Dariusz W. Szczepanik1,2
1 Department of Theoretical Chemistry, Jagiellonian University
Faculty of Chemistry, Gronostajowa 2, 30-387 Krakow, Poland
2 Institute of Computational Chemistry and Catalysis, University of Girona
C/ Maria Aurèlia Capmany, 69, 17003 Girona, Catalonia, Spain
Naphthalene at S0 - Input files
The current version of RunEDDB requires two input files: the formatted checkpoint file (.fchk) and the DMNAO/AONAO file (.49) file. They can be generated using Gaussian and NBO programs by specifying in the Gaussian route section Pop=NBORead and in the $NBO section $NBO SKIPBO FILE=DMNAO AONAO=W49 DMNAO=W49 $END. It is strongly recommended to install and use the newest version of NBO, i.e. 6 or 7 (Pop=NBO7Read), especially when diffuse functions are used or the calculation involves a post-HF wavefunction (in this case adding Density=Current in the Gaussian route section and the FIXDM keyword in the $NBO section is also required). When problems with linear dependence occur during the NBO calculations involving diffuse functions adding IOP(3/32=2) into the Gaussian route section should help. An exemplary Gaussian 16 input file that can be used to perform the EDDB analysis for naphthalene at S0 state is as follows (nap_s0.gjf):
# CAM-B3LYP/6-311G(d,p) Pop(NBORead)
Naphthalene at S0
C 0.00000 1.24008 1.39429
C 0.00000 2.41940 0.70603
C 0.00000 2.41940 -0.70603
C 0.00000 1.24008 -1.39429
C 0.00000 0.00000 -0.70953
C 0.00000 0.00000 0.70953
C 0.00000 -1.24008 1.39429
C 0.00000 -2.41940 0.70603
C 0.00000 -2.41940 -0.70603
C 0.00000 -1.24008 -1.39429
H 0.00000 1.23660 2.47868
H 0.00000 3.36162 1.24086
H 0.00000 3.36162 -1.24086
H 0.00000 1.23660 -2.47868
H 0.00000 -1.23660 2.47868
H 0.00000 -3.36162 1.24086
H 0.00000 -3.36162 -1.24086
H 0.00000 -1.23660 -2.47868
$NBO SKIPBO FILE=nap_s0 DMNAO=W49 AONAO=W49 $END
To generate nap_s0.fchk and nap_s0.49 required for the EDDB analysis simply run:
formchk -3 nap_s0.chk
It should be noticed that any other program that is capable of generating .fchk files and has a built-in interface to the NBO software (e.g. Q-Chem) can be used to perform the EDDB analysis; another way is to use tools like MultiWFN to generate .fchk file, or import converged MOs from another program into Gaussian ( Guess=(Cards,Only) ).
Naphthalene at S0 - Performing calculations of different EDDB functions
Types of the EDDB function:
By default, RunEDDB runs in interactive mode which allows user to select different options during the program execution. It is much more practical, however, to disable this mode and use the command-line options and redirect the output into the file:
- EDDBG - electrons delocalized through the system of all chemical bonds in a molecule (Global delocalization).
- EDDBH - electrons delocalized through the system of all chemical bonds involving only Heavy atoms.
To study global π-delocalization it is recommended to use this function rather than EDDBG because the bond orbitals involving hydrogen atoms tend to conjugate with the adjacent σ-bond orbitals noticeably increasing delocalization in the σ-subsystem.
- EDDBF - electrons delocalized through the system of chemical bonds in particular molecular Fragment.
- EDDBE - similar to EDDBF, but here the density of electrons delocalized in selected fragment is 'extracted' from the EDDBG function, and thus it includes also the External (non-local) conjugations.
- EDDBP - electrons delocalized along selected Pathway.
For instance, to calculate global EDDBG(r) and EDDBH(r) functions as well as local EDDBE(r), EDDBF(r) and EDDBP(r) functions for a single benzenoid unit in naphthalene, to perform the corresponding electron population analyses, and finally to export the results into new .fchk and .out (text) files run the following commands:
- -q ......................................................... disable interactive mode
- -i [e.g. MOLECULE.FCHK DMNAO.49] ................................. select input files
- -g ....................................................... select the EDDB_G function
- -h ....................................................... select the EDDB_H function
- -f [molecular fragment, e.g. 1:4,7,8] .................... select the EDDB_F function
- -e [molecular fragment, e.g. 1:4,7,8] .................... select the EDDB_E function
- -p [delocalization pathway, e.g. 1-2-3-4-5-6-1] .......... select the EDDB_P function
- -o [e.g. EDDB_X.FCHK] ....... export the calculated EDDB_X into a new .FCHK file
runeddb -q -i nap_s0.fchk nap_s0.49 -g -o nap_s0.EDDB_G.fchk >& nap_s0.EDDB_G.out
runeddb -q -i nap_s0.fchk nap_s0.49 -h -o nap_s0.EDDB_H.fchk >& nap_s0.EDDB_H.out
runeddb -q -i nap_s0.fchk nap_s0.49 -e 1:6 -o nap_s0.EDDB_E.fchk >& nap_s0.EDDB_E.out
runeddb -q -i nap_s0.fchk nap_s0.49 -f 1:6 -o nap_s0.EDDB_F.fchk >& nap_s0.EDDB_F.out
runeddb -q -i nap_s0.fchk nap_s0.49 -p 1-2-3-4-5-6-1 -o nap_s0.EDDB_P.fchk >& nap_s0.EDDB_P.out
Naphthalene at S0 - Structure of the output file
Naphthalene at S0 - Visualization of the EDDB functions
The generated new checkpoint files (nap_s0.EDDB_X.fchk) are copies of the original one (nap_s0.fchk) in which Alpha MO energies and coefficients as well as the Total SCF densities (and Spin SCF densities for open-shell systems) are replaced by the (spinless) Natural Orbital for Bond Delocalization (NOBD) occupation numbers, NOBD coefficients, and the total EDDB densities (and spin EDDB densities for open-shell systems, abbrev. SDDB), respectively. These new .fchk files can be used to generate cube files using Cubegen program from the Gaussian package. Alternatively, one can use Avogadro to visualize the EDDB functions. To do that open the fchk file containing the EDDB function and in the program menu select Extensions → Create Surfaces → Surface Type: "Electron Density", Iso Values: from 0.015 to 0.020, and click the Calculate button. To visualize NOBDs, use the toolbar Orbitals on the right site of the program window (the toolbar can be turned on/off in the menu Settings → Toolbars → Orbitals). The NOBDs are ordered by decreasing occupation number; thus, e.g. in the case of π-aromatic systems the π-NOBDs are expected to be at the beginning of the list.
To generate cube files for all the calculated EDDB functions using the Cubegen tool from Gaussian, run the following commands:
cubegen 1 FDensity=SCF nap_s0.EDDB_G.fchk nap_s0.EDDB_G.cube 100 h
cubegen 1 FDensity=SCF nap_s0.EDDB_H.fchk nap_s0.EDDB_H.cube 100 h
cubegen 1 FDensity=SCF nap_s0.EDDB_E.fchk nap_s0.EDDB_E.cube 100 h
cubegen 1 FDensity=SCF nap_s0.EDDB_F.fchk nap_s0.EDDB_F.cube 100 h
cubegen 1 FDensity=SCF nap_s0.EDDB_P.fchk nap_s0.EDDB_P.cube 100 h
The generated cube files can be visualized using e.g. Avogadro (Iso Value: 0.015):
Naphthalene at S0 - Interpretation of the results
Naphthalene at S0 - Dissection into σ- and π-components