A laplace transform wave function for the hydrogen molecule ion ground state

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The H + 2 ground state energy is calculated over the range of internuclear separation from R = 0.2 au to R = 8.0 au, using a Laplace transform-type wave function. The integral transform is made on Slater-type functions with the weighting function f(ν, p, α) = α (ν+3)/2 exp (− pα/2). The electronic energy E = −1.0833 au for the equilibrium internuclear distance ( R = 2.0 au) is obtained with incomplete optimization. Still lower energy is expected for larger values of the parameters v and p. The difference between the calculated and the exact energies is not excessive over the whole range of internuclear separations considered.