Pag.

Chemical Concepts from Density Functional Theory

Paul Geerlings, Stijn Fias, ZinoBoisdenghien, Thijs Stuyver, Frank De

Proft

General Chemistry, Vrije Universiteit Brussel, Brussels, Belgium

ICCMSE 2016

Athens, March 17 – 20, 2016

21/09/2016 1

Chemistry from the Linear Response Function

Pag.

0. Introduction : the ongoing need for interpretational concepts and models in quantum chemistry

21/09/2016 2

• Chemistry as an experimental science → accumulation of data of countless number of molecules (CA > 100.000.000 Substances!)

Need for unifying theories, concepts, models to rationalize, interpret, predict …… in order to avoid an encylopaedic “science”.

• Nowadays: Computational Chemistry is flourishing (e.g. WATOC Conferences)

Accumulation of accurate data on countless number of molecules, reactions,…

Aren’t we generating a new encyclopaedia??

STILL need for unifying concepts and models to systematize the theoretical data.

Pag.21/09/2016 3

Looking back

• many concepts are MO/VB based cf. HOMO/LUMO, frontier MO theory rationalization of the Woodward Hoffmann rules, …

• Nowadays DFT is the workhorse par excellence for computational studies on medium and large systems

Isn’t there a need for density based concepts?

Part of DFT founded by RG Parr (1978)

CONCEPTUAL DFT

CHEMICAL DFT or CHEMICAL REACTIVITY DFTor

Pag.21/09/2016 4

Today’s talk

1. - A very brief introduction to Conceptual DFT

1. - Concentrating on the linear response function

• Evaluation

• Representation

• Chemistry from the linear response function

- Concepts: inductive and mesomeric effects, aromaticity,…

- Substrates: carbon chains, organic rings, inorganic rings,…

- An excursion into Alchemical Derivatives: exploring Chemical Space

3. – Electrical Conductivity: Molecular Electronic Devices

4. – Conclusions

Pag.

1. Conceptual DFT

Fundamentals of DFT : the Electron Density Function as Carrier of Information

Hohenberg Kohn Theorems (P. Hohenberg, W. Kohn, Phys. Rev. B136, 864 (1964))

ρ(r) as basic variable:

21/09/2016 5

( )v r( )rρ

N

opH “everything”

Pag.21/09/2016 6

•

•

• • •

•

•

•

••

•

compatiblewith asingle v(r)

ρ(r) for a givenground state

- nuclei- position/charge

electrons

v(r)

Visualisation of the HK Theorem

Pag.

• Variational Principle

FHK Universal HohenbergKohn functional

Lagrangian Multiplier

• Practical implementation : Kohn Sham equations

Computational breakthrough

v(r)+δFHK

δρ(r)=µ

21/09/2016 7

( ) ( ) ( )HKE r v r dr + F r= ρ ρ ∫

Pag.

Starting point for DFT perturbative approach to chemical reactivity

E = E[N,v]Consider Atomic, molecular system, perturbed in number of electrons and/or external potential

dE =∂E

∂N

v(r)

dN +δE

δv(r)

∫

N

δv(r)dr

identification first order perturbation theory

identification

ρ r( )

Electronic Chemical Potential (R.G. Parr et al, J. Chem. Phys., 68, 3801 (1978))

= - χ (Iczkowski - Margrave electronegativity)

μ

21/09/2016 8

Pag.21-9-2016 921-9-2016 9

Chemical hardnessFukui function

∂E

∂N

v(r)

= µ

∂2E

∂N2

v(r)

= η∂2E

∂Nδv(r)=

δµ

δv(r)

N

=∂ρ(r)

∂N

v

E[N,v]

= f(r)

Identification of two first derivatives of E with respect to N and v in a DFT context → response functions in reactivity theory

Linear response Function

2

N

E(r, r ')

v(r) v(r ')

δ= χ

δ δ

= −

Electro-negativityElectronic

Chemical Potential

χN

E(r)

v(r)

δ= ρ

δ

• P. Geerlings, F. De Proft, W. Langenaeker, Chem. Rev. , 103, 1793, 2003

• P. Geerlings, F. De Proft, PCCP, 10, 3028 (Third order derivatives)

• P. Geerlings, P.W. Ayers, A. Toro Labbé, P.K. Chattaraj, F. De Proft, Acc. Chem. Res., 55, 2012 (WH rules)

21/09/2016 9

Pag.

Hardness and fukui function have been widely explored but what about the remaining second order derivative?

: linear response function

• Well known in its frequency dependent form in solid slate physics and in the time dependent DFT community.

• “Chemistry” content relatively unexplored

• Fundamental Importance: Information about propagation in the density of an (external potential) perturbation on position r’ throughout the system

( )χ r,r'

( ) ( )( )

( )

2

' '

N N

δρ rδ E= =δv r δv r δv r

21/09/2016 10

Pag.

2. The Linear Response Function

• Work on formal aspects and mathematical aspects (Parr, Senet, Cohen, Ayers)

• Some numerical work (Coulson, Baekelandt, Cioslowski)

• NO direct, practical, generally applicable, nearly exact approach available and/or exploited

2.1. Introduction

21/09/2016 11

“Hückel MO Theory: mutual atom-atom polarizability πr,s =

C.A. Coulson and H.C. Longuet Higgins, Proc.Roy.Soc.LondonA, 192, 16, (1947)

∂qr/ ∂α

s

Pag.

2.2. A simple perturbational approach; an independent particle model

(P.W.Ayers, Faraday Discussions, 135, 161, 2007)

: occupied orbitals : unoccupied orbitals : orbital energies

( )( )

( )( ) ( ) ( ) ( )* *N 2

i a a i

i=1 a=N 2+1 i aN

δρ r φ r φ r φ r' φ r' = χ r,r' =4 δv r' ε -ε

∞

∑ ∑

iφ aφ i aε ,ε

2.2.1. Preliminaries

• Numerical evaluation: time consuming → benchmark

• Can we calculate in a simpler way?

• Closed shell N-electron system in the KS ansatz; frozen orbital approach

• 1st order Perturbation Theory → → taking functional derivative w.r.t

( )χ r,r'

( ) ( )1ρ r ( )v r

21/09/2016 12

P.W Ayers, F. De Proft, A. Borgoo, P. Geerlings, JCP, 126, 224107, 2007.

N. Sablon, F. De Proft, P.W. Ayers, P. Geerlings, JCP, 126, 224108, 2007.

Pag.

2.2.2. Atoms revisited

• Earlier work: A. Savin, F. Colonna, M. Allavena, J. Chem. Phys, 115, 6827, 2001

some light elements

• Light elements (KS ansatz; PBE). Spherical potential perturbation

. plot : radial distribution of the linear response kernel( )2 ' '2r χ r,r r

He Be

• Similar to Savin’s plots

• Positive and negative region, for He, duplicated in Be shell structure

21/09/2016 13

Along diagonal: increasing depletion of ( )v r ( )rρ

alternating signs χ(r, r ')dr ' = 0∫

Pag.

One dimensional version for a fixed ( )2 'r χ r,r ( )r'=0 2r' r χ r,0→

He

Be

( ) ( ) ( )ρ r dr' χ r,r' δv r'∆ = ∫( ) ( )δv r' Aδ r ' 0 A>0= −Pointlike

perturbation

( ) ( )ρ r Aχ r,0∆ =

Alternating positive and negative regions due to conservation of number of electrons

also in 2D plot

21/09/2016 14

Pag.

Extending → the noble gases

21/09/2016 15

Shell structure of atoms

Pag.

χ(r,0) for Ar in the x,y plane

21/09/2016 16

Pag.

A direct application → polarizability calculations

αij= - dr∫ dr' r

i χ r,r'( ) r'

j i,j= x,y,z

• Comparison with high level calculations

• Absolute values deviate, trend is respected

21/09/2016 17

Z. Boisdenghien, C. Van Alsenoy, F. De Proft, P. Geerlings,J. Chem. Theor. Comp. 9, 1007 (2013)

Pag.21/09/2016 18

Z., Boisdenghien, S. Fias, F. Da Pieve, F. De Proft, P. Geerlings Mol. Phys. 113, 1890, 2015

Pag.21/09/2016 19

Extension to open shell atoms/ Spin polarized linear Response

Transition to a spin-polarized version of in the context of spin polarized conceptual DFT

(F. De Proft, E. Chamorro, P. Perez, M. Duque, F. De Vleeschouwer, P.Geerlings,

Chem. Modell. 6, 63-111 (2009))

( )r, r 'χ

N, Ns representation [ ]s sE E N, N , v, v=

vs

=1

2(v

α− v

β)

v =1

2(v

α+ v

β)

sN N Nα β= −

( )r, r 'χ ( )( ) ( )

( )( )

s s

2

NN

N,N N,N

rEr, r '

v r v r ' v r '

δρδχ = =

δ δ δ

usual DFT potential

related to B vs

= µB

B(r)

Pag.21/09/2016 20

Introduction of

χNS

r, r '( ) =δ2E

δv r( )δvs

r '( )

N,Ns

=δρ

s

δv r '( )

N,Ns

s α βρ = ρ − ρ

( )( )

( )( )

( )NS

rrr, r '

v r ' v r '

βαδρδρ

χ = −δ δ

: two terms can be expanded (IPM)

Pag.21/09/2016 21

Li

α − β α β

• Symmetry r, r’

• Middle region negative: sensitivity of to larger than that of

Aρ v∆

βρ

(cf. )N Nα β>

~ ( ) of Be α + β

cf. ground state configuration

~ ( ) of He but contracted

α + β

(higher Z)

Z. Boisdeghien, S. Fias, F. De Proft, P. Geerlings, PCCP, 16, 14614 (2014)S. Fias, Z. Boisdenghien, F. De Proft, P. Geerlings, J.Chem. Phys, 141, 184107 (2014)

Pag.

How to extend its use for molecules to look for chemical information

condensation at stake in a first approach

21/09/2016 22

M. Torrent-Sucarat, P. Salvador, M. Solà, P. Geerlings, J. Comp. Chem., 29, 1064, 2008

2.2.3. From atoms to molecules

Pag.

An example: : atom condensed values

Numerical methodPresent method

Correlation coefficient between the matrix elements of the two methods:

H C O H2

H -1.22

C 0.68 -4.35

O 0.34 2.99 -3.67

H 0.19 0.68 0.34 -1.22

H2CO

Y = 0.99x - 0.01 R2= 0.96 Slope ∼ 1

H C O H2

H -1.21

C 1.19 -4.82

O 0.42 2.45 -3.28

H -0.40 1.19 0.42 -1.21

N. Sablon, P.W.Ayers, F. De Proft, P. Geerlings, J.Chem.Theor. Comp., 6, 3671, 2010

For other simple molecules (H2O, NH3, CO, HCN, NNO) always a high correlation coefficient is obtained with a very small intercept; the slope varies between 1 and 2.

21/09/2016 23

Pag.

Transmission of a perturbation through a carbon chain

NXχOXχ

Saturated systems

• density response of C atoms on heteroatom perturbation decreases monotonously with distance

• exponential fit: r2= 0.982 ( vide infra) Characterizing and quantifying the inductive effect.

(X= C0, C1, C2 …)

Inductive and mesomeric effects

21/09/2016 24

Pag.

Unsaturated systems

• alternating values• C1, C3, C5 of the chain: minimaC0, C2, C4, C6 : maxima

R= OH, NH2: resonance structures

C1, C3, C5 : mesomeric passive atoms→ follow same trend as alkane structures (inductive effect)

C0, C2, C4, C6 : mesomeric active atoms → effect remains consistently large even after 6 bonds (small decrease due to

superposition of inductive and mesomeric effect)

135

6 4 2

N. Sablon, F. De Proft, P. Geerlings, JPCLett., 1, 1228, 2010

21/09/2016 25

Pag.

Substituted benzenes vs cyclohexanes

• cyclohexane:

1 iC Cχ (i= 2,3,...6)=

• decreases exponentially (inductive effect)• influence of OH small

χ

• benzene: • maxima at C2, C4, C6: mesomerically active atoms (mesomeric effect)• minima at C3, C5 : mesomerically inactive atoms

Reminiscent of (1,4) Para Delocalisation Index. Sola et al,

Chem. Eur. J. 9, 400 (2003) as a criterion of aromaticity

N. Sablon, F. De Proft, P. Geerlings, Chem.Phys.Lett., 498, 192, 2010

21/09/2016 26

• Does Linear response function contain similar information?1,4χ

Pag.

16 non equivalent sixrings studied by Sola et al.

21/09/2016 27

Pag.

• typical benzene-type pattern encountered before

21/09/2016 28

Pag.

→ Linear response function as an “electronic” descriptor of aromaticity→ Unsold’s theorem, resolution of the identity

21/09/2016 29

Pag.

Benzene

• Decreasing σ contribution (cfr. Cyclohexane)

• Zig/zag for π and total

• Anti-aromatic molecules:Cyclobutadiene, COT

“inverted zig zag”

S. Fias, P. Geerlings, P. Ayers, F. De Proft, PCCP, 15, 2882 (2013)

21/09/2016 30

Digging further in aromaticity →→→→ σσσσ,ππππ aromaticity (applying σσσσ,ππππ separation)

Pag.

Inorganic rings

21/09/2016 31

Pag.

Valence Bond Structures

X= NH, O, PH

Resonance Energy (kJ mol-1) and weights W of the four Valence Bond Structures.

Molecule Eres W(I) W(II) W(III) W(IV)

B3N3H6 61.6 0.05 0.05 0.90 0.00

B3O3H3 27.6 0.02 0.02 0.96 0.00

B3P3H6 132.6 0.21 0.21 0.58 0.00

C6H6 161.4 0.47 0.47 0.03 0.03

J. Engelberts, R. Havenith, J. Van Lenthe, L. Jenneskens, P. Fowler, Inorg. Chem., 44, 5266, 2005

21/09/2016 32

Pag.

Borazine

• Typical resonance pattern observed in aromatic systems is recovered if one of the N-atoms is chosen

as the reference atom.

• Purely inductive behaviour (exponential decay of electron delocalization with internuclear distance)

is recovered if one of the B-atoms is chosen as the reference atom.

Dual picture of aromatic character of borazine (cfr. ongoing debate in the literature)

N. Sablon, F. De Proft, M. Sola, P. Geerlings, PCCP, 14, 3960 (2012)

21/09/2016 33

Pag.3421/09/2016

Reactions

• Evolution of the �, � LRF upon cyclisation reactions:the trimerization of acetylene to benzene

• Total PLR (Para Linear Response) function maximum at TS• Essentially � in nature � � aromaticity• � contribution only becomes significant when the � framework is returned to a more localized state

Pag.21/09/2016 35

2.3. Beyond the independent Particle Model

• Using a CPKS approach

( ) ( ) ( ) ( ) ( ) ( )ia , jb

1 * *

i a b j

i,a, j,b,

r, r ' 2 M r r r ' r 'σ τ

−σ σ τ τ

σ τ

χ = − ϕ ϕ ϕ ϕ∑∑

• Independent particle:

• Random Phase:

• General CPKS:

( )ia , jb b j ij abM σ τ στ= ε − ε δ δ δ

( ) ( )ia , jb b j ij abM 2 ia | jbσ τ στ= ε − ε δ δ δ + σ τ

( ) ( ) ( )( )ia , jb b j ij ab xcM 2 ia | jb 2 ia | f r, r ' | jbσ τ στ= ε − ε δ δ δ + σ τ + σ τ

( )( ) ( )

2

xcxc

Ef r, r '

r r '

δ=

δρ δρ

W. Yang, A.J.Cohen, F. De Proft, P. Geerlings, J.Chem.Phys. 136, 144110 (2012)

Home made program (S. Fias) ���� Unintegrated Plots

Pag.

Planar Metallic Systems: Unintegrated plots

Aromaticity order2- - + 2+

4 3 2 2 3 4Al > Al Ge ³ Al Ge AlGe < Ge≥ ≤

Expected order (Feixas et al)

Mainly σ aromatic (∼ 65%)

Insertion of C: decreasing aromaticity, sequence unaltered; but increasing σ component

21/09/2016 36

• The use of unintegrated plots

Benzene 2-

4Al

σ

• in plane• perturbation

at top nucleus

π

• 0.5 au above plane• perturbation in that

plane at top nucleus

σ π

Delocalized Nature of the linear Response more pronounced in the σ electron density

σ Aromatic character

S. Fias, Z. Boisdenghien, T. Stuyver, M. Audiffred, G. Merino, P. Geerlings, F. De Proft, J. Phys. Chem. A, 2013, 117, 3556

( )13 241χ + χ

2→

Pag.21/09/2016 37

2.4 An extension to Alchemical Derivatives:exploring Chemical Space

• Alchemical derivatives ( O.A. Von Lilienfeld, R.D. Lins, U. Röthlisberger, Phys.Rev.Lett., 95, 153002 (2005)

MN,Z ,

E

Zβ

α

∂

∂ ℝ

: change in molecular energy upon changing atomic nuclear charge

alchemical potential cf

M MZ ,R v

E E

N N

∂ ∂ = = µ

∂ ∂ electronic chemical potential

2

2

N,Z ,R

E

Z Zγ

α β

∂ ∂ ∂

cf

2

2

v

E

N

∂= η

∂ electronic chemical hardness

alchemical hardness

Pag.21/09/2016 38

Chemical Significance: navigation through the huge Chemical Compound Space for tracing interesting compounds by “Transmutation Reactions”

N=cte

∆Z= ± 1

Chemical Compound Space: set of all possible combinations of chemical elements prone to form stable compounds

P. Kirkpatrick, C. Ellis, Nature, 432, 823 (2004)

Pag.21/09/2016 39

Instead of calculating the energy of each of the “transmutants”, concentrate on the central compound and its alchemical derivatives

2

N,Z , N,Z ,

E EdZ dZ dZ ...

Z Z Zβ γ

α α βα α βα α β

∂ ∂= + + ∂ ∂ ∂ ∑ ∑∑

ℝ ℝ

alchemical potential alchemical hardness ( diagonal and off-diagonal)

electronic part electronic part

( )rdr

r Rα

ρ−

−∫( )

N,...

rZ

d rr R

β

α

∂ρ ∂

−∫

Pag.21/09/2016 40

Connection with linear response function

( ) ( )( ) ( )2 2

'

N N

v r v r 'E E dr dr '

Z Z Z Zv r v rα α ββ

∂ ∂∂ δ= ∂ ∂ ∂ ∂δ δ ∫ ∫

( )1 1

r, r ' dr dr'r R r Rα β

= χ− −

∫

Pag.21/09/2016 41

Evaluation of the alchemical potential and hardness

Coupled Perturbed Kohn Sham Theory (cf linear response function)

M.Lesiuk, R. Balawender, J. Zachara, J.Chem.Phys., 136, 034104(2012)

Prediction of energies of molecules with charge of the central nuclei changed by ± 1

( ) ( ) ( )iN

i

ii 1

1 EE Z 1 E Z 1

i! Z=

∂± = + ±

∂ ∑

‖

0E

Cf CH4

(HF)

0E 40.214 au= −E

14.752 auZ

∂= −

∂

2

2

E 3.023 au

Z

∂= −

∂

3

3

E 0.135 au

Z

∂= −

∂

( ) ( )0 0 4E Z 1 E NH - 56.500++ = =

( ) ( )0 0 4E Z 1 E BH - 26.950−− = =

cf “exact” 56.565−

26.987−

Pag.21/09/2016 42

For the complete series of six N2 transmutation reactions (B3LYP/cc-pVTZ) an error between “vertical” and alchemical transmutation energies of 0.03 a.u. was obtained

N2 → CO case: 0.004 au ~ 2.5 kcal mol-1

Not “chemical accuracy” yet but the ordering of the energy of the compounds comes out correctly

Straightforward procedure for looking at neighbouring structures when exploring chemical space

Recent quantum chemical interest in Molecular Design

(cf W. Yang et al, JACS, 128, 3228 (2006))

Pag.21/09/2016 43

A more involved application: transmutation of benzene

( ) nn C H N azines− → →

( ) ( )n n

C C B N azoborines− → − →

iso-electronic transmutations

Azoborines • n-sequence correctly reproduced

• sequence of isomers n=1 (3)n=2 (11) n=3 (3)

correctly reproduced

Transmutation energies and alchemical derivates effective tools for stability prediction and exploring CCS

Present work: CC → BN substitution in fullerenes, graphene, …

R. Balawender, M.A. Welearegay, M. Lesiuk, F. De Proft, P. Geerlings, J. Chem.Theor.Comp., 9,5327,(2013)

Pag.21/09/2016 44

3. Molecular Eletrical Conductivity: Molecular Electronic Devices

• Coulson’s atom – atom polarizability as a forerunner of the linear response function

• Coulson – Longuet Higgins (Proc. Roy. Soc, 191, 39 (1947))

qr

HMO =∂Ε

∂αr

πr,s =

∂qr

∂αs

� π r,s =∂2Ε

∂αs∂αr

=∂2Ε

∂αr∂αs

Cfr. χ r( , r ') =δ 2 Ε

δν r( )δν r '( )

Ν

∆ z( ) = Hückel secular determinant

∆ r,r: row r and column r omitted

1

2πi

z∆ '(z)

∆(z)− n

γ

∫ dz = Eπ = 2 ε j

j

occ

∑

qr =1−1

π

∆r,r (iy)

∆(iy)−∞

+∞

∫ dy

Pag.21/09/2016 45

» Transmission: Molecule connected with two semi – infinite contacts

Approximations

• Source – sink potential (B.T. Pickup, P.W. Fowler, Chem. Phys.Lett., 459, 198, (2008))

• Fermi level

• Wide band limit

� Transmission identified with the integrand in the expression for the atom-atom polarizability

T. Stuyver, S. Fias, F. De Proft, P.W. Fowler, P. Geerlings, J.Chem.Phys. 142, 094103 (2015)

∂qr

∂αs

� πr,s =1

π −∞

+∞

∫∆r,r∆s,s − ∆∆rs,rs

∆2dy =

1

π −∞

+∞

∫∆2

rs

∆2dy

Tr,s 0( ) =1

π −∞

+∞

∫∆r,r∆s,s − ∆∆rs,rs

∆2dy =

∆r,s

2 (0)

∆2 (0)

Pag.21/09/2016 46

Pag.21/09/2016 47

A selection rule for nonsingular alternant hydrocarbones was derived through study of X(z) =∆

r ,s(Z)

2

∆2(z)

• Same partite sets: negative atom-atom polarizabilities � devices with insulation at the Fermi level: no transmission

• Opposite sets � positive atom-atom polarizability: conduction or insultation depending whether or not

• Conduction at the Fermi level requires a positive atom-atom polarizability

∆ r,s = 0

Pag.21/09/2016 48

? Intuitive Rationalization which Molecules will conduct under small bias and what the influence is of the positions of the contacts

� ?Need for simple pictorial insight

? Relation to Molecular Reactivity

� Bridging the gap between Molecular Reactivity and Molecular Electronics

Pag.21/09/2016 49

Trs

0( ) = 42

β∆2r,s(0)

∆2(0)

• Introducing Pauling bond order Prs for adjacent atoms r and s of a conjugated system: fraction of resonancestructures with r and s double bounded

• Graph theoretical formulation

Prs

P =K GΘrs( )

K G( )

K= # Kekulé Structures

G= Molecular Graph (C-Skeleton), N.S. Ham, J.Chem. Phys., 29, 1229, (1958)

• Extension: to non adjacent atoms � long bond order (T. Morkawa, S. Narito, D.J. Klein, Chem. Phys. Lett., 402, 554 (2005)

Now: K2 (G) = ∆(0) K2(GΘrs)

=

Prs

P( )2

=∆r, s(0)

∆(0)

2

~ Trs(0)

K(GΘrs)

K(G)

2

= ∆rs,rs

(0)

Transmission � Pauling Bond Order

Pag.21/09/2016 50

Consider Benzene: Kekulé Structure for (GΘr,s) say (GΘ1,4)

� If no curly arrows drawing can be made of the electron displacements between the two atoms

�Pauling long bond order is zero � transmission probability of MED is zero

�Trs Ξ T14 ≠ 0 � transmission

G Θ 1,4

G

Displacement of Electron Pairs in the Kekulé structures of G from r�s (contact atoms)

Pag.21/09/2016 51

The use of curly arrows opens up a connection to the widely used concepts of resonance effects in reactivity theory

Selection RuleAtom-AtomPolarizability

Pag.21/09/2016 52

Application in Photo-, Thermo and Redoxswitches

- Oligo (phenylenevinylene)quinone redox switch

(Q – OPV)

- Conductance ratio: 40, S. Tsoi et al., A.C.S. Nano, 2, 1289 (2008)

T. Stuyver, S. Fias, F. De Proft, P. Geerlings, Chem. Phys. Lett., 630, 51 (2015)T. Stuyver, S. Fias, F. De Proft, P. Geerlings, J. Phys. Chem.C., 119, 26390 (2015)

Pag.21/09/2016 53

Pag.

4. Conclusions

• Conceptual DFT offers a broad spectrum of reactivity descriptors in line with the need for unifying concepts.

• The “missing” second order derivative, the “linear response function”, comes within reach with various techniques of increasing complexity. It is a tool to see how ∆v perturbations are propagated through an atom or molecule. Its physical relevance becomes apparent, thanks to various representations of the kernel for atoms revealing atomic shell structure, and extensions in the context of spin polarized Conceptual DFT

• The computational results on molecules reveal that important chemical information can be retrieved from the linear response function: from inductive and mesomeric effects to the aromatic character of organic and inorganic rings including its evolution during reactions. In the context of alchemical derivatives it opens the gate for exploring chemical compound space in an efficient way.

•An important step towards the link between the linear response function and electrical conductivity has been taken, retrieving the curly arrow approach of organic chemistry.

21/09/2016 54

Pag.

Acknowledgements

Acknowledgements

Prof. Frank De Proft, Dr. Stijn Fias, Dr. Zino Boisdenghien, Dr. Freija De Vleeschouwer

Dr. Nick Sablon

Prof. Paul W. Ayers (Mc Master University, Hamilton, Canada)

Prof. Weitao Yang (Duke University, USA) and Dr. A. J. Cohen (Cambridge, UK)

Dr. R. Balawender and Drs. M. Welearegay (Warsaw, Poland)

Dr. M. Torrent – Sucarrat (Brussels, Girona)

Prof. C. Van Alsenoy (Antwerp, Belgium)

Prof. M. Sola (Girona), Prof. Gabriel Merino (aromaticity)

Fund for Scientific Research-Flanders (Belgium) (FWO)

and the VUB (Strategic Research Program)

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