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