Applications of multireference perturbation theory to potential energy surfaces by optimal partitioning of H: Intruder states avoidance and convergence enhancement

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Abstract
The minimum basis set hydrogen rectangular system (HRS), consisting of four hydrogen atoms arranged in a rectangle, is examined using a variety of partitionings of the Hamiltonian H for high order single and double reference perturbation computations. The potential energy surface is mapped out over a range of geometries in which the length L of one side of the rectangle is varied. Several criteria are derived governing the necessary conditions for perturbative convergence of two‐state systems, and these criteria are useful in explaining the behavior of the HRS for the range of geometries and partitioning methods investigated. The divergence caused by intruder states, observed by Zarrabian and Paldus [Int. J Quantum Chem. 38, 761 (1990)] for the nondegenerate, double reference space perturbation expansions at L=3.0 a.u. with traditional partitioning methods, is shown to correspond to avoided crossings with negative real values of the perturbation parameter—backdoor intruder states. These intruder state induced divergences result from too small zeroth order energy differences between the high lying reference space state and an orthogonal space intruder state whose identity depends on the partitioning method. Forcing the valence orbitals to be degenerate enlarges these zeroth order energy differences and, thus, yields a convergent perturbative expansion for L=3.0 a.u. The convergent or divergent behavior of all the partitioning method computations and the locations of their avoided crossings are accurately predicted by using two‐state models composed of the high lying reference space state and the intruder state. A partitioning method is introduced in which the zeroth order state energies are selected to optimize the convergence in low orders of the perturbation expansion. This optimization method yields perturbative convergence which is both rapid and free of intruder state for geometries between L=2.0 and 3.0 a.u. The divergent behavior for various partitioning methods at L=5.0 a.u., also observed by Zarrabian and Paldus, is caused by one or more orthogonal space states and the high lying reference space state that are strongly coupled and have close expectation values of H. The two‐state model illustrates why no partitioning choice with a double reference space can yield a satisfactory rate of perturbative convergence for L=5.0. Therefore, the entire potential energy surface is treated using more than one reference space: a double reference space for L≤3.0 a.u. and a single reference space for L≳3.0 a.u. The entire potential surface of interest, which is generated with the optimized partitioning method and the two different reference spaces, is very accurate by third order, with eigenvalues for all geometries considered differing from the FCI by no more than 1 kcal/mol.

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