## Hyperfine and Spin-rotation Interactions in the Hydrogen Molecule-ion |

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Page 73

... orbital node; the d -types are described by four spherical gaussians centered

xy at the corners of a square, and a d 2 orbital is approximated with six lobes, two

to describe the axial charge density and four to mimic the torroidal ring of charge.

Two

consisting of a set of contracted orbital s, for which a rough optimization of orbital

exponents could be performed, and

functions, ...

... orbital node; the d -types are described by four spherical gaussians centered

xy at the corners of a square, and a d 2 orbital is approximated with six lobes, two

to describe the axial charge density and four to mimic the torroidal ring of charge.

Two

**basis sets**were used in this study, a small prototypical basis,**Basis Set**I,consisting of a set of contracted orbital s, for which a rough optimization of orbital

exponents could be performed, and

**Basis Set**II, a larger production set offunctions, ...

Page 79

type functions. It was found that the 2s-type functions were of only slight value in

the expansions and became even less important when the ls set was

uncontracted. They were therefore eliminated in

character was bolstered by substituting Huzinaga's ten component ls orbital for

the eight component orbital of

used for

**Basis Set**II is essentially an uncontracted version of**Basis Set**I enriched with d 2-type functions. It was found that the 2s-type functions were of only slight value in

the expansions and became even less important when the ls set was

uncontracted. They were therefore eliminated in

**Basis Set**II, and the s-typecharacter was bolstered by substituting Huzinaga's ten component ls orbital for

the eight component orbital of

**Basis Set**I. In all cases the same scaling factors asused for

**Basis Set**...Page 82

When these findings are compared with results obtained with the exact wave

function, the differences, as reported in the columns headed Ay' . reflect the

superiority of

for

. In the context of assessing the capabilities of an approximate wave function in a

calculation of y' » the observations to be made on the basis of Table V.5 are

promising, ...

When these findings are compared with results obtained with the exact wave

function, the differences, as reported in the columns headed Ay' . reflect the

superiority of

**Basis Set**II over**Basis Set**I, especially at small R . The errors in y'for

**Basis Set**II are generally 0.1-0.2% while those for**Basis Set**I range from 1-5%. In the context of assessing the capabilities of an approximate wave function in a

calculation of y' » the observations to be made on the basis of Table V.5 are

promising, ...

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### Contents

Solution of Nonrelativistic Electronic | 15 |

Solution of Nuclear Schrodinger | 24 |

The Effective Spectroscopic Hamiltonian | 42 |

6 other sections not shown

### Common terms and phrases

accuracy angular momentum Appendix atomic units Basis Set bH CH Bishop and Wetmore Born-Oppenheimer approximation calculation Chapter Chem CM CM continued K bH convergence Cooley-Cashion curve diagonal eigenfunctions eigenvalues eigenvectors electric field electron spin electronic and nuclear electronic energy elliptical coordinates evaluation expectation value experimental Figure first-order function of internuclear g factor H2 and HD hamiltonian hyperfine components hyperfine constants hyperfine energy levels hyperfine interactions hyperfine levels hyperfine structure infrared interaction coefficients interaction functions internuclear separation interpolation lattice Lett matrix elements Menasian molecular rotation momenta Morse potential nonrelativistic electronic nuclei one-electron diatomic molecule Pauli equation perturbation Phys Poisson sum formula quantum numbers reference diagram relative intensities representation ROGER DEAN rovibrational transitions simple product basis simulated solution spectra spectroscopic constants spherical spin-rotation interaction surface unit cell Table VI.1 theoretical transition frequencies transition intensity variation vector vibrational-rotational VM(R wave function Wigner-Eckart theorem