Pag.
Chemical Concepts from Density Functional Theory
Paul Geerlings
General Chemistry, Vrije Universiteit Brussel, Brussels, Belgium
55th Sanibel Symposium
February 15-20, 2015
13/04/2015 1
Chemistry from the Linear Response Function
Pag.
0. Introduction Interpretive Chemistry : the ongoing need for interpretational concepts and models in quantum chemistry
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• Chemistry as an experimental science → accumulation of data of countless number of molecules (CA > 50.000.000 Substances!)
Need for unifying theories, concepts, models to rationalize, interpret, predict …… in order to avoid an encylopaedic “science”.
• Nowadays: Computational Chemistry (WATOC …)
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.13/04/2015 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.13/04/2015 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. – 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:
13/04/2015 5
( )v r( )rρ
N
opH “everything”
Pag.13/04/2015 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
HKF
v(r)+ =(r)
δµ
δρ
13/04/2015 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, R.A. Donnelly, M.Levy, W.E. Palke, J. Chem. Phys., 68,
3801 (1978))
= - χ (Iczkowski - Margrave electronegativity)
μ
13/04/2015 8
Pag.13-4-2015 913-4-2015 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)
13/04/2015 9
Pag.
Hardness and fukui function have been widely explored but what about the remaining second order derivative?
: linear response function
Fundamental Importance: Information about propagation in the density throughout the system of an (external potential) perturbation at position r’
( )χ r,r'
( ) ( )( )
( )
2
' '
N N
δρ rδ E= =δv r δv r δv r
13/04/2015 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
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Hückel MO Theory: mutual atom-atom polarizability πrs = ∂qr/ ∂αs
C.A. Coulson and H.C. Longuet Higgins, Proc.Roy.Soc.LondonA, 192, 16 (1947)
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
∗∗∗∗
( ) ( )( )KS Nδρ r δv r'∗∗∗∗ Zeroth order approximation to the linear response kernel for
the interacting system
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
13/04/2015 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
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Along diagonal: increasing depletion of ( )v r ( )rρ
Pag.
One dimensional version for a fixed ( )2 'r χ r,r ( )r'=0 2r' r χ r,0→
He
Be
• Positive perturbation δv(r’) v(r’) becomes less negative electron density depletion in the vicinity of the nucleus
• ( ) ( ) ( )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
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Pag.
Extending → the noble gases
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Pag.
χ(r,0) for Ar in the x,y plane
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A direct application → polarizability calculations
( )ij i jα = - dr dr' r χ r,r' r'∫ i,j= x,y,z
• Comparison with high level calculations
• Absolute values deviate, trend is respected
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Z. Boisdenghien, C. Van Alsenoy, F. De Proft, P. Geerlings,J. Chem. Theor. Comp. 9, 1007 (2013)
Pag.13/04/2015 18
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=
s
1v (v v )
2α β= −
1v (v v )
2α 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 s B zv B (r)= µ
Pag.13/04/2015 19
Introduction of
( )( ) ( ) ( )
s s
2
sNS
s N,N N,N
Er, r '
v r v r ' v r '
δ δρχ = =
δ δ δ s α βρ = ρ − ρ
( )( )
( )( )
( )NS
rrr, r '
v r ' v r '
βαδρδρ
χ = −δ δ
: two terms can be expanded (IPM)
Pag.13/04/2015 20
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)
Pag.13/04/2015 21
Li B O
Decreasing difference in sensitivity
NSχ
Difference in n Difference in l No (n,l) difference
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
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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.
13/04/2015 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
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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
13/04/2015 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
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Pag.
Aromaticity
Relation with the para delocalization index (PDI) derived from AIM
Exchange correlation density; integration over atomic basins
• quantitative idea of the number of electrons delocalized or shared between A and B
(X. Fradera, M.A. Austen, R.F.W Bader, JPCA, 103, 304, 1999.)
• investigated as a potential index of aromaticity
(J. Poater, X. Fradera, M. Duran, M. Sola, Chem.Eur. J. , 9, 400, 2003)
• six membered rings of planar PAH’s• successful correlation of the (1,4) (para) delocalization index with NICS, HOMA, …
AB 14δ = δ
1
2
3
4
para
• Does Linear response function contain similar information?1,4χ
( ) ( )1 2 1 2
A B XC
δ A,B = -2 r ,r dr drΓ∫ ∫
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Pag.
16 non equivalent sixrings studied by Sola et al.
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Pag.
• typical benzene-type pattern encountered before
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Pag.
→ Linear response function as an “electronic” descriptor of aromaticity
13/04/2015 30
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)
13/04/2015 31
Digging further in aromaticity →→→→ σσσσ,ππππ aromaticity (applying σσσσ,ππππ separation)
Pag.
Inorganic rings
13/04/2015 32
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
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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)
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Pag.13/04/2015 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)
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
13/04/2015 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, 117, 3556 (2013)
( )13 241χ + χ
2→
Pag.13/04/2015 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)O.A. Von Lilienfeld, IJQC, 13, 1676 (2013)
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.13/04/2015 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.13/04/2015 39
Instead of calculating the energy of each of the “transmutants”, concentrate on the central compound and its alchemical derivatives
M M M M MdE E N, d , E N, , = + − ℤ ℤ ℝ ℤ ℝ
( )M
1 2 MZ , Z ...Z=ℤ nuclear charge vector
( )M
1 2 MR , R ...R=ℝ nuclear position vector
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.13/04/2015 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.13/04/2015 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.13/04/2015 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 M.Wang, X.Hu, D.N. Beratan, W.Yang, JACS, 128, 3228 (2006))
Pag.13/04/2015 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 stabilityprediction 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.
3. 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. In the context of alchemical derivatives it opens the gate for exploring chemical compound space in an efficient way.
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Pag.13/04/2015 45
Ongoing
• The role of the linear response function in conduction of molecular electronic devices.
First results: � atom – atom polarizabilities( Hückel-π-type approach)
T.Stuyver, S.Fias, F.De Proft, P.W.Fowler, P.Geerlings, J.Chem.Phys, 147, xxx, 2015
• The role of DFT based reactivity descriptors in molecular design
Inverse design of stable radicals with highly electrophilic or nucleophilic charachter: roleof the electrophilicity ( ² / 2 )ω µ η=
F.De Vleeschouwer, A.Chankisjijev, W. Yang, P.Geerlings, F. De Proft, J. Org. Chem., 73, 9109 (2013)F.De Vleeschouwer, A.Chankisjijev, P.Geerlings, F.De Proft, Eur.J.Org.Chem,506 (2015)
χ
Pag.
Acknowledgements
Acknowledgements
Prof. Frank De Proft, Dr. Stijn Fias, Drs. 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 (Mexico)
Fund for Scientific Research-Flanders (Belgium) (FWO)
and the VUB (Strategic Research Program)
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Pag.13/04/2015 48
Inverse Molecular Design
Introduction
• Previous part: application of concepts and indices to understand electronic structure and its relation to reactivity for atoms and indices
• Alchemical Derivatives : a first step towards exploring chemical space
• Exploring the properties of molecules encountered upon navigating through molecular space : molecule � property
• Now: design of new compounds with optimized reactivity indices : property� molecule� Inverse Molecular Design
• Case study: design of stable organic radicals
Pag.
• Homolytic bond cleavage of the molecule A-B into the radicals A and B
A − B → A• + B•
• Characterized by the bond dissociation enthalpy (BDE)
• Use BDE to quantify radical stability through a model
stab: intrinsic stability of the radical
Intrinsic Radical Stability Scale
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Pag.
enhanced electrophilicities
(ω=μ²/2η; ωref=2: borderline betweenelectrophilic and nucleophilic radicals
Intrinsic stabilities
Computed BDE (B3P86/6-311+G**)
enhanced electronegativities
χref=3 (~medium value betweenhighest and lowest Pauling.Electronegativity in database)
Performance of the model:
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Pag.
F.De Vleeschouwer, V.Van Speybroeck, M.Waroquier, P.Geerlings, F.De Proft, J. Org. Chem. 2008, 739109
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Pag.
• Use of this model (against H in A-B) to design stable organic radicals� Start from BDE (A-H)
• Inverse molecular design: find an optimal external potential of the system, generating a molecular system with the associated target properties (cfr W.Yang, X.Hu, D.N.Beratan, W.Yang, J.Am.Chem.Soc., 128, 3228 (2006)
• Challenge ! large number of possible structures accessible through the systematic variation of the composition of the molecular system
e.g. for a given framework : 5 sites and 21 substituents yield 215 combinations ~4x106
Inverse design approach
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Pag.
Approach:
1. Choice of a molecular framework of interest
• determine number of sites that can be modified
• determine number of substituents per site
2. Define property of interest to be optimized (here: stab values)
3. Choice of property optimizing method
M.L.Wang, X.Hu, D.N. Beratan, W. Yang, J. Am. Chem. Soc., 128, 3228 (2006)F.De Vleeschouwer, W. Yang, D.N. Beratan, P. Geerlings, F. De Proft, Phys. Chem. Chem. Phys. 14, 16002
(2012)
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Pag.
Molecular framework: thiadiazenyl structure
J.Zienkiewicz, P.Kaszynski, J. Org. Chem., 69, 7525 (2004)
Stable radical: stab = 70 kJ mol−1
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Pag.
5 sites and 21 substituents per site:
size of chemical space = 215 ≅ 4 x 106 molecules
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Pag.
• Choice of property optimizing method: Best-First-Search Methodology
• Algorithm:
• optimizes the property of a molecule by making chemical changes and evaluating the influence of those changes on the property of interest
• chemical changes brought in through the independent site approximation, so the various sites are optimized individually
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(C)-NHCH3
(C)-SOCH3
(C)-OCH3
(C)-SCH3
(C)-SO3H
(C)-COOH
(C)-CF3
(C)-CH3
(C)-CHO
(C)-CFO
(C)-OOH
(C)-SOH
(C)-NH2
(C)-OH
(C)-SH
(C)-CN
(C)-H
(C)-F
(C)-Cl
(C)-Br
(N)
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Results: most stable radicals
stab = 13 kJ mol−1
stab = 19 kJ mol−1
stab = 32 kJ mol−1
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Comparison with other stable organic radicals
20 kJ mol−1 82 kJ mol−1 86 kJ mol−1
33 kJ mol−1 34 kJ mol−1
F.De Vleeschouwer, A.Chankisjijev, W. Yang, P.Geerlings, F. De Proft, J. Org. Chem., 73, 9109 (2013)F.De Vleeschouwer, A.Chankisjijev, P.Geerlings, F.De Proft, Eur.J.Org.Chem, 506 (2015)
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Triphenylmethyl Phenalenyl N,N-diphenyl-N’ - picrylhydrazyl
1,5 - diphenylverdazyl 1,3,5 - triphenylverdazyl
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