12.7.7 ALMO-EDA with non-aufbau Electronic Configurations

Q-Chem also supports ALMO-EDA calculations with one or multiple fragments in non-aufbau electronic configurations.^Mao:2021c This method is particularly useful for cases where the energetically most stable electronic state of a given fragment changes upon the formation of intermolecular complex, which is common for systems involving open-shell species such as carbenes, transition metal cations, etc. For example, the lowest-energy electronic configuration of an isolated Ba${}^{+}$ radical cation is 6s${}^1$; however, when it is ligated with CO, the complex is more stable when the unpaired electron of Ba${}^{+}$ is promoted from 6s${}^1$ to 5d${}^1$, which is thus in a non-aufbau state relative to the isolated Ba${}^{+}$ cation. A sensible strategy to study the formation of such a complex is to perform an ALMO-EDA calculation with Ba${}^{+}$ in the 5d${}^1$ electronic configuration, and then evaluate the energy difference between Ba${}^{+}$(5d${}^1$) and Ba${}^{+}$(6s${}^1$) and interpret that as the monomer “electronic preparation” energy. To ensure that the system stays in a given non-aufbau electronic configuration throughout, the Maximum Overlap Method ³⁶¹ (MOM, see Sec. 4.5.12 for details) is applied to almost all stages in ALMO-EDA, including (i) isolated fragment calculations, (ii) calculation for the polarized wavefunction, and (iii) full SCF calculation for the whole system. Among them, (i) and (iii) are standard SCF calculations using MOM, while (ii) involves the application of MOM to an SCFMI calculation,⁷⁴¹ which is compatible with the use of DIIS algorithm to solve locally projected SCF equations (with FRGM_METHOD = STOLL or GIA, see Section 12.4).

Specifically, an ALMO-EDA calculation for a complex within a non-aufbau electronic configuration (assuming only one of the fragments is excited) comprises the following steps:

• •

  Perform ground-state SCF calculations for all fragments

• •

  Calculate the non-aufbau electronic configuration for the fragment as specified in the input using MOM: the energy consumed to excite this fragment is reported in the output as the preparation energy ($E_{\mathrm{prp}}$); construct the frozen state for the system with that one fragment in the non-aufbau state and the rest in ground state

• •

  Starting from the frozen state, perform an SCFMI calculation with MOM to obtain the polarized state within the non-aufbau electronic configuration

• •

  Perform a full SCF calculation with MOM, starting from the polarized wavefunction in the non-aufbau state

Such a calculation requires EDA2_MOM = TRUE in addition to the setup of standard EDA2 jobs. The non-aufbau electronic state is specified through the $scfmi_mom input section, which has the following format:

$scfmi_mom
frag_idx1   X_1   Y_1   spin_1
frag_idx2   X_2   Y_2   spin_2
...
$end

In each row, the first entry specifies the index of the non-aufbau fragment (starting from 1). The second and third entries specify the non-aufbau electronic configuration, which is prepared by promoting an electron from a given fragment’s HOMO$-$X to LUMO$+$Y once the ground-state SCF calculation of that fragment is finished. The last entry specifies the spin of the occupied and virtual orbitals that are being swapped (“a” for $\alpha$ electrons and “b” for $\beta$ electrons, and $\alpha$ orbitals will be used by default if the fourth entry is left blank). For instance, for a HOMO$\to$LUMO excitation on the first fragment, this section would simply look like

$scfmi_mom
1  0  0  a
$end

Q-Chem 5 also allows one to perform SCFMI calculations for non-aufbau electronic configurations,⁷⁴¹ without going through the entire ALMO-EDA procedure. To do that, one can simply add SCFMI_MOM = TRUE to the $rem setup of an SCFMI calculation (see Section 12.7.2). The non-aufbau electronic configuration can be specified through the $scfmi_mom section in the same way.

Note that EDA2_MOM and SCFMI_MOM can be used without explicitly setting the $scfmi_mom section, where the electronic configuration of the frozen state constructed from two ground-state fragments will be preserved in the SCFMI or ALMO-EDA calculation.