Two-surface Monte Carlo with basin hopping: quantum mechanical trajectory and multiple stationary points of water cluster

The efficiency of the two-surface monte carlo (TSMC) method depends on the closeness of the actual potential and the biasing potential used to propagate the system of interest. In this work, it is shown that by combining the basin hopping method with TSMC, the efficiency of the method can be increased by several folds. TSMC with basin hopping is used to generate quantum mechanical trajectory and large number of stationary points of water clusters.     

Ab initio potential energy and dipole moment surfaces of (H2O)2

A full-dimensional ab initio potential energy surface (PES) and dipole moment surface (DMS) are reported for the water dimer, (H2O)2. The CCSD(T)-PES is a very precise fit to 19,805 ab initio energies obtained with the coupled-cluster (CCSD(T)) method, using an aug-cc-pVTZ basis. The standard counterpoise correction was applied to approximately eliminate basis set superposition errors. The fit is based on an approach that incorporates the permutational symmetry of identical atoms [Huang, X.; Braams, B.; Bowman, J. M. J. Chem.Phys. 2005, 122, 044308]. The DMS is a fit to the dipole moment obtained with M?ller-Plesset (MP2) theory, using an aug-cc-pVTZ basis. The PES has an RMS fitting error of 31 cm(-1) for energies below 20,000 cm(-1), relative to the global minimum. This surface can describe various internal floppy motions, including various monomer inversions, and isomerization pathways. Ten characteristic stationary points have been located on the surface, four of which are transition structures and the rest are higher order saddle points. Their geometrical and vibrational properties are presented and compared with available previous theoretical work. The CCSD(T)-PES and MP2-DMS dissociate correctly (and symmetrically) to two H2O monomers, with D(e) = 1665.7 cm(-1) (19.93 kJ/mol). Accurate quantum calculations of the zero-point energy of the dimer (using diffusion Monte Carlo) and the monomers (using a vibrational configuration interaction approach) are reported, and these together with D(e) give a value of D0 of 1042 cm(-1) (12.44 kJ/mol). A best estimated value is 1130 cm(-1) (13.5 kJ/mol).     

Global potential energy minima of C60(H2O)n clusters

Likely candidates for the global potential energy minima of C60(H2O)n clusters with n < or = 21 are found using basin-hopping global optimization. The potential energy surfaces are constructed using the TIP4P intermolecular potential for the water molecules, a Lennard-Jones water-fullerene potential, and a water-fullerene polarization potential, which depends on the first few nonvanishing C60 multipole polarizabilities. This combination produces a rather hydrophobic water-fullerene interaction. As a consequence, the water component of the lowest C60(H2O)n minima is quite closely related to low-lying minima of the corresponding TIP4P (H2O)n clusters. In most cases, the geometrical substructure of the water molecules in the C60(H2O)n global minimum coincides with that of the corresponding free water cluster. Exceptions occur when the interaction with C60 induces a change in geometry. This qualitative picture does not change significantly if we use the TIP3P model for the water-water interaction. Structures such as C60@(H2O)60, in which the water molecules surround the C60 fullerene, correspond to local minima with much higher potential energies. For such a structure to become the global minimum, the magnitude of the water-fullerene interaction must be increased to an unphysical value.     

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.     

Water clusters: the (H2O)64 case

Minimum energy structures and dynamics of (H₂O)₆₄ cluster are investigated by molecular dynamics techniques and an empirical potential energy surface. Using plots of the cluster, the oxygen-oxygen distance distribution function, and power spectra, we show the existence of minima with deformed cubic arrangement. These results together with previous calculations on smaller clusters support the conclusion that the cubic type geometries are common among water aggregates.     

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.     

Electronic basis of the comparable hydrogen bond properties of small H2CO/(H2O)n and H2NO/(H2O)n systems (n = 1, 2)

The electronic and structural properties of dihydronitroxide/water clusters are investigated and compared to the properties of formaldehyde/water clusters. Exploring the stationary points of their potential energy surfaces (structurally, vibrationally, and energetically) and characterizing their hydrogen bonds (by both atoms in molecules and natural bond orbitals methods) clearly reveal the strong similarity between these two kind of molecular systems. The main difference involves the nature of the hydrogen bond taking place between the X-H bond and the oxygen atom of a water molecule. All the properties of the hydrogen bonds occurring in both kind of clusters can be easily interpreted in terms of competition between intermolecular and intramolecular hyperconjugative interactions.     

New ab initio potential energy surface and the vibration-rotation-tunneling levels of (H2O)2 and (D2O)2

We report a new full-dimensional potential energy surface (PES) for the water dimer, based on fitting energies at roughly 30,000 configurations obtained with the coupled-cluster single and double, and perturbative treatment of triple excitations method using an augmented, correlation consistent, polarized triple zeta basis set. A global dipole moment surface based on Moller-Plesset perturbation theory results at these configurations is also reported. The PES is used in rigorous quantum calculations of intermolecular vibrational frequencies, tunneling splittings, and rotational constants for (H2O)2 and (D2O)2, using the rigid monomer approximation. Agreement with experiment is excellent and is at the highest level reported to date. The validity of this approximation is examined by comparing tunneling barriers within that model with those from fully relaxed calculations.     

Intermolecular interactions: basis set and intramolecular correlation effects on semiempirical methods. Application to (C2H2)2, (C2H2)3 and (C2H4)2

A detailed study of the intrinsic consistency of the semiempirical method of P. Claverie namely, the effects of the basis set and intramolecular correlation on the multipole distributions of molecular subunits and the influence of the electronic population of each atom in the molecular subunit on its van der Waals radius, is performed on some van der Waals dimers. The validity, limits of this model and the appropriate way to use it is established. In particular, the dependence of the geometry and the interaction energy on the basis set chosen and the intramolecular correlation shows that the multipole distribution involved in the calculation of the electrostatic and polarization terms must be derived from a correlated wave function within an extended basis set. Associated to non local methods for finding stationary points, the method of P. Claverie reproduce reliably the intermolecular geometrical parameters observed for the equilibrium structures and the transition states of the dimer and trimer of acetylene. In addition, a study of the equilibrium structures of the ethylene dimer is presented, the aim of being to clarify the considerable uncertainty in their number and their geometry.     

Ab initio molecular dynamics studies of ionic dissolution and precipitation of sodium chloride and silver chloride in water clusters, NaCl(H2O)n and AgCl(H2O)n, n = 6, 10, and 14

An ab initio molecular dynamics method was used to compare the ionic dissolution of soluble sodium chloride (NaCl) in water clusters with the highly insoluble silver chloride (AgCl). The investigations focused on the solvation structures, dynamics, and energetics of the contact ion pair (CIP) and of the solvent-separated ion pair (SSIP) in NaCl(H(2)O)(n) and AgCl(H(2)O)(n) with cluster sizes of n = 6, 10 and 14. We found that the minimum cluster size required to stabilize the SSIP configuration in NaCl(H(2)O)(n) is temperature-dependent. For n = 6, both configurations are present as two distinct local minima on the free-energy profile at 100 K, whereas SSIP is unstable at 300 K. Both configurations, separated by a low barrier (<10 kJ mol(-1)), are identifiable on the free energy profiles of NaCl(H(2)O)(n) for n = 10 and 14 at 300 K, with the Na(+)/Cl(-) pairs being internally solvated in the water cluster and the SSIP configuration being slightly higher in energy (<5 kJ mol(-1)). In agreement with the low bulk solubility of AgCl, no SSIP minimum is observed on the free-energy profiles of finite AgCl(H(2)O)(n) clusters. The AgCl interaction is more covalent in nature, and is less affected by the water solvent. Unlike NaCl, AgCl is mainly solvated on the surface in finite water clusters, and ionic dissolution requires a significant reorganization of the solvent structure.     

An ab initio correlated study of the potential energy surface for the HOBr.H2O complex

The potential energy surface (PES) for the HOBr.H(2)O complex has been investigated using second- and fourth-order M?ller-Plesset perturbation theory (MP2, MP4) and coupled cluster theory with single and doubles excitations (CCSD), and a perturbative approximation of triple excitations (CCSD-T), correlated ab initio levels of theory employing basis sets of triple zeta quality with polarization and diffuse functions up to the 6-311++G(3dp,3df ) standard Pople's basis set. Six stationary points being three minima, two first-order transition state (TS) structures and one second-order TS were located on the PES. The global minimum syn and the anti equilibrium structure are virtually degenerated [DeltaE(ele-nuc) approximately 0.3 kcal mol(-1), CCSD-T/6-311++G(3df,3pd) value], with the third minima being approximately 4 kcal mol(-1) away. IRC analysis was performed to confirm the correct connectivity of the two first-order TS structures. The CCSD-T/6-311++G(3df,3pd)//MP2/6-311G(d,p) barrier for the syn<-->anti interconversion is 0.3 kcal mol(-1), indicating that a mixture of the syn and anti forms of the HOBr.H(2)O complex is likely to exist.     

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.     

Photochemistry of water: the (H2O)5 cluster

The structures of the cyclic water pentamer, the H3O+(H2O)3OH- zwitterion, and the H3O(H2O)3OH biradical form of the (H2O)5 cluster have been determined with the second-order M?ller-Plesset method and with density-functional theory (DFT). The vertical singlet excitation energies of these structures have been calculated with the second-order approximated coupled-cluster method and with time-dependent DFT, respectively. The molecular and electronic structures of the H3O(H2O)3OH biradical have been characterized for the first time. The lowest electronic states of the biradical are slightly lower in energy than the vertically excited states of the covalent and zwitterionic (H2O)5 clusters and therefore are photochemically accessible from the latter. The electronic absorption spectrum of the biradical exhibits the characteristic features of the absorption spectrum of the hydrated electron. It is argued that the basic mechanisms of the photochemistry of water, in particular the generation of the hydrated electron by UV photons, can be unraveled by relatively straightforward electronic structure and dynamics calculations for finite-size water clusters.     

Simulated annealing to locate various stationary points in semiempirical methods

In this work, an algorithm was developed to study the potential energy surfaces in the coordinate spaces of molecules by a nonlocal way, in contrast to classic energy minimizers as the BFGS or the DFP method. This algorithm, based on the specificities of semiempirical methods, mixes simulated annealing and local searches to reduce computation costs. By this technique, the global energy minimum can be localized. Moreover, local minima that are close in energy to the global minimum are also obtained. If the search is not only for minima but for all stationary points (minima, saddle points…), then the energy is replaced by the gradient norm, which reaches its minimum values at stationary points. The annealing process is stopped before having accurately reached the global minimum and generates a list of geometries whose energies (respectively, whose gradients) are optimized by local minimizers. This list of geometries is shortened from the nearly equivalent geometries by a dynamic single-clustering analysis. The energy/gradient local minimizers act on the clustered list to produce a set of minima/stationary points. A targeted search of these points and reduction of the costs are reached by the way of several penalty functions. They eliminate—without energy calculation—most of the points generated by random walks on the potential energy surface. These penalty functions (on the total moment of inertia or on interatomic distances) are specific to the class of problem studied. They account for the nonrupture of either specific chemical bonds or rings in cyclic molecules, they assure that molecular systems are kept bonded, and they avoid the collapsing of atoms. © 1992 John Wiley & Sons, Inc.     

Potential energy surface of O2-(H2O) and factors controlling water-to-O2- binding motifs

The potential energy surface (PES) of O(2)(-)(H(2)O) is investigated by varying the interoxygen distance of O(2)(-) via ab initio calculations with a large basis set. Although two stationary points, C(s) and C(2v) conformers, are found along the interoxygen-distance coordinate, only the C(s) conformer is identified as a minimum-energy species. We find a critical distance, r(c), separating these two conformers in the PES. The C(s) conformer prevails at interoxygen distances of O(2)(-) that are less than r(c), while the C(2v) conformer dominates at the distances larger than r(c). The structural features of these two conformers are also discussed. Although the water deformation energy is shown to be the stabilization source responsible for the prevalence of the C(s) cluster conformer at the interoxygen distances of O(2)(-) less than r(c), the ionic hydrogen bonding is the major driving force for transformation of the water binding motif from C(s) to C(2v) when the interoxygen distance of O(2)(-) increases.     

Quantum chemistry study of H+(H2O)8: a global search for its isomers by the scaled hypersphere search method, and its thermal behavior

The structures of the protonated water cluster H+(H2O)8 have been globally explored by the scaled hypersphere search method. On the Hartree-Fock potential energy surface 174 isomers were found, among which 168 were computed to be minima at the B3LYP/6-31+G** level, and their energies were further refined at the level of MP2/6-311++G(3df,2p). The global minimum on the potential energy surface computed at the B3LYP/6-31+G** level shows a cagelike structure with the "Eigen" motif, while the lowest-free-energy isomer has a five-membered-ring structure at 170 K and a chain form at 273 K. The present results are well in line with previous experimental findings. In addition, the ADMP (atom-centered density matrix propagation) simulation indicates that the extra proton in the lowest-free-energy isomer (170 K), which has a five-membered ring and the "Zundel" feature, is often in an asymmetrical hydrogen bond.     

Toward the infrared spectroscopic observation of SiH5: the silanium ion

Ab initio quantum mechanical methods, including the self-consistent field, single and double excitation configuration interaction, and single and double excitation coupled cluster, have been applied to six stationary points on the SiH⁺₅ potential energy hypersurface. Equilibrium geometries were determined using analytic energy first derivative techniques. Relative energies of stationary points have been obtained. Harmonic vibrational frequencies of the global minimum were obtained at all levels of theory. Basis sets used include double-zeta plus polarization and triple-zeta plus double polarization. SiH⁺₅ should be regarded as involving weakly bound H₂ and SiH⁺₃ subunits, with a dissociation energy of only about 10 kcal/mol. Pseudorotation was found to be unfavorable in the SiH⁺₅ ion.     

Structural, electronic, and magnetic properties of fe(3)c(2) cluster

On the basis of density-functional theory and all-electron numerical basis set, 20 stable isomers of Fe(3)C(2) cluster are found through optimization calculations and frequency analysis from 108 initial structures. A nonplanar C(s) structure with nonet spin multiplicity and 482.978 kcal/mol of binding energy is found as the candidate of global minimum geometry of Fe(3)C(2) cluster. The binding energies, the energy gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, and the magnetic moments of all the isomers are reported. The relationship between the molecular properties and geometrical structures is also investigated.     

Multiscale approach to explore the potential energy surface of water clusters (H2O)nn <or= 8

We propose a multiscale method to explore the energy landscape of water clusters. An asynchronous genetic algorithm is employed to explore the potential energy surface (PES) of OSS2 and TTM2.1-F models. Local minimum structures are collected on the fly, and the ultrafast shape recognition algorithm was used to remove duplicate structures. These structures are then refined at the B3LYP/6-31+G* level. The number of distinct local minima we found (21, 76, 369, 1443, and 3563 isomers for n = 4-8, respectively) reflects the complexity of the PES of water clusters.     

Effect of solvation on the vertical ionization energy of thymine: from microhydration to bulk

The effect of hydration on the vertical ionization energy (VIE) of thymine was characterized using equation-of-motion ionization potential coupled-cluster (EOM-IP-CCSD) and effective fragment potential (EFP) methods. We considered several microsolvated clusters as well as thymine solvated in bulk water. The VIE in bulk water was computed by averaging over solvent-solute configurations obtained from equilibrium molecular dynamics trajectories at 300 K. The effect of microsolvation was analyzed and contrasted against the combined effect of the first solvation shell in bulk water. Microsolvation reduces the ionization energy (IE) by about 0.1 eV per water molecule, while the first solvation shell increases the IE by 0.1 eV. The subsequent solvation lowers the IE, and the bulk value of the solvent-induced shift of thymine's VIE is approximately -0.9 eV. The combined effect of the first solvation shell was explained in terms of specific solute-solvent interactions, which were investigated using model structures. The convergence of IE to the bulk value requires the hydration sphere of approximately 13.5 ? radius. The performance of the EOM-IP-CCSD/EFP scheme was benchmarked against full EOM-IP-CCSD using microhydrated structures. The errors were found to be less than 0.01-0.02 eV. The relative importance of the polarization and higher multipole moments in EFP model was also investigated.