Small ScCn cyclic clusters: a density functional study of their structure and stability

A theoretical study of the ScCn, ScCn+, and ScCn- (n = 1-10) cyclic clusters has been carried out employing the B3LYP density functional method. Predictions for several molecular properties that could help in their possible experimental characterization, such as equilibrium geometries, electronic structures, dipole moments, and vibrational frequencies, are reported. All ScCn cyclic clusters are predicted to have doublet ground states. For cationic clusters the ground state is alternate between singlets (n-even species) and triplets (n-odd members). In the case of anionic clusters the singlet-triplet separation is relatively small, with the singlets being favored in most cases. In general, even-odd parity effects are also observed for different properties, such as incremental binding energies, ionization energies, and electron affinities. For all neutral, cationic, and anionic clusters it is found that cyclic species are more stable than their open-chain counterparts. Therefore, cyclic structures are the most interesting possible targets for an experimental search of scandium-doped carbon clusters.     

Geometries and stabilities of the carbon clusters with the rhodium impurity: a computational investigation

A density functional study of the RhCn(n = 1-6) clusters with different spin states has been carried out systematically by using the B3LYP/Lan2DZ method. The equilibrium geometries associated with total energies and natural populations of RhCn (n = 1-6) clusters are calculated and presented. Stabilities and electronic properties are discussed in detail. The relative stabilities in term of the calculated fragmentation energies show that the lowest-energy RhCn clusters with rhodium atom being located at terminal of carbon chain are the linear geometries and the ground states of the RhCn clusters alternate between doublet (for n-odd members) and quartet (for n-even members) states. Furthermore, the calculated fragmentation energies of the RhCn show strong even-odd alternations: the RhCn clusters with an odd number of carbon atoms are more stable than those with an even number ones. In addition, we comment on the charge transfer and chemical bonding properties within the clusters.     

Au-doped carbon clusters AuC n with n = 1–11: a theoretical investigation

The hybrid HF/DFT method B3LYP has been employed to investigate the geometrical and electronic structures of AuC _n (n = 1–11) clusters. The properties such as geometrical parameters and electronic energies are determined for open-chain and cyclic species. Our results indicate that the open-chain structures with low spin states (doublet) are more stable than the cyclic ones for the small sizes clusters (n ≤ 9), as the cluster sizes increase (n = 10, 11), the cyclic species are more stable. The incremental binding energies show a smooth even–odd alternation phenomenon for open-chain species, n-even (n is the numbers of C atom in the clusters) species have the stronger stabilities relative to the adjacent odd-numbered ones. In addition, the most favorable dissociation channels are determined by calculating the fragmentation energies accompanying various possible pathways. The studied clusters incline to be dissociated to Au + C _n and AuC _n?3 + C₃ fragments.     

Structures, spectra, and energies of niobium clusters from Nb13 to Nb20

A comprehensive theoretical investigation on structures and properties of niobium clusters in the range from 13 to 20 atoms, in three different charged states, is performed by using the BPW91 and M06 functionals and the cc-pVDZ-PP basis set. These species are predicted to prefer low spin ground state, i.e., singlet (for even electron) and doublet (for odd electron) systems. In terms of growth mechanism, a compact structure with one Nb encapsulated by a cage formed from five and six triangles is found to be favored over an icosahedral evolution. Unlike many 3d metals, whose volumes are much smaller, 13 and 19 Nb atoms clusters do not exist as icosahedra and double-icosahedra. A distinct case is Nb(15) as it bears a slightly distorted bcc structure. For some systems, several lower lying isomers are computed to be so close in energy that DFT computations cannot clearly establish their ground electronic states. The existence of structural isomers with comparable energy content is established for Nb(n) species with n = 13, 18, 19, and 20 in both neutral and charged states. The vibrational (IR) spectra are also calculated. While the spectra of smaller systems are strongly dependent on addition or removal of an electron from the neutral, the spectra of the larger size clusters are mostly independent of the charged state. The neutrals and their corresponding ions usually have a quite similar IR pattern. Electron affinities (EA), ionization energies (IE), average binding energies, dissociation energies, and frontier orbital energy gaps are evaluated. The computed EAs and IEs are generally in fair agreement with experiment. The Nb(15) system is observed to be stable and it can form a highly symmetric structure in all charged states with both open and closed electron shells.     

Theoretical study of the electronic states of Nb4, Nb5 clusters and their anions (Nb4-,Nb5-)

Geometries and energy separations of the various low-lying electronic states of Nb(n) and Nb(n) (-) (n=4,5) clusters with various structural arrangements have been investigated. The complete active space multiconfiguration self-consistent field method followed by multireference singles and doubles configuration interaction (MRSDCI) calculations that included up to 52x10(6) configuration spin functions have been used to compute several electronic states of these clusters. The ground states of both Nb(4) ((1)A('), pyramidal) and Nb(4) (-) ((2)B(3g), rhombus) are low-spin states at the MRSDCI level. The ground state of Nb(5) cluster is a doublet with a distorted trigonal bipyramid (DTB) structure. The anionic cluster of Nb(5) has two competitive ground states with singlet and triplet multiplicities (DTB). The low-lying electronic states of these clusters have been found to be distorted due to Jahn-Teller effect. On the basis of the energy separations of our computed electronic states of Nb(4) and Nb(5), we have assigned the observed photoelectron spectrum of Nb(n) (-) (n=4,5) clusters. We have also compared our MRSDCI results with density functional calculations. The electron affinity, ionization potential, dissociation and atomization energies of Nb(4) and Nb(5) have been calculated and the results have been found to be in excellent agreement with the experiment.     

Trends in structural, electronic and energetic properties of bimetallic vanadium-gold clusters Au(n)V with n = 1-14

A systematic quantum chemical investigation on the electronic, geometric and energetic properties of Au(n)V clusters with n = 1-14 in both neutral and anionic states is performed using BP86/cc-pVTZ-PP calculations. Most clusters having an even number of electrons prefer a high spin state. For odd-electron systems, a quartet state is consistently favoured as the ground state up to Au(8)V. The larger sized Au(10)V, Au(12)V and Au(14)V prefer a doublet state. The clusters prefer 2D geometries up to Au(8)V involving a weak charge transfer. The larger systems bear 3D conformations with a more effective electron transfer from Au to V. The lowest-energy structure of a size Au(n)V is built upon the most stable form of Au(n-1)V. During the growth, V is endohedrally doped in order to maximize its coordination numbers and augment the charge transfer. Energetic properties, including the binding energies, embedding energies and second-order energy differences, show that the presence of a V atom enhances considerably the thermodynamic stability of odd-numbered gold clusters but reduces that of even-numbered systems. The atomic shape has an apparently more important effect on the clusters stability than the electronic structure. Especially, if both atomic shape and electronic condition are satisfied, the resulting cluster becomes particularly stable such as the anion Au(12)V(-), which can thus combine with the cation Au(+) to form a superatomic molecule of the type [Au(12)V]Au. Numerous lower-lying electronic states of these clusters are very close in energy, in such a way that DFT computations cannot clearly establish their ground electronic states. Calculated results demonstrate the existence of structural isomers with comparable energy content for several species including Au(9)V, Au(10)V, Au(13)V and Au(14)V.     

Excess electron localization sites in neutral water clusters

We present approximate pseudopotential quantum-mechanical calculations of the excess electron states of equilibrated neutral water clusters sampled by classical molecular dynamics simulations. The internal energy of the clusters are representative of those present at temperatures of 200 and 300 K. Correlated electronic structure calculations are used to validate the pseudopotential for this purpose. We find that the neutral clusters support localized, bound excess electron ground states in about 50% of the configurations for the smallest cluster size studied (n = 20), and in almost all configurations for larger clusters (n > 66). The state is always exterior to the molecular frame, forming typically a diffuse surface state. Both cluster size and temperature dependence of energetic and structural properties of the clusters and the electron distribution are explored. We show that the stabilization of the electron is strongly correlated with the preexisting instantaneous dipole moment of the neutral clusters, and its ground state energy is reflected in the electronic radius. The findings are consistent with electron attachment via an initial surface state. The hypothetical spectral dynamics following such attachment is also discussed.     

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.     

Transverse acoustic modes of biogenic and alpha,omega-polyamines: a study by inelastic neutron scattering and Raman spectroscopies coupled to DFT calculations

A complete analysis of the transverse acoustic modes (TAMs) for the homologous series of alpha,omega-diamines (H2N(CH2)nNH2) (n = 2-10, n = 12) as well as for the biogenic polyamines spermidine and spermine was undertaken, by Raman and inelastic neutron scattering (INS) spectroscopies combined with density functional theory (DFT) calculations. A complete assignment of the whole set of TAMs was carried out, for both the undeuterated and N-deuterated species. 1,2-Diaminoethane was found to display exceptional behavior, probably due to the formation of dimers in the solid state. An n-even/n-odd dependence of the low frequency INS pattern was observed for these polyamines. The very good accordance between their INS experimental TAMs and the ones previously reported for the corresponding n-alkanes suggest a close conformational similarity between these systems.     

Optical properties of (GaAs)n clusters (n = 2-16)

The electronic and geometrical structures of the lowest triplet states of (GaAs) n clusters ( n = 2-16) are studied using density functional theory with generalized gradient approximation (DFT-GGA). It is found that the triplet-state geometries are different from the corresponding singlet-state geometries; for n = 2-8, 10, and 11, the triplets and singlets have different topologies, while the (GaAs) 9, (GaAs) 12, (GaAs) 15, and (GaAs) 16 triplets possess a reduced symmetry, due to Jahn-Teller distortions. Except for GaAs, the singlet states are the ground states. Excitation energies and oscillator strengths are computed for excitations from the ground state to ten singlet states of all (GaAs) n clusters using time-dependent density functional theory. The adiabatic singlet-triplet gap is compared to the vertical gap, and the difference in the eigenvalues of the highest-occupied and lowest-unoccupied molecular orbitals (the HOMO-LUMO gap). While these three values show large oscillations for small n, they approach each other as the cluster size grows. Thus, the HOMO-LUMO gap computed using the DFT-GGA approach presents a rather reliable estimate of the adiabatic singlet-triplet gap.     

Probing the structural and electronic properties of small vanadium monoxide clusters

The structural evolution and bonding of a series of early transition-metal oxide clusters, V(n)O(q) (n = 3-9, q = 0,-1), have been investigated with the aid of previous photoelectron spectroscopy (PES) and theoretical calculations. For each vanadium monoxide cluster, many low-lying isomers are generated using the Saunders "Kick" global minimum stochastic search method. Theoretical electron detachment energies (both vertical and adiabatic) were compared with the experimental measurements to verify the ground states of the vanadium monoxide clusters obtained from the DFT calculations. The results demonstrate that the combination of photoelectron spectroscopy experiments and DFT calculation is not only powerful for obtaining the electronic and atomic structures of size-selected clusters, but also valuable in resolving structurally and energetically close isomers. The second difference energies and adsorption energies as a function of the cluster size exhibit a pronounced even-odd alternation phenomenon. The adsorption energies of one O atom on the anionic (6.64 → 8.16 eV) and neutral (6.41 → 8.13 eV) host vanadium clusters are shown to be surprisingly high, suggesting strong capabilities to activate O by structural defects in vanadium oxides.     

Electronic structure calculations of small Al n (n=2–8) clusters

The electronic states of small Al _n (n=2–8) clusters have been calculated with a relativistic ab-initio MO-LCAO Dirac-Fock-Slater method using numerical atomic DFS wave-functions. The excitation energies were obtained from a ground state calculation of neutral clusters, and in addition from negative clusters charged by half an electron in order to account for part of the relaxation. These energies are compared with experimental photo-electron spectra.     

Ground state, growth, and electronic properties of small lanthanum clusters

The DMol cluster method based on density-functional theory has been employed to study the structural stability and electronic structure of La(n) (n=2-14) clusters. The ground states have been found out for lanthanum clusters. The Jahn-Teller effect plays an important role in this process because there are many isomers near the ground state. The magnetism is not sensitive to interatomic spacing when the change of interatomic spacing is in a small range. Lanthanum clusters grow in an icosahedral pattern. The results of the mean binding energy, of the second derivative of binding energy, and of the formation energy show strong odd-even alternation and that 7- and 13-atom clusters are magic. Further, the HOMO-LUMO gap, the mean nearest bond lengths, and the mean magnetic moments suggest that the convergence to bulk is slow and it shows an oscillatory behavior for small lanthanum clusters.     

Quantum chemical modeling of photoadsorption properties of the nitrogen-vacancy point defect in diamond

Quantum chemical calculations of geometric and electronic structure and vertical transition energies for several low-lying excited states of the neutral and negatively charged nitrogen-vacancy point defect in diamond (NV(0) and NV(-)) have been performed employing various theoretical methods and basis sets and using finite model NC(n)H(m) clusters. Unpaired electrons in the ground doublet state of NV(0) and triplet state of NV(-) are found to be localized mainly on three carbon atoms around the vacancy and the electronic density on the nitrogen and rest of C atoms is only weakly disturbed. The lowest excited states involve different electronic distributions on molecular orbitals localized close to the vacancy and their wave functions exhibit a strong multireference character with significant contributions from diffuse functions. CASSCF calculations underestimate excitation energies for the anionic defect and overestimate those for the neutral system. The inclusion of dynamic electronic correlation at the CASPT2 level leads to a reasonable agreement (within 0.25 eV) of the calculated transition energy to the lowest excited state with experiment for both systems. Several excited states for NV(-) are found in the energy range of 2-3 eV, but only for the 1(3)E and 5(3)E states the excitation probabilities from the ground state are significant, with the first absorption band calculated at approximately 1.9 eV and the second lying 0.8-1 eV higher in energy than the first one. For NV(0), we predict the following order of electronic states: 1(2)E (0.0), 1(2)A(2) (approximately 2.4 eV), 2(2)E (2.7-2.8 eV), 1(2)A(1), 3(2)E (approximately 3.2 eV and higher).     

Geometric, electronic, and bonding properties of AuNM (N = 1-7, M = Ni, Pd, Pt) clusters

Employing first-principles methods, based on density functional theory, we report the ground state geometric and electronic structures of gold clusters doped with platinum group atoms, Au(N)M (N = 1-7, M = Ni, Pd, Pt). The stability and electronic properties of Ni-doped gold clusters are similar to that of pure gold clusters with an enhancement of bond strength. Due to the strong d-d or s-d interplay between impurities and gold atoms originating in the relativistic effects and unique properties of dopant delocalized s-electrons in Pd- and Pt-doped gold clusters, the dopant atoms markedly change the geometric and electronic properties of gold clusters, and stronger bond energies are found in Pt-doped clusters. The Mulliken populations analysis of impurities and detailed decompositions of bond energies as well as a variety of density of states of the most stable dopant gold clusters are given to understand the different effects of individual dopant atom on bonding and electronic properties of dopant gold clusters. From the electronic properties of dopant gold clusters, the different chemical reactivity toward O(2), CO, or NO molecule is predicted in transition metal-doped gold clusters compared to pure gold clusters.     

Strong spin-orbit effects in small Pt clusters: geometric structure, magnetic isomers and anisotropy

Ab initio density functional calculations including spin-orbit coupling (SOC) have been performed for Pt(n), n = 2-6 clusters. The strong SOC tends to stabilize planar structures for n = 2-5, whereas for clusters consisting of six atoms, three-dimensional structures remain preferred. SOC leads to the formation of large orbital magnetic moments and to a mixing of different spin states. Due to the spin-mixing the total magnetic moment may be larger or smaller than the spin moment in the absence of SOC. Both spin and orbital moments are found to be anisotropic. Because of the strong SOC the energy differences between coexisting magnetic isomers can be comparable to or even smaller than their magnetic anisotropy energies. In this case the lowest barrier for magnetization reversal can be determined by a magnetic isomer which is different from the ground state configuration.     

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.     

Structural and electronic properties of boron-doped lithium clusters: ab initio and DFT studies

The lowest-energy structures and electronic properties of the BLi(n) (n = 1-7) clusters are reported using the B3LYP, MP2, and CCSD(T) methods with the aug-cc-pVDZ basis set. Though the results at the B3LYP level agree well with those at the CCSD(T) level, the MP2 method is rather unsatisfactory. The first three-dimensional ground state in the BLi(n) clusters occurs for BLi(4), and the impurity B atom is seen to be trapped in a Li cage from the BLi(6) cluster onwards. The evolution of the binding energies, vertical ionization potentials, and polarizability with size of cluster shows the BLi(5) cluster to be most stable among the BLi(n) clusters. Besides, the BLi(5) cluster is also found to have the largest reaction enthalpy (49.8 kcal/mol) upon losing a Li atom, which is different from the previous prediction. The unique stability of the 8-valence electron BLi(5) can be understood from the cluster electronic shell model (CSM). However, in contradiction to the prediction of the CSM, the 2s level is filled prior to the 1d level in the BLi(n) clusters.     

On the triplet ground state of tetrahedral X4 clusters (X = Li, Na, K, Cu)

The lowest electronic state of distorted tetrahedral X(4) clusters (with X = Li, Na, K, Cu) is studied at coupled-cluster level using high-quality atomic basis sets. The ground state is found to have a triplet spin symmetry for this kind of geometry and for all the considered atomic species. The equilibrium geometries correspond to Jahn-Teller-distorted oblate tetrahedra having D(2d) symmetry, and tetrahedric structures are local minima on the potential-energy surfaces for the triplet states. Their energies lie between 0.2 eV (for the K(4) cluster) and 0.9 eV (for Cu(4)) above the absolute minimum of the corresponding systems, which is a spin singlet having a rhombus geometry.     

Structure of small TiCn clusters: A theoretical study

A theoretical study of the TiC_n (n = 1–8) clusters has been carried out at the B3LYP/6-311+G(d) level. Molecular properties for three different isomers, namely linear, cyclic, and fan species, have been determined. The fan isomers, where the titanium atom is essentially side-bonded to the entire C_n unit, are predicted to be more stable than both linear and cyclic isomers. Only for the largest studied species, TiC₈, the cyclic isomer is located lower in energy. An even–odd parity effect in the incremental binding energies is observed for the three isomers, n-even species being in general more stable for linear and fan isomers, whereas for the cyclic species n-odd clusters are favoured. A topological analysis of the electronic charge density shows that all cyclic isomers correspond to true monocyclic rings, whereas for the fan species a variety of different connectivities has been observed.