H2+, HeH and H2: Approximating potential curves, calculating r

Abstract

Analytic consideration of the Bohr-Oppenheimer (BO) approximation for diatomic molecules is proposed: accurate analytic interpolation for potential curve consistent with its rovibrational spectra is found.It is shown that in the Bohr-Oppenheimer approximation for four lowest electronic states 1sσ g and 2pσ u , 2pπ u and 3dπ g of H + 2 , the ground state X 2 Σ + of HeH and the two lowest states 1 Σ + g and 3 Σ + u of H 2 , the potential curves can be analytically interpolated in full range of internuclear distances R with not less than 4-5-6 figures. Approximation based on matching the Taylor-type expansion at small R and a combination of the multipole expansion with one-instanton type contribution at large distances R is given by two-point Padé approximant. The position of minimum, when exists, is predicted within 1% or better.For the molecular ion H + 2 in the Lagrange mesh method, the spectra of vibrational, rotational and rovibrational states (ν, L) associated with 1sσ g and 2pσ u , 2pπ u and 3dπ g potential curves is calculated. In general, it coincides with spectra found via numerical solution of the Schrödinger equation (when available) within six figures. It is shown that 1sσ g curve contains 19 vibrational states (ν, 0), while 2pσ u curve contains a single one (0, 0) and 2pπ u state contains 12 vibrational states (ν, 0). In general, 1sσ g electronic curve contains 420 rovibrational states, which increases up to 423 when we are beyond BO approximation. For the state 2pσ u the total number of rovibrational states (all with ν = 0) is equal to 3, within or beyond Bohr-Oppenheimer approximation. As for the state 2pπ u within the Bohr-Oppenheimer approximation the total number of the rovibrational bound states is equal to 284. The state 3dπ g is repulsive, no rovibrational state is found.It is confirmed in Lagrange mesh formalism the statement that the ground state potential curve of the heteronuclear molecule HeH does not support rovibrational states.Accurate analytical expression for the potential curves of the hydrogen molecule H 2 for the states 1 Σ + g and 3 Σ + u is presented. The ground state 1 Σ + g contains 15 vibrational states (ν, 0), ν = 0 − 14.In general, this state supports 301 rovibrational states. The potential curve of the state 3 Σ + u has a shallow minimum: it does not support any rovibrational state, it is repulsive. * Electronic address: horop@xanum.uam.mx † Electronic address: turbiner@nucleares.unam.mx

On the Problem of He–He Bond in the Endohedral Fullerene He2@C60

“…The values obtained for Δ ZPE (He 2 ) are in good agreement with the results of Luo et al [100][101][102], Gdanitz [103], Zhao and Truhlar [104], and Szalewicz et al [105,106]. For example, Δ ZPE (He 2 ) = −10.980 ± 0.004 K at (He − He) = 2.9634Å [103] and Δ ZPE (He 2 ) = −11.0006(2) K at (He − He) = 2.9634Å [105] [93,94] and references therein). It has the van der Waals minimum = 4.720 cm −1 = 6.79 K at the equilibrium interatomic H-He distance = 3.548Å.…”

“…It has the van der Waals minimum = 4.720 cm −1 = 6.79 K at the equilibrium interatomic H-He distance = 3.548Å. It was proved [93,94] that the small depth of a potential well cannot provide the existence of any bound state, including the ground one. Therefore, the ground electron state 2 Σ + of the HeH system is unstable.…”

The hydrogen molecule H2 in inclined configuration in a weak magnetic field

“…and inclinations θ = 0, 45 • , 90 • are built from variational results obtained in the domain R ∈ [1, 2] a.u. and extended beyond following the procedure discussed in [22] for approximating potential curves in diatomic molecules (see also references therein). It is evident that the asymptotic behavior of the electronic energy of H 2 at small distances R → 0 is given by…”

On the Existence of HeHe Bond in the Endohedral Fullerene Hе2@C60

“…In the ground X 2 Σ + ‐electronic state, its potential energy curve (PEC) revealing the van der Waals minium D e = 4.720 cm −1 = 6.79 K at the equlibrium HHe distance R e = 3.548 Å is very shallow (see Refs. [ and ] and references therein). It is proved that due to its shallowness this PEC is unable to support any bound state, in particular the ground one.…”

“…[ and ] and references therein). It is proved that due to its shallowness this PEC is unable to support any bound state, in particular the ground one. Therefore, the ground X 2 Σ + ‐electronic state of HeH is unstable.…”