Analysis of the equation-of-motion theory of electron affinities and ionization potentials

An analysis of the equation-of-motion (EOM) method for computing molecular electron affinities and ionization potentials is presented. The method is compared with the Dyson equation approach of Green function theory. Particular emphasis is devoted to clarifying the similarities between these two theories when carried out to second and to third order. The Epstein—Nesbet hamiltonian and the notion of diagonal scattering renormalization have been used to systematize this comparison.     

Magnetic screening of nuclei by electrons as manifestation of geometric vector potential

Summary The usual Born-Oppenheimer approach to a molecule in a magnetic field leads to an effective nuclear hamiltonian in which bare nuclei interact with the field. We show that the geometric phase, which has been the object of much interest in recent years, is capable of correcting this defect, accounting for corrections to the molecular charge and magnetic moment due to the electron cloud accompanying the nuclei.     

The single particle dynamics of iodine in the Sachs-Teller regime: an inelastic x-ray scattering study

The high frequency dynamics of liquid iodine has been investigated by deep inelastic x-ray scattering at exchanged wave-vectors (q) ranging from 2.5 to 15 A?(-1). The experimental data have been analyzed in the frame of the Sachs-Teller theory of the molecular spectrum while accounting for final state corrections to the lineshape. The performed data analysis carries insights on physical quantities as relevant as the mean rototranslational kinetic energy and the mean square Laplacian of the intermolecular potential. In both cases the measured values are consistent with corresponding theoretical expectations.     

Superfine and hyperfine structures in the v3 band of 32SF6

We present a first detailed account of our theoretical approach to reproduce observed superfine and hyperfine structures in the ν₃ band of SF₆ and we display various observed and calculated patterns of superfine clusters exhibiting hyperfine effects. The main operators of the hamiltonian are derived and the associated constants are related to molecular parameters. We show that, owing to the off-diagonal terms in the hyperfine hamiltonian, a mixing occurs between vibration—rotation states with different point-group symmetry species. As a consequence, superfine and hyperfine structures have to be considered simultaneously and hyperfine hamiltonian matrices connecting several vibration—rotation states need to be diagonalized to reproduce the spectra. We analyse in greater detail a few typical examples from which several molecular constants have been determined (e.g. t₀₄₄, c_d). For the first time, the sign c_d is obtained. Also an effective change, Δc_d, is found between upper and lower levels which can be readily interpreted as a manifestation of the tensor spin—vibration interaction.     

Relativistic corrections in the multiple-scattering method

We show how to introduce the Foldy-Wouthuysen relativistic corrections in the multiple-scattering method, for the determination of the electronic energy levels of molecules. The present derivation begins from a variational expression where the Foldy-Wouthuysen hamiltonian is inserted, instead of the Schrödinger hamiltonian. The resulting secular equation becomes identical with the standard multiple-scattering secular equation, if one neglects the relativistic correction terms.     

Rotation energies for deuterated H+3 oscillators in zero-point states of vibration

Previous ab initio studies of deuterated H⁺₃ molecular ions are extended to include rotational modes for the zero-point states of vibration. Rotation energies are obtained using direct numerical diagonalization of vibration—rotation hamiltonian matrices, and nuclear wavefunctions as superpositions of mode-coupled anharmonic rotationless vibrators and related prolate symmetric top eigenfunctions. Relevance to recent searches for interstellar H₂D⁺ is noted.     

Low energy (e,2e) measurements of CH4 and neon in the perpendicular plane

Low energy experimental and theoretical triple differential cross sections for the highest occupied molecular orbital of methane (1t(2)) and for the 2p atomic orbital of neon are presented and compared. These targets are iso-electronic, each containing 10 electrons and the chosen orbital within each target has p-electron character. Observation of the differences and similarities of the cross sections for these two species hence gives insight into the different scattering mechanisms occurring for atomic and molecular targets. The experiments used perpendicular, symmetric kinematics with outgoing electron energies between 1.5 eV and 30 eV for CH(4) and 2.5 eV and 25 eV for neon. The experimental data from these targets are compared with theoretical predictions using a distorted-wave Born approximation. Reasonably good agreement is seen between the experiment and theory for neon while mixed results are observed for CH(4). This is most likely due to approximations of the target orientation made within the model.     

Approximate analytic evaluation of distorted-wave matrix elements for inverse power potentials

A method for approximate analytic evaluation of distorted-wave matrix elements for inverse power potentials is presented. Preliminary results are very encouraging. The method is computationally extremely fast and, with the exponential distorted-wave approximation, should make it possible to solve many currently intractable molecular collision problems.     

A simple approach to predicting resonance levels

We propose a modification of Hazi and Taylor's stabilization method for calculating resonance energies by adding a positive definite operator to the hamiltonian. The purpose of this operator is to raise the energies of scattering states while not significantly affecting the bound or resonance states. The method has advantages over the ordinary stabilization techniques. We treat two model problems and discuss possible applications to atomic and molecular systems.     

Quantum effects on adsorption and diffusion of hydrogen and deuterium in microporous materials

Monte Carlo and molecular dynamics simulations and neutron scattering experiments are used to study the adsorption and diffusion of hydrogen and deuterium in zeolite Rho in the temperature range of 30-150 K. In the molecular simulations, quantum effects are incorporated via the Feynman-Hibbs variational approach. We suggest a new set of potential parameters for hydrogen, which can be used when Feynman-Hibbs variational approach is used for quantum corrections. The dynamic properties obtained from molecular dynamics simulations are in excellent agreement with the experimental results and show significant quantum effects on the transport at very low temperature. The molecular dynamics simulation results show that the quantum effect is very sensitive to pore dimensions and under suitable conditions can lead to a reverse kinetic molecular sieving with deuterium diffusing faster than hydrogen.     

Electronic effect on the rotational energy of a diatomic molecule

The rotational hamiltonian for a diatomic molecule has been rederived from the total classical hamiltonian. This procedure directly introduces the effect of electronic motion which is ordinarily neglected in zero-order approximation. Kronig's rotational hamiltonian is discussed and shown to be an approximation of our findings. Our general result is then specialized to ¹Σ states, and the theory tested by calculating the observed fractional discrepancy between the experimentally determined H³⁵Cl energy level constant Y₀₂ and its predicted value from Dunham's theory. When all corrections are summed, the results are in good agreement with experiment.     

Analysis of exact valence shell hamiltonian: Nonclassical terms and molecular based parameters

The exact valence shell effective hamiltonian is analyzed for one- and two-valence orbital systems using a second quantized formulation. The exact solutions of the exact effective hamiltonian are used, to display the meaning of each of its terms. The well-known α_υ = ?I_p and γ_υυ = I_p ? A_f relations are provided a molecular basis for certain special cases, thereby enabling molecular definitions for molecular “integrals” and allowing the determination of the molecule and bond length dependence of traditional semi-empirical “integrals”. It is shown how the presence of nonclassical terms in the effective hamiltonian destroys the pairing symmetry of alternate hydrocarbons.     

Structure-parameter and force-field refinement for lead dihalide molecules

Conclusions It has been shown for PbF₂ that one can process electron-diffraction data for molecules containing heavy atoms on the basis of atomic scattering amplitudes calculated with a relativistic approximation for the atomic electron density. The errors in calculating the atomicscattering amplitudes explain the previous discrepancies in the observed values for the Pb-Cl amplitudes in PbCl₂ derived in two independent researches. The differences between those values are now not so considerable, and they may be explained as due to experimental error or to the processing of the measurements in Hungary for most of the scattering angles having been performed without the relativistic corrections to the electron density.Our mean-square vibration amplitudes and the measured frequencies can be used with our semiempirical relationships for the force constants to determine the potential-energy parameters for those molecules and to estimate the vibrational frequencies for PbI₂, which have not been measured.I am indebted to Professor V. P. Spiridonov and staff at the vapor electron-diffraction laboratory at Moscow University for providing the observed values for the reduced molecular component of the scattering intensities for lead dihalides and for valuable comments in discussion on the draft.High-Temperature Institute, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 1, pp. 54–59, January–February, 1991.     

Urbach rule in the optical spectra of crystalline and amorphous organic-solids

In this paper we explore the effects of microscopic structural disorder on the low energy optical absorption edges in some crystalline and amorphous organic solids. We advance a theoretical model which incorporates the simultaneous effects of static disorder and of exciton—phonon coupling on Frenkel exciton states. Explicit theoretical expressions were derived for the self energy and for the absorption lineshapes by the introduction of a two-step effective-field approximation, defining an effective exciton—phonon hamiltonian which was subsequently utilized within the framework of a single site average t-matrix approximation for disorder scattering. Numerical results for the low energy lineshapes over a broad temperature range demonstrate that exciton scattering by a static disorder field results in Urbach type low energy absorption tails, where the Urbach slope is temperature independent.     

The derivation of relativistic corrections to the hamiltonian for two electrons

Use of the relativistic equation for two electrons in the presence of a radiation field gives corrections to the non-relativistic hamiltonian with less difficulty than use of the Dirac or Breit equation.     

Neutron diffraction and simulation studies of the exocyclic hydroxymethyl conformation of glucose

The techniques of neutron diffraction with isotopic substitution (NDIS) and molecular dynamics (MD) simulations have been used to examine the rotational conformation of the exocyclic hydroxymethyl group of D-glucopyranose. First order H/D NDIS experiments were performed on the H6 position in 3m aqueous glucose solutions where the average coherent scattering length of the exchangeable hydrogen atoms was zero (i.e., all correlations between exchangeable hydrogen atoms and other atoms cancel and thus are not present in the scattering data). This H6 experimental result suggests that no single conformation for the C4-C5-C6-O6 dihedral reproduces the observed scattering data well, but that a mixture of the gg and gt conformations, which has been suggested by NMR experiments, gives a reasonable agreement between the MD and experimental data.     

Atom-molecule scattering with the average wavefunction method

The average wavefunction method (AWM) is applied to atom-molecule scattering. In its simplest form the labor involved in solving the AWM equations is equivalent to that involved for elastic scattering in the same formulation. As an initial illustration, explicit expressions for the T-matrix are derived for the scattering of an atom and a rigid rotor. Results are presented for low-energy scattering and corrections to the Born approximation are clearly evident. In general, the AWM is particularly suited to polyatom scattering due to its reduction of the potential in terms of a separable atom-atom potential.     

Spin asymmetry in near threshold (e, 2e) process for lithium and hydrogen

The singlet and triplet cross sections and the asymmetry parameter for e-H and e-Li ionization have been calculated in a distorted-wave Born approximation for incident energies in the range 0.5 to 20 eV above the ionization threshold. The two final-state continuum electrons are assumed to share equal energy and to come out 180° apart. The variation with respect to the angle of scattering is found to be qualitatively very different in the two cases. It is found that, in the case of lithium, the ¹D and ³F components in the scattering amplitude are quite significant even at very low energies.     

Exponential perturbation theories for inelastic scattering

An Exponential Perturbation Theory (EPT) is derived whereby one calculates a phase-shift matrix by an nth order perturbation theory and then exponentiates it to obtain the scattering matrix. The theory has been developed to include high-order terms, closed channels and resonances. The radial wavefunctions used are WKB solutions which are generalized to cases where there are multiple turning points. The orbital angular momentum may be treated exactly or in the classical or sudden limits. Calculations are done for the rotationally inelastic scattering in He + H₂, Ar + N₂ and Ar + HCl. The first two systems give fair to good agreement with accurate calculations; the last case gives poor agreement. The first-order EPT is very much better than the first-order distorted-wave approximation.     

Some aspects of scaling factor calculations for quantum-mechanical molecular force fields

Stages of the scaling procedure for correcting molecular force fields obtained in rough quantum chemical calculations are discussed. The procedure includes selection of the number of scaling factors and their determination using experimental vibration frequencies of isotopomers and related molecules. It is stated that the difference in anharmonicity corrections for light molecules and their heavy analogs is to be taken into account along with possible errors in vibration frequency assignments of both isotopomers and more complex related molecules.