electronic spectroscopy ch 11 mchale 21... · electronic spectroscopy ch 11 mchale. ... –...

Electronic Spectroscopy CH 11 McHale

What does the spectrum look like?

• gas phase– Vibrational and rotational structure can be

resolved (in many systems). – Electronic spectrum often looks like

progressions of energy differences for allowed transitions from the ground and other thermally populated states to a series of excited vibrational levels (as set by the Franck-Condon factors).

– Dissociation/Predissociation

Potential surfaces for NO

C∞v symmetry group

Note irreducible reps of this group are label Σ, Π, Δ, Φ,

etc.

Ground State: XFirst excited state of same Mulitplicity: AThen B, C, D, …

First excited state of different multiplicity: aThen b, c, d, …

State Symmetries

• Text provides a good overview of how to go about accounting for number of energy levels and their degeneracy for LCAO in diatomics.

• In general can apply technology we developed in Group theory to derive irreducible rep for any wavefunction.

Selection Rules/Intensity• Use group theory as an aid. Recalling that

transition dipole moment transforms as x, y, z.

• Intensity ∝

<f|μ|i>2 ~|< Ψef |μ

| Ψei ><vf |vi >|2

this assumes dipole moment can be treated as independent of R. An OK approximation.

Franck-Condon factorΣf |<vf |vi >|2=1


X→A

X←A


X→B

X←B

Journal of Quantitative Spectroscopy &Radiative Transfer 90 (2005) 275–289

www.elsevier.com/locate/jqsrt

Experimental study and calculations of nitric oxide absorptionin the �(0; 0) and �(1; 0) bands for strong temperature

conditions

H. Trada ;∗, P. Higelina, N. Djeba12li-Chaumeixb, C. Mounaim-RousselleaaLaboratoire de M�ecanique et Energ�etique, Ecole Polytechnique d’Orl�eans, Site L�eonard de Vinci,

8 rue L�eonard de Vinci, Orl�eans Cedex 2 45072, FrancebLaboratoire de Combustion et Syst&emes R�eactifs, CNRS, 1C avenue de la recherche scienti,que,

Orl�eans Cedex 2 45071, France

Received 9 September 2003; accepted 13 March 2004

Abstract

Absorption spectra of nitric oxide in the �(0; 0) and �(1; 0) bands have been measured for hard temperatureconditions up to 1700 K in order to validate a model for the simulation of these two bands. The goodagreement between experiments and calculations (relative errors of 2–5% for the �(0; 0) band and 10–15%for the �(1; 0) band) consolidates the two important assumptions concerning the intermediate Hund’s casebetween (a) and (b) for the X2� state of the �(0; 0) and �(1; 0) absorption bands and the use of collisionalbroadening parameters of �(0; 0) to simulate the �(1; 0) band. Using this simulation, a study of the Beer–Lambert law behavior at high temperature has been carried out. With the instrument resolution used for theseexperiments, it was shown that a correction of the Beer–Lambert law is necessary. To apply this techniquefor the measurements of NO concentrations inside the combustion chamber of an optical SI engine, a newformulation of the Beer–Lambert law has been introduced, since the modiDed form proposed in the literatureis no longer applicable in the total column range of interest.? 2004 Elsevier Ltd. All rights reserved.

Keywords: UV absorption spectroscopy; Nitric oxide; Spectra simulation

1. Introduction

To better understand the NO formation inside the combustion chamber of IC engines, severaloptical techniques have been developed. These techniques have always been confronted to many

∗ Corresponding author. Tel.: +33-238417050; fax: +33-238417383.E-mail address: [email protected] (H. Trad).URL: http://www.univ-orleans.fr/ESEM/LME

0022-4073/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.jqsrt.2004.03.017

mailto:[email protected]

http://www.univ-orleans.fr/ESEM/LME

H. Trad et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 90 (2005) 275–289 277

is thought to be due to a missing of pressure broadening and shift data. However, using parametersof the �(0; 0) band to calculate the �(1; 0) one appears to be a good alternative since it has beenproven that this assumption works well for excitation and Quorescence spectra [22].In this section, we present a detailed overview on the �(0; 0) and �(1; 0) NO absorption bands

calculation. VeriDcation with experimental results will be presented in the last section of this work.

2.1. Simulation of the �(0; 0) band

Absorption structure has been Drst computed from the integrated absorption coeKcient of rotationallines expression used by Nicholls [23]:

ktot =∫line

kv d�=�e2

mc2f00

Sj′j′′

2J ′′ + 1N (J ′′); (1)

where m and e are, respectively, the electron mass and charge and c the light celerity, expressed inthe electrostatic unit system (ergs). f00(4:01 10−4) is the �(0; 0) band absorption oscillator strength,measured by Farmer et al. [15] with an accuracy of ±5%. SJ ′J ′′ are the H1onl–London factors, ob-tained from the LIFBASE database [24] which calculates Einstein emission coeKcients and transitionfrequencies according, respectively, to Schadee [25] and Brown et al. [26] and uses formulas derivedby Kovaks [27] and Earls [28] to calculate SJ ′J ′′ , whereas N (J ′′) is the population of the groundstate. As the lower level X2� is composed of two sub-states X2�1=2 and X2�3=2 (spin doublet), thepopulation should be calculated for each sub-level using the rotational energy F(J ′′) correspondingto each one, respectively. Besides, NO is a heteronuclear molecule, and then dissymmetrical, thetwo possible orientations of the electronic rotation angular momentum vector produces two diOerentenergy levels (� doublet) for each of the two sub-states X2�3=2 and X2�1=2.The four expressions of F(J ′′) are presented by Reisel et al. [29]. N (J ′′) is expressed as follows:

N (J ′′) = n0(2J ′′ + 1)

Qrexp

[−hcF(J ′′)kT

]; (2)

where n0 is the number of molecules per cm3 at the pressure and temperature conditions of theexperiment, k and h are, respectively, the Boltzmann and Planck constants. Qr is the rotationalpartition function expressed as

Qr =∑J ′′(2J ′′ + 1)

[exp

(−hcF(J ′′; X 2�1=2; c)kT

)+ exp

(−hcF(J ′′; X 2�1=2; d)kT

)

+exp(−hcF(J ′′; X 2�3=2; c)

kT

)+ exp

(−hcF(J ′′; X 2�1=2; d)kT

)]: (3)

The absorption cross-section �(cm2) is then determined using the absorption coeKcient and n0,as noticed Okabe [30]

�tot =ktotn0

: (4)

278 H. Trad et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 90 (2005) 275–289

The broadening eOects are then applied to the obtained line absorption structure. Only Doppler(temperature) and Lorentz (pressure) broadenings are considered in this work. The natural line widthis neglected because it is about 5000 times lower than the Doppler one at ambient temperature.Holtsmark broadening (due to collisions with atoms of the same kind) was included in the Lorentzone.Voigt proDle has, therefore, been used while it combines temperature and pressure eOects. The

analytical form of this proDle is too computationally intensive, an empirical expression determinedby Whitting [31] was then used. It presents only a maximum error less than 3% in the ranges oftemperature and pressure of interest:

Fv(�) =1

avWv

{(1− Wc

Wv

)exp(−4 ln(2)�2) +

(Wc

Wv

)1

1 + 4�2

+0:016(1− Wc

Wv

) (Wc

Wv

) [exp(−0:4�2:25)− 10

10 + �2:25

]}; (5)

where �= (�− �0)=Wv and Wc and Wv are, respectively, the pressure broadening and Voigt proDleFWHM expressed as follows:

Wv =Wc

2+

√W 2c

2+Wd (6)

and av is the Voigt line shape factor:

av = 1:065 + 0:447Wc

Wv+ 0:058

(Wc

Wv

)2: (7)

It should be noted that∫line Fv(�) d�= 1.

Wd is the temperature broadening, which is well known thanks to the Maxwell–Boltzmann velocitydistribution of atoms. It is given by the formula [30,32]

Wd =2√2R ln(2)c

�0

√TM= 7:1623× 10−7�0

√TM

; (8)

where R is the ideal gas constant, �0 the wave number at the center of the absorption line, T thetemperature and M the molecular weight.Whereas the Doppler broadening depends only on temperature of the mixture, the collision

eOect depends also on pressure and mixture composition. In the assumption of binary intermolecularcollisions, this broadening parameter is proportional to pressure [33,34]. It is calculated as [35]

Wc =q∑

i=1

2�NO−iXiP; (9)

where q is the number of foreign species, Xi the molar fraction of each foreign species and P thetotal pressure. 2�i is the full-width at half-maximum associated to the species i for pressure equalto one. Its general form was given by [36]

2�i = 2�0

(TrefT

)n

: (10)


Table 1Collision broadening parameters, gathered from the literature, for diOerent background gases, at Tref = 295 K

Species 2�0 n

N2 0.585 0.75Ar 0.505 0.65CO2 0.585 0.75CO 0.585 0.75O2 0.530 0.66H2O 0.790 0.79NO 0.550 —

Tref is the reference temperature at which the value of 2�0 is known. n typically varies between 0.5and 1.The collision broadening parameters are usually determined experimentally for each individual

background gas. Parameters, concerning the �(0; 0) band, for some NO collider partners have beenfound in the literature. Values for N2, Ar [35], CO2, CO [37], O2 and H2O [38] are gathered inTable 1. Data concerning NO are only available for room temperature of 295 K [38]. The samevalues were applied for all rotational lines since Chang et al. [35] showed that they are independentof the rotational quantum number J ′′. Di Rosa et al. [37] noticed that values of 2�0 and n for N2 areapplicable with a good match for CO and CO2, and that explains the values in Table 1 concerningthese two molecules.Besides the broadening eOect, pressure generates shift of rotational lines. However, as it was

demonstrated by Chang et al. [35], rotational line shifts do not depend on the line itself. In thatway all the lines will shift of the same quantity and this will only results in a simple translation ofthe Dnal spectrum. Then the shift eOect has not been included in the Voigt function. Results of the�(0; 0) band simulation at 300 and 1500 K and pressure of 1 bar are shown in Fig. 1.Using the absorption cross-section spectrum, light transmittance has been calculated through the

classic Beer–Lambert law, for the corresponding total column. Finally, in order to get a represen-tative spectrum of what was measured, the instrument line shape of the used spectrometer (0:3 nmresolution) has been convoluted with the obtained transmittance. The slit function (Fs) was obtainedusing a calibration low-pressure mercury lamp (Oriel Inst.) to record the line proDle at 253:65 nm.Then, it is compensated for a slightly lower spectrometer dispersion at 226:3 nm. The obtainedfunction was, Dnally, normalized to its integral

∫Fs(#) d#= 1: (11)

Convoluting Fs by the transmittance appeared to be a very heavy computing task which executingtime depends on the sizes of the two matrices. For that reason, a calculation step ($l) of 10−1 cm−1was used instead of 10−2 cm−1 without losing information that could eOect the Dnal result. Moreover,the limits for the Voigt function wings (which go down to zero at the inDnity) were Dxed to 10−4($2).Below this limit the Dnal result deviated as shown in Fig. 2.


225 225.2 225.4225.6 225.8 226 226.2 226.4226.6 226.8 2270

2

4

6A

bsor

ptio

n C

ross

Sec

tion

(cm

2 )

221 222 223 224 225 226 2270

1

2

3

4

5

6× 10-18× 10-18

λ (nm)λ (nm)

Abs

orpt

ion

Cro

ss S

ectio

n (c

m2 )

(a) (b)

Fig. 1. (a) NO absorption cross-section in the �(0; 0) band at 300 K and 1 bar. (b) NO absorption cross-section in the�(0; 0) band at 1500 K and 1 bar.

225 225.5 226 226.5 2270

0.2

0.4

0.6

0.8

1

1.2

1.4

λ (nm)

Cal

cula

ted

Abs

orpt

ion

Cro

ss S

ectio

n (c

m2 )

ε1 = 10-1, ε2 = 10-3

ε1 = 10-1, ε2 = 10-4

ε1 = 10-1, ε2 = 10-6

ε1 = 10-2, ε2 = 10-4

10-310-4

10-510-61.25

1.255

1.26

1.265

1.27

1.275

1.28

1.285× 10-18× 10-18

ε2

Abs

orpt

ion

cros

s se

ctio

n at

the

pea

k of

the

ban

d

(a) (b)

Fig. 2. (a) Calculated absorption cross-section at 300 K; 30 bar and 6:7×1017 cm−2, for diOerent calculation steps ($1 and$2). (b) Evolution of the band peak at 226 · 28 nm against the limit for the Voigt function wings ($2), at 300 K; 30 barand 6:7× 1017 cm−2.

2.2. Simulation of the �(1; 0) band

The same procedure as for the �(0; 0) band was followed to calculate the �(1; 0) one. The absorp-tion oscillator strength (f10 = 8:09× 10−1) is taken from [15] whereas the H1onl–London factors areobtained from the LIFBASE database [24]. Two very important assumptions were made to do thesecalculations. First is that the rotational energy function has the same form as that of the �(0; 0) band,


PG-200

L2

D-H Lamp 190 – 400 nm

ICCD Camera

Jobin-Yvon spectrometer

PC

L1L2

Shock tube

Pressureprobe

Synch.card

Fig. 3. Experimental set-up for the absorption spectra measurements of NO at high temperatures.

but using parameters of the �(1; 0) band, obtained from [29,39–41]. The second is that the pressurebroadening parameter values are the same as of the �(0; 0) band. The results of the calculations arediscussed in the last section where they are compared to measurements.

3. Experimental setup

A 78 W broadband deuterium halogen light source (DH-2000) is used to produce UV light in the190–400 nm range. Due to the high dependence of the lens refractive index on the light wavelengthin the UV range, a Drst plano-convex lens L1 (UV synthetic fused-silica, 25 mm focal length,15 mm diameter) is used to focus the beam on a pinhole (0:55 mm). This spatial Dlter eliminatesthe undesirable wavelengths (outside the 200–230 nm region). A second lens L2 (UV syntheticfused-silica, 75 mm focal length, 50 mm diameter) is placed at 70 mm on the opposite side of thepinhole. The transmitted parallel beam (2 mm diameter) is then focused at the entrance slit of thespectrometer, using a lens (L2). This single beam is suKcient to make absorption measurementswith a good signal to noise ratio SNR, of about 400.The detection system is composed of a spectrometer (190 mm focal length Jobin–Yvon, with

Czerny turner conDguration) equipped with an unpolarized plane ruled grating (1200 gr=mm, blazedat 250 nm). The width of the entrance slit was set to 50 �m allowing a good agreement betweenthe light energy passing into the spectrometer and the resolution (∼0:3 nm at 226:28 nm). Thetransmitted light is then detected by a 12-bit intensiDed CCD Pentamax camera (Princeton Inst.).With the 4:63 nm=mm dispersion of the grating, it was possible to observe a range of 42 nm on theCCD, allowing to display the two absorption bands of NO, �(0; 0) and �(1; 0) on the same image.Each individual spectrum is recorded with a gate width of 350 �s. A scheme of the experimentaldevice is displayed in Fig. 3.The shock tube used for these experiments is made of high-purity stainless steel (circular cross-

section of 40 mm diameter) that has been extensively used at the LCSR (CNRS, OrlVeans) forhigh-temperature measurements of chemical reaction rates [42,43]. The tube is Dtted on both sideswith suprasil synthetic windows (10 mm thick, 10 mm in diameter, yield of about 95% each, in theregion 200–230 nm) to allow the light beam to cross the gas mixture.Two mixtures of 0.3% and 1% pure NO in Argon were used to make spectra acquisitions. Spectra

measurements have been synchronized with the reQected shock wave when crossing the light beam,using the pressure signal of the probe placed at the same location as the light beam.


224.5 225 225.5 226 226.5 227 227.50.5

0.6

0.7

0.8

0.9

1

Tra

nsm

ittan

ce

SimulationExperiment

224.5 225 225.5 226 226.5 227 227.5

-0.07

-0.04

0

0.04

nm

Dis

crep

ancy

224.5 225 225.5 226 226.5 227 227.50.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Tra

nsm

ittan

ce


224.5 225 225.5 226 226.5 227 227.5

-0.04

-0.02

0

0.02

0.04

nm

Dis

crep

ancy

224.5 225 225.5 226 226.5 227 227.50.7

0.75

0.8

0.85

0.9

0.95

1

Tra

nsm

ittan

ce


224.5 225 225.5 226 226.5 227 227.5-0.03

0

0.03

nm

Dis

crep

ancy

224.5 225 225.5 226 226.5 227 227.50.7

0.75

0.8

0.85

0.9

0.95

1

Tra

nsm

ittan

ce


224.5 225 225.5 226 226.5 227 227.5-0.1

0

0.1

nm

Dis

crep

ancy

224.5 225 225.5 226 226.5 227 227.50.9

0.92

0.94

0.96

0.98

1

Tra

nsm

ittan

ce


224.5 225 225.5 226 226.5 227 227.5-0.05

0

0.05

nm

Dis

crep

ancy

T=734 K, P=3 bar, [NO]=O.50 mol/m3 T=968 K, P=3.5 bar, [NO]=O.42 mol/m3

T=1350 K, P=3.3 bar, [NO]=O.29 mol/m3 T=1484 K, P=3.1 bar, [NO]=O.25 mol/m3

T=1712 K, P=2.8 bar, [NO]=O.06 mol/m3

Fig. 7. Measured and simulated absorption spectra of the nitric oxide �(0; 0) band for diOerent temperature and concen-tration conditions.


213.5 214 214.5 215 215.5 2160.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Tra

nsm

ittan

ce


213.5 214 214.5 215 215.5 216-0.04

-0.02

0

0.02

0.04

nm

Dis

crep

ancy

213.5 214 214.5 215 215.5 2160.4

0.5

0.6

0.7

0.8

0.9

1

Tra

nsm

ittan

ce


213.5 214 214.5 215 215.5 216-0.05

0

0.05

nm

Dis

crep

ancy

213.5 214 214.5 215 215.5 2160.5

0.6

0.7

0.8

0.9

1

Tra

nsm

ittan

ce


213.5 214 214.5 215 215.5 216

-0.1

0

0.1

nm

Dis

crep

ancy

213.5 214 214.5 215 215.5 2160.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Tra

nsm

ittan

ce


213.5 214 214.5 215 215.5 216

-0.1

0

0.1

nm

Dis

crep

ancy

213.5 214 214.5 215 215.5 2160.8

0.85

0.9

0.95

1

Tra

nsm

ittan

ce


213.5 214 214.5 215 215.5 216-0.1

0

0.1

nm

Dis

crep

ancy

T=734 K, P=3 bar, [NO]=O.50 mol/m3 T=968 K, P=3.5 bar, [NO]=O.42 mol/m3

T=1350 K, P=3.3 bar, [NO]=O.29 mol/m3 T=1484 K, P=3.1 bar, [NO]=O.25 mol/m3

T=1712 K, P=2.8 bar, [NO]=O.06 mol/m3

Fig. 8. Measured and simulated absorption spectra of the nitric oxide �(1; 0) band for diOerent temperature and concen-tration conditions.

Dissociation and predissociation

What features of the spectrum could we use to determine the dissociation energy of the ground and excited states?

Ground State: (1a1 )2 (2a1 )2(1b2 )2 (3a1 )2 (1b1 )2 (4a1 )0(2b2 )0

Oxygen 1s →1a1

All orbitals doubly occupied 1A1 . What are the spin/symmetry of the first two excited states?

H2 O

J. Phys. R: A

tom. M

olec. Phys.. Vol. 11, N

o. 6. @ 1978--E

Ishigtrro ~t ctl

[facing page 9941

Absorption spectra of H,O and D z O in the vuv region 995

Ib, -B npal

I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ,

1000 1050 1100

Wavelength (A ) Figure 2. A densitometer trace of the absorption spectrum of H 2 0 in the 1140-980 a region. The ordinate indicates the absorption intensity in arbitrary units. The C series is assigned to the l b , -+ nda, Rydberg series, the C' series to the lb , ---f nda, series and the D series to both lb , -+ ndb, and l b , -+ nda, series, according to Goddard and Hunt (1974).

experiment. Numerous bands can be seen throughout the region from 1130 to 650 A. We shall divide the spectrum observed into three regions and consider them separ- ately.

3.1. 1 1 30-980 A region 3.1.1. l b , -+nd Rydberg series. Figures 2 and 3 show densitometer traces of the absorption spectra of H 2 0 and D 2 0 in the 1130-980 A region, respectively. Intense

Ib, + npa, Ib,+nd 6 5 n=4

1000 1050 1100

Wavelength $4 Figure 3. A densitometer trace of the absorption spectrum of D 2 0 in the 1140-980 region. The C, C' and D series are assigned to four optically allowed l b l -+ nd Rydberg series (see the caption of figure 2 ) .

998 E Islziguro et a1

Table 2. Vibrational bands associated with lb l + nd Rydberg series (CC'D series).

H 2 0 DZO

Vibrational €ohs "1 l a b s €ohs V 1

i i Series assignment (A) (cm-') (cm-') (A) (cm-') (cm-')

3 c

C'

D

4 c

C'

D

5 c

C'

D

6 CC'D

7 CC'D

1128.1 109057 l055.0t

1122.0 1083.8

1113.8 1075.7 1038.1 1004.2

1057.0 1022.8

1055.0 1021.4

1052.8 1019,Ot

1027.5 995.0

1013.2 981.7

1005.1 973.6

88645 91701 94787

89127 92268

89783 92963 96330 99582

94607 97771

94787 97905

94985 98135

97324 100503

98697 101864

99493 102712

3056 3086

3141

3180 3367 3252

3164

3118

3150

3179

3167

3219

1127.5 1098.7 1072.4

1121.3 1093.0 1065.3

1113.0 1084.9 1057.5 1031.7

1055.9 1030.8

1054.5 1028.9

1052.6 1028.0

1027.2 1003.1

1026.8 1002.7

1026.4 1002.1

1012.0 988.9

1003.8 98 1.0

88692 91017 93249

89182 91491 93870

89847 92114 94563 96921

94706 97012

94832 97191

95003 91216

91352 99691

97390 99731

97428 99790

98814 101122

99621 101937

2325 2232

2309 2379

2321 2389 2364

2306

2359

2273

2339

2341

2362

2308

2316

t Indicates indefinite band (overlapping with other transitions).

absorption spectrum of D 2 0 in the 1130-105OA region has not been published hit herto.

In the present experiment, many vibrational bands which relate with the CC'D series are observed. The wavelengths of these bands in H 2 0 and D 2 0 and the vibrational assignments are given in table 2. A comparison between the fundamental vibrational frequencies in various electronic states is shown in table 3. The bands giving the bending mode v 2 and the anti-stretching mode v g have not been observed.

3.1.3. ' B , ( l b l --+ npa,) Rydberg series. The bands at 1090.5 and 1042.8 8, in the H 2 0 spectrum are the second and third members of the 'A' Rydberg series of Price, the first member of which (at 1240.6 A) was attributed to the 'Bl(lbl -+ 3pal) t x 'Al transition by Johns (1963). Additional higher members of the l b l --+ npa, Rydberg series have been observed in the present spectrum. The wavelengths and other information about these bands are given in table 4.

Absorption spectra of H 2 0 and D 2 0 in the vuv region 999

Table 3. A comparison between fundamental vibrational frequencies in various electronic states.

v1 (cm-') v 2 (cm-') v 3 (cm-')

Ground statea x 'Al

'Bl(lbl -+ 3 ~ a , ) ~

'Bl(lb, -+ 3dal)'

'B2(lbl -+ 3da2)"

'Al(lbl -+ 3dbl)' 'Bl(lbl -+ 3da9

2Bl(lb; ') Ionic stated

3657 2671

3179 2338

3268 2381

30563 2325

3141 2309

3180 2311

3242 2363

1595 1178

1407 1038

1636 1223

1428 1065

3756 2788

32387 2427t

3335t 2483t

32997 2444t

Benedict (1956) Bell (1965).

E Present work. Karlsson et al (1975).

t Calculated from v 1 and v 2 on the basis of valence force approximation. $ Uncertain.

In the DzO spectrum, a vibrational band with origin at 1088.8 A, the second member of the 'Bl(lbl -+ npal) series, has been observed at 1061.3 A. This band is assigned to the (100) band with v1 = 2380cm-l. The corresponding I lzO band cannot be seen clearly because it is obscured by the strong C2C;D2 bands.

3.1.4. Unassigned bunds. Several bands which could not be assigned here are listed in table 5.

The band of HzO at 1067.0 A was tentatively assigned to the 'Bl(lbl-+ 5sal) +- x ' A I transition by Goddard and Hunt (1974). However, the band arising from this

Table 4. 'Bl(lbl -+npal) Rydberg series

Lobs €obi Quantum ' €ohs Quantum (cm- l) defect n (4 (cm-') defect

3 1240.6-F 80606 0.72 1238.6T 80736 0.72 4 1090.5 91701 0.70 1088.8 91844 0.70 5 1042.8 95896 0.68 1042.0 95969 0.71 6 1019.2 98116 0.52 1020.2 98020 0.70 7 1009.0 99108 0.58 1008.5 99157 0.71 8 1001.9 99810 0.52 1001.3 99870 0.70 CO (101770) (101930)

t Taken from Bell (1965)

1000 E Ishiguro et a1

Table 5. Unassigned bands (A) in the 1130-980 8, region,

HZO D2O

-1109 1103.6 1098.0 1079.7 1095.2 1017.0 1067.0 1015,2 1025.0

transition would probably be less intense because the band at 1166A observed by Bell (1965), which was attributed to the l b l -+ 4sal transition by Goddard and Hunt, is very weak in our experiment.

3.2. 980-800 A region

3.2.1. 3 a I --+ nd Rydberg series. Densitometer traces of the absorption spectra of H 2 0 and D 2 0 in this region are shown in figures 4 and 5. The spectra have a number of bands which are superimposed on a continuum spreading over this region.

The photoelectron spectrum corresponding to ionisation to the 2A,(3a; ') ionic state has a long vibrational progression with the mean band-to-band interval of 975cm-I for H 2 0 and of 715cm-' for D 2 0 (Brundle and Turner 1968). These frequencies are of the bending mode v 2 .

Wavelength 6) Figure 4. A densitometer trace of the absorption spectrum of H,O in the 980-810 A region. The bands in this region are assigned to an optically allowed 3a, + nd Rydberg series accompanied by vibrationally excited states. The asterisks signify bands corresponding to vertical transitions to the (3a, + nd) states (converging to the band at 14.745 eV in the Z A 1 ( 3 a ; 1 ) + ~ 'Al photoelectron spectrum of H20). The weaker bands in the region around 950 8, are tentatively assigned to the 301 + 4sal transition. The continuum lying in the lOOG8008, region is attributed to the 1bZ + 3sai transition. The arrows denote the absorption bands of Nz.

What does the spectrum look like?

• Liquids– Rotational structure cannot be resolved

contributes to apparent width. Vibrational progressions often still identifiable but if not also contribute to width.

electronic spectroscopy ch 11 mchale 21... · electronic spectroscopy ch 11 mchale. ... –...

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