Lability of a mixture of metal complexes under steady-state planar diffusion in a finite domain

The rigorous analytical solution for the fluxes from a mixture of 1:1 metal complexes toward an active surface under steady-state planar diffusion in a finite domain and excess ligand conditions allows for the computation of the global degree of lability of the system as well as particular degrees of lability of each complex in the mixture. This kind of system is found in a variety of fields ranging from electrochemical techniques (such as stripping chronopotentiometry at scanned deposition potential, SSCP) to analytical devices (such as diffusion gradients in thin-film gels, DGT). Among the specific effects arising from the presence of a mixture of ligands competing for the metal we highlight the following: (i) The degree of lability of a complex in the mixture differs from its degree of lability in an unmixed system with the same ligand concentration, and (ii) the degree of lability of one complex depends on (i.e., can be modified with) the concentrations of the ligands in the mixture. The impact of these characteristics on the metal flux crossing the active surface reaches the highest value when both complexes are partially labile. The complex contribution to the metal flux goes through a maximum when the thickness of the diffusion domain is varied. Thus, the thickness of the diffusion domain can be chosen to enhance the contribution of one particular complex. Lability criteria for each complex of the mixture within the reaction layer approximation are also reported. In particular, the reaction layer formulation for a complex is discussed in detail for two limiting cases: the rest of complexes are all nonlabile or the rest of complexes are all labile.     

Roles of dynamic metal speciation and membrane permeability in metal flux through lipophilic membranes: general theory and experimental validation with nonlabile complexes

The study of the role of dynamic metal speciation in lipophilic membrane permeability in aqueous solution requires accurate interpretation of experimental data. To meet this goal, a general theory is derived for describing 1:1 metal complex flux, under steady-state and ligand excess conditions, through a permeation liquid membrane (PLM). The theory is applicable to fluxes through any lipophilic membrane. From this theory, fluxes in the three rate-limiting conditions for metal transport are readily derived, corresponding, namely, to (i) diffusion in the source solution, (ii) diffusion in the membrane, and (iii) the chemical kinetics of formation/dissociation of the metal complex in the interfacial reaction layer. The theory enables discussion of the reaction layer concept in a more general frame and also provides unambiguous criteria for the definition of an inert metal complex. The theoretical flux equations for fully labile complexes were validated in a previous paper. The general theory for semi- or nonlabile complexes is validated here by studying the flux of Pb(II) through PLMs in contact with solutions of Pb(II)-NTA and Pb(II)-TMDTA at different pHs and flow rates.     

Chromium(III): Extra nonlability of its 1:1 chelates of polycarbonylic ligands

Decomplexation rates of chromium(III) chelates of dicarbonylic and tricarbonylic ligands in aqueous solution have been evaluated. Results show an extreme nonlability of these metal complexes that does not depend on the chelating ligand structure. A more extensive analysis including structurally similar complexes of first‐row transition metal ions [Ni(II), Co(II), and Cu(II)] shows decomplexation rate values at least 10⁴ times higher than the rate constants of previously mentioned chromium metal complexes. Correlations between the decomplexation rate constants and the deprotonation capability of the enol tautomer suggest that the decomplexation rates of a structurally similar 1:1 chelate of quoted metal ions may be predicted from the ligand dissociation constant. © 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 178–183, 2000     

Metal flux through consuming interfaces in ligand mixtures: boundary conditions do not influence the lability and relative contributions of metal species

In a mixture of metal ions and complexes, it is difficult to predict ecological risk without understanding the contribution of each metal species to biouptake. For microorganisms, the rate of uptake (internalization flux) has not only a major influence on the total metal flux but also on the bioavailability of the various metal species and their relative contributions to the total flux. In this paper, the microorganism is considered as a consuming interface, which interacts with the metal ion, M, via the Michaelis-Menten boundary conditions. The contribution of each metal complex to the overall metal flux, in relation to its lability, is examined for a number of important boundary parameters (the equilibrium constant K(a) of metal with transport sites, internalization rate constant k(int) and total transport sites concentration {R}(t)). Computations were performed for Cu(II) complexes, in a multicomponent culture medium for microoganisms. For a one-ligand system, results were acquired using rigorous mathematical expressions, whereas approximate expressions, based on the reaction layer approximation (RLA) and rigorous numerical computations (computer codes MHEDYN and FLUXY), were employed for ligand mixtures. Under the condition of ligand excess, as often found in the natural environment, the relative contribution of each metal species to the total flux is shown to be independent of the boundary conditions. This finding has important implications, including an improved basis for relating the analytical signals of dynamic metal speciation sensors to metal bioavailability.     

Full-dimensional vibrational calculations for H5O2+ using an ab initio potential energy surface

We report quantum diffusion Monte Carlo (DMC) and variational calculations in full dimensionality for selected vibrational states of H(5)O(2) (+) using a new ab initio potential energy surface [X. Huang, B. Braams, and J. M. Bowman, J. Chem. Phys. 122, 044308 (2005)]. The energy and properties of the zero-point state are focused on in the rigorous DMC calculations. OH-stretch fundamentals are also calculated using "fixed-node" DMC calculations and variationally using two versions of the code MULTIMODE. These results are compared with infrared multiphoton dissociation measurements of Yeh et al. [L. I. Yeh, M. Okumura, J. D. Myers, J. M. Price, and Y. T. Lee, J. Chem. Phys. 91, 7319 (1989)]. Some preliminary results for the energies of several modes of the shared hydrogen are also reported.     

Quasirelativistic theory for the magnetic shielding constant. III. Quasirelativistic second-order Møller-Plesset perturbation theory and its application to tellurium compounds

The quasirelativistic (QR) generalized unrestricted Hartree-Fock method for the magnetic shielding constant [R. Fukuda, M. Hada, and H. Nakatsuji, J. Chem. Phys. 118, 1015 (2003); R. Fukuda, M. Hada, and H. Nakatsuji, J. Chem. Phys.118, 1027 (2003)] has been extended to include the electron correlation effect in the level of the second-order M?ller-Plesset perturbation theory (MP2). We have implemented the energy gradient and finite-perturbation methods to calculate the magnetic shielding constant at the QR MP2 level and applied to the magnetic shielding constants and the NMR chemical shifts of 125Te nucleus in various tellurium compounds. The calculated magnetic shielding constants and NMR chemical shifts well reproduced the experimental values. The relations of the chemical shifts with the natures of ligands, and the tellurium oxidation states were investigated. The chemical shifts in different valence states were explained by the paramagnetic shielding and spin-orbit terms. The tellurium 5p electrons are the dominant origin of the chemical shifts in the Te I and Te II compounds and the chemical shifts were explained by the p-hole mechanism. The tellurium d electrons also play an important role in the chemical shifts of the hypervalent compounds.     

The structure and binding energies of the van der Waals complexes of Ar and N2 with phenol and its cation, studied by high level ab initio and density functional theory calculations

We have investigated, using both ab initio and density functional theory methods, the minimum energy structures and corresponding binding energies of the van der Waals complexes between phenol and argon or the nitrogen molecule, and the corresponding complexes involving the phenol cation. Structures were obtained at the MP2 level using a large basis, and the corresponding energies were corrected for basis set superposition error (BSSE), higher order electron correlation effects, and for basis set size. The structures of the global minima were further refined for the effects of BSSE and the corresponding binding energies were evaluated. For each neutral species, we find only a single true minimum, pi bonded for argon and OH bonded for nitrogen. For both cationic species, we find that the OH-bonded complex is preferred over other minima which we have identified as having Ar or N(2) between exogeneous atoms. The ab initio calculations are generally in excellent agreement with experimental binding energies and rotational constants. We find that the B3LYP functional is particularly poor at describing these complexes, while a density functional theory (DFT) method with an empirical correction for dispersive interactions (DFT-D) is very successful, as are some of the new functionals proposed by Zhao and Truhlar [J. Phys. Chem. A 109, 5656 (2005); J. Chem. Theory Comput. 2, 1009 (2006); Phys. Chem. Chem. Phys. 7, 2701 (2005); J. Phys. Chem. A 108, 6908 (2004)]. Both the ab initio and DFT-D methods accurately predict the intermolecular vibrational modes.     

Complex formation of polyethyleneimine with copper(II), nickel(II), and cobalt(II) ions

An influence of the structure of a globule of polyethyleneimine on the complex formation of one with the copper(II), nickel(II), and cobalt(II) ions is described. A change of the coordination number from the pH of solution for complexes of ethylenediamine, diethylenetriamine, and polyethyleneimine with metal ions was found. The fraction of monomer links, bound with metal ions, depends on the volume of the globule of macromolecule as well as the condition of the proceeding reaction. The reaction of complex formation is controlled by the diffusion of metal ions into the polymer globule in solution. The effective equilibrium constants of complex formation were found. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 914–922, 2002; DOI 10.1002/pola.10157     

Bound state potential energy surface construction: ab initio zero-point energies and vibrationally averaged rotational constants

Collins' method of interpolating a potential energy surface (PES) from quantum chemical calculations for reactive systems (Jordan, M. J. T.; Thompson, K. C.; Collins, M. A. J. Chem. Phys. 1995, 102, 5647. Thompson, K. C.; Jordan, M. J. T.; Collins, M. A. J. Chem. Phys. 1998, 108, 8302. Bettens, R. P. A.; Collins, M. A. J. Chem. Phys. 1999, 111, 816) has been applied to a bound state problem. The interpolation method has been combined for the first time with quantum diffusion Monte Carlo calculations to obtain an accurate ground state zero-point energy, the vibrationally average rotational constants, and the vibrationally averaged internal coordinates. In particular, the system studied was fluoromethane using a composite method approximating the QCISD(T)/6-311++G(2df,2p) level of theory. The approach adopted in this work (a) is fully automated, (b) is fully ab initio, (c) includes all nine nuclear degrees of freedom, (d) requires no assumption of the functional form of the PES, (e) possesses the full symmetry of the system, (f) does not involve fitting any parameters of any kind, and (g) is generally applicable to any system amenable to quantum chemical calculations and Collins' interpolation method. The calculated zero-point energy agrees to within 0.2% of its current best estimate. A0 and B0 are within 0.9 and 0.3%, respectively, of experiment.     

Quantum transition state theory for the full three-dimensional H+H2 reaction

A recently developed quantum transition state theory (QTST) [E. Pollak and J. L. Liao, J. Chem. Phys. 108, 2733 (1998)] for calculating thermal rate constants of chemical reactions is applied to the full three-dimensional hydrogen exchange reaction. Results are compared with other numerical results, for temperatures ranging from T=300 K to T=1500 K. The QTST rate is almost exact at high temperature and is 20% greater than the exact rate at T=300 K, where there is extensive tunneling.     

Dynamic coupling between coordinates in a model for biomolecular isomerization

To understand a complex reaction, it is necessary to project the dynamics of the system onto a low-dimensional subspace of physically meaningful coordinates. We recently introduced an automatic method for identifying coordinates that relate closely to stable-state commitment probabilities and successfully applied it to a model for biomolecular isomerization, the C(7eq)-->alpha(R) transition of the alanine dipeptide [A. Ma and A. R. Dinner, J. Phys. Chem. B 109, 6769 (2005)]. Here, we explore approximate means for estimating diffusion tensors for systems subject to restraints in one and two dimensions and then use the results together with an extension of Kramers theory for unimolecular reaction rates [A. Berezhkovskii and A. Szabo, J. Chem. Phys. 122, 014503 (2005)] to show explicitly that both the potential of mean force and the diffusion tensor are essential for describing the dynamics of the alanine dipeptide quantitatively. In particular, the signficance of off-diagonal elements of the diffusion tensor suggests that the coordinates of interest are coupled by the hydrodynamic-like response of the bath of remaining degrees of freedom.     

Anharmonicity of water stretching vibrations in series of isomorphous crystalline hydrates Copper and manganese saccharinates hexahydrates

On the basis of the experimentally obtained frequencies of isotopically isolated OH and OD species, the anharmonicity constants, as well as the harmonic eigenvalues of the OH and OD stretching vibrations for two members of the isomorphous series of metal(II) saccharinates hexahydrates (those of Mn and Cu) were calculated using several theoretical models [B. Berglund, J. Lindgren, J. Tegenfeldt, J. Mol. Struct. 43 (1978) 169, M.G. Sceats, S.A. Rice, J. Chem. Phys. 71 (1979) 973, H. Engstrom, J.B. Bates, L.A. Boatner, J. Chem. Phys. 73 (1980) 1073]. The anharmonicity constants and the nu(OH)/nu(OD) isotopic ratios correlate well with the stretching frequencies of the isotopically isolated OH and OD oscillators. Both anharmonicity constants and isotopic ratios as criteria for the anharmonicity of the OH (OD) vibrations show that, with a very few exceptions, it increases with the increase in the hydrogen bond strength. The exceptions from the trend are explained in terms of local electrostatic field differences and force constant changes due to the coordination to the metal ion. The obtained regression equations were used to predict the anharmonicity constants of the nu(OD) modes in other members of the series. Within the three-particle model of the hydrogen bonded complex, the parameters characterising the coupling of the nu(OH)/nu(OD)/modes with the low-frequency nu(Ocdots, three dots, centeredO) ones were estimated. The positions of the overtones of OH and OD stretching vibrations in the compounds of copper and manganese were estimated using the calculated anharmonicity parameters. The predicted values for the OD oscillators were compared with the experimentally obtained data. Model calculations of the described type are shown to be valuable in the assignment of the second-order transitions, especially in complex systems.     

Electronically unsaturated three-coordinate chloride and methyl complexes of iron,cobalt, and nickel

Three-coordinate organometallic complexes are rare, especially with the prototypical methyl ligand. Using a hindered, rigid bidentate ligand (L), it is possible to create 12-electron methyliron(II) and 13-electron methylcobalt(II) complexes. These complexes are thermally stable, and (1)H NMR spectra suggest that the low coordination number is maintained in solution. Attempts to create the 14-electron LNiCH(3) led instead to the three-coordinate nickel(I) complex LNi(THF). Single crystals of LMCH(3) are isomorphous with the new three-coordinate chloride complexes LNiCl and LCoCl. Along with the recently reported LFeCl (Smith, J. M.; Lachicotte, R. J.; Holland, P. L. Chem. Commun. 2001, 1542), these are the only examples of three-coordinate iron(II), cobalt(II), and nickel(II) complexes with terminal chloride ligands, enabling the systematic evaluation of the effect of coordination number and metal identity on M-Cl bond lengths. Electronic structure calculations predict the ground states of the trigonal complexes.     

Effects of the anion salt nature on the rate constants of the aqueous proton exchange reactions

The proton-transfer ground-state rate constants of the xanthenic dye 9-[1-(2-methyl-4-methoxyphenyl)]-6-hydroxy-3H-xanthen-3-one (TG-II), recovered by Fluorescence Lifetime Correlation Spectroscopy (FLCS), have proven to be useful to quantitatively reflect specific cation effects in aqueous solutions (J. M. Paredes, L. Crovetto, A. Orte, J. M. Alvarez-Pez and E. M. Talavera, Phys. Chem. Chem. Phys., 2011, 13, 1685-1694). Since these phenomena are more sensitive to anions than to cations, in this paper we have accounted for the influence of salts with the sodium cation in common, and the anion classified according to the empirical Hofmeister series, on the proton transfer rate constants of TG-II. We demonstrate that the presence of ions accelerates the rate of the ground-state proton-exchange reaction in the same order than ions that affect ion solvation in water. The combination of FLCS with a fluorophore undergoing proton transfer reactions in the ground state, along with the desirable feature of a pseudo-dark state when the dye is protonated, allows one unique direct determination of kinetic rate constants of the proton exchange chemical reaction.     

Imaging translational and rotational diffusion of single anisotropic nanoparticles with planar illumination microscopy

Here we demonstrated a simple yet powerful method, planar illumination microscopy, to directly track the rotational and translational diffusion dynamics of individual anisotropic nanoparticles in solution and living cells. By illuminating gold nanorods (GNRs) with two orthogonal sheets of light and resolving the polarized scattering signal with a birefringent crystal, we readily achieved three-dimensional angular resolving capability for single GNRs in noisy surroundings. The rotational dynamics of individual GNRs dispersed in glycerol/water mixtures with different chemical modification were tracked, and the measured rotational diffusion coefficient was well fitted to a previously reported theoretical model (Torre, J. G. d. l.; Martinez, M. C. L. Macromolecules 1987, 20, 661-666; Tirado, M. M.; Torre, J. G. d. l. J. Chem. Phys. 1980, 73, 1986-1993). In addition, the translational and rotational movements of individual GNRs transported by kinesin motor protein on microtubules inside living cells were directly imaged. Compared to its motion in free solution, a GNR attached to motor-protein did not rotate significantly while moving forward. Our method can be further generalized to allow determination of three-dimensional orientation of single dipoles using many different illumination modes.     

Lability criteria for successive metal complexes in steady-state planar diffusion

The lability of sequential metal complexes, ML, ML2, ML3, ... , up to a general 1:n metal/ligand stoichiometric ratio is considered for the case of metal ions (M) being accumulated at a surface (analytical sensor or organism). The analytical solution for the steady-state diffusion of M within a sequential complexation scheme allows quantification of the contribution from the dissociation of all of the complex species to the metal flux through the so-called lability degree, xi. A lability degree for each sequential complexation step is also defined which, due to the sequential character of the complexation scheme, depends not only on the proper kinetic constants of the given complexation step but also on the kinetics of the previous ones. When all contributions from the complexes are diffusion limited, the system is fully labile and xi=1. To provide simple lability criteria, the reaction layer approximation is extended to specifically deal with this sequential complexation scheme, so that a reaction layer thickness is defined when the existence of one particular rate-limiting step is assumed. Expressions for the classical lability parameter, L, are formulated using the reaction layer approximation. The change of the lability of the system as the diffusion layer thickness is modified is analyzed in detail. The contribution of the complex flux reflects the evolution of the system from labile to inert as the thickness of the sensor is appropriately decreased.     

Communication: rigorous calculation of dissociation energies (D0) of the water trimer, (H2O)3 and (D2O)3

Using a recent, full-dimensional, ab initio potential energy surface [Y. Wang, X. Huang, B. C. Shepler, B. J. Braams, and J. M. Bowman, J. Chem. Phys. 134, 094509 (2011)] together with rigorous diffusion Monte Carlo calculations of the zero-point energy of the water trimer, we report dissociation energies, D(0), to form one monomer plus the water dimer and three monomers. The calculations make use of essentially exact zero-point energies for the water trimer, dimer, and monomer, and benchmark values of the electronic dissociation energies, D(e), of the water trimer [J. A. Anderson, K. Crager, L. Fedoroff, and G. S. Tschumper, J. Chem. Phys. 121, 11023 (2004)]. The D(0) results are 3855 and 2726 cm(-1) for the 3H(2)O and H(2)O + (H(2)O)(2) dissociation channels, respectively, and 4206 and 2947 cm(-1) for 3D(2)O and D(2)O + (D(2)O)(2) dissociation channels, respectively. The results have estimated uncertainties of 20 and 30 cm(-1) for the monomer plus dimer and three monomer of dissociation channels, respectively.     

Pyridine and phosphonate containing ligands for stable lanthanide complexation. An experimental and theoretical study to assess the solution structure

We report an experimental and theoretical study of the stability and solution structure of lanthanide complexes with two novel ligands containing pyridine units and phosphonate pendant arms on either ethane-1,2-diamine (L2) or cyclohexane-1,2-diamine (L3) backbones. Potentiometric studies have been carried out to determine the protonation constants of the ligands and the stability constants of the complexes with Gd(III) and the endogenous metal ions Zn(II) and Cu(II). While the stability constant of the GdL2 complex is too high to be determined by direct pH-potentiometric titrations, the cyclohexyl derivative GdL3 has a lower and assessable stability (log K(GdL3)=17.62). Due to the presence of the phosphonate groups, various protonated species can be detected up to pH approximately 8 for both ligands and all metal ions studied. The molecular clusters [Ln(L)(H2O)](3-).19H2O (Ln=La, Nd, Ho or Lu; L=L2 or L3) were characterized by theoretical calculations at the HF level. Our calculations provide two minimum energy geometries where the ligand adopts different conformations: twist-wrap (tw), in which the ligand wraps around the metal ion by twisting the pyridyl units relative to each other, and twist-fold (tf), where the slight twisting of the pyridyl units is accompanied by an overall folding of the two pyridine units towards one of the phosphonate groups. The relative free energies of the tw and tf conformations of [Ln(L)(H2O)]3- (L=L2, L3) complexes calculated in aqueous solution (C-PCM) by using the B3LYP model indicate that the tw form is the most stable one along the whole lanthanide series for the complexes of L3, while for those of L2 only the Gd(III) complex is more stable in the tf conformation by ca. 0.5 kcal mol-1. 1H NMR studies of the Eu(III) complex of L3 show the initial formation of the tf complex in aqueous solution, which slowly converts to the thermodynamically stable tw form. The structures calculated for the Nd(III) complexes are in reasonably good agreement with the experimental solution structures, as demonstrated by Nd(III)-induced relaxation rate enhancement effects in the 1H NMR spectra.     

Application of permeation liquid membrane and scanned stripping chronopotentiometry to metal speciation analysis of colloidal complexes

The potential of permeation liquid membrane (PLM) to obtain dynamic metal speciation information for colloidal complexes is evaluated by measurements of lead(II) and copper(II) complexation by carboxyl modified latex nanospheres of different radii (15, 35, 40 and 65 nm). The results are compared with those obtained by a well characterized technique: stripping chronopotentiometry at scanned deposition potential (SSCP). Under the PLM conditions employed, and for large particles or macromolecular ligands, membrane diffusion is the rate-limiting step. That is, the flux is proportional to the free metal ion concentration with only a small contribution from labile complexes. In the absence of ligand aggregation in the PLM channels, good agreement was obtained between the stability constants determined by PLM and SSCP for both metals.     

Semiclassical calculation of nonadiabatic thermal rate constants: application to condensed phase reactions

The nonadiabatic transition state theory proposed recently by Zhao et al. [J. Chem. Phys. 121, 8854 (2004)] is extended to calculate rate constants of complex systems by using the Monte Carlo and umbrella sampling methods. Surface hopping molecular dynamics technique is incorporated to take into account the dynamic recrossing effect. A nontrivial benchmark model of the nonadiabatic reaction in the condensed phase is used for the numerical test. It is found that our semiclassical results agree well with those produced by the rigorous quantum mechanical method. Comparing with available analytical approaches, we find that the simple statistical theory proposed by Straub and Berne [J. Chem. Phys. 87, 6111 (1987)] is applicable for a wide friction region although their formula is obtained using Landau-Zener [Phys. Z. Sowjetunion 2, 46 (1932); Proc. R. Soc. London, Ser. A 137, 696 (1932)] nonadiabatic transition probability along a one-dimensional diffusive coordinate. We also investigate how the nuclear tunneling events affect the dependence of the rate constant on the friction.