4.4.2 Initial Guess Types

Core Hamiltonian

The core Hamiltonian guess simply obtains the guess MO coefficients by diagonalizing the core Hamiltonian matrix in Eq. (4.19). It is also commonly known as the one-electron guess, as it completely ignores interelectronic interactions. Although the guess is exact for one-electron systems, the lack of repulsion effects leads to incorrect shell structure of atoms as well as all electrons crowding onto the heaviest atom in the system; see Ref.  752 Lehtola S.
J. Chem. Theory Comput.
(2019), 15, pp. 1593. Link for a discussion. Due to these effects, the core guess is typically extremely inaccurate and should only be used as a last resort; much better alternatives are provided by the various SAD and SAP guesses.

Superposition of Atomic Densities (SAD)

The SAD guess ⁷⁵⁶ Lenthe J. H. Van et al.
J. Comput. Chem.
(2006), 27, pp. 926. Link is constructed by summing together pretabulated, spherically averaged atomic density matrices. The SAD guess generally yields robust convergence, and its use is particularly important when large basis sets and/or large molecules are employed. There are three issues associated with the SAD guess to be aware of:

1. 1.

   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. It can, however, be generated on-the-fly for general basis sets (BASIS = GEN), as described below, though not for mixed basis sets (BASIS = MIXED).

2. 2.

   The SAD guess is not available for general (read-in) basis sets (pretabulated guesses exist for all internal basis sets); and

3. 3.

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

Purified Superposition of Atomic Densities (SADMO)

The purified SAD guess (called “SADMO” in Ref.  752 Lehtola S.
J. Chem. Theory Comput.
(2019), 15, pp. 1593. Link ), is otherwise the same as the SAD guess except that it removes the issues 1 and 3 above. The SADMO guess obtains guess orbitals and corresponding occupation numbers by diagonalizing the non-idempotent SAD density matrix, after which an idempotent density matrix is recreated by aufbau occupation of the SAD natural orbitals. Since the initial density matrix is created with the SAD guess, the SADMO guess is not available for a general (read-in) basis set, either.

Superposition of Atomic Potentials (SAP)

The SAP guess ⁷⁵² Lehtola S.
J. Chem. Theory Comput.
(2019), 15, pp. 1593. Link is a major improvement on the core guess as it correctly describes atomic shell structure while retaining a simple form. The SAP guess introduces the interelectronic interactions missing from the core guess with a superposition of pretabulated atomic potentials, which have been derived with fully numerical calculations; ⁷⁵³ Lehtola S.
Int. J. Quantum Chem.
(2019), 119, pp. e25945. Link ^{, 754} Lehtola S.
Phys. Rev. A
(2020), 101, pp. 012516. Link the atomic potentials used in Q-Chem are derived from non-relativistic exchange-only LDA calculations employing spherically averaged densities. ⁷⁵⁴ Lehtola S.
Phys. Rev. A
(2020), 101, pp. 012516. Link As suggested in Ref.  752 Lehtola S.
J. Chem. Theory Comput.
(2019), 15, pp. 1593. Link , the atomic potential matrix is evaluated through quadrature on a molecular grid analogous to the one used in DFT calculations; the grid is controlled by the $rem variable GUESS_GRID. Importantly, the SAP guess is noniterative, available for all elements in the periodic table from H to Og, and can be used with both internal and general (read-in) basis sets, thereby offering reasonably accurate initial guesses also in the case when the other options fail to work. Note SAP guess is not available in the old SCF code but only in GEN_SCFMAN.

On-the-fly (Automated) Superposition of Atomic Densities (AUTOSAD)

In contrast to the SAD option that relies on pretabulated density matrices, the AUTOSAD guess provides a means of obtaining a method-specific SAD guess on-the-fly by running separate atomic calculations on all non-equivalent atoms in the system. As a 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. Unlike the SAD option, AUTOSAD can be used for both internally defined and user-defined (general) basis sets, but is currently unavailable for mixed basis. Note that use of AUTOSAD is not necessary when using a single internal basis set with wave function methods, as in this case the AUTOSAD density is simply equivalent to the pretabulated SAD density. The pretabulated SAD guess is based on Hartree-Fock atomic densities whereas AUTOSAD uses the SCF method specified in $rem.

Generalized Wolfsberg-Helmholtz (GWH)

The GWH guess procedure ¹³⁸³ Wolfsberg M., Helmholtz L.
J. Chem. Phys.
(1952), 20, pp. 837. Link 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 even worse than the core Hamiltonian. ⁷⁵² Lehtola S.
J. Chem. Theory Comput.
(2019), 15, pp. 1593. Link It is constructed according to

$$H_{\mu \upsilon }=c_x{S}_{\mu \upsilon }(H_{\mu \mu }+\frac{1}{2}{H}_{\upsilon \upsilon }).$$

(4.29)

where $c_x$ is a constant, typically $c_x=1.75$.

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