Quantum-Mechanical Study of Some Three-Center Two-Electron Systems. I. Energy Calculations

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Abstract
Recent work on H3+ has been carried over to an investigation of a series of pseudomolecular ions of the form ZHZ+2Z−1. This was done in the hope of obtaining some understanding of the three‐center, two‐electron bonds of which the ``bridge'' bond in diborane is one possible example. The two‐electron systems, studied here, may be regarded as an approximate representation of a fragment of a more complex molecule. Therefore, noninteger Z values were used in an attempt to make some allowance for the nuclear shielding caused by the presence of other electrons which were otherwise unaccounted for in the present calculations. The effective nuclear charge Z was allowed to take values of 0.8 (0.2) 2.2 and the optimum bond angle ZHZ was studied as a function of Z. For each Z, a study was also made of the angular dependence of the molecular energy for a fixed value of the bond length Z—H. Within a limited basis set the present treatment is a complete configuration‐interaction calculation. The study gave rise to several interesting features, two of which are the sizeable initial decrease in the bond angle as Z is increased and the occurrence of a double minimum in the molecular energy as a function of the bond angle for Z∼1.8. Therefore, for Z=1.8, the dependence of the molecular energy upon the bond angle ZHZ was also investigated for different values of the bond length. Although Part II contains a natural spin—orbital analysis of the wavefunction for each system, it was felt obligatory, at this stage, to offer a tentative interpretation of the present results. This was performed in terms of the movement of charge density components as a function of the bond angle and Z.

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