Structure and energy of Mo27SxCy clusters: a density functional theory study

For understanding the carburization processes of MoSx catalysts, the structures and energies of Mo27SxCy cluster models have been computed at the level of density functional theory. The surface sulfur atoms on the Mo edge and S edge as well as bulky sulfur atoms have been replaced by atomic carbon, and the corresponding structures have S/C ratios in the range of 0.8-55. The formation of all Mo27SxCy structures is favored thermodynamically. It is also found that the formation of CS and C2 bridging units is more favored than the individual or separated replacements and that the formation of C2 bridging units is more favored than that of CS units. In contrast, the replacement of sulfur on the Mo edge is least favored. Furthermore, the replacement of the bulky sulfur on the Mo edge is equally favored as those of sulfur on the S edge. For aiding further experimental studies, the C=S and C=C stretching frequencies have been computed.     

Ab-initio molecular dynamics based on non-local density functional procedure with Gaussian basis; study of structural and temperature behaviour of metallic clusters

An ab-initio molecular dynamics procedure without precalculation of the Born-Oppenheimer energy surface based on an iterative non-local density functional method employing Gaussian atomic basis has been developed. Analytical gradients are calculated and used for the propagation of nuclei. Sufficiently long trajectories can be calculated at an acceptable computational cost, allowing for analysis of dynamical behaviour of small metallic clusters. This is illustrated on an example of the Li₈ cluster. Temperature behaviour of different type of isomers has been investigated. Calculated power spectra allow to identify the presence of more than one isomeric forms along the given trajectories.     

BFW: a density functional for transition metal clusters

Ionization potentials (IPs) or electron affinities (EAs) for transition metal clusters are an important property that can be used to identify and differentiate between clusters. Accurate calculation of these values is therefore vital. Previous attempts using a variety of DFT models have correctly predicted trends, but have relied on the use of scaling factors to compare to experimental IPs. In this paper, we introduce a new density functional (BFW) that is explicitly designed to yield accurate, absolute IPs for transition metal clusters. This paper presents the numerical results for a selection of transition metal clusters and their carbides, nitrides, and oxides for which experimental IPs are known. When tested on transition metal clusters, the BFW functional is found to be significantly more accurate than B3LYP and B3PW91.     

Four-dimensional density and energy density functional

The relations based on an external one-electron operator V( r ) are examined from two view-points, i.e., from the Hohenberg–Kohn approach and the four-dimensional density concept introduced by Wilson and Frost, and extensively studied by Parr and Politzer. The object being to obtain, with the help of the Hellmann–Feynman theorem, new formulas for the energy of atoms and molecules, and to discuss the construction of the universal energy density functional on the basis of the four-dimensional density.     

Dipole polarizabilities of germanium clusters

Dipole polarizabilities of Ge_n clusters with 2–25 atoms are calculated using finite field (FF) method within density functional theory. The dipole moments and polarizabilities of clusters are sensitively dependent on the cluster geometries and electronic structures. The clusters with low symmetry and large HOMO–LUMO gap prefer to large dipole moments. The polarizabilities of the Ge_n clusters increase rapidly in the size range of 2–5 atoms and then fluctuate around the bulk value. The larger HOMO–LUMO gap may lead to smaller polarizability. As compared with the compact structure and diamond structure, the prolate cluster structure corresponds to a larger polarizability.     

Time-dependent density functional study of the electronic potential energy curves and excitation spectrum of the oxygen molecule

Orbital energies, ionization potentials, molecular constants, potential energy curves, and the excitation spectrum of O(2) are calculated using time-dependent density functional theory (TDDFT) with Tamm-Dancoff approximation (TDA). The calculated negative highest occupied molecular orbital energy (-epsilon(HOMO)) is compared with the energy difference ionization potential for five exchange correlation functionals consisting of the local density approximation (LDAxc), gradient corrected Becke exchange plus Perdew correlation (B(88X)+P(86C)), gradient regulated asymptotic correction (GRAC), statistical average of orbital potentials (SAOP), and van Leeuwen and Baerends asymptotically correct potential (LB94). The potential energy curves calculated using TDDFT with the TDA at internuclear distances from 1.0 to 1.8 A are divided into three groups according to the electron configurations. The 1pi(u) (4)1pi(g) (2) electron configuration gives rise to the X (3)Sigma(g) (-), a (1)Delta(g), and b (1)Sigma(g) (+) states; the 1pi(u) (3)1pi(g) (3) electron configuration gives rise to the c (1)Sigma(u) (-), C (3)Delta(u), and A (3)Sigma(u) (+) states; and the B (3)Sigma(u) (-), A (1)Delta(u), and f (1)Sigma(u) (+) states are determined by the mixing of two or more electron configurations. The excitation spectrum of the oxygen molecule, calculated with the aforementioned exchange correlation functionals, shows that the results are quite sensitive to the choice of functional. The LDAxc and the B(88X)+P(86C) functionals produce similar spectroscopic patterns with a single strongly absorbing band positioned at 19.82 and 19.72 eV, respectively, while the asymptotically corrected exchange correlation functionals of the SAOP and the LB94 varieties yield similar excitation spectra where the computed strongly absorbing band is located at 16.09 and 16.42 eV, respectively. However, all of the exchange correlation functionals yield only one strongly absorbing band (oscillator strength greater than 0.1) in the energy interval of 0-20 eV, which is assigned to a X (3)Sigma(g) (-) to (3)Sigma(u) (-) transition. Furthermore, the oxygen molecule has a rich spectrum in the energy range of 14-20 eV and no spin allowed absorption bands are predicted to be observed in the range of 0-6 eV.     

A short-range correlation energy density functional with multi-determinantal reference

We introduce a short-range correlation density functional defined with respect to a multi-determinantal reference which is meant to be used in a multi-determinantal extension of the Kohn–Sham scheme of density functional theory based on a long-range/short-range decomposition of the Coulomb electron–electron interaction. We construct the local density approximation for this functional and discuss its performance on the He atom.     

Two hydrogen ligands on tetrairidium clusters: a relativistic density functional study

Structural and energetic properties of Ir(4)H(2) have been determined by applying a relativistic density functional method. As previously obtained for Ir(4)H, terminal coordination of H ligands is preferred, in contrast to some other transition metals. Square-planar Ir(4) isomers with an H binding energy of up to 318 kJ mol(-1) per atom were determined as the most stable structures of Ir(4)H(2). Isomers with a tetrahedral or butterfly structure of the metal framework exhibit average H atom binding energies of up to approximately 300 kJ mol(-1). For all three types of isomers, a surprisingly large number of stable minima was identified. Unexpectedly, structural as well as energetic properties of Ir(4)H(2) complexes are very similar to Ir(4)H. Thus binding of an H atom to Ir(4) is only slightly affected by the presence of a second H ligand. In all cases examined, the reaction H(2)+ Ir(4)--> H(2)Ir(4) was found to be exothermic with reaction energies of up to 170 kJ mol(-1).     

Time-dependent four-component relativistic density functional theory for excitation energies

Time-dependent four-component relativistic density functional theory within the linear response regime is developed for calculating excitation energies of heavy element containing systems. Since spin is no longer a good quantum number in this context, we resort to time-reversal adapted Kramers basis when deriving the coupled Dirac-Kohn-Sham equation. The particular implementation of the formalism into the Beijing density functional program package utilizes the multipolar expansion of the induced density to facilitate the construction of the induced Coulomb potential. As the first application, pilot calculations on the valence excitation energies and fine structures of the rare gas (Ne to Rn) and Group 12 (Zn to Hg) atoms are reported. To the best of our knowledge, it is the first time to be able to account for spin-orbit coupling within time-dependent density functional theory for excitation energies.     

Average excitation energies from time-dependent density functional response theory

The authors present an occupation number averaging scheme for time-dependent density functional response theory (TD-DFRT) in frequency domain. The known problem that TD-DFRT within the local (spin) density approximation (LDA/LSDA) inaccurately predicts Rydberg and charge-transfer excitation energies has been reexamined from the methodology of linear response, without explicit correction of the exchange-correlation potential. The working equations of TD-DFRT are adapted to treat arbitrary difference of orbital occupation numbers, using the nonsymmetric matrix form of Casida's formulation of TD-DFRT [M. E. Casida, in Recent Advances in Density Functional Methods, edited by D. P. Chong (World Scientific, Singapore, 1995), Pt. I, p. 155]. The authors' scheme is applied to typical closed-shell and open-shell molecular systems by examining the dependence of excitation energies on the fraction of excited electron. Good performance of this modified linear response scheme is shown, and is consistent with the authors' previous examination by the real-time propagation approach, suggesting that the calculation of average excitation energies might be one of the ways to better decode excitation energies from LDA/LSDA. Different techniques for treating singlet, triplet, and doublet states are discussed.     

Octacoordinate carbons encaged inside carborane clusters: a density functional theory investigation

This work focuses on the computational design and characterization of a novel series of endohedral carborane clusters containing octacoordinate carbon centers. The structural and bonding features and the thermodynamic and kinetic stabilities are discussed extensively based on density functional theory calculations. These nonclassical carboranes are fascinating in structure not only for the octacoordinate carbon center but also for the surrounding carbon and boron ligands with inverted bonding configuration. These endohedral carboranes are higher in energy than the corresponding exohedral isomers due to the high strain in the system. A new stability rule based on the donor-acceptor model is proposed to predict the stability ordering for these carborane isomers. In addition, some of these octacoordinate carboranes might have relatively high kinetic stabilities, which is rather hopeful for the experimental syntheses.     

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.     

A density functional study on the aggregation of alumina clusters

A calculation has been performed to explore the mechanism of aggregation reaction between two small molecular clusters [(Al₂O₃) _n1 and (Al₂O₃) _n2] by the density functional theory method. Five pathways of aggregation reactions between two different (Al₂O₃)₁ clusters isomers were identified. The detailed process of (Al₂O₃)₁ interaction with (Al₂O₃)₂ were also obtained. All the products of the aggregation reactions between two cage structures are cage-dimer structures. We calculated the thermodynamic properties of all the aggregate clusters. The Gibbs free energy changes of aggregation reactions in 0–1000 K were negative and increased with the temperature increase. The energy changes of enthalpy and entropy were also obtained.     

On the accuracy of density functional theory for iron-sulfur clusters

A simple, yet powerful wave function manipulation method was introduced utilizing a generalized ionic fragment approach that allows for systematic mapping of the wave function space for multispin systems with antiferromagnetic coupling. The use of this method was demonstrated for developing ground state electronic wave function for [2Fe-2S] and [Mo-3Fe-4S] clusters. Using well-defined ionic wave functions for ferrous and ferric irons, sulfide, and thiolate fragments, the accuracy of various density functionals and basis sets including effective core potentials were evaluated on a [4Fe-4S] cluster by comparing the calculated geometric and electronic structures with crystallographic data and experimental atomic spin densities from X-ray absorption spectroscopy, respectively. We found that the most reasonable agreement for both geometry and atomic spin densities is obtained by a hybrid functional with 5% HF exchange and 95% density functional exchange supplemented with Perdew's 1986 correlation functional. The basis set seems to saturate only at the triple-zeta level with polarization and diffuse functions. Reasonably preoptimized structures can be obtained by employing computationally less expensive effective core potentials, such as the Stuttgart-Dresden potential with a triple-zeta valence basis set. The extension of the described calibration methodology to other biologically important and more complex iron-sulfur clusters, such as hydrogenase H-cluster and nitrogenase FeMo-co will follow.     

A density functional study of bare and hydrogenated platinum clusters

We perform density functional theory calculations using Gaussian atomic-orbital methods within the generalized gradient approximation for the exchange and correlation to study the interactions in the bare and hydrogenated platinum clusters. The minimum-energy structures, binding energies, relative stabilities, vibrational frequencies and the highest occupied and lowest unoccupied molecular-orbital gaps of Pt_nH_m (n = 1–5, m = 0–2) clusters are calculated and compared with previously studied pure platinum and hydrogenated platinum clusters. We investigate any magic behavior in hydrogenated platinum clusters and find that Pt₄H₂ is more stable than its neighboring sizes. The lowest energy structure of Pt₄ is found to be a distorted tetrahedron and that of Pt₅ is found to be a bridge site capped tetrahedron which is a new global minimum for Pt₅ cluster. The successive addition of H atoms to Pt_n clusters leads to an oscillatory change in the magnetic moment of Pt₃–Pt₅ clusters.     

Gradient corrections in the energy density functional

It is shown, by calculations in He and Ne with HF densities, that the improvement obtained when gradient corrections are added to the local approximation to the kinetic energy, arises from a detailed improvement in the kinetic energy density.