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.
The SAD guess
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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:
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).
The SAD guess is not available for general (read-in) basis sets (pretabulated guesses exist for all internal basis sets); and
The SAD guess is not idempotent and thus requires at least two SCF iterations to ensure proper SCF convergence (idempotency of the density).
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.
The SAP guess
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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;
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the atomic
potentials used in Q-Chem are derived from non-relativistic
exchange-only LDA calculations employing spherically averaged
densities.
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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.
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.
The GWH guess
procedure
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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.
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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 chosen as ${c}_{x}=1.75$.
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
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(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
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SAP
Superposition of atomic potentials
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(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, $Y=2{N}^{2}$.
RECOMMENDATION:
Larger grids may be required if the SAP guess is poor.