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Spectra reflecting the formation of single-site double-core-hole pre-edge states involving the N 1s and C 1s core levels of acetonitrile have been recorded by means of high-resolution single-channel photoelectron spectroscopy using hard X-ray excitation. The data are interpreted with the aid of ab initio quantum chemical calculations, which take into account the direct or conjugate nature of this type of electronic states. Furthermore, the photoelectron spectra of N 1s and C 1s singly core-ionized states have been measured. From these spectra, the chemical shift between the two C 1s−1 states is estimated. Finally, by utilizing C 1s single and double core-ionization potentials, initial and final state effects for the two inequivalent carbon atoms have been investigated.

We show that using the Colle–Salvetti correlation-energy functional (Colle and Salvetti in Theoret Chim Acta 37:329, 1975) in the Hartree–Fock-type procedure suggested by Kohn and Sham (Phys Rev 140:A1133PR, 1965), one can calculate quite accurately electronic properties of systems in which the “dynamical” correlation energy is dominant. We compare our results with those obtained by Grabo and Gross (Chem Phys Lett 240:141, 1995) using the optimized effective potential method, and we discuss characteristics and advantages of our procedure.

The behavior of electrons in general many-electronic systems throughout the density functionals of energy is reviewed. The basic physico-chemical concepts of density functional theory are employed to highlight the energy role in chemical structure while its extended influence in electronic localization function helps in chemical bonding understanding. In this context the energy functionals accompanied by electronic localization functions may provide a comprehensive description of the global-local levels electronic structures in general and of chemical bonds in special. Becke-Edgecombe and author’s Markovian electronic localization functions are discussed at atomic, molecular and solid state levels. Then, the analytical survey of the main workable kinetic, exchange, and correlation density functionals within local and gradient density approximations is undertaken. The hierarchy of various energy functionals is formulated by employing both the parabolic and statistical correlation degree of them with the electronegativity and chemical hardness indices by means of quantitative structure-property relationship (QSPR) analysis for basic atomic and molecular systems.

International audience; At the hand of the adsorption of the metal atoms Zn, Cd and Hg on a graphene sheet, we propose a combination of range-separated hybrid density-functional theory in combination with the incremental scheme in localised orbitals and extrapolation procedures for the description of this type of extended systems. Using only dispersion terms for the long-range part, we were able to obtain results comparable to incremental coupled-cluster calculations with singles, doubles and perturbative triples (CCSD(T)). Repulsive three-centre increments reduce the overall correlation contribution to the binding energy by 20 %.

The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi approximation in the non-relativistic semiclassical (or large-$Z$) limit for all matter, i.e, the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms supports the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that the correlation energy tends to $-A_c Z ln Z + B_c Z$ as $Z$ tends to infinity, where $Z$ is the atomic number, $A_c$ is known, and we estimate $B_c$ to be about 37 millihartrees. The local density approximation yields $A_c$ exactly, but a very incorrect value for $B_c$, showing that the local approximation is less relevant for correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-$Z$ limit generally takes this form, but with $B_c$ a functional of the TF density for the system. The implications for construction of approximate density functionals are discussed., 17 pages, 10 figures

International audience

The nonlocal dynamical polarisability of two arbitrarily shaped objects coupled by long-range Coulomb forces, when overlap of their electron densities is negligible, is calculated by expressing it in terms of the response functions of separate objects. That enables us to extend the Density Functional Theory approach within the Kohn-Sham scheme to such systems. The method is applied to the system consisting of two metallic slabs within the jellium model. The obtained response function of the total system is used to calculate the correlation energy of a static test charge placed in the system.

The ground state total and correlation energies of a negative ion-electron and electron-electron systems in a parabolic QD with standard dispersion law are theoretically investigated in an external magnetic field by a variational approach. Both cases of finite and infinite potential barrier on the spherical surface of the QD are considered. The negative ion-electron system energies in a A3B5 semiconductor QD with nonparabolic (Kane's) dispersion law is also investigated. © 2006 WILEY-VCH Verlag GmbH & Co. KGaA. 3 532 535 Conference code: 67231

Here we propose an accurate approach to the description of the electron liquid model in the electron and plasmon terms. Our ideas in the present paper are close to the conception of the collective variables which was developed in the papers of Bohm and Pines. However we use another body of mathematics in the transition to the expanded space of variable particles and plasmons realized by the transition operator. It is evident that in the Random Phase Approximation (RPA), the model which consists of two interactive subsystems of electrons and plasmons is equivalent to the electron liquid model with Coulomb interaction. Запропоновано строгий підхід до опису моделі електронної рідини в термінах електронів і плазмонів. Концептуально наша робота близька до підходу колективних змінних, який розроблявся в роботах Бома і Пайнса. Проте ми використовуємо інший математичний апарат, в якому перехід до розширеного простору змінних частинок та плазмонів виконується за допомогою оператора переходу. Доведено, що у наближенні хаотичних фаз модель, яка складається із двох взаємодіючих між собою підсистем електронів і плазмонів, цілком еквівалентна моделі електронної рідини з кулонівською взаємодією.

We propose a compact perturbative approach that reveals the physical origin of the singularity occurring in the density dependence of correlation energy: like fermions, elementary bosons have a singular correlation energy which comes from the accumulation, through Feynman "bubble" diagrams, of the same non-zero momentum transfer excitations from the free particle ground state, that is, the Fermi sea for fermions and the Bose-Einstein condensate for bosons. This understanding paves the way toward deriving the correlation energy of composite bosons like atomic dimers and semiconductor excitons, by suggesting Shiva diagrams that have similarity with Feynman "bubble" diagrams, the previous elementary boson approaches, which hide this physics, being difficult to do so., Comment: 16 pages, 22 figures

We found, by using the theoretical MP2 model, that correlation energy of the valence electrons in a large number of 3D organic molecules follows a very simple additivity rule resembling that established earlier in planar π-systems. Namely, it turns out that the total correlation energy is a multilinear function of the number of atoms of each element entering a molecule. Extrapolating the calculated correlation energies to the complete basis set (CBS) values, it occurs that the additivity holds for E(CBS)corr too. We believe that computational methods more rigorous than MP2 will confirm the additivity in the future and show that it is a genuine molecular property. The additivity formula for the valence electrons correlation energies could serve as a diagnostic tool to identify cases where significant nonadditivity takes place. In such situations the electronic structure apparently exhibits some subtleties, which are not present in other, more or less related molecules, thus deserving a meticulous scrutiny....

In this thesis are shown developments in the random phase approximation (RPA) in the context of range-separated theories. We present advances in the formalism of the RPA in general, and particularly in the ''dielectric matrix'' formulation of RPA, which is explored in details. We show a summary of a work on the RPA equations with localised orbitals, especially developments of the virtual localized orbitals that are the ''projected oscillatory orbitals'' (POO).A program has been written to calculate functions such as the exchange hole, the response function, etc on real space grid (parallelepipedic or of the ''DFT'' type) ; some of those visualisations are shown here. In the real space, we offer an adaptation of the effective energy denominator approximation (EED), originally developped in the reciprocal space in solid physics. The analytical gradients of the RPA correlation energies in the context of range separation has been derived. The formalism developped here with a lagrangian allows an all-in-one derivation of the short- and long-range terms that emerge in the expressions of the gradient. These terms show interesting parallels. Geometry optimisations at the RSH+dRPA-I and RSH+SOSEX levels on a set of 16 molecules are shown, as well as calculations and visualisations of correlated densities at the RSH+dRPA-I level.; Dans cette thèse sont montrés des développements de l'approximation de la phase aléatoire (RPA) dans le contexte de théories à séparation de portée. On présente des travaux sur le formalisme de la RPA en général, et en particulier sur le formalisme ''matrice diélectrique'' qui est exploré de manière systématique. On montre un résumé d'un travail sur les équations RPA dans le contexte d'orbitales localisées, notamment des développements des orbitales virtuelles localisées que sont les ''orbitales oscillantes projetées'' (POO). Un programme a été écrit pour calculer des fonctions telles que le trou de d'échange, la fonction de réponse, etc sur des grilles de l'espace réel (grilles parallélépipédiques ou de type ''DFT''). On montre certaines de ces visualisations. Dans l'espace réel, on expose une adaptation de l'approximation du dénominateur effectif (EED), développée originellement dans l'espace réciproque en physique du solide. Également, les gradients analytiques des énergies de corrélation RPA dans le contexte de la séparation de portée sont dérivés. Le formalisme développé ici à l'aide d'un lagrangien permet une dérivation tout-en-un des termes courte- et longue-portée qui émergent dans les expression du gradient, et qui montrent un parallèle intéressant. Des applications sont montrées, telles que des optimisations de géométries aux niveaux RSH+dRPA-I et RSH+SOSEX d'un ensemble de 16 petites molécules, ou encore le calcul et la visualisation des densités corrélées au niveau RSH+dRPA-I.

The ground state energies of non-magnetic, ferromagnetic and antiferromagnetic phases of 3D electron crystals corresponding to hcp structure are computed. In each case, the possibility of the Wigner electrons having cubic or spherical constant energy surface (the region of integration in momentum space) is investigated. The role of correlation energy is suitably taken into account. The range of the low density region favourable for Wigner electron crystallization is found. The structure dependent Wannier functions, which give proper localized representation for the Wigner electrons in the crystal, are employed in the calculation.

This thesis focuses on development of three novel multiconfigurational quantum chemical methods, to study strongly correlated systems: GASSCF, SplitCAS and SplitGAS. By GASSCF it is possible to eliminate ineffective configurations from the CI expansion by choosing an arbitrary number of active spaces and by tuning the interspace excitations. By SplitCAS and SplitGAS, the CI wave function generated by CAS or GAS type of active spaces is partitioned into two parts: a principal part containing few relevant configurations and an extended part containing less relevant configurations. The two methods differ in the criteria for the splitting. Lowdin's partitioning technique is used to reduce the secular problem to the size of the principal space. These methods allow for an enlargement of the active space with respect to the CASSCF method. Theory, algorithmic details and test calculations are presented. Based on this work, the ‘scaling catastrophe' of the CASSCF approach is partially solved.

Density functional theory uses the electron density n(r), instead of the electronic wavefunction. We side-step the kinetic energy functional by constructing a thermodynamically equivalent classical map (CM). A classical Coulomb fluid whose zeroth-order pair-distribution function (PDF) g0(r) that agrees with the quantum g0, and interacting via a “Pauli exclusion potential” reproduces the thermodynamics of the electron fluid, when the classical-fluid temperature Tcf is chosen optimally. This Tcf is chosen so that the correlation energy of the classical fluid is the Kohn–Sham correlation energy. Then, the PDFs of the classical fluid closely agree with the PDFs of the two-dimensional (2D) and 3D uniform electron systems. Can we calculate sensitive Fermi-liquid properties (e.g., quasiparticle mass m*, Lande g-factor) of interacting electrons via this CM? Given the wide interest in the effective mass m* of electrons in 2D layers, we chose the 2D system for this study. Analytical and numerical results are used to define a partially regularized m* valid to logarithmic accuracy in the sense of Landau for the Hartree–Fock (H–F) approximation. The resulting H–F m* decreases linearly with the electron-disk radius rs. The m* including correlation is calculated via a physically transparent formula. This uses the CM of the 2D PDF and its finite-T exchange-correlation free energy Fxc(T). Our results for m* fall well within the results from recent quantum Monte-Carlo simulations at T = 0, and other theoretical and experimental results. © 2012 Wiley Periodicals, Inc.

Electronic structure calculations have emerged as a key contributor in modern heterogeneous catalysis research, though their application in chemical reaction engineering remains largely limited to academia. This perspective aims at encouraging the judicious use of first-principles kinetic models in industrial settings based on a critical discussion of present-day best practices, identifying existing gaps, and defining where further progress is needed.

Using the wave-vector analysis of the jellium exchange-correlation surface energy, we show that the PBEint generalized gradient approximation (GGA) of Fabiano et al. [Phys. Rev. B 82, 113104 (2010)] is one of the most accurate density functionals for jellium surfaces, being able to describe both exchange and correlation parts of the surface energy, without error compensations. We show that the stabilized jellium model allows us to achieve a realistic description of the correlation surface energy of simple metals at any wave vector $k$. The PBEint correlation is then used to construct a meta-GGA correlation functional, modifying the one-electron self-correlation-free Tao-Perdew-Staroverov-Scuseria (TPSS) one. We find that this new functional (named JS) performs in agreement with fixed-node diffusion Monte Carlo estimates of the jellium surfaces, and is accurate for spherical atoms and ions of different spin-polarization and for Hooke's atom for any value of the spring constant.

The random phase approximation (RPA) for the electron correlation energy, combined with the exact-exchange energy, represents the state-of-the-art exchange-correlation functional within density-functional theory (DFT). However, the standard RPA practice -- evaluating both the exact-exchange and the RPA correlation energy using local or semilocal Kohn-Sham (KS) orbitals -- leads to a systematic underbinding of molecules and solids. Here we demonstrate that this behavior is largely corrected by adding a "single excitation" (SE) contribution, so far not included in the standard RPA scheme. A similar improvement can also be achieved by replacing the non-self-consistent exact-exchange total energy by the corresponding self-consistent Hartree-Fock total energy, while retaining the RPA correlation energy evaluated using Kohn-Sham orbitals. Both schemes achieve chemical accuracy for a standard benchmark set of non-covalent intermolecular interactions., Comment: 5 pages, 4 figures, and an additional supplementary material

We find that the spin susceptibility of a two-dimensional electron system with valley degeneracy does not grow critically at low densities, at variance with experimental results [ A. Shashkin et al. Phys. Rev. Lett. 96 036403 (2006)]. We ascribe this apparent discrepancy to the weak disorder present in experimental samples. Our prediction is obtained from accurate correlation energies computed with state-of-the-art diffusion Monte Carlo simulations and fitted with an analytical expression which also provides a local spin density functional for the system under investigation.