Low-lying electronic states of M(3)O(9)(-) and M(3)O(9)(2-) (M = Mo, W)

Multiple low-lying electronic states of M(3)O(9)(-) and M(3)O(9)(2-) (M = Mo, W) arise from the occupation of the near-degenerate low-lying virtual orbitals in the neutral clusters. We used density functional theory (DFT) and coupled cluster theory (CCSD(T)) with correlation consistent basis sets to study the structures and energetics of the electronic states of these anions. The adiabatic and vertical electron detachment energies (ADEs and VDEs) of the anionic clusters were calculated with 27 exchange-correlation functionals including one local spin density approximation functional, 13 generalized gradient approximation (GGA) functionals, and 13 hybrid GGA functionals, as well as the CCSD(T) method. For M(3)O(9)(-), CCSD(T) and nearly all of the DFT exchange-correlation functionals studied predict the (2)A(1) state arising from the Jahn-Teller distortion due to singly occupying the degenerate e' orbital to be lower in energy than the (2)A(1)' state arising from singly occupying the nondegenerate a(1)' orbital. For W(3)O(9)(-), the (2)A(1) state was predicted to have essentially the same energy as the (2)A(1)' state at the CCSD(T) level with core-valence correlation corrections included and to be higher in energy or essentially isoenergetic with most DFT methods. The calculated VDEs from the CCSD(T) method are in reasonable agreement with the experimental values for both electronic states if estimates for the corrections due to basis set incompleteness are included. For M(3)O(9)(2-), the singlet state arising from doubly occupying the nondegenerate a(1)' orbital was predicted to be the most stable state for both M = Mo and W. However, whereas M(3)O(9)(2-) was predicted to be less stable than M(3)O(9)(-), W(3)O(9)(2-) was predicted to be more stable than W(3)O(9)(-).     

C24和B12N12团簇的结构与稳定性

本文采用量子化学密度泛函理论的B3LYP/6-31G*方法,对C24和B12N12团簇的12种异构体进行了优化,并对它们的几何构型、振动频率、核独立化学位移(NICS)和结合能进行了理论探讨, 比较了C24和B12N12团簇结构的稳定性。研究表明:C24团簇的最稳定几何构型为类石墨结构d,B12N12团簇的最稳定结构为4/6笼状结构g。C24异构体的稳定性大小顺序为d > b > f > c > a > e。B12N12团簇异构体稳定性大小顺序为a > f> c> d > e >b。     

Cu3C4-: a new sandwich molecule with two revolving C2(2-) units

A combined photoelectron spectroscopy (PES) and ab initio study was carried out on a novel copper carbide cluster in the gas phase: Cu(3)C(4)(-). It was generated in a laser vaporization cluster source and appeared to exhibit enhanced stability among the Cu(3)C(n)(-) series. Its PES spectra were obtained at several photon energies, showing numerous well-resolved bands. Extensive ab initio calculations were performed on Cu(3)C(4)(-), and two isomers were identified: a C(2) structure ((1)A) with a Cu(3)(3+) triangular group sandwiched by two C(2)(2-) units and a linear CuCCCuCCCu structure (D(infinity)(h), (1)Sigma(g)(+)). A comparison of ab initio PES spectra with experimental data showed that the sandwich Cu(3)C(4)(-) cluster was solely responsible for the observed spectra and the linear isomer was not present, suggesting that the C(2) structure is the global minimum in accordance with CCSD(T)/6-311+G predictions. Interestingly, a relatively low barrier (0.4-0.6 kcal/mol) was found for the internal rotation of the C(2)(2-) units in the sandwich Cu(3)C(4)(-). To test different levels of theory in describing the Cu(m)C(n)(-) systems and lay foundations for the validity of the theoretical methods, extensive calculations at a variety of levels were also carried out on a simpler copper carbide species CuC(2)(-), where two isomers were found to be close in energy: a linear one (C(infinity)(v), (1)Sigma(+)) and a triangular one (C(2)(v), (1)A(1)). The calculated electronic transitions for CuC(2)(-) were also compared with the PES data, in which both isomers were present.     

Polarizability of small carbon cluster anions from first principles

We examine the applicability of density functional theory (DFT) to the polarizability of Cn- (n = 3-9) cluster anions. This was achieved by comparing DFT calculations using two different exchange-correlation functionals (the non-empirical local density approximation, LDA, and the semiempirical hybrid functional B97-1) to quantum chemical calculations using the coupled cluster method in the CCSD(T) "gold standard" approximation. We find that, unless the extra electron is not bound at all by DFT, both LDA and B97-1 agree with the CCSD(T) calculation to within 5-10%, allowing for a meaningful qualitative and semiquantitative analysis. Furthermore, the polarizability is found to increase monotonically with chain size, consistent with the trend inferred from electron detachment experiments.     

Structures and properties of neutral gallium clusters: a theoretical investigation

A systematic and unbiased structure search based on a genetic algorithm in combination with density functional theory (DFT) procedures has been carried out to locate low-energy isomers of Ga(n) up to n = 25. For the smaller clusters up to n = 8 results are checked by coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) employing a quadruple zeta type basis set. The CCSD(T) calculations confirm a (3)Π(u) ground state for the dimer. Ga(3) has a doublet ground state 0.2 eV below two quartet states, whereas two isoenergetic triplet states are predicted for Ga(4) with D(4h) and a rhombus structure (D(2h)). Three low-lying isomers with doublet electronic states are found for Ga(5): a W-structure (C(2v)), a planar envelope (C(s)) at 0.015 eV, and a non-planar envelope (C(1)) 0.086 eV above the ground state. A triplet state for a trigonal prism (D(3h)) and a singlet for an open prism (C(2v)) are computed with virtually identical energy for Ga(6). The global minimum for Ga(7) is a capped trigonal prism (C(s)) and that for Ga(8) a distorted cube in D(2h). DFT provides a fair agreement with CCSD(T), deviations in dissociation energies are up to 0.2 eV for n ≤ 8. The structures for Ga(n) are mostly irregular for n ≥ 9, those for Ga(12) to Ga(17) can be derived from the truncated decahedron with D(5h) symmetry though highly distorted by Jahn-Teller effects, for example. For Ga(18) to Ga(23) we find stacks of five- and six-membered rings as global minima, e.g., 5-1-5-1-6 for Ga(18). Ga(24) and Ga(25) consist of layers with packing sequence ABCBA similar to those found for clusters of aluminum. The most important feature of computed cohesive energies is a rapid increase with n: for Ga(25) it reaches 2.46 eV, the experimental bulk value is 2.84 eV. Particularly stable clusters for Ga(n) are seen for n = 7, 14, and 20.     

Au10团簇结构与电性质的理论研究

使用4种流行的泛函(BPW91, B3PW91, PW91和B3LYP)考查了若干Au10团簇结构的稳定结构, 获得了能量最有利的6种异构体(其中2种以前未见报道), 并在此基础上进一步用MP2方法校准了它们的相对稳定性, 分析了它们的电子性质以及最稳定异构体与氧分子的化学反应性能. 计算结果表明Au10团簇异构体的相对稳定性明显依赖所使用的理论方法和泛函, 密度泛函结果显示Au10倾向于采用平面结构, 且不同的泛函给出异构体的相对稳定性次序也不相同, 而MP2计算则显示三维空间结构的Au10团簇更稳定, Au10可能是金团簇从二维结构到三维结构演化的一个临界点.     

Unique CO chemisorption properties of gold hexamer: Au6(CO)n- (n = 0-3)

Elucidating the chemisorption properties of CO on gold clusters is essential to understanding the catalytic mechanisms of gold nanoparticles. Gold hexamer Au(6) is a highly stable cluster, known to possess a D(3)(h) triangular ground state structure with an extremely large HOMO-LUMO gap. Here we report a photoelectron spectroscopy (PES) and quasi-relativistic density functional theory (DFT) study of Au(6)-CO complexes, Au(6)(CO)(n)(-) and Au(6)(CO)(n) (n = 0-3). CO chemisorption on Au(6) is observed to be highly unusual. While the electron donor capability of CO is known to decrease the electron binding energies of Au(m)(CO)(n)(-) complexes, CO chemisorption on Au(6) is observed to have very little effect on the electron binding energies of the first PES band of Au(6)(CO)(n)(-) (n = 1-3). Extensive DFT calculations show that the first three CO successively chemisorb to the three apex sites of the D(3)(h) Au(6). It is shown that the LUMO of the Au(6)-CO complexes is located in the inner triangle. Thus CO chemisorption on the apex sites (outer triangle) has little effect on this orbital, resulting in the roughly constant electron binding energies for the first PES band in Au(6)(CO)(n)(-) (n = 0-3). Detailed molecular orbital analyses lead to decisive information about chemisorption interactions between CO and a model Au cluster.     

Performance of multi-configurational calculations for a 1,4-bis(phenylethynyl)benzene derivative conjugated molecule.

The theoretical challenge of finding a single method that quantitatively reproduces both the experimental low-lying excitation energies and the torsional barrier of a prototypical conjugated molecule, which could act as a molecular wire, has been addressed here. The results indicate that this goal can be reasonably achieved when multi-reference perturbation theory up to second order (MRMP2) based on a complete active space self-consistent field (CASSCF) wave function using large active spaces is used. The results obtained were also used to compare with less expensive Kohn-Sham (KS) density functional theory (DFT) calculations when applied to these properties. The results obtained with BLYP and B3LYP exchange-correlation functionals indicate that quantitative agreement with all the experimental data cannot be obtained with this methodology, with a clear dependence on the exchange-correlation form selected. We thus encourage a careful testing of pure and hybrid density functionals whenever KS DFT is used for the rational design of conjugated materials for charge conduits.     

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: benchmarks approaching the complete basis set limit

The ability of several density-functional theory (DFT) exchange-correlation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order Moller-Plesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the nonhybrid generalized gradient approximation functionals, mPWLYP and PBE1W perform best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.     

Density functional theory study of 11-atom germanium clusters: effect of electron count on cluster geometry

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge(11)(z) (z = -6, -4, -2, 0, +2, +4, +6) starting from eight different initial configurations. The global minimum within the Ge(11)(2-) set is an elongated pentacapped trigonal prism distorted from D(3)(h) to C(2v) symmetry. However, the much more spherical edge-coalesced icosahedron, also of C(2v) symmetry, expected by the Wade-Mingos rules for a 2n + 2 skeletal electron system and found experimentally in B(11)H(11)(2-) and isoelectronic carboranes, is of only slightly higher energy (+5.2 kcal/mol). Even more elongated D(3)(h) pentacapped trigonal prisms are the global minima for the electron-rich structures Ge(11)(4-) and Ge(11)(6-). For Ge(11)(4-) the C(5v) 5-capped pentagonal antiprism analogous to the dicarbollide ligand C(2)B(9)H(11)(2-) is of significantly higher energy (approximately 28 kcal/mol) than the D(3h) global minimum. The C(2v) edge-coalesced icosahedron is also the global minimum for the electron-poor Ge(11) similar to its occurrence in experimentally known 11-vertex "isocloso" metallaboranes of the type (eta(6)-arene)RuB(10)H(10). The lowest energy polyhedral structures computed for the more hypoelectronic Ge(11)(4+) and Ge(11)(6+) clusters are very similar to those found experimentally for the isoelectronic ions E(11)(7-) (E = Ga, In, Tl) and Tl(9)Au(2)(9-) in intermetallics in the case of Ge(11)(4+) and Ge(11)(6+), respectively. These DFT studies predict an interesting D(5h) centered pentagonal prismatic structure for Ge(11)(2+) and isoelectronic metal clusters.     

On the electronic structure and chemical bonding in the tantalum trimer cluster

The electronic structure and chemical bonding in the Ta 3 (-) cluster are investigated using photoelectron spectroscopy and density functional theory calculations. Photoelectron spectra are obtained for Ta 3 (-) at four photon energies: 532, 355, 266, and 193 nm. While congested spectra are observed at high electron binding energies, several low-lying electronic transitions are well resolved and compared with the theoretical calculations. The electron affinity of Ta 3 is determined to be 1.35 +/- 0.03 eV. Extensive density functional calculations are performed at the B3LYP/Stuttgart +2f1g level to locate the ground-state and low-lying isomers for Ta 3 and Ta 3 (-). The ground-state for the Ta 3 (-) anion is shown to be a quintet ( (5)A 1') with D 3 h symmetry, whereas two nearly isoenergetic states, C 2 v ( (4)A 1) and D 3 h ( (6)A 1'), are found to compete for the ground-state for neutral Ta 3. A detailed molecular orbital analysis is performed to elucidate the chemical boding in Ta 3 (-), which is found to possess multiple d-orbital aromaticity, commensurate with its highly symmetric D 3 h structure.     

Six-dimensional potential energy surface for H2 at Ru(0001)

The six-dimensional (6D) potential energy surface (PES) for the H(2) molecule interacting with a clean Ru(0001) surface has been computed accurately for the first time. Density functional theory (DFT) and a pseudopotential based periodic plane-wave approach have been used to calculate the electronic interactions between the molecule and the surface. Two different generalized gradient approximation (GGA) exchange-correlation functionals, PW91 and RPBE, have been adopted. Based on the DFT/GGA calculated potential energies, an analytical 6D PES has been constructed using the corrugation reducing procedure. A very accurate representation of the DFT/GGA data has been achieved, with an average error in the interpolation of about 3 meV and a maximum error not larger than about 30 meV. The top site is found to be the most reactive site for both functionals used, but PW91 predicts a higher reactivity than RPBE, with lower-energy and earlier-located dissociation barriers. The energetic corrugation displayed by the RPBE PES is larger than the PW91 PES while the geometric corrugation is smaller. The differences between the two PESs increase as the distance of the molecular center of mass to the surface decreases. A direct comparison with experimental investigations on H(2)/Ru(0001) could shed light on the suitability of these XC potentials often used in DFT calculations.     

Photoelectron spectroscopy and density functional calculations of CuSi(n)- (n = 4-18) clusters

We conducted a combined anion photoelectron spectroscopy and density functional theory study on the structural evolution of copper-doped silicon clusters, CuSi(n)(-) (n = 4-18). Based on the comparison between the experiments and theoretical calculations, CuSi(12)(-) is suggested to be the smallest fully endohedral cluster. The low-lying isomers of CuSi(n)(-) with n ≥ 12 are dominated by endohedral structures, those of CuSi(n)(-) with n < 12 are dominated by exohedral structures. The most stable structure of CuSi(12)(-) is a double-chair endohedral structure with the copper atom sandwiched between two chair-style Si(6) rings or, in another word, encapsulated in a distorted Si(12) hexagonal prism cage. CuSi(14)(-) has an interesting C(3h) symmetry structure, in which the Si(14) cage is composed by three four-membered rings and six five-membered rings.     

Assessment of the accuracy of density functionals for prediction of relative energies and geometries of low-lying isomers of water hexamers

Water hexamers provide a critical testing ground for validating potential energy surface predictions because they contain structural motifs not present in smaller clusters. We tested the ability of 11 density functionals (four of which are local and seven of which are nonlocal) to accurately predict the relative energies of a series of low-lying water hexamers, relative to the CCSD(T)/aug'-cc-pVTZ level of theory, where CCSD(T) denotes coupled cluster theory with an interative treatment of single and double excitations and a quasi-perturbative treatment of connected triple excitations. Five of the density functionals were tested with two different basis sets, making a total of 16 levels of density functional theory (DFT) tested. When single-point energy calculations are carried out on geometries obtained with second-order M?ller-Plesset perturbation theory (MP2), only three density functionals, M06-L, M05-2X, and M06-2X, are able to correctly predict the relative energy ordering of the hexamers. These three functionals predict that the range of energies spanned by the six isomers is 3.2-5.6 kcal/mol, whereas the other eight functionals predict ranges of 1.0-2.4 kcal/mol; the benchmark value for this range is 3.1 kcal/mol. When the hexamers are optimized at each level of theory, all methods are able to reproduce the MP2 geometries well for all isomers except the boat and bag isomers, and DFT optimization changes the energy ordering for seven of the 16 methods tested. The addition of zero-point energy changes the energy ordering for all of the density functionals studied except for M05-2X and M06-2X. The variation in relative energies predicted by the different methods highlights the necessity for exercising caution in the choice of density functionals used in future studies. Of the 11 density functionals tested, the most accurate results for energies were obtained with the PWB6K, MPWB1K, and M05-2X functionals.     

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.     

Density functional study of 8- and 11-vertex polyhedral borane structures: comparison with bare germanium clusters

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the polyhedral boranes B(n)H(n)(z) (n = 8 and 11, z = -2, -4, and -6) for comparison with isoelectronic germanium clusters Ge(n)(z). The energy differences between the global minima and other higher energy borane structures are much larger relative to the case of the corresponding bare germanium clusters. Furthermore, for both B(8)H(8)(2-) and B(11)H(11)(2-), the lowest energy computed structures are the corresponding experimentally observed most spherical deltahedra predicted by the Wade-Mingos rules, namely the D(2)(d) bisdisphenoid and the C(2)(v) edge-coalesced icosahedron, respectively. Only in the case of B(8)H(8)(2-) is there a second structure close (+2.6 kcal/mol) to the D(2)(d) bisdisphenoid global minimum, namely the C(2)(v) bicapped trigonal prism corresponding to the "square" intermediate in a single diamond-square-diamond process that can lead to the experimentally observed room temperature fluxionality of B(8)H(8)(2-). Stable borane structures with 3-fold symmetry (e.g., D(3)(h), C(3)(v), etc.) are not found for boranes with 8- and 11-vertices, in contrast to the corresponding germanium clusters where stable structures derived from the D(3)(d) bicapped octahedron and D(3)(h) pentacapped trigonal prism are found for the 8- and 11-vertex systems, respectively. The lowest energy structures found for the electron-rich boranes B(8)H(8)(4-) and B(11)H(11)(4-) are nido polyhedra derived from a closo deltahedron by removal of a relatively high degree vertex, as predicted by the Wade-Mingos rules. They relate to isoelectronic species found experimentally, e.g., B(8)H(12) and R(4)C(4)B(4)H(4) for B(8)H(8)(4-) and C(2)B(9)H(11)(2-) for B(11)H(11)(4-). Three structures were found for B(11)H(11)(6-) with arachno type geometry having two open faces in accord with the Wade-Mingos rules.     

First principles study on the solvation and structure of C2O4(2-)(H2O)n, n = 6-12

The structures and energies of hydrated oxalate clusters, C2O4(2-)(H2O)n, n = 6-12, are obtained by density functional theory (DFT) calculations and compared to SO4(2-)(H2O)n. Although the evolution of the cluster structure with size is similar to that of SO4(2-)(H2O)n, there are a number of important and distinctive futures in C2O4(2-)(H2O)n, including the separation of the two charges due to the C-C bond in C2O4(2-), the lower symmetry around C2O4(2-), and the torsion along the C-C bond, that affect both the structure and the solvation energy. The solvation dynamics for the isomers of C2O4(2-)(H2O)12 are also examined by DFT based ab initio molecular dynamics.     

Theoretical Study of the Molecular Electrostatic Potential of C_(50)

1 INTRODUCTION All fullerenes made so far obey the isolated pentagon (IPR)[1], which governs the stability of fullerenes comprising hexagons and exact 12 pen- tagons. Smaller fullerenes, which violate the IPR, are predicted to have high instability and especially difficult isolation due to their condensed pentagons and increased strain. The production of smaller fullerene C36 has been reported[2]. However, the definite characterization of a C36-based solid is in doubt. Moreover, variou…     

Computational study of the Stone-Wales transformation in C36

The transition of the D6h neutral and charged isomers to D2d isomers of C36 via Stone-Wales transformation has been studied by means of the hybrid density functional method (B3LYP). The results show that the transition state (TS) and reaction pathway could be identified for the rearrangement from C36-D6h to C36-D2d on the potential energy surface. We found that the neutral and charged transition states all have C2 molecular point group symmetry with the two migrating carbon atoms remaining close to the fullerene surface. The other kind of possible TS with a carbene-like structure along the stepwise reaction path does not exist as a stationary point with the density functionals utilized here. The classical barriers are 6.23 eV through the neutral TS, 6.37 eV through the anionic TS, and 6.29 eV through the cationic TS at the B3LYP/6-31G level of theory.     

Cyclic boron clusters enclosing planar hypercoordinate cobalt, iron, and nickel

Planar cyclic boron clusters with cobalt, iron, and nickel atoms at their centerssinglet D(8h) CoB(8)(-), D(9h) FeB(9)(-), CoB(9), and NiB(9)(+)are computed to be stable minima at the BP86/TZVPP DFT level. Stochastic searches of the singlet and triplet potential energy surfaces show the planar hypercoordinate D(8h) CoB(8)(-) (1) and D(9h) FeB(9)(-) (2) singlet isomers to be the global minima. Their double aromatic character with 6 pi and 10 radial electrons is documented by detailed NICS(zz) grid and CMO-NICS(zz) analyses at PW91/TZVPP. These results encourage gas phase investigations of these two exotic anions. Although isoelectronic with D(9h) FeB(9)(-) (2), CoB(9) and NiB(9)(+) prefer nonplanar structures, triplet 3-aT for the former and singlet 4-a for the latter.