8.7 Complex Basis Sets 8.7 Complex Basis Sets 8.8 Auxiliary Basis Sets for RI (Density Fitting)

8.7.1 Overview

(September 1, 2024)

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. An alternative way to specify the scaled functions is the scaling variable in the $complex_ccman section. If a scaling independent of the BASIS is desired, this variable accepts a comma-separated list of the indices of the shells to be scaled. This requires the COMPLEX_CCMAN variable to be set to 1 so that the scaling string is recognized. The indices are referring to the order in which they appear in the basis set file or respectively, in the $zbasis section. Furthermore, in the case of multiple centers, basis functions on different centers are enumerated separately, in the order as the centers are listed in the $molecule section, which allows different scaling of basis functions even when centered at atoms of the same type. As an example, in a calculation with two atoms which each possess 10 shells, the shells of the first atom would be given the indices 1–10 and the shells of the second atom 11–20. The following $complex_ccman section is an example for this, in which the scaling of shells 5, 6, 15 and 16 is requested.

$rem
...
complex_ccman 1
...
$end

$complex_ccman
   CS_THETA  0
   CS_ALPHA  1000
   scaling 5,6,15,16
$end

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

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. ¹³⁵⁴ White A. F., Head-Gordon M., McCurdy C. W.
J. Chem. Phys.
(2015), 142, pp. 054103. Link and the Basis Set Exchange.

COMPLEX_THETA

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. ¹³⁵⁴ White A. F., Head-Gordon M., McCurdy C. W.
J. Chem. Phys.
(2015), 142, pp. 054103. Link . Usually calculations at several different values of $\theta$ (a “ $\theta$ -trajectory”) should be performed.

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8.7.1 Overview