The use of the FERF model for the evaluation of polarization energy and the further decomposition of the frozen term define the second generation of the ALMO-EDA method. Meanwhile, under the same code structure, the original AO-block based ALMO model and other related methods (such as the constrained relaxation of the frozen wave functionHorn:2016a which renders the frozen energy variationally computed, and the polMO modelAzar:2013 that arguably gives a lower limit to the polarization contribution) are also available. This entire set of methods implemented in Q-Chem based on GEN_SCFMAN (see Section 4.3) is referred to as “EDA2". In Q-Chem 5.2 and after, “EDA2" is used as the default ALMO-EDA driver when “JOBTYPE = EDA" is requested.
The job control for EDA2 is largely simplified by a series of preset options provided by the developers. The option number is set through the EDA2 $rem variable (introduced below). Besides that, for the sake of flexibility, users are allowed to overwrite the values of part of the preset $rem variables:
Related to the isolated fragment calculations:
EDA_CHILD_SUPER_BASIS: use the super-system basis for fragment calculations (default: FALSE).
FRAGMO_GUESS_MODE: as introduced in Section 12.3 (default: 0).
Related to the decomposition of the FRZ term:
FRZ_ORTHO_DECOMP: it can be turned off by setting its value to -1 in the $rem section
FRZ_ORTHO_DECOMP_CONV: as introduced in Section 12.7.3 (default: 6).
EDA_CLS_DISP: as introduced in Section 12.7.3 (default: FALSE).
DISP_FREE_X: as introduced in Section 12.7.3 (default: HF).
DISP_FREE_C: as introduced in Section 12.7.3 (default: NONE).
Related to the evaluation of CT and BSSE:
EDA_NO_CT: skip the evaluation of the CT term in the EDA procedure
(default: FALSE (automatically turned on when SCFMI_FREEZE_SS = TRUE)).
EDA_BSSE: use counterpoise-corrected monomer calculations to evaluate the BSSE
EDA_PCT_A: turn on perturbative charge transfer analysis (Roothaan step based).
EDA_COVP: perform COVP analysis for charge transfer (see Section 12.5).
EDA_PRINT_COVP: dump COVPs to the MO coefficient file (see Section 12.5). Note: EDA2 can automatically generate the cubes for the dominant complementary occupied-virtual orbitals for each pair of donor and acceptor fragments when EDA_PRINT_COVP is greater than 1.
Note that for Q-Chem 5.2 and after, if “JOBTYPE = EDA" is requested while the EDA2 $rem variable is not specified by the user, it automatically sets EDA2 = 2 and EDA_PCT_A = TRUE as the default option.
In cases where the radical is a single atom (e.g. Cl) or of a highly symmetric geometry (e.g. OH), there can be multiple degenerate electronic configurations with the unpaired electron residing in different orbitals, resulting in arbitrariness in the definition of the frozen state. For such systems, it is desirable to obtain the orientation of fragment spin that leads to the lowest-energy frozen state. This can be achieved by employing a “polarize-then-depolarize" (PtD) approach Mao:2020, using interfragment polarization to resolve the degeneracy of radical’s electronic states: one first converges the polarization (SCF-MI) calculation for the full system, and then recalculates the SCF solutions for each isolated fragment using their corresponding blocks in the ALMO coefficient matrix as the initial guess. To ensure that the “depolarized” fragments are of the same electronic configuration as in the fully polarized wavefunction, the initial maximum overlap method (IMOM) Barca:2018 is utilized in these fragment calculations. The fragment orbitals obtained therefrom then uniquely determine the frozen wavefunction.
In Q-Chem 5.2 and after, the procedure described above is performed for unrestricted ALMO-EDA calculations by default. It can also be manually requested by setting EDA_ALIGN_FRGM_SPIN to values. Note that this setting further ensures that one obtains a stable SCF-MI solution in the initial polarization step (see below), which is crucial for the success of this approach. Occasionally, one may find that the frozen state constructed from “spin-aligned” fragments is of a higher energy than the initial one. This indicates that the fragment spin alignment procedure is not functioning well, and in such cases we recommend the user to run EDA2 calculation without this procedure by setting FRZ_RELAX = -1.
Another feature that can be useful for systems involving open-shell species is the capability of performing stability analysis on user-specified fragments, since it is important to ensure the stability of each fragment’s SCF solution. This can be done through the $frgm_stability input section:
$frgm_stability [frgm_idx1] [frgm_idx2] ... $end
where one simply puts the indexes of fragments that require stability analysis.
$molecule 0 1 -- 0 1 N 0.000000 0.000000 -0.727325 H 0.947371 0.000000 -1.091577 H -0.473685 -0.820448 -1.091577 H -0.473685 0.820448 -1.091577 -- 0 1 B 0.000000 0.000000 0.930725 H -1.165774 0.000000 1.243063 H 0.582887 -1.009590 1.243063 H 0.582887 1.009590 1.243063 $end $rem JOBTYPE eda EDA2 1 METHOD wB97M-V BASIS def2-TZVPPD SYMMETRY false MEM_TOTAL 4000 MEM_STATIC 1000 THRESH 14 SCF_CONVERGENCE 8 XC_GRID 000099000590 NL_GRID 1 FD_MAT_VEC_PROD false $end
$molecule 0 1 -- 0 1 H1 O1 H1 0.95641 H2 O1 0.96500 H1 104.77306 -- 0 1 O2 H2 dist O1 171.85474 H1 180.000 H3 O2 0.95822 H2 111.79807 O1 -58.587 H4 O2 0.95822 H2 111.79807 O1 58.587 dist = 2.0 $end $rem JOBTYPE eda EDA2 2 METHOD b97m-v BASIS def2-svpd SCF_CONVERGENCE 8 THRESH 14 SYMMETRY false DISP_FREE_X revPBE DISP_FREE_C PBE EDA_BSSE true $end
$molecule 0 2 -- 0 2 Cl 0.00127 0.00000 -0.88139 -- 0 1 O -0.06700 0.00000 1.72173 H 0.50943 -0.76061 1.83598 H 0.50943 0.76061 1.83598 $end $rem jobtype eda eda2 2 method m06-2x basis 6-31+g(d) unrestricted true scf_algorithm diis scf_convergence 8 max_scf_cycles 200 thresh 14 symmetry false sym_ignore true eda_bsse true eda_align_frgm_spin 2 $end