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(May 16, 2021)

Complex basis function (CBF) methods for describing meta-stable electronic states (see Section 4.9.5) require the user to specify a basis set in which the most diffuse functions have a complex-scaled exponent. The real-valued basis functions are specified using the standard *$rem* keyword BASIS. The complex basis set is specified using the *$rem* keyword COMPLEX_BASIS, and it should be a superset of the real basis.
If the basis is specified as general or mixed, the user-defined basis should be entered in an an additional *$zbasis* input section in the same format as the *$basis* section.

Q-Chem will automatically determine the additional basis functions in the complex basis and scales the exponents of those functions. For example, if BASIS is specified as “cc-pVTZ” and COMPLEX_BASIS is specified as “aug-cc-pVTZ”, the augmenting functions will have complex-scaled exponents. The scaling is done according to

$$\alpha \to \alpha {e}^{-2i\theta}$$ | (8.1) |

where $\alpha $ is the exponent of a particular basis function and $\theta $ is specified by the *$rem* keyword COMPLEX_THETA.

COMPLEX_BASIS

Defines the complex basis.

TYPE:

STRING

DEFAULT:

No default complex basis set

OPTIONS:

Symbol
Use a standard basis set
ZBASIS_GENERAL, ZBASIS_GEN
User-defined. As for BASIS
ZBASIS_MIXED
User-defined mixed basis

RECOMMENDATION:

Consult Ref.
^{
1170
}
J. Chem. Phys.

(2015),
142,
pp. 054103.
Link
and the Basis Set Exchange.

COMPLEX_THETA

Sets the value of $\theta $ in degrees for a calculation with complex basis functions.

TYPE:

INTEGER

DEFAULT:

0

OPTIONS:

$n$
$\theta =n/10$ (degrees)

RECOMMENDATION:

Consult Ref.
^{
1170
}
J. Chem. Phys.

(2015),
142,
pp. 054103.
Link
. Usually calculations at several different values of $\theta $ (a “$\theta $-trajectory”) should be performed.