DIRECT POTENTIAL FITTING FOR THE A31u and X1+g STATES
Transcript of DIRECT POTENTIAL FITTING FOR THE A31u and X1+g STATES
DIRECT POTENTIAL FITTING FOR THE A 3Π1u andX 1Σ+g STATES OF Br2
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
June 21, 2012
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 1 / 17
Our ResearchThe A − X system of ICl(1),(2), IBr(3),(4), I(5)
2 and Br(6),(7)2 have been
studied in the 0.8µm region.
The line positions of these spectra were determined in order toestablish a frequency standard.
Potential energy curves and spectroscopic constants of the Aand X state are determined.
(1) N. Nishimiya et al., “Nuclear Quadrupole Coupling Effect in the A-X System and Spectroscopic Constants for v=2′-4′′ ,3′-5′′
and 4′-5′′ Progressions of ICl”, JMS, 163, 43(1994).(2) T. Yukiya et al., “ Doppler-limited spectroscopy of the A3Π1–X1Σ+ system of ICl in the 0.8µm region using a Ti:sapphire ring
laser”, JMS 269, 193(2011).(3) N. Nishimiya et al., “Laser Spectroscopy of the A3Π1–X1Σ+ System of IBr”, JMS, 173,8(1995).(4) T. Yukiya et al., “ High-Resolution Laser Spectroscopy of the A3Π1–X1Σ+ System of IBr with a Titanium: Sapphire Ring Laser”,
JMS 214, 132( 2002).(5) T. Yukiya et al., “High-Resolution Laser Spectroscopy of the A3Π1u–X1Σ+g System of I2 with Ti: Sapphire Ring Laser”, JMS,
182, 271(1997).(6) N. Nishimiya et al., “High-Resolution Laser Spectroscopy of the A3Π1–X1Σ+ of Br2”, OHIO Columnbus Meeting (2005).(7) N. Nishimiya et al., “Improvement of Spectroscopic Constants for the A3Π1–X1Σ+ System of Br2”, OHIO Columnbus Meeting
(2011).
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 2 / 17
Previous WorkM.A.A.Clyne and J.A.Coxon,“The Emission Spectra of Br2 and IBr Formedin Atomic Recombination Processes”, J.Mol.Spectroscopy, 23, 58 (1967).
P.Venkateswarlu, V.N.Sarma, and Y.V.Rao, “Resonance series of Br2 in thevacuum ultraviolet“, J.Mol.Spectrosc., 96, 247 (1982).
M. Saute,et. al., ”Coefficients d’interaction à grande distance C5 et C6 pourles 23 états moléculaires de Cl2 et de Br2”, Mol. Phys., 51, 1459 (1984).
S. Gerstenkorn and P. Luc, ”Analysis of the long range potential of 79Br2 inthe B3Π0+u state and molecular constants of the three isotopic brominespecies 79Br2, 79Br81Br2 and 81Br2”, J. Phys. (France), 50, 1417 (1989).
C. D. Boone, ” Magnetic rotation study of the A3Π1u − X1Σ+g system of Br2”,Thesis (PhD), British Columbia (1999).
C. Focsa, H. Li, and P. F. Bernath, “Characterization of the Ground State ofBr2 by Laser-Induced Fluorescence Fourier Transform Spectroscopy of theB3ΠO+u − X1Σ+g system”,J.Mol.Spectroscopy, 200, 104 (2000).
D.J.Postell,“Laser Induced Fluorescence Spectroscopy of Br2:Observations of Emission to High Vibrational Levels in the Ground X(1Σ+g )State”, Thesis(Master of Science), Wright State University, 2005.
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 3 / 17
Block diagram of Ti:sapphire ring laser spectrometer.
91MHz
100kHz
Br2
Local Bus
PC
Function
Generator
Sweep Sig.
D/A
Etalon Drive Sig.
Servo Amp.
Laser
Cntrl.
Ti:Al2O3 Laser Ar+ LaserM
BS
BS
Chopper
F.P.I
ref.
Det.
Wavelength
Meter
Lock-in
Amp.
Chopper
Cntrl.
Function Gen.
RF Gen.
Balanced
MixerBurst Signal
Det.
E.O.M.
ref.
Lock-inAmp.
GP-IB
Bus
To BRF
White type CellM
amp.
ModulationMethod
:Tone Burst
EOM :191 MHz
Cell Temp. :150C
Path length :13.6 m
Gas Pressure:10 Torr
WavelengthMeter
:BurleighWA-1500
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 4 / 17
Example of Br2 Spectrum
12711.0 12711.5 12712.0 12712.5 12713.0 12713.5
14 18
39
68
31
66
69
23
89
15 13 17
64
3427
32
14 12
68
91
30
38
13
56
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 5 / 17
Assigned Bands for the A State
0
5
10
15
20
25
30
35
0 1 2 3 4 5 6 7 8
A s
tate
X state
Q
PR
Boone Q
Boone PR
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 6 / 17
Assigned Ro-vibrational Levels in the A State
0
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20 25 30 35 40
J'
v'
This Work
Boone
Boone(QB)
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 7 / 17
Bυ′ and the First Differences for the A State
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0.050
0.055
0.060
0 10 20 30 40
B' v
cm
-1
v'
79,79Br2
79,81Br2
81,81Br2
-2.2
-2.0
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
0 10 20 30 40
B
' vx1
03cm
-1
v'
79,79Br2
79,81Br2
81,81Br2
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0 5 10 15 20 25 30
qv'x105cm-1
v'
79,79Br2
79,81Br2
81,81Br2
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 8 / 17
Schrödinger equation and Potential Function.Schrödinger equation..
......
− ~
2
2µα
d2
dr2 +[V1ad(r) + ∆V (α)
ad (r)] +~2[J(J + 1) − Λ2]
2µαr2 [1 + g(α)(r)]
+ sgΛ(e/ f )∆V (α)Ω
(r)[J(J + 1)]Λψv,J(r) = Ev,Jψv,J(r)
.Potential Function(Morse Long Range)..
......
VMLR(r) = De
1 − µLR(r)
µLR(re)e−β(r)·yp(r;re)
2
µLR(r) =last∑i=1
Dmi (r)Cmi
rmi, Dm(r) =
(1 − exp
−b · (ρr)
m− c · (ρr)2
√m
)m
β(r) = βMLR(yp(r; rref)) = yp(r; rref)β∞ + [1 − yp(r; rref)]NS ,NL∑
i=0
βi · yq(r; rref)i
yp(r; rref) =rp − rref
p
rp + rrefp , yq(r; rref) =
rq − rrefq
rq + rrefq
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 et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 9 / 17
Born–Oppenheimer Breakdown Correction and Λ–Doubling Functions.Born–Oppenheimer Breakdown Correction..
......
∆V (α)ad (r) =
∆M(α)A
M(α)A
S Aad(r) +
∆M(α)B
MαB
S Bad(r), g(α)(r) =
∆M(1)A
MαA
RAna(r) +
∆M(1)B
M(α)B
RBna(r)
S Aad(r) = [1 − ypad (r; re)]
NAad∑
i=0
uAi yqad (r; re)i + uA
∞ypad (r; re)
RAna(r) = [1 − ypna (r; re)]
NAna∑
i=0
tAi yqna (r; re)i + tA
∞ypna (r; re)
∆M(α)A = M(α)
A − M(1)A
.Λ–Doubling Functions..
......
∆V (α)Ω
(r) =(~2
2µαr2
)2Ω
fΩ(r)
fΩ(r) =NΩ∑i=0
ωΩi yqΩ(r; re)i
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 10 / 17
Dimensionless Root-Mean-Square Deviation(dd)
dd =
1N
N∑i=1
ycalc(i) − yobs(i)
unc(i)
2
1/2
yobs(i) : measured valueycalc(i) : calculated valueunc(i) : The estimated uncertainty of datumN : The total number of data
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 11 / 17
Choosing of a Potential Model minimizing DRMS andNumber of Parameters.
0.914
0.916
0.918
0.920
0.922
0.924
0.926
0.928
0.930
3.0 3.2 3.4 3.6 3.8 4.0
dd
rref
N12 p=5 q=4N12 p=5 q=5N13 p=5 q=4N13 p=5 q=5N14 p=5 q=4N14 p=5 q=5
0.910
0.915
0.920
0.925
0.930
0.935
0.940
0.945
0.950
0.955
0.960
2.8 3.0 3.2 3.4 3.6
dd
rref
N10 p5 q6N11 p5 q6N12 p5 q6N10 p5 q5N11 p5 q5N12 p5 q5
(a) A State (b)X State
Number of β terms , p and q values of Morse Long Range(MLR) potential functionin the A and X state were changed in this calculation. C5 ,C6 and C8 of the X stateand C6 and C8 of the A state are constrained at values reported by M. Saute. Teand C5 of the A state, De , Re and β were computed by DPotFita . In the A state,Born – Oppenheimer Breakdown term t1 ∼ t6 and Λ doubling term ω0 ∼ ω3 wereused. The lines of the v′=27 in A state were not included in this calculation.
ahttp://scienide2.uwaterloo.ca/∼rleroy/dpotfit/
X-State C5 cm−1Å5 : -0.0033×105
C6 cm−1Å6 : 6.274 ×105
C8 cm−1Å8 : 1.55 ×107
A-State C5 cm−1Å5 : 0.32 ×105
C6 cm−1Å6 : 6.37 ×105
C8 cm−1Å8 : 1.55 ×107
M. Saute (Mol. Phys., 51, 1459(1984)).
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 12 / 17
Long-Range Extrapolation behavior of the Potential
0.0x100
5.0x104
1.0x105
1.5x105
2.0x105
2.5x105
3.0x105
0.00 0.05 0.10 0.15 0.20
-(V
(r)-
D)*
r5=
C5+
C6/r
(A
Sta
te)
1/r [Ang.-1
]
Data
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 13 / 17
Number of Λ-Type Doubling Constants and CentrifugalBorn–Oppenheimer Breakdown Terms
1.0
2.0
3.0
4.0
5.0
0 1 2 3 4 5 6
dd
N
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
0.0 5.0 10.0 15.0 20.0
V
/r**
4 x
10
4
Å
N
=0123456
(a) Number of Lambda-Type Doubling terms (b) ∆VΩ(r) function
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
0 1 2 3 4 5 6 7 8 9
dd
Nna
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
0.0 5.0 10.0 15.0 20.0
Rnax 1
04
Å
Nna=12
3
4
5
6
7
8
9
(a) Number of Centrifugal BOB terms (b) Centrifugal BOB function
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 14 / 17
Potential Function Parameters for the A and X state.For the A-Sate: MLR N=13, p=5, q=4 , Rre f =3.3..
......
Values Error Values Error Values ErrorTe 13909.01274 0.023 De 2147.9239 0.014 Re 2.7046951 2.1×10−5
C5 3.72212×104 720 C6 6.37×105 – C8 1.55×107 –β0 1.1604 6.2×10−4 β1 0.60688 0.0028 β2 -3.12787 0.005β3 -3.4697 0.012 β4 10.3542 0.025 β5 14.758 0.081β6 -42.133 0.31 β7 -47.605 0.54 β8 142.91 1.9β9 64.24 2.2 β10 -295.0 5.6 β11 42.8 3.8β12 260.0 7.0 β13 -147.0 4.7
t0 0.0 – t1 0.00171 6.4×10−4 t2 -0.0174 0.00545t3 -0.036 0.025 t4 1.205 0.24 t5 -5.99 0.93t6 12.84 1.7 t7 -12.9 1.6 t8 5.0 0.55ω0 0.00386 5.0×10−5 ω1 -0.0122 0.0042 ω2 0.037 0.011ω3 0.312 0.0084
The lines of the v′=27 in A state were not included in this calculation.
.For the X-Sate: MLR N=11, p=5, q=6, Rre f =3.12..
......
Values Error Values Error Values ErrorDe 16056.93664 0.0088 Re 2.28102682 6.9×10−7
C5 -3.3×102 – C6 6.274×105 – C8 1.55×107 –β0 1.0418061 3.8×10−5 β1 0.860947 1.7×10−4 β2 1.24355 7.4×10−4
β3 0.16568 0.0035 β4 1.48566 0.0076 β5 -1.9265 0.025β6 0.5507 0.043 β7 3.806 0.061 β8 2.972 0.12β9 -1.523 0.048 β10 -3.38 0.11 β11 -1.43 0.057u0 0.323 0.0068
.Overall..
......
No. of Data: 16916v′=27 is not included
No. of Param.:45
dd: 0.896
vmin(A): 2
vmax(A): 37
D-vmax(A): 2.0 cm−1
vmin(X): 0
vmax(X): 76
D-vmax(X): 116 cm−1
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 15 / 17
Band Constant Calculated by Parameter Fits and by Direct-Potential
Fits
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0 10 20 30
Bv'/
cm
-1
-2.0
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
0 10 20 30
B
v' x 1
03/
cm
-1
79,79Br2(BOB)
79,79Br2(No C-BOB)
ParameterFitting Coxon(J.M.S.1972)
v ' v '
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 16 / 17
Conclusion
Spectra in the new bands weremeasured and assigned in 0.71 –0.83 µm region.Irregular behavior of Bv′ for the Astate were confirmed.Electronic isotope shift andcentrifugal Born – Oppenheimerbreakdown terms were determinedfor the first time.Accurate MLR potential function forthe A and X state were determined.
-15
-10
-5
0
5
2.0 3.0 4.0 5.0
R [Å]x1
00
0 c
m-1
T.YUKIYA et al. (Tokyo Polytechnic University) Potential Fitting for Br2 June 21, 2012 17 / 17