8 Basis Sets and Effective Core Potentials

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

ααe-2iθ (8.1)

where α is the exponent of a particular basis function and θ 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. White:2015 and the EMSL.

COMPLEX_THETA
       Sets the value of θ in degrees for a calculation with complex basis functions.
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       n θ=n/100 (degrees)
RECOMMENDATION:
       Consult Ref. White:2015. Usually calculations at several different values of θ (a “θ-trajectory") should be performed.