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12.6 The Second-Generation ALMO-EDA Method

12.6.9 Visualization Tools Associated with ALMO-EDA

(April 13, 2024)

The following visualization tools are enabled in EDA2:

  • Automated generation of complementary occupied-virtual pairs (COVP)

  • Electron density difference (EDD) maps between intermediate states (FRZPOL, POLFull)

  • Plots for Natural Orbitals for Chemical Valence (NOCV)

  • Plots of frozen and polarized ALMOs

As introduced in Sec. 12.5.4, the COVPs can help elucidate the details of a charge-transfer process by showing the chemically most relevant donor-acceptor orbitals. In its implementation in EDA2, we enabled an automated selection of the most significant occupied-virtual pairs (based on a threshold on singular values). The MO cube files of these selected COVPs are then generated, and thus there is no need to specify which orbitals to plot. This new feature can be turned on by setting EDA_COVP_PRINT = AUTOMATED. Also, both the old and new formats of the $plots section are supported for automated COVP cube generation in EDA2. The old format requires MAKE_CUBE_FILES = TRUE and the new format requires PLOTS = TRUE. The plotted COVPs are indexed as covp_a.N.cube and covp_b.N.cube and the energetic significance of each of them can be looked up from the output file.

EDA2 also enabled electron density difference (EDD) plots to show the redistribution of electron density upon polarization (Δ𝐏pol=𝐏pol-𝐏frz) and charge transfer (Δ𝐏ct=𝐏full-𝐏pol). For unrestricted ALMO-EDA calculations, the spin density at FRZ, POL, and fully relaxed states are plotted together. Another related quantity that can be visualized is the so-called natural orbitals for chemical valence (NOCV), 856 Mitoraj M. P., Michalak A., Ziegler T.
J. Chem. Theory Comput.
(2008), 5, pp. 962.
Link
which are defined as the eigenvectors of Δ𝐏=𝐏full-𝐏frz. The NOCVs appear in pairs ψk and ψ-k, whose associated eigenvalues are nk and -nk, respectively. The energy lowering associated with each pair of NOCVs can be calculated using the extended transition state (ETS) approach (see Ref.  856 Mitoraj M. P., Michalak A., Ziegler T.
J. Chem. Theory Comput.
(2008), 5, pp. 962.
Link
for details). The NOCVs are useful tools for illustrating the underlying orbital interactions, including both polarization and charge transfer, in chemical bonding.

In EDA2, the EDD maps are plotted when EDA_PLOT_DIFF_DEN = TRUE. The calculation of NOCVs are performed when EDA_NOCV >0. The most significant NOCVs are automatically selected based on a threshold on the eigenvalues {nk}. When EDA_NOCV = 1, Q-Chem will only plot the contribution from each significant NOCV pair (ψ-k, ψk) to the density deformation (Δρk):

Δρk(𝐫)=-nk|ψ-k(𝐫)|2+nk|ψk(𝐫)|2 (12.21)

When EDA_NOCV = 2, Q-Chem will plot not only the NOCV pair contributions to density deformation but also the NOCVs themselves. Note that the new format of the $plots section is required for these visualizations (see Sec. 10.5.4.1 for details).

Finally, Q-Chem 5.2.2 enables the visualization of frozen and polarized ALMOs, which is controlled by $rem variables PLOT_ALMO_FRZ and PLOT_ALMO_POL. The user needs to specify which orbitals to plot for each fragment through the $almo_print section:

$almo_print
   frgm_idx1   orb1  orb2 ... (spin)
   frgm_idx2   orb1  orb2 ... (spin)
   . . .
$end

One can use the format “orb1:orb2” to specify a range of orbitals to plot for each fragment. For unrestricted cases, at the end of each line one can write “a” or “b” to specify whether alpha or beta orbitals are plotted (alpha orbitals will be plotted by default if there is no specification). As above, a $plots section with its new format is required for the visualization of ALMOs.

In the following table, we summarize the names of the cube files generated by each type of plots. Note that for the EDD plots, “0” refers to the EDD between POL and FRZ states, while “1” refers to the EDD between full SCF and POL states; for the spin density plots, “0”, ”1”, and ”2” correspond to the FRZ, POL, and fully relaxed states, respectively.

Table 12.1: Cube file names generated by visualization tools in EDA2
Plot type Orbital type Cube file name
COVP R covp_a.N.cube
U covp_a.N.cube, covp_b.N.cube
EDD R dens.0.cube, dens.1.cube
U dens_alpha.0.cube, dens_alpha.1.cube
dens_beta.0.cube, dens_beta.1.cube
dens_spin.0.cube, dens_spin.1.cube, dens_spin.2.cube
NOCV R nocv_diffden_a.N.cube, nocv_a.N.cube
U nocv_diffden_a.N.cube, nocv_a.N.cube
nocv_diffden_b.N.cube, nocv_b.N.cube
ALMO R almo_frz_a.N.cube, almo_pol_a.N.cube
U almo_frz_a.N.cube, almo_frz_b.N.cube
almo_pol_a.N.cube, almo_pol_b.N.cube

EDA_PLOT_DIFF_DEN

EDA_PLOT_DIFF_DEN
       Plot changes in electron density due to POL and CT
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       FALSE Do not make EDD plots TRUE Make EDD plots
RECOMMENDATION:
       None

EDA_NOCV

EDA_NOCV
       Perform the NOCV analysis and plot the significant NOCVs
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 Do not perform NOCV analysis 1 Plot NOCV pair contributions to density deformation 2 Plot both NOCV pair contribution to density deformation and NOCV orbitals
RECOMMENDATION:
       None

PLOT_ALMO_FRZ

PLOT_ALMO_FRZ
       Plot ALMOs at the frozen stage of EDA2 calculations
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       FALSE Do not plot frozen ALMOs TRUE Plot frozen ALMOs
RECOMMENDATION:
       None

PLOT_ALMO_POL

PLOT_ALMO_POL
       Plot ALMOs after the polarization calculation
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       FALSE Do not plot polarized ALMOs TRUE Plot polarized ALMOs
RECOMMENDATION:
       None

Example 12.24  Performing perturbative CTA through EDA2 (using the default settings). The automatic COVP generation is enabled by setting EDA_PRINT_COVP = AUTOMATED, which plots the most significant COVPs automatically. The new format of the $plots section is used by setting PLOTS = TRUE, and there is no need to specify how many orbitals to plot.

$molecule
0 1
--
0 1
O          -1.521720    0.129941    0.000000
H          -1.924536   -0.737533    0.000000
H          -0.571766   -0.039961    0.000000
--
0 1
O           1.362840   -0.099704    0.000000
H           1.727645    0.357101   -0.759281
H           1.727645    0.357101    0.759281
$end

$rem
   JOBTYPE               EDA
   METHOD                B3LYP
   BASIS                 6-31+G(d)
integral_symmetry FALSE
point_group_symmetry True
   MEM_TOTAL             8000
   MEM_STATIC            2000
   BASIS_LIN_DEP_THRESH  6
   THRESH                14
   SCF_CONVERGENCE       8
   MAXSCF                200
   EDA_COVP              TRUE
   EDA_PRINT_COVP        AUTOMATED !auto-generation of covp cube files
   MAKE_CUBE_FILES       TRUE
   PLOTS                 TRUE  !new format for the plot section
$end

$plots
grid_points 100 100 100
$end

Example 12.25  Electron density difference (EDD) plots and NOCV analysis for the NH3BH3 complex. Both the significant NOCV pairs and each pair’s contribution to density deformation due to orbital interaction (polarization and charge transfer) are plotted.

$molecule
0 1
--
0 1
N         0.0000001517    0.7279666667    0.0000000000
H         0.9488005016    1.0881357449    0.0000000000
H        -0.4743994984    1.0881371276   -0.8216800000
H        -0.4743994984    1.0881371276    0.8216800000
--
0 1
B        -0.0000014567   -0.9275533333    0.0000000000
H        -1.1719117610   -1.2408021948    0.0000000000
H         0.5859582390   -1.2408039026   -1.0149100000
H         0.5859582390   -1.2408039026    1.0149100000
$end

$rem
   JOBTYPE                 eda
   EDA2                    2   !ALMO-POL
   METHOD                  b3lyp
   BASIS                   6-31g(d)
   SCF_ALGORITHM           diis
   XC_GRID                 1
   SCF_CONVERGENCE         8
   MAX_SCF_CYCLES          200
   THRESH                  14
integral_symmetry false
point_group_symmetry False
   EDA_PLOT_DIFF_DEN TRUE  !plot EDD maps
   EDA_NOCV  2             !NOCV analysis
$end

$plots
grid_points 100 100 100
$end

Example 12.26  Plot HOMO and LUMO for each fragment (frozen and polarized ALMOs) in an EDA2 calculation

$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
   METHOD           b3lyp
   BASIS            6-31g
   EDA2             2   !ALMO-POL
   UNRESTRICTED     false
   SCF_ALGORITHM    diis
   SCF_CONVERGENCE  8
   MAX_SCF_CYCLES   200
   THRESH           14
integral_symmetry false
point_group_symmetry False
   PLOT_ALMO_FRZ    true
   PLOT_ALMO_POL    true
$end

$almo_print
1 5:6
2 5:6
$end

$plots
grid_points 60 60 60
$end