1. 3-Dimensional Intermolecular Potential Energy Surface of Ar-SH(2Pi)
Y. Sumiyoshi　and　Y. Endo
The Univ. of Tokyo

2. 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

3. 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 = Å

4. 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

5. 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 = MHz
g = MHz
B = MHz
g = 2109 MHz 2 1

6. 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

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

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

9. 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 : X sec. by P4-3.2 GHz

10. 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

11. 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” = , lines
FTMW
Ar-SH
Transitions of D P = 1 :
P = 1/2 ← 3/2, N” = , lines
weighted by 0.01
Double
Resonance
Pure rotational transitions :
P = 3/2 ← 3/2, J” = , lines
FTMW
Ar-SD
Transitions of D P = 1 :
P = 1/2 ← 3/2, N” = , lines
weighted by 0.01
Double
Resonance

12. 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 !

13. The Average potential q0 q1 q2 Fitted Ab initio Fitted Ab initio
/ cm-1 -
7.380 (61)
(21)
(15)
7.4556
0.1351
2.0208 -
-5.81 (47)
4.3049
8.3933
6.9223 e1 e2 e3 e4 e5 e6
Rm0
/ Å
(27)
(13)
(31)
(32) -
3.9955
0.0886
0.0323
0.1516
0.0370
(81)
(94) -
0.1144
0.3642
0.3085
0.2088
0.0142
0.1020
0.1578
Rm1
Rm2
Rm3
Rm4
Rm5
Rm6 m0
(38) -
0.6523
1.3638
1.3152
0.3654 -
1.0350 m1 m2 m3 m4 m5 m6 g - -

14. The Difference potentialq0 q1
Fitted
Ab initio
Ab initio
V22
/ cm-1
/ Å
/ Å6
(52)
(89)
-4.85 (50) -
0.357 (24)
0.1129
2.9041
5.2550
0.2248
V23
V24
V25 a b k
The Potential of SH a)
Ab initio
16 parameters
s = 9.9 kHz
/ Å-2cm
/ Å-3cm
/ Å-4cm
/ Å-5cm
/ Å k2 k3 k4 k5 re
a) Fixed to the ab initio values

15. 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.

16. 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

17. q-Dependence of the PESR 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.

18. 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

19. 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.

20. 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