A. Core ionization energies
The calculated core ionization energies obtained at the ⌬MP2 and ⌬SCF levels are given in Table I and compared with the ⌬SCF results of Carravetta et al. 关8兴 and the XPS experimental values 关 31 兴. Since in MP2 calculations, several possible definitions of the zero-order Hamiltonian for open- shell systems are possible 关32兴, the ⌬MP2 values of the present work were obtained using three different models: RMP 关 33,34 兴, ZAPT 关 35,36 兴, and CIPSI. The two ⌬SCF are nearly identical because Carravetta et al. 关 8 兴 employed the same basis set as in the present work. While RMP and ZAPT methods are very similar, the CIPSI values are slightly dif- ferent. All results are within 0.5 eV of the experimental val- ues.
and ΔG seg surf .
1 However, while the analysis for the DFT studies was made assuming that the solute
remained in the same site during fracture, such a constraint is not possible during the experimental measurements of segregation behavior. Thermodynamically, the imposition of a constraint guaran- tees that the work needed to perform a process is larger than in the absence of the constraint. Thus, the experimentally measured embrittling potencies should be considered an upper bound when compared with the theoretically computed embrittling potencies. Despite this difference, previous authors have shown that the embrittling potencies computed from a theoretical and experimental perspective are in fair agreement [2 , 6] .
Fig. 4. - Interatomic
distances between nearest neighbours in positive ions (relaxed conformations). V, V UHF abinitio
calculation. A, A model calculation. re Mg2 experimental re. dm metallic nearest neighbour distance.
It seems likely that for larger and larger clusters the number of competing minima will increase and their
6 I. Introduction
2.1. Surface rumpling and relaxation
In crystalline bulk, the equilibrium positions of the atoms result from a balance be- tween the forces generated by all the neighbors. At the surface, the atoms have a different environment: some neighbors are missing with respect to the bulk. Thus, the atoms relax to equilibrium positions different from the bulk ones. Given the transla- tional symmetry parallel to the surface plane, the new equilibrium positions of the surface atoms involve displacements perpendicular to the surface (in this thesis we do not discuss the possibility of surface reconstruction or faceting). For ionic crystals and ionocovalent crystals such as BaTiO 3 , the relative displacements of the cations with respect to the anions normal to the surface defines the rumpling. It usually consists of anions displaced outwards with respect to cations which are on the contrary displaced inwards. This was measured by low-energy electron diffraction (LEED) [ 20 ] and by re- flection high-energy electron diffraction (RHEED) [ 21 ] on SrTiO 3 , of similar perovskite structure as BaTiO 3 . First-principles calculations [ 22 – 25 ] agree with the experimental observations on SrTiO 3 and show similar results for BaTiO 3 surfaces [ 26 – 28 ], and other perovskite structures [ 29 ]. The relative displacements induced by the rumpling corresponds to polar displacements which allows foreseeing a potential interplay between rumpling and ferroelectric polarization at the surface.
three different kinetic laws of the literature for deposition from silane. Note that these calculations have been performed using the inlet partial pressures of silane. The straight line in Fig. 1 corresponds to equality between experimental and theoretical values. Using pure silane, the law of Wilke et al.  is the most suitable one to predict deposition rate of conventional thickness as already observed  . But in conditions of high dilution of silane, we found that this law under-estimates experimental deposition rates whereas that of Jensen et al  over-estimates them. In the opposite, choosing the minimum parameters of the Roenigk et al. law  gives agreement with experimental values in high dilution conditions whereas maximum parameters of these authors give the highest over-estimations. It is worth noting that the Roenigk et al. law with its minimum parameters and the Wilke et al. law provide convenient results at temperatures as low as 500 and 550 °C. Thus the Roenigk et al. law with its minimum parameters has been retained to simulate by CFD silicon deposition in high dilution conditions.
Semi-empirical calculations of optical properties
In a spectroscopic experiment the sample is excited from its ground state: the re- sponse to the perturbation is the object of both experimental measurements and theoretical calculations. A big variety of phenomena can occur. In Fig. 4.1 we show three model excitations: direct photoemission, inverse photoemission, and absorp- tion. Direct/inverse photoemission processes are one-quasi-particle excitations: a quantum of energy hν is absorbed/emitted while an electron is ejected/absorbed. The ejected/incoming electron is supposed to be completely decoupled from the sys- tem after/before the process takes place. These kinds of experiments give insight, respectively, on the density of occupied and unoccupied states. Here we are more interested in absorption processes in solids. In a naive picture, the incoming ra- diation causes the transition of an electron from an occupied state in the valence band to an empty state in the conduction band. However, even if one uses quasi- particle instead of one-electron states, one faces the problem that this process is not the simple combination of an inverse photoemission and a direct photoemission process, because the electron does not leave the sample and continues interacting with it. The electron which has undergone a transition to the conduction band and the relative hole left in valence band feel each other via a Coulomb interaction: this is the so-called excitonic effect, which introduces the main complexity in computa- tions, since it forces to abandon the independent quasi-particle picture, to move to
As a conclusion, a full coupled TDSE-UPPE propagation model has been developed and used to investigate the propa- gation of an ultrashort, high-intensity laser pulse over 5 mm. Simulations over such a distance have been made possible by an efficient abinitio TDSE solver based on the B-spline basis set. The consideration of harmonics and their relative dephasing up to the ninth strongly influences the propagation of ultrashort pulses, and especially their harmonic generation and ionization yield. Our results illustrate that empirical mod- els based on a complex envelope and phenomenological coef- ficients for ionization and the Kerr effect cannot adequately reproduce the complex behavior of the high-field–atom in- teraction. The emergence of single attosecond pulses may allow one to probe the propagation at the sub-fs scale, i.e., at the sub-optical-cycle scale [ 76 ], therefore providing direct experimental comparison with our calculations, especially if the propagation is considered in two dimensions. Such a 2D + z extension, implementing a transverse resolution, to- gether with radial symmetry and efficient parallelization of the propagation steps, will allow its application to filamentation.
3.1. Energy levels
Calculated energy levels obtained with the HFR+CPOL method are compared to available experimental values in
table 1 . The largest LS-components of the wavefunctions are also reported in that table. One can observe that many of these levels are strongly mixed, the average LS-purities being equal to 89% and 68% for even and odd parities, respectively. For comparison, it is interesting to note that the fully relativistic MCDF calculations gave average purities in j j-coupling equal to 84% for 5d 2 + 5d6s and 88% for 5d6p. For these configurations, the correlation between LS and j j designations are given in table 2 together with a comparison between experimental energies and those obtained using different computational approaches. While, as expected and already mentioned above, the two semi-empirical HFR models are in excellent agreement with experiment, rather large discrepancies are observed, in some cases, when considering the abinitio methods for which the average deviations E = |E exp − E calc | are of the order of 1376, 1882 and 3930 cm −1 for
By comparing high-level abinitio electronic structure calculations with time-resolved experimental measurements of dissociative ionization in CHBr 2 COCF 3 , we have devel- oped a detailed picture of the fragmentation dynamics initi- ated by shaped and unshaped ultrafast laser pulses. We find that while the ground state of the ion has multiple barriers to dissociation, the initial wave packet launched via strong field ionization has sufficient energy to go over barriers along the C – CF 3 and C – CHBr 2 coordinates, producing the ionic frag- ments CHBr 2 + , CHBr 2 CO + , and CF 3 + . For dissociation along the C – CF 3 coordinate, the positive charge of the molecular ion is mostly localized on the acetyl 共CHBr 2 CO兲 fragment. However, the first excited state of the ion corresponds to a charge transfer state, with the positive charge mostly on the methyl 共CF 3 兲 fragment. Since the first excited state of the ion comes into resonance 共1.5 eV separation兲 with the ground state as the dissociative wave packet moves out along the C – CF 3 coordinate, a probe pulse following the ionization pulse can promote the wave packet to the first excited state of the ion, leading to a depletion of the CHBr 2 CO + and CHBr 2 + yields and an enhancement of the CF 3 + yield. In order to generalize our result, we interpret a comparison of the electronic spectra of two different molecular ions in terms of the ease with which one can move the unpaired electron left by ionization around the molecule.
After relaxing all the SQS cells, we compared the geo- metries and the density of states of the supercells of different sizes corresponding to the same stoichiometry. We observed that SQS supercells with 40 atoms already give bond lengths that differ by less than 0.002 A ˚ and density of states substan- tially identical to those of the 64 atom supercells. In view of that, all results shown in the following were obtained with the 40-atom SQS cells. A further validation of our model structures comes from the comparison with EXAFS meas- urements of CIGS alloys, which yield the element-specific atomic-scale structure, in particular, the Cu-S, Ga-S, and In- S distances. 12 The atomic positions obtained with the HSE functional always yield bond lengths in excellent agreement with experimental data (see Table 1 of the supplementary
II. MOLECULAR-BEAM-EPITAXY-GROWN Co /Ni(111) LAYERS
A. Sample preparation
The ﬁrst series of samples were prepared by using molecu- lar beam epitaxy (MBE). The Co/Ni(111) layers are deposited on a seed layer constituted of ﬁrst V(110) and second Au(111) seed layers grown on sapphire substrates. The Co and Ni thicknesses were accurately controlled by using reﬂection high energy electron diffraction (RHEED). By recording the intensity of the RHEED truncation rods during the growth, we observed intensity oscillations (called RHEED oscillations) during the growth of Ni on the Au(111) buffer layer and during the growth of Co on Ni. This means that Ni (Co) grows layer by layer on Au (Ni). The period of the oscillations is exactly the time to complete an atomic plane and takes around 40 sec for Ni and 80 sec for Co in our experimental conditions. Such low growth rates allow us to control the deposition time and consequently the thicknesses with an accuracy better than 0.1 ML. The Co/Ni layers are deposited at room temperature, and no thermal intermixing is observed. More details about the growth are given in Ref. 10 . Two kinds of samples were prepared by MBE. First, (Co x / Ni y )xN SLs were grown varying
This paper presents a surface structure determination by SXRD of a quasicrystalline approximant, the Al 13 Co 4 phase,
a complex intermetallic compound with more than 100 atoms in its unit cell. This achievement was only possible due to the large experimental data set that could be recorded—the largest experimental data set ever analyzed with SXRD—a consequence of the high density of crystal truncation rods and of the relatively low symmetry of the system (124 symmetry- nonequivalent CTRs). Fits of the SXRD data allowed us to discriminate among various surface models and pointed toward a bulk truncated surface at dense Al-rich puckered planes where protruding surface Co atoms are missing. Surface relaxations and exact atomic positions obtained by SXRD and complementary DFT calculations are very similar and give
Our preliminary fits also indicated, that it is necessary to impose some other constraints regarding the FWHMs. For some fitting para- meters, when left completely free, non-physically small values were obtained together with unrealistic fluctuations between the composi- tions. They cannot be completely fixed either, since such fixing leads to bad fits. The calculated disorder-dependent contribution to the FWHMs are smaller then the rest of contributions to the peak FWHM (as esti- mated in previous section) for the TiO 2 and SiO 2 parts, and comparable
6. Vanadium dioxide
function. In their calculation, the details of the band structure are somewhat different, since they used the theoretical lattice structure of Wentzcovitch et al. [ 286 ], but the differences remain of the same size as what has been already found at LDA level (see Fig. 6.9 ). Also in their case the GW corrections don’t affect much the shape of the bands (see the upper panel of Fig. 6.16 ). Their qualitative picture agrees well with the present self- consistent quasiparticle calculations. The results illustrated in this section represent hence a fully parameter-free validation of their model calculations. The bottom panel of Fig. 6.23 shows that the experimental spectrum for the metallic phase is already well reproduced by the LDA density of states. The task in this case for LDA was easier. The metal is electronically more isotropic than the insulator, and LDA and quasiparticle wavefunctions are much more similar. Further GW calculations induce only small changes, still improving the agreement with the experiment, especially concerning the position of the O 2p bands.
The comparison with experimental geometries, for three complexes of the [Ln(tpy)(H 2 O) n Cl] 2+ series,
showed systematically slightly longer calculated bond lengths. The deviations may be due to the eect of crystal packing forces in the solid, which induce shorter LnAligand distances than those calculated in the gas phase. Furthermore, calculations taking better into ac- count the electron correlation could also result in shorter bond lengths, as shown in the MP2 calculations of [Ln(tpy)] 3+ complexes even if this shortening is not
As we know that there are no previous experimental studies have yet been published for the FrH molecule and there is two theoretical adiabatic studies have been examined by Hill et al. 1 and Noro et al. 2 using the new correlation consistent (cc) basis sets. So, this method is based on Pseudo-Potential (PP) Hamiltonian, which is contracted from double to quintuple Zeta quality. Moreover, for these alkali-metal, the Gaussian-type function sets have been contracted by application the two approach which are the exact 2-component (X2C) scalar relativistic Hamiltonians 50-55 and third-order Douglas-Kroll-Hess (DK3) approximation 56 . In addition, we compare our results with the other alkali hydrides systems (Li-Cs)H 3-7 . In 2006, Aymar et al. 49 have studied the electronic structure of Fr 2 , FrRb and FrCs molecules and their cations. Then,
In this thesis, we propose to push the linear-response approach to its limit and appreciate his range of validity to evaluate the random electronic stopping power (RESP). We aim at exploring the power of the calculations to predict experimental results, since the experimental data are scarce for non-elemental crystals. Due to the slow convergence of the practical calculations, we produce, to the best of our knowledge, the first fully converged abinitio electronic stopping power within linear-response theory. The comparison against time- propagation results is surprisingly good as we will show. We furthermore evaluate the validity of a few rule of thumbs empirically used in practice, such as the Bragg’s additivity rule or the bond effect. In addition, to have a deep understanding of the RESP results, we will answer the following two questions: Can we take the phase insensitivity for granted? Also, can we safely ignore the anisotropy of anisotropic materials?
Here, we study the phonon modes and dielectric properties of both methylamonium
(CH 3 NH 3 PbI 3 ) and cesium (CsPbI 3 ) lead iodide perovskite structures using DFT (Density Functional Theory)
calculations. Phonon frequencies for both the cubic (T>600K) and orthorhombic (T<530K) phases of CsPbI3 are derived using the linear response approach (DFPT). As for the orthorhombic phase (figure 1), we find that CsPbI 3 shows a very flat energy profile around its equilibrium structure (figure 2). We derive