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Atoms and the Periodic Table of the Elements
Published in Franco Battaglia, Thomas F. George, Understanding Molecules, 2018
Franco Battaglia, Thomas F. George
It is convenient at this stage to make use of units suitable to the values pertaining to atomic and molecular systems, namely, atomic units (a.u.). These are defined by assigning unit value to the elementary charge, e, the electron mass, me, the Planck constant, ħ, and the constant factor appearing in the Coulomb force: ℏ=e=me=4πϵ0≡1.
κ transition metal dielectrics: applications to interfacial band offset energies and electronically active defects
Published in Michel Houssa, κ Gate Dielectrics, 2003
Gerald Lucovsky, Jerry L Whitten
and contains kinetic energy (1/2∇i2), nuclear–electron attraction (−Zk/rik) and electron–electron repulsion (1/rij) contributions. Equation (4.2.1) is formulated in atomic units (a.u.): 1 a.u. (distance) = 1 Bohr = a0 = 0.5292 Å; 1 a.u. (energy) = 1 Hartree = e2/a0 = 27.21 eV.
Formation, Growth Mechanism and Electronic Structures of Ge Films on Si Substrates
Published in Kuan Yew Cheong, Two-Dimensional Nanostructures for Energy-Related Applications, 2017
Here, the atomic units |e| = m = h/2π = 1 are used, where e, m and h are the electron charge, electron mass and Plank’s constant, respectively. For the exchange-correlation energy Exc, the Local Density Approximation (LDA) (Perdew and Zunger 1981) and the Generalized Gradient Approximation (GGA) (Perdew et al. 1996) are typically employed.
Consequences of approximating electron correlation effects
Published in Molecular Physics, 2023
Adam L. Baskerville, Philippa U. Cox, Hazel Cox
The singlet ground states of helium and helium-like systems, within the clamped nucleus approximation, are investigated. The details of the implementation used for the FC method is described in [27], for the HF method in [16], and for the CS method in [4,9]. Atomic units (a.u.) are used throughout, where , and the atomic unit of energy is the Hartree () and the atomic unit of length is the Bohr (). Figure 1 shows the coordinates referred to throughout this investigation, the interparticle coordinates and the Jacobi coordinates, .
An excited state coupled-cluster study on indigo dyes
Published in Molecular Physics, 2021
Marvin H. Lechner, Frank Neese, Róbert Izsák
Geometry optimizations were performed at the DFT level using the B3LYP functional [72] with the def2-TZVP basis set [73] and the matching auxiliary basis set [74]. The D3 dispersion correction as parametrised by Grimme and co-workers was also applied [75]. The B3LYP functional has already been used with success to obtain geometries in our earlier studies on other families of dyes [52]. The geometries obtained in this study are provided in the Supplementary Material. The RIJCOSX [76,77] approach applying the resolution of identity (RI) approximation to the Coulomb part and the chain of spheres (COS) seminumerical integration algorithm to the exchange term was also used to accelerate the optimisation process. Harmonic vibrational frequencies were computed at the same level of theory. The TightSCF keyword was used to set convergence criteria for energy calculations (thresholds in atomic units: for energy and for the orbital gradient) and the TightOpt keyword for geometry optimizations (thresholds in atomic units: for energy and for the maximum component of the gradient). The DFT grid was set to DEFGRID2 (Lebedev angular grid with 302 points and a Gauss–Chebyshev radial grid with a radial integration accuracy of 4.67) and all the other parameters were chosen as default.
Photoelectron angular distributions in photodetachment from polarised d-like states: the case of HO2 −
Published in Molecular Physics, 2021
Christopher C. Blackstone, Adam A. Wallace, Andrei Sanov
According to the derivation in Ref. [41], given ζ2p and ζ3d, the three Hanstorp coefficients A1,A2, and B2 can be expressed in terms of just these two parameters: All three coefficients in (6) are given in atomic units (of reciprocal energy). These expressions appeared in Equation (43) in Ref. [41], but due to a typographical error the B2 formula there included an incorrect power of ζ2p (2 instead of the correct 9). Given the parametrization of A1,A2, and B2 in terms of ζ2p and ζ3d, the number of parameters in Equation (3) is reduced to three total: ζ2p, ζ3d, and . Among these, can be determined from ab initio calculations, leaving the effective charges ζ2p and ζ3d as the only free model parameters to be deduced from the experimental data.