1. Ab Initio Calculations of the Ground Electronic States of the C 3 Ar and C 3 Ne Complexes Yi-Ren Chen, Yi-Jen Wang, and Yen-Chu Hsu Institute of Atomic and Molecular Sciences Academia Sinica Taiwan, R. O. C. National Science Council, R. O. C.

2. The equilibrium geometry of the ground electronic state of the C 3 -Ar vdW complex has been determined by ab initio calculation at the level of CCSD(T)/cc-pVQZ. 3.916Å Ar C C C 1.298Å 73.73 o 179.3 o Zhang et.al., J. Chem. Phys.120, 3189(2004).

3. Chao et.al., J. Chem. Phys.134, 074313(2011).

4. PHO Model

6. The levels observed in the C 3 -Ne complex cannot be assigned by this model!! But,

7. Zhang et. al., Mol. Phys. (2008) CCSD(T)/cc-pVTZ, 3S3P2d  C-C-C=180°, ℓ (C-C)=1.29497 Å 2D-DVR

8. The A rotational constant of C 3 Ar should be the same as the B rotational constant of free C 3, assuming the Ar atom only affects the bonding in the C 3 part slightly. A(C 3 Ar) is found to be larger than B(C 3 ) 0.4549 cm  0.4305 cm  Therefore the top of the T is tilted. With these values of A and B, simple geometry shows that the tilt angle is 12.4 o C C C Ar 12.4 o MI09

9. Computation Details 1.Potential energy obtained from ab initio calculations C 3 Ar, CCSD(T)/cc-pVQZ using Molpro program 46550 points in the internal coordinates: ρ (the bond angle of C 3 )=112-248°, C r(C-C bond length of C 3 )= 1.2981Å, Ar R (the vdW bond length between Ar and the r (fixed)  center of mass of C 3 )=3.4-6.0 Å, R azimuth angle  (the angle between the vector  R and the principal axis of C 3 )=0-180°, Z colatitudes angle  =0-90°. r (fixed) C Equilibrium geometry of C 3 Ar: ρ=179.5°, R=3.9 Å, r= 1.2981Å,  =74°, and  =7° C ρ

10. Fig. 3 Contour plot of the calculated energies of C 3 -Ar complex with a fixed  C-C-C(=173.75º). The in-plane bending angle varies from 0-360 degrees, and the bond length of the Ar atom to the center of mass of C 3 varies from 3.4 to 4.4Å.

12. Fig. 7. Contour plot of the calculated energies of C 3 -Ar complex with a fixed  C-C-C(=160º) and a fixed bond length (3.6Å) between the Ar atom to the C. M. of C 3. The in-plane bending angle varies from 0 to 360 degrees, and the out-of-plane bending angle varies from 0 to 90 degrees.

13. The obtained potential energy points covering energies up to 19,736.8 cm -1 were fitted to an analytical function in terms of internal coordinates with one σ of 0.63 cm -1., where,, R 0 =3.9 and 3.7Å for the Ar and Ne complexes, respectively. Assuming that the presence of the rare gas atom would not change the C-C stretch potential, the stretch potential of C 3 monomer was added to the 4-D potential to obtain a full 6-D potential of C 3 -Rg. V (r 1,r 2,R, , θ,  )≈V( R, , θ,  )+V( r 1,r 2,  )- V(  ) Therein the stretch-bending potential of C 3 was calculated at CCSD(T)/aug-cc-pVQZ in the range of (C-C) =1.1-1.5 Å and  C-C-C=70-179.5 . This gives additional vibrational energy up to 7756cm -1. One standard deviation of the fitting error of C 3 potential is 2.6cm -1.

14. C 3 Ar C 3 Ne basis set cc-pVQZ aug-cc-pVQZ method CCSD(T) CCSD(T) with the correction of the basis-set superposition error vdW bond length, R 3.4-6.0 Å 3.0-7.0 Å azimuth angle,  0-180  colatitudes angle,  0-90  C-C bond length, r 1.2981Å ∠ C-C-C,  112-248  106-254  # of ab initio points 46550 62178 Equilibrium geometry ρ=179.5°, R=3.9 Å, r= 1.2981Å,  =74°, and  =7° ρ=170°, R=3.6 Å, r= 1.2981Å,  =80°, and  =0°. Energy range 0-19736.8 cm -1 0-26252 cm -1 PE fitting error 0.63 cm -1 0.86 cm -1

15. Conclusions 1. The 4D-potential energy functions of C 3 Ar and C 3 Ne were calculated at the level of CCSD(T)/cc-pVQZ or aug-cc-pVQZ. The C-C stretch potential energies were added to the 4D potential energies by assuming the vdW bend and stretch energies do not depend upon the C-C bond distances. This assumption was made because we are interested in the vibrational level structures of these two complexes for the first 800 cm -1 region. 2. An improved potential energy fit of C 3 Ne has been made by dividing the calculated PE into two regions such as energies below 200 cm -1 and energies above 200 cm -1. For instance, 67475 points were fit by 6384 parameters with one standard deviation of fit of 0.22 cm -1. 3. The equilibrium vdW bond length of C 3 Ar calculated by us is 3.9 Å, longer than that (3.8Å) reported Zhang et. al.