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6.6 Auxiliary Basis (Resolution of the Identity) MP2 Methods

6.6.10 RI-MP2 Method for Complex Basis Functions

(April 13, 2024)

Based on the general implementation of complex basis functions in libqints by White, Head-Gordon, and McCurdy, 1306 White A. F., Head-Gordon M., McCurdy C. W.
 J. Chem. Phys.
 (2015), 142, pp. 054103. Link , 1307 White A. F., McCurdy C. W., Head-Gordon M.
 J. Chem. Phys.
 (2015), 143, pp. 074103. Link (see Section 4.9.5) an RI-MP2 method for complex resonance energies has been implemented. 1256 Vera M. Hernandez, Jagau T.-C.
 J. Chem. Phys.
 (2019), 151, pp. 111101. Link , 1257 Vera M. Hernandez, Jagau T.-C.
 J. Chem. Phys.
 (2020), 152, pp. 174103. Link This method is currently limited to closed-shell cases. The RI approximation can be applied to the complex MP2 energy as well as to the Coulomb and exchange parts of the complex HF energy. The use of the RI approximation is particularly advantageous for electronic resonances since their treatment using complex-scaled methods requires large bases with many diffuse functions. In many cases, RI reduces computation times by a factor of 10 or more. Also, there is no need to include complex-scaled functions in the auxiliary basis set; standard auxiliary bases provide excellent results. 1257 Vera M. Hernandez, Jagau T.-C.
 J. Chem. Phys.
 (2020), 152, pp. 174103. Link

The full basis set is supplied through the keyword COMPLEX_BASIS, while BASIS specifies the unscaled part thereof. This process is described in Section 8.7. In complete analogy, the auxiliary basis set is specified using the keywords COMPLEX_AUX_BASIS and AUX_BASIS. The keyword COMPLEX_RI_JK controls whether the RI approximation is invoked only for the MP2 part or for the HF reference as well.

See Sections 4.9.5 and 7.11.9 for more information about electronic resonances, functionalities offered by Q-Chem in this context, and the corresponding keywords.

Example 6.19  Q-Chem input for an RI-MP2 calculation of the complex resonance energy (= Stark-shifted energy and tunnel ionization rate) of N2 in a static electric field of a strength of 0.1 a.u.

$molecule
   0 1
   N  0.00  0.00  0.55
   N  0.00  0.00 -0.55
$end

$rem
   CORRELATION           RIMP2
   BASIS                 6-31G
   COMPLEX_BASIS         6-31G*
   AUX_BASIS             rimp2-aug-cc-pVDZ
   COMPLEX_AUX_BASIS     rimp2-aug-cc-pVDZ
   COMPLEX_RI_JK         true
   COMPLEX_CCMAN         true
   SCF_GUESS             gwh
   SCF_CONVERGENCE       10
   COMPLEX_EXPONENTS     1
   COMPLEX_THETA         80
   COMPLEX_SCF           1
   COMPLEX_SCF_GUESS     1
   COMPLEX_N_ELECTRONS   0
   COMPLEX_METSCF        1
   GEN_SCFMAN            true
integral_symmetry false
point_group_symmetry False
   THRESH                14
   PURECART              1111
$end

$complex_ccman
   stark_z   1000
   cs_alpha  1000
   cs_theta  0
$end