# 4.4 SCF Initial Guess

(June 30, 2021)

The Roothaan-Hall and Pople-Nesbet equations of SCF theory are non-linear in the molecular orbital coefficients. Like many mathematical problems involving non-linear equations, prior to the application of a technique to search for a numerical solution, an initial guess for the solution must be generated. If the guess is poor, the iterative procedure applied to determine the numerical solutions may converge very slowly, requiring a large number of iterations, or at worst, the procedure may diverge.

Thus, in an ab initio SCF procedure, the quality of the initial guess is of utmost importance for (at least) two main reasons:

• To ensure that the SCF converges to an appropriate ground state. Often SCF calculations can converge to different local minima in wave function space, depending upon which part of “LCAO space” in which the initial guess lands.

• When considering jobs with many basis functions requiring the recalculation of ERIs at each iteration, using a good initial guess that is close to the final solution can reduce the total job time significantly by decreasing the number of SCF iterations.

For these reasons, sooner or later most users will find it helpful to have some understanding of the different options available for customizing the initial guess. Q-Chem currently offers six options for the initial guess:

• Superposition of Atomic Densities (SAD)

• Superposition of Atomic Potentials (SAP, only available with GEN_SCFMAN = TRUE)

• On-the-fly (automated) Superposition of Atomic Densities (AUTOSAD)