Total Absorption Cross-Section for UV Excitation of Sulfur Monoxide

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Total Absorption Cross-Section for UV Excitation of Sulfur Monoxide Karolis Sarka, and Shinkoh Nanbu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b01921 • Publication Date (Web): 10 Apr 2019 Downloaded from http://pubs.acs.org on April 11, 2019

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The Journal of Physical Chemistry

Total Absorption Cross-Section for UV Excitation of Sulfur Monoxide Karolis Sarka∗ and Shinkoh Nanbu Department of Materials and Life Science, Sophia University, Tokyo 102-8554, Japan E-mail: [email protected]

1

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract In a new study on sulfur monoxide, new ab-initio potential energy curves are developed for excited states: A3 Π, B3 Σ− , C3 Π, C03 Π, and three unassigned in literature states that we name numerically: 33 Σ− , 43 Π, 53 Π. All these excited states have allowed transitions from ground state, X3 Σ− . The ab initio calculations were performed using MRCI-F12+Q/aug-cc-pV(5+d)Z level of theory implemented in MOLPRO2015. Based on close-coupling R-matrix theory, fine structure absorption cross-sections of isotopically substituted sulfur monoxide are calculated for wavelengths of 190–300 nm. The spectra are shown at highest possible resolution (FWHH ≈ 0.15 − 0.18cm−1 ) for reference and future studies. The effects of self-shielding and possible mutual-shielding are discussed.

1

Introduction

2

Sulfur monoxide, SO, is a highly reactive radical species, present in most combustion re-

3

actions of sulfur-containing molecules and an important part of present, 1 Archean, 2 and

4

extraterrestrial atmospheres. 3–6 It is also a precursor for formation of SO dimer (OSSO) 7

5

and a part of interstellar medium. 8 It’s photochemical activity in present troposphere is

6

limited, because of the UV-absorbing ozone layer, but it is introduced to the stratosphere

7

through photodissociation of SO2 . 9 The mass-independent isotopic fractionation pattern ob-

8

served during SO2 photolysis is shown to be consistent with the data from stratospheric

9

aerosols, 9 but no such effects are considered for SO, which largely shares the same excitation

10

energy region.

11

In addition, SO has a major role in atmospheric sulfur cycle of anoxic atmospheres, where

12

it is formed by photodissociation of SO2 emitted through volcanic outgassing, and leads to

13

production of gaseous elemental sulfur. Sulfur monoxide shares a part of the absorption

14

spectrum with S2 (230–270 nm), 10 reinforcing shielding effects through mutual-shielding on

15

top of the self-shielding based mass-independent isotopic fractionation of S2 . SO also absorbs 2


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16

light in the same wavelength range (190–220 nm) 11 as it’s chemical source - SO2 - introducing

17

self- and mutual-shielding interactions in this region as well.

18

Sulfur monoxide has been subject to many studies so far. Numerous experimental works

19

analyze the rotational spectroscopy. 12–16 Liu et al. have recorded absorption spectra and

20

rotational analysis using degenerate four-wave mixing (DFWM) experiments. 17 Elks and

21

Western studied fluorescence, excitation lifetimes and rotational constants on A3 Π state using

22

multiphoton ionization techniques. 18 A computational work by Yu and Bian 19 analyzes the

23

excited electronic state potentials as well as the spin-orbit coupling between them. Works

24

by Borin and Ornellas analyzed the potential energy curves of low-lying singlet and triplet

25

electronic states of SO 20 and A3 Π ←−− X3 Σ− transition. 21 A study by Phillips et al. 22

26

presents low resolution UV spectra for B3 Σ− − X3 Σ− transition, which has been replicated

27

accurately by Danielache et al. 23

28

Because of implied short lifetime of a radical species, sulfur monoxide is generally not

29

considered as a contributor to isotopic fractionation of sulfur in atmospheres and it is clear

30

that it’s incredibly difficult to measure UV properties of SO in laboratory setting with many

31

competing absorbers and high reactivity with itself. The reaction rates 24,25 indicate that it

32

may have a lifetime long enough (strongly dependent on the concentration of SO itself) to

33

be photoactive: 3

cm k=3.5e−15 molecule·s

SO + SO −−−−−−−−−−−−→ SO2 + S k=4.41e−31

cm6 molecule2 ·s

SO + SO + M −−−−−−−−−−−−−→ OSSO + M, 34

which, with an assumed concentration of [SO] = 2.5 × 1013 molecule and bath gas at [M] = cm3

35

2.5 × 1019 molecule , gives lifetimes of τ ≈ 11.4 s and 3.6 ms respectively. As such, the molecule cm3

36

should not be negated in isotopic fractionation considerations.

37

In this study, we show new ab-initio potential energy curves. Based on the reported re-

38

sults of other studies, both numerical and experimental, 12–16,19–21 the spectroscopic constants

39

from our study falls within range of previously reported data. Based on improved method-

40

ology of Danielache et al., 23 we present high resolution total absorption cross-sections for 3



Page 4 of 20

41

A3 Π ←−− X3 Σ− transition, and two nonadiabatically-coupled-potential ([C3 Π − C03 Π] ←−−

42

X3 Σ− , and [B3 Σ− − 3 3 Σ− ] ←−− X3 Σ− ) transitions. The present study improves on the

43

previous theoretical work of SO by Danielache et al. 23 by including ground state vibrational

44

modes v = 0 . . . 3 and rotational levels J = 0 . . . 90 (compared to v = 0 and J = 0 . . . 29).

45

In addition, the previous study did not include C3 Π ←−− X3 Σ− transition for bound-state

46

calculations. The nonadiabatic coupling matrix elements are now calculated using same level

47

of theory as the potential energy curves, improving their position and magnitude. Calcu-

48

lated spectra for all four sulfur-substituted isotopologues of SO are presented. Based on

49

the structure of absorption spectra lines, implications for self-shielding effect are shown and

50

discussed in detail.

51

Computational details

52

Ab-initio potential energy curves

53

The potential energy curves (PECs) were calculated with MOLPRO2015 26 quantum chem-

54

istry package using MRCI-F12+Q 27–29 /aug-cc-pV(5+d)Z 30 method (multireference config-

55

uration interaction with explicit correlation, and using Davidson-corrected energies, with a

56

tight-d augmented correlation-consistent, polarized valence quintuple-ζ basis set). The cal-

57

culations were performed on a uniform grid of 141 points in 1.1–2.5 range and 90 points in

58

2.55–7.0 for 4 lowest-lying states in A1 irreducible representation of C2v symmetry, and 5

59

states in each of A2 , B1 , B2 irreducible representations. The nonadiabatic coupling matrix

60

matrix elements were calculated using three-point DDR procedure. For this study, only

61

allowed transitions in triplet multiplicity were considered.

62

63

The rotational state energies for each electronic state at a particular vibrational level were calculated as: Ev,J = Ev,0 + hBe J(J + 1) − hαe (v + 0.5)J(J + 1) − hDe (J(J + 1))2 4


(1)

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where Ev,0 is a solution for a discrete state problem shown in next subsection and substitutes 2 the V (re )+hωe v + 21 −hωe χe v + 12 terms seen in the common expression for anharmonic potential; the spectroscopic constants used for the potential and evaluation of the quality of PECs were obtained as: h ¯ 4πµre2 s 1 d2 V (re ) 1 = 2π µ dr2 " # 2 Be2 re4 10Be re2 d3 V (re ) d4 V (re ) = − 4¯hωe2 3¯ hωe2 dr3 dr4 2Be2 2Be re3 d3 V (re ) +3 =− ωe h ¯ ωe2 dr3 4B 3 = 2e ωe " 2 # Be2 re4 d4 V (re ) 14re2 Be d3 V (re ) = − 16¯ hωe2 dr4 9¯ hωe2 dr3

Be =

(2a)

ωe

(2b)

ωe χ e αe De Y00

EZP E = hY00 +

hωe hωe χe − 2 4

(2c) (2d) (2e) (2f) (2g)

64

R-Matrix theory

65

For one-dimensional systems, one of the most prominent and accurate methods is the time-

66

independent R-matrix theory. The Schrödinger equation for the system including nonadia-

67

batic coupling can be expressed as: 1 1 d2 d 1 d − I 2 + V(r) − EI − M(r) + M(r) ψE (r) = 0, 2µ dr µ dr µ dr

(3)

68

where I is the identity matrix, V(r) is diagonal matrix of adiabatic potentials, and M(r) is

69

the matrix of nonadiabatic coupling elements. For a bound interval r ∈ [ri , rf ], the above

5



70

Page 6 of 20

expression can be rewritten as:

ˆ + V(r) − EI − U ˆ ψE (r) = L ˆ+D ˆ ψE (r), K

(4)

where → ← − − 2 1 d I d d ˆ =− I ˆ= K +L 2 2µ dr dr 2µ dr 1 d 1 d ˆ L=I δ(r − rf ) − δ(r − ri ) 2µ dr 2µ dr ← − − → ˆ = d M(r) − M(r) d U dr µ µ dr ˆ = M(r) (δ(r − rf ) − δ(r − ri )) D 2µ

(5a) (5b) (5c) (5d)

71

By selecting an orthonormal on all interval set of Nb basis functions ϕn (r), we can introduce

72

the eigenproblem:

ˆ + V(r) − εn I − U ˆ ϕn (r) = 0 K

(6)

73

To solve the Eq. 6 we expand the basis functions in terms of discrete value representation

74

(DVR) functions πj (r): ϕn (r) =

Nb X

(7)

cnj πj (r)

j=1 75

and we get a simple eigenproblem: (8)

Wdn = εn dn ,

76

where





 c1     d=  ··· ,   cNb

  W1,1 · · · W1,Nb  W= ··· ···  ···  WNb ,1 · · · WNb ,Nb

6


     

(9)

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77


and matrix elements Wi,j are: Z

rf

Wi,j =

(10)

ˆ + V(r) − U)π ˆ j (r)dr πi (r)(K

ri

78

Similarly, the solution to Eq. 4 can then be written as:

ψE (r) =

Nb X

(11)

Cn (E)ϕn (r)

n=1

79

The solution is then: ˜ r,ri (E)ψE0 (rf ) + ˜ r,r (E)ψE0 (rf ) + R ψE (r) = R f ˜ r,r (E)M(rf )ψE (rf ) + R ˜ r,ri (E)M(ri )ψE (ri ), R f

80

where ψE0 is the derivative of the wavefunction, and

˜ xz (E) = R

Nb X

(1 − 2δxz )

n=1

81

ϕn (rx )ϕTn (rz ) 2µ(En − E)

(13)

The wavefunctions can then be obtained through R-matrix propagation as: 



82

(12)





ψE0 (rf )



  ψE (rf )   Rf f (E) Rf i (E)   ,  =  Rif (E) Rii (E) ψE0 (ri ) ψE (ri )

(14)

−1  ˜ ˜  Rf f (E) Rf i (E)   I − Rf f (E)M(rf ) −Rf i (E)M(ri )    =   ˜ if (E)M(rf ) I − R ˜ ii (E)M(ri ) Rif (E) Rii (E) −R

 ˜ ˜ Rf f (E) Rf i (E)   ˜ if (E) R ˜ ii (E) R

where 





(15) 83

The discrete state energy levels are found by finding solution to: det[Q(r) (E) − Q(l) (E)] = 0

7


(16)


84

where l and r indicate the direction of approach towards the sector containing the minimum

85

of potential, (ri , rs ) and (rs , rf ). The Q matrices are expanded as follows: (l)

(l)

(l)

(l)

Q(l) (E) = Rf i (E)Pi (E)[I − Rii (E)Pi (E)]−1 Rif (E) + Rf f (E) (r)

(r)

(r)

(r)

Q(r) (E) = Rif (E)Pf (E)[I − Rf f (E)Pf (E)]−1 Rf i (E) + Rii (E) p Pi (E) = δ 2µ(V(ri ) − E) q Pf (E) = δ 2µ(V(rf ) − E)

86

Results and discussion

87

Potential energy curves 80000 Potential Energy / cm−1

70000

3 −

3 Σ

’3

60000

C Π B3Σ−

50000

O(3P) + S(1D)

C3Π

40000

(17)

53Π

43Π

O(3P) + S(3P)

3

A Π

30000 20000

µ / a.u.

10000

3 −

X Σ

0 1 0.5 0

C3Π

3

4 Π

A3Π

B3Σ− 33Σ−

’3

C Π

NACME / cm

−1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 20

43Π − 53Π

C3Π − C’3Π

10

C’3Π − 43Π B3Σ− − 33Σ− 0

1

1.5

2 2.5 Internuclear Distance / Å

3

3.5

Figure 1: Potential energy curves for bright electronic states of triplet SO 88

The potential energy curves were calculated based on MRCI-F12+Q/aug-cc-pV(5+d)Z

89

theory implemented in MOLPRO2015 and are shown in Fig. 1. The adiabatic electronic

90

states form two groups of nonadiabatically-coupled (NAC) potentials, in 3 Σ (B3 Σ− − 3 3 Σ – ) 8


Page 9 of 20

55000

3 −

3 Σ ’3

C Π 50000 Potential Energy / cm−1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3 −

C3Π

B Σ

45000

40000 A3Π 3 −

X Σ 35000

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Internuclear Distance / Å

3

Figure 2: Discrete state energy levels for

32

SO

91

and 3 Π (C3 Π − C03 Π, C03 Π − 4 3 Π, 4 3 Π − 5 3 Π) symmetries. For the purpose of the spectra

92

discussed in this article, the calculations included following transitions: single potential

93

transition to A3 Π ←−− X3 Σ− , and two coupled-potential transitions for [C3 Π − C03 Π] ←−−

94

X3 Σ− , and [B3 Σ− −3 3 Σ− ] ←−− X3 Σ− states. There is a visible hump on the potential energy

95

curve of 3 3 Σ− state at ≈ 1.7 Å, which is a result of a nonadiabatic coupling with a higher

96

3

Σ− state, but it could not be included in the ab-initio calculations due to convergence issues.

97

This limitation does not affect the end results, since it is a dissociative state with transition

98

energies above the energy range we are considering for this study.

99

The density of states increases significantly above the avoided crossing point for the B3 Σ−

100

potential at 50 900 cm−1 (196.46 nm). The potential well of the adiabatic state changes profile

101

from deep and narrow potential to broad and shallow, allowing for the increase in density.

102

Close to the top of potential barrier on C3 Π adiabatic state, where it is coupled with a

103

dissociative C03 Π state, a resonant behavior can be observed, as a result of narrow barrier

104

between bound and dissociative states, starting at 48 892 cm−1 (204.53 nm), as shown in

105

Fig. 2.

106

To evaluate the quality of the potential energy curves, spectroscopic constants were cal-

107

culated based on the approach shown in Eqs. 2a to 2g and are presented in Table 1. As

9



108

can be seen, the potential energy curves are in good agreement with the previous studies,

109

both experimental and computational. One thing that our calculation adds that is essential

110

for our work, but missing from all other studies, (making the calculations necessary in the

111

first place) are the nonadiabatic coupling matrix elements between coupled states, allow-

112

ing further exploration of the system on a purely theoretical basis. Work by Danielache et

113

al. 23 did include nonadiabatic couplings, but they were calculated at different level of the-

114

ory than the potential energy curves (MRCI for PEC, versus CASSCF for NACs) and their

115

reported values of ωe (1095.24 cm−1 for

116

(see Table 1).

32

SO) are significantly different from other studies

10


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Table 1: Spectroscopic constants for isotopically-substituted SO potential energy curves Isotopologue State 32 16 S O X3 Σ− Calc. 19 Calc. 20 Calc. 21 Expt. 12 Expt. 13 Expt. 14 Expt. 15

S O

33 16

S O

34 16

S O

36 16

Te , cm−1 0 0 0 0 0 0

re , Å ωe , cm−1 1.492 1150.48 1.4865 1149.9 1.481 1153 1.493 1137 1.481 1148 1.481 1149 1150.695

ωe χe , cm−1 6.56 6.16 5.77 5.84 6.12 5.6 6.377

A3 Π Calc. 19 Calc. 21 Calc. 20 Expt. 12

38879.3 38334 38880 38931 38455

1.593 438.59 1.6196 408 1.613 420 1.719 371 1.609 413.3

1.562 1.98 1.84

0.62 0.60 0.62

1.6

0.6107

C3 Π Calc. 19 Calc. 20 Expt. 16

44908.9 44033 44038 44381

1.671 736.92 1.6692 713.3 1.681 747 1.654 694.2

5.25 5.71 21.6

0.566 0.5675 0.5596 0.578

B 3 Σ− Calc. 19 Calc. 20 Expt. 13 Expt. 14

41706.5 41314 41206 41629 41639.2

1.785 1.782 1.794 1.775

633.06 631.7 687 630.4 622.5

4.04 4.16

0.496 0.4959

4.79 2.6

0.5245 0.502

X3 Σ− Expt. 15

0

1.492

1144.65

6.49

0.703 0.7107

A3 Π C3 Π B3 Σ−

38879.3 44908.9 41706.5

1.593 1.671 1.785

436.37 733.19 629.85

1.546 5.197 4.00

0.62 0.56 0.491

X3 Σ− Expt. 15

0

1.492

1139.15

6.43

0.696 0.7039

A3 Π C3 Π B3 Σ−

38879.3 44908.9 41706.5

1.593 1.671 1.785

434.28 729.67 626.83

1.53 5.147 3.966

0.62 0.555 0.486

X3 Σ− A3 Π C3 Π B3 Σ−

0 38879.3 44908.9 41706.5

1.492 1.593 1.671 1.785

1128.97 430.39 723.14 621.22

6.32 1.50 5.06 3.895

0.684 0.62 0.545 0.478

11


Be , cm−1 0.71 0.7152 0.721 0.7208 0.7208 0.7179


117

Absorption cross-sections

118

The absorption cross-sections for four isotopologues of SO, with isotopically-substituted sul-

119

fur atom were calculated ignoring all external broadening factors except for thermal broad-

120

ening, applied at T = 300 K. As seen in Fig. 3, the absorption cross-section features two

121

distinct absorption regions. The shorter wavelength bands, located at 191–235 nm range are

122

composed of transitions to [C3 Π − C03 Π] and [B3 Σ− − 3 3 Σ− ] groups of coupled potentials,

123

leads to the split in electronic state of the sulfur atom production, with a possibility to

124

obtain both through the nonadiabatic coupling between potentials. The other excitation

125

region, 235–300 nm range, consists of transitions to the A3 Π state, with a slight overlap with

126

the [B3 Σ− − 3 3 Σ− ] group, starting at ≈ 240 nm for the transitions from v = 0 , J = 0 state

127

of ground state and going up to ≈ 277 nm for v = 3 , J = 90. 10−16

σ / cm2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 20

10

−18

10

−20

10−22 10−24 10−26 10−28 10−30

32 SO 33 SO 34 SO 36

SO

200

220

240

260

280

300

λ / nm

Figure 3: Total absorption cross-section of sulfur monoxide at T = 300 K.

128

As a result of purely thermal broadening at T = 300 K, the simulated linewidths (FWHH)

129

are ≈ 0.18 cm−1 at λ = 260 nm and ≈ 0.15 cm−1 at λ = 200 nm. It is obvious that the

130

simulation of self-shielding effects are very sensitive to the resolution of the spectra, due

131

to proximity of absorption bands of different isotopologues and all competing absorbers, 12


Page 13 of 20

σ / cm2

10−16

10

−17

10

−18

10−16

32

a

10−19

σ / cm2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


199.98 32

b

SO

33

SO

34

200 SO

33

SO

SO

36

SO

200.02 34

SO

36

32

SO

S2

10−18 10−20 10−22

251.88

251.9 λ / nm

251.92

Figure 4: Excitation wavelength sensitivity for (a) self-shielding of SO; (b) self- and mutualshielding of SO (solid lines) and 32 S2 (red, dashed lines). 132

as indicated by Figs. 4a and 4b. It can be seen in Fig. 4a that even in the case of high-

133

resolution spectra of competing absorbers missing, the isotopologue-specific absorption needs

134

to be taken into account when modeling complex photochemical systems. Fig. 4b shows the

135

absorption cross-sections of isotopically-substituted SO overlapped with the spectrum of one

136

of the competing absorbers in an anoxic atmosphere –

137

effect is even more wavelength-dependent as a result of mutual-shielding caused by the

138

continuum band of S2 . While self-shielding and mutual-shielding are expected to be very

139

significant under interstellar conditions, in atmospheres they have to be considered with care.

140

Based purely on the spectra it is evident that the shielding effects are expected to be very

141

large, however they also depend on the vertical distribution of the absorbers and the vertical

142

flux of species in question. The spectra are also susceptible to the variation in potential

143

energy curves: different anharmonic potentials would provide slightly shifted spectra and

144

result in different isotopic fractionation factors.

13

S S. 10 In this case the shielding

32 32



145

Conclusions

146

Based on new ab-initio potential energy curves of sulfur monoxide, we have calculated high-

147

resolution absorption cross-sections for four sulfur-isotope-substituted SO molecules. We

148

have shown that the density of discrete states is significantly greater at excitation energies

149

close to avoided crossings for nonadiabatically-coupled electronic states. The high-resolution

150

absorption cross-sections contribute to the ongoing studies of isotopic fractionation and self-

151

shielding, which is worth considering both in isolation of a single species, as shown at λ ≈

152

200 nm wavelength, as well as in combination of both self-shielding and mutual-shielding of

153

competing absorbers, as shown at wavelength of λ ≈ 251.9 nm. The absorption cross-sections

154

shown in this study can be used as a reference for groups trying to measure the absorption

155

spectra of sulfur monoxide, as well as modeling community studying isotopic effects, and

156

self-shielding in atmospheric photochemistry.

157

Acknowledgement

158

The authors thank the anonymous referees for their great comments on improving the article.

159

This work was supported by a Grant-in-Aid for Scientific Research (S) (No. 17H06105) from

160

the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan and

161

The Sophia University Special Grant for Academic Research, Research on Optional Subjects.

162

Karolis Sarka is supported by a Japanese Ministry of Education, Culture, Sports, Science,

163

and Technology (Monbukagakusho: MEXT) Scholarship.

164

Supporting Information Available

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The potential energy curves are available to download as Supporting Information. Authors

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are happy to provide the full resolution absorption cross-sections upon request.

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The following files are available free of charge. 14


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• Potential energy curves for each electronic state

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• Electronic transition dipole moments from ground state

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• Nonadiabatic coupling matrix elements for all coupled states

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References (1) Seinfeld, J. H.; Pandis, S. N. Atmospheric Chemistry and Physics: From Air Pollution to Climate Change; John Wiley & Sons, 2016.

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(3) Jessup, K. L.; Spencer, J.; Yelle, R. Sulfur Volcanism on Io. Icarus 2007, 192, 24–40.

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(30) Dunning Jr, T. H.; Peterson, K. A.; Wilson, A. K. Gaussian Basis Sets for Use in

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Graphical TOC Entry 55000

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Potential Energy / cm−1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


33Σ−

C’3Π 50000

3 −

B Σ C3Π

45000 40000 35000

A3Π 1.2

1.4

1.6

X3Σ−

1.8 2 2.2 2.4 Internuclear Distance / Å

19


2.6

2.8

3

Potential Energy / cm−1

55000 1 2 3 4 5 6 7 8 9 10 11 12 13 14

The Journal of Physical Chemistry 33Σ− ’3

Page 20 of 20

C Π

50000

B3Σ− C3Π

45000 40000 35000

A3Π 1.2

1.4

1.6


1.8 2 2.2 2.4 Internuclear Distance / Å

X3Σ− 2.6

2.8

3

Total Absorption Cross-Section for UV Excitation of Sulfur Monoxide

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