12.7 The Second-Generation ALMO-EDA Method

12.7.4 Job Control for EDA2

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
      (default: TRUE).

    • 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 POL:

    • CHILD_MP_ORDERS: as introduced in Section 12.7.2 (default: 232 (DQ)).

    • SCFMI_FREEZE_SS: as introduced in Section 12.7.1 (default: 0).

  • 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
      (default: FALSE).

    • 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.

EDA2
       Switch on EDA2 and specify the option set number.
TYPE:
       INTEGER
DEFAULT:
       2
OPTIONS:
       0 Do not run through EDA2. 1 Frozen energy decomposition + nDQ-FERF polarization (the standard EDA2 option) 2 Frozen energy decomposition + (AO-block-based) ALMO polarization (old scheme with the addition of frozen decomposition) 3 Frozen energy decomposition + oDQ-FERF polarization (NOT commonly used) 4 Frozen wave function relaxation + Frozen energy decomposition + nDQ-FERF polarization (NOT commonly used) 5 Frozen energy decomposition + polMO polarization (NOT commonly used). 10 No preset. Completely controlled by user’s $rem input (for developers only)
RECOMMENDATION:
       Turn on EDA2 for Q-Chem’s ALMO-EDA jobs unless CTA with the old scheme is desired. Option 1 is recommended in general, especially when substantially large basis sets are employed. The original ALMO scheme (option 2) can be used when the employed basis set is of small or medium size (arguably no larger than augmented triple-ζ). The other options are rarely used for routine applications.

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 >0 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.

EDA_ALIGN_FRGM_SPIN
       Turn on the fragment spin alignment procedure
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 Do not performed the spin alignment procedure (turned on by default in unrestricted cases) 1 Perform fragment spin alignment; use GDM for the polarization step preceding the MOM calculations 2 Perform fragment spin alignment; use GDM and perform stability analysis for the polarization step
RECOMMENDATION:
       Use 1 or 2 when the radical is of highly symmetric structure

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.

Example 12.14  Energy decomposition analysis for the ammonia-borane complex. The FERF-nDQ model is used for the POL term (as very large basis set is employed here), and decomposition of the frozen interaction energy is performed (Hartree-Fock is employed as the DFXC functional by default).

$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

Example 12.15  Energy decomposition analysis of the water dimer with a low-cost model chemistry. The original ALMO model is used for the evaluation of polarization energy, and revPBE is chosen as the DFXC functional. Counterpoise correction for the BSSE is applied.

$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

Example 12.16  Unrestricted EDA calculation for the H2OCl complex. The fragment spin alignment procedure is performed to ensure the uniqueness of the frozen wavefunction (EDA_ALIGN_FRGM_SPIN = 2).

$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