Variational principle,energetic method

Hartree-Fock-Roothaan methods have often been quite successful in the calculation of properties despite the fact that the variational principle upon which they are based ensures only the best total energy. In particular, other energetic properties such as force constants and charge-distribution properties such as electron-density distributions and electric-field gradients are well reproduced. 

Figure 4.9 The initial state selected reaction probability for D+H2(u,i) — DH+H at the total energy E = 0.9 eV, from all energetically accessible initial states. The solid hnes are the present calculation, and the dashed Hnes are from the 5-matrix Kohn variational principle calculations of Groenenboom and Colbert, in which the state-to-state reaction probabiHties are summed for comparison. The larger probabilities are from the u = 0 vibrational state, and the smaller (multiplied by 20) are from the = 1 vibrational state. Excellent agreement is obtained for all initial states, even those with small probabilities which are most challenging for the ABC method.

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