4.4 SCF Initial Guess

4.4.2 Simple Initial Guesses

There are four simple initial guesses available in Q-Chem. While they are all simple, they are by no means equal in quality, as we discuss below.

  1. 1.

    Superposition of Atomic Densities (SAD): The SAD guess is almost trivially constructed by summing together atomic densities that have been spherically averaged to yield a trial density matrix. The SAD guess is far superior to the other two options below, particularly when large basis sets and/or large molecules are employed. There are three issues associated with the SAD guess to be aware of:

    1. (a)

      No molecular orbitals are obtained, which means that SCF algorithms requiring orbitals (the direct minimization methods discussed in Section 4.5) cannot directly use the SAD guess, and,

    2. (b)

      The SAD guess is not available for general (read-in) basis sets. All internal basis sets support the SAD guess.

    3. (c)

      The SAD guess is not idempotent and thus requires at least two SCF iterations to ensure proper SCF convergence (idempotency of the density).

  2. 2.

    On-the-fly (Automated) Superposition of Atomic Densities (AUTOSAD): The SAD guess is constructed from sphericalized Hartree-Fock atomic densities that are stored on disk. While normally a very good initial guess, SAD can lead to slow convergence, or even convergence failures if the electronic structure of the system is sufficiently different from a superposition of Hartree-Fock atomic densities. The AUTOSAD guess provides a means of obtaining a method-specific SAD guess on-the-fly. Like the SAD guess, the AUTOSAD density matrix is not idempotent and the guess will not produce molecular orbitals, so direct minimization methods cannot be directly used. However, AUTOSAD can be used with mixed basis sets (unlike the SAD guess), so long as the basis sets are internally defined. In general, it is not advised to use AUTOSAD if using a single, internal basis set for wavefunction methods, as the AUTOSAD density is equivalent to the SAD density at the level of Hartree-Fock.

  3. 3.

    Purified Superposition of Atomic Densities (SADMO): This guess, described in 553 as SADNO, is similar to the SAD guess, with two critical differences, namely, the removal of issues 1a and 1c above. The functional difference to the SAD guess is that the density matrix obtained from the superposition is diagonalized to obtain natural molecular orbitals, after which an idempotent density matrix is created by aufbau occupation of the natural orbitals. Since the initial density matrix is created with the SAD guess, the SADMO guess is not available either for a general (read-in) basis set.

  4. 4.

    Core Hamiltonian: The core Hamiltonian guess simply obtains the guess MO coefficients by diagonalizing the core Hamiltonian matrix in Eq. (4.19). This approach works best with small basis sets, and degrades as both the molecule size and the basis set size are increased.

  5. 5.

    Generalized Wolfsberg-Helmholtz (GWH): The GWH guess procedure999 uses a combination of the overlap matrix elements in Eq. (4.12), and the diagonal elements of the Core Hamiltonian matrix in Eq. (4.19). This initial guess is usually worse than the core Hamiltonian 553. It is constructed according to the relation given below, where cx is a constant typically chosen as cx=1.75.

    Hμυ=cxSμυ(Hμμ+Hυυ)/2. (4.29)

The selection of these choices (or whether to read in the orbitals) is controlled by the following $rem variables:

       Specifies the initial guess procedure to use for the SCF.
       SAD Superposition of atomic densities (available only with standard basis sets) AUTOSAD For internally defined general basis sets GWH For ROHF where a set of orbitals are required. FRAGMO For a fragment MO calculation
       CORE Diagonalize core Hamiltonian SAD Superposition of atomic density AUTOSAD On-the-fly superposition of atomic densities SADMO Purified superposition of atomic densities (available only with standard basis sets) GWH Apply generalized Wolfsberg-Helmholtz approximation READ Read previous MOs from disk FRAGMO Superimposing converged fragment MOs
       SAD, AUTOSAD, or SADMO guess for standard basis sets. For general basis sets, it is best to use the BASIS2 $rem. For mixed (standard) basis sets, use AUTOSAD. Alternatively, try the GWH or core Hamiltonian guess. For ROHF it can be useful to READ guesses from an SCF calculation on the corresponding cation or anion. Note that because the density is made spherical, this may favor an undesired state for atomic systems, especially transition metals. Use FRAGMO in a fragment MO calculation.

       Switch to force the regeneration of a new initial guess for each series of SCF iterations (for use in geometry optimization).
       False Do not generate a new guess for each series of SCF iterations in an optimization; use MOs from the previous SCF calculation for the guess, if available. True Generate a new guess for each series of SCF iterations in a geometry optimization.
       Use the default unless SCF convergence issues arise