Binary clusters AuPt and Au6Pt: structure and reactivity within density functional theory

Within density functional theory with the general gradient approximation for the exchange and correlation, the bimetallic clusters AuPt and Au(6)Pt have been studied for their structure and reactivity. The bond strength of AuPt lies between those of Au(2) and Pt(2), and it is closer to that of Au(2). The Pt atom is the reactive center in both AuPt and AuPt(+) according to electronic structure analysis. AuPt(+) is more stable than AuPt. Au(6)Pt prefers electronic states with low multiplicity. The most stable conformation of Au(6)Pt is a singlet and has quasi-planar hexagonal frame with Pt lying at the hexagonal center. The doping of Pt in Au cluster enhances the chemical regioselectivity of the Au cluster. The Pt atom essentially serves as electron donor and the Au atoms bonded to the Pt atom acts as electron acceptor in Au(6)Pt. The lowest triplet of edge-capped rhombus Au(6)Pt clusters is readily accessible with very small singlet-triplet energy gap (0.32 eV). O(2) prefers to adsorb on Au and CO prefers to adsorb on Pt. O(2) and CO have stronger adsorption on AuPt than they do on Au(6)Pt. CO has a much stronger adsorption on AuPt bimetallic cluster than O(2) does. The adsorption of CO on Pt modifies the geometry of AuPt bimetallic clusters.     

Determination of structures, stabilities, and electronic properties for bimetallic cesium-doped gold clusters: a density functional theory study

The equilibrium geometric structures, stabilities, and electronic properties of bimetallic Au(n)Cs (n = 1-10) and pure gold Au(n) (n ≤ 11) clusters have been systematically investigated by using density functional theory with meta-generalized gradient approximation. The optimized geometries show that one Au atom capped on Au(n-1)Cs structures and Cs atom capped Au(n) structures for different sized Au(n)Cs (n = 1-10) clusters are two dominant growth patterns. Theoretical calculated results indicate that the most stable isomers have three-dimensional structures at n = 4 and 6-10. Averaged atomic binding energies, fragmentation energies, and second-order difference of energies exhibit a pronounced even-odd alternations phenomenon. The same even-odd alternations are found in the highest occupied-lowest unoccupied molecular orbital gaps, vertical ionization potential, vertical electron affinity, and hardnesses. In addition, it is found that the charge in corresponding Au(n)Cs clusters transfers from the Cs atom to the Au(n) host in the range of 0.851-1.036 electrons.     

Towards rational syntheses of the elusive metallocarbohedrenes: density functional prescriptions for electronic and geometric structures

The metallocarbohedrenes are binary molecular clusters containing metal atoms linked by acetylenediide C(2) groups. Hundreds of these molecules have been generated, detected and reacted in the gas phase since the prototype, [Ti(8)(C(2))(6)], was reported in 1992, but none has yet been synthesised pure in bulk: the time gap between detection and preparation increasingly exceeds that of the fullerenes. We report here the results of density functional calculations of geometrical and electronic structure of more than 150 postulated metallocarbohedrenes, stabilised by terminal ligation, in order to recognise the more electronically favourable and less reactive targets. At least 38 metallocarbohedrenes have been identified as having a spin singlet ground state, with a relatively large (> 0.5 eV) energy gap between HOMO and LUMO, and an appropriate HOMO energy. In addition, a considerable number of electronically stable metallocarbohedrenes are predicted to have highly paramagnetic ground states, potentially useful in molecular magnetism. The geometrical principles for enclosing but unstrained coordination of metal sites by terminal ligands are outlined. Mechanisms for rational syntheses are considered in the context of reaction type and precursor selection, including issues of oxidation and reduction, and kinetic versus thermodynamic control. This leads to many diverse reactions suggested for the rational syntheses of metallocarbohedrenes. Some preliminary experimental results are presented.     

Stable structures and absorption spectra for SixOy molecular clusters using density functional theory

Structural Chemistry - Calculations are presented of vibrational absorption spectra for energy minimized structures of SixOy molecular clusters using density functional theory (DFT). The size of...     

Effect of adsorption site, size, and composition of Pt/Au bimetallic clusters on the CO frequency: a density functional theory study

Density functional theory (DFT) calculations were performed to investigate the C-O stretching frequency changes when a CO molecule was adsorbed to Pt/Au clusters of 2-4 atoms. Our calculations show that the adsorption site is the most sensitive quantity to the C-O stretching frequency shifts. All the bridge site adsorptions yield a CO frequency band of 1737-1927 cm-1 with the CO bond distance of 1.167-1.204 A regardless of cluster composition and size, and all the atop site adsorptions yield a CO frequency band of 2000-2091 cm-1 with the CO bond distance of 1.151-1.167 A. More detailed analysis of the two frequency bands shows that each band may consist of two emerging subbands with the lower frequencies corresponding to the CO adsorption to Pt atoms and the higher frequencies to the CO adsorption to Au atoms. The insensitivity of the CO frequency shift to the cluster size indicates that the trend discussed here for small clusters may be used to interpret the experimental observations for nanoparticles. Our results also illustrated that the Fourier transform infrared spectroscopy measurement may be used as a sensitive tool to identify adsorption sites of the Pt/Au nanoparticles using CO adsorption as the probe.     

Methane activation on Pt and Pt4: a density functional theory study

The activation mechanisms of a methane molecule on a Pt atom (CH4-Pt) and on a Pt tetramer (CH4-Pt4) were investigated using density functional theory (B3LYP and PW91) calculations. The results from these two functionals are different mostly in predicting the reaction barrier, in particular for the CH4-Pt system. A new lower energy pathway was identified for the CH4 dehydrogenation on a Pt atom. In the new pathway, the PtCH2 + H2 products were formed via a transition state, in which the Pt atom forms a complex with carbene and both dissociated hydrogen atoms. We report here the first theoretical study of methane activation on a Pt4 cluster. Among the five single steps toward dehydrogenation, our results show that the rate-limiting step is the third step, that is, breaking the second C-H bond, which requires overcoming an energy barrier of 28 kcal/mol. On the other hand, the cleavage of the first C-H bond, that is, the first reaction step, requires overcoming an energy barrier of 4 kcal/mol.     

Atomistic and electronic structure of bimetallic cobalt/rhenium clusters from density functional theory calculations

We have carried out computational density functional investigations of Co I Re J (J=0,1,2; I+J=14) metal atom clusters. Through thorough optimization of geometry, spin polarization, and electronic configuration, the most stable structures for each cluster have been identified. While the global minima are found to be well defined and energetically well separated from other local minima, the study reveals a plethora of different structures and symmetries only moderately higher in energy. A key point of interest is the effect of doping the cobalt clusters with rhenium. Aside from significant structural reorganizations, rhenium is found to stabilize the clusters and couple down the spin. Furthermore, the most stable clusters comprise highly coordinated rhenium and, in the case of Co 12 Re 2, Re-Re bonding. Our results are compared to earlier experimental and computational data.     

Methanol activation catalyzed by Pt7, Pt3Cu4, and Cu7 clusters: A density functional theory investigation

Metal clusters were considered as excellent catalysts for methanol dissociation. In this work, two main decomposition mechanisms of methanol on Pt₇, Pt₃Cu₄, and Cu₇ clusters were investigated by the density functional theory. One was methanol direct dehydrogenation, and the other was non‐CO‐involved oxidation. Stable adsorption configurations, elementary reaction barriers, the potential energy surface (PES), and the charge analysis were elucidated. The results showed that on Pt₇ cluster, methanol was favorable for direct decomposition. On Pt₃Cu₄ and Cu₇ clusters, methanol was inclined to the pathway of non‐CO‐involved oxidation. All the transition‐state energies and the final‐state energies were related in a linear, including those for the clusters. The results may be useful for computational design and catalysts optimization.     

Acrolein hydrogenation on Pt(211) and Au(211) surfaces: a density functional theory study

Partial hydrogenation of acrolein, the simplest α,β-unsaturated aldehyde, is not only a model system to understand the selectivity in heterogeneous catalysis, but also technologically an important reaction. In this work, the reaction on Pt(211) and Au(211) surfaces is thoroughly investigated using density functional theory calculations. The formation routes of three partial hydrogenation products, namely propenol, propanal and enol, on both metals are studied. It is found that the pathway to produce enol is kinetically favoured on Pt while on Au the route of forming propenol is preferred. Our calculations also show that the propanal formation follows an indirect pathway on Pt(211). An energy decomposition method to analyze the barrier is utilized to understand the selectivities at Pt(211) and Au(211), which reveals that the interaction energies between the reactants involved in the transition states play a key role in determining the selectivity difference.     

Differentiability of Lieb functional in electronic density functional theory

A solid understanding of the Lieb functional F_L is important because of its centrality in the foundations of electronic density functional theory. A basic question is whether directional derivatives of F_L at an ensemble‐V‐representable density are given by (minus) the potential. A widely accepted purported proof that F_L is Gâteaux differentiable at EV‐representable densities would say, “yes.” But that proof is fallacious, as shown here. F_L is not Gâteaux differentiable in the normal sense, nor is it continuous. By means of a constructive approach, however, we are able to show that the derivative of F_L at an EV‐representable density ρ₀ in the direction of ρ₁ is given by the potential if ρ₀ and ρ₁ are everywhere strictly greater than zero, and they and the ground state wave function have square integrable derivatives through second order. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Atomic and electronic structures of neutral and charged Pbn clusters (n=2-15): theoretical investigation based on density functional theory

The geometric and electronic structures of the Pbn+ clusters (n=2-15) have been investigated and compared with neutral clusters. The search for several low-lying isomers was carried out under the framework of the density functional theory formalism using the generalized gradient approximation for the exchange correlation energy. The wave functions were expanded using a plane wave basis set and the electron-ion interactions have been described by the projector augmented wave method. The ground state geometries of the singly positively charged Pbn+ clusters showed compact growth pattern as those observed for neutrals with small local distortions. Based on the total energy of the lowest energy isomers, a systematic analysis was carried out to obtain the physicochemical properties, viz., binding energy, second order difference in energy, and fragmentation behavior. It is found that n=4, 7, 10, and 13 clusters are more stable than their neighbors, reflecting good agreement with experimental observation. The chemical stability of these clusters was analyzed by evaluating their energy gap between the highest occupied and lowest unoccupied molecular orbitals and adiabatic ionization potentials. The results revealed that, although Pb13 showed higher stability from the total energy analysis, its energy gap and ionization potential do not follow the trend. Albeit of higher stability in terms of binding energy, the lower ionization potential of Pb13 is interesting which has been explained based on its electronic structure through the density of states and electron shell filling model of spherical clusters.     

Molecular analysis of water clusters: Calculation of the cluster structures and vibrational spectrum using density functional theory

Density functional theory (DFT) is applied to obtain absorption spectra at THz frequencies for molecular clusters of H₂O. The vibrational modes of the clusters are calculated. Coupling among molecular vibrational modes explains their spectral features associated with THz excitation. THz excitation is associated with vibrational frequencies which are here calculated within the DFT approximation of electronic states. This is done for both isolated molecules and collections of molecules in a cluster. The principal result of the paper is that a crystal-like cluster of 38 water molecules together with a continuum solvent background is sufficient to replicate well the experimental vibrational frequencies.     

Comparison between the geometric and electronic structures and reactivities of [FeNO]7 and [FeO2]8 complexes: a density functional theory study

In a previous study, we analyzed the electronic structure of S = 3/2 [FeNO](7) model complexes [Brown et al. J. Am. Chem. Soc. 1995, 117, 715-732]. The combined spectroscopic data and SCF-X alpha-SW electronic structure calculations are best described in terms of Fe(III) (S = 5/2) antiferromagnetically coupled to NO(-) (S = 1). Many nitrosyl derivatives of non-heme iron enzymes have spectroscopic properties similar to those of these model complexes. These NO derivatives can serve as stable analogues of highly labile oxygen intermediates. It is thus essential to establish a reliable density functional theory (DFT) methodology for the geometry and energetics of [FeNO](7) complexes, based on detailed experimental data. This methodology can then be extended to the study of [FeO(2)](8) complexes, followed by investigations into the reaction mechanisms of non-heme iron enzymes. Here, we have used the model complex Fe(Me(3)TACN)(NO)(N(3))(2) as an experimental marker and determined that a pure density functional BP86 with 10% hybrid character and a mixed triple-zeta/double-zeta basis set lead to agreement between experimental and computational data. This methodology is then applied to optimize the hypothetical Fe(Me(3)TACN)(O(2))(N(3))(2) complex, where the NO moiety is replaced by O(2). The main geometric differences are an elongated Fe[bond]O(2) and a steeper Fe[bond]O[bond]O angle in the [FeO(2)](8) complex. The electronic structure of [FeO(2)](8) corresponds to Fe(III) (S = 5/2) antiferromagnetically coupled to O(2)(-) (S = 1/2), and, consistent with the extended bond length, the [FeO(2)](8) unit has only one Fe(III)-O(2)(-) bonding interaction, while the [FeNO](7) unit has both sigma and pi type Fe(III)-NO(-) bonds. This is in agreement with experiment as NO forms a more stable Fe(III)-NO(-) adduct relative to O(2)(-). Although NO is, in fact, harder to reduce, the resultant NO(-) species forms a more stable bond to Fe(III) relative to O(2)(-) due to the different bonding interactions.     

Growth pattern and electronic properties of acetonitrile clusters: a density functional study

We report a systematic theoretical study on the growth pattern and electronic properties of acetonitrile clusters [(CH(3)CN)(n) (n = 1, 9, 12)] using density functional approach at the B3LYP6-31++G(d,p) level. Although we have considered a large number of configurations for each cluster, the stability of the lowest energy isomer was verified from the Hessian calculation. It is found that the lowest energy isomer of the dimer adopts an antiparallel configuration. For trimer and tetramer, cyclic ring structures were found to be favored over the dipole stabilized structure. In general, it is found that the intermolecular CH...N interactions play a significant role in the stabilization of the cyclic layered geometry of acetonitrile clusters. A critical comparison between trimer and tetramer clusters suggests that the three member cyclic ring is more stable than four member rings. The growth motif for larger clusters (n = 5-9, 12) follows a layered pattern consisting of three or four membered rings, which, in fact, is used as the building block. Based on the stability analysis, it is found that clusters with an even number of molecular entities are more stable than the odd clusters, except trimer and nonamer. The exceptional stability of these two clusters is attributed to the formation of trimembered cyclic rings, which have been found to form the building blocks for larger clusters.     

Geometries, stabilities, and electronic properties of small anion Mg-doped gold clusters: a density functional theory study

First-principle density functional theory is used for studying the anion gold clusters doped with magnesium atom. By performing geometry optimizations, the equilibrium geometries, relative stabilities, and electronic and magnetic properties of [Au(n)Mg]? (n = 1-8) clusters have been investigated systematically in comparison with pure gold clusters. The results show that doping with a single Mg atom dramatically affects the geometries of the ground-state Au(n+1)? clusters for n = 2-7. Here, the relative stabilities are investigated in terms of the calculated fragmentation energies, second-order difference of energies, and highest occupied?lowest unoccupied molecular orbital energy gaps, manifesting that the ground-state [Au(n)Mg]? and Au(n+1)? clusters with odd-number gold atoms have a higher relative stability. In particular, it should be noted that the [Au?Mg]? cluster has the most enhanced chemical stability. The natural population analysis reveals that the charges in [Au(n)Mg]? (n = 2-8) clusters transfer from the Mg atom to the Au frames. In addition, the total magnetic moments of [Au(n)Mg]? clusters exhibit an odd-even oscillation as a function of cluster size, and the magnetic effects mainly come from the Au atoms.     

Paramagnetic NMR spectroscopy and density functional calculations in the analysis of the geometric and electronic structures of iron-sulfur proteins

Paramagnetic NMR spectroscopy has been underutilized in the study of metalloproteins. One difficulty of the technique is that paramagnetic relaxation broadens signals from nuclei near paramagnetic centers. In systems with low electronic relaxation rates, this makes such signals difficult to observe or impossible to assign by traditional methods. We show how the challenges of detecting and assigning signals from nuclei near the metal center can be overcome through the combination of uniform and selective 2H, 13C, and 15N isotopic labeling with NMR experiments that utilize direct one-dimensional (2H, 13C, and 15N) and two-dimensional (13C-X) detection. We have developed methods for calculating NMR chemical shifts and relaxation rates by density functional theory (DFT) approaches. We use the correspondence between experimental NMR parameters and those calculated from structural models of iron-sulfur clusters derived from X-ray crystallography to validate the computational approach and to investigate how structural differences are manifested in these values. We have applied this strategy to three iron-sulfur proteins: Clostridium pasteurianum rubredoxin, Anabaena [2Fe-2S] ferredoxin, and human [2Fe-2S] ferredoxin. Provided that an accurate structural model of the iron-sulfur cluster and surrounding residues is available from diffraction data, our results show that DFT calculations can return NMR observables with excellent accuracy. This suggests that it might be possible to use calculations to refine structures or to generate structural models of active sites when crystal structures are unavailable. The approach has yielded insights into the electronic structures of these iron-sulfur proteins. In rubredoxin, the results show that substantial unpaired electron spin is delocalized across NH...S hydrogen bonds and that the reduction potential can be changed by 77 mV simply by altering the strength of one of these hydrogen bonds. In reduced [2Fe-2S] ferredoxins, hyperfine shift data have provided quantitative information on the degree of valence trapping. The approach described here for iron-sulfur proteins offers new avenues for detailed studies of these and other metalloprotein systems.     

Mechanisms of Staudinger reactions within density functional theory

The Staudinger reactions of substituted phosphanes and azides have been investigated by using density functional theory. Four different initial reaction mechanisms have been found. All systems studied go through a cis-transition state rather than a trans-transition state or a one-step transition state. The one-step pathway of the phosphorus atom attacking the substituted nitrogen atom is always unfavorable energetically. Depending on the substituents on the azide and the phosphane, the reaction mechanism with the lowest initial reaction barrier can be classified into three categories: (1). like the parent reaction, PH(3) + N(3)H, the reaction goes through a cis-transition state, approaches a cis-intermediate, overcomes a PN-bond-shifting transition state, reaches a four-membered ring intermediate, dissociates N(2) by overcoming a small barrier, and results in the final products: N(2) and a phosphazene; (2). once reaching the cis-intermediate, the reaction goes through the N(2)-eliminating transition state and produces the final products; (3). the reaction has a concerted initial cis-transition state, in which the phosphorus atom attacks the first and the third nitrogen atoms of the azide simultaneously and reaches an intermediate, and then the reaction goes through similar steps of the first reaction mechanism. In contrast to the previous predictions on the relative stability of the unsubstituted cis-configured phosphazide intermediate and the unsubstituted trans-configured phosphazide intermediate, the total energy of the substituted trans-configured phosphazide intermediate is close to that of the substituted cis-configured phosphazide intermediate. The preference of the initial cis-transition state reaction pathway is thoroughly discussed. The relative stability of the cis- and the trans-intermediates is explored and analyzed with the aid of molecular orbitals. The effects of substituents and solvent effects on the reaction mechanisms of the Staudinger reactions are discussed in detail.     

Time-dependent density functional theory investigation of the electronic spectra of hexanuclear chalcohalide rhenium(III) clusters

The UV-vis spectra of the hexanuclear chalcohalide rhenium(III) clusters of formula [Re(6)S(8)X(6)](4-) (X(-) = Cl(-), Br(-), I(-)) were investigated at the time-dependent density functional theory (TD-DFT) level employing B3LYP, PBE1PBE, and the double-hybrid B2PLYP functional in combination with the LANL2DZ basis set. We were able to reproduce the red shift experimentally observed when the halide changes from chloride to iodide. However, some discrepancies between experimental results and theory were found. First, we did not observe a remarkable dependence of the experimental ill-resolved bands on the solvent. Indeed, similar spectra were obtained taken CH(2)Cl(2) or CH(3)CN as solvents into account. Second, all calculations explained the origin of the band peaked at the low-energy region in contraposition with the one experimentally assumed by R. Long et al. (J. Am. Chem. Soc. 1996, 118, 4603), and theoretically made available by Arratia-Pe?rez et al. (J. Chem. Phys. 1999, 110, 2529). These authors have proposed a ligand-to-cluster charge transfer (LCCT) for all title complexes. Our findings undoubtedly allow such origin to be discarded. While the HGGA functionals lead to a cluster-to-halide ligand charge transfer (CLCT), an intracluster charge transfer (ICCT) has been considered by employing B2PLYP. This contribution showed B2PLYP in the presence of the solvent to be the best performer in studying the UV-vis spectra of large complexes of rhenium(III) containing the Re-S bond. We strongly recommended the use of the double-hybrid B2PLYP in studying UV-vis spectrum of rhenium complexes of size making the computational cost affordable. We expect that our work stimulates new experimental and theoretical investigations of the title complexes to confirm our assignment.