ERKALE—A flexible program package for X‐ray properties of atoms and molecules

Lehtola, Susi; Hakala, Mikko; Sakko, Arto; Hämäläinen, K.

doi:10.1002/jcc.22987

Cited by 85 publications

(110 citation statements)

References 127 publications

(159 reference statements)

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“…0n (O) (66) and find that this contribution is indeed independent of the choice of the origin. In fact, it can be shown that for each order, the higher-order contributions to the oscillator strengths are origin independent if all terms that are of the same order in the wave vector k are included.…”

Section: Origin Independence Of Oscillator Strengthsmentioning

confidence: 78%

Origin-independent calculation of quadrupole intensities in X-ray spectroscopy

Bernadotte

Atkins

Jacob

2012

The Journal of Chemical Physics

146

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For electronic excitations in the ultraviolet and visible range of the electromagnetic spectrum, the intensities are usually calculated within the dipole approximation, which assumes that the oscillating electric field is constant over the length scale of the transition. For the short wavelengths used in hard X-ray spectroscopy, the dipole approximation may not be adequate. In particular, for metal K-edge X-ray absorption spectroscopy (XAS), it becomes necessary to include higher-order contributions. In quantum-chemical approaches to X-ray spectroscopy, these socalled quadrupole intensities have so far been calculated by including contributions depending on the square of the electric-quadrupole and magnetic-dipole transition moments. However, the resulting quadrupole intensities depend on the choice of the origin of the coordinate system. Here, we show that for obtaining an originindependent theory, one has to include all contributions that are of the same order in the wave vector consistently. This leads to two additional contributions depending on products of the electric-dipole andelectric-octupole and of the electric-dipole and magnetic-quadrupole transition moments, respectively. We have implemented such an origin-independent calculation of quadrupole intensities in XAS within timedependent density-functional theory, and demonstrate its usefulness for the calculation of metal and ligand K-edge XAS spectra of transition metal complexes.2

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Section: Origin Independence Of Oscillator Strengthsmentioning

confidence: 78%

Origin-independent calculation of quadrupole intensities in X-ray spectroscopy

Bernadotte

Atkins

Jacob

2012

The Journal of Chemical Physics

146

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“…The IGLO-III basis set (73) was used for the excited oxygen site, whereas Dunning's augmented correlation consistent polarized valence double zeta basis set (74) was used for all other atoms. The localization of the core hole was enforced by freezing the other oxygen core orbitals in the system (68). Broyden mixing (75) of the Kohn-Sham-Fock matrix was used in solving the self consistent field (SCF) equations.…”

Section: Methodsmentioning

confidence: 99%

Microscopic structure of water at elevated pressures and temperatures

Sahle

Sternemann

Schmidt

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

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128

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We report on the microscopic structure of water at sub-and supercritical conditions studied using X-ray Raman spectroscopy, ab initio molecular dynamics simulations, and density functional theory. Systematic changes in the X-ray Raman spectra with increasing pressure and temperature are observed. Throughout the studied thermodynamic range, the experimental spectra can be interpreted with a structural model obtained from the molecular dynamics simulations. A spatial statistical analysis using Ripley's K-function shows that this model is homogeneous on the nanometer length scale. According to the simulations, distortions of the hydrogenbond network increase dramatically when temperature and pressure increase to the supercritical regime. In particular, the average number of hydrogen bonds per molecule decreases to ≈0.6 at 600°C and p = 134 MPa.supercritical water | water structure | X-ray scattering | X-ray scattering spectroscopy

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“…We use here the all-electron ERKALE program [16,17,6] to test the accuracy of the calculated atomization energy for 35 molecules and make a comparison with results of high-level quantum chemistry calculations of chemical accuracy [11]. The atomization energy of the following molecules was calculated: H 2 , BeF 2 , BeCl 2 , BH, BH 3 , B 2 H 6 , BF, CH 2 (singlet), CH 2 (triplet), C 2 H 2 , C 2 H 4 , C 2 H 6 , NH 2 , NH 3 , N 2 , H 2 O, O 2 , HF, F 2 , AlH, AlH 3 , AlF, AlCl, SiH, SiH 4 , SiO, SiF, PH 3 , P 2 , H 2 S, SO, SO 2 , ClO, ClF and Cl 2 The calculations are variational and selfconsistent, in that we minimize the energy of the PZ-SIC energy functional with the chosen GGA expression for the functional.…”

Section: Calculations Of Atomization Energymentioning

confidence: 99%

Towards an Optimal Gradient-dependent Energy Functional of the PZ-SIC Form

Jónsson

Lehtola

Jónsson

2015

Procedia Computer Science

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Results of Perdew-Zunger self-interaction corrected (PZ-SIC) density functional theory calculations of the atomization energy of 35 molecules are compared to those of high-level quantum chemistry calculations. While the PBE functional, which is commonly used in calculations of condensed matter, is known to predict on average too high atomization energy (overbinding of the molecules), the application of PZ-SIC gives a large overcorrection and leads to significant underestimation of the atomization energy. The exchange enhancement factor that is optimal for the generalized gradient approximation within the Kohn-Sham (KS) approach may not be optimal for the self-interaction corrected functional. The PBEsol functional, where the exchange enhancement factor was optimized for solids, gives poor results for molecules in KS but turns out to work better than PBE in PZ-SIC calculations. The exchange enhancement is weaker in PBEsol and the functional is closer to the local density approximation. Furthermore, the drop in the exchange enhancement factor for increasing reduced gradient in the PW91 functional gives more accurate results than the plateaued enhancement in the PBE functional. A step towards an optimal exchange enhancement factor for a gradient dependent functional of the PZ-SIC form is taken by constructing an exchange enhancement factor that mimics PBEsol for small values of the reduced gradient, and PW91 for large values. The average atomization energy is then in closer agreement with the high-level quantum chemistry calculations, but the variance is still large, the F 2 molecule being a notable outlier.

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ERKALE—A flexible program package for X‐ray properties of atoms and molecules

Cited by 85 publications

References 127 publications

Origin-independent calculation of quadrupole intensities in X-ray spectroscopy

Origin-independent calculation of quadrupole intensities in X-ray spectroscopy

Microscopic structure of water at elevated pressures and temperatures

Towards an Optimal Gradient-dependent Energy Functional of the PZ-SIC Form

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