1) The document summarizes research on the bonding in the carbon dimer (C2) molecule and analogous eight valence electron species. 2) Computational studies using DFT, CASSCF, and full configuration interaction methods show that C2 has multi-reference character in its ground state with a bond order between 2 and 3. 3) Thermodynamic calculations estimate the bond dissociation energy of the proposed fourth bond in C2 to be 12-17 kcal/mol, supporting its existence. 4) Similar quadruple bonding may exist in other isoelectronic molecules and higher carbides based on computational evidence.

1. STUDY OF BONDING IN C2 AND
ANALOGOUS EIGHT VALENCE
SPECIES
SAYANTAN MONDAL
Roll- 91/CEM/131027
Reg. No. A01-1112-0634-10
Department of Chemistry
University of Calcutta
1

2. DEPARTMENT OF CHEMISTRY
University of Calcutta
UNIVERSITY COLLEGE OF SCIENCE, TECHNOLOGY AND
AGRICULTURE
92 A.P.C. ROAD, KOL-700 009
2

3. One Molecule, Two Atoms, Three Views, Four Bonds?**
Sason Shaik,* Henry S. Rzepa,* and Roald Hoffman*
Angewandte
And Finally
Chemical Bonding
3

4. Existence of C2 Molecule
 Blue Colour of hot hydrocarbon flames (Emission
from excited C2).
 Astrophysical environment (Responsible for the aqua
hue in some Comets).
COMET ISON
Discovered on 21st
Sept. 2012 (Russia)
4

5. Valence molecular orbitals of C2 at Ground State
(The energy scale is schematic, 1s combinations are omitted)
Bond Order = 2
E
5

6. Carbon-Carbon Bond lengths
1.54 Å 1.34 Å 1.20 Å
(ethane) (ethelene) (acytelene)
In Diatomic Carbon the equilibrium bond length is
1.243 Å
Ref : “Bond length and bond multiplicity : σ-bonds prevent short π-bonds”
E.D.Jemmis, B.Pathak, R.B.King, H.F. Schaefer; Chem. Comm. 2006 (2164-2166)
6

7. Possible Causes :
1. The suspended π bonds are shorter than σ+π bonds
2. The antibonding MO (2σu) is less antibonding i.e it can
not compensate the bonding effect of the bonding MO
(2σg )
If so, The bond order would be close to THREE !
7

8. Inverted bond
C2 Molecule [1.1.1] propellane
Ref : W . Wu, J. Gu, J. Song, S. Shaik, P.C. Hiberty; Angew. Chem. 2009, 121,
(1435-1438) 8

9. Ref : R. S. Mulliken, Phys. Rev. 1939, 56, 778 – 781.
Mulliken’s Foresight
9

10. Ref : R. S. Mulliken, Phys. Rev. 1939, 56, 778 – 781.
Mulliken’s Foresight
Diatomic Carbon is Quadruply Bonded in a High Lying Excited State
10

11. C-C distances in some extended carbides containing C2 units.
Ref : W. Jeitschko, M. H. Gerss, R. Hoffmann, S. Lee, J. Less-Common Met. 1989, 156, 397 – 412.
J. Li, R. Hoffmann, Chem. Mater.. 1989, 1, 83 – 101; H.-J. Meyer,R. Hoffmann, Z. Anorg. Allg.
Chem. 1992, 607, 57–71; J.R.
Long, J.-F. Halet, J.-Y. Saillard, R. Hoffmann, H.- J. Meyer, New J. Chem. 1992, 16, 839 – 846; H.
Deng, R. Hoffmann, Inorg.
Chem. 1993, 32, 1991 – 1996; E. F. Merschrod, S. H. Tang, R. Hoffmann, Z. Naturforsch. B 1998,
53, 322. 11

12. Bond lengths in CaC2 in different phases
1.242Å
1.065Å
1.19Å
1.216Å
Space group ‘P 1 21/a1'
Space group 'C 12/c1' Space Group ‘14/m m m'
Space Group ‘P 1 21/a1'
12

13. Calcium Carbide is used to send TIN-CAN ROCKETS !
13

14. Molecule Wiberg Bond Order Equilibrium Bond Dist. (Ǻ)
C2 3.7660 1.26
Si2 3.1450 2.07
Ge2 2.0093 2.16
BN 3.0524 1.24
CN+ 3.5889 1.18
BC- 3.6777 1.39
Wiberg Bond Order Analysis
DFT Calculations (Gaussian 09 outputs)
B3LYP/6-31+G(d,p)
14

15. DFT Calculations
B3LYP/6-31+G(d,p)
C2 Singlet Energy = -75.888 a.u
C2 Triplet (first excited) Energy= -75.925 a.u
This level is showing OPEN SHELL diradical structure
Contradicting many previous studies on the same molecule
15

16. NEED TO CHECK MULTI-REFERENCE
CHARACTER (IF ANY )
TOOLS :
• Full Configurational Interaction (FCI)
• Complete Active Space Self Consistent Field (CASSCF)
• Multi Reference Configurational Interaction (MRCI)
16

17. CASSCF (8/8) Results
Str. No Configuration Coefficcient Weight(%)
1 KK(2σg)2(2σu)2(1πu)4 0.8525036 72.25
2 KK(2σg)2(1πu)4 (3σg)2 -0.3364305 11.29
3 KK(2σg)2(2σu)1(1πu)1(1πu)2 (3σg)1(1πu)1 0.1934542 03.74
4 KK(2σg)2(2σu)1(1πu)2 (1πu)1 (3σg)1(1πu)1 -0.1934542 03.74
5 KK(2σg)2(2σu)2(1πu)2 (1πu)2 -0.1224776 01.49
Basis Set : 6-31+G(d,p)
17

18. Significant Contributions
Config. 1 Config. 2
Coefficient = 0.8525036 Coefficient = -0.3364305
% Weight = 72.25 % Weight = 11.29
18

19. CASSCF Shows ---
Energy of C2 Singlet = -75.60 a.u
Energy of C2 Triplet = -75.58 a.u
Singlet state is more stable than triplet by 0.02 a.u that is,
12.54 Kcal/mol energy
19

20. The Ground State of C2 Shows distinct
Multi-Reference Character
Bond Order in between 2 and 3
20

21. Is there a fourth bond?
• Dimerisation of C2 to form C4 (:C=C=C=C:) is exothermic by
~170 Kcal/mol
(Source : NIST webbook)
• If it is a diradical, there should be hardly any barrier to dimerise.
• This fact accounts for another bond !
21

22. Calculation using Thermodynamic Data
• Using consecutive BDEs of C-H bonds of Acetylene
The first BDE of HCCH is 130-134 Kcal/mol
(HCCH HCC٠+٠H)
the second BDE is 110-117 Kcal/mol
(HCC٠ ٠CC٠+٠H)
• BDE of 4th Bond (!) = 14-30 Kcal/mol
22

23. BDE of the 4th bond can be thought of as the
energy required to untangle the singlet pair to the
next triplet
ΔE=12.54 Kcal/mol
C C
C C
Energy of the Fourth Bond in C2
is ~ 12-17 Kcal/mol
(Full CI result;
Nature Chem. March. 2012, Vol. 4)
23

24. 24
Conclusions:
• C2 has multi reference character in its ground state
and excited states.
• The higher analogues like Si2 and Ge2 , due to their
larger size can not form multiple bonds (higher
than 3)
• Other first row isoelectronic molecules (including
C2) may show quadruple bonds. (Full CI must be
done; already reported)

25. Similar quadruple bonding in isoelectronic species
*Ref : S. Shaik, D. Danovich, W. Wu, P. Su, H. S. Rzepa, P. C. Hiberty,
Nat. Chem. 2012, 4, 195 – 200.
25
Full CI study of analogous eight valence species*

26. References :
[1] J. Chem. Theo. Comput. 2011, 7, 121-130; Bonding Conundrums in the
C2 Molecule : A Valence Bond Study ; P.Su, J.Wu, J.Gu, Wei Wu, Sason Shaik
and Phillippe C. Hiberty
[2] W. Wu, J. Gu, J. Song, S. Shaik, P. C. Hiberty, Angew. Chem. 2009, 121,
1435 – 1438;
Angew. Chem. Int. Ed. 2008, 48, 1407 –1410.
[3] R. S. Mulliken. Phys. Rev. 1939, 56, 778-781
[4] Journal of Molecular Structure: THEOCHEM; Symmetry decomposition
of quantum chemical bond orders; Olga V. Sizova *, Leonid V. Skripnikov,
Alexander Yu. Sokolov
26

27. [5] Grimme, S. Semiempirical hybrid density functional with perturbative
second order correlation. J. Chem. Phys. 124, 034108 (2006).
[6] Quadruple bonding in C2 and analogous eight-valence electron species :
Sason Shaik*, David Danovich, WeiWu, Peifeng Su, Henry S. Rzepa and Philippe
C. Hiberty, 2012, Nature Chemistry. Vol. 4 (195-200)
[7] R. I. Kaiser, M. Goswami, P. Maksyutenko, F. Zhang, Y. S. Kim, A. Landera, A.
M. Mebel, J. Phys. Chem. A 2011, 115, 10251 –10258.
27

28. Project Supervisor
Dr. Ayan Datta
Associate Professor
Department of Spectroscopy
Indian Association for the Cultivation of Science
Jadavpur, Kolkata
Saied Md Pratik
Sarmistha Karmakar
My Teachers and Friends
28

29. 29