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• W2801161017 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 $1ssigma_g$ and $2psigma_u$, $2p pi_u$ and $3d pi_g$ of H$_2^+$, the ground state X$^2Sigma^+$ of HeH and the two lowest states $^1Sigma^+_g$ and $^3Sigma^+_u$ 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 Pad'e 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 $(nu,L)$ associated with $1ssigma_g$ and $2psigma_u$, $2p pi_u$ and $3d pi_g$ potential curves is calculated. In general, $1ssigma_g$ electronic curve contains 420 rovibrational states, which increases up to 423 when we are beyond BO approximation. For the state $2psigma_u$ the total number of rovibrational states (all with $nu=0$) is equal to 3, within or beyond Bohr-Oppenheimer approximation. As for the state $2ppi_u$ within the Bohr-Oppenheimer approximation the total number of the rovibrational bound states is equal to 284. The state $3dpi_g$ is repulsive, no rovibrational state is found. 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 $^1Sigma^+_g$ and $^3Sigma^+_u$ is presented." @default.
• W2801161017 created "2018-05-17" @default.
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• W2801161017 date "2018-06-01" @default.
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• W2801161017 title "H<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=mml110 display=inline overflow=scroll altimg=si1.gif><mml:msubsup><mml:mrow /><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup></mml:math>, HeH and H<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=mml111 display=inline overflow=scroll altimg=si35.gif><mml:msub><mml:mrow /><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>: Approximating potential curves…" @default.
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• W2801161017 doi "https://doi.org/10.1016/j.aop.2018.04.021" @default.
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