Introduction to Computational Quantum Chemistry
Intermolecular interactions II: Density-based methods
Jan Novotny (NCBR) Intermolecular interactions November 2, 2021 1 / 7
Electron deformation density(EDD)
Upon formation of complex redistribution of electron density
occurs(polarisation, charge transfer):
∆ρ = ρcomplex − ρfragments (1)
in inputs of both fragment the atoms of missing partner is
represented by ghost centers (indicated by Bq label) ⇒
preservation of occupied space
cubgen utility produces 3D density output (*.cube format/xplor) by
processing formatted checkpoint file (*.chk) from Gaussian SP
calculation
Jan Novotny (NCBR) Intermolecular interactions November 2, 2021 2 / 7
Topological analysis of electron density using QTAIM
approach
molecular space divided in atomic basins bordered by zero-flux surfaces
ρ · n = 0 of gradient of electron density
Bond critical points (BCPs) = local stationary points of vanishing density
gradient and maximized density in two directions perpendicular to
interatomic vector A-B ⇒ (3,-1) Hessian tensor
various density-based descriptors can be analysed to evaluate character
of interaction between atoms A and B (local density ρ(r),Laplacian
2
ρ(r), delocalisation index DI(A,B))
Jan Novotny (NCBR) Intermolecular interactions November 2, 2021 3 / 7
HOMEWORK: Bifurcated hydrogen bond
1 The aim is to analyze set of H-bonded complexes of HF attached to
substituted dimethoxybenzene (see attached figure, BLYP/def2TZVPP
optimized geometries of -NH2 and -CHO derivatives available in IS)
2 Calculate interaction energies (∆E for all 6 complexes and for 2
extremes plot the electron deformation energies(∆ρ, slide 5) and map of
Laplacian of electron density ( 2
ρ, slide 6).
3 Run basic QTAIM calculation for all complexes, extract values of density,
Laplacian of electron density and delocalisation index (DI) associated
with BCPs between (F)H and O(CH3) atoms.
4 Try to correlate ∆E versus ρ, 2
ρ, DI, DI/r(O-C)
Jan Novotny (NCBR) Intermolecular interactions November 2, 2021 4 / 7
Electron deformation density
Gaussian input for organic fragment
%chk=f1.chk
#p B3LYP/def2TZVPP scf=conver=6
Integral=UltraFine
SP of f1
0 1
H 0.6778488 1.2270278 2.1895466
C 0.1339051 1.3019980 1.2510536
C -1.2613796 1.3725016 1.2677278
H -1.7993284 1.3529764 2.2128579
C -1.9692784 1.4687435 0.0645759
C -3.3941682 1.5428919 0.0703788
...
H-Bq 3.0768960 1.2302657 -1.6848812
F-Bq 3.8684785 1.1731588 -2.2005430
N -4.5586668 1.6046640 0.0695014
run script
module add gaussian
#COMPLEX
g09 complex.com
formchk -3 complex.chk complex.fchk
cubgen "ncpus" density=SCF complex.fchk
complex.cube -3
#FRAGMENT 1
g09 f1.com
formchk -3 f1.chk f1.fchk
cubgen "ncpus" density=SCF f1.fchk f1.cube
-3
#FRAGMENT 2
g09 f1.com
formchk -3 f2.chk f2.fchk
cubgen "ncpus" density=SCF f2.fchk f2.cube
-3
use interactive tool CUBMAN for processing cube files:
1. Add f1.cube and f2.cube to get temporary sum.cube.
2. SUbstract complex.cube minus sum.cube to get final difference map.
3. Use VMD isosurface representation to show positive and negative regions
of ∆ρ.
Jan Novotny (NCBR) Intermolecular interactions November 2, 2021 5 / 7
OTAIM
Gaussian input: BSSE-corrected interaction energy + generation
of wavefunction file *wfx
%chk=complex.chk
#p B3LYP/def2TZVPP scf=conver=6
Integral=UltraFine Counterpoise=2 output=wfx
SP of complex
0 1 0 1 0 1
H 0.6778488 1.2270278 2.1895466 1
C 0.1339051 1.3019980 1.2510536 1
C -1.2613796 1.3725016 1.2677278 1
...
H 3.0768960 1.2302657 -1.6848812 2
F 3.8684785 1.1731588 -2.2005430 2
N -4.5586668 1.6046640 0.0695014 1
complex.wfx
Commands for performing QTAIM analysis in AIMALL
program based on Gaussian wavefunction
module add gaussian
# start job
g16 complex.com
formchk -3 complex.chk complex.fchk
# clean
rm -f core
# QTAIM
module add aimall
aimqb.ish -nogui -nproc=3
-atlaprhocps=true -encomp=1 -usetwoe=0
complex.fchk
Plotting the Laplacian using Aimstudio GUI
1. Run in terminal aimstudio.ish complex.sumviz.
2. Use Counters/New 2D Grid option, select Function DelSqRho, copy
coordinates of 3 ring atoms(right click on selected atom in structure).
3. Open complex.g2dvi in current window and export png picture.
Jan Novotny (NCBR) Intermolecular interactions November 2, 2021 6 / 7
Extracting data from *sumviz file
Open complex.sumviz and find relevant BCPs (H–O, or O–H),
save corresponding values of ρ, 2ρ.
Find the section listing delocalisation indexes (table with DI(A,B)
heading) and save these values.
Extract H–O distances from structure.
Prepare correlation plots.
Jan Novotny (NCBR) Intermolecular interactions November 2, 2021 7 / 7