The Flipping of CO Ligand Groups in Metal Carbonyl Compounds and its Frequency in Fe(CO)5

It has been proven qualitatively by a number of authors using variable temperature NMR experiments that most metal carbonyl complexes are nonrigid. A quantitative determination of the ligand exchange frequency v_e is often achieved by a line shape analysis or by measurement of the transverse relaxation time T₂ using the Carr-Purcell method. In the case of a “very fast” exchange, however, both methods prove unsuccessful. It is shown in this study that a simultaneous fit of IR or Raman spectra on the one hand and NMR spectra on the other can make possible the determination of v_e for the “very fast” exchange and can also facilitate the determination of v_e in “slow” and “medium” exchange cases considerably. The ligand exchange frequency thus found for Fe(CO)₅, 1.1 × 10¹⁰s^?1, is unexpectedly high; comparison with variable temperature measurements on solid Fe(CO)₅, yields similar energy barriers. A mechanism of exchange closely related to the “Berry mechanism” is proposed. Finally the consequences of this surprisingly large ligand exchange rate are discussed with respect to IR band assignments for molecular “fragments” M(CO)^x (where x=coordination number, and M is a transition metal, typically lanthanoid or actinoid).     

On the “New possibility of chemical bonding”: Anti-resonance phenomena

A chemical bond in the absence of a local minimum in the potential surface has been obtained recently by Pollak, Manz, Meyer and Römelt for the I-HI complex. We associate this “new chemical bond” with Simon's proof that a discrete spectrum can be obtained even for a quantum Hamiltonian for which the volume |(P, q)|P² + V(q) ? El is infinite and therefore an infinite number of classical trajectories lead to dissociation (an “anti-resonance” phenomenon). A simple model Hamiltonian which yields for any given E an infinite number of classical dissociative trajectories and also has a discrete spectrum in quantum mechanics, is presented.     

The complex coordinate scattering theroy and its application to the study of the surface asymmetry effect in helium diffraction from copper

The Complex Coordinate Scattering Theory is reformulated for the general case of a time-independent Hamiltonian. It is applied to scattering of He atoms from a Cu(115) crystal surface by constracting the Green operator for the T-matrix from the eigenvectors of both the complex scaled Hamiltonian and its transposed (“right” and “left” eigenvectors), which are different in this case. The weakly asymmetric corrugation function describing the (115) face of Cu is shown to cause a strong dependence of the calculated diffraction intensities upon the direction of the incident atomic beam. The calculated transition probabilities are in excellent agreement with the experimentally measured ones, previously obtained by Perreau and Lapujoulade. We show that additional information about the gas atom/surface physisorption interaction potential can be obtained if the incident angle of the atomic beam (the angles between the beam and the surface normal) is changed from γ to ?γ. © 1993 John Wiley & Sons, Inc.     

A “classical” trajectory driven nuclear dynamics by a parallelized quantum‐classical approach to a realistic model Hamiltonian of benzene radical cation

We explore the workability of a parallelized algorithm of time‐dependent discrete variable representation (TDDVR) methodology formulated by involving “classical” trajectories on each DOF of a multi‐mode multi‐state Hamiltonian to reproduce the population dynamics, photoabsorption spectra and nuclear dynamics of the benzene radical cation. To perform such dynamics, we have used a realistic model Hamiltonian consists of five lowest electronic states (X²E_1g, B²E_2g, C²A_2u, D²E_1u, and E²B_2u) which are interconnected through several conical intersections with nine vibrational modes. The calculated nuclear dynamics and photoabsorption spectra with the advent of our parallelized TDDVR approach show excellent agreement with the results obtained by multiconfiguration time‐dependent Hartree method and experimental findings, respectively. The major focus of this article is to demonstrate how the “classical” trajectories for the different modes and the “classical” energy functional for those modes on each surface can enlight the time‐dependent feature of nuclear density and its' nodal structure. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Internal dynamics of nonrigid molecules. I. Application to acetone

The group theory for nonrigid molecules is used for studying the internal dynamics of the two equivalent C_3v rotor “bent” molecules. Special emphasis is given to the deduction of the symmetry basis vectors which represent in box form the Hamiltonian operator. It is shown that these basis vectors may be advantageously employed in order to simplify the resolution of the two-rotor equation. The procedure is applied to the acetone molecule. It is found that the lowest solutions are clustered into groups of four. The four lowest levels are related to vibrational states, the upper 64 to vibro–rotational states, in which the rotors are rotating in a restricted manner. Only few states show some cogwheel effect. Internal rotation contributions to the principal thermodynamic parameters of acetone are also computed.     

Potentiometric methods for determination of autoprotolysis constants of amphiprotic nonaqueous solvents: Part II. Titration of a weak protolyte with another weak protolyte

A method for the determination of autoprotolysis constants of nonaqueous amphiprotic solvents is proposed, which makes use of the data of a potentiometric titration of a weak acid with a weak base. The method is based on a least-squares treatment of the data combined with the “pit-mapping” procedure developed by Sillén. The acid-base constants of the two weak protolytes along with the autoprotolysis constant are obtained simultaneously. The method is checked by determination of the autoprotolysis constant of the classical amophiprotic solvent-water. The pK_W^T-values as well as the acid-base constants of acetic. acid, ammonia, monochloroacetic acid, triethylamine and potassium biphthalate obtained by the proposed method are in a good agreement with the data reported by other authors.     

Connections between perturbation theory and the unitary transformation methods of deriving effective Hamiltonians

The connections between open shell Brillouin–Wigner perturbation theory and the Van Vleck unitary transformation formalisms for generating effective Hamiltonians are explored. An explicit expression is obtained relating the generator ? of the unitary transformation e^i? with the amplitudes to be found from perturbation theory. The “renormalization effects” needed to produce the explicit “orthogonal-Hermitian” form of the effective Hamiltonian in perturbation theory are related directly to the generator of the unitary transformation. The conclusions reached previously by Jørgensen and Brandow regarding the identity of the effective Hamiltonians of the formalisms are explicitly verified for the case that the generator ? satisfied the Kemble condition. The procedure suggests how the powerful techniques of perturbation theory can be used within the unitary transformation framework to guarantee properly renormalized wave functions.     

Improved intermolecular SCF theory and the BSSE problem

Analytical and numerical studies are performed concerning the exclusion of the basis set superposition error (BSSE ) from the SCF calculations of intermolecular interactions. Based on these studies a new procedure is proposed, which consists of the following steps: (1) determine the orbitals by the SCF scheme based on the recent “chemical Hamiltonian approach” (CHA-SCF method), i.e., excluding the delocalization effects caused by BSSE , and then (2) calculate the usual energy expectation value. (This gives results superior to those obtained by the previous nonsymmetric CHA energy formula.) The actual numerical calculations performed for different simple systems (He₂, water dimer) by using various basis sets indicate that the CHA/CE (CHA with “conventional energy” formula) potential curves are well-balanced and are close to those obtained by the Boys–Bernardi (BB ) method and usually (but not necessarily) go slightly beyond the latter. So our method gives results better than (or close to) those given by the BB method by performing only a single ～N⁴ calculation at each geometrical arrangement of the system.     

Na*(3p)-Formation under grazing scattering of Na+-ions at an Al(111) surface

Excited Na*(3p)-atoms are observed in grazing surface-collision experiments with Na⁺-beams. Such atoms can be formed beyond a certain threshold velocity via resonant electron transfer between atomic and metallic conduction band levels due to motion of the atom relative to the surface of the metal (“kinematic resonance”). This mechanism is studied here theoretically employing two different techniques: the nonperturbative “Coupled Angular Mode” (CAM) method and the approximate “Transfer Hamiltonian” (TH) method. The calculated Na*(3p)-populations agree well with recent experimental results. Moreover, the complete density matrix of the Na*(3p)-subspace has been computed with the TH-method for ion-energies between 10 and 300 keV.     

Electrochemical investigation of the chemical diffusion,partial ionic conductivities,and other kinetic parameters in Li3Sb and Li3Bi

The galvanostatic intermittent titration technique (GITT) has been used to electrochemically determine the chemical and component diffusion coefficients, the electrical and general lithium mobilities, the partial lithium ionic conductivity, the parabolic tarnishing rate constant, and the thermodynamic enhancement factor in “Li₃Sb” and “Li₃Bi” as a function of stoichiometry in the temperature range from 360 to 600°C. LiCl, KCl eutectic mixtures were used as molten salt electrolytes and Al, “LiAl” two-phase mixtures as solid reference and counterelectrodes. The stoichiometric range of the antimony compound is rather small, 7 × 10^?3 at 360°C, whereas the bismuth compound has a range of 0.22 (380°C), mostly on the lithium deficit side of the ideal composition. The thermodynamic enhancement factor in “Li₃Sb” depends strongly on the stoichiometry, and has a peak value of nearly 70 000; for “Li₃Bi” it rises more smoothly to a maximum of 360. The chemical diffusion coefficient for “Li₃Sb” is 2 × 10^?5 cm² sec^?1 at negative deviations from the ideal stoichiometry and increases by about an order of magnitude in the presence of excess lithium at 360°C. The corresponding value for “Li₃Bi” is 10^?4 cm² sec^?1 with high lithium deficit, and increases markedly when approaching ideal stoichiometry. The activation energies are small, 0.1–0.3 eV, depending on the stoichiometry, in both phases. The mobility of lithium in “Li₃Bi” is about 500 times greater than in “Li₃Sb” with a lithium deficit. The ionic conductivity in “Li₃Sb” increases from about 10^?4 Ω^?1 cm^?1 in the vacancy transport region to about 2 × 10^?3 where transport is probably by interstial motion at 360°C. For “Li₃Bi” a practically constant value of nearly 10^?1 Ω^?1 cm^?1 is found at 380°C. The parabolic tarnishing rate constant shows a sharp increase at higher lithium activities in “Li₃Sb” whereas in “Li₃Bi” it has a roughly linear dependence upon the logarithm of the lithium activity. The tarnishing process is about 2 orders of magnitude slower for “Li₃Sb” than for “Li₃Bi.” Because of the fast ionic transport in these mixed conducting materials, “Li₃Sb” and “Li₃Bi” may be called “fast electrodes.”     

Conformational and energetic properties of the ammonia dimer—comparison of post-Hartree—Fock and density functional methods

The equilibrium structure of the ammonia dimer has been investigated with density functional and MP2 calculations. We used Slater- and Becke-exchange functionals combined with correlation functionals as recommended by Vosko-Wilk-Nusair, by Perdew, and by Lee-Yang-Parr, respectively. The potential energy surfaces was investigated. The asymmetric cyclic “microwave” structure could be identified as a minimum. Optimization of the intermolecular parameters showed that this structure has nearly the same energy as the centrosymmetric cyclic structure. Full optimization transformed the asymmetric cyclic structure into the linear structure. The interaction energies in the dimer were corrected for the basis set superposition error using the Boys-Bernardi counterpoise method and the a priori chemical Hamiltonian approach, respectively. © 1996 by John Wiley & Sons, Inc.     

Polymer-Bromine Interactions. I. Interactions with Polyacrylonitrile

The present paper deals with the interactions of bromine with poly-acrylonitrile (PAN). Kinetics and equilibria of the sorption of Br₂ on PAN were studied at a concentration range of 0.01–0.1 mol/L and a temperature range of 25–40°C. Two kinds of sorption were found: a “reversible” sorption removable by water and an “irreversible” sorption removable by aqueous ammonia solutions. The irreversibly sorbed bromine is presumably linked by charge transfer to the nitrile groups of the PAN, as evidenced by UV spectra. The irreversible sorption follows the reversible sorption and is slower. Partition coefficients obtained from the linear Freundlich isotherms increased with temperature and, at 40°C, the values obtained were 97, 65, and 32 L/kg for the total, irreversible, and reversible sorptions, respectively. At 25°C the chemical potential, enthalpy, and change in entropy for the irreversible sorption were ?2.0 kcal/mol, 9.4 kcal/mol, and 38 cal·mol^?1·K^?1. Effects of a 6-day Br₂ treatment and ammonia rinse were: decrease in dry T _g from 74.5 to 61°C and in water from 38 to 35°C; no significant decrease in M _W ; decrease in tensile strength measured after the bromine stage, and improvement after ammonia stage; increased swollen dimensions from 57% in water to 75%; and stabilization of swollen dimensions upon drying. The results support the existence of two phases in the less ordered regions of PAN.     

REACTION OF α-CHLOROTOLUENE WITH ELEMENTAL SULFUR IN LIQUID AMMONIA

Abstract

α-Chlorotoluene (1) reacts with elemental sulfur in liquid ammonia affording dibenzyl disulfide (2), dibenzyl trisulfide (3), dibenzyl tetrasulfide (4), dibenzyl pentasulfide (5) and benzylidene benzylimide (6) at a low temperature such as 20°C. This reaction is presumed to be initiated by the nucleophilic attack of ammonium thioaminohydroxylate, “H₂NS^-NH₄ ⁺,” or dithioaminohydroxylate, “H₂NSS^-NH₄,” formed upon treating elemental sulfur in liquid ammonia, on α-chlorotoluene (1). Benzylidene benzylimide (6) is presumed to be formed from benzylamine, which can be formed by treatment of α-chlorotoluene (1) with ammonia.     

New generation of semiempirical methods of molecular modeling based on the theory of group functions

The semiempirical methods of modeling the molecular systems using the group function approximation for electronic structure calculations have been used by the author for many years. The review discusses the general structure of the semiempirical method that uses the group functions and the results obtained by the particular methods, namely, the crystal field effective Hamiltonian method designed for systems containing transition metal ions and methods based on the strictly local geminal approximation designed for modeling the “organic” molecules.     

EPR on tetrabutylammonium tetraiodo-nitrosyltechnetate(II), (Bu4N)[Tc(NO)I4]

An EPR study on tetrabutylammonium tetraiodo-nitrosyltechnetate(II), (Bu₄N)[Tc(NO)I₄], is reported. The frozen solution EPR spectrum is described by an axially symmetric spin Hamiltonian. The ⁹⁹Tc hyperfine interaction is used to estimate the spin density distribution in the MO of the unpaired electron which is of “in-plane-π-type”.     

Enhancing the Sensitivity of Aptameric Detection of Lysozyme with a “Feed‐Forward” Network of DNA‐Related Reaction Cycles

In this study, a network of DNA‐related reaction cycles was established to enhance the sensitivity of lysozyme detection with dual signal amplification, and aptamer‐based reactions were integrated into this system to provide high specificity. The network was organized in a feed‐forward manner: the “upstream cycles” recognized the lysozyme (the target) and released the “messenger strands” from probe A (a DNA construct); the “downstream cycles” received them and then released the “signal strands” from another DNA construct, probe B, in multiplied quantities to that of the original inputted lysozyme. The upstream cycles centered on “target‐displacement polymerization”, which circulates the lysozyme to provide primary amplification; the downstream cycles centered on “strand‐displacement polymerization”, which circulates the messenger strand to provide further amplification. There were also several “nicking–polymerization” cycles in both reaction groups that provide extra signal amplification. In total, the network enclosed eight interconnected and autonomic reaction cycles, with only two probes, two primers, and two enzymes needed as raw feeds, and the network can be operated simply in one‐pot mode. With this network, lysozyme could be quantified at lysozyme concentrations as low as 2.0×10^?14 M , with a detection limit of 3.6×10^?15 M (3σ rule), which was seven orders of magnitude lower than that obtained without any amplification(1.8×10^?8 M ). Detection of lysozyme in real serum samples confirmed the reliability and practicality of the assay based on this reported reaction network.     

Towards a “Chemical” Hamiltonian

An analysis of the LCAO Hamiltonian is performed in terms of a “mixed” formulation of the second quantization for nonorthogonal orbitals, compressing the different interactions to one- and two-center terms as far as possible by performing appropriate projections. For this purpose an operator of atomic charge is also introduced, the expectation values of which are the Mulliken gross atomic populations on the individual atoms. The LCAO Hamiltonian is decomposed into terms having different physical meaning and significance: (i) sum of effective atomic Hamiltonians; (ii) the electrostatic interactions in the point-charge approximation; (iii) the electrostatic effects connected with the deviation of the actual charge distribution from the pointlike one; (iv) two-center overlap effects; (v) finite basis (“counterpoise”) correction terms related to the individual atoms; and (vi) similar finite basis correction terms with respect to the two-center interactions. Only terms of types (i) to (iv), containing no three- or four-center integrals, are considered as having physical significance. Based on the analysis of the Hamiltonian, an energy partitioning scheme is developed, and explicit expressions are given for one- and two-center (and basis extension) components of the SCF energy. The approach is also applied to the problem of intermolecular interactions, and an explicit formula is given permitting calculation of the “counterpoise” part of the supermolecule energy by properly taking into account that it depends not only on the extension of the basis, but also on the occupation of the additional orbitals in the intervening molecule—a factor completely overlooked in the usual scheme of calculations.     

Note on the atomic correlation energy

In the introductory section, we compare the total, kinetic, nuclear-electron, Coulomb, exchange, and correlation energies of ground-state atoms. From the analyses of the data, one can conclude that the Hartree-Fock (HF) model is notably good and might require only a small perturbation to become essentially an “accurate” model. For this reason and considering past literature, we present a semiempirical extension of the HF model. We start with a calibration of three independent models, each one with an effective Hamiltonian, which introduces a small perturbation on the kinetic, the nuclear-electron, or the Coulomb HF operators. The perturbations are expressed as very simple functions of products of orbital probability density. The three perturbations yield very equivalent results and the computed ground-state energies are reasonably near to the accurate nonrelativistic energies recently provided by E. Davidson and his collaborators for the 2–18 electron systems and the estimates by Clementi and his collaborators for the 19–54 electron systems. The first ionization potentials from He to Cs, the second ionization potentials from Li to Zn, and excitation energies for npⁿ, 3dⁿ, and 4s¹3dⁿ configurations are used as additional verification and validation. The above three effective Hamiltonians are then combined in order to redistribute the correlation energy correction in a way which exactly satisfies the virial theorem and maintains the HF energy ratios between kinetic, nuclear-electron, and electron-electron interaction energies; the resulting effective Hamiltonian, named “virial constrained,” yields good quality data comparable to those obtained from the three independent effective operators. Concerning excitation energies, these effective Hamiltonians yield values only in modest agreement with experimental data, even if definitively superior to HF computations. To further improve the computed excitation energies, we applied an empirical scaling in the vector coupling coefficient; this correction yields very reasonable excitations for all the configurations that we have considered. We conclude that the use of effective potentials to introduce small perturbations density-dependent onto the HF model constitutes a broad class of practical and reliable semiempirical solutions to atomic many-electron problems, can provide an alternative to popular proposals from density functional theory, and should prepare the ground for “generalized HF models.” © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 571–591, 1997     

Electrochemical Synthesis of Organic Polysulfides from Disulfides by Sulfur Insertion from S8 and an Unexpected Solvent Effect on the Product Distribution

An electrochemical synthesis of organic polysulfides through sulfur insertion from elemental sulfur to disulfides or thiols is introduced. The highly economic, low-sensitive and low-priced reaction gives a mixture of polysulfides, whose distribution can be influenced by the addition of different amounts of carbon disulfide as co-solvent. To describe the variable distribution function of the polysulfides, a novel parameter, the “absorbance average s ulfur a mount in p olysulfides” (SAP) was introduced and defined on the basis of the “number average molar mass” used in polymer chemistry. Various organic polysulfides were synthesized with variable volume fractions of carbon disulfide, and the yield of each polysulfide was determined by quantitative ¹³C NMR. Moreover, by using two symmetrical disulfides or a disulfide and a thiol as starting materials, a mixture of symmetrical and asymmetrical polysulfides could be obtained.