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-

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