Finite Cluster Approach Research Articles

Modeling the spectral properties of poly(x-phenylenediamine) conducting polymers using a combined TD-DFT and electrostatic embedding approach.

The absorption spectra of polymers derived from ortho, meta and para phenylenediamines (o-PDA, m-PDA and p-PDA) have been simulated combining periodic density functional theory (DFT) calculations with time-dependent DFT simulations. These latter have been carried out on finite clusters embedded in a set of point charges devised to exactly reproduce the electrostatic potential of the periodic chains. The results are compared with those obtained for solvated o-PDA, m-PDA and p-PDA oligomers of increasing sizes extracted from the periodic structures. The electronic transitions involved have been investigated by a qualitative analysis based on isodensity maps completed by a quantitative analysis based on the density-based index (DCT ). For poly-(o)- and poly-(p)- phenylenediamines the agreement with the experimental data is achieved already by modeling solvated dimers whereas the inclusion of long-range electrostatic effects is mandatory for poly-(m)-phenylenediamine highlighting the importance of an accurate treatment of the electrostatic environment when a finite cluster approach is considered.

First-principles melting of krypton and xenon based on many-body relativistic coupled-cluster interaction potentials

The solid-to-liquid phase transition for krypton and xenon is studied by means of parallel-tempering Monte Carlo simulations based on an accurate description of the atomic interactions within a many-body ansatz using relativistic coupled-cluster theory. These high-level data were subsequently fitted to computationally efficient extended Lennard-Jones and extended Axilrod-Teller-Muto types of interaction potentials. Solid-state calculations demonstrate that the many-body decomposition of the interaction energy converges well for the heavier rare gas solids, leading to solid-state properties in good agreement with experiment. The results show that it suffices to include two- and three-body interactions only for the melting simulation. The melting of the bulk is simulated for cells with cubic periodic boundary conditions, as well as within a finite cluster approach. For the latter, melting of spherical magic number clusters with increasing cluster size is studied, and the melting temperatures are obtained from extrapolation to the bulk. The calculated melting temperatures for the cluster extrapolation (the periodic approach values corrected for superheating are set in parentheses) are ${T}_{m}=113.7$ K (110.9 K) and ${T}_{m}=160.8$ K (156.1 K) for krypton and xenon, respectively. Both are in very good agreement with corresponding experimental values of 115.75 and 161.40 K.

Absorption in Finite-Length Chevron-Type Graphene Nanoribbons

Using a combination of the density functional theory and tight-binding calculations, we study electronic and optical properties of asymmetric chevron-type graphene nanoribbons recently synthesized with atomic precision. We demonstrate that the low-energy optical selection rules in such infinite chiral ribbons are more reminiscent of those for zigzag rather than for armchair ribbons. It is also shown that, starting from about 25 nm long ribbons, the low-energy absorption and therefore the selection rules of infinitely long ribbons are well reproduced in the finite cluster approach. Hence, ribbons longer than 25 nm (about 28 unit cells) can be treated as infinitely long ones.

A Hundred-Year-Old Experiment Re-evaluated: Accurate Ab Initio Monte Carlo Simulations of the Melting of Radon.

State-of-the-art relativistic coupled-cluster theory is used to construct many-body potentials for the noble-gas element radon to determine its bulk properties including the solid-to-liquid phase transition from parallel tempering Monte Carlo simulations through either direct sampling of the bulk or from a finite cluster approach. The calculated melting temperature are 200(3) K and 200(6) K from bulk simulations and from extrapolation of finite cluster values, respectively. This is in excellent agreement with the often debated (but widely cited) and only available value of 202 K, dating back to measurements by Gray and Ramsay in 1909.

A Finite Cluster Approach to an Extended Transition Metal Oxide: A Wave Function Based Study

An accurate finite cluster approach based on localized Wannier orbitals is applied here to bulk TiO2 as a prototypical extended transition metal oxide. The quasi-particle band structure, an extended property of the infinite solid, is successfully reproduced within a finite local cluster approach at the Hartree–Fock level. Post-Hartree–Fock calculations on selected clusters are then performed to account for correlation effects. The computational implementation, which is a modified version of the “cluster-in-solid” embedding technique (Birkenheuer, U., Fulde, P.; Stoll, H. Theor. Chem. Acc.2006, 116, 398) along with the frozen local hole approximation (Pahl, E.; Birkenheuer, U. J. Chem. Phys.2006, 124 214101), is described and possible further extensions to calculate local defects in bulk materials and excited states in adsorbate/metal oxide surfaces are discussed.

The O–H(D) stretching potentials of the hydrogen bonded water molecules in MCl2·2H2O (M∈{Mn, Co, Fe}). Ab initio and density functional study

The uncoupled anharmonic O–H(D) stretching vibrations of the hydrogen bonded water molecules with local C2 symmetry in compounds of the type MCl2·2H2O (where M∈{Mn, Co, Fe}) were studied at various levels of theory, within the finite-cluster approach. The studied clusters consisted of one water molecule coordinated to the metal atom and hydrogen bonded to two chloride anions. The vibrational potential energy curves for the uncoupled OH stretching vibrations were obtained from pointwise energy calculations at HF, MP2 and gradient-corrected B3-LYP density functional levels of theory. To solve the HF or the Kohn–Sham equations, the standard 6-311G(d,p) basis set was used on O, H and Cl, while the transition metal atoms were treated within the LANL2DZ basis, employing an effective core potential (ECP) description of the inner shell electrons. From the calculated energies of the vibrational eigenstates, both the fundamental anharmonic and harmonic vibrational frequencies, as well as the anharmonicity constants were computed.

Potential-dependent chemisorption of carbon monoxide on platinum electrodes: new insight from quantum-chemical calculations combined with vibrational spectroscopy

Abstract Density functional theory (DFT) using the finite cluster approach is utilized to compute binding energies, bond geometries, and vibrational properties of carbon monoxide adsorbed on Pt(111) as a function of the external interfacial field, focusing attention on the metal–CO bond itself. Comparison with electrode potential-dependent frequencies for the metal–CO ( ν M–CO ) as well as the much-studied intramolecular CO ( ν CO ) vibration, as measured by in-situ Raman and infrared spectroscopy, facilitate their interpretation in terms of metal-chemisorbate bonding for this archetypal electrochemical system. Decomposing the calculated metal–CO binding energy and vibrational frequencies into individual orbital and steric repulsion components enables the role of such quantum-chemical interactions to the field- (and hence potential-) dependent bonding to be assessed. No simple relationship between the field( F )-dependent binding energies and the ν M–CO frequencies is evident. While the DFT ν M–CO – F slopes are negative at positive and small–moderate negative fields, reflecting the prevailing influence of back-donation, a ν M–CO – F maximum is obtained at larger negative fields for atop CO, and a plateau for hollow-site CO. This Stark-tuning behavior reflects largely offsetting field-dependent contributions from π and σ surface bonding, and can also be rationalized on the basis of changes in the electrostatic component of ν M–CO from increasing M–CO charge polarization. A rough correlation between the field-dependent ν M–CO frequencies and the corresponding bond distances, r M–CO , is observed for hollow and atop CO in that r M–CO shortens towards less positive fields, but becomes near-constant at moderate–large negative fields. A more quantitative correlation between the field-dependent CO frequencies and bond lengths is also evident. In harmony with earlier findings (and unlike the ν M–CO – F behavior), the ν CO – F dependence is due chiefly to changes in the back-donation bonding component. The overall vibrational frequency-field behavior predicted by DFT is also in semi-quantitative concordance with experimental potential-dependent spectra.

A real-space finite cluster approach to the correlated electron problem

A new finite-cluster method for the correlated electron problem has been applied to Hubbard and Heisenberg models and shown to yield accurate solutions for the ground-state and low-lying excited states of finite systems. Interating this method results in much improved estimates of ground-state energy densities in the thermodynamic limit compared with the usual numerical renormalisation group approach.

A simulated annealing based algorithm for eigenvalue problems

We present a simple, iterative algorithm to find the lowest (few) eigenvalue(s) and eigenvector(s) of a large sparse real Hermitian matrix. The algorithm is an application of the simulated annealing technique implemented via molecular dynamics. We also demonstrate that the slow rate of convergence, characteristic of the late-time behaviour of such annealing based methods, can be considerably improved by using simple gradient minimization schemes. Our studies are based on a large number of real Hermitian matrices of dimensions up to 15876 arising out of our investigations of strongly-correlated systems using the finite-cluster approach. We also investigate the effect of the controlling parameters (time step and fictitious mass) on the convergence and suggest a way to choose these parameters a priori.

The Electronic Structure of Crystalline Li21Si5. A Cluster Approach to a γ-Brass Structure

The electronic structure of crystalline Li21Si5 is investigated by semiempirical MO (molecular orbital) calculations of the INDO (intermediate neglect of differential overlap) type in the framework of a finite cluster approach. The complex solid-state ensemble with 416 atoms per unit cell is divided into 16 cluster units M26 that form the three-dimensional structure. These M26 clusters have two different chemical compositions and act as formal donor and acceptor fragments, namely D = (Li20Si6) and A = (Li22Si4), having the formal net charges q(D ) = - 4 and q(A) = + 4. The electronic structures of these finite building units are rationalized by the semiempirical MO model. The one-electron energies of (Li20Si6)4- and (Li22Si4)4+ are derived on the basis of fragment interactions between the site sets (tetrahedral, octahedral, cube-octahedral) that build up the different M26 units. The canonical MO’s are transformed by means of the Edmiston-Ruedenberg localization procedure in order to come to a clear representation of the chemical bond in the two clusters. In (Li20Si6)4- a coincidence of the classical valence rules and the existence of nonclassical many-center bonds is found. (Li22Si4)4+ on the other side violates the counting schemes because of an excess of 2 electrons (electron octets at Si). The model calculations show however that the octet rule is strictly fulfilled in the Si subspace. The Li centers allow for the formation of an additional bonding cage orbital due to in-phase interactions between the Li 2s AO’s. This MO is occupied by the two excess electrons which are left after filling the valence orbitals associated to Si. The formation of such a one-electron level is not considered in classical models. The Li-Si interaction in Li21Si5 is of covalent nature and is comparable to the metal-nonmetal bonds in other lithium silicides. The Li-Li contacts are nonbonding in the framework of the Hartree-Fock approximation. The observed solid-state structure of the binary phase can be explained by intercluster interactions between the different donor and acceptor fragments.

A finite cluster approach to the electron-hole pair damping of the adsorbate vibration: CO adsorbed on Cu(100)

A finite cluster method is applied to describe the energy transfer from the adsorbate vibrations to the electron-hole pair excitations. For CO stretch vibration on Cu(100) surface a value of 0.5 meV is found for the consequent damping (corresponding to the lifetime of 1.3·10 −12- s) in an agreement with a recently measured vibrational line width. The mechanism behind the electron-hole pair excitations is found to be charge oscillations between the molecular 2π ★ resonance and the substrate, caused by the molecular vibration. Cluster size effects have been found to be negligible.

Theory of localized magnetic moments in metals I finite cluster approach

The origin of localized magnetic moments formation in metals is investigated theoretically using a self-consistent local spin density molecular cluster approach. Clusters with up to 55 atoms are employed to describe isolated impurity local moment behavior in the cases of Fe Ag and Fe Pd . Densities of states and spin magnetic moments were determined and compared with results of spectroscopic (notably photoemission) and magnetization measurements, respectively. In the case of a noble metal host, the spin magnetization density is found to be highly localized around the Fe site; the iron moment is ≈ 3.9μ B and the polarization of the host Ag atoms is small. In the case of a transition metal host, the iron moment is ≈ 3.2 μ B but here the strong hybridization of the Fe-3d and Pd-4d states results in a large induced magnetic moment in the host PD metal — in essential agreement with experiment for this giant moment system.

A renormalisation group approach for two-dimensional percolating systems: Honeycomb bond lattice and Kagome lattice

A renormalisation group approach to two-dimensional percolation problems on the honeycomb lattice (bond) and the Kagome lattice (site and bond) is developed using a scaling transformation in real space. A finite cluster approach, called the electrode method, gives the location of the fixed point p*, the eigenvalue lambda and the correlation length critical exponent nu ; the results are p*=0.6308, lambda =1.669 and nu =1.353 for both the honeycomb lattice (bond) and the Kagome lattice (site), and p*=0.4697, lambda =1.577 and nu =1.522 for the Kagome lattice (bond). The fixed point p* for the honeycomb lattice (bond) and the Kagome lattice (site) is in good agreement with the exact critical percolation probability obtained by Sykes and Essam (1964).