The optimized lattice constant is 6.49 ˚ A, which is in excellent agreement with the experimental value of 6.48 ˚ A[14]. For the **ab** **initio** molecular dynamics, we used a time step of 1 fs with PBEsol and a Langevin thermostat (PS-L) at 300 K. The Berendsen thermostat (PS-B) was also considered to evaluate the sensitivity of our predictions to different thermostats. Along the same lines, we have also considered the Armiento- Mattsson 2005 exchange correlation functional (AM05)[15] with both Berendsen (AM05- B) and Langevin (AM05-L) thermostats. Newton’s equations of motion were integrated using the Verlet algorithm [16]. A 54-atom supercell (3×3×3 of the fcc unit cell) for the AIMD simulations was considered, and a 128-atom supercell (4×4×4) was used to study the size effect for few particular calculations. The lattice thermal conductivity and linear thermal expansion is calculated with numerical integration on q 25×25×25 Monkhorst-Pack[17] q-point grid to ensure convergence.

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The first excited state also changes dramatically, crossing the entire n = 2 manifold in the diabatic representation, which is due to the coupling F 23 (see figure 16 ). However, one must remember that the non-adiabatic coupling between the two first 1 + states is of the Rosen–Zener type, and that therefore the diabatic representation of those states has little physical significance. Likewise, the influence of the two first 1 + states on the diabatic representation of the n = 2 states is very important but has little effect on the non-adiabatic dynamics in the n = 2 manifold, as has been observed in the **calculation** of charge exchange cross section between He + and H at low energies (Loreau et al 2010 ). To our knowledge, the only other work on the diabatic representation of the PEC of the HeH + ion has been done by Kl¨uner et al ( 1999 ) using the quasi-diabatization procedure proposed by Pacher et al ( 1988 ). These authors compare a 3-state (the three lowest n = 2 states) and a 4-state (adding the second n = 1 state) diabatization in a small interval of internuclear distances (0.8 au R 5.4 au). It is concluded that the inclusion of the n = 1 state does not modify the diabatic PEC of the n = 2 manifold, and this state is therefore neglected in wavepacket simulations of charge exchange processes involving n = 2 states. Although we arrive at the same conclusion regarding the dynamics, our method gives significantly different diagonal as well as non- diagonal matrix elements of the electronic Hamiltonian in the diabatic representation.

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Cohen (0.31). For Co the drastic reduction of λ tr with respect to λ is due to the Fermi
velocity factors in α 2 F tr . In cobalt the coupling constants and spectral functions are
anisotropic, and the directional dependency in Eq. 5 yields two inequivalent directions for Co (xx = yy 6= zz). The tensors should stay diagonal for both systems: the calculated cross terms give an estimate of the numerical accuracy of the **calculation**, and are about 100 times smaller than the diagonal terms (no explicit symmetrization of the σ matrix is imposed, as a check).

Figure 5.6: Generelized stacking fault energies from [ 23 ], showing the energy variation for a glide in the plane containing H (GSF1), the nearest neighbor plane (GSF2) and the next
,nearest plane (GSF3). The reference without H is also shown.
While the high degree of technicality of these works is undeniable and their results, in complex crack tip configurations, are relevant to transgranular cracking, they still do not investigate in detail the impact of H on the incipient dislocation, in the simplest case where the effect of the ledge is negligible. This aspect is of general interest since it will contribute to modeling H effect on dislocation emission from grain boundaries ahead of the crack tip (intergranular fracture). Several groups have already done the **calculation** of the influence of H on the γ surface and found qualitatively different results depending on the way the relaxations are included, and also which concentration of H is used. H, in tetrahedral position (most favorable position at ground state for Al) in the glide plane, was found to greatly increase the barrier to glide [ 22 , 23 ]. Lu et al. [ 22 ] proposed that the energy in octahedral position becomes more favorable above a critical shear. Therefore, H could jump from distorted tetrahedral position to a distorted octahedral position during the shear process, giving a lower effective barrier to glide. However, a different behavior is reported by Apostol et al. [ 23 ]: H induces a reconstruction and glide becomes easy in the next nearest glide plane. Thus H effect on γ us is not fully understood. Further calculations involving

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(Received 5 February 2011; accepted 21 June 2011; published online 11 July 2011)
**Ab** **initio** techniques are used to calculate the effective work function (Weff ) of a TiN/HfO 2 /SiO 2 /Si stack representing a metal-oxide-semiconductor (MOS) transistor gate taking into account first order many body effects. The required band offsets were calculated at each interface varying its composition. Finally, the transitivity of local density approximation (LDA) calculated bulk band lineups were used and completed by many body perturbation theory (MBPT) bulk corrections for the terminating materials (Si and TiN) of the MOS stack. With these corrections the **ab** **initio** calculations predict a W eff of a TiN metal gate on HfO 2 to be close to 5.0 eV. V C 2011 American

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*E-mail : achouaih@gmail.com
ABSTRACT
Electrostatic atomic and molecular properties of the 1,2-dimethyl-3-nitrobenzene are derived from both experimental data and **ab** **initio** theoretical investigation. The molecular dipolar moment obtained by both methods is around 6 Debye and its orientation shows clearly the direction of the intra-molecular charge transfer. The obtained net atomic charges and the derived electrostatic potential show that the electronegative potential is located on the side on the nitro group region whereas the electropositive potential is on the side of the methyl groups. The experimental electrostatic potential is derived from high-resolution single-crystal X-ray diffraction data. The crystallographic investigations are carried out using the multipolar model of Hansen and Coppens in order to take into account the non-spherical part of the atomic electron charge density distribution. In addition to the structural analysis, a thermal motion analysis is carried out in terms of rigid blocks in order to improve the accuracy of obtained results. The experimental results are compared to **ab** **initio** theoretical Hartree-Fock (HF) and density functional theory (DFT) predictions, using two different large basis sets. Both DFT and HF calculations gave a molecular dipole moment in good agreement with the extracted one from the X-ray diffraction data (value of 6.57 D). The theoretical investigations are found to reproduce well the experimental molecular electrostatic potential. In the present work, the intermolecular hydrogen bonds are also subjected to a detailed experimental topological analysis.

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the uncertainties in the required inputs leads to a highly non-Gaussian distribution of σ 806 MeV [35] .)
In summary, lattice QCD calculations have been used to determine the short-distance two-nucleon interactions with the electromagnetic field (meson-exchange currents in the context of nuclear potential models) that make significant contributions to the low-energy cross sections for np → dγ and γ ðÞ d → np. This was facilitated by the pionless effective field theory which provides a clean separation of long-distance and short-distance effects along with a concise analytic expression for the near-threshold cross sections. A (naive) extrapolation of the LQCD results to the physical pion mass is in agreement with the experimental determinations of the np → dγ cross section, within the uncertainties of the **calculation** and of the experiment. Calculations were performed at a single lattice spacing and volume, introducing systematic uncertainties in ¯ L 1 that are

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Within that theoretical scheme, which reproduces by construction the experimental energies of the main fragments in 37 S to 35 Si once full correlations are included, the ESPE spin-orbit[r]

Convergence of the equilibrium CH distance of methane, of the quartic force constants of modes ν 3 and ν 4 , and of the non-zero first order derivatives of the electric dipole moment z-component
with orbital basis set. The derivatives are with respect to the mass-weighted, Cartesian, normal coordinates of the Lee, Martin and Taylor force field [1], however, as noted in the main material, these coordinates are essentially basis set independent. The derivatives were obtained by finite difference at the equilibrium geometry with a step of 1 atomic unit. This is in contrast with the values actually used in the study, which were derived from fitting grid points extending over the range where the vibrational ground state product function has a non negligible weight at the harmonic level of approximation (typically more than or in the order of 10 −2 , that is to say 10 −4 for the square of the wave function), as this is more appropriate in view of computing expectation values. MRCI calculations were performed with frozen core for the VQZ basis set and full core excitations for the ACVnZ basis sets. The CI space for the ACV6Z **calculation** is spanned by about 16 Million CSFs. It is clear from this table that a full core treatment of correlation is necessary to obtain a value of the equilibrium distance to the m˚ A accuracy. If the significant digits of ∂µ z

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[ 30 ], and [ 31 ], some of these couplings behave asymptotically as R, a phenomenon that cannot be avoided by changing the origin of electronic coordinates. Due to the factor 1/R 2 in
Eq. ( 6 ), these couplings will thus decrease as 1/R, much more slowly than the radial couplings, which decrease to 0 extremely rapidly outside the interaction region. This causes a problem in the **calculation** of the cross sections, as it implies the use of very large numerical grids that increase the **calculation** time tremendously. To solve this problem, we modified the problematic rotational couplings outside the interaction region, where we required that they decrease to 0 (i.e., their atomic values). We have tried various switching functions to find a set of parameters that had no effect on the cross sections. This approximation is also justified in our case by the fact that the linear rotational couplings usually connect two states in the same atomic configuration, so that the modification will not influence the charge-transfer cross sections.

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3 Department of Physics, Wake Forest University, Winston-Salem, North Carolina 27109, USA
共Received 4 March 2010; published 20 May 2010 兲
We extend the recently developed converse NMR approach 关Thonhauser et al., J. Chem. Phys. 131, 101101 共2009兲兴 such that it can be used in conjunction with norm-conserving, nonlocal pseudopotentials. This exten- sion permits the efficient **ab** **initio** **calculation** of NMR chemical shifts for elements other than hydrogen within the convenience of a plane-wave pseudopotential approach. We have tested our approach on several finite and periodic systems, finding very good agreement with established methods and experimental results.

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4. Conclusion
To conclude, we have generalized the density matrix approach to Gutzwiller method for the degenerate Hubbard Hamiltonian. We have shown that we can express the total energy in the Gutzwiller state in terms of the different probabilities of configurations. Moreover to apply the method to cases of physical interest we have developed this method for inequivalent sites and for different orbital symmetries. In this way we have given the expression of the different q factors which renormalize the hopping terms and an expression to renormalize the on-site energies in the Gutzwiller context. This method is limited to ground state properties but can extend to finite temperature and low-frequency excitations in analogy with the work of Gebhard [47]. Of course, as a quasiparticle approach, this method is limited to cases where the Fermi-liquid theory is valid, i.e. close to Fermi energy. Thereafter we have have described a simple implementation of our method in a **ab**-**initio** **calculation** as the LMTO method. To give an example, we have applied this technique to the particular case of Pu in fcc structure. In despite of the simplicity of our model, we were able to extract interesting results such as the double-well feature in the energy-volume curve and more generally improve the LDA results. Our results compare well with previous works.

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Li
Figure 7.6: The electrons RESP of Li within ALDA in linear-response (dashed red line) compared to the available experimental data. Experiments (probably bcc crystal) by Janni [42] (orange line) and Eppacher et al. [28] (brown line). Is LDA RESP a valid alternative to the full evaluation of core elec- trons? We also considered the opportunity to have a cheap evaluation of the core contribution using the LDA based on the Lindhard stopping power. In the upper panel of Fig. 7.5, the LDA RESP is calculated for both the valence electronic density and the valence plus core electronic density. The difference between the two can be compared with the full **ab** **initio** **calculation** in the lower panel. The LDA technique is not perfectly adequate to describe the core contribution. Indeed, the stopping power continuously increases starting from the lowest velocities. In other words, the LDA core misses the shell effect: the core contribution should be zero up to the minimum velocity that allows the core electrons to be excited.

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1. Introduction
**Ab** **initio** molecular dynamics (AIMD) is an irreplaceable technique for the realistic simulation of complex molecular systems and processes associated with biological organisms [1, 2] such as monoclonal antibodies as illustrated in Figure 1. With **ab** **initio** molecular dynamics, it is possible to predict in silico phenomena for which an in vivo experiment is either too diicult or expensive, or even currently deemed infeasible [3, 4]. **Ab** **initio** molecular dynamics essentially difers from molecular dynamics (MD) in two ways. Firstly, AIMD is based on the quantum Schr¨odinger equation while its clas- sical counterpart relies on Newton’s equation. Secondly, MD relies on semiempirical efective potentials which approxi- mate quantum efects, while AIMD is based on the real physi- cal potentials.

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These typically fall into categories of either using transition state theory and calculating attempt frequencies and activation energies, or simulating atomic motion [r]

Dans ce chapitre nous tentons d’expliquer le principe des méthodes ab initio et la méthode de la théorie de la fonctionnelle de la densité (DFT) que nous avons utilisé dans notre ét[r]

Photochemically initiated thiol-ene emulsion polymerization has several advantageous features, that are successively highlighted in the following section: (i) temporal control[r]

Chapter 2
**Ab**-**initio** calculations
Due to the difficulties found in the direct solution of the Schr¨odinger equation dif- ferent simplified approaches were proposed and are nowadays widely used. Among them, the most usually employed are the Hartree-Fock and the Density Functional Theory, that we revisit in the present chapter. The former makes use of nonstandard numerical approximations in order to calculate the wavefunction while circumvent- ing the curse of dimensionality whereas the latter involves the electronic density that is now defined in three dimensions but that requires deeper analyses to retain in a ‘coarse” 3D model the most relevant features present in the wavefunction descrip- tion.

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The subject of this master’s thesis is the **ab** **initio** study of carbon nanotubes. First, an in- troduction to the subject is presented. It covers the history, the geometric and electronic structure and potential applications of carbon nanotubes. Second, the energy stability of double-walled carbon nanotubes and their electronic structure are studied. It is found that the change of hybridization causes a lowering in the energy of the highest occu- pied molecular orbital’s level for small nanotubes. Thirdly, a study of the diameter and metallicity dependence for the bromophenyl bonding energy on the carbon nanotubes is presented. The main conclusion is that it is easier to functionalize the nanotubes of small diameter since they already have some sp 3 hybridization in their electronic structure. Fi- nally, the last chapter discusses the burning of carbon nanotubes with carbon dioxide. It is found that combustion can not begin on a pristine surface or by a oxygen bridge due to the large amount of energy required. The favored reaction is then burning the ends of nanotubes. We suggest a path of reaction for which a diameter selectivity is apparent.

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Méthodes **ab**-**initio** utilisées
La description des matériaux présentant des fortes corrélations électroniques est di- cile et des modèles simples, dédiés aux traitement spécique de la corrélation sont large- ment employés pour tenter de décrire les propriétés physiques de ces matériaux. Bien sur, en partant des premiers principes, il est en théorie possible de décrire ces matériaux et c'est ce que tente de faire le calcul **ab**-**initio**. Cependant les méthodes partant d'approximation monoélectronique, telles que la DFT, rencontrent des dicultés pour traiter les eets de corrélations dès lors qu'ils se sont plus perturbatifs par rapport aux eets de délocali- sation. C'est le cas dans les matériaux auxquels nous nous intéressons. D'un autre coté, les méthodes de calcul **ab**-**initio** en fonction d'onde permettent de traiter correctement le caractère multi-référence de ces systèmes fortement corrélés. Elles sont malheureuse- ment limitées aux traitement d'un petit nombre d'atomes. La méthode usuelle utilisée consiste alors à décrire ces systèmes par des hamiltoniens modèles et nous verrons com- ment le calcul **ab**-**initio** en fonction d'onde utilisé dans ce travail permet de déterminer avec précision les degrés de liberté pertinents et les interactions utilisées dans ces modèles. On peut se convaincre que ces interactions eectives ne nécessitent pour leur évaluation que l'évaluation préalable d'intégrales mono et bi-électroniques entres orbitales localisées spatialement proches [50]. Cela aura pour conséquence, qu'une évaluation des interactions eectives au sein de petits fragments du cristal, représentera quantitativement cette même interaction dans le système inni si les électrons, les orbitales qui médient l'interaction eective ainsi que les orbitales responsables de l'écrantage sont convenablement traitées dans le fragment. Pour cela, on utilisera les méthodes de la chimie quantique qui sont capables de traiter correctement les eets de corrélation, même forte, et de calculer les états fondamental et excités des fragments. A partir de la connaissance de ces états et de leur énergie il est possible d'extraire les valeurs des interactions eectives.

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