4.4 SCF Initial Guess

4.4.4 Basis Set Projection

(May 16, 2021)

Q-Chem also includes a novel basis set projection method developed by Dr Jing Kong of Q-Chem Inc. It permits a calculation in a large basis set to bootstrap itself up via a calculation in a small basis set that is automatically spawned when the user requests this option. When basis set projection is requested (by providing a valid small basis for BASIS2), the program executes the following steps:

  • A simple DFT calculation is performed in the small basis, BASIS2, yielding a converged density matrix in this basis.

  • The large basis set SCF calculation (with different values of EXCHANGE and CORRELATION set by the input) begins by constructing the DFT Fock operator in the large basis but with the density matrix obtained from the small basis set.

  • By diagonalizing this matrix, an accurate initial guess for the density matrix in the large basis is obtained, and the target SCF calculation commences.

Two different methods of projection are available and can be set using the BASISPROJTYPE $rem. The OVPROJECTION option expands the MOs from the BASIS2 calculation in the larger basis, while the FOPPROJECTION option constructs the Fock matrix in the larger basis using the density matrix from the initial, smaller basis set calculation. Basis set projection is a very effective option for general basis sets, where the SAD guess is not available. In detail, this initial guess is controlled by the following $rem variables:

BASIS2
       Sets the small basis set to use in basis set projection.
TYPE:
       STRING
DEFAULT:
       No second basis set default.
OPTIONS:
       Symbol. Use standard basis sets as per Chapter 8. BASIS2_GEN General BASIS2 BASIS2_MIXED Mixed BASIS2
RECOMMENDATION:
       BASIS2 should be smaller than BASIS. There is little advantage to using a basis larger than a minimal basis when BASIS2 is used for initial guess purposes. Larger, standardized BASIS2 options are available for dual-basis calculations (see Section 4.7).

BASISPROJTYPE
       Determines which method to use when projecting the density matrix of BASIS2
TYPE:
       STRING
DEFAULT:
       FOPPROJECTION (when DUAL_BASIS_ENERGY=false) OVPROJECTION (when DUAL_BASIS_ENERGY=true)
OPTIONS:
       FOPPROJECTION Construct the Fock matrix in the second basis OVPROJECTION Projects MOs from BASIS2 to BASIS.
RECOMMENDATION:
       None

Note:  BASIS2 sometimes affects post-Hartree-Fock calculations. It is recommended to split such jobs into two subsequent one, such that in the first job a desired Hartree-Fock solution is found using BASIS2, and in the second job, which performs a post-HF calculation, SCF_GUESS = READ is invoked.

Example 4.7  Input where basis set projection is used to generate a good initial guess for a calculation employing a general basis set, for which the default initial guess is not available.

$molecule
   0  1
   O
   H  1  r
   H  1  r  2  a

   r    0.9
   a  104.0
$end

$rem
   METHOD        mp2
   BASIS         general
   BASIS2        sto-3g
$end

$basis
   O   0
   S   3   1.000000
           3.22037000E+02   5.92394000E-02
           4.84308000E+01   3.51500000E-01
           1.04206000E+01   7.07658000E-01
   SP  2   1.000000
           7.40294000E+00  -4.04453000E-01   2.44586000E-01
           1.57620000E+00   1.22156000E+00   8.53955000E-01
   SP  1   1.000000
           3.73684000E-01   1.00000000E+00   1.00000000E+00
   SP  1   1.000000
           8.45000000E-02   1.00000000E+00   1.00000000E+00
****
   H   0
   S   2   1.000000
           5.44717800E+00   1.56285000E-01
           8.24547000E-01   9.04691000E-01
   S   1   1.000000
           1.83192000E-01   1.00000000E+00
****
$end

View output