Relativistic energies of the ground state of the hydrogen molecule

Wolniewicz, L.

doi:10.1063/1.465303

Cited by 314 publications

(253 citation statements)

References 27 publications

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“…Further tests performed on a set of 30 closedshell molecules (see Fig. 4 [35][36][37], with E GM evaluated from sc-GW , G 0 W 0 @HF, and G 0 W 0 @PBE. PBE total energies are included for comparison.…”

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confidence: 99%

Unified description of ground and excited states of finite systems: The self-consistentGWapproach

et al. 2012

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GW calculations with a fully self-consistent Green's function G and screened interaction W -based on the iterative solution of the Dyson equation-provide a consistent framework for the description of groundand excited-state properties of interacting many-body systems. We show that for closed-shell systems selfconsistent GW reaches the same final Green's function regardless of the initial reference state. Self-consistency systematically improves ionization energies and total energies of closed-shell systems compared to G 0 W 0 based on Hartree-Fock and (semi)local density-functional theory. These improvements also translate to the electron density, as exemplified by an improved description of dipole moments, and permit us to assess the quality of ground-state properties such as bond lengths and vibrational frequencies. Many-body perturbation theory (MBPT) 1 in the GW approximation of the electronic self-energy 2,3 is presently the state-of-the-art method for describing the spectral properties of solids. 4,5 Recently, it has steadily gained popularity for molecules and nanosystems. 6 In addition, MBPT provides a prescription to extract total energies and structural properties from the GW approximation and therefore is a consistent theoretical framework for single-particle spectra and total energies.Due to its numerical cost and algorithmic difficulties, the GW method has only recently been applied self-consistently (i.e., nonperturbatively) to atoms, 7 molecules, 8 and molecular transport. 6 Predominantly, GW calculations are still performed perturbatively (one-shot G 0 W 0 ) on a set of singleparticle orbitals and eigenvalues obtained from a preceding density-functional theory 9 (DFT) or Hartree-Fock (HF) calculation. This procedure introduces a considerable starting-point dependence, 10-12 which can be eliminated by iterating the Dyson equation to self-consistency. [6][7][8]13 The resulting selfconsistent GW (sc-GW ) framework is a conserving approximation in the sense of Baym and Kadanoff 14 (i.e., it satisfies momentum, energy, and particle number conservation laws). sc-GW gives total energies 15 free from the ambiguities of the G 0 W 0 scheme, in which the results depend on the chosen total energy functional. 7 However, as in any self-consistent theory, the question remains if the self-consistent solution of the Dyson equation is unique. This issue is fundamentally different from the initial-state dependence of G 0 W 0 . For HF (Ref. 16) and local-density approximation (LDA)/generalized gradient approximation + U (GGA + U ) (Ref. 17) calculations, it is well known that the self-consistency cycle can reach many local minima instead of the global minimum. Moreover, a previous sc-GW study for the Be atom showed that normconserving pseudopotential calculations do not produce the same final GW Green's function (and the corresponding ionization potential) as all-electron calculations. 18 In this Rapid Communication, we demonstrate certain key aspects of the sc-GW approximation for closed-shell molecules that make...

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confidence: 99%

Unified description of ground and excited states of finite systems: The self-consistentGWapproach

et al. 2012

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“…We presented the first full calculation of photon-energy dependent Raman association cross sections including all rovibrational resonances associated with the intermediate states, based on the accurate electronic potential energy surfaces and properties computed by Wolniewicz and Staszewska. [18][19][20][21] We compared the exact results with those of the Placzek-Teller approximation and we showed that …”

Section: Discussionmentioning

confidence: 99%

“…The ab initio potential energy curves and electronic dipole transition moments are taken from calculations by Wolniewicz and Staszewska. [18][19][20][21] We use the vibrationally resolved lifetimes from the work by Fantz and Wu¨nderlich 22 where the sum of the initial state energy and the energy of the incoming photon exceeds the dissociation limit of an intermediate electronic state, we use the Green function absorbing boundary condition (ABC) method [23][24][25] to prevent the matrix in eqn (10) from becoming singular. The ABC method consists of replacing the constant ½G m by an r-dependent function g(r), thus effectively augmenting the potential V nO (r) with a negative imaginary potential which absorbs the wave function in the physically non-relevant outer region.…”

Section: Methodsmentioning

confidence: 99%

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Raman association of H2 in the early universe

et al. 2006

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We investigate the contribution made by Raman scattering to the formation of molecular hydrogen in astrophysical environments characteristic of the early stages of the evolution of the universe. In the Raman process that we study, a photon is scattered by a pair of colliding hydrogen atoms leaving a hydrogen molecule that is stabilized by the transfer of kinetic and binding energy to the photon. We use a formulation for calculating the photon scattering cross section in which an infinite sum of matrix elements over rovibrational levels of dipole accessible electronic states is replaced by a single matrix element of a Green's function. We evaluate this matrix element by using a discrete variable representation.

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“…One of their attractive features is the capability of incorporating finite nuclear mass/isotope and spin statistic effects directly into the electronic wave-function, in a contrast with BO treatments where these finite-mass effects are usually incorporated as corrections, either adiabatic or non-adiabatic, to the electronic energies only (see, e.g., Ref. 16). In fact, approaches going beyond the BO approximation and enabling a simultaneous description of electrons and nuclei are very useful when the nuclear de-localization has a marked influence onto the electronic wave-function itself (e.g., proton-coupled electron transfer processes).…”

Section: Introductionmentioning

confidence: 99%

Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems

Aguirre

Villarreal

Delgado‐Barrio

et al. 2013

The Journal of Chemical Physics

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An interface between the APMO code and the electronic structure package MOLPRO is presented. The any particle molecular orbital APMO code [González et al., Int. J. Quantum Chem. 108, 1742 implements the model where electrons and light nuclei are treated simultaneously at Hartree-Fock or second-order Möller-Plesset levels of theory. The APMO-MOLPRO interface allows to include highlevel electronic correlation as implemented in the MOLPRO package and to describe nuclear quantum effects at Hartree-Fock level of theory with the APMO code. Different model systems illustrate the implementation: 4 He 2 dimer as a protype of a weakly bound van der Waals system; isotopomers of [He-H-He] + molecule as an example of a hydrogen bonded system; and molecular hydrogen to compare with very accurate non-Born-Oppenheimer calculations. The possible improvements and future developments are outlined.

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Relativistic energies of the ground state of the hydrogen molecule

Cited by 314 publications

References 27 publications

Unified description of ground and excited states of finite systems: The self-consistentGWapproach

Unified description of ground and excited states of finite systems: The self-consistentGWapproach

Raman association of H2 in the early universe

Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems

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