# 8.7 Complex Basis Sets

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

 $\alpha\rightarrow\alpha e^{-2i\theta}$ (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. 1034 and the EMSL.

COMPLEX_THETA
Sets the value of $\theta$ in degrees for a calculation with complex basis functions.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
$n$ $\theta=n/100$ (degrees)
RECOMMENDATION:
Consult Ref. 1034. Usually calculations at several different values of $\theta$ (a “$\theta$-trajectory") should be performed.