1 Vrije Universiteit Brussel Molecular Quantum Similarity of Enantiomers: Chiral Axis vs Asymmetric Centra Molecular Quantum Similarity of Enantiomers: Chiral Axis vs Asymmetric Centra Janssens S., Boon G., Geerlings P. Onderzoeksgroep Algemene Chemie (ALGC), Faculteit Wetenschappen, Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium.

2 Vrije Universiteit Brussel 1. Introduction Similarity  Fundamental concept in chemistry / pharmacology Chirality  Lots of pharmacologically important molecules Assume: degree of chirality linked to (dis)similarity of 2 enantiomers dissimilarity = 1- similarity How quantify molecular similarity?

3 Vrije Universiteit Brussel Quantify dissimilarity of enantiomers Global & local similarity indices Orientation! Conformations! Illustration Mezey’s “Holographic Electron Density Theorem”  sp 3, sp 2, sp 1 carbon chirality dissimilarity link 2. Objectives

4 Vrije Universiteit Brussel 3. Similarity indices Carbó index: generalized cosine index MQSM perfect similarity Use next to  (r) also eliminates dominant effect of core electrons

5 Vrije Universiteit Brussel Local SI Hohenberg – Kohn Mezey: Holographic Electron Density Theorem compatible with a single (r)  (r) for a given ground state electrons (r) nuclei E=E  (r), N E=E     (finite, arbitrary subdomain) (r)(r) (positions & charges)

6 Vrije Universiteit Brussel Hirshfeld partitioning Total electron density  (r)  atomic contributions  A (r) Global index converted to local analogue: Promolecular density Contribution C* to total  R (r) Contribution C* to product  R (r)  S (r)

7 Vrije Universiteit Brussel Orientation dependency Translational problem Relative orientation Maximal similarity? Several alignment methods Physico-chemical features Topological-geometrical features  TGSA Maximize similarity  QSSA Align backbone atoms  BB QSSA BB

8 Vrije Universiteit Brussel SI for conformers Boltzmann weighted (BW) SI: BW specific rotation :

9 Vrije Universiteit Brussel 4. Applications Chiral axis 1,3-disubstituted allenes: chiral structures without C* XHC=C=CX’H with XX’=FF, ClCl, BrBr, FCl, FBr, ClBr No conformational flexibility   X H H X C CC   H X H X C CC

10 Vrije Universiteit Brussel Selected alignment 0° 180° 5 7   H X H X CC C   X H H X C C C   H X H X CC C   H X X H C C C

11 Vrije Universiteit Brussel 5. Results: Global SI XHC=C=CX’H BB alignment constraint BB 180° B3LYP/6-31G*  heavy atoms at large distance  global SI  coinciding  global SI  average “non-diagonal” dihalogen allenes 0°  HH, FF, HCl, HCl 180° HF, HF, HH, ClCl

12 Vrije Universiteit Brussel Global SI XHC=C=CX’H BB alignment constraint BB 180° B3LYP/6-31G*  intermediate values  effect heavy halogens cancels out ≠ due to not fully perfect sp 2 character C1, C3 “diagonal” dihalogen allenes 0°  HH, FF, HF, HF 180° HF, HF, HH, FF

13 Vrije Universiteit Brussel Global SI XHC=C=CX’H with XX’=FF, ClCl, BrBr, FCl, FBr, ClBr SI: BrBr < ClBr ≈ FBr < ClCl < FCl < FF sequence of “size” of atoms, follows chemical intuition In line with CHFClBr: coinciding atoms ClCBr > FCBr > HCBr > FCCl > HCCl > HCF heavier halogens superimposed  SI 

14 Vrije Universiteit Brussel Local SI XHC=C=CX’H BB alignment constraint BB 180° B3LYP/6-31G* Extra constraint C1/C3 perfect sp 2 Numerical illustration of Mezey’s Theorem on sp 2 /sp 1 C- atoms Substituent values all =1 within precision considered

15 Vrije Universiteit Brussel Local SI XHC=C=CX’H BB alignment constraint BB 180° B3LYP/6-31G* Extra constraint C1/C3 perfect sp 2 substituents on C at large distance  SI smaller = (FF) or ≠ (FCl) substituents  value = or ≠

16 Vrije Universiteit Brussel Chiral axis vs. chiral center (Boon et al.) Halomethane CHFClBr sp 3 C-atom similar values Simple amino acids: Ala, Asp, Cys, Leu, Ser, Val similar values Boltzmann weighted SI R-C*-COOH NH 2 H sp 2 ≥ sp 1 > sp 3 Chiral axis: less direct chirality source  Mezey’s Theorem less pronounced for allenes

17 Vrije Universiteit Brussel “Calibration” curve RR’C=C=CR”R’”: exp data* of molar rotation  R=CH 3 R’=H R”=CH 3 R’”=H R=CH 3 R’=H R”=CH 2 OH R’”=H R=Ph R’=H R”=CH 3 R’”=H R=Ph R’=CH 3 R”=COOH R’”=CH 3 R=Ph R’=CH 3 R”=COOH R’”=H R=Ph R’=H R”=COOH R’”=H R=Ph R’=H R”=Ph R’”=H *W.Runge, In The Chemistry of Ketenes, Allenes and Related Compounds, Part 1, Editor: S.Patai, Wiley, 1980, p.99

18 Vrije Universiteit Brussel “Calibration” curve exp  theor  theor  reliable y = x R2R2 = y = x =  theor.  exp. B3LYP/6-31G* B3LYP/ G (and solvent effect) R2R2

19 Vrije Universiteit Brussel Link SI - [  ] D XHC=C=CX’H Calculated specific rotation [  ] D  global SI [  ] D SI ‘Mirror’ image pattern, exact nature of correlation not known FFFClFBrClClClBrBrBr FFFClFBrClClClBrBrBr

20 Vrije Universiteit Brussel 6. Outlook 2C*, halogen substituted ethanes X 1 X 2 X 3 C―CY 1 Y 2 Y 3 with X 1,X 2,X 3,Y 1,Y 2,Y 3 = H, F, Cl, Br Conformational flexibility  Boltzmann weighted SI Backbone alignment with C 1, C 2, X, Y superimposed

21 Vrije Universiteit Brussel 7. Conclusions Extension similarity 1C*  0C*, 2C* sp 3  sp 2, sp 1 Global/local SI based on  /   complementary info Numerical illustration of Mezey’s ‘Holographic Electron Density Theorem’ Reliable  due to comparison theory  exp chirality dissimilarity link

22 Vrije Universiteit Brussel Publications G.Boon, C.Van Alsenoy, F.De Proft, P.Bultinck, P.Geerlings, J. Phys. Chem. A, 107, (2003) G.Boon, C.Van Alsenoy, F.De Proft, P.Bultinck, P.Geerlings, J. Phys. Chem. A, 110, 5114 (2006) S.Janssens, G.Boon, P.Geerlings, J. Phys. Chem. A, 110, 9267 (2006) S.Janssens, G.Boon, P.Geerlings, Lecture Series in Computer and Computational Sciences, xxx (2006)

23 Vrije Universiteit Brussel Acknowledgements Prof. Dr. P. Geerlings Dr. G. Boon Thank you for your attention!