# 6.6.8 RI-MP2 Method for Complex Basis Functions

Based on the general implementation of complex basis functions in libqints by White, Head-Gordon, and McCurdy,1034, 1035 (see Section 4.9.5) an RI-MP2 method for complex resonance energies has been implemented.992, 993 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.993

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

Example 6.16  Q-Chem input for an RI-MP2 calculation of the complex resonance energy (= Stark-shifted energy and tunnel ionization rate) of N${}_{2}$ 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

$rem jobtype sp correlation RIMP2 basis 6-31G complex_basis 6-31G* aux_basis rimp2-aug-cc-pVDZ complex_aux_basis rimp2-aug-cc-pVDZ complex_ri_jk true complex_ccman true scf_guess gwh scf_convergence 10 complex_exponents 1 complex_theta 80 complex_scf 1 complex_scf_guess 1 complex_n_electrons 0 complex_metscf 1 gen_scfman true symmetry false sym_ignore true thresh 14 purecart 111111$end

$complex_ccman stark_z 1000 cs_alpha 1000 cs_theta 0$end