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 ⁵⁶⁶ 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 procedure¹⁰⁵⁹ 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 ⁵⁶⁶. It is constructed according to the relation given below, where $c_x$ is a constant typically chosen as $c_x=1.75$.

   $$H_{\mu \upsilon }=c_x{S}_{\mu \upsilon }(H_{\mu \mu }+H_{\upsilon \upsilon })/2.$$

   (4.29)

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