Frozen-density embedding-based many-body expansions

Fragmentation methods allow for the accurate quantum chemical (QC) treatment of large molecular clusters and materials. Here we explore the combination of two complementary approaches to the development of such fragmentation methods: the many-body expansion (MBE) on the one hand, and subsystem density-functional theory (DFT) or frozen-density embedding (FDE) theory on the other hand. First, we assess potential benefits of using FDE to account for the environment in the subsystem calculations performed within the MBE. Second, we use subsystem DFT to derive a density-based MBE, in which a many-body expansion of the electron density is used to calculate the system's total energy. This provides a correction to the energies calculated with a conventional energy-based MBE that depends only on the subsystem's electron densities. For the test case of clusters of water and of aspirin, we show that such a density-based MBE converges faster than the conventional energy-based MBE. For our test cases, truncation errors in the interaction energies are below chemical accuracy already with a two-body expansion. The density-based MBE thus provides a promising avenue for accurate QC calculation of molecular clusters and materials.     

Interaction energies of large clusters from many-body expansion

In the canonical supermolecular approach, calculations of interaction energies for molecular clusters involve a calculation of the whole cluster, which becomes expensive as the cluster size increases. We propose a novel approach to this task by demonstrating that interaction energies of such clusters can be constructed from those of small subclusters with a much lower computational cost by applying progressively lower-level methods for subsequent terms in the many-body expansion. The efficiency of such "stratified approximation" many-body approach (SAMBA) is due to the rapid convergence of the many-body expansion for typical molecular clusters. The method has been applied to water clusters (H(2)O)(n), n = 6, 16, 24. For the hexamer, the best results that can be obtained with current computational resources in the canonical supermolecular method were reproduced to within about one tenth of the uncertainty of the canonical approach while using 24 times less computer time in the many-body expansion calculations. For (H(2)O)(24), SAMBA is particularly beneficial and we report interaction energies with accuracy that is currently impossible to obtain with the canonical supermolecular approach. Moreover, our results were computed using two orders of magnitude smaller computer resources than used in the previous best calculations for this system. We also show that the basis-set superposition errors should be removed in calculations for large clusters.     

水团簇(H2O)n中多体作用强度与水分子间距的关系

使用高精度从头算方法(含基组重叠误差校正)计算了水团簇(H₂O)_n (n = 8, 10, 16, 20, 22, 24)中的所有二体、三体和四体作用能,分析了水团簇中的多体效应.研究表明,二体作用对体系总作用能的贡献高达70%以上,三体作用对总作用能的贡献可高达25%,四体作用在总作用能中所占比例不超过3%,五体及以上多体作用能在总作用能中所占比例更小,不超过0.5%.本文研究还表明,两个水分子间距小于0.68 nm的二体作用、三个和四个水分子中最近的两个水分子间距小于0.31 nm的三体和四体作用对体系总作用能的贡献高达99.4%.因此,以生物体系为对象的分子模拟方法应该具备准确地模拟两个水分子间距小于0.68 nm的二体作用、三个和四个水分子中最近的两个分子间距小于0.31 nm的三体和四体作用的能力.     

Pdn(n=1-7)团簇及其与甲烷相互作用的密度泛函理论研究

用密度泛函理论(DFT)的B3LYP方法, 对Pdn(n=1-7)团簇的几何结构、振动频率及其与甲烷分子间的相互作用进行了理论研究. 结果表明, 随着Pd原子数增多, 团簇结构对团簇大小的依赖性减弱, 结构参数向金属晶体趋近. 在Pdn(n=1-7)团簇上, 甲烷的表面吸附作用较弱. Pd2CH4中, 甲烷受到两个Pd原子的活化作用, 活化程度增强, 吸附能增大. 在PdnCH4 (n=1, 3-7)体系中, 甲烷的吸附能随着团簇模型的增大而减小, 趋近于其在金属晶面上的吸附能.     

Fully retarded van der Waals interaction between dielectric nanoclusters

The van der Waals (dispersion) interaction between an atom and a cluster or between two clusters at large separation is calculated by considering each cluster as a point particle, characterized by a polarizability tensor. For the extreme limit of very large separation, the fully retarded regime, one needs to know just the static polarizability in order to determine the interaction. This polarizability is evaluated by including all many-body (MB) intracluster atomic interactions self-consistently. The results of these calculations are compared with those obtained from various alternative methods. One is to consider each cluster as a collection of many atoms and evaluate the sum of two-body interatomic interactions, a common assumption. An alternative method is to include three-body atomic interactions as a MB correction term in the total energy. A comparison of these results reveals that the contribution of the higher-than-three-body MB interactions is always attractive and non-negligible even at such a large separation, in contrast to common assumptions. The procedure employed is quite general and is applicable, in principle, to any shape or size of dielectric cluster. We present numerical results for clusters composed of atoms with polarizability consistent with silica, for which the higher-than-three-body MB correction term can be as high as 42% of the atomic pairwise sum. This result is quite sensitive to the anisotropy and orientation of the cluster, in contrast to the result found in the additive case. We also present a power law expansion of the total van der Waals interaction as a series of n-body interaction terms.     

On the Role of Charge Transfer in Many-Body Non-Covalent Interactions**

Charge transfer is one of the mechanisms involved in non-covalent interactions. In molecular dimers, its contribution to pairwise interaction energies has been studied extensively using a variety of interaction energy decomposition schemes. In polar interactions such as hydrogen bonds, it can contribute ten or several tens of percent of the interaction energy. Less is known about its importance in higher-order interactions in many-body systems, mainly because of the lack of methods applicable to this problem. In this work, we extend our method for the quantification of the charge-transfer energy based on constrained DFT to many-body cases and apply it to model trimers extracted from molecular crystals. Our calculations show that charge transfer can account for a large fraction of the total three-body interaction energy. This also has implications for DFT calculations of many-body interactions in general as it is known that many DFT functionals struggle to describe charge-transfer effects correctly.     

Pair interaction energy decomposition analysis

The energy decomposition analysis (EDA) by Kitaura and Morokuma was redeveloped in the framework of the fragment molecular orbital method (FMO). The proposed pair interaction energy decomposition analysis (PIEDA) can treat large molecular clusters and the systems in which fragments are connected by covalent bonds, such as proteins. The interaction energy in PIEDA is divided into the same contributions as in EDA: the electrostatic, exchange-repulsion, and charge transfer energies, to which the correlation (dispersion) term was added. The careful comparison to the ab initio EDA interaction energies for water clusters with 2-16 molecules revealed that PIEDA has the error of at most 1.2 kcal/mol (or about 1%). The analysis was applied to (H2O)1024, the alpha helix, beta turn, and beta strand of polyalanine (ALA)10, as well as to the synthetic protein (PDB code 1L2Y) with 20 residues. The comparative aspects of the polypeptide isomer stability are discussed in detail.     

Growth and Formation of Fullerene Clusters

Theoretical studies on the stability and electronic structure of small carbon clusters assuming chain, ring, bowl, and fullerene structures have been carried out using a linear combination of atomic orbitals molecular orbital approach within a density functional formalism. Our studies on clusters containing between 12 and 60 atoms indicate three regimes for the growth and formation of carbon clusters. In clusters containing less than 20 atoms, the most stable geometry is the ring arrangements. Between 20 and 28 atoms, clusters with very different geometry have comparable energies. For clusters with larger than 30 atoms, the fullerene structures are the most stable structures. An analysis of the electronic structure shows a distinct correlation between the geometry and the nature of electronic states.     

Strain Energies in Homoatomic Nitrogen Clusters N(4), N(6), and N(8)

Strain energies and resonance energies can be obtained as the energy changes for appropriate homodesmotic reactions using ab initio calculated total energies as the energies of the reactants and products involved. Homodesmotic reactions conserve bond types and preserve valence environments at all atoms, requirements that favor the cancellation of basis set and electron correlation errors in the ab initio energies. In this paper we calculate strain energies and resonance energies for N(4), N(6), and N(8) clusters in a number of chemically significant but, for nitrogen, hypothetical structural forms. The nitrogen cluster strain energies are generally of the same order of magnitude as those of isostructural hydrocarbon clusters, and individual differences can be explained by using the ring strain additivity rule and recognizing the effect of the presence of lone pairs of electrons on nitrogen clusters but not on the hydrocarbons. Resonance energies of the nitrogen clusters are much smaller than those of the comparable aromatic hydrocarbons. The differences can be rationalized by considering the relative strengths of CC and NN single and double bonds. Strain and resonance energies of nitrogen clusters are compared with those previously reported for homoatomic clusters of phosphorus and arsenic. Trends through the series are remarkably similar, but strain energies for clusters from lower periods are progressively smaller. Strain and resonance have been important organizing concepts in organic chemistry for many years. Estimates of corresponding parameters for inorganic analogs are only now becoming available.     

水分子团簇分子力场方法的比较研究

采用传统水分子力场模型(SPC, TIPnP(n=3-5))和极化模型(POL3, AMOEBA, SPC-FQ, TIP4P-FQ)对水分子二聚体团簇性质进行了比较和研究. 以从头计算和实验数据为依据, 分析水分子在外场作用下体系的静电极化, 电荷转移和分子结构变化. 通过水分子二聚体结合能和各分解能量项评价极化静电势能在双分子结合能中的地位和作用, 以及各水分子力场的适用性. 通过水分子团簇多体相互作用能的计算,展示不同极化水分子力场定量计算极化能量的实际能力. 通过对力场模型结果的对比和分析, 为进一步发展极化力场模型, 并应用到其他体系提供借鉴和依据.     

Development of a 3-body:many-body integrated fragmentation method for weakly bound clusters and application to water clusters (H2O)(n = 3-10, 16, 17)

A 3-body:many-body integrated quantum mechanical (QM) fragmentation method for non-covalent clusters is introduced within the ONIOM formalism. The technique captures all 1-, 2-, and 3-body interactions with a high-level electronic structure method, while a less demanding low-level method is employed to recover 4-body and higher-order interactions. When systematically applied to 40 low-lying (H(2)O)(n) isomers ranging in size from n = 3 to 10, the CCSD(T):MP2 3-body:many-body fragmentation scheme deviates from the full CCSD(T) interaction energy by no more than 0.07 kcal mol(-1) (or <0.01 kcal mol(-1) per water). The errors for this QM:QM method increase only slightly for various low-lying isomers of (H(2)O)(16) and (H(2)O)(17) (always within 0.13 kcal mol(-1) of the recently reported canonical CCSD(T)/aug-cc-pVTZ energies). The 3-body:many-body CCSD(T):MP2 procedure is also very efficient because the CCSD(T) computations only need to be performed on subsets of the cluster containing 1, 2, or 3 monomers, which in the current context means the largest CCSD(T) calculations are for 3 water molecules, regardless of the cluster size.     

Modeling intercalation through the sandwich‐type interactions between benzene and 14 polyaromatic molecules: DFT and ab initio results

We use second order Moller Plesset perturbation theory and several density functional theory methods to calculate the counterpoise corrected electronic interaction energies between benzene and a series of polyaromatic molecules. These systems serve as a simple model for DNA intercalation. We show that addition of nitrogen atoms to the polyaromatic molecules always increases sandwich‐type interactions, and that, of the density functional theory methods studied, only SVWN can mimic the interaction energies and optimal separations obtained with perturbation theory. SVWN reproduces the optimal molecular distances obtained with perturbation theory very well, and often comes within less than 10% of the interaction energy. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Evolution of the electronic structure of Be clusters

Using a modified symbiotic genetic algorithm approach and many-body interatomic potential derived from first principles, we have calculated equilibrium geometries and binding energies of the ground-state and low-lying isomers of Be clusters containing up to 41 atoms. Molecular-dynamics study was also carried out to study the frequency of occurrence of the various geometrical isomers as these clusters are annealed during the simulation process. For a selected group of these clusters, higher-energy isomers were more often found than their ground-state structures due to large catchment areas. The accuracy of the above ground-state geometries and their corresponding binding energies were verified by carrying out separate ab initio calculations based on molecular-orbital approach and density-functional theory with generalized gradient approximation for exchange and correlation. The atomic orbitals were represented by a Gaussian 6-311G** basis, and the geometry optimization was carried out using the GAUSSIAN 98 code without any symmetry constraint. While the ground-state geometries and their corresponding binding energies obtained from ab initio calculations do not differ much from those obtained using the molecular-dynamics approach, the relative stability of the clusters and the energy gap between the highest occupied and the lowest unoccupied molecular orbitals show significant differences. The energy gaps, calculated using the density-functional theory, show distinct shell closure effects, namely, sharp drops in their values for Be clusters containing 2, 8, 20, 34, and 40 electrons. While these features may suggest that small Be clusters behave free-electron-like and, hence, are metallic, the evolution of the structure, binding energies, coordination numbers, and nearest-neighbor distances do not show any sign of convergence towards the bulk value. We also conclude that molecular-dynamics simulation based on many-body interatomic potentials may not always give the correct picture of the evolution of the structure and energetics of clusters although they may serve as a useful tool for obtaining starting geometries by efficiently searching a large part of the phase space.     

Visualizing internal stabilization in weakly bound systems using atomic energies: hydrogen bonding in small water clusters

Atomic energies are used to visualize the local stabilizing and destabilizing energy changes in water clusters. Small clusters, (H(2)O)(n), from n = 2-5, at MP2/aug-cc-pVTZ geometries are evaluated using energies defined by the quantum theory of atoms in molecules (QTAIM). The atomic energies reproduce MP2 total energies to within 0.005 kcal mol(-1). Oxygen atoms are stabilized for all systems and hydrogen atoms are destabilized. The increased stability of the water clusters due to hydrogen bond cooperativity is demonstrated at an atomic level. Variations in atomic energies within the clusters are correlated to the geometry of the waters and reveal variations in the hydrogen bond strengths. The method of visualization of the energy changes applied here is especially suited for application to large biomolecules.     

Rapid computation of intermolecular interactions in molecular and ionic clusters: self-consistent polarization plus symmetry-adapted perturbation theory

A method that we have recently introduced for rapid computation of intermolecular interaction energies is reformulated and subjected to further tests. The method employs monomer-based self-consistent field calculations with an electrostatic embedding designed to capture many-body polarization (the "XPol" procedure), augmented by pairwise symmetry-adapted perturbation theory (SAPT) to capture dispersion and exchange interactions along with any remaining induction effects. A rigorous derivation of the XPol+SAPT methodology is presented here, which demonstrates that the method is systematically improvable, and moreover introduces some additional intermolecular interactions as compared to the more heuristic derivation that was presented previously. Applications to various non-covalent complexes and clusters are presented, including geometry optimizations and one-dimensional potential energy scans. The performance of the XPol+SAPT methodology in its present form (based on second-order intermolecular perturbation theory and neglecting intramolecular electron correlation) is qualitatively acceptable across a wide variety of systems-and quantitatively quite good in certain cases-but the quality of the results is rather sensitive to the choice of one-particle basis set. Basis sets that work well for dispersion-bound systems offer less-than-optimal performance for clusters dominated by induction and electrostatic interactions, and vice versa. A compromise basis set is identified that affords good results for both induction and dispersion interactions, although this favorable performance ultimately relies on error cancellation, as in traditional low-order SAPT. Suggestions for future improvements to the methodology are discussed.     

原子团簇P10模型的理论计算

用分子图形学方法设计出26种P10模型,并对其进行了分子力学、PM3半经验量子化学和Hartree-Fock从头算优化。在P10原子团簇模型设计中,磷原子采用一、二、三或四配位。大部分P10的模型是在P9+和P8的模型上分别增加1、2个原子生成的。这些模型包括15种在势能面上局域极小点和11种鞍点（或过渡态）。从模型优化后的能量比较可知,2个四面体P4与1个P2通过4个单键连接的桥式结构最稳定。从最稳定楔状P8可以派生多种构型,其中有一种的能量也相当低。由正四面体P4和楔状P8派生出的结构具有能量优势,它们是构造大分子磷原子团簇的重要的结构基元。在模型几何优化中,得到了带有2个一配位原子的特殊结构,它含有2个三键（1.95A）。     

Force fields for metallic clusters and nanoparticles

Atomic force fields for simulating copper, silver, and gold clusters and nanoparticles are developed. Potential energy functions are obtained for both monatomic and binary metallic systems using an embedded atom method. Many cluster configurations of varying size and shape are used to constrain the parametrization for each system. Binding energies for these training clusters were computed using density functional theory (DFT) with the Perdew-Wang exchange-correlation functional in the generalized gradients approximation. Extensive testing shows that the many-body potentials are able to reproduce the DFT energies for most of the structures that were included in the training set. The force fields were used to calculate surface energies, bulk structures, and thermodynamic properties. The results are in good agreement with the DFT values and consistent with the available experimental data.     

[He3H]＋分子基态势能面的从头计算研究

使用CCSD(T)/aug-cc-pVTZ从头计算方法，对[He3H]＋分子的一些特殊构型的电子基态势能进行扫描，并以此为基础对三体相互作用势在惰性气体质子簇中的影响进行了讨论.结果表明即使在这样一个简单的体系中三体相互作用的影响都是不能忽略的.另一方面，在[He3H]＋分子稳定构型附近仅将势能展开至三体相互作用项便可提供较精确的相互作用信息，但在强排斥区域更高阶作用的影响变得越来越突出.本文同时讨论了[He4H]＋的稳态结构. [He3H]＋与[He4H]＋的稳态结构表明,[HenH]＋簇中存在着一个[He2H]＋核.     

Density functional theory study of the properties of N-H...N, non-cooperativities, and intermolecular interactions in linear trans-diazene clusters up to ten molecules

We investigate aspects of N-H...N hydrogen bonding in the linear trans-diazene clusters (n=2-10) such as the N...H and N-H lengths, n(N) --> sigma(N-H) interactions, N...H strengths, and frequencies of the N-H stretching vibrations utilizing the DFT/B3LYP theory, the natural bond orbital (NBO) method, and the theory of atoms in molecules (AIM). Our calculations indicate that the structure and energetics are qualitatively different from the conventional H-bonded systems, which usually exhibit distinct cooperative effects, as cluster size increases. First, a shortening rather than lengthening of the N-H bond is found and thus a blue rather than red shift is predicted. Second, for the title clusters, any sizable cooperative changes in the N-H and N...H lengths, n(N) --> sigma(N-H) charge transfers, N...H strengths, and frequencies of the N-H stretching vibrations for the linear H-bonded trans-diazene clusters do not exist. Because the n(N) --> sigma(N-H) interaction hardly exhibits cooperative effects, the capability of the linear trans-diazene cluster to localize electrons at the N...H bond critical point is almost independent of cluster size and thereby leads to the noncooperative changes in the N...H lengths and strengths and the N-H stretching frequencies. Third, the dispersion energy is sizable and important; more than 30% of short-range dispersion energy not being reproduced by the DFT leads to the underestimation of the interaction energies by DFT/B3LYP. The calculated nonadditive interaction energies show that, unlike the conventional H-boned systems, the trans-diazene clusters indeed exhibit very weak nonadditive interactions.