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The hydrogen molecules H 2 and ( ) H 2 2 are analyzed with electronic correlations taken into account between the s 1 electrons in an exact manner. The optimal single-particle Slater orbitals are evaluated in the correlated state of H 2 by combining their variational determination with the diagonalization of the full Hamiltonian in the second-quantization language. All electron-ion coupling constants are determined explicitly and their relative importance is discussed. Sizable zero-point motion amplitude and the corresponding energy are then evaluated by taking into account the anharmonic contributions up to the ninth order in the relative displacement of the ions from their static equilibrium value. The applicability of the model to solid molecular hydrogen is briefly analyzed by calculating intermolecular microscopic parameters for the × H 2 2 rectangular configuration, as well its ground state energy.Keywords: hydrogen molecules, electron-proton coupling for hydrogen molecule, electronic correlations for hydrogen molecule, intermolecular hopping and interaction parameters MotivationThe few-site models of correlated fermions play an important role in singling out, in an exact manner, the role of various local intra-and inter-site interactions against hopping (i.e., containing both covalent and the ionic factors) and thus, in establishing the optimal correlated state of fermions [1-8] on a local (nanoscopic) scale. The model has also been used to obtain a realistic analytic estimate of the hydrogen-molecule energies of the ground and the excited states in the correlated state [9]. For this purpose, we have developed the so-called EDABI method, which combines Exact Diagonalization in the Fock space with a concomitant Ab Initio determination of the single-particle basis in the Hilbert space. So far, the method has been implemented by taking only s 1 Slater orbitals, one per site [10]. The method contains no parameters; the only approximation made is taking a truncated single-particle basis (i.e., one Slater orbital per site) when constructing the field operator, that in turn is used to derive the starting Hamiltonian in the second-quantization representation. This Hamiltonian represents an extended Hubbard Hamiltonian, with all two-site interactions taken into account and the solution comprises not only the exact eigenvalues of the few-site Hamiltonian, but also at the same time an evaluation of the adjustable single-particle wave functions in the correlated state. Also, the calculated thermodynamic properties rigorously exemplify [12,11] the low-and highenergy scales, corresponding to spin and local charge fluctuations, respectively. The former represents the precursory magnetic-ordering effect whereas the latter represents local effects accompanying the Mott-Hubbard transition. In general, our approach follows the tradition of accounting for interelectronic correlations via the second-quantization procedure, with the adjustment of single-particle wave functions, contained in microscopic parameters of the startin...

An efficient computational scheme devised for investigations of ground state properties of the electronically correlated systems is presented. As an example, (H2)n chain is considered with the long-range electron-electron interactions taken into account. The implemented procedure covers: (i) single-particle Wannier wave-function basis construction in the correlated state, (ii) microscopic parameters calculation, and (iii) ground state energy optimization. The optimization loop is based on highly effective process-pool solution -specific root-workers approach. The hierarchical, two-level parallelism was applied: both shared (by use of Open Multi-Processing) and distributed (by use of Message Passing Interface) memory models were utilized. We discuss in detail the feature that such approach results in a substantial increase of the calculation speed reaching factor of 300 for the fully parallelized solution. The elaborated in detail scheme reflects the situation in which the most demanding task is the single-particle basis optimization. I. PHYSICAL MOTIVATION: EXACT DIAGONALIZATION + AB INITIO METHODElectronically correlated systems are important both from the point of view of their unique physical properties and from nontrivial computational methods developed to determine them. The latter cover methods based on the Density Functional Theory (DFT) with the energy functional enriched by the correlation terms -the on-site repulsion U in the Hubbard model [1] and the Hund's rule term in the case of orbital degeneracy. Often, they are incorporated into either DFT or the Dynamic Mean Field Theory (DMFT) approach supplemented with the LDA-type calculations (see e.g. [2]). On the other hand, the Configuration-Interaction (CI) method does not suffer from the well-known double counting problem [1,2], inherent in the DFT+U or LDA+DMFT methods. Another approach, similar in its spirit to the CI method, formulated as a combination of the first-and second quantization (FQ, SQ respectively) formalisms was elaborated in our group in the last decade and termed the Exact Diagonalization Ab Intito (EDABI) approach [3,4]. This method allows for a natural incorporation of the correlation effects consistently by the advantages of using the SQ language so that the double-counting problem does not arise at all. Also, by construction, it includes the Pauli principle for the fermionic systems. In contrast to CI the EDABI approach avoids any direct dealing * andrzej.biborski@agh.edu.pl † kadzielawa@th.if.uj.edu.pl ‡ ufspalek@if.uj.edu.pl with the many-body wave function expressed via a linear combination of the Slater determinants [5]. Instead, it is based on the many-particle quantum states constructed in the occupation number representation [5] -standard procedure for the SQ formulated problems.The application of EDABI was found promising in view of research devoted to the hydrogen molecular systems with inclusion of interelectronic correlations [6], nano-clusters [7], and to atomic hydrogen metallization [8]. As the many-particle state i...