1. The Three-dimensional Potential Energy
Surface of Ar-CO
Yoshihiro Sumiyoshi1, 　Yasuki Endo2
1. Faculty of Science and Technology, Gunma University
2. Graduate School of Arts and Sciences, University of Tokyo

2. Previous studies on Ar-CO
T. Ogata, et al., J. Chem. Phys. 98, 9399 (1993)
W. Jaeger, et al., J. Chem. Phys. 102, 3578 (1995)
V. N. Markov, et al., Rev. Sci. Inst. 69, 4061 (1998)
M. Hepp, et al., J. Mol. Spectrosc. 176, 58 (1996)
M. Hepp, et al., Mol. Phys. 92, 229 (1997)
M. Hepp, et al., J. Mol. Spectrosc. 183, 295 (1997)
R. Gendriesch, et al., J. Mol. Spectrosc. 196, 139 (1999)
L. A. Surin, et al., Rev. Sci. Inst. 72, 2535 (2001)
D. G. Melnik, et al., J. Chem. Phys. 114, 6100 (2001) MW
& mmW
R. W. McKellar, J. Mol. Spectrosc. 153, 475 (1992)
Y. Xu, et al., Mol. Phys. 88, 859 (1996)
Y. Xu, et al., Mol. Phys. 87, 1071 (1996)
S. Koenig, et al., Mol. Phys. 91, 265 (1997)
A. R. W. McKellar, Mol. Phys. 98, 111 (2000)
I. Scheele, et al., Mol. Phys. 99, 197 (2001)
I. Scheele, et al., Mol. Phys. 99, 205 (2001)
I. Scheele, et al., Mol. Phys. 101, 1423 (2003) IR
R. R. Toczylowski , et al., J. Chem. Phys. 112, 4604 (2000)
CCSD(T) / aug-cc-pVTZ
T. B. Pederson, et al., J. Chem. Phys. 117, 6562 (2002)
CCSD(T) / aug-cc-pVQZ
Ab initio

3. Previous studies on Ar-CO
L. H. Coudert, et al., J. Chem. Phys. 121, 4691 (2004)
M. Havenith and G. W. Schwaab,
Z. Phys. Chem. 219, 1053 (2005)
2D-IPES
(fitting)
Attacking a Small Beast: Ar-CO, a Prototype for Intermolecular Forces
“No satisfactory analysis has been carried out.”
Intermolecular potential energy surface (3D-IPES)
by directly fitting all available transition frequencies

4. Coupling Scheme C r q K R G Ar O j L J G : The center of mass of CO
R : Distance between G and Rg.
r : CO bond length.
q : Angle between R and r.

5. Observed ro-vibrational levels
MW & mmW : ~ 200 lines
IR : ~ 830 lines 80
(0, 6, 6)*
(vvdW, j, K) 60
(3, 1, 0)*
(0, 5, 5)
Energy / cm-1 40
(0, 4, 4)
(1, 2, 0)*
(0, 3, 2)*
(1, 1, 0)*
(0, 3, 3)
(1, 1, 1)* 20
(0, 2, 1)
(1, 0, 0)
(0, 1, 0)
(0, 2, 2)
(vvdW, j, K) vco = 0, 1
(vvdW, j, K)* vco = 1
(vvdW, j, K)** vco = 0, 1, 2
(0, 1, 1)**
(0, 0, 0)**

6. upper lower n0 N weight Ar-12CO mmW: 5 IR: 25 Ar-13CO
(vCO, vvdW, j, K)
(vCO, vvdW, j, K) n0 N
weight
Ar-12CO
mmW: 5 * * *
Pederson, et al., J. Chem. Phys.
117, 6562 (2002) * *
IR: 25
Ar-13CO

7. Ab initio calculations
An initial 3-D potential by ab initio calculations
CCSD(T) -F12b/ aug-cc-pV5Z
2450 points
R : 3.3 ～ 15.0 Å
r : 1.00 ～ 1.35 Å
q : 0 ～ 180 °
Molpro

8. Total Hamiltonian ～3D analysis ～
Htotal = HArCO + HCO

9. Potential terms ～3D IPES ～
Short range term
Legendre polynomial
Asymptotic term
A total of 46 parameters are used
to fit the ab initio potential surfaces
s : 0.32 cm-1

10. 3 Dimensional Potential
/13C
q ’ G’ r’ R’
V(R’, r’, q ’)
3D potential surfaces
IR data
12C r r’
12CO
13CO
Ar-12CO
Ar-13CO
MW data r G q Rg R O
V(R, r, q )

11. Eigenvalue calculation
Total function:
1. Rotation: Rotation matrix
jmax = 18
2. Vibration: anharmonic/harmonic oscillator
vdW stretching vibration
vmax = 15/40
CO vibration
vsmax = 7/35
Hamiltonian matrices to be diagonalized: ≈ 20000
Discrete variable representation(DVR)

12. Least-squares fitting
Direct fit of observed transition frequencies
MW data (12 lines) : 1.0
mmW data (195 lines) : 1.0 x 10-2 ~ 1.0 x 10-4
IR data (831 lines) : 1.0 x 10-6 ~ 1.0 x 10-8
Total : 1038 lines:
20 potential parameters were optimized
rms(MW) : 32 kHz (Ar-12CO / 13CO)
rms(mmW) : 970 kHz
rms(IR) : cm-1

13. PES of Ar-CO O Ar C C O Ar O Ar C
R / Å
q /deg.

14. Potential curve fitted CCSD(T)-F12/ AV5Z Rmin(q) CCSD(T)/ AVQZ(33211)
Re = 3.72 Å
Dn (J = 2-1) 0.9%
R / Å
Re = 3.68 Å at = 85° C O Ar
q /deg. O Ar C
The present ab initio PES predicts transition frequency
for J = 2-1 at 8284 MHz within 0.026%.

15. Potential curve fitted CCSD(T)-F12/ AV5Z V(Re, q, q = 0)
CCSD(T)/ AVQZ(33211)
De = 102 cm-1
De = 107 cm-1
D0 = 83 cm-1
De = 108 cm-1
E / cm-1
q /deg.

16. Observed ro-vibrational levels
IR transition
(vCO, vvdW, j, K)
(1, 0, 6, 6)
(0, 0, 5, 5)
Rotational state with J’ = 14
has been observed J’ 14 85
Present: 84.5 cm-1 13
D0 (vCO = 1) 80
CCSD(T) / AVQZ(33211):
79 cm-1 9 6

17. Comparison of Energy levels in VCO = 1

18. Bending excited states with vCO = 1
Y2 > 5%
(4% step)
J = 1(-)
(1, 1, 1)
Bending excited states
with vCO = 1
R / Å
E / cm-1
+40
(vvdW, j, K)
(1, 2, 0)
(0, 3, 2)
(1, 1, 0)
(1, 1, 1)
+20
(1, 1, 0)
(0, 2, 1)
(0, 1, 0)
3141.6
R / Å
q /deg.

19. Summary All the spectroscopic data (1038 lines),
MW(Ar-12CO, Ar-13CO), mmW, and IR(vCO=1, 2),
have been fitted simultaneously, and the 3D-IPES
has been determined.
Unobserved states have been predicted.
(vCO, vvdW, j, K)
(1, 1, 2, 1)
Higher by 35 cm-1 than
the state (1, 0, 0, 0)
(1, 1, 2, 2)