Excited states of linear polyenes in the SCF–RPA method

In the framework of the PPP Hamiltonian, we have studied the low-lying spectra of all trans linear polyenes with the dielectirc function method. It is shown that higher order processes, not included in the RPA scheme as local field correction (LFC) and self-energy (SE) effects can be introduced in a effective way by a suitable parametrization of the residual coulomb interaction. This parametrization is fixed along the polyene series both for singlet and triplet states, at variance with previous RPA calculations. Comparison with the most refined CI calculations, as well as with the experimental findings shows very good agreement. Furthermore, chain length and geometry dependence of the electron–electron correlation is briefly discussed.     

Vibrational–rotational energies of all H2 isotopomers using Monte Carlo methods

Using variational Monte Carlo techniques, we have computed several of the lowest rotational–vibrational energies of all the hydrogen molecule isotopomers (H₂, HD, HT, D₂, DT, and T₂). These calculations do not require the excited states to be explicitly orthogonalized. We have examined both the usual Gaussian wave function form as well as a rapidly convergent Padé form. The high‐quality potential energy surfaces used in these calculations are taken from our earlier work and include the Born–Oppenheimer energy, the diagonal correction to the Born–Oppenheimer approximation, and the lowest‐order relativistic corrections at 24 internuclear points. Our energies are in good agreement with those determined by other methods. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Calculations of electron inelastic mean free paths. XI. Data for liquid water for energies from 50 eV to 30 keV

We calculated electron inelastic mean free paths (IMFPs) for liquid water from its optical energy‐loss function (ELF) for electron energies from 50 eV to 30 keV. These calculations were made with the relativistic full Penn algorithm that has been used for previous IMFP and electron stopping‐power calculations for many elemental solids. We also calculated IMFPs of water with three additional algorithms: the relativistic single‐pole approximation, the relativistic simplified single‐pole approximation, and the relativistic extended Mermin method. These calculations were made by using the same optical ELF in order to assess any differences of the IMFPs arising from choice of the algorithm. We found good agreement among the IMFPs from the four algorithms for energies over 300 eV. For energies less than 100 eV, however, large differences became apparent. IMFPs from the relativistic TPP‐2M equation for predicting IMFPs were in good agreement with IMFPs from the four algorithms for energies between 300 eV and 30 keV, but there was poorer agreement for lower energies. We calculated values of the static structure factor as a function of momentum transfer from the full Penn algorithm. The resulting values were in good agreement with results from first‐principle calculations and with inelastic X‐ray scattering spectroscopy experiments. We made comparisons of our IMFPs with earlier calculations from authors who had used different algorithms and different ELF data sets. IMFP differences could then be analyzed in terms of the algorithms and the data sets. Finally, we compared our IMFPs with measurements of IMFPs and of a related quantity, the effective attenuation length. There were large variations in the measured IMFPs and effective attenuation lengths (as well as their dependence on electron energy). Further measurements are therefore required to establish consistent data sets and for more detailed comparisons with calculated IMFPs. Copyright © 2016 John Wiley & Sons, Ltd.     

Generalized Born model with a simple, robust molecular volume correction

Generalized Born (GB) models provide a computationally efficient means of representing the electrostatic effects of solvent and are widely used, especially in molecular dynamics (MD). A class of particularly fast GB models is based on integration over an interior volume approximated as a pairwise union of atom spheres-effectively, the interior is defined by a van der Waals rather than Lee-Richards molecular surface. The approximation is computationally efficient, but if uncorrected, allows for high dielectric (water) regions smaller than a water molecule between atoms, leading to decreased accuracy. Here, an earlier pairwise GB model is extended by a simple analytic correction term that largely alleviates the problem by correctly describing the solvent-excluded volume of each pair of atoms. The correction term introduces a free energy barrier to the separation of non-bonded atoms. This free energy barrier is seen in explicit solvent and Lee-Richards molecular surface implicit solvent calculations, but has been absent from earlier pairwise GB models. When used in MD, the correction term yields protein hydrogen bond length distributions and polypeptide conformational ensembles that are in better agreement with explicit solvent results than earlier pairwise models. The robustness and simplicity of the correction preserves the efficiency of the pairwise GB models while making them a better approximation to reality.     

Stopping powers and inelastic mean free path from quantitative analysis of experimental REELS spectra for electrons in Ti,Fe, Ni,and Pd

Stopping power (SP) and inelastic mean free path (IMFP) of electrons in Ti, Fe, Ni, and Pd have been determined by using dielectric models. We have used energy loss function (ELF) determined from quantitative analysis of experimental reflection electron energy loss spectroscopy (REELS) spectra as the input parameter for this model. ELF in this study was determined from the previously published quantitative analysis of REELS spectra. The SP of Fe, Ni, Pd, and Ti was compared with several calculation methods for energies from 100 eV to 10 keV and shows SP in this study, which are in best agreement for medium to high energies (greater than or equal to 300 eV). The IMFP obtained in this study shows the best agreement with online database TPP2M and NIST and also calculation by Tanuma with a root mean square (rms ) less than 12%. The present approach shows ELF from quantitative analysis of REELS spectra has a high potential for the experimental determination of SP and IMFP of metals.     

The equations-of-motion method for F2: Transition energies,oscillator strengths and born cross sections

The equations-of-motion method has been used to study various electronic states of F₂. The transition energies have been found in both the random phase approximation (RPA) and higher random approximation (HRPA) using single particle—hole components in the excitation operators. We have also computed generalized oscillator strengths (Born cross sections) for the scattering of high energy electrons by F₂.     

Characteristic and non-characteristic X-ray emission from SF6 and SO2 molecules by electron impact

Cross sections for K-shell ionization of sulphur in collisions of electrons with kinetic energies of 3.5–14.0 keV with SF₆ and SO₂ gases have been measured. In addition, the impact energy dependence of the bremsstrahlung radiation emitted at different photon energies was investigated. The experimental results are compared with theoretical calculations in plane wave Born approximation and with the available semi-empirical models.     

Post collision interaction effects in the ionisation of helium and hydrogen by fast electrons

Conspicuous effects from a weak post collision interaction have been identified in triply differential cross sections for the ionisation of helium and hydrogen by fast electrons. A classical correction to a first Born approximation describes experimental data at smaller values of the momentum transfer.     

Effect of semi-empirical parameters on the simple random-phase approximation calculations of conjugated hydrocarbons

Singlet-singlet transition energies, oscillator strengths, triplet energy levels, and the ground state correlation energy of a number of conjugated hydrocarbons have been calculated by the simple random-phase approximation (RPA ) within the framework of the Pariser-Parr-Pople (PPP ) model. The effect of semi-empirical parameters in such calculations has been examined in detail. A set of parameters has been deduced from these parametric studies which is found to yield results for the singlet spectra of the molecules in excellent agreement with experiment. It is, however, not possible to treat the triplet states using these same parameters, since they produce triplet instabilities in all the molecules. The triplet instability problem associated with semi-empirical RPA calculations has been discussed in detail.     

Accuracy of basis-set extrapolation schemes for DFT-RPA correlation energies in molecular calculations

We construct a reference benchmark set for atomic and molecular random phase approximation (RPA) correlation energies in a density functional theory framework at the complete basis-set limit. This set is used to evaluate the accuracy of some popular extrapolation schemes for RPA all-electron molecular calculations. The results indicate that for absolute energies, accurate results, clearly outperforming raw data, are achievable with two-point extrapolation schemes based on quintuple- and sextuple-zeta basis sets. Moreover, we show that results in good agreement with the benchmark can also be obtained by using a semiempirical extrapolation procedure based on quadruple- and quintuple-zeta basis sets. Finally, we analyze the performance of different extrapolation schemes for atomization energies.     

Bremsstrahlung cross-section with screening and Coulomb corrections at high energies

Using analytical formulae which are exact in Born approximation, the doubly differential bremsstrahlung cross-section with form-factor screening is calculated. For the atomic form factor parameters are applied which approximate self-consistent Dirac–Hartree–Fock–Slater calculations. The evaluation of the bremsstrahlung spectrum requires a single numerical integration. The results are superior to the customary Bethe approximation, in particular at the high-energy part of the spectrum. At high energies the screening correction can be added to any Coulomb-corrected cross-section without screening. In the present work, we are using a cross-section calculated by means of Sommerfeld–Maue functions with additional higher-order terms.     

A consistent approach to construction of the model valence electron hamiltonian: M2, M = Li,Na, K,Rb, Cs

A consistent procedure is considered for the development of a correct model Hamiltonian for many-electron diatomic molecules in the framework of the Rayleigh-Schrödinger perturbation theoy with zero approximation model potential and with corrections for the exchange-correlation effects as high order effects. Using the pseudopotential approach, we have calculated some molecular constants, in particular, the dissociation energy of homo- and heteronuclear diatomic alkaline molecules. It is shown that an accurate correction for the principal correlation effects (the polarization interaction of valence electrons via the polarized core and mutual screening of outer particles) is critical for obtaining a reasonable calculation accuracy. We suggest ways to improve the accuracy of calculations by using (in zero approximation of the perturbation theoy) reliable empirical information about simple systems, such as the M₂ ⁺ ions (M = Li, Na, K, Rb, Cs).Hydrometeorological Institute, Ukraine. Translated fromZhurnal Strukturnoi Khimii Vol. 34, No. 5, pp. 3–11, September–October, 1993.Translated by I. Zilberberg     

A simple but fully nonlocal correction to the random phase approximation

The random phase approximation (RPA) stands on the top rung of the ladder of ground-state density functional approximations. The simple or direct RPA has been found to predict accurately many isoelectronic energy differences. A nonempirical local or semilocal correction to this direct RPA leaves isoelectronic energy differences almost unchanged, while improving total energies, ionization energies, etc., but fails to correct the RPA underestimation of molecular atomization energies. Direct RPA and its semilocal correction may miss part of the middle-range multicenter nonlocality of the correlation energy in a molecule. Here we propose a fully nonlocal, hybrid-functional-like addition to the semilocal correction. The added full nonlocality is important in molecules, but not in atoms. Under uniform-density scaling, this fully nonlocal correction scales like the second-order-exchange contribution to the correlation energy, an important part of the correction to direct RPA, and like the semilocal correction itself. For the atomization energies of ten molecules, and with the help of one fit parameter, it performs much better than the elaborate second-order screened exchange correction.     

Continuum solvation models in the linear interaction energy method

The linear interaction energy (LIE) method in combination with two different continuum solvent models has been applied to calculate protein-ligand binding free energies for a set of inhibitors against the malarial aspartic protease plasmepsin II. Ligand-water interaction energies are calculated from both Poisson-Boltzmann (PB) and Generalized Born (GB) continuum models using snapshots from explicit solvent simulations of the ligand and protein-ligand complex. These are compared to explicit solvent calculations, and we find close agreement between the explicit water and PB solvation models. The GB model overestimates the change in solvation energy, and this is caused by consistent underestimation of the effective Born radii in the protein-ligand complex. The explicit solvent LIE calculations and LIE-PB, with our standard parametrization, reproduce absolute experimental binding free energies with an average unsigned error of 0.5 and 0.7 kcal/mol, respectively. The LIE-GB method, however, requires a constant offset to approach the same level of accuracy.