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.

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 Å Ar C C C 1.298Å o o Zhang et.al., J. Chem. Phys.120, 3189(2004).

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

PHO Model

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

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

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 ) cm  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

Computation Details 1.Potential energy obtained from ab initio calculations C 3 Ar, CCSD(T)/cc-pVQZ using Molpro program points in the internal coordinates: ρ (the bond angle of C 3 )= °, C r(C-C bond length of C 3 )= Å, Ar R (the vdW bond length between Ar and the r (fixed)  center of mass of C 3 )= 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= Å,  =74°, and  =7° C ρ

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 degrees, and the bond length of the Ar atom to the center of mass of C 3 varies from 3.4 to 4.4Å.

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.

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) = Å and  C-C-C= . This gives additional vibrational energy up to 7756cm -1. One standard deviation of the fitting error of C 3 potential is 2.6cm -1.

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 Å Å azimuth angle,   colatitudes angle,  0-90  C-C bond length, r Å ∠ C-C-C,    # of ab initio points Equilibrium geometry ρ=179.5°, R=3.9 Å, r= Å,  =74°, and  =7° ρ=170°, R=3.6 Å, r= Å,  =80°, and  =0°. Energy range cm cm -1 PE fitting error 0.63 cm cm -1

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, points were fit by 6384 parameters with one standard deviation of fit of 0.22 cm 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.