4.4 SCF Initial Guess

4.4.1 Initial Guess Types

(June 30, 2021)
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. 644 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 648 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. 644), 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 644 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; 645 Lehtola S.
Int. J. Quantum Chem.
(2019), 119, pp. e25945.
Link
, 646 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. 646 Lehtola S.
Phys. Rev. A
(2020), 101, pp. 012516.
Link
As suggested in Ref. 644, 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. At variance to the SAD option, AUTOSAD can be used for both internally defined and user-customized general basis sets. However, AUTOSAD 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.

Generalized Wolfsberg-Helmholtz (GWH)

The GWH guess procedure 1195 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. 644 Lehtola S.
J. Chem. Theory Comput.
(2019), 15, pp. 1593.
Link
It is constructed according to

Hμυ=cxSμυ(Hμμ+12Hυυ). (4.29)

where cx is a constant, typically chosen as cx=1.75.

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

SCF_GUESS
       Specifies the initial guess procedure to use for the SCF.
TYPE:
       STRING
DEFAULT:
       SAD Superposition of atomic densities 648 Lenthe J. H. Van et al.
J. Comput. Chem.
(2006), 27, pp. 926.
Link
(default for internal basis sets)
AUTOSAD For internally defined or user-customized general basis sets GWH For ROHF jobs with GEN_SCFMAN = FALSE which require a set of orbitals FRAGMO For fragment jobs such as ALMO-based calculations CORE Currently used as default for Mixed basis

OPTIONS:
       CORE Diagonalize core Hamiltonian SAD Superposition of atomic density 648 Lenthe J. H. Van et al.
J. Comput. Chem.
(2006), 27, pp. 926.
Link
SAP Superposition of atomic potentials 644 Lehtola S.
J. Chem. Theory Comput.
(2019), 15, pp. 1593.
Link
(only available with GEN_SCFMAN = TRUE)
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 (see Section 12.3)

RECOMMENDATION:
       SAD, AUTOSAD, or SADMO guess for standard basis sets. For either standard or user-customized general basis sets, AUTOSAD is recommended and used as default. If these options fail, use the SAP guess; try the GWH or core Hamiltonian guess only as a last resort. For mixed basis sets, only the AUTOSAD, SAP, GWH, and core Hamiltonian guesses are currently available. 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.

SCF_GUESS_ALWAYS
       Switch to force the regeneration of a new initial guess for each series of SCF iterations (for use in geometry optimization).
TYPE:
       LOGICAL
DEFAULT:
       False
OPTIONS:
       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.
RECOMMENDATION:
       Use the default unless SCF convergence issues arise

GUESS_GRID
       Specifies the type of grid to use for SAP guess generation. The options are the same as those of the $rem variable XC_GRID.
TYPE:
       INTEGER
DEFAULT:
       1
OPTIONS:
       0 Use SG-0 for H, C, N, and O; SG-1 for all other atoms. n Use SG-n for all atoms, n=1,2, or 3 XY A string of two six-digit integers X and Y, where X is the number of radial points and Y is the number of angular points where possible numbers of Lebedev angular points, which must be an allowed value from Table 5.2 in Section 5.5. -XY Similar format for Gauss-Legendre grids, with the six-digit integer X corresponding to the number of radial points and the six-digit integer Y providing the number of Gauss-Legendre angular points, Y=2N2.
RECOMMENDATION:
       Larger grids may be required if the SAP guess is poor.