The Coulomb Attenuated Schrödinger Equation (CASE)
approximation^{25} follows from the KWIK
algorithm^{237} 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.