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(May 16, 2021)

The Coulomb Attenuated Schrödinger Equation (CASE)
approximation
^{
24
}
Chem. Phys. Lett.

(1996),
254,
pp. 329.
Link
follows from the KWIK
algorithm
^{
284
}
J. Phys. Chem.

(1996),
100,
pp. 6272.
Link
in which the Coulomb operator is separated into
two pieces using the error function, Eq. (5.12). Whereas in
Section 5.6 this partition of the Coulomb operator was used to
incorporate long-range Hartree-Fock exchange into DFT, within the CASE
approximation it is used to attenuate all occurrences of the Coulomb operator
in Eq. (4.2), by neglecting the long-range portion of the
identity in Eq. (5.12). The parameter $\omega $ in
Eq. (5.12) is used to tune the level of attenuation.
Although the total energies from Coulomb attenuated calculations are
significantly different from non-attenuated energies, it is found that relative
energies, correlation energies and, in particular, wave functions, are not,
provided a reasonable value of $\omega $ is chosen.

By virtue of the exponential decay of the attenuated operator, ERIs can be neglected on a proximity basis yielding a rigorous $\mathcal{O}(N)$ algorithm for single point energies. CASE may also be applied in geometry optimizations and frequency calculations.

OMEGA

Controls the degree of attenuation of the Coulomb operator.

TYPE:

INTEGER

DEFAULT:

No default

OPTIONS:

$n$
Corresponding to $\omega =n/1000$, in units of bohr${}^{-1}$

RECOMMENDATION:

None

INTEGRAL_2E_OPR

Determines the two-electron operator.

TYPE:

INTEGER

DEFAULT:

-2
Coulomb Operator.

OPTIONS:

-1
Apply the CASE approximation.
-2
Coulomb Operator.

RECOMMENDATION:

Use the default unless the CASE operator is desired.