## ACCURATE PREDICTION OF THE VIBRATION-ROTATION CONSTANTS OF DIATOMIC MOLECULES

dc.creator | Calder, V. | en_US |

dc.creator | Hansen, Dick | en_US |

dc.creator | Hoffman, D. K. | en_US |

dc.creator | Ruedenberg, Klaus | en_US |

dc.date.accessioned | 2006-06-15T13:28:52Z | |

dc.date.available | 2006-06-15T13:28:52Z | |

dc.date.issued | 1972 | en_US |

dc.identifier | 1972-AA-4 | en_US |

dc.identifier.uri | http://hdl.handle.net/1811/8894 | |

dc.description | $^{1}$ G.V. Calder and Klaus Ruedenberg, J. Chem. Phys., 49, 5399 (1968)."" | en_US |

dc.description | Author Institution: Ames Laboratory, USAEC, Iowa State University | en_US |

dc.description.abstract | Two empirical observations about diatomic ground state potentials are made: (1) The coefficients $a_{1}, a_{2}$, etc. in the Dunham potential energy expansion: $$ V(\rho) = a_{0} \rho^{2} [1 + a_{1} \rho + a_{2}\rho^{2}+\cdots ], (\rho =(R-R_{e})/R_{e}) $$ are essentially constant for a large class of diatomic molecules, and (2) the coefficient $a_{i}$ is related to $a_{1}$ by the expression: $$ a_{i} = {(-1)}^{i-1} ia_{1}.$$ Correlations between the spectroscopic coefficients $\beta_{e}$, $\alpha_{e}$, $\omega_{e}$ and $\omega_{e}X_{e}$ have been derived previously using the first $observation^{1}$; however the correlations, although accurate, are isotopically inconsistent. New, useful interrelations between the vibration-rotation spectroscopic constants can be deduced by recasting the energy level expansion: $$ E(V,J) = \Sigma_{\ell , m} Y_{\ell m}\left(V+\frac{1}{2}\right)^\ell [J(J+1)]^{m} $$ in terms of mass reduced quantum numbers $\mu^{-1/2}$ V and $a^{-1/2} J$ and mass independent coefficients: $$ Y_{\ell m}^{*} = Y_{\ell m}\mu^{(\ell/2+m)} $$ For diatomic molecules formed from atoms from any two columns of the periodic table, an appropriate plot of the coefficients $Y_{\ell m}^{*}$ form a grid with molecules occuring at the intersections. Thus it is possible to predict the spectroscopic constants of a diatomic molecule to within a few percent even when no data are available on that molecule. The second observation is used to derive a ``universal’’ three parameter function: $$ V(\rho) = a_{0} \rho^{2} \left[ 1 + \frac{a_{1}\rho}{(1+\rho)^{2}}\right ] $$ which is shown to fit the observed energy levels of a test molecule, $I_{2}$, over a wide range of $\rho$. | en_US |

dc.format.extent | 169907 bytes | |

dc.format.mimetype | image/jpeg | |

dc.language.iso | English | en_US |

dc.publisher | Ohio State University | en_US |

dc.title | ACCURATE PREDICTION OF THE VIBRATION-ROTATION CONSTANTS OF DIATOMIC MOLECULES | en_US |

dc.type | article | en_US |

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