The Three-dimensional Potential Energy

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Presentation transcript:

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

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

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

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.

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)**

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

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 2010.1

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

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

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 )

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)

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) : 0.0026 cm-1

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

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%.

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.

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

Comparison of Energy levels in VCO = 1

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.

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)