The Contracted Schrödinger Equation: Some Results

Convergence enhancement in the iterative solution of the second‐order contracted Schrödinger equation

“…Since most of these steps have been published previously [20,23,34,38], this report focuses on the new regulating device introduced.…”

“…When contracting the matrix form of the Schrö-dinger equation into the two-electron space, one obtains [16,23]:…”

“…As already mentioned, in the method proposed by Colmenero and Valdemoro [18 -20], and in those further proposed by Nakatsuji and Yasuda [21,22] and by Mazziotti [24,47], a set of algorithms for approximating the higher-order RDMs in terms of the lower-order RDMs [17][18][19] allows this equation to be solved iteratively until converging to a self-consistent solution. In our approach, the form of the used equation is that given in [23,38], where the spin functions appear explicitly and where the 2-CSE has been coupled with the second-order contracted spin equation [23].…”

“…where ᏺ represents a renormalization operation [20,23]; the matrix 2 ⌬ is the second-order cumulant [9, 10, 24 -26, 28, 59 -63] and the 3 D appearing in it is calculated as in Ref. [23], using the 3 ⌬ approximation given by Valdemoro et al [34].…”

“…First, our algorithms, in contrast to those proposed by Mazziotti [24,31,47], need not be evaluated on a specific basis set. Second, the 4-RDM elements are neither calculated as such nor stored in memory, which diminishes the computational cost of the calculation [23,38].…”