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.     

A quasiclassical trajectory study of vibrational energy transfer in collisions involving intermolecular attraction of moderate strength

Monte Carlo selected, quasiclassical trajectories have been computed on six potential energy hypersurfaces possessing potential minima or “wells” up to 50 kJ mol^?1 deep. The aim of the investigation has been to examine how vibrational energy transfer in A + BC(υ = 1) collisions is promoted by intermolecular attraction of moderate strength. Here results are reported for the mass combination m_A = 20 u, m_B = 1 u, m_C = u. The results show that even quite slight intermolecular attraction can enhance energy transfer, as long as the attraction does not just depend on the separation of A from the center-of-mass of BC. The mean loss of vibrational energy does not depend only the well depth but also on its “location” (in particular, the difference in r_BC at the minimum and in isolated BC) and on the angular anisotropy of the potential. Large transfers of energy do not occur only in complex-forming collisions; indeed, a high fraction of trajectories on all surfaces are direct but show similar transfer of energy as in the more complex trajectories on the same surface. The results of the calculations are discussed in relation to the mechanisms and rates of vibrational relaxation in collisions between radicals and between species. such as HF + HF, capable of forming hydrogen bonds.     

Orbiting trajectories and the adiabatic approximation to the capture cross section

For the potentialV(R)=CR ^?4(1+ε(cos²??1/2)) and a planar geometry we compute classical trajectories, which are a good approximation to those trapped orbits which separate collisions with “capture” from those without. Two possible types of such trajectories (rotating or librating in the rotating reference frame) and the transition between both types are discussed. From the limiting impact parameters accurate capture cross sections may be calculated. They can be compared with the popular approximation known as ADO — (average dipole orientation) — theory, but an analysis of the latter shows that it is theoretically not justified. Instead, the adiabatic approximation for planar collisions is developed with and without angular momentum conservation. It fits numerical calculations very well as long as the transition from rotation to libration lies inside the centrifugal wall, i.e. the separating orbit is a rotation. In the opposite case only qualitative agreement is obtained. Finally, a simple approximation to get 3D capture cross sections from planar calculations is discussed.     

Second order charge overlap effects and damping functions for isotropic atomic and molecular interactions

Second order charge overlap effects and the related dispersion energy damping functions have been evaluated for the H-(1s)-H(1s) interaction through partial wave indices l_a+l_b such that (l_a+l_b) ? 13. These results are a substantial improvement on, or addition to, previous literature results and are important since they can be used, following several available scaling approaches, to construct damping functions for other interactions. They also indicate that the “spherical” energies are not an insignificant part of the total second order Coulomb energy until R becomes reasonably large. The various approaches for evaluating the non-expanded second order Coulomb energy are compared and the difficulties associated with the accurate determination of these energies, and the related damping functions, for general interactions are discussed in some detail.     

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     

Effects of electron–electron interaction on the band structure in polydiacetylenes

The ground‐state band structure of polydiacetylenes is theoretically studied with the extensional Su–Schriffer–Heeger model supplemented by electron–electron interactions. The results show the following. First, the interval of valence bands (conduction bands) increases because of the electron–electron interactions. Second, the effect of the on‐site Coulomb energy (U) is different from that of the nearest neighbor Coulomb repulsion (V); the competition between U and V shows that U makes the bandwidth narrower and the gap broader, whereas V makes the bandwidth broader and the gap narrower. There is a critical value of U/V. Third, the whole band width (E_w) decreases when the U/V ratio is less than 1.0 and increases when the U/V ratio is greater than 1.0 at V = 2.0 eV. Thus, the ground‐state band structure is sensitive to the U/V ratio. The results also show that electron–electron interactions can play an important role in the band structure of polydiacetylenes. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1656–1661, 2000     

The lack of leaving-atom isotope effects on rotational state distributions in M* + H2 (HD) → MH(ν, N)+H (D) reactions: “Half-collision” classical trajectories on model H-M-H anisotropic potential surfaces

Simple “half-collision” classical trajectories on model potential surfaces show that the lack of leaving-atom isotope effects on initial rotational state distributions P(N) in reactions of the type M + H₂ (HD) → MH (ν, N)+H (D) would result from decomposition of H-M-H (D) intermediates on anisotropic potential surfaces.     

Thermodynamics of molecular interactions in binary mixtures of non-electrolytes. Molar excess volumes

Molar excess volumes, V^E, for pyridine (A) + α-picoline (B), + β-picoline (B) and + γ-picoline (B) and benzene (A) + toluene (B), + o-xylene (B) and + p-xylene (B) and carbon tetrachloride (A) + n-heptane (B) have been measured dilatometrically as a function of temperature and composition and have been utilized to study B—B and B—B—B interactions in the presence of A via the Mayer—McMillan approach. A model has also been presented to account for these B—B and B—B—B interactions. The V^E data at 308.15 K have also been analysed in terms of the “graph theoretical” approach which describes the V^E data well for all these mixtures at 308.15 K. The “graph theoretical” approach has further been extended to successfully evaluate V^E data for a mixture at any temperature, T₂, when the V^E data at T₁ are known.     

Trinuclear Schiff base complexes with uranium(V) and copper(II) or zinc(II) ions

Treatment of the uranium(IV) complexes [{ML¹(py)}₂U^IV] (M = Cu, Zn; L¹ = N,N′-bis(3-hydroxysalicylidene)-1,3-propanediamine) with silver nitrate in pyridine led to the formation of the corresponding cationic uranium(V) species which were found to be thermally unstable and were converted back into the parent U^IV complexes; no electron transfer was observed in solution between the U^IV and U^V compounds. In the crystals of [{ML¹(py)}₂U^IV][{ML¹(py)}₂U^V][NO₃], the neutral U^IV and cationic U^V species are clearly identified by the distinct U–O distances. Similar reaction of [{ZnL²(py)}₂U^IV] [L² = N,N′-bis(3-hydroxysalicylidene)-1,4-butanediamine] with AgNO₃ gave crystals of [{ZnL²(py)}U^V{ZnL²(py)₂}][NO₃] but the copper counterpart was not isolated. Crystals of [{ZnL¹(py)}₂U^V][OTf] · THF (OTf = OSO₂CF₃) were obtained fortuitously from the reaction of [Zn(H₂L¹)] and U(OTf)₃.     

Physical aspects of charge transfer theory

The possible shapes of the ground (U_I) and first excited (U_II) adiabatic potentials are discussed in connection with the electron transfer problem. If U_I has two minima the electron transfer process is adiabatic, regardless of the value of the gap 2Γ between U_I and U_II; the transfer rate W has the form W = B exp(?E_A/T), the pre-exponential factor B can be influenced by the size of the gap, especially when Γ is small. For the fluctuation model of the medium in the case of purely adiabatic transfer (large Γ) the value of W corresponds to diffusional penetration through the potential barrier. A barrier of arbitrary shape is considered and an expression for W obtained, which matches with the corresponding expression for the “hindered adiabatic” case of small Γ.     

Spectra of atomic Rydberg states in strong magnetic fields

Transition frequencies and intensities for exited states of atomic hydrogen in a strong magnetic field are calculated by Fourier transformation of dipole moments computed using classical trajectories. We consider states with n = 30 and L_z = 1 for fields of up to 7 T. Spectra for states labeled as librators and rotators are found to be qualitatively different, especially for the spectral component perpendicular to the field. In addition to the zero-field Kepler line, a new intra-manifold transition is located at low frequency. The frequencies and intensities are found to be sensitive functions of the field strength, and of the particular state of the Coulomb manifold involved.     

Foundations of the relativistic theory of many-electron bound states

Most of the existing calculations of relativistic effects in many-electron atoms or molecules are based on the Dirac–Coulomb Hamiltonian H_DC. However, because the electron–electron interaction mixes positive- and negative-energy states, the operator H_DC has no normalizable eigenfunctions. This fact undermines the quantum-theoretic rationale for the Dirac–Hartree–Fock (DHF ) equations and therefore that of the relativistic configuration-interaction (RCI ) and multiconfiguration Dirac–Fock (MCDF ) methods. An approach to this problem based on quantum electrodynamics is reviewed. It leads to a configuration-space Hamilton H which involves positive-energy projection operators dependent on an external potential U; identification of U with the nuclear potential V_ext corresponds to use of the Furry bound-state interaction picture. It is shown that the RCI method can be reinterpreted as an approximation scheme for finding eigenvalues of a Hamiltonian H, with U identified as the DHF potential; the theoretical interpretation of the MCDF method needs further clarification. It is emphasized that if U differs from V_ext one must consider the effects of virtual-pair creation by the difference potential δU = V_ext ? U; an approximate formula for the level-shift arising from δU is derived. Some ideas for dealing with the technical problems introduced by the projection operators are discussed and relativistic virial theorems are given. Finally, a possible scheme for adapting current MCDF methods to Hamiltonians involving projection operators is described.     

Détermination des modèles d'imperfections de différentes variétés allotropiques du sulfure cuivreux (digénite cubique,chalcocite hexagonale “haute et basse température”, chalcocite orthorhombique)

From the study of the CuCuBrCu_2?εSC solid cell in the range of cubic digenite and “high temperature” hexagonal chalcocite we have deduced the laws of variation of the deviation from stoichiometry and the holes concentration with the equilibrium partial pressure of sulfur (δ and p are found to be proportional to ). The electronic model corresponding to the formation of associations (V^×_CuV′_Cu) in the presence of neutral vacancies V^×_Cu allows one to explain these laws. In the low temperature range (range of “low temperature” hexagonal chalcocite and orthorhombic chalcocite) the study of thermal variations of Hall coefficient permits us to propose the following models: (a) the deviation from stoichiometry of the “low temperature” hexagonal chalcocite is due to the simple ionized vacancies V′_Cu; (b) the deviation from stoichiometry of the orthorhombic chalcocite is due to the vacancies V′_Cu and to the associations (V^×_CuV^×_Cu).     

Schrödinger equation for a dirac bubble potential

The quantum-mechanical problem of a particle moving in a “Dirac bubble potential” U(r) = (λ/r_o)δ(r - r_o) is solved exactly for both bound and continuum states by making use of partial wave Green's functions G_l(r, r₀, k). Phase shifts are expressed in a compact form related to those for an impenetrable sphere.     

On the intrinsic anisochrony of diastereotopic nuclei in chiral ethanes and but-2-ynes

A theory for intrinsic magnetic shielding non-equivalence of the geminal nucleiU_a and U_b in ethanes CXYZ-CU_aU_bV and but-2-ynes CXYZ-CC-CU_aU_bV is developed and illustrated with the aid of symmetry auguments and mechanistic models. Special attention is given to mechanisms which survive when internal rotation is free and to the attenuation of intrinsic anisochrony with increasing separation between the chiral perturbing group and the sensor nuclei.     

The Fermi doublet V2−V3 + V4 of CH3CN as a probe of molecular interactions

The Fermi doublet V₂?V₃ + V₄ of CH₃CN in basic, inert and acidic solvents has been studied by IR and Raman spectroscopy. The values of W, the Fermi coupling coefficient, obtained from IR spectra varies with the nature of the solvent while W evaluated from Raman data remains constant at 12.5 ± 0.5 cm^?1. The similar effects of Bronsted and Lewis acids on the band frequencies and intensities is evidence that the CN group complexes with acids via the N atom “n” electron pair and not the π bond.     

Asymmetric torsional potential function and conformational analysis of furfural by far infrared and Raman spectroscopy

The far i.r. (400-50 cm⁻¹) spectra of gaseous and solid furfural (2-furancarboxaldehyde), c-C₄H₃O (CHO), have been recorded. Additionally, the Raman (3500-20 cm⁻¹) spectra of the gas and liquid have been obtained at variable temperatures and the spectrum of the solid at 25 K. These data have been interpreted on the basis that the molecule exists in two different conformations in the fluid states and that the conformation which has the two oxygen atoms oriented in a trans configuration, OO-trans, is most stable (ΔH ⩽ 1 kcal/mol) in the gas; however, the conformation which has the two oxygen atoms oriented cis, OO-cis, is preferred in the liquid (ΔH = 1.07 ± 0.03 kcal/mol) and is the only rotamer present in the spectra of the solid. The asymmetric torsional fundamental for the OO-trans rotamer has been observed at 146.25 cm⁻¹ in the far i.r. spectrum of the vapor and has five accompanying “hot bands”. The corresponding fundamental for the OO-cis rotamer has been observed at 127.86 cm⁻¹ along with a “hot band” which occurs at 127.46 cm⁻¹. From these data a cosine-based potential function governing internal rotation of the CHO top has been determined and the potential coefficients have values of V₁ = 173 ± 2, V₂ = 3112 ± 20, V₃ = 113 ± 2 and V₄ = −198 ± 6 cm⁻¹. This potential is consistent with an enthalpy difference between the more stable OO-trans and high energy OO-cis conformers being 286 ± 24 cm⁻¹ (818 ± 67 cal/mol) and a trans to cis barrier height of 3255 ± 20 cm⁻¹ (9.31 ± 0.06 kcal/mol). These results are compared to the corresponding quantities obtained previously from microwave spectroscopy and theoretical methods.     

La methode polarovoltrique : Principes généraux et bases de la méthode

The various steps in the development of the polarovoltric method and its utilisation in an automatic titration apparatus employing 2 polarized platinum electrodes are described. The method is based on the use of 2 types of polarization relationships applied to different chemical systems. These relationships are of the type I = f(V) and V = f(U), where V is the potential measured at the electrodes and U the potential applied to the electrodes across a resistance R, and are obtained directly from 2 indicating electrodes without the need for a reference electrode.The advantage of these relationships over the classic I= f(E) curves, where E is the potential of the indicating electrode with respect to a reference electrode, is to facilitate the prediction of the titration curves as a function of the resistance R and the applied voltage U. The use of these relationships has shown that a fixed applied voltage U of 3 V and a fixed series resistance R of 0.5 megohm are the most suitable for a differential polarovoltmeter for semi-automatic titrations.A symbolic notation is described which indicates the origin of the observed variations in potential. This notation permits a simple interpretation of polarovoltric curves and the rational use of unsymmetrical electrode arrangements.     

Electric dipole oscillator strengths: length and velocity!

Whenever approximate wavefunctions are employed in calculations of electric dipole oscillator strengths (f values). so that “length” and “velocity” forms ? and ? differ, an appropriate linear combination of transition moments may yield and f value which is usually close to (and often more accurate than) the better of f_L and f_V. Sample calculations on the helium isoelectronic sequence and the boron atom demonstrate the effectiveness of the procedure.     

Subtle Interactions and Electron Transfer between UIII,NpIII, or PuIII and Uranyl Mediated by the Oxo Group

A dramatic difference in the ability of the reducing An^III center in AnCp₃ (An=U, Np, Pu; Cp=C₅H₅) to oxo‐bind and reduce the uranyl(VI) dication in the complex [(UO₂)(THF)(H₂L)] (L=“Pacman” Schiff‐base polypyrrolic macrocycle), is found and explained. These are the first selective functionalizations of the uranyl oxo by another actinide cation. At‐first contradictory electronic structural data are explained by combining theory and experiment. Complete one‐electron transfer from Cp₃U forms the U^IV‐uranyl(V) compound that behaves as a U^V‐localized single molecule magnet below 4 K. The extent of reduction by the Cp₃Np group upon oxo‐coordination is much less, with a Np^III‐uranyl(VI) dative bond assigned. Solution NMR and NIR spectroscopy suggest Np^IVU^V but single‐crystal X‐ray diffraction and SQUID magnetometry suggest a Np^III‐U^VI assignment. DFT‐calculated Hirshfeld charge and spin density analyses suggest half an electron has transferred, and these explain the strongly shifted NMR spectra by spin density contributions at the hydrogen nuclei. The Pu^III–U^VI interaction is too weak to be observed in THF solvent, in agreement with calculated predictions.