3 years ago

# H2+, HeH and H2: Approximating potential curves, calculating rovibrational states

Horacio Olivares-Pilón, Alexander V. Turbiner
Analytic consideration of the Bohr–Oppenheimer (BO) potential curves for diatomic molecules is proposed: accurate analytic interpolation for a potential curve consistent with its rovibrational spectra is found. It is shown that in the BO approximation for four lowest electronic states $1 s σ g$ and $2 p σ u$, $2 p π u$ and $3 d π g$ 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 s.d. Approximation based on matching the Laurant-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 $1 s σ g$ and $2 p σ u$, $2 p π u$ and $3 d π g$ potential curves are calculated. In general, it coincides with spectra found via numerical solution of the Schrödinger equation (when available) within six s.d. It is shown that $1 s σ g$ curve contains 19 vibrational states $( ν , 0 )$, while $2 p σ u$ curve contains a single one $( 0 , 0 )$ and $2 p π u -Abstract Truncated-$

DOI: S0003491618301088

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