Theoretical Study of the Potential Surface for the H4 System by Double-Zeta Configuration-Interaction Calculations

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Abstract
A number of shapes of the H4 system have been studied by ab initio full-CI calculations, using a scale-optimized, eight-orbital (1s, 1s′) basis set. The scale optimization consisted of the simultaneous variation of all the orbital exponents, keeping their relative values constant. Potential-energy curves were obtained for the uniform stretching of the square (1B1g, 3A2g, 1A1g, 1B2g), the rectangle with a 5:4 side ratio (1Ag, 3B1g, 1B1g), the tetrahedron (1E, 3T1, 1T2, 1A1), and the linear equidistant configuration (1Σg+, 1Σu+), while a more limited study was made of the rhombus with a 70° apex angle (1B1g, 3B1g, 1Ag). The order obtained for the energy levels of each shape is as listed above. The lowest energy for each shape, relative to the energy of two H2 molecules, was 43 kcal/mole for the linear case, 109 for the rectangle, 142 for the square, 151 for the rhombus, and 188 kcal/mole for the terahedron. It seems unlikely that the square configuration can be a transition state in a four-center exchange reaction H2 + D2→2HD, for the required energy is considerably above that needed to dissociate one hydrogen molecule and carry out a three-center exchange. Possible transition-state shapes which have not been studied include the isoceles trapezoid (suggested by the low energy of the linear form) and the kite.