Spin-Orbit coupling in aromatic hydrocarbons: A semiempirical evaluation of the radiative lifetimes of naphtalene and anthracene

Singlet-triplet spin-orbit matrix elements, which govern the lowest ³B_1u ← ¹A_g transition in typical aromatic molecules like naphtalene and anthracene, are calculated with INDO molecular orbitals and the conventional spin-orbit one-electron hamiltonian. The correct order of magnitude of the triplet radiative lifetimes is obtained for the two molecules, when INDO MO coefficients are referred to a symmetrically orthogonalized basis. The possibility of using the semiempirical Hamiltonian is explored using ab initio wave-functions for a few test cases. Reasonably accurate doublet-doublet and singlet-triplet matrix elements have been computed.     

Unitary group tensor operator algebras for many-electron systems: II. One- and two-body matrix elements

Relying on our earlier results in the unitary group Racah-Wigner algebra, specifically designed to facilitate quantum chemical calculations of molecular electronic structure, the tensor operator formalism required for an efficient evaluation of one- and two-body matrix elements of molecular electronic Hamiltonians within the spin-adapted Gel'fand-Tsetlin basis is developed. Introducing the second quantization-like creation and annihilation vector operators at the unitary group [U(n)] level, appropriate two-box symmetric and antisymmetric irreducible tensor operators as well as adjoint tensors are defined and their matrix elements evaluated in the electronic Gel'fand-Tsetlin basis as single products of segment values. Using these tensor operators, the matrix elements of one- and two-body components of a general electronic Hamiltonian are found. Explicit expressions for all relevant quantities pertaining to at most two-column irreducible representations that are required in molecular electronic structure calculations are given. Relationships with other approaches and possible future extensions of the formalism to partitioned bases or spin-dependent Hamiltonians are discussed.On leave from: Department of Chemistry, Xiamen University, Xiamen, Fujian, PR China.     

Ab initio copper–water interaction potential for the simulation of aqueous solutions

A new ab initio effective two-body potential that aims at mimicking the average copper–water interaction energy of the first solvation shell was developed. This new potential, together with the MCY water–water potential and a three-body ion–water–water induction potential, is tested in simulations of gas-phase clusters [Cu²⁺? (H₂O)₂₀] and diluted solutions [Cu²⁺? (H₂O)₂₀₀] at T = 298 K. The results of simulations with conventional ab initio pair potentials, with and without three-body induction corrections, are also presented. The different types of copper–water interaction potentials are evaluated comparatively and the efficiency of the newly proposed effective pair potential is discussed. © 1993 John Wiley & Sons, Inc.     

Spin-free approach for evaluation of electronic matrix elements using character operators of ℒN

A spin-free method is presented for evaluating electronic matrix elements over a spin-independent many-electron Hamiltonian. The spin-adapted basis of configuration state functions is obtained using a nonorthogonal spin basis consisting of projected spin eigenfunctions. The general expressions for the matrix elements are given explicitly, and it is demonstrated how the matrix elements may be obtained simply from the knowledge of the irreducible characters of the permutation group ℒ_N. The presented formulas are very general and may be applied in connection with both spin-coupled valence bond studies and in conventional configuration interaction (CI) methods based on an orthonormal orbital basis. © 1996 John Wiley & Sons, Inc.     

Unitary group approach to the many-electron problem. II. Adjoint tensor operators for U(n)

In this paper we present a derivation of the U(n) adjoint coupling coefficients for the representations appropriate to many-electron systems. Since the states of a many-fermion system are to comprise the totally antisymmetric Nth rank tensor representation of U(2n), the work of this paper enables the matrix elements of the U(2n) generators to be evaluated directly in the U(n) × U(2) (i.e., spin orbit) basis using their transformation properties as adjoint tensor operators. A connection between the adjoint coupling coefficients, as derived in this paper, and the matrix elements of certain (spin independent) two-body operators is also presented. This indicates that in CI calculations, one may obtain the matrix elements of spin-dependent operators from the known matrix elements of certain spin-independent two-body operators. In particular this implies a segment-level formula for the matrix elements of the U(2n) generators in the spin-orbit basis.     

Valence bond approach exploiting Clifford algebra realization of Rumer–Weyl basis

A detailed algorithm is described that enables an implementation of a general valence bond (VB ) method using the Clifford algebra unitary group approach (CAUGA ). In particular, a convenient scheme for the generation and labeling of classical Rumer–Weyl basis (up to a phase) is formulated, and simple rules are given for the evaluation of matrix elements of unitary group generators, and thus of any spin-independent operator, in this basis. The case of both orthogonal and nonrothogonal atomic orbital bases is considered, so that the proposed algorithm can also be exploited in molecular orbital configuration interaction calculations, if desired, enabling a greater flexibility for N-electron basis-set truncation than is possible with the standard Gel'fand–Tsetlin basis. Finally, an exploitation of this formalism for the VB method, based on semiempirical Pariser–Parr–Pople (PPP )-type Hamiltonian and nonorthogonal overlap-enhanced atomic orbital basis, and its computer implementation, enabling us to carry out arbitrarily truncated or full VB calculations, is described in detail.     

Molecular treatment of charge transfer cross sections in N5+ collisions with H2

We present cross sections for electron capture in N⁵⁺+H₂ collisions in the energy range 100 eV/amu≤E≤6 keV/amu. We employ a model potential aproximation to treat the interaction of the active electron with the cores, and a recently proposed method, which applies the independent particle model to evaluate the Hamiltonian matrix elements. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Gitterschwingungsspektren. LXIII. Be(lO3)2 · 4 H2O,ein Hydrat mit ungewöhnlicher Bindungsstruktur und Gitterdynamik

Lattice Vibration Spectra. LXIII. Be(IO₃)₂ · 4 H₂O, a Hydrate with Unusual Bonding and Lattice Dynamics The IR and Raman spectra (4000–50 cm^?1) of Be(IO₃)₂ · 4 H₂O and of deuterated specimens are recorded at 90 and 300 K and discussed in terms of the unusual relations of the masses of the atoms involved and the large polarization power of the beryllium ions. Thus, the translatory modes of the Be²⁺ ions (BeO₄ skeleton vibrations), the librations of the H₂O molecules, and the internal vibrations of the IO₃^? ions in the spectral regions of 300–400 and 600–1000 cm^?1 couple and coincide producing unusual v_H/v_D isotopic ratios of partly < 1. The H-bond donor strengths of the water molecules is so much increased (due to the very large ionic potential of Be²⁺ ions, viz. 49 e nm^?1) (synergetic effect) that the H-bonds formed are similar in strength as those in hydrates of hydroxides with the very strong H-bond acceptor group OH^? (v_OD of matrix isolated HDO molecules 2 074 and 2 244 (H₂O I) and 2 206 and 2 349 cm^?1 (H₂O II))     

Modeling the solvation shell of complexes in solution for quantum chemical calculations of electronic spectra

A procedure that allows for solvation effects is suggested; it is designed for quantum chemical calculations of the electronic spectra of complex compounds. Based on Monte Carlo (MC) simulation of the solvation shell one can calculate the electrostatic potential created by the solvation shell at the sites of all atoms of the complex; appropriate corrections are added to the diagonal elements of the Fock matrix and to the matrix elements of the Hamiltonian in the configuration interaction method. The method suggested has been implemented based on the semiempirical (CINDO) version of the CI (configuration interaction) technique and tested on the following compounds: [Ru(NH₃)₅(py)]²⁺, [Ru(NH₃)₅(pyz)]²⁺, [Ru(bpy)(CN)₄]^2?, [Ru(NO)(py)₄-NC-Ru(py)₄(CN)]³⁺.     

A semiempirical method based on geminal functions

An attempt has been made to develop a semiempirical method which considers only the n- and π-electrons, with the eigenfunctions expressed as an antisymmetrized product of two-electron functions or geminals. These geminals are expressed as a linear combination of products of Hückel-type MO's and the matrix elements are evaluated assuming the strong orthogonality condition to hold among the geminals, with an average effective Hamiltonian where the interaction between paired electrons is explicitly included. A first application of the method to N₂, HCN, C₂H₂, and C₂H^? was carried out without the introduction of parameters adjustable to best fit. A parametric approximation was then used for studying the electronic structure of diazabarrelene, an unknown molecule containing three pairs of π-electrons and two pairs of n-electrons. It is concluded that the explicit introduction of (π,π) and (n-π)-electron interaction describes the ground state more realistically than the simplest Hückel method. The separation of the energy levels was also affected, but the calculated transitions compared rather poorly with the spectroscopic observations. Diazabarrelene is expected to be not less stable than barrelene and attempts to its synthesis should be considered worthy of being made.     

Experimental study of the D + H2 (v = 1) reaction by CARS spectroscopy

The reactions D + H₂ (v = 0, 1) → HD (v = 0, 1) + H have been studiedin a discharge flow reactor by CARS-spectroscopy. For H₂(v = 0) molecules a rate constant of (4, 0 ± 1, 0) 10^?16 cm³ s^?1 is obtained at 310 K from measured HD (v = 0, 1) product yields. Keeping the degree of vibrational excitation of H₂in the microwave discharge in the range of 1% from the increase of the HD (v = 0, 1) CARS signals a rate of k_{2a, b} = (1, 0 ± 0, 4) 10^?13cm³ s^?1 is derived. The total consumption of H₂ (v = 1) in the presence of D atoms gives a rate k₂ = (1, 9 ± 0, 2) 10^?13 cm³ s^?1 at 310 K. The resultsare discussed in regard to previous measurements and theoretical treatments.     

Exact solution of indefinitely growing self-avoiding and Hamiltonian walk on fractals in four dimensions

The exponent v and the connectivity constant μ of an indefinitely growing self-avoiding walk and the μ_H for Hamiltonian walk in five simplex fractal have been calculated. We show that v is a decreasing function of d and that d = 4 is not the critical dimension. © 1996 John Wiley & Sons, Inc.     

Optimization of parameters for semiempirical methods. III Extension of PM3 to Be,Mg, Zn,Ga, Ge,As, Se,Cd, In,Sn, Sb,Te, Hg,Tl, Pb,and Bi

Using a recently developed procedure for optimizing parameters for semiempirical methods,¹ PM3 has been extended to a total of 28 elements. Average ΔH_f errors for the newly parameterized elements are Be: 8.6, Mg: 8.4, Zn: 5.8, Ga: 14.9, Ge: 11.4, As: 8.5, Se: 11.1, Cd: 2.6, In: 11.3, Sn: 9.0, Sb: 13.7, Te: 11.3, Hg: 6.8, Tl: 6.5, Pb: 7.4, and Bi: 10.9 kcal/mol. For some elements the paucity of data has resulted in a method, which, while highly accurate, is likely to be only poorly predictive.     

Configuration interaction matrix elements for atoms using permutation group algebra

A procedure is described for the efficient evaluation of the energy matrix elements necessary for atomic configuration-interaction calculations. With the orbital configurations of an N electron system in spin state S written as the irreducible representations [2^1/2N?S, 1^2S] of the permutation group S( N ), it is possible to evaluate readily the energy matrix elements of a spin-free Hamiltonian expressed in terms of the generators of the unitary group. We show how the use of angular momentum ladder operators permits the effective generation of a basis of eigenstates of ??², ??_z as well as ??² and ??_z, for which the energy matrix elements may be evaluated with ease.     

Unitary group approach to general system partitioning. II. U(n) matrix element evaluation in a composite basis

An explicit segment level formalism is derived for the matrix elements of the U(n) generators in an arbitrary (multishell) composite basis. The results of this paper, which contain the usual (spin-independent) unitary calculus approach as a limiting case, yield a more powerful and versatile algorithm than the traditional (spin-independent) unitary group formalism.     

Perturbative calculation of intermolecular interactions in orthogonalized or biorthogonal basis sets

Two versions of a many-body perturbation theory for the computation of molecular interaction energies are investigated. The methods are based on the partitioning of the second-quantized form of the dimer Hamiltonian written either in the orthogonalized basis of the monomer MOs, or, alternatively, in the original non-orthogonal dimer basis set handling the overlap by the biorthogonal formalism. The zeroth-order Hamiltonian H ⁰ is the sum of effective monomer Fockians and the zeroth-order wave functions are exact eigenfunctions of H ⁰. Full antisymmetry is ensured by the second-quantized formalism. Basis set superposition error is accounted for by the counterpoise correction recipe. Results for He₂, (H₂)₂ and (H₂O)₂ indicate the reliability of the biorthogonal technique.     

Concentration-dependence of faradaic currents and conductivity in a polystyrene sulfonic latex suspension

The conductivity, κ, in a suspension of polystyrene sulfonic latex without supporting electrolyte showed a linear dependence on the volume fraction, v_f, of the latex for v_f<0.03 with a finite intercept. In contrast, this deviated upward from the linear line for v_f>0.03. These variations were qualitatively consistent with the dependence of the voltammetric reduction current of H⁺ on v_f without supporting electrolyte. The current values were only a few percent of the theoretical diffusion-controlled current that could be observed in the suspension with supporting electrolyte. This fact indicates the electrostatic immobilization of the hydrogen ions by sulfonic latex particles. A plot of the current against κ at common values of v_f showed that the current for v_f>0.07 was smaller than the value predicted from the conductivity. This can be explained in terms of a combination of the increase in electrostatically unbounded H⁺ estimated by conductance measurements and electric migration in which the electrochemical depletion of [H⁺] also causes the depletion of the latex.     

Long-range interactions between atoms and molecules

The refractive index data for various gases are fitted to analytical formulae from which may be calculated the coefficient of the leading term of the long-range two-body interactions and the coefficient of the leading term of the long-range non-additive three-body interactions. Coefficients are obtained for mixtures of the gases He, Ne, A, Kr, Xe, H₂, N₂ and CH₄, the probable error being 5%.     

Electronic quantum motions in hydrogen molecule ion

The hydrogen molecule ion is a two‐center force system expressed under the prolate spheroidal coordinates, whose quantum motions and quantum trajectories have never been addressed in the literature before. The momentum operators in this coordinate system are derived for the first time from the Hamilton equations of motion and used to construct the Hamiltonian operator. The resulting Hamiltonian comprises a kinetic energy T and a total potential V_Total consisting of the Coulomb potential and a quantum potential. It is shown that the participation of the quantum potential and the accompanied quantum forces in the force interaction within H₂⁺ is essential to develop an electronic motion consistent with the prediction of the probability density function |Ψ|². The motion of the electron in H₂⁺ can be either described by the Hamilton equations derived from the Hamiltonian H = T_K + V_Total or by the Lagrange equations derived from the Lagrangian H = T_K ? V_Total. Solving the equations of motion with different initial positions, we show that the solutions yield an assembly of electronic quantum trajectories whose distribution and concentration reconstruct the σ and π molecular orbitals in H₂⁺. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011