li2 dopant. Some significant consequences on the Li2 behavior in larger clusters and droplets are drawn from the above findings.     

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.     

Dynamics of the concerted triple proton transfer in cyclic water trimer using the multiconfiguration molecular mechanics algorithm

Cyclic water clusters are important molecular species to understand the nature of hydrogen bonded networks. Theoretical studies for the dynamics of triple proton transfer in the cyclic water trimer were performed. The potential energy surface (PES) of triple proton transfer is generated by the multiconfiguration molecular mechanics (MCMM) algorithm. We have used the MP2/6-31G(d,p) level for high-level ab initio data (energies, gradients, and Hessians), which are used in the Shepard interpolation. Eight high-level reference points were added step by step, including two points for the critical configurations of the large curvature tunneling paths. The more high-level points are used, the better the potential energy surfaces become. The rate constant and kinetic isotope effect (KIE) for the triple proton transfer at 300 K, which have been calculated by the canonical variational transition-state theory with microcanonical optimized multidimensional semiclassical tunneling approximation, are 1.6 x 10(-3) s(-1) and 230, respectively. Tunneling is very important not only for the triple proton transfer but also for the triple deuterium transfer. The MCMM results show good agreement with those from the direct ab initio dynamics calculations.     

Probing the electronic structure and band gap evolution of titanium oxide clusters (TiO(2))(n)(-) (n = 1-10) using photoelectron spectroscopy

TiO2 is a wide-band-gap semiconductor, and it is an important material for photocatalysis. Here we report an experimental investigation of the electronic structure of (TiO2)n clusters and how their band gap evolves as a function of size using anion photoelectron spectroscopy (PES). PES spectra of (TiO2)n- clusters for n = 1-10 have been obtained at 193 nm (6.424 eV) and 157 nm (7.866 eV). The high photon energy at 157 nm allows the band gap of the TiO2 clusters to be clearly revealed up to n = 10. The band gap is observed to be strongly size-dependent for n < 7, but it rapidly approaches the bulk limit at n = 7 and remains constant up to n = 10. All PES features are observed to be very broad, suggesting large geometry changes between the anions and the neutral clusters due to the localized nature of the extra electron in the anions. The measured electron affinities and the energy gaps are compared with available theoretical calculations. The extra electron in the (TiO2)n- clusters for n > 1 appears to be localized in a tricoordinated Ti atom, creating a single Ti3+ site and making these clusters ideal molecular models for mechanistic understanding of TiO2 surface defects and photocatalytic properties.     

Theoretical study of stable structures and photoelectron spectra of mass-selected Al12Cs-, Al11Cs2-, and Al10Cs3- clusters

The geometric and electronic structures of the ground and low-lying states for the Al(12)Cs(-), Al(11)Cs(2) (-), and Al(10)Cs(3) (-) clusters were examined using the density functional theory. Semi-icosahedral structures of the Al(12)Cs(-) and Al(11)Cs(2) (-) clusters were found as the ground state. The most stable structure of the Al(10)Cs(3) (-) cluster is a distorted icosahedron structure. The vertical detachment energy of these clusters and the anion photoelectron spectra (PES) were compared. The peaks of the anion PES were assigned on the basis of the shell model. The single peak of 3.1-3.2 or 2.5-2.7 eV for the Al(12)Cs(-) or Al(11)Cs(2) (-) cluster, respectively, is observed due to the electron detachment from the 2p or 1f or 1f+2p shells. Two large peaks of 2.1 eV and 3.1-3.3 eV correspond to the electron detachments from the 1f+2p and 2p, and 1d+1f shells, respectively. It was found that a second peak appears with the hybridization of the 1d and 1f shells due to the distortion from the icosahedral structure in the Al(10)Cs(3) (-) cluster.     

Competition between linear and cyclic structures in monochromium carbide clusters CrCn- and CrCn (n = 2-8): a photoelectron spectroscopy and density functional study

Photoelectron spectroscopy (PES) is combined with density functional theory (DFT) to study the monochromium carbide clusters CrCn- and CrCn (n = 2-8). Well-resolved PES spectra were obtained, yielding structural, electronic, and vibrational information about both the anionic and neutral clusters. Experimental evidence was observed for the coexistence of two isomers for CrC2-, CrC3-, CrC4-, and CrC6-. Sharp and well-resolved PES spectra were observed for CrCn- (n = 4,6,8), whereas broad spectra were observed for CrC5- and CrC7-. Extensive DFT calculations using the generalized gradient approximation were carried out for the ground and low-lying excited states of all the CrCn- and CrCn species, as well as coupled-cluster calculations for CrC2- and CrC2. Theoretical electron affinities and vertical detachment energies were calculated and compared with the experimental data to help the assignment of the ground states and obtain structural information. We found that CrC2- and CrC3- each possess a close-lying cyclic and linear structure, which were both populated experimentally. For the larger CrCn- clusters with n = 4, 6, 8, linear structures are the overwhelming favorite, giving rise to the sharp PES spectral features. CrC7- was found to have a cyclic structure. The broad PES spectra of CrC5- suggested a cyclic structure, whereas the DFT results predicted a linear one.     

Structural evolution of small gold clusters doped by one and two boron atoms

The potential energy surfaces (PES) of a series of gold–boron clusters with formula Au_nB (n = 1–8) and Au_mB₂ (m = 1–7) have been explored using a modified stochastic search algorithm. Despite the complexity of the PES of these clusters, there are well‐defined growth patterns. The bonding of these clusters is analyzed using the adaptive natural density partitioning and the natural bonding orbital analyses. Reactivity is studied in terms of the molecular electrostatic potential. © 2014 Wiley Periodicals, Inc.     

Phenyl-coinage metal (Ag, Au) complexes: an anion photoelectron spectroscopy and density functional study

The important intermediate phenyl-coinage metal complexes (Ag(m)C6H5(-), Au(m)C6H5(-)), which are produced from the reactions between coinage metal clusters formed by laser ablation and the benzene molecules seeded in argon carrier gas, are studied by PES (photoelectron spectroscopy) and DFT (density functional theory). The EAs (adiabatic electron affinities) of these complexes are obtained from PES at both 308 and 193 nm photon energies and show odd-even alternation. Calculations with DFT are carried out on the structural and electronic properties of Ag(m)C6H5(-) and Au(m)C6H5(-); the adiabatic detachment energy and the calculated DOS (density of states) for the ground state of a given anion are in good agreement with the experimental PES results. The observed spectra are also compared with those of the pure coinage metal clusters, which reveal that there are some similarities between them and the phenyl acts like an additional metal atom in the clusters. Furthermore, the bonding between phenyl and metal is analyzed, suggesting that phenyl group binds perpendicularly on metal clusters through C-M sigma bond.     

Electronic structure and chemical bonding in MO(n)- and MO(n) clusters (M = Mo, W; n = 3-5): a photoelectron spectroscopy and ab initio study

Photoelectron spectroscopy (PES) and ab initio calculations are combined to investigate the electronic structure of MO(n)- clusters (M = W, Mo; n = 3-5). Similar PES spectra were observed between the W and Mo species. A large energy gap between the first and second PES bands was observed for MO3- and correlated with a stable closed-shell MO3 neutral cluster. The electron binding energies of MO4- increase significantly relative to those of MO3-, and there is also an abrupt spectral pattern change between MO3- and MO4-. Both MO4- and MO5- give PES features with extremely high electron binding energies (>5.0 eV) due to oxygen-2p-based orbitals. The experimental results are compared with extensive density functional and ab initio [CCSD(T)] calculations, which were performed to elucidate the electronic and structural evolution for the tungsten oxide clusters. WO3 is found to be a closed-shell, nonplanar molecule with C3v symmetry. WO4 is shown to have a triplet ground state (3A2) with D2d symmetry, whereas WO5 is found to be an unusual charge-transfer complex, (O2-)WO3+. WO4 and WO5 are shown to possess W-O* and O2-* radical characters, respectively.     

Structures of water octamers (H2O)8: exploration on ab initio potential energy surfaces by the scaled hypersphere search method

The potential energy surface (PES) of water octamers has been explored by the scaled hypersphere search method. Among 164 minima on the PES (based on MP2/6-311++G(3df,2p)//B3LYP/6-311+G(d,p) calculations), the cubic structure with D2d symmetry has been confirmed to be the global minimum. In a thermodynamic simulation using these 164 structures, the cubic structure with S4 symmetry has the highest population at low temperature, though double rings can become dominant as temperature going up, in good accord with a recent Monte Carlo simulation using an empirical potential. A transition temperature from cubic to noncubic has significantly been underestimated when potential energy data of B3LYP/6-311+G(d,p) calculations are employed in the simulation. This serious discrepancy between the MP2 and the B3LYP results suggests an importance of dispersion interactions for discussions on thermodynamics of water octamers.     

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.     

Theoretical modeling of dissociative addition of an H<Subscript>2</Subscript> molecule to doped aluminum clusters FeAl<Subscript>12</Subscript> and CoAl<Subscript>12</Subscript>

The potential energy surfaces (PES) of the reactions FeAl₁₂ + Н₂ → FeН₂Al₁₂ (1) and CoAl₁₂ + Н₂ → CoН₂Al₁₂ (2) of dissociative addition of an H₂ molecule to Fe- and Co-doped aluminum clusters have been calculated by the density functional theory method. Local minima on the PES in the vicinity of low-lying isomers, intermediates, and transition states have been found, and their structural and spectroscopic characteristics and energies have been calculated. The energies of the successive stages of the catalytic cycle have been evaluated, and the channels corresponding to the minimum energy path of the reactions have been studied. Differences between the structural characteristics and energies of key structures in reactions (1) and (2) have been considered. The results are compared with previous calculations of the PES of hydrogenation reactions performed for related clusters doped with nickel and titanium atoms.     

Energy landscape study of water splitting and H2 evolution at a ruthenium(II) pincer complex

A bird's-eye view of the water splitting and H₂ generation at a ruthenium(II) pincer complex is presented. Using a combination of density functional theory and efficient algorithms for exploration of potential energy hypersurface (PES), a total of 197 local minima and 186 transition states are identified, and a new mechanism for water splitting and H₂ evolution via hydroxycarbonyl intermediates is presented. Furthermore, a global feature of the reaction PES, so-called potential energy landscape, is discussed on analyzing the obtained structures. As a result, the landscape is characterized by hierarchical structure, namely, PES consists of many “superbasins (SBs)” that are separated by relatively high energy barriers corresponding to bond breaking around Ru(II) center. Each SB involves a set of conformational isomers that can be interchanged with each other through relatively small barriers. To the best of our best knowledge, this is the first report on the quantum chemical computation of the hierarchical structure of PES for a realistic, catalytic reaction system.     

Ab initio calculations on low-energy conformers of alpha-cyclodextrin

In this article we carried out a comprehensive investigation of true minima on the potential energy surface (PES) for the alpha-cyclodextrin molecule using ab initio Hartree-Fock (HF) and density functional theory (DFT) quantum chemical methods, employing basis sets ranging from 6-31 G(d,p) to 6-311++G(2d,2p) triple-zeta quality. Thermodynamic quantities and the solvent effect were evaluated at the DFT level of theory. We believe that the most relevant conformers present on the multidimensional PES were sampled in our work, using an adequate treatment of electron correlation effects to describe the intramolecular hydrogen bonds that are present in cyclodextrin species. We present new structures not reported so far and discuss, in detail, the relevance of the DFT gas-phase equilibrium structures for the experimental and theoretical studies involving cyclodextrins and corresponding inclusion complexes, in the condensed phase. In addition, among the various true minimum energy structures located on the DFT PES, the preferred structures in the gas phase and aqueous media, needed to be used as representative minima on the PES in further studies involving the interaction of alpha-cyclodextrin with other species, were unambiguously identified.     

Probing the electronic and structural properties of doped aluminum clusters: MAl12- (M=Li, Cu, and Au)

Photoelectron spectroscopy (PES) is combined with theoretical calculations to investigate the electronic and atomic structures of three doped aluminum clusters, MAl12- (M=Li, Cu, and Au). Well-resolved PES spectra have been obtained at two detachment photon energies, 266 nm (4.661 eV) and 193 nm (6.424 eV). Basin-hopping global optimization method in combination with density-functional theory calculations has been used for the structural searches. Good agreement between the measured PES spectra and theoretical simulations helps to identify the global minimum structures. It is found that LiAl12- (C(5nu)) can be viewed as replacing a surface Al atom by Li on an icosahedral Al13-, whereas Cu prefers the central site to form the encapsulated D3d-Cu@Al12-. For AuAl12- (C1), Au also prefers the central site, but severely distorts the Al12 cage due to its large size.