Force field for copper clusters and nanoparticles

An atomic force field for simulating copper clusters and nanoparticles is developed. More than 2000 cluster configurations of varying size and shape are used to constrain the parametrization of the copper force field. Binding energies for these training clusters were computed using density functional theory. Extensive testing shows that the copper force field is fast and reliable for near‐equilibrium structures of clusters, ranging from only a few atoms to large nanoparticles that approach bulk structure. Nonequilibrium dissociation and compression structures that are included in the training set are also well described by the force field. Implications for molecular dynamics simulations and extensions to other metallic and covalent systems are discussed. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

A sobering assessment of small‐molecule force field methods for low energy conformer predictions

We have carried out a large scale computational investigation to assess the utility of common small‐molecule force fields for computational screening of low energy conformers of typical organic molecules. Using statistical analyses on the energies and relative rankings of up to 250 diverse conformers of 700 different molecular structures, we find that energies from widely used classical force fields (MMFF94, UFF, and GAFF) show unconditionally poor energy and rank correlation with semiempirical (PM7) and Kohn–Sham density functional theory (DFT) energies calculated at PM7 and DFT optimized geometries. In contrast, semiempirical PM7 calculations show significantly better correlation with DFT calculations and generally better geometries. With these results, we make recommendations to more reliably carry out conformer screening.     

氧化锆小团簇的结构和稳定性

利用密度泛函理论在广义梯度近似(GGA)和Perdew-Wang交换关联泛函条件下研究了小团簇Zr_mOn (1≤m≤5, 1≤n≤2m)的几何结构和稳定性. 结果表明: 所有团簇的最低能量结构可通过锆团簇的连续氧化获得, 一般情况下O原子占据在Zr团簇的桥位. (ZrO₂)₃和(ZrO₂)₅团簇的基态结构符合配位数规则和成键规律. 此外, 讨论了氧化锆团簇的分解通道和分解能, 值得指出的是在Zr原子数相同时Zr_mO_2m-1团簇(除了Zr₄O₇)存在最大的分解能.     

Energies of ions in water and nanopores within density functional theory

Accurate calculations of electrostatic potentials and treatment of substrate polarizability are critical for predicting the permeation of ions inside water-filled nanopores. The ab initio molecular dynamics method, based on density functional theory (DFT), accounts for the polarizability of materials, water, and solutes, and it should be the method of choice for predicting accurate electrostatic energies of ions. In practice, DFT coupled with the use of periodic boundary conditions in a charged system leads to large energy shifts. Results obtained using different DFT packages may vary because of the way pseudopotentials and long-range electrostatics are implemented. Using maximally localized Wannier functions, we apply robust corrections that yield relatively unambiguous ion energies in select molecular and aqueous systems and inside carbon nanotubes. Large binding energies are predicted for ions in metallic carbon nanotube arrays, while Na+ and Cl- energies are found to exhibit asymmetry in water that is smaller than but comparable with those computed using nonpolarizable water force fields.     

Electronic and structural evolution and chemical bonding in ditungsten oxide clusters: W2O(n)- and W2O(n) (n = 1-6)

We report a systematic and comprehensive investigation of the electronic structures and chemical bonding in a series of ditungsten oxide clusters, W2O(n)- and W2O(n) (n = 1-6), using anion photoelectron spectroscopy and density functional theory (DFT) calculations. Well-resolved photoelectron spectra were obtained at several photon energies (2.331, 3.496, 4.661, 6.424, and 7.866 eV), and W 5d-based spectral features were clearly observed and distinguished from O 2p-based features. More complicated spectral features were observed for the oxygen-deficient clusters because of the W 5d electrons. With increasing oxygen content in W2O(n)-, the photoelectron spectra were observed to shift gradually to higher binding energies, accompanied by a decreasing number of W 5d-derived features. A behavior of sequential oxidation as a result of charge transfers from W to O was clearly observed. A large energy gap (2.8 eV) was observed in the spectrum of W2O6-, indicating the high electronic stability of the stoichiometric W2O6 molecule. Extensive DFT calculations were carried out to search for the most stable structures of both the anion and neutral clusters. Time-dependent DFT method was used to compute the vertical detachment energies and compare to the experimental data. Molecular orbitals were used to analyze the chemical bonding in the ditungsten oxide clusters and to elucidate their electronic and structural evolution.     

Theoretical study of selenium and tellurium impurities in (ZnO)6 clusters using DFT and TDDFT

Zinc oxide (ZnO) nanostructures have attracted much interest due to their potential applications in various fields including optoelectronics, glass industries, and solar cells. These compounds hold the promise of creating new materials that can advance energy technologies. In this work, a series of (ZnO)₆ clusters with selenium and tellurium applied as substitutional impurities has been studied. The investigated structures have been produced through the doping of (ZnO)₆ clusters by replacing an oxygen atom with a selenium or a tellurium atom at each time. The ground state geometric parameters of (ZnO)₆ structures, containing selenium or tellurium atoms as substitutional impurities, were calculated using density functional theory (DFT) with B3LYP and LanL2DZ basis set. Excited state energies and absorption wavelengths were computed using time‐dependent‐DFT (TDDFT). For the calculation of emission wavelengths, Hartree–Fock configuration interaction singles (HF/CIS) has been used in order to perform the excited state geometry optimization. This work led to some important results that can be helpful for developing novel THz sensitive materials and imaging detectors that may be an alternative to x‐rays detectors for radiology as well as for the development of solar cells and electroluminescent diodes. Zinc oxide (ZnO) nanostructures have attracted growing interest due to their potential applications in many technological fields, including optoelectronics, the glass industry, and energy. The presence of impurities, in particular selenium and tellurium, in ZnO‐based clusters can affect their structural and spectroscopic properties. Some of these doped nanostructures have favorable Terahertz emission characteristics that make them good candidates for applications in biology and medicine.     

Structural and electronic properties of reduced transition metal oxide clusters, M4O10 and M4O10- (M = Cr, W), from photoelectron spectroscopy and quantum chemical calculations

Anion photoelectron spectroscopy and quantum chemical calculations at the density functional theory (DFT), coupled cluster theory (CCSD(T)), and complete active space self-consistent field (CASSCF) theory levels are employed to study the reduced transition metal oxide clusters M(4)O(10)(-) (M = Cr, W) and their neutrals. Photoelectron spectra are obtained at 193 and 157 nm photon energies, revealing very different electronic structures for the Cr versus W oxide clusters. The electron affinity and HOMO-LUMO gap are measured to be 3.68 ± 0.05 and 0.7 eV, respectively, for the Cr(4)O(10) neutral cluster, as compared to 4.41 ± 0.04 and 1.3 eV for W(4)O(10). A comprehensive search is performed to determine the ground-state structures for M(4)O(10) and M(4)O(10)(-), in terms of geometry and electronic states by carefully examining the calculated relative energies at the DFT, CCSD(T), and CASSCF levels. The ground states of Cr(4)O(10) and Cr(4)O(10)(-) have tetrahedral structures similar to that of P(4)O(10) with the anion having a lower symmetry due to a Jahn-Teller distortion. The ground states of W(4)O(10) and W(4)O(10)(-) have butterfly shape structures, featuring two fused five-member rings with a metal-metal multiple bond between the central metal atoms. The much stronger WW bonding than the CrCr bonding is found to be the primary cause for the different ground state structures of the reduced Cr(4)O(10)(0/-) versus W(4)O(10)(0/-) oxide clusters. The photoelectron spectra are assigned by comparing the experimental and theoretical adiabatic and vertical electron detachment energies, further confirming the determination of the ground electronic states of M(4)O(10) and M(4)O(10)(-). The time-dependent DFT method is used to calculate the excitation energies of M(4)O(10). The TD-DFT results in combination with the self-consistently calculated vertical detachment energies for some of the excited states at the DFT and CCSD(T) levels are used to assign the higher energy bands. Accurate clustering energies and heats of formation of M(4)O(10) are calculated and used to calculate accurate reaction energies for the reduction of M(4)O(12) to M(4)O(10) by CH(3)OH, as well as for the oxidation of M(4)O(10) to M(4)O(12) by O(2). The performance of the DFT method with the B3LYP and BP86 functionals in the calculations of the relative energies, electron detachment energies, and excitation energies are evaluated, and the BP86 functional is found to give superior results for most of these energetic properties.     

Molecular structures and energetics of the (TiO2)n (n = 1-4) clusters and their anions

The (TiO2)n clusters and their anions for n = 1-4 have been studied with coupled cluster theory [CCSD(T)] and density functional theory (DFT). For n > 1, numerous conformations are located for both the neutral and anionic clusters, and their relative energies are calculated at both the DFT and CCSD(T) levels. The CCSD(T) energies are extrapolated to the complete basis set limit for the monomer and dimer and calculated up to the triple-zeta level for the trimer and tetramer. The adiabatic and vertical electron detachment energies of the anionic clusters to the ground and first excited states of the neutral clusters are calculated at both levels and compared with the experimental results. The comparison allows for the definitive assignment of the ground-state structures of the anionic clusters. Anions of the dimer and tetramer are found to have very closely lying conformations within 2 kcal/mol at the CCSD(T) level, whereas that of the trimer does not. In addition, accurate clustering energies and heats of formation are calculated for the neutral clusters and compared with the available experimental data. Estimates of the titanium-oxygen bond energies show that they are stronger than the group VIB transition metal-oxygen bonds except for tungsten. The atomization energies of these clusters display much stronger basis set dependence than the clustering energies. This allows the calculation of more accurate heats of formation for larger clusters on the basis of calculated clustering energies.     

第一原理对AlPm和AlPm-(m = 2～9)团簇结构与稳定性的研究

用密度泛函理论(DFT)的B3LYP方法,在6-311G*水平上对AlPm和AlPm(m = 2～9)团簇的几何构型,电子结构和振动频率等性质进行了理论研究,给出了一种以Pm团簇作为设计AlPm类结构的母体,考虑在不同位置上结合Al原子的结构,可以较快找到AlPm类团簇基态结构的方法. 通过对基态结构的第一离解能和能量二次差分讨论,得到m为奇数的AlPm团簇比m为偶数的稳定,对基态结构的HOMO-LUMO能隙和绝热电子亲合势的讨论表明,AlP3,AlP5和AlP7团簇结构较稳定.     

BAND NN: A Deep Learning Framework for Energy Prediction and Geometry Optimization of Organic Small Molecules

Recent advances in artificial intelligence along with the development of large data sets of energies calculated using quantum mechanical (QM)/density functional theory (DFT) methods have enabled prediction of accurate molecular energies at reasonably low computational cost. However, machine learning models that have been reported so far require the atomic positions obtained from geometry optimizations using high-level QM/DFT methods as input in order to predict the energies and do not allow for geometry optimization. In this study, a transferable and molecule size-independent machine learning model bonds (B), angles (A), nonbonded (N) interactions, and dihedrals (D) neural network (BAND NN) based on a chemically intuitive representation inspired by molecular mechanics force fields is presented. The model predicts the atomization energies of equilibrium and nonequilibrium structures as sum of energy contributions from bonds (B), angles (A), nonbonds (N), and dihedrals (D) at remarkable accuracy. The robustness of the proposed model is further validated by calculations that span over the conformational, configurational, and reaction space. The transferability of this model on systems larger than the ones in the data set is demonstrated by performing calculations on selected large molecules. Importantly, employing the BAND NN model, it is possible to perform geometry optimizations starting from nonequilibrium structures along with predicting their energies. © 2019 Wiley Periodicals, Inc.     

Binding energies of five molecular pincers calculated by explicit and implicit solvent models

Molecular pincers or tweezers are designed to hold and release the target molecule. Potential applications involve drug distribution in medicine, environment technologies, or microindustrial techniques. Typically, the binding is dominated by van der Waals forces. Modeling of such complexes can significantly enhance their design; yet obtaining accurate complexation energies by theory is difficult. In this study, density functional theory (DFT) computations combined with dielectric continuum solvent model are compared with the potential of mean force approach using umbrella sampling and the weighted histogram analysis method (WHAM) with molecular dynamics (MD) simulations. For DFT, functional and basis set effects are discussed. The computed results are compared to experimental data based on NMR spectroscopic measurements of five synthesized tweezers based on the Tröger's basis. Whereas the DFT computations correctly provided the observed trends in complex stability, they failed to produce realistic magnitudes of complexation energies. Typically, the binding was overestimated by DFT if compared to experiment. The simpler semiempirical PM6‐DH2X scheme proposed lately yielded better magnitudes of the binding energies than DFT but not the right order. The MD‐WHAM simulations provided the most realistic Gibbs binding energies, although the approximate MD force fields were not able to reproduce completely the ordering of relative stabilities of model complexes found by NMR. Yet the modeling provides interesting insight into the complex geometry and flexibility and appears as a useful tool in the tweezers' design. © 2012 Wiley Periodicals, Inc.     

Tailor-made force fields for crystal-structure prediction

A general procedure is presented to derive a complete set of force-field parameters for flexible molecules in the crystalline state on a case-by-case basis. The force-field parameters are fitted to the electrostatic potential as well as to accurate energies and forces generated by means of a hybrid method that combines solid-state density functional theory (DFT) calculations with an empirical van der Waals correction. All DFT calculations are carried out with the VASP program. The mathematical structure of the force field, the generation of reference data, the choice of the figure of merit, the optimization algorithm, and the parameter-refinement strategy are discussed in detail. The approach is applied to cyclohexane-1,4-dione, a small flexible ring. The tailor-made force field obtained for cyclohexane-1,4-dione is used to search for low-energy crystal packings in all 230 space groups with one molecule per asymmetric unit, and the most stable crystal structures are reoptimized in a second step with the hybrid method. The experimental crystal structure is found as the most stable predicted crystal structure both with the tailor-made force field and the hybrid method. The same methodology has also been applied successfully to the four compounds of the fourth CCDC blind test on crystal-structure prediction. For the five aforementioned compounds, the root-mean-square deviations between lattice energies calculated with the tailor-made force fields and the hybrid method range from 0.024 to 0.053 kcal/mol per atom around an average value of 0.034 kcal/mol per atom.     

Molecular and electronic structures, Brönsted basicities, and Lewis acidities of group VIB transition metal oxide clusters

The structures and properties of transition metal oxide (TMO) clusters of the group VIB metals, (MO(3))(n) (M = Cr, Mo, W; n = 1-6), have been studied with density functional theory (DFT) methods. Geometry optimizations and frequency calculations were carried out at the local and nonlocal DFT levels with polarized valence double-zeta quality basis sets, and final energies were calculated at nonlocal DFT levels with polarized valence triple-zeta quality basis sets at the local and nonlocal DFT geometries. Effective core potentials were used to treat the transition metal atoms. Two types of clusters were investigated, the ring and the chain, with the ring being lower in energy. Large ring structures (n > 3) were shown to be fluxional in their out of plane deformations. Long chain structures (n > 3) of (CrO(3))(n) were predicted to be weakly bound complexes of the smaller clusters at the nonlocal DFT levels. For M(6)O(18), two additional isomers were also studied, the cage and the inverted cage. The relative stability of the different conformations of M(6)O(18) depends on the transition metal as well as the level of theory. Normalized and differential clustering energies of the ring structures were calculated and were shown to vary with respect to the cluster size. Br?nsted basicities and Lewis acidities based on a fluoride affinity scale were also calculated. The Br?nsted basicities as well as the Lewis acidities depend on the size of the cluster and the site to which the proton or the fluoride anion binds. These clusters are fairly weak Br?nsted bases with gas phase basicities comparable to those of H(2)O and NH(3). The clusters are, however, very strong Lewis acids and many of them are stronger than strong Lewis acids such as SbF(5). Br?nsted acidities of M(6)O(19)H(2) and M(6)O(18)FH were calculated for M = Mo and W and these compounds were shown to be very strong acids in the gas phase. The acid/base properties of these TMO clusters are expected to play important roles in their catalytic activities.     

Accurate interaction energies of hydrogen-bonded nucleic acid base pairs

Hydrogen-bonded nucleic acids base pairs substantially contribute to the structure and stability of nucleic acids. The study presents reference ab initio structures and interaction energies of selected base pairs with binding energies ranging from -5 to -47 kcal/mol. The molecular structures are obtained using the RI-MP2 (resolution of identity MP2) method with extended cc-pVTZ basis set of atomic orbitals. The RI-MP2 method provides results essentially identical with the standard MP2 method. The interaction energies are calculated using the Complete Basis Set (CBS) extrapolation at the RI-MP2 level. For some base pairs, Coupled-Cluster corrections with inclusion of noniterative triple contributions (CCSD(T)) are given. The calculations are compared with selected medium quality methods. The PW91 DFT functional with the 6-31G basis set matches well the RI-MP2/CBS absolute interaction energies and reproduces the relative values of base pairing energies with a maximum relative error of 2.6 kcal/mol when applied with Becke3LYP-optimized geometries. The Becke3LYP DFT functional underestimates the interaction energies by few kcal/mol with relative error of 2.2 kcal/mol. Very good performance of nonpolarizable Cornell et al. force field is confirmed and this indirectly supports the view that H-bonded base pairs are primarily stabilized by electrostatic interactions.     

Copper cation interactions with biologically essential types of ligands: a computational DFT study

This work presents a systematic theoretical study on Cu(I) and Cu(II) cations in variable hydrogen sulfide-aqua-ammine ligand fields. These ligands model the biologically most common environment for Cu ions. Molecular structures of the complexes were optimized at the density functional theory (DFT) level. Subsequent thorough energy analyses revealed the following trends: (i) The ammine complexes are the most stable, followed by those containing the aqua and hydrogen sulfide ligands, which are characterized by similar stabilization energies. (ii) The most preferred Cu(I) coordination number is 2 in ammine or aqua ligand fields. A qualitatively different binding picture was obtained for complexes with H(2)S ligands where the 4-coordination is favored. (iii) The 4- and 5-coordinated structures belong to the most stable complexes for Cu(II), regardless of the ligand types. Vertical and adiabatic ionization potentials of Cu(I) complexes were calculated. Charge distribution (using the natural population analysis (NPA) method) and molecular orbital analyses were performed to elucidate the nature of bonding in the examined systems. The results provide in-depth insight into the Cu-binding properties and can be, among others, used for the calibration of bioinorganic force fields.     

High level of ab initio and density functional theory computational study of structural and energetic properties of tetrafluorhydrazine rotamers

The HF, MP2, MP3, MP4, and QCISD ab initio methods were compared with local, hybrid, and gradient-corrected density functional theory (DFT) methods for computing structures and energies of N2F4 rotamers. In all DFT calculations 6-311 + G(2d) basis set was used. The generated structures energies of trans- and gauche-N₂F₄ rotamers, and their dissociation energies to nitrogen difluoride were compared with experimental data. Suitable hybrid and gradient-corrected DFT methods for determining structures and energies for these and similar molecular systems were discussed.     

A theoretical study of small copper oxide clusters: Cu2Ox (x = 1 - 4)

Density functional theory (DFT) calculations are performed to study Cu2Ox (x = 1 - 4) clusters in their neutral, anionic and cationic states. The ground state structures are obtained and found to exhibit linear or near linear structures, which are different from the two- or three-dimensional ones suggested by the previous theoretical calculations. The calculated electron affinities of the clusters are in good agreement with the experimental ones. The low-lying excited states for the clusters are calculated using time-dependent DFT and used to assign the features in the photoelectron spectra. Our results compare well with the available experimental data.     

Enhanced stability by three-dimensional aromaticity of endohedrally doped clusters X(10)M(0/-) with X = Ge, Sn, Pb and M = Cu, Ag, Au

The group 14 clusters encapsulated by coinage metals in neutral and anionic states X(10)M(0/-) (X = Ge, Sn, Pb and M = Cu, Ag, Au) are investigated using quantum chemical calculations with the DFT/B3LYP functional and coupled-cluster CCSD(T) theory. Addition of transition metals into the empty cages forms high symmetry endohedral structures, except for Ge(10)Ag(0/-). In agreement with experiments available for X(10)Cu, the D(4d) global minima of the anions are calculated to be magic clusters with large frontier orbital gaps, high vertical and adiabatic detachment energies, and large embedding energies and binding energies as compared to those of the empty cages X(10)(2-). The enhanced stability of these magic clusters can be rationalized by the three-dimensional aromaticity.     

Comprehensive analysis of the hydrogen bond network morphology and OH stretching vibrations in protonated methanol-water mixed clusters, H(+)(MeOH)1(H2O)n (n = 1-8)

Density functional theory (DFT) calculations of protonated methanol-water mixed clusters, H (+)(MeOH) 1(H 2O) n ( n = 1-8), were extensively carried out to analyze the hydrogen bond structures of the clusters. Various structural isomers were energy optimized, and their relative energies with zero point energy corrections and temperature dependence of the free energies were examined. Coexistence of different morphological isomers was suggested. Infrared spectra were simulated on the basis of the optimized structures. The infrared spectra were also experimentally measured for n = 3-9 in the OH stretching vibrational region. The observed broad bands in the hydrogen-bonded OH stretch region were assigned in comparison with the simulations. From the DFT calculations, the preferential proton location was also investigated. Clear correlations between the excess proton location and the cluster morphology were found.