3-Dimensional Intermolecular Potential Energy Surface of Ar-SH(2Pi) Y. Sumiyoshi　and　Y. Endo The Univ. of Tokyo

Introduction I High-resolution spectroscopy of radical-complexes Rg-OH, Rg-SH, Ar-HO2, H2O-OH Pure rotational transitions of ArSH and ArSD in the ground state by FTMW spectroscopy Two-dimensional PES of Ar-SH 1. JCP, 113, 10121, 2000 2. JMS, 222, 22, 2003

Introduction II Procedure 1. A PES by ab initio at RCCSD(T)/aVTZ+332 2. Solve the 2D Schrödinger equation on the PES Optimize the 2D PES to reproduce the FTMW data of Ar-SH & Ar-SD Effective correction term for R : R + dR for Ar-SD dR = -0.034 Å

How to investigate the PES A state Energy level structures defined by P Ar Ar-OH J 20 P P Energy / cm-1 S H w Ar-SH 10 -1/2 SEP spectroscopy -3/2 ～10 cm-1 (300 GHz) 1/2 Berry et al. J.Chem.Phys. 96, 7890 (1992) P = 3/2 ～3 cm-1 (90 GHz) Millimeter wave

Energy level structures P = 3/2 3/2 5/2 J =7/2 e f Case a Ar H S ArSH ArSD 5 e Ar N = 5 e f N = 5 e f 4 4 f P = 1/2 H S e 4 e f 3 Case b f e 2 e 3 f f e 1 e 3 2 e f f e 1 Energy / cm-1 e f B = 1724.4 MHz g = 792 MHz B = 1719.3 MHz g = 2109 MHz 2 1

Hamiltonian ～3D analysis ～ Coupling scheme j n = r + l, j = n + s, J = j + L, F = J + I L Ar J r P S H w Total Hamiltonian j + q = r - re

Potential terms ～3D analysis ～ 1. Average potential : ½(VA’+VA”) Expanded by Legendre functions

Potential terms ～3D analysis ～ 2. Difference potential : ½(VA’ -VA”) 3. Coordinate transformation H / D q’ R’ d rC Ar R q S

Basis functions ～3D analysis ～ Total function: 1. Rotation Couple the nuclear spin, I 2. Vibration Intermolecular : Monomer vibration : Gauss-Hermite functions vmax = 17, jmax = 7.5, vs max = 9 Hmax : 48678 X 48678 207 sec. by P4-3.2 GHz

Ab initio calculation ～3D analysis ～ An initial 3-D potential by ab initio calculations RCCSD(T) / aug-cc-pVTZ with bond functions (3sp, 2df, 1g) Total of 1806 points for A’ and A” R : 3.3 ～ 8.0 Å r : 1.21 ～ 1.51 Å q : 0 ～ 180 ° by Molpro 2002

115 lines with parity doublings & Data set to be fitted 115 lines with parity doublings & hyperfine components Pure rotational transitions : P = 3/2 ← 3/2, J” = 1.5 - 7.5, 25 lines FTMW Ar-SH Transitions of D P = 1 : P = 1/2 ← 3/2, N” = 0 - 4, 31 lines weighted by 0.01 Double Resonance Pure rotational transitions : P = 3/2 ← 3/2, J” = 1.5 - 7.5, 36 lines FTMW Ar-SD Transitions of D P = 1 : P = 1/2 ← 3/2, N” = 1 - 4, 23 lines weighted by 0.01 Double Resonance

Least-squares analysis Ar-SH Ar-SD FTMW 0.2 0.1 0.0 O-C / MHz -0.1 -0.2 J’ = 5/2 9/2 13/2 17/2 J’ = 5/2 9/2 13/2 17/2 mmW 0.2 0.1 O-C / MHz 0.0 -0.1 -0.2 J’ = 1/2 3/2 5/2 7/2 9/2 J’ = 1/2 3/2 5/2 7/2 s = 9.9 kHz Without effective correction terms !

The Average potential q0 q1 q2 Fitted Ab initio Fitted Ab initio / cm-1 - 7.380 (61) 14.856 (21) -12.511 (15) 117.9214 7.4556 14.0354 -12.8798 -1.6877 0.1351 2.0208 - -5.81 (47) 20.1060 -15.8818 -5.4035 -18.0012 4.3049 8.3933 6.9223 30.5485 e1 e2 e3 e4 e5 e6 Rm0 / Å 3.96730 (27) 0.08983 (13) 0.03480 (31) 0.14691 (32) - 3.9955 0.0886 0.0323 0.1516 0.0370 -0.0041 -0.0110 0.0176 (81) 0.4884 (94) - 0.1144 0.3642 0.3085 0.2088 0.0142 -0.0464 -0.0290 0.1020 0.1578 Rm1 Rm2 Rm3 Rm4 Rm5 Rm6 m0 13.111 (38) - 12.9371 0.6523 1.3638 1.3152 0.3654 -0.2572 -0.2065 - -0.7377 1.0350 m1 m2 m3 m4 m5 m6 g - 14.2594 - 2.967658

The Difference potential q0 q1 Fitted Ab initio Ab initio V22 / cm-1 / Å / Å6 -68.888(52) -3.415 (89) -4.85 (50) - 0.357 (24) -74.581 -3.0392 -5.0343 -0.7611 0.1129 2.9041 -146205.499 -3.8308 5.2550 -2.4627 0.2248 -0.1386 V23 V24 V25 a b k The Potential of SH a) Ab initio 16 parameters s = 9.9 kHz / Å-2cm-1 209624.021 / Å-3cm-1 -1119853.149 / Å-4cm-1 4980100.247 / Å-5cm-1 -13683020.268 / Å 1.346282 k2 k3 k4 k5 re a) Fixed to the ab initio values

PESs of ArSH : Average & Difference potentials 5.5 -50 (VA’ + VA’’)/2 : VP (R, q = 0, q ) -70 4.5 R / ang. -90 -110 -110 -130 3.5 5.5 R / ang. (VA’ - VA’’)/2 : V2(R, q = 0, q ) 4.5 -20 -40 -300 3.5 60 120 180 q / deg.

Comparison of potentials Minimum energy path at re Ab initio fitted 4.2 R / ang. 4.0 Ar-OH -3/2 -1/2 Ar-SH 3.8 -85 -95 Ar-SH -105 -1/2 E / cm-1 -115 -3/2 -125 1/2 P = 3/2 -135 -145 60 q / deg. 120 180

q-Dependence of the PES R Ar R Ar H S q = -0.1 0.0 0.1 H S q = 0 q = 60 -40 E / cm-1 -80 -120 3.5 4.5 5.5 3.5 4.5 5.5 R / ang. R / ang.

Summary Energy level structure of the P = 1/2 state has been characterized: (i) Hund’s case (b), (ii) Significantly different between Ar-SH and Ar-SD. All data of Ar-SH and Ar-SD have been reproduced without the effective correction terms 3. The 3D-PES of Ar-SH has been determined. Future 1. Observation of the P = –1/2 and –3/2 states of Ar-SH 2. Rg-SH, Rg-OH

q = 0 q = -0.1 0.0 0.1 Ar-SH Ar-OH -40 -60 E / cm-1 -100 -80 -120 -140 3.5 4.5 5.5 3.0 4.0 5.0 R / ang. R / ang.

Dipole moment SH OH Exp. m / Debye Exp. R / ang. R / ang. 0.80 1.70 0.76 1.66 m / Debye Exp. 0.72 1.62 1.26 1.36 1.46 0.90 1.00 1.10 R / ang. R / ang. RCCSD(T)/av5z