12.7.9 Visualization Tools Associated with ALMO-EDA

The following visualization tools are enabled in EDA2:

• •

  Automated generation of complementary occupied-virtual pairs (COVP)

• •

  Electron density difference (EDD) maps between intermediate states (FRZ$\to$POL, POL$\to$Full)

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  Plots for Natural Orbitals for Chemical Valence (NOCV)

• •

  Plots of frozen and polarized ALMOs

As introduced in Sec. 12.5.2, 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 ($\mathrm{\Delta }{𝐏}_{\mathrm{pol}}={𝐏}_{\mathrm{pol}}-{𝐏}_{\mathrm{frz}}$) and charge transfer ($\mathrm{\Delta }{𝐏}_{\mathrm{ct}}={𝐏}_{\mathrm{full}}-{𝐏}_{\mathrm{pol}}$). 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), ⁷⁸⁸ which are defined as the eigenvectors of $\mathrm{\Delta }𝐏={𝐏}_{\mathrm{full}}-{𝐏}_{\mathrm{frz}}$. The NOCVs appear in pairs ${\psi }_k$ and ${\psi }_{-k}$, whose associated eigenvalues are $n_k$ and $-n_k$, respectively. The energy lowering associated with each pair of NOCVs can be calculated using the extended transition state (ETS) approach (see Ref. 788 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 $\{n_k\}$. When EDA_NOCV = 1, Q-Chem will only plot the contribution from each significant NOCV pair (${\psi }_{-k}$, ${\psi }_k$) to the density deformation ($\mathrm{\Delta }{\rho }_k$):

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.