Search results for "Wave function"
showing 10 items of 395 documents
Coupled-Cluster study of ‘no-pair’ bonding in the tetrahedral Cu4 cluster
2011
Abstract Ab initio Coupled-Cluster calculations with single and double excitations and perturbative correction to the triple, CCSD(T), have been carried out for the high-spin electronic state, ( 5 A 2 ) , of the copper cluster Cu 4 in its tetrahedral arrangement. Like alkali metals clusters, tetrahedral Cu 4 presents a bound quintet state, i.e., a situation where all the valence electrons are unpaired. This rather exotic wavefunction, also known as no-pair bonding state, is examined in detail. The influence of the basis set is also analyzed, as well as the importance of the core correlation and the effect of the basis-set superposition errors.
High excitations in coupled-cluster series: vibrational energy levels of ammonia
2004
The ammonia molecule containing large amplitude inversion motion is a revealing system in examining high-order correlation effects on potential energy surfaces. Correlation contributions to the equilibrium and saddle point geometries, inversion barrier height and vibrational energy levels, including inversion splittings, have been investigated. A six-dimensional Taylor-type series expansion of the Born–Oppenheimer potential energy surface, which is scaled to different levels of theory, is used to determine vibrational energy levels and inversion splittings variationally. The electronic energies are calculated by coupled-cluster methods, combining explicitly correlated R12 theory (which incl…
Tuning the Electronic Properties of the Dative N-B Bond with Associated O-B Interaction: Electron Localizability Indicator from X-Ray Wavefunction Re…
2016
Despite the immense growth in interest in difluoroborate dyes, the nature of the interactions of the boron atom within the N-BF2 -O kernel is not yet fully understood. Herein, a set of real-space bonding indicators is used to quantify the electronic characteristics of the dative N-B bond in difluoroborate derivatives. The atoms-in-molecules (AIM) partitioning scheme is complemented by the electron localizability indicator (ELI-D) approach, and both were applied to experimental and theoretical electron-density distributions (X-ray constrained wavefunction fitting vs. DFT calculations). Additionally, Fermi orbital analysis was introduced for small DFT models to support and extend the findings…
Mapping an electron wave function by a local electron scattering probe
2015
A technique is developed which allows for the detailed mapping of the electronic wave function in two-dimensional electron gases with low-temperature mobilities up to $15\times {10}^{6}\;{\mathrm{cm}}^{2}\;{{\rm{V}}}^{-1}\;{{\rm{s}}}^{-1}$. Thin ('delta') layers of aluminium are placed into the regions where the electrons reside. This causes electron scattering which depends very locally on the amplitude of the electron wave function at the position of the Al δ-layer. By changing the distance of this layer from the interface we map the shape of the wave function perpendicular to the interface. Despite having a profound effect on the electron mobiliy, the δ-layers do not cause a widening of …
Multiple scattering approach for two-electron resonant emission studied by angle-resolved coincidence spectroscopy.
2008
International audience; We have developed a generalization of the multiple-scattering formalism to deal with Auger-photoelectron coincidence spectroscopy APECS in the solid state. We have merged the exact atomic treatment of the angular correlations between the two electrons and the single-particle approach, on which the multiplescattering description of condensed matter relies. This allows the recovering, even in extended systems, of the entangled form of the electron-pair wave function characterizing the coincidence angular diffraction pattern. In the atomic limit our formalism correctly reproduces the cross section, as calculated within the statistical-tensors approach, usually employed …
Size-consistent ab initio calculation of the electric quadrupole moment of Cl2
2003
Abstract The molecular electric quadrupole moment ( Θ ) of Cl 2 has been calculated using SDCI, and (SC) 2 -SDCI wave functions as well as CCSD, CCSD(T), and CC3 methods. All these correlation methods are single reference. All of them, but SDCI, are free of the size-extensivity error. The variation of Θ from the separated atoms to the equilibrium region is reported. The present results leads to an estimated value of 2.3520 a.u. (10.55 × 10 −40 Cm 2 ) corresponding to a CC(3) calculation at the CBS approach and including the ro-vibrational and thermal averaging corrections. This value is compatible with two experimental values and points to one of them as slightly more reliable.
Reply to comment on “A MRCI PS and CASSCF study of the ground state MgO dissociation energy”
1993
To compute the dissociation energy of MgO, the relationship among the size of the active space in CASSCF wavefunctions, the computed De and the continuity of ∂E/∂r is studied. Basis set influence is also considered. Finally, it is concluded that the dissociation energy of MgO referred to ground state atoms is 2.32±0.1 eV.
A modified ansatz for explicitly correlated coupled-cluster wave functions that is suitable for response theory
2009
A modified ansatz for explicitly correlated coupled-cluster wave functions with a single correlation factor is set forward. It is based on the fixed amplitude ansatz of Ten-no [Chem. Phys. Lett. 398, 56 (2004)] to which an extra term is added that allows for the explicitly correlated description of singly excited configurations. The new approach has been implemented for coupled-cluster singles and doubles with the aid of automated techniques. Numerical results are presented for vertical excitation energies, and ground and excited state equilibrium distances and harmonic frequencies of diatomics. The new approach is shown to provide a nearly unbiased description of ground and predominantly s…
Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment
2014
Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions and near degeneracy static correlations. In this work we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function $f(r_{12})$ depending on the interelectronic distance $r_{12}$. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems we make an analysis of the wave function in t…
Long-range interactions and the sign of natural amplitudes in two-electron systems
2013
In singlet two-electron systems the natural occupation numbers of the one-particle reduced density matrix are given as squares of the natural amplitudes which are defined as the expansion coefficients of the two-electron wave function in a natural orbital basis. In this work we relate the sign of the natural amplitudes to the nature of the two-body interaction. We show that long-range Coulomb-type interactions are responsible for the appearance of positive amplitudes and give both analytical and numerical examples that illustrate how the long-distance structure of the wave function affects these amplitudes. We further demonstrate that the amplitudes show an avoided crossing behavior as func…