Universal tight binding model for chemical reactions in solution and at surfaces. I. Organic molecules

As is now well established, a first order expansion of the Hohenberg-Kohn total energy density functional about a trial input density, namely, the Harris-Foulkes functional, can be used to rationalize a non self consistent tight binding model. If the expansion is taken to second order then the energy and electron density matrix need to be calculated self consistently and from this functional one can derive a charge self consistent tight binding theory. In this paper we have used this to describe a polarizable ion tight binding model which has the benefit of treating charge transfer in point multipoles. This admits a ready description of ionic polarizability and crystal field splitting. It is necessary in constructing such a model to find a number of parameters that mimic their more exact counterparts in the density functional theory. We describe in detail how this is done using a combination of intuition, exact analytical fitting, and a genetic optimization algorithm. Having obtained model parameters we show that this constitutes a transferable scheme that can be applied rather universally to small and medium sized organic molecules. We have shown that the model gives a good account of static structural and dynamic vibrational properties of a library of molecules, and finally we demonstrate the model's capability by showing a real time simulation of an enolization reaction in aqueous solution. In two subsequent papers, we show that the model is a great deal more general in that it will describe solvents and solid substrates and that therefore we have created a self consistent quantum mechanical scheme that may be applied to simulations in heterogeneous catalysis.

Lien entre les matrices de transfert de spins et de boucles du modèle de Potts sur le tore

Le lien entre le spectre de la matrice de transfert de la formulation de spins du modèle de Potts critique et celui de la matrice de transfert double-ligne de la formulation de boucles est établi. La relation entre la trace des deux opérateurs est obtenue dans deux représentations de l'algèbre de Temperley-Lieb cyclique, dont la matrice de transfert de boucles est un élément. Le résultat est exprimé en termes des traces modifiées, qui correspondent à des traces effectuées dans le sous-espace de l'espace de représentation des N-liens se transformant selon la m ième représentation irréductible du groupe cyclique. Le mémoire comporte trois chapitres. Dans le premier chapitre, les résultats essentiels concernant les formulations de spins et de boucles du modèle de Potts sont rappelés. Dans le second chapitre, les propriétés de l'algèbre de Temperley-Lieb cyclique et de ses représentations sont étudiées. Enfin, le lien entre les deux traces est construit dans le troisième chapitre. Le résultat final s'apparente à celui obtenu par Richard et Jacobsen en 2007, mais une nouvelle représentation n'ayant pas été étudiée est aussi investiguée.

Far-infrared spectroscopy of nanoscopic InAs rings

We have employed time-dependent local-spin-density theory to analyze the far-infrared transmission spectrum of InAs self-assembled nanoscopic rings recently reported [A. Lorke et al., Phys. Rev. Lett. (to be published)]. The overall agreement between theory and experiment is fairly good, which on the one hand confirms that the experimental peaks indeed reflect the ringlike structure of the sample, and on the other hand, asseses the suitability of the theoretical method to describe such nanostructures. The addition energies of one- and two-electron rings are also reported and compared with the corresponding capacitance spectra

Integer filling facfor phases and isospin in vertical diatomic artificial molecules

Integer filling factor phases of many-electron vertically coupled diatomic artificial quantum dot molecules are investigated for different values of the interdot coupling. The experimental results are analyzed within local-spin density functional theory for which we have determined a simple lateral confining potential law that can be scaled for the different coupling regimes, and Hartree-Fock theory. Maximum density droplets composed of electrons in both bonding and antibonding or just bonding states are revealed, and interesting isospin-flip physics appears for weak interdot coupling when the systematic depopulation of antibonding states leads to changes in isospin.

Magnetic-field dependence of hole levels in self-assembled InGaAs quantum dots

Recent magnetotransport experiments of holes in InGaAs quantum dots [D. Reuter, P. Kailuweit, A. D. Wieck, U. Zeitler, O. Wibbelhoff, C. Meier, A. Lorke, and J. C. Maan, Phys. Rev. Lett. 94, 026808 (2005)] are interpreted by employing a multiband k¿p Hamiltonian, which considers the interaction between heavy hole and light hole subbands explicitly. No need of invoking an incomplete energy shell filling is required within this model. The crucial role we ascribe to the heavy hole-light hole interaction is further supported by one-band local-spin-density functional calculations, which show that Coulomb interactions do not induce any incomplete hole shell filling and therefore cannot account for the experimental magnetic field dispersion.

Electronic structure of few-electron concentric double quantum rings

The ground state structure of few-electron concentric double quantum rings is investigated within the local spin density approximation. Signatures of inter-ring coupling in the addition energy spectrum are identified and discussed. We show that the electronic configurations in these structures can be greatly modulated by the inter-ring distance: At short and long distances the low-lying electron states localize in the inner and outer rings, respectively, and the energy structure is essentially that of an isolated single quantum ring. However, at intermediate distances the electron states localized in the inner and the outer ring become quasidegenerate and a rather entangled, strongly-correlated system is formed.

Vertically coupled double quantum rings at zero magnetic field

Within local-spin-density functional theory, we have investigated the ¿dissociation¿ of few-electron circular vertical semiconductor double quantum ring artificial molecules at zero magnetic field as a function of interring distance. In a first step, the molecules are constituted by two identical quantum rings. When the rings are quantum mechanically strongly coupled, the electronic states are substantially delocalized, and the addition energy spectra of the artificial molecule resemble those of a single quantum ring in the few-electron limit. When the rings are quantum mechanically weakly coupled, the electronic states in the molecule are substantially localized in one ring or the other, although the rings can be electrostatically coupled. The effect of a slight mismatch introduced in the molecules from nominally identical quantum wells, or from changes in the inner radius of the constituent rings, induces localization by offsetting the energy levels in the quantum rings. This plays a crucial role in the appearance of the addition spectra as a function of coupling strength particularly in the weak coupling limit.

Effective mass and dielectric constant mismatch effects in spherical multishell quantum dots

The role of effective mass and dielectric mismatches on chemical potentials and addition energies of many-electron multishell quantum dots (QDs) is explored within the framework of a recent extension of the spin density functional theory. It is shown that although the gross electronic density is located in the wells of these multishell QDs, taking position-dependent effective mass and dielectric constant into account can lead to the appearance of relevant differences in chemical potential and addition energies as compared to standard calculations in which the effective mass and the dielectric constant of the well is assumed for the whole multishell structure.

First-principles electronic theory of non-collinear magnetic order in transition-metal nanowires

The structural, electronic and magnetic properties of one-dimensional 3d transition-metal (TM) monoatomic chains having linear, zigzag and ladder geometries are investigated in the frame-work of first-principles density-functional theory. The stability of long-range magnetic order along the nanowires is determined by computing the corresponding frozen-magnon dispersion relations as a function of the 'spin-wave' vector q. First, we show that the ground-state magnetic orders of V, Mn and Fe linear chains at the equilibrium interatomic distances are non-collinear (NC) spin-density waves (SDWs) with characteristic equilibrium wave vectors q that depend on the composition and interatomic distance. The electronic and magnetic properties of these novel spin-spiral structures are discussed from a local perspective by analyzing the spin-polarized electronic densities of states, the local magnetic moments and the spin-density distributions for representative values q. Second, we investigate the stability of NC spin arrangements in Fe zigzag chains and ladders. We find that the non-collinear SDWs are remarkably stable in the biatomic chains (square ladder), whereas ferromagnetic order (q =0) dominates in zigzag chains (triangular ladders). The different magnetic structures are interpreted in terms of the corresponding effective exchange interactions J(ij) between the local magnetic moments μ(i) and μ(j) at atoms i and j. The effective couplings are derived by fitting a classical Heisenberg model to the ab initio magnon dispersion relations. In addition they are analyzed in the framework of general magnetic phase diagrams having arbitrary first, second, and third nearest-neighbor (NN) interactions J(ij). The effect of external electric fields (EFs) on the stability of NC magnetic order has been quantified for representative monoatomic free-standing and deposited chains. We find that an external EF, which is applied perpendicular to the chains, favors non-collinear order in V chains, whereas it stabilizes the ferromagnetic (FM) order in Fe chains. Moreover, our calculations reveal a change in the magnetic order of V chains deposited on the Cu(110) surface in the presence of external EFs. In this case the NC spiral order, which was unstable in the absence of EF, becomes the most favorable one when perpendicular fields of the order of 0.1 V/Å are applied. As a final application of the theory we study the magnetic interactions within monoatomic TM chains deposited on graphene sheets. One observes that even weak chain substrate hybridizations can modify the magnetic order. Mn and Fe chains show incommensurable NC spin configurations. Remarkably, V chains show a transition from a spiral magnetic order in the freestanding geometry to FM order when they are deposited on a graphene sheet. Some TM-terminated zigzag graphene-nanoribbons, for example V and Fe terminated nanoribbons, also show NC spin configurations. Finally, the magnetic anisotropy energies (MAEs) of TM chains on graphene are investigated. It is shown that Co and Fe chains exhibit significant MAEs and orbital magnetic moments with in-plane easy magnetization axis. The remarkable changes in the magnetic properties of chains on graphene are correlated to charge transfers from the TMs to NN carbon atoms. Goals and limitations of this study and the resulting perspectives of future investigations are discussed.

Diorganoruthenium complexes incorporating noninnocent [C6H2(CH2ER2)2-3,5]22-(E = N, P) Bis-Pincer bridging ligands: synthesis, spectroelectrochemistry, and DFT studies

The dinuclear complex [(tpy)Ru-II(PCP-PCP)Ru-II(tPY)]Cl-2 (bridging PCP-PCP = 3,3',5,5'-tetrakis(diphenylphosphinomethyl)biphenyl, [C6H2(CH2PPh2)(2)-3,5](2)(2-)) was prepared via a transcyclometalation reaction of the bis-pincer ligand [PC(H)P-PC(H)P] and the Ru(II) precursor [Ru(NCN)(tpy)]Cl (NCN = [C6H3(CH2NMe2)(2)-2,6](-)) followed by a reaction with 2,2':6',2 ''-terpyridine (tpy). Electrochemical and spectroscopic properties of [(tpy)Ru-II(PCP-PCP)Ru-II(tPY)]Cl-2 are compared with those of the closely related [(tpy)Ru-II(NCN-NCN)Ru-II(tpy)](PF6)(2) (NCN-NCN = [C6H2(CH2- NMe2)(2)-3,5](2)(2-)) obtained by two-electron reduction of [(tpy)Ru-III(NCN-NCN)Ru-III(tpy)](PF6)(4). The molecular structure of the latter complex has been determined by single-crystal X-ray structure determination. One-electron reduction of [(tpy)Ru-III(NCN-NCN)Ru-III(tpy)](PF6)(4) and one-electron oxidation of [(tpy)Ru-II(PCP-PCP)RUII(tpy)]Cl-2 yielded the mixed-valence species [(tpy)Ru-III(NCN-NCN)RUII(tpy)](3+) and [(tpy)Ru-III(PCP-PCP)RUII(tpy)](3+), respectively. The comproportionation equilibrium constants K-c (900 and 748 for [(tpy)Ru-III(NCN-NCN)Ru-III(tpy)](4+) and [(tpy)Ru-II(PCP-PCP)RUII(tpy)](2+), respectively) determined from cyclic voltammetric data reveal comparable stability of the [Ru-III-Ru-II] state of both complexes. Spectroelectrochemical measurements and near-infrared (NIR) spectroscopy were employed to further characterize the different redox states with special focus on the mixed-valence species and their NIR bands. Analysis of these bands in the framework of Hush theory indicates that the mixed-valence complexes [(tpy)Ru-III(PCP-PCP)RUII(tpy)](3+) and [(tpy)Ru-III(NCN-NCN)RUII(tpy)](3+) belong to strongly coupled borderline Class II/Class III and intrinsically coupled Class III systems, respectively. Preliminary DFT calculations suggest that extensive delocalization of the spin density over the metal centers and the bridging ligand exists. TD-DFT calculations then suggested a substantial MLCT character of the NIR electronic transitions. The results obtained in this study point to a decreased metal-metal electronic interaction accommodated by the double-cyclometalated bis-pincer bridge when strong sigma-donor NMe2 groups are replaced by weak sigma-donor, pi-acceptor PPh2 groups

Structure and magnetic properties of a tetranuclear Cu(II) complex containing the 2-(pyridine-2-yliminomethyl)-phenol ligand

A tetranuclear Cu(II) complex [Cu4L4(H2O)4](ClO4)4 has been synthesized using the terdentate Schiff base 2-(pyridine-2-yliminomethyl)-phenol (HL) (the condensation product of salicylaldehyde and 2-aminopyridine) and copper perchlorate. Chemical characterizations such as IR and UV/Vis of the complex have been carried out. A single-crystal diffraction study shows that the complex contains a nearly planar tetranuclear core containing four copper atoms, which occupy four equivalent five-coordinate sites with a square pyramidal environment. Magnetic measurements have been carried out over the temperature range 2–300K and with 100Oe field strengths. Analysis of magnetic susceptibility data indicates a strong antiferromagnetic (J1=−638cm−1) exchange interaction between diphenoxo-bridged Cu(II) centers and a moderate antiferromagnetic (J2=−34cm−1) interaction between N–C–N bridged Cu(II) centers. Magnetic exchange interactions (J’s) are also discussed on the basis of a computational study using DFT methodology. The spin density distribution (singlet ground state) is calculated to visualize the effect of delocalization of spin density through bridging groups.

Bridge-localized HOMO-binding character of divinylanthracene-bridged dinuclear ruthenium carbonyl complexes: spectroscopic, spectroelectrochemical, and computational studies

The electronic properties of four divinylanthracene-bridged diruthenium carbonyl complexes [{RuCl(CO)(PMe3)3}2(μ[BOND]CH[DOUBLE BOND]CHArCH[DOUBLE BOND]CH)] (Ar=9,10-anthracene (1), 1,5-anthracene (2), 2,6-anthracene (3), 1,8-anthracene (4)) obtained by molecular spectroscopic methods (IR, UV/Vis/near-IR, and EPR spectroscopy) and DFT calculations are reported. IR spectroelectrochemical studies have revealed that these complexes are first oxidized at the noninnocent bridging ligand, which is in line with the very small ν(C[TRIPLE BOND]O) wavenumber shift that accompanies this process and also supported by DFT calculations. Because of poor conjugation in complex 1, except oxidized 1+, the electronic absorption spectra of complexes 2+, 3+, and 4+ all display the characteristic near-IR band envelopes that have been deconvoluted into three Gaussian sub-bands. Two of the sub-bands belong mainly to metal-to-ligand charge-transfer (MLCT) transitions according to results from time-dependent DFT calculations. EPR spectroscopy of chemically generated 1+–4+ proves largely ligand-centered spin density, again in accordance with IR spectra and DFT calculations results.

Direct probing of photoinduced electron transfer in a self- assembled biomimetic [2Fe2S]-hydrogenase complex using ultrafast vibrational spectroscopy

A pyridyl-functionalized diiron dithiolate complex, [μ-(4-pyCH2−NMI-S2)Fe2(CO)6] (3, py = pyridine(ligand), NMI = naphthalene monoimide) was synthesized and fully characterized. In the presence of zinc tetraphenylporphyrin (ZnTPP), a self-assembled 3·ZnTPP complex was readily formed in CH2Cl2 by the coordination of the pyridyl nitrogen to the porphyrin zinc center. Ultrafast photoinduced electron transfer from excited ZnTPP to complex 3 in the supramolecular assembly was observed in real time by monitoring the ν(CO) and ν(CO)NMI spectral changes with femtosecond time-resolved infrared (TRIR) spectroscopy. We have confirmed that photoinduced charge separation produced the monoreduced species by comparing the time-resolved IR spectra with the conventional IR spectra of 3•− generated by reversible electrochemical reduction. The lifetimes for the charge separation and charge recombination processes were found to be τCS = 40 ± 3 ps and τCR = 205 ± 14 ps, respectively. The charge recombination is much slower than that in an analogous covalent complex, demonstrating the potential of a supramolecular approach to extend the lifetime of the chargeseparated state in photocatalytic complexes. The observed vibrational frequency shifts provide a very sensitive probe of the delocalization of the electron-spin density over the different parts of the Fe2S2 complex. The TR and spectro-electrochemical IR spectra, electron paramagnetic resonance spectra, and density functional theory calculations all show that the spin density in 3•− is delocalized over the diiron core and the NMI bridge. This delocalization explains why the complex exhibits low catalytic dihydrogen production even though it features a very efficient photoinduced electron transfer. The ultrafast porphyrin-to-NMIS2−Fe2(CO)6 photoinduced electron transfer is the first reported example of a supramolecular Fe2S2-hydrogenase model studied by femtosecond TRIR spectroscopy. Our results show that TRIR spectroscopy is a powerful tool to investigate photoinduced electron transfer in potential dihydrogen-producing catalytic complexes, and that way to optimize their performance by rational approaches.

Isostructural M(RL)(2)(hfac)(2) complexes with RL=5-(4-[N-tert-butyl-N-aminoxyl]phenyl)pyrimidine

5-(4-(N-tert-Butyl-N-aminoxylphenyl)) pyrimidine (RL, 4PPN) forms crystallographically isostructural and isomorphic pseudo-octahedral M(RL)(2)(hfac)(2) complexes with M(hfac)(2), M = Zn, Cu, Ni, Co, and Mn. Multiple close contacts occur between sites of significant spin density of the organic radical units. Magnetic behavior of the Zn, Cu, Ni, Co complexes appears to involve multiple exchange pathways, with multiple close crystallographic contacts between sites that EPR (of 4PPN) indicates to have observable spin density. Powder EPR spectra at room temperature and low temperature are reported for each complex. Near room temperature, the magnetic moments of the complexes are roughly equal to those expected by a sum of non-interacting moments (two radicals plus ion). As temperature decreases, AFM exchange interactions become evident in all of the complexes. The closest fits to the magnetic data were found for a 1-D Heisenberg AFM chain model in the Zn(II) complex (J/k = (-)7 K), and for three-spin RL-M-RL exchange in the other complexes (J/k = (-)26 K, (-)3 K, (-) 6 K, for Cu(II), Ni(II), and Co(II) complexes, respectively). (C) 2008 Elsevier B.V. All rights reserved.

Entanglement degree measure and a criterion for sudden death as a phase transition in bipartite systems

We propose a method to compute the entanglement degree E of bipartite systems having dimension 2 x 2 and demonstrate that the partial transposition of density matrix, the Peres criterion, arise as a consequence Of Our method. Differently from other existing measures of entanglement, the one presented here makes possible the derivation of a criterion to verify if an arbitrary bipartite entanglement will suffers sudden death (SD) based only on the initial-state parameters. Our method also makes possible to characterize the SD as a dynamical quantum phase transition, with order parameter epsilon. having a universal critical exponent -1/2. (C) 2009 Elsevier Inc. All rights reserved.