ACCURATE ANALYTIC POTENTIAL FUNCTIONS FOR THE A31 and …
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ACCURATE ANALYTIC POTENTIAL FUNCTIONS FOR THE A 3 Π 1 and X 1 Σ + STATES OF IBr T.Yukiya * , N. Nishimiya * , M.Suzuki * , and R. J. LeRoy ** *Dept. of Electronics and Information Technology, Tokyo Polytechnic University, Iiyama 1583, Atsugi City, Kanagawa 243-0297, Japan ** Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada Jun. 16, 2014 T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 1 / 22
Transcript of ACCURATE ANALYTIC POTENTIAL FUNCTIONS FOR THE A31 and …
ACCURATE ANALYTIC POTENTIAL FUNCTIONS FOR THE A31 and X1+ STATES OF
IBr ACCURATE ANALYTIC POTENTIAL FUNCTIONS FOR THE A 3Π1 and X 1Σ+
STATES OF IBr
T.Yukiya∗, N. Nishimiya∗, M.Suzuki∗, and R. J. Le Roy∗∗
*Dept. of Electronics and Information Technology, Tokyo Polytechnic University, Iiyama 1583, Atsugi City, Kanagawa 243-0297, Japan
** Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Jun. 16, 2014
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 1 / 22
Our Objectives
Define frequency standards based on the A–X transition of IBr Determine reliable spectroscopic constants for calculation of line positions Provide realistic predictions for the unobserved levels of IBr Obtain accurate analytic potential energy functions for the A and X state
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 2 / 22
References
the A –X system 1932 W.G. Brown, "Absorption Spectrum of Iodine Bromide"
1962 L.E.Selin, "Analysis of the absorption spectrum of IBr "
1967 M.A.A.CLYNE AND J.A.COXON, "The Emission Spectra of Br and IBr Formed in Atomic Recombination Processes"
1994 D. R. T. Appadoo, P. F. Bernath, Robert J. Le Roy , "High-resolution visible spectrum for the A 3Π1 ← X 1Σ+ system of IBr"
1995 N. Nishimiya , T .Yukiya and M .Suzuki, "Laser Spectroscopy of the A 3Π1 ← X 1Σ+ System of IBr"
2002 T. Yukiya, N. Nishimiya and M. Suzuki , "High-Resolution Laser Spectroscopy of the A 3Π1 ← X 1Σ+ System of IBr with a Titanium:Sapphire Ring Laser"
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 3 / 22
References
the X state 1975 E.Tiemann and Th.Möller,"Rotational Spectrum of IBr"
1976 E. M. Weinstock ,"The laser-induced fluorescence of IBr79"
1993 J. M. Campbell, P. F. Bernath,"Vibration-rotation spectrum of iodine monobromide"
1998 B. Nelander, V. Sablinskas, M. Dulick, V.Braun and P. F. Bernath,"High resolution far infrared spectroscopy of IBr using a synchrotron source"
Related Research on the A state 1982 M. Saute, M. Aubert–Frécon,"Calculated long-range potential-energy curves for the 23 molecular states of I2"
1986 F. Martin, R. Bacis, S. Churassy, J. Vergès, "Laser-induced-fluorescence Fourier transform spectrometry of the X0g
+ state of I2: Extensive analysis of the B0u + → X0g
+
1994 J.O.Clevenger, Q.P.Ray, J.Tellinghuisen, X.Zheng and M.C.Heaven ,"Spectroscopy of metastable species in a free-jet expansion: the β← A transition in IBr"
2000 E. Wrede, S. Laubach, S. Schulenburg, A. J. Orr-Ewing, M. N. R. Ashfold, Velocity map imaging of the near-threshold photodissociation of IBr: accurate determination of De(I–Br)
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 4 / 22
Experimental system
Ar +Ion Laser
GP−IB BusOsc.
Lock−in Amp.
Lock−in Amp.
Lock−in Amp.
Lock−in Amp.
Room Temparature
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 5 / 22
Absorption Spectrum of IBr near 12568 cm−1
12567.0 12568.0 12569.0 12570.0
I79Br8-2 R(96)
I79Br10-3 Q(71)
I81Br8-2 P(92)
I79Br10-3 R(73)
I79Br10-3 P(69)
I81Br8-2 Q(94)
I81Br12-4 R(31)
I79Br11-3 Q(98)
I81Br12-4 Q(29)
I81Br13-4 R(72)
I79Br12-4 R(30)
I79Br12-4 Q(28)
I81Br14-4 Q(92)
I81Br12-4 P(27)
I79Br14-4 Q(91)
I81Br8-2 R(96)
I79Br12-4 P(26)
I79Br13-4 R(71)
I81Br7-2 Q(54)
I81Br10-3 Q(71)
I81Br10-3 R(73)
I81Br13-4 Q(70)
I79Br11-3 P(96)
I81Br10-3 P(69)
I79Br7-2 Q(54)
I81Br12-4 R(30)
I81Br12-4 Q(28)
I79Br12-4 R(29)
I79Br13-4 Q(69)
I79Br12-4 Q(27)
I81Br12-4 P(26)
I79Br12-4 P(25)
I81Br13-4 P(68)
I79Br8-2 P(91)
I81Br14-4 P(90)
I81Br12-4 R(29)
I81Br12-4 Q(27)
I79Br14-4 P(89)
I79Br13-4 P(67)
I79Br12-4 R(28)
I79Br8-2 Q(93)
I79Br10-3 Q(70)
I79Br12-4 Q(26)
I81Br11-3 Q(98)
I79Br10-3 R(72)
I81Br7-2 Q(53)
I81Br12-4 P(25)
I79Br10-3 P(68)
I79Br12-4 P(24)
I81Br14-4 R(93)
I79Br14-4 R(92)
I79Br7-2 Q(53)
I79Br8-2 R(95)
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 6 / 22
Observed Band System of I79/81Br
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
v '
Appadoo Q PR
New Data
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 7 / 22
Rotational levels assigned for the A state.
0
20
40
60
80
100
120
J’
v’
Yukiya Appadoo
New Data
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 8 / 22
Bands constants of the A state The Band Constants for the A State of I79Br
v′ T ′v B′v q′v × 105 D′v × 107 H′v × 1011
3 12821.6070 (51) 0.0408629 (78) -0.195 (31) 0.000 (35) 4 12943.1777 (19) 0.0404527 (22) 0.290(45) -0.2050(69) -0.0050(59) 5 13061.1857 (12) 0.0400228 (14) 0.430(24) -0.2184(39) -0.0050(30) 6 13175.51370(93) 0.0395677 (11) 0.490(20) -0.2292(32) -0.0070(24) 7 13286.00970(94) 0.0390916 (11) 0.530(24) -0.2476(31) -0.0070(24) 8 13392.53260(87) 0.03858700(100) 0.550(17) -0.2646(30) -0.0100(24) 9 13494.92630(89) 0.03805470(95) 0.590(15) -0.2900(26) -0.0100(19)
10 13593.03060(93) 0.03748860(99) 0.630(16) -0.3157(27) -0.0130(20) 11 13686.68470(84) 0.03688550(93) 0.670(16) -0.3458(26) -0.0160(19) 12 13775.72750(92) 0.03624380(98) 0.740(16) -0.3832(26) -0.0190(19) 13 13860.00310(89) 0.03555770(100) 0.770(18) -0.4199(28) -0.0280(21) 14 13939.3795 (12) 0.0348267 (13) 0.920(25) -0.4667(35) -0.0330(27) 15 14013.7549 (12) 0.0340503 (13) 0.990(21) -0.5210(35) -0.0410(26) 16 14083.0733 (12) 0.0332291 (13) 1.100(23) -0.5818(37) -0.0490(28) 17 14147.3447 (18) 0.0323658 (22) 1.250(49) -0.6421(62) -0.0610(45) 18 14206.6706 (24) 0.0314677 (32) 1.400(55) -0.696 (11) -0.080 (11) 19 14261.2366 (15) 0.0305500 (20) 1.360(48) -0.7630(61) -0.0840(47) 20 14311.3259 (14) 0.0296241 (19) 1.700(100) -0.8240(59) -0.0890(44) 21 14357.2655 (23) 0.0287231 (19) 1.690(85) -0.9650(34) 22 14399.4560 (45) 0.0278190 (47) 1.90 (14) -1.0090(99) 23 14438.2680 (25) 0.0269300 (38) 2.60 (19) -1.0510(84) 24 14474.0480 (32) 0.0260500 (60) 2.90 (35) -1.050 (22) 25 14507.0719 (20) 0.0252258 (33) 6.50 (16) -1.1060(98) 26 14537.584 (15) 0.024399 (18) -1.340 (52) 27 14565.8190 (28) 0.0236100 (39) 2.70 (14) -1.9090(93) 28 14591.9560 (42) 0.0227920 (54) 10.80 (21) -3.920 (12) 29 14615.9180 (63) 0.021883 (16) 5.70 (59) -4.620 (75)
in cm−1 and σ in parentheses DRMS:1.486
-10.0
-9.0
-8.0
-7.0
-6.0
-5.0
-4.0
-3.0
B v 'x 1 0 4 c m -1
v'
I 79 Br
I 81 Br
ν(υ′, J′; υ′′, J′′) = Tυ′ + (Bυ′ ± qυ′/2){J′(J′ + 1) −2} − Dυ′ {J′(J′ + 1) −2}2 + Hυ′ {J′(J′ + 1) −2}3
− ∑ l=1
∑ m=0
Y′′l,m
{J′′(J′′ + 1)}m
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 9 / 22
Bands constants for the A state
The Band Constant for the A State of I81Br v′ T ′v B′v q′v × 105 D′v × 107 H′v × 1011
3 12818.3050 (76) 0.040250 (10) -0.188 (40) 0.000 (45) 4 12939.0514 (19) 0.0398515 (21) 0.470(56) -0.1970(59) -0.0060(47) 5 13056.2946 (14) 0.0394323 (16) 0.470(25) -0.2129(45) -0.0030(35) 6 13169.9185 (10) 0.0389888 (11) 0.470(19) -0.2229(31) -0.0060(22) 7 13279.7775 (10) 0.0385244 (11) 0.510(21) -0.2392(28) -0.0070(20) 8 13385.73300(94) 0.03803240(100) 0.530(20) -0.2555(29) -0.0090(22) 9 13487.62930(97) 0.03751520(100) 0.560(16) -0.2798(28) -0.0100(21)
10 13585.3158 (10) 0.0369637 (11) 0.610(21) -0.3030(29) -0.0130(21) 11 13678.63330(91) 0.03637630(100) 0.620(17) -0.3295(28) -0.0170(21) 12 13767.42060(94) 0.0357534 (11) 0.710(17) -0.3653(29) -0.0200(22) 13 13851.5276 (10) 0.0350885 (12) 0.730(24) -0.4036(34) -0.0260(26) 14 13930.8247 (12) 0.0343770 (13) 0.810(26) -0.4437(37) -0.0340(29) 15 14005.2063 (12) 0.0336216 (13) 0.980(27) -0.4902(37) -0.0440(28) 16 14074.6095 (15) 0.0328267 (17) 1.080(31) -0.5580(52) -0.0430(43) 17 14139.0356 (16) 0.0319866 (19) 1.210(46) -0.6107(55) -0.0580(40) 18 14198.5730 (19) 0.0311155 (26) 1.370(66) -0.6710(85) -0.0700(73) 19 14253.3897 (16) 0.0302243 (18) 1.390(43) -0.7423(53) -0.0710(40) 20 14303.7648 (20) 0.0293131 (23) 1.700(95) -0.7860(68) -0.0860(49) 21 14349.9860 (14) 0.0284341 (13) 1.390(95) -0.9350(22) 22 14392.4510 (32) 0.0275461 (37) 1.800(100) -0.9670(82) 23 14431.5266 (17) 0.0266746 (21) 2.050(81) -1.0150(49) 24 14467.5579 (21) 0.0258187 (32) 2.320(96) -1.040 (10) 25 14500.8380 (22) 0.0249901 (33) 2.40 (11) -1.097 (10) 26 14531.5990 (72) 0.0242080 (98) 3.10 (33) -1.280 (29) 27 14560.1000 (48) 0.0233770 (69) 2.70 (25) -1.370 (19) 28 14586.4670 (60) 0.022541 (11) 3.00 (34) -1.530 (40) 29 14610.8750 (86) 0.021663 (20) 2.10 (59) -1.750 (89)
in cm−1 and σ in parentheses DRMS:1.486
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 10 / 22
Schrödinger equation and Potential Function . Schrödinger equation ..
......
{ − ~
ad (r)] + ~2[J(J + 1) − Λ2]
2µαr2 [1 + g(α)(r)]
(r)[J(J + 1)]Λ ψv,J(r) = Ev,Jψv,J(r)
......
β(r) = βMLR(yp(r; rref)) = yp(r; rref)β∞ + [1 − yp(r; rref)] NS ,NL∑
i=0
rq − rref q
rq + rref q
Robert J. Le Roy et al. “Long-range damping functions improve the short-range behaviour of ’MLR’ potential energy functions”, Mol.
Phys. 109, p435(2011)
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 11 / 22
Born–Oppenheimer Breakdown Correction Functions and Λ–Doubling
. Λ–Doubling for the A state ..
......
......
∞ypad (r; re) + [1 − ypad (r, rref)] NA
ad∑ i=0
RA na(r) = RA
na∑ i=0
M(α) A = M(α)
A − M(1) A
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 12 / 22
Condition of the Calculating Potential Function Parameter
© For the X state: De of the X state is constrained as 14797.9 cm−1 reported by Wrede(2000).
the Coefficients C5, C6, C8 of the X state I2 Br2 IBr
C5 cm−1Å5 0.045 × 105(a) 0.0033 × 105 (b) 0.0122 × 105
C6 cm−1Å6 −2.11 × 106(a) −0.6274 × 106(b) −1.1565 × 106
C8 cm−1Å8 −3.8 × 107(c) −1.55 × 107(b) −2.42 × 107
© For the A state: the Coefficients C5, C6, C8 of the A state
I2 Br2 IBr C5 cm−1Å5 −5.95 × 104(a) −3.2 × 104 (b) −4.36 × 104
C6 cm−1Å6 −2.01 × 106(a) −6.37 × 105(b) −1.13 × 106
C8 cm−1Å8 −3.8 × 107(c) −1.55 × 107(b) −2.42 × 107
a M. Saute, M. Aubert–Frécon, J. Chern. Phys. 77(11),1 (1982)
b M. Saute, B. Bussery, M. Aubert–Frécon, Mol.Phys, 51, No.6, 1459-1474(1984)
c F. Martin, R. Bacis, S. Churassy, J. Vergès, J. Mol.Spectrosc 116, 71–100(1986)
DPotFit1 is used in this calculation.
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 13 / 22
Which vibrational levels have trouble?
1.4
1.6
1.8
2.0
2.2
DRMS of Parfit
d d
v v=25 means that the uncertain of the v(A)=0–25 are not modified but uncertainly 2.0 cm−1 is given to those of the v(A)=26–29.
Calculation Process
First Calculate the potential of the X state. The A state is to be represented by term values, to avoid the behavior of the A-state.
Second Calculate the potential of the A state using the frozen parameter of the X state. At that time, Large uncertainty is given to the data having high vibrational levels.
Third Chose the initial data set. In this time, the lines having v(A)=0–25 have normal uncertainty, uncertainty 2.0cm−1 is given to the data belonging to v(A)=26–29.
Fourth Calculate the initial parameter set of the potential of the A state.
Fifth Calculate the potential of the A state, using ’Robust’ weights and the initial parameter set of above.
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 14 / 22
Relation of Rref and Dimensionless RMS
0.920
0.930
0.940
0.950
0.960
0.970
0.980
0.990
1.000
rref
N11 p=5 q=4 N11 p=5 q=5 N11 p=5 q=6 N12 p=5 q=4 N12 p=5 q=5 N12 p=5 q=6
(R o b
u s t
w e ig
N5 p6q3 N5 p5q3 N5 p5q4 N6 p5q3 N6 p5q4
(n o rm
dd =
yobs(i) :measured value ycalc(i):calculated value unc(i) :The estimated
uncertainty of datum N :The total number of data w(i) :the normal data weights wrob(i):the robust weights
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 15 / 22
Long-Range Extrapolation behavior of the Potential
The long-range extrapolation behaviour of a number of fitted MLR models for the A 3Π1 state of IBr T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 16 / 22
Number of Λ-Type Doubling Constants
Number of Lambda-Type Doubling terms V(r) function
Robust weights
V
/r **
Data
Region
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
V
/r **
Data
Region
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 17 / 22
Number of Centrifugal Born–Oppenheimer Breakdown Terms
Number of Centrifugal BOB terms Centrifugal BOB function
Robust weights
UNC of v(A)=26- 29 are 2.0cm−1.
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 18 / 22
......
Values Error Values Error Values Error Te 12369.6142 0.0097 De 2428.2870 0.0084 Re 2.8653212 2.2×10−5
C5 4.3635×104 – C6 1.132 ×106 – C8 2.42×107 – De(X) 14797.90124 0.00086 uBr
0 (X) 0.241 0.0041 β0 1.1080742 0.00016 β1 0.403637 0.00013 β2 -1.33961 0.00023 β3 -0.70070 0.00090 β4 1.6983 0.0041 β5 1.2010 0.017 β6 -1.9160 0.039 β7 -4.1465 0.13 β8 1.50 0.10 β9 9.7 0.34 β10 -1.3230 0.088 β11 -8.687 0.29 tBr 0 0.0 – tBr
1 -0.0048 0.00034 tBr 2 0.0209 0.00069
ω0 0.00288 8.6×10−5 ω1 -0.069 0.011 ω2 0.17 0.038 ω3 0.513 0.037
’Robust’ is used in this calculation. The constants β0 ∼ β6 of the X were constrained into below values.
......
Values Error Values Error Values Error C5 -1.21×103 – C6 1.156 ×106 – C8 2.42×107 – De 14797.9* Re 2.46898596 6.1×10−8
β0 0.32025489 1.0×10−6 β1 -1.132183 5.5×10−5 β2 -0.652405 5.2×10−4
β3 0.262 7.3×10−3 β4 1.519 0.045 β5 3.41 0.28 β6 5.6 0.79
uBr 0 0.202 0.17
De was constrained into the value reported by E. Wrede. All level of the A state were independent term values in this calculation.
. Overall ..
......
For the A State No. of Data: 20741 No. of Param.: 30
dd: 0.93 vmin( A): 3 vmax( A): 29
D-vmax(A): 181 cm−1
For the X State No. of Data: 12103 No. of Param.: 6
dd: 0.735 vmin(X): 0 vmax (X): 19 D-vmax(X): 9880.7cm−1
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 19 / 22
Bυ′ and the first differences for the A state
0.020
0.025
0.030
0.035
0.040
0.045
B v 'c m -1
v'
B v 'x 1 0 4 c m -1
v'
Black lines indicate the parameter generated by DPotFit.
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 20 / 22
Which Bands have trouble?
c a
lc -o
I 79
Br26 f
I 81
Br26 f
I 81
Br26 e
I 79
Br27 f
I 81
Br27 f
I 79
Br27 e
I 81
Br27 e
I 79
Br28 f
I 81
Br28 f
I 79
Br28 e
I 81
Br28 e
I 79
Br29 f
I 81
Br29 f
I 79
Br29 e
I 81
Br29 e
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 21 / 22
Conclusion
Potential function parameter are determined for the A and X state.
First differential of the Bv of the A state which is calculated by potfit are compared with parameter calculated by parameter fitting.
Found that there are something trouble in v(A)=27–29 of I79Br.
We need to measure the high vibrational level of the A state to improve accuracy of the potential.
-14.0
-12.0
-10.0
-8.0
-6.0
-4.0
-2.0
0.0
x 1 0 0 0 c m -1
D e = 1 4 7 9 7 .9 c m -1
v"=19
v"=0
v'=3
v'=29
v'=25
Re=2.46898595(6)
Re=2.86530(2) D e = 2 4 2 8 .2 9 4 (8 )c m -1
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 22 / 22
Introduction
Purpose
Potential Function for the A and X states
Direct Potential Fitting
T.Yukiya∗, N. Nishimiya∗, M.Suzuki∗, and R. J. Le Roy∗∗
*Dept. of Electronics and Information Technology, Tokyo Polytechnic University, Iiyama 1583, Atsugi City, Kanagawa 243-0297, Japan
** Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Jun. 16, 2014
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 1 / 22
Our Objectives
Define frequency standards based on the A–X transition of IBr Determine reliable spectroscopic constants for calculation of line positions Provide realistic predictions for the unobserved levels of IBr Obtain accurate analytic potential energy functions for the A and X state
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 2 / 22
References
the A –X system 1932 W.G. Brown, "Absorption Spectrum of Iodine Bromide"
1962 L.E.Selin, "Analysis of the absorption spectrum of IBr "
1967 M.A.A.CLYNE AND J.A.COXON, "The Emission Spectra of Br and IBr Formed in Atomic Recombination Processes"
1994 D. R. T. Appadoo, P. F. Bernath, Robert J. Le Roy , "High-resolution visible spectrum for the A 3Π1 ← X 1Σ+ system of IBr"
1995 N. Nishimiya , T .Yukiya and M .Suzuki, "Laser Spectroscopy of the A 3Π1 ← X 1Σ+ System of IBr"
2002 T. Yukiya, N. Nishimiya and M. Suzuki , "High-Resolution Laser Spectroscopy of the A 3Π1 ← X 1Σ+ System of IBr with a Titanium:Sapphire Ring Laser"
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 3 / 22
References
the X state 1975 E.Tiemann and Th.Möller,"Rotational Spectrum of IBr"
1976 E. M. Weinstock ,"The laser-induced fluorescence of IBr79"
1993 J. M. Campbell, P. F. Bernath,"Vibration-rotation spectrum of iodine monobromide"
1998 B. Nelander, V. Sablinskas, M. Dulick, V.Braun and P. F. Bernath,"High resolution far infrared spectroscopy of IBr using a synchrotron source"
Related Research on the A state 1982 M. Saute, M. Aubert–Frécon,"Calculated long-range potential-energy curves for the 23 molecular states of I2"
1986 F. Martin, R. Bacis, S. Churassy, J. Vergès, "Laser-induced-fluorescence Fourier transform spectrometry of the X0g
+ state of I2: Extensive analysis of the B0u + → X0g
+
1994 J.O.Clevenger, Q.P.Ray, J.Tellinghuisen, X.Zheng and M.C.Heaven ,"Spectroscopy of metastable species in a free-jet expansion: the β← A transition in IBr"
2000 E. Wrede, S. Laubach, S. Schulenburg, A. J. Orr-Ewing, M. N. R. Ashfold, Velocity map imaging of the near-threshold photodissociation of IBr: accurate determination of De(I–Br)
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 4 / 22
Experimental system
Ar +Ion Laser
GP−IB BusOsc.
Lock−in Amp.
Lock−in Amp.
Lock−in Amp.
Lock−in Amp.
Room Temparature
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 5 / 22
Absorption Spectrum of IBr near 12568 cm−1
12567.0 12568.0 12569.0 12570.0
I79Br8-2 R(96)
I79Br10-3 Q(71)
I81Br8-2 P(92)
I79Br10-3 R(73)
I79Br10-3 P(69)
I81Br8-2 Q(94)
I81Br12-4 R(31)
I79Br11-3 Q(98)
I81Br12-4 Q(29)
I81Br13-4 R(72)
I79Br12-4 R(30)
I79Br12-4 Q(28)
I81Br14-4 Q(92)
I81Br12-4 P(27)
I79Br14-4 Q(91)
I81Br8-2 R(96)
I79Br12-4 P(26)
I79Br13-4 R(71)
I81Br7-2 Q(54)
I81Br10-3 Q(71)
I81Br10-3 R(73)
I81Br13-4 Q(70)
I79Br11-3 P(96)
I81Br10-3 P(69)
I79Br7-2 Q(54)
I81Br12-4 R(30)
I81Br12-4 Q(28)
I79Br12-4 R(29)
I79Br13-4 Q(69)
I79Br12-4 Q(27)
I81Br12-4 P(26)
I79Br12-4 P(25)
I81Br13-4 P(68)
I79Br8-2 P(91)
I81Br14-4 P(90)
I81Br12-4 R(29)
I81Br12-4 Q(27)
I79Br14-4 P(89)
I79Br13-4 P(67)
I79Br12-4 R(28)
I79Br8-2 Q(93)
I79Br10-3 Q(70)
I79Br12-4 Q(26)
I81Br11-3 Q(98)
I79Br10-3 R(72)
I81Br7-2 Q(53)
I81Br12-4 P(25)
I79Br10-3 P(68)
I79Br12-4 P(24)
I81Br14-4 R(93)
I79Br14-4 R(92)
I79Br7-2 Q(53)
I79Br8-2 R(95)
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 6 / 22
Observed Band System of I79/81Br
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
v '
Appadoo Q PR
New Data
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 7 / 22
Rotational levels assigned for the A state.
0
20
40
60
80
100
120
J’
v’
Yukiya Appadoo
New Data
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 8 / 22
Bands constants of the A state The Band Constants for the A State of I79Br
v′ T ′v B′v q′v × 105 D′v × 107 H′v × 1011
3 12821.6070 (51) 0.0408629 (78) -0.195 (31) 0.000 (35) 4 12943.1777 (19) 0.0404527 (22) 0.290(45) -0.2050(69) -0.0050(59) 5 13061.1857 (12) 0.0400228 (14) 0.430(24) -0.2184(39) -0.0050(30) 6 13175.51370(93) 0.0395677 (11) 0.490(20) -0.2292(32) -0.0070(24) 7 13286.00970(94) 0.0390916 (11) 0.530(24) -0.2476(31) -0.0070(24) 8 13392.53260(87) 0.03858700(100) 0.550(17) -0.2646(30) -0.0100(24) 9 13494.92630(89) 0.03805470(95) 0.590(15) -0.2900(26) -0.0100(19)
10 13593.03060(93) 0.03748860(99) 0.630(16) -0.3157(27) -0.0130(20) 11 13686.68470(84) 0.03688550(93) 0.670(16) -0.3458(26) -0.0160(19) 12 13775.72750(92) 0.03624380(98) 0.740(16) -0.3832(26) -0.0190(19) 13 13860.00310(89) 0.03555770(100) 0.770(18) -0.4199(28) -0.0280(21) 14 13939.3795 (12) 0.0348267 (13) 0.920(25) -0.4667(35) -0.0330(27) 15 14013.7549 (12) 0.0340503 (13) 0.990(21) -0.5210(35) -0.0410(26) 16 14083.0733 (12) 0.0332291 (13) 1.100(23) -0.5818(37) -0.0490(28) 17 14147.3447 (18) 0.0323658 (22) 1.250(49) -0.6421(62) -0.0610(45) 18 14206.6706 (24) 0.0314677 (32) 1.400(55) -0.696 (11) -0.080 (11) 19 14261.2366 (15) 0.0305500 (20) 1.360(48) -0.7630(61) -0.0840(47) 20 14311.3259 (14) 0.0296241 (19) 1.700(100) -0.8240(59) -0.0890(44) 21 14357.2655 (23) 0.0287231 (19) 1.690(85) -0.9650(34) 22 14399.4560 (45) 0.0278190 (47) 1.90 (14) -1.0090(99) 23 14438.2680 (25) 0.0269300 (38) 2.60 (19) -1.0510(84) 24 14474.0480 (32) 0.0260500 (60) 2.90 (35) -1.050 (22) 25 14507.0719 (20) 0.0252258 (33) 6.50 (16) -1.1060(98) 26 14537.584 (15) 0.024399 (18) -1.340 (52) 27 14565.8190 (28) 0.0236100 (39) 2.70 (14) -1.9090(93) 28 14591.9560 (42) 0.0227920 (54) 10.80 (21) -3.920 (12) 29 14615.9180 (63) 0.021883 (16) 5.70 (59) -4.620 (75)
in cm−1 and σ in parentheses DRMS:1.486
-10.0
-9.0
-8.0
-7.0
-6.0
-5.0
-4.0
-3.0
B v 'x 1 0 4 c m -1
v'
I 79 Br
I 81 Br
ν(υ′, J′; υ′′, J′′) = Tυ′ + (Bυ′ ± qυ′/2){J′(J′ + 1) −2} − Dυ′ {J′(J′ + 1) −2}2 + Hυ′ {J′(J′ + 1) −2}3
− ∑ l=1
∑ m=0
Y′′l,m
{J′′(J′′ + 1)}m
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 9 / 22
Bands constants for the A state
The Band Constant for the A State of I81Br v′ T ′v B′v q′v × 105 D′v × 107 H′v × 1011
3 12818.3050 (76) 0.040250 (10) -0.188 (40) 0.000 (45) 4 12939.0514 (19) 0.0398515 (21) 0.470(56) -0.1970(59) -0.0060(47) 5 13056.2946 (14) 0.0394323 (16) 0.470(25) -0.2129(45) -0.0030(35) 6 13169.9185 (10) 0.0389888 (11) 0.470(19) -0.2229(31) -0.0060(22) 7 13279.7775 (10) 0.0385244 (11) 0.510(21) -0.2392(28) -0.0070(20) 8 13385.73300(94) 0.03803240(100) 0.530(20) -0.2555(29) -0.0090(22) 9 13487.62930(97) 0.03751520(100) 0.560(16) -0.2798(28) -0.0100(21)
10 13585.3158 (10) 0.0369637 (11) 0.610(21) -0.3030(29) -0.0130(21) 11 13678.63330(91) 0.03637630(100) 0.620(17) -0.3295(28) -0.0170(21) 12 13767.42060(94) 0.0357534 (11) 0.710(17) -0.3653(29) -0.0200(22) 13 13851.5276 (10) 0.0350885 (12) 0.730(24) -0.4036(34) -0.0260(26) 14 13930.8247 (12) 0.0343770 (13) 0.810(26) -0.4437(37) -0.0340(29) 15 14005.2063 (12) 0.0336216 (13) 0.980(27) -0.4902(37) -0.0440(28) 16 14074.6095 (15) 0.0328267 (17) 1.080(31) -0.5580(52) -0.0430(43) 17 14139.0356 (16) 0.0319866 (19) 1.210(46) -0.6107(55) -0.0580(40) 18 14198.5730 (19) 0.0311155 (26) 1.370(66) -0.6710(85) -0.0700(73) 19 14253.3897 (16) 0.0302243 (18) 1.390(43) -0.7423(53) -0.0710(40) 20 14303.7648 (20) 0.0293131 (23) 1.700(95) -0.7860(68) -0.0860(49) 21 14349.9860 (14) 0.0284341 (13) 1.390(95) -0.9350(22) 22 14392.4510 (32) 0.0275461 (37) 1.800(100) -0.9670(82) 23 14431.5266 (17) 0.0266746 (21) 2.050(81) -1.0150(49) 24 14467.5579 (21) 0.0258187 (32) 2.320(96) -1.040 (10) 25 14500.8380 (22) 0.0249901 (33) 2.40 (11) -1.097 (10) 26 14531.5990 (72) 0.0242080 (98) 3.10 (33) -1.280 (29) 27 14560.1000 (48) 0.0233770 (69) 2.70 (25) -1.370 (19) 28 14586.4670 (60) 0.022541 (11) 3.00 (34) -1.530 (40) 29 14610.8750 (86) 0.021663 (20) 2.10 (59) -1.750 (89)
in cm−1 and σ in parentheses DRMS:1.486
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 10 / 22
Schrödinger equation and Potential Function . Schrödinger equation ..
......
{ − ~
ad (r)] + ~2[J(J + 1) − Λ2]
2µαr2 [1 + g(α)(r)]
(r)[J(J + 1)]Λ ψv,J(r) = Ev,Jψv,J(r)
......
β(r) = βMLR(yp(r; rref)) = yp(r; rref)β∞ + [1 − yp(r; rref)] NS ,NL∑
i=0
rq − rref q
rq + rref q
Robert J. Le Roy et al. “Long-range damping functions improve the short-range behaviour of ’MLR’ potential energy functions”, Mol.
Phys. 109, p435(2011)
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 11 / 22
Born–Oppenheimer Breakdown Correction Functions and Λ–Doubling
. Λ–Doubling for the A state ..
......
......
∞ypad (r; re) + [1 − ypad (r, rref)] NA
ad∑ i=0
RA na(r) = RA
na∑ i=0
M(α) A = M(α)
A − M(1) A
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 12 / 22
Condition of the Calculating Potential Function Parameter
© For the X state: De of the X state is constrained as 14797.9 cm−1 reported by Wrede(2000).
the Coefficients C5, C6, C8 of the X state I2 Br2 IBr
C5 cm−1Å5 0.045 × 105(a) 0.0033 × 105 (b) 0.0122 × 105
C6 cm−1Å6 −2.11 × 106(a) −0.6274 × 106(b) −1.1565 × 106
C8 cm−1Å8 −3.8 × 107(c) −1.55 × 107(b) −2.42 × 107
© For the A state: the Coefficients C5, C6, C8 of the A state
I2 Br2 IBr C5 cm−1Å5 −5.95 × 104(a) −3.2 × 104 (b) −4.36 × 104
C6 cm−1Å6 −2.01 × 106(a) −6.37 × 105(b) −1.13 × 106
C8 cm−1Å8 −3.8 × 107(c) −1.55 × 107(b) −2.42 × 107
a M. Saute, M. Aubert–Frécon, J. Chern. Phys. 77(11),1 (1982)
b M. Saute, B. Bussery, M. Aubert–Frécon, Mol.Phys, 51, No.6, 1459-1474(1984)
c F. Martin, R. Bacis, S. Churassy, J. Vergès, J. Mol.Spectrosc 116, 71–100(1986)
DPotFit1 is used in this calculation.
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 13 / 22
Which vibrational levels have trouble?
1.4
1.6
1.8
2.0
2.2
DRMS of Parfit
d d
v v=25 means that the uncertain of the v(A)=0–25 are not modified but uncertainly 2.0 cm−1 is given to those of the v(A)=26–29.
Calculation Process
First Calculate the potential of the X state. The A state is to be represented by term values, to avoid the behavior of the A-state.
Second Calculate the potential of the A state using the frozen parameter of the X state. At that time, Large uncertainty is given to the data having high vibrational levels.
Third Chose the initial data set. In this time, the lines having v(A)=0–25 have normal uncertainty, uncertainty 2.0cm−1 is given to the data belonging to v(A)=26–29.
Fourth Calculate the initial parameter set of the potential of the A state.
Fifth Calculate the potential of the A state, using ’Robust’ weights and the initial parameter set of above.
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 14 / 22
Relation of Rref and Dimensionless RMS
0.920
0.930
0.940
0.950
0.960
0.970
0.980
0.990
1.000
rref
N11 p=5 q=4 N11 p=5 q=5 N11 p=5 q=6 N12 p=5 q=4 N12 p=5 q=5 N12 p=5 q=6
(R o b
u s t
w e ig
N5 p6q3 N5 p5q3 N5 p5q4 N6 p5q3 N6 p5q4
(n o rm
dd =
yobs(i) :measured value ycalc(i):calculated value unc(i) :The estimated
uncertainty of datum N :The total number of data w(i) :the normal data weights wrob(i):the robust weights
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 15 / 22
Long-Range Extrapolation behavior of the Potential
The long-range extrapolation behaviour of a number of fitted MLR models for the A 3Π1 state of IBr T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 16 / 22
Number of Λ-Type Doubling Constants
Number of Lambda-Type Doubling terms V(r) function
Robust weights
V
/r **
Data
Region
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
V
/r **
Data
Region
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 17 / 22
Number of Centrifugal Born–Oppenheimer Breakdown Terms
Number of Centrifugal BOB terms Centrifugal BOB function
Robust weights
UNC of v(A)=26- 29 are 2.0cm−1.
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 18 / 22
......
Values Error Values Error Values Error Te 12369.6142 0.0097 De 2428.2870 0.0084 Re 2.8653212 2.2×10−5
C5 4.3635×104 – C6 1.132 ×106 – C8 2.42×107 – De(X) 14797.90124 0.00086 uBr
0 (X) 0.241 0.0041 β0 1.1080742 0.00016 β1 0.403637 0.00013 β2 -1.33961 0.00023 β3 -0.70070 0.00090 β4 1.6983 0.0041 β5 1.2010 0.017 β6 -1.9160 0.039 β7 -4.1465 0.13 β8 1.50 0.10 β9 9.7 0.34 β10 -1.3230 0.088 β11 -8.687 0.29 tBr 0 0.0 – tBr
1 -0.0048 0.00034 tBr 2 0.0209 0.00069
ω0 0.00288 8.6×10−5 ω1 -0.069 0.011 ω2 0.17 0.038 ω3 0.513 0.037
’Robust’ is used in this calculation. The constants β0 ∼ β6 of the X were constrained into below values.
......
Values Error Values Error Values Error C5 -1.21×103 – C6 1.156 ×106 – C8 2.42×107 – De 14797.9* Re 2.46898596 6.1×10−8
β0 0.32025489 1.0×10−6 β1 -1.132183 5.5×10−5 β2 -0.652405 5.2×10−4
β3 0.262 7.3×10−3 β4 1.519 0.045 β5 3.41 0.28 β6 5.6 0.79
uBr 0 0.202 0.17
De was constrained into the value reported by E. Wrede. All level of the A state were independent term values in this calculation.
. Overall ..
......
For the A State No. of Data: 20741 No. of Param.: 30
dd: 0.93 vmin( A): 3 vmax( A): 29
D-vmax(A): 181 cm−1
For the X State No. of Data: 12103 No. of Param.: 6
dd: 0.735 vmin(X): 0 vmax (X): 19 D-vmax(X): 9880.7cm−1
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 19 / 22
Bυ′ and the first differences for the A state
0.020
0.025
0.030
0.035
0.040
0.045
B v 'c m -1
v'
B v 'x 1 0 4 c m -1
v'
Black lines indicate the parameter generated by DPotFit.
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 20 / 22
Which Bands have trouble?
c a
lc -o
I 79
Br26 f
I 81
Br26 f
I 81
Br26 e
I 79
Br27 f
I 81
Br27 f
I 79
Br27 e
I 81
Br27 e
I 79
Br28 f
I 81
Br28 f
I 79
Br28 e
I 81
Br28 e
I 79
Br29 f
I 81
Br29 f
I 79
Br29 e
I 81
Br29 e
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 21 / 22
Conclusion
Potential function parameter are determined for the A and X state.
First differential of the Bv of the A state which is calculated by potfit are compared with parameter calculated by parameter fitting.
Found that there are something trouble in v(A)=27–29 of I79Br.
We need to measure the high vibrational level of the A state to improve accuracy of the potential.
-14.0
-12.0
-10.0
-8.0
-6.0
-4.0
-2.0
0.0
x 1 0 0 0 c m -1
D e = 1 4 7 9 7 .9 c m -1
v"=19
v"=0
v'=3
v'=29
v'=25
Re=2.46898595(6)
Re=2.86530(2) D e = 2 4 2 8 .2 9 4 (8 )c m -1
T.Yukiya (Tokyo Polytechnic University) The A-X System of IBr Jun. 16, 2014 22 / 22
Introduction
Purpose
Potential Function for the A and X states
Direct Potential Fitting
