Energy and density analysis of the H2 molecule from the united atom to dissociation: The Σ3g+ and Σ3u+ states

There are well-established mathematical relationships for the energy of a diatomic molecule (the exact energy, but also both the Hartree-Fock and Thomas-Fermi energies) in the limit of large nuclear charge of the atoms and small internuclear distances. We present calculated energies for a number of homonuclear diatomic molecules at short internuclear distances for numerical comparison with these established relationships. Intriguingly, they hold in practice for relatively small nuclear charges and for relatively long internuclear distances.

Section: Methodsmentioning

confidence: 75%

Behavior of the Hartree‐Fock energy at short internuclear distances

Gilka

Solovej

Taylor

2011

“…Thus, the wavefunctions of the H 2 system, composed of both covalent and ionic components, can be partitioned into two wavefunctions, the first one, of H + H − , composed, by construction, only of ionic structures, and the second one, of H 2 , composed only of covalent structures. This partitioning is possible with the HL‐CI method . As reported by Slater, in the H 2 molecule the HL covalent and ionic wavefunctions, although orthogonal at infinity, are highly nonorthogonal at equilibrium and at shorter distances; actually, the shorter the internuclear distance, the more the two functions resemble one another, and indeed the two functions must become identical at the united atom.…”

Section: Ionic and Covalent Charactermentioning

confidence: 87%

“…The computations have been performed, within the Born–Oppenheimer approximation, with full Configuration Interaction (CI), a well‐tested approximation of the Schrödinger equation. As previously done, both full molecular orbital (MO) CI and full atomic orbital (AO) CI [referred to as Hartree–Fock CI (HF‐CI) and Heitler–London CI (HL‐CI), respectively] are considered. As known, the two approaches yield, for a given basis set, exactly the same energy but the HL‐CI technique is most convenient for the exploration of H + H − ionic states …”

Section: Computational Detailsmentioning

confidence: 99%

“…In this work, we present for the H 2 molecule the PECs for the first 10 doubly excited states of the

{{}^{1,3}Σ}_{g}^{-}

and

{{}^{1,3}Σ}_{u}^{-}

manifolds with electronic configurations He(2p2p) up to He(2p8g) at the united atom and dissociation products H 2 (2p + 2p) up to H 2 (2p + 6ℓ). We have followed the methodology previously used for the study of the

Σ, Π, Δ, Φ, normala normaln normald Γ

manifolds of the H 2 singly excited states …”

Section: Introductionmentioning

confidence: 99%

“…We have followed the methodology previously used for the study of the R; P; D; U; and C manifolds of the H 2 singly excited states. [7][8][9][10] The H 2 R 2 states are non-autoionizing and are located in the energy region delimited by two PECs of the H 1 2 ion, precisely those of the 2 R u 1 2pr u ð Þ and the 2 P u 2pp u ð Þ states. This energy region is about 26 eV above the ground state of the H 2 molecule.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Unexpected properties of non‐autoionizing doubly excited states of the H₂ molecule

Corongiu

2016

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We present accurate calculations of the non‐autoionizing Σ1,3g− and Σ1,3u− doubly excited states of the H2 molecule using full configuration interaction with Hartree–Fock molecular orbitals and Heitler–London atomic orbitals. We consider the united atom configurations from He(2p2p) up to He(2p8g) and dissociation products from H2(2p + 2p) up to H2(2p + 6ℓ). Born–Oppenheimer calculations are carried out with extended and optimized Slater‐type orbitals for a total of 40 states, 10 for each symmetry, covering the internuclear distances from the united atom to dissociation, which, for some states, is reached beyond 100 a0. Occurrences of repulsive states cleanly interlaced between bound states with many vibrational levels are reported. Some of the potential minima are deep enough to accommodate many vibrational levels (up to 50). Noteworthy large equilibrium minima, like Req = 46.0 a0 in the Σ3u− state dissociating as (2p + 6h) and with 18 vibrational levels. The occurrence of vertical excitations from the singly excited manifolds is analyzed. Several states present double minima generated by avoided crossings, some with a strong ionic character. © 2016 Wiley Periodicals, Inc.

Energy and density analysis on the H₂ molecule from the united atom to dissociation: The Σ, Π, Δ, ϕ, and Γ manifolds

Corongiu

Clementi

2010

Self Cite

We present 140 accurate potential energy curves, PECs, for the R, P, D, U, and C manifolds for the H 2 molecule, mapping all the states with energy below the H þ 2 ground state. The full configuration interaction, nonrelativistic Born-Oppenheimer computations are performed with large and optimized basis sets of Slater-type and spherical Gaussian functions; these new basis sets are somewhat larger than those used in recent published studies on the 60 R state PECs. The full CI computations are performed twice, with Hartree-Fock and with Heitler-London-type functions, allowing the identification of the ionic component in the total energy. The computed energies are within 10 À5 hartree from the most accurate PECs in literature. We aim (a) at the evaluation of the PECs starting at very short and unexplored internuclear distances (0.01 bohrs) and ending at full dissociation, (b) at the systematic prediction of high excited state PECs dissociating as 1s þ 4l and 1s þ 5l, and (c) at the characterization of the evolution of the 140 PEC electronic densities from united atom to dissociation. With this work we fill a gap in today literature, which has dealt mainly with low excited states, generally excluding short internuclear distances. The electronic configuration at the united atom persists as dominant configuration well beyond the equilibrium separation, and it switches to that at dissociation often with energy patterns seemingly irregular, in particular when the values of the principal quantum number at dissociation and at the united atom differ by one or more unit. The Hund's singlettriplet splitting, which propagates from the united atom to the molecule, is discussed. The singlet and triplet states are rather close in energy in the P manifolds, and approach degeneracy in the D and U manifolds, to become fully degenerate in the C manifolds. Discussions on the correlation energy correction, adiabatic correction, spectroscopic constants and on general features of the H 2 excited states are presented. The H 2 molecule is a system, which-to be understood-needs consideration of both the very short internuclear distances in approaching the united atom and of the very high excited states below H þ 2 .