Module 2 of LUMPAC acts as a graphical interface for the ORCA program,[1] enabling the calculation of the singlet and triplet excited states of the ligands in the compound (Figure 1). The excited states energies are important for calculating the energy transfer and back-transfer rates between the ligands, which act as an antenna, and the lanthanide ion. The lanthanide ion is conveniently replaced by a 3e+ point charge to calculate the excited states of the ligands using the semiempirical INDO/S model (Intermediate Neglect of Differential Overlap),[2,3] implemented in ORCA.
Figure 1. Module for calculating the excited states energies of the ligands using the ORCA program.
ORCA is a modern computational package for electronic structure calculations developed by Prof. Frank Neese (Universität Bonn). The ORCA development project benefits from contributions by numerous research groups and is made freely available to academics. Users can download the ORCA installer by registering on the website, https://orcaforum.kofo.mpg.de/app.php/portal, with no password required. Newer versions of ORCA increasingly require more storage space due to added features. For example, ORCA version 5.0.4 for Windows requires approximately 24 GB of storage space. The latest version, 6.0, includes an installer that allows users to select specific packages for installation. Regardless of the version, all files must be located within a single directory.
As LUMPAC uses command lines to execute ORCA, placing the ORCA executable files in a short-named directory (e.g., C:\ORCA) it is strongly recommended to prevent interaction issues.
The ORCA program can perform a wide variety of calculations, from geometry optimization to spectral parameters calculations, using various levels of theory. Despite this extensive functionality, LUMPAC uses ORCA only for calculating the excited states of ligands using the configuration interaction singles (CIS) method, applying the semiempirical INDO/S model. Because the ORCA program is not public domain like MOPAC, LUMPAC cannot distribute it. Therefore, users are required to obtain ORCA via the procedure described above.
Procedure for Calculating Excited States using LUMPAC
1.Specify the directory of the external ORCA program (Figure 2), using the procedure previously demonstrated for the geometry optimization module.
2.After defining the directory containing the ORCA program, click on button (Figure 2) to open the MOPAC output file (.out) created by the geometry optimization described earlier.
Figure 2. ORCA program integration in LUMPAC and the various input file formats supported for excited states calculations.
Figure 3). Optionally, the number of excited states and the range of orbitals considered in the configuration interaction singles (CIS) can be modified. The button (Figure 2) will be enabled once the MOPAC output file is opened.
Figure 3. Editor for setting the parameters of the excited states calculations using ORCA.
Before LUMPAC executes ORCA, the ORCA input file is created with the same name as the corresponding MOPAC output file, but with the .orcinp extension. The ORCA input file created for the [Eu(btfa)3(bpy)] compound can be viewed in Figure 4, and the ORCA output file will have the .orcout extension.
Figure 4. .orcinp file created by LUMPAC from the MOPAC output file of [Eu(btfa)3(bpy)] and used as the ORCA input file.
The number of excited states (nroots) to be calculated is specified in the seventh line of the .orcinp file (Figure 4). The eighth line displays the size of the Configuration Interaction (CI) matrix used in the CIS calculation. As shown in Figure 4, the sixteenth line indicates the filename for the .pointcharge file, which stores the point charges replacing the lanthanide. Therefore, the .orcinp file contains only the atomic coordinates of the organic ligands. Because the [Eu(btfa)3(bpy)] complex contains a single Eu3+ ion, only one point charge will be used (Figure 5).
Figure 5. .pointcharge file containing the +3e point charge used to replace the lanthanide ion.
Warning: The .pointcharge file provides the Cartesian coordinates of the lanthanide ion when the .orcout file is used as input for LUMPAC. Therefore, the .pointcharge file must be in the same directory and have the same name as the corresponding .orcout file.
The seventeenth line of the .orcinp file (Figure 4) specifies the coordinate type, compound charge, and multiplicity (considering only the ligands). A multiplicity of 1 (singlet) indicates paired electrons; therefore, the first line shows the RHF (Restricted Hartree-Fock) keyword, indicating a closed-shell calculation. ORCA will report an error and terminate the calculation if the charge is incorrect. To minimize errors, LUMPAC automatically transfers the charge from geometry optimization to the ORCA input file. Thus, users must verify the charge from defined in Module 1.
4.The ORCA output file will have the same name as the .orcinp file, but with the .orcout extension.
Figure 6 shows the ORCA output file in the LUMPAC file viewer. The .orcout file can also be viewed with any text editor.
Figure 6. ORCA output file displayed in the LUMPAC file viewer.
LUMPAC enables excited states calculations using an existing ORCA input file (.orcinp). As LUMPAC does not provide editing capabilities for the .orcinp file keywords, users must utilize a text editor if modifications are required.
The “Select Excitation Window” option (Figure 3) allows users to customize the molecular orbital range considered in the CIS calculation. By default, LUMPAC uses a 20×20 excitation window, which includes the 20 highest energy occupied and the next 20 lowest energy unoccupied molecular orbitals.
Figure 7 shows the section of the ORCA output file containing the energies of the molecular orbitals calculated for [Eu(btfa)3(bpy)].
The OCC column in Figure 7 indicates the orbital occupation: 2.0000 for occupied and 0.0000 for unoccupied orbital. Thus, orbital 148 corresponds to the highest energy occupied orbital (HOMO), and orbital 149 is the lowest energy unoccupied orbital (LUMO).
Figure 7. Section of the .orcout output file displaying the energies of the molecular orbitals used to select the orbital range will be used in the CIS calculation.
A single-point SCF (Self-Consistent Field) calculation determines the orbital energies before a CIS calculation. Figure 7 illustrates the orbital window used in the CIS calculation for the case study: orbitals 129 (-0.415580 Eh) and 168 (0.073982 Eh), highlighted in bold, correspond to the lower and upper limits of the excitation window, respectively. The sixth line of Figure 4 demonstrates how the orbital range was specified to define a 20×20 excitation window.
The excited states are calculated from single excitations involving the orbitals included in the defined excitation window (Figure 8). The RL quantity, representing the distance between the energy donor center (located on the ligands) and the lanthanide ion (energy density acceptor), is calculated using the coefficients of the atomic orbital contributions for the molecular orbital formation and the distances between the corresponding atoms and the lanthanide ion. These coefficients are presented in another section of the ORCA output file (not shown here).
A calculation is successfully completed only when the phrase ORCA TERMINATED NORMALLY appears, as shown in Figure 8.
Figure 8. Singlet and triplet state energies and individual excitations that form the respective excited states in the .orcout file.
References
[1] F. Neese, Software update: The ORCA program system—Version 5.0, Wiley Interdisciplinary Reviews: Computational Molecular Science, 12. 2022.
[2] J. Ridley, M. Zerner, Theor. Chim. Acta, 1973, 32, 111–134.
[3] J. E. Ridley, M. C. Zerner, Theor.Chim. Acta, 1976, 42, 223–236.
(Figure 2) to open the MOPAC output file (.out) created by the geometry optimization described earlier.
(Figure 2) will be enabled once the MOPAC output file is opened.
