ISSN 0036�0244, Russian Journal of Physical Chemistry A, 2013, Vol. 87, No. 13, pp. 2225–2230. © Pleiades Publishing, Ltd., 2013.

2225

1 INTRODUCTION

The electronic spectrum of boron monoxide (BO)chiefly consists of three extensive band systems involv�

ing ground�state transitions: A2Πi– , B2Σ+– ,

and C2Πr– . The A–X and B–X systems, knownas the α and β systems, which are situated in theregions of ~350–650 and ~220–330 nm, respectively,were first identified and analyzed by Mulliken, as earlyas 1925 [1]. The C–X or γ system, lying below 230 nm,was discovered by Chretien in 1950 [2]. Since theirfirst observations, all three systems of both 10BO and11BO isotopologues, which are always present in thegas phase of natural boron because it is a mixture of 10B(19%) and 11B (81%), were the subject of many stud�ies, which yielded accurate spectroscopic constantsfor the electronic states of these transitions, i.e., forthe X, A, B, and C states [3–13]. A summary of theconstants obtained through 1978 is given in the com�pilation of Huber and Herzberg [14].

In addition to the red�degraded A–X and B–Xbands, Mulliken recognized in all photographs of theA–X system, between 455 and 600 nm, weak bands ofa peculiar structure, which looked like a group of linesor band heads, some of which were clearly shaded toviolet. Mulliken identified these bands as 10BO and11BO combination bands resulting in transitions fromthe B to the A states, and gave vibrational assignmentsfor about 20 bands of both isotopologues. To the best

1 The article is published in the original.

X2Σg

+X

2Σg

+

X2Σg

+

of our knowledge, the only other data concerningthese bands that can be found in the literature thus far,are those of Nicholls et al. [15], who calculatedapproximate Morse Franck–Condon (FC) factors forseveral bands with certainty on the second decimalplace using the spectroscopic constants from [16].This is surprising in view of the astrophysical interestin the BO spectrum [17, 18] and its significance incombustion processes [19], and the suggestion that theBO radical could be the basis of a chemical laser [20,21]. The data dearth is probably related to the seriousdifficulties of their experimental observation, as theB–A bands lie within the region of the much strongerA–X bands, some of which overlap them.

In this report, we present our simulated B–A spec�trum of BO based on computed FC factors and bandorigin positions, with the aim of providing additionalinformation about these bands.

METHODOLOGY

The simulation of our emission B–A band spec�trum of BO is based on computed FC factors for v'–v''bands, q

v'v'', and band origin wavenumbers, νv'v''. The

product (qv'v'' ) was used for computation of the

relative intensities of the bands, assuming the powerintensities, rather than based on the number of pho�tons per time unit. It is useful, but, in some cases, acrude approximation of the relative band intensity,Iv'v'', which is, in fact, proportional to the product:

νv'v''4

Nv'pv'v''νv'v''

4N

v'Re2

rv'v''( )q

v'v''νv'v''4

,=

STRUCTURE OF MATTERAND QUANTUM CHEMISTRY

Franck�Condon Simulation of the B–A Bands of BO1

A. Anti �Jovanovi a, M. Kuzmanovi a, M. A. Khakoob, and R. R. Laherc

aFaculty of Physical Chemistry, University of Belgrade, P.O. Box 47,11158 Belgrad 118, SerbiabDepartment of Physics, California State University Fullerton, Fullerton, CA 92834 USA

cSpitzer Science Center, California Institute of Technology, M/S 314�6, Pasadena, CA 91125 USAe�mail: ankica@ffh.bg.ac.rsReceived December 26, 2012

Abstract—Franck�Condon simulation of the emission B–A band system of boron monoxide are given. Thecomputed band origin wavenumbers are found to be in good agreement with those derived from measured bandhead positions. In the absence of intensity measurements for the B–A bands, the simulated intensities weretested by calculation of the relative intensities of the well known A–X bands under the assumption that the elec�tronic transition moment function is constant. The resulting good agreement between the simulated and exper�imentally obtained intensity patterns for A–X bands supports the reliability of our simulated B–A spectrum.

Keywords: boron monoxide (BO) molecule, B–A band system, Franck–Condon factors, Franck–Condonsimulation of vibronic bands, relative band intensity.

DOI: 10.1134/S0036024413130049

c c c

2226

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 87 No. 13 2013

ANTI �JOVANOVI et al.C� C�

where pv'v'' = (r

v'v'')qv'v'' is the relative vibrational

transition probability of the v'–v'' band, and Re(rv'v'')

is the electronic transition moment function (ETMF). According to above relation, I

v'v'' is also propor�tional to the product:

sometimes called “the intensity at infinite tempera�ture,” I

∞, v'v'', at which the number of emitting mole�cules N

v' in all upper levels become equal. The product

( ) applies in the cases where Re(rv'v'') is

unknown, as in the case of the present B–A system,where it is considered to be constant and is absorbedinto the factor of proportionality.

Our FC factors and band origins were computedfrom Rydberg–Klein–Rees (RKR) potential energycurves for the A, B, and X states, using the latest avail�able molecular constants from [9] as input data toEspy’s computer program [22]. As the available inten�sity data were given in terms of power, the above equa�tion has the additional power of ν

v'v''; cf. Eq. (9) of[22]. Our calculations were done for the more abun�dant 11B16O isotopologue.

RESULTS AND DISCUSSION

FC factors and band�origin positions (wavelengthsand wavenumbers) of the 11B16O B–A band systemwere computed for the first time for transitions involv�ing v' and v'' levels up to 20. Table contains a portionof the computed values of both parameters in the formof the Deslandres scheme, for transitions between v'and v'' levels ≤10. The full data set is too large to bepresented here; however, it may be obtained uponrequest. The measured band origin wavenumbers,which we calculated from the A1 and B1 band head mea�surements of Mulliken [1], are listed also in table,together with our simulated relative intensities,

, of the B–A bands. The later were normalizedto the value 10 for the 0–0 band, which is theoreticallypredicted to be the strongest band in the spectrum.

Re2

pv'v''νv'v''

4,

pv'v''νv'v''

4

qv'v''νv'v''

4

A close survey of table, as well as of the full set ofcomputed FC factors, reveals that only five sequencesin the B–A system, i.e., the Δv = 0, ±1, and ±2sequences, can be expected in the experimental spec�trum.

The results indicate the 0–0 band as the strongestone in the system followed by the bands in the samesequence (i.e., Δv = 0), whose intensity falls off rap�idly as v' and v'' increase up to 6. For the bands with v'and v'' > 7, the FC factors grow very slowly, predictingthat only the first seven members of this sequence maybe experimentally observed. The distribution of theprominent FC factors above and below the diagonal ofthe v', v'' scheme predict more bands for the neigh�boring Δv = ±1 sequences than in the Δv = 0sequence, since the values of FC factors becomehigher with increasing v' and v''. The Δv = ±2sequence bands are predicted to be weaker with grad�ually growing of intensity for the higher members ofsequences.

According to our computed band origin positions,the Δv = 0, +1, –1, and –2 sequences extend from aninitial band to the violet, and the bands in thosesequences are approximately equidistant (due to a verysmall difference between and ), withmutual separations of about 6, 1, 15, and 23 Å (~20, 2,40, and 65 cm–1), respectively, and with the tendency ofslowly increasing for the members with v' and v'' > 10.As seen from table, band origin positions indicate theexistence of the turning point in the Δv = –2 sequenceat the position of the band having v'' = 6, up to whichit proceeds to the red. The successive sequence mem�bers come quite close to one another with increasing v'and v'' up to 8–6 band, after which the higher mem�bers extend in opposite direction with graduallyincreasing mutual separations.

The fourth entry in each row of values in table indi�

cates the simulated relative intensity, , forcorresponding B–A bands on the relative scale fromzero to 10. Figure 1 depicts the simulated B–A bandsystem based on our calculated FC factors and bandpositions.

ωe' xe' ωe''xe''

qv'v''νv'v''

4

23

10

0

5

0Rel

. in

ten

sity

213

24

16832

~ ~ ~ ~ ~ ~ ~ ~

18048 19287 20548 21788

01

12

23

34

0011223344

21

10

43

53423120

0.32.5 1.3 2.3 0.1A−X

B−A

Wavenumber, cm−1

v'v''

Fig. 1. Franck–Condon simulation of the B–A bands of 11B16O. Above are marked positions of the bands of A–X system situatedin the region of B–A bands.

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 87 No. 13 2013

FRANCK�CONDON SIMULATION OF THE B–A BANDS OF BO 2227

Com

pute

d ba

nd

orig

in p

osit

ion

s in

μm

(a)

an

d cm

–1 (

b),

FC

fac

tors

(c)

, re

lati

ve i

nte

nsi

ties

(pr

opor

tion

al t

o q v

'v''

) (d

), a

nd

ban

d or

igin

pos

itio

ns

(in

cm

–1 ),

deri

ved

from

mea

sure

d ba

nd

hea

ds (

e),

for

sele

ct B

–A

ban

ds o

f th

e 11

B16

O is

otop

olog

ue

v'

v''

01

23

45

67

89

10

00.

5185

a0.

5541

0.59

410.

6395

0.69

140.

7513

0.82

120.

9038

1.00

281.

1236

1.27

45

1928

7.1b

1804

8.5

1683

1.7

1563

6.5

1446

2.5

1330

9.5

1217

7.0

1106

4.8

9972

.588

99.7

7846

.3

7.58

91 ×

10–

1c1.

8723

× 1

0–1

4.17

86 ×

10–

29.

2942

× 1

0–3

2.11

65 ×

10–

34.

9908

× 1

0–4

1.22

49 ×

10–

43.

1363

× 1

0–5

8.38

56 ×

10–

62.

3422

× 1

0–6

6.83

45 ×

10–

7

10.0

d1.

90.

3<

0.1

<0.

1<

0.1

<0.

1<

0.1

<0.

1<

0.1

<0.

1

1928

4.4e

1804

4.5*

1682

6.6

––

––

––

––

10.

4867

0.51

790.

5527

0.59

180.

6360

0.68

630.

7442

0.81

130.

8902

0.98

421.

0980

2054

8.1

1930

9.5

1809

2.7

1689

7.5

1572

3.6

1457

0.5

1343

8.0

1232

5.8

1123

3.5

1016

0.8

9107

.3

2.27

52 ×

10–

14.

0939

× 1

0–1

2.41

98 ×

10–

18.

5076

× 1

0–2

2.57

17 ×

10–

27.

3744

× 1

0–3

2.09

05 ×

10–

35.

9790

× 1

0–4

1.74

45 ×

10–

45.

2269

× 1

0–5

1.61

48 ×

10–

5

3.9

5.4

2.5

0.7

0.2

<0.

1<

0.1

<0.

1<

0.1

<0.

1<

0.1

2054

5.5*

1930

6.0*

1809

0.0

1689

4.5

––

––

––

–

20.

4590

0.48

660.

5173

0.55

140.

5895

0.63

250.

6813

0.73

720.

8017

0.87

720.

9665

2178

7.6

2054

9.0

1933

2.2

1813

7.0

1696

3.0

1581

0.0

1467

7.5

1356

5.3

1247

2.9

1140

0.2

1034

6.8

1.35

31 ×

10–

23.

6779

× 1

0–1

2.04

33 ×

10–

12.

3187

× 1

0–1

1.15

08 ×

10–

14.

4408

× 1

0–2

1.54

00 ×

10–

25.

1014

× 1

0–3

1.66

48 ×

10–

35.

4458

× 1

0–4

1.80

47 ×

10–

4

0.3

6.3

2.7

2.4

0.9

0.3

<0.

1<

0.1

<0.

1<

0.1

<0.

1

2178

3.7

2054

5.5*

1932

8.3

1813

4.0

1695

9.7

––

––

––

30.

4347

0.45

940.

4866

0.51

660.

5500

0.58

720.

6291

0.67

640.

7304

0.79

240.

8646

2300

6.5

2176

7.9

2055

1.1

1935

5.9

1818

1.9

1702

8.9

1589

6.4

1478

4.2

1369

1.8

1261

9.1

1156

5.7

4.27

45 ×

10–

53.

5432

× 1

0–2

4.49

40 ×

10–

18.

9884

× 1

0–2

1.94

79 ×

10–

11.

2926

× 1

0–1

6.12

76 ×

10–

22.

4994

× 1

0–2

9.47

53 ×

10–

33.

4714

× 1

0–3

1.25

66 ×

10–

3

<0.

10.

87.

61.

22.

01.

00.

40.

1<

0.1

<0.

1<

0.1

–21

763.

320

546.

4*19

343.

2*18

177.

2*–

––

––

–

40.

4131

0.43

540.

4598

0.48

650.

5160

0.54

860.

5849

0.62

560.

6715

0.72

370.

7834

2420

5.9

2296

7.2

2175

0.5

2055

5.3

1938

1.3

1822

8.2

1709

5.8

1598

3.5

1489

1.2

1381

8.5

1276

5.0

2.63

55 ×

10–

61.

3835

× 1

0–4

6.21

92 ×

10–

24.

9192

× 1

0–1

3.11

83 ×

10–

21.

5087

× 1

0–1

1.30

20 ×

10–

17.

3917

× 1

0–2

3.47

57 ×

10–

21.

4841

× 1

0–2

6.02

55 ×

10–

3

<0.

1<

0.1

1.3

8.4

0.4

1.6

1.1

0.5

0.2

<0.

1<

0.1

––

2175

1.8

–19

377.

7*–

––

––

–

50.

3939

0.41

410.

4361

0.46

010.

4863

0.51

520.

5471

0.58

260.

6222

0.66

670.

7171

2538

6.7

2414

8.1

2293

1.3

2173

6.1

2056

2.1

1940

9.1

1827

6.6

1716

4.4

1607

2.1

1499

9.3

1394

5.9

2.51

65 ×

10–

81.

1083

× 1

0–5

2.82

60 ×

10–

49.

1437

× 1

0–2

5.08

77 ×

10–

15.

9149

× 1

0–3

1.09

91 ×

10–

11.

2196

× 1

0–1

8.14

87 ×

10–

24.

3507

× 1

0–2

2.06

59 ×

10–

2

<0.

1<

0.1

<0.

11.

98.

70.

11.

21.

00.

50.

2<

0.1

––

–21

732.

1–

1940

5.4

––

––

–

νv

'v''

4

2228

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 87 No. 13 2013

ANTI �JOVANOVI et al.C� C�

Tabl

e.(C

ontd

.)

v'

v''

01

23

45

67

89

10

60.

3766

0.39

510.

4150

0.43

670.

4603

0.48

610.

5144

0.54

560.

5802

0.61

870.

6618

2655

0.1

2531

1.4

4094

.722

899.

521

725.

520

572.

519

440.

018

327.

717

235.

416

162.

715

109.

3

1.39

79 ×

10–

91.

8926

× 1

0–7

2.72

68 ×

10–

54.

6791

× 1

0–4

1.21

58 ×

10–

15.

0904

× 1

0–1

1.42

37 ×

10–

57.

5866

× 1

0–2

1.08

42 ×

10–

18.

4225

× 1

0–2

5.04

60 ×

10–

2

<0.

1<

0.1

<0.

1<

0.1

2.6

8.7

<0.

10.

80.

90.

50.

3

––

––

––

––

––

–

70.

3611

0.37

800.

3962

0.41

590.

4372

0.46

040.

4857

0.51

350.

5440

0.57

770.

6152

2769

7.0

2645

8.3

2524

1.6

2404

6.4

2287

2.4

2171

9.4

2058

6.9

1947

4.6

1838

2.3

1730

9.6

1625

6.2

2.98

14 ×

10–

105.

3818

× 1

0–9

7.76

35 ×

10–

75.

0633

× 1

0–5

6.89

44 ×

10–

41.

5156

× 1

0–1

4.98

85 ×

10–

14.

7968

× 1

0–3

4.96

20 ×

10–

29.

2624

× 1

0–2

8.29

73 ×

10–

2

<0.

1<

0.1

<0.

1<

0.1

<0.

13.

28.

4<

0.1

0.5

0.8

0.4

––

––

––

––

––

–

80.

3469

0.36

250.

3792

0.39

720.

4166

0.43

760.

4604

0.48

530.

5125

0.54

230.

5751

2882

8.4

2758

9.7

2637

3.0

2517

7.8

2400

3.8

2285

0.8

2171

8.3

2060

6.0

1951

3.7

1844

1.0

1738

7.6

1.16

21 ×

10–

111.

9619

× 1

0–9

9.55

58 ×

10–

92.

2956

× 1

0–6

7.76

92 ×

10–

59.

4875

× 1

0–4

1.80

73 ×

10–

14.

8223

× 1

0–1

1.50

65 ×

10–

23.

0544

× 1

0–2

7.67

06 ×

10–

2

<0.

1<

0.1

<0.

1<

0.1

<0.

1<

0.1

3.8

8.3

0.2

0.3

0.7

––

––

––

––

––

–

90.

3339

0.34

840.

3638

0.38

030.

3981

0.41

720.

4379

0.46

030.

4847

0.51

130.

5404

2994

5.3

2870

6.6

2748

9.9

2629

4.7

2512

0.7

2396

7.6

2283

5.1

2172

2.9

2063

0.6

1955

7.9

1850

4.4

1.22

95 ×

10–

151.

1212

× 1

0–10

6.93

21 ×

10–

98.

3196

× 1

0–9

5.47

74 ×

10–

61.

0237

× 1

0–4

1.25

77 ×

10–

32.

0871

× 1

0–1

4.61

73 ×

10–

12.

7862

× 1

0–2

1.74

09 ×

10–

2

<0.

1<

0.1

<0.

1<

0.1

<0.

1<

0.1

<0.

14.

48.

00.

40.

2

––

––

––

––

––

–

100.

3221

0.33

550.

3497

0.36

500.

3813

0.39

890.

4177

0.43

810.

4601

0.48

400.

5100

3104

8.4

2980

9.8

2859

3.0

2739

7.8

2622

3.9

2507

0.8

2393

8.3

2282

6.1

2173

3.8

2066

1.1

1960

7.6

1.02

82 ×

10–

136.

7654

× 1

0–13

5.85

26 ×

10–

101.

7009

× 1

0–8

1.11

02 ×

10–

91.

1183

× 1

0–5

1.17

41 ×

10–

41.

6402

× 1

0–3

2.35

31 ×

10–

14.

3884

× 1

0–1

4.16

54 ×

10–

2

<0.

1<

0.1

<0.

1<

0.1

<0.

1<

0.1

<0.

1<

0.1

5.0

7.6

0.6

––

––

––

––

––

–

*S

uper

pose

d or

mas

ked

ban

ds.

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 87 No. 13 2013

FRANCK�CONDON SIMULATION OF THE B–A BANDS OF BO 2229

To verify the reliability of the predicted spectrum,we used Mulliken’s experimental data for comparison.Mulliken measured A1 and B1 heads of about 20 bandsof the B–A system recorded in his emission spectrum,which were identified as the members of four violet�extended Δv = 0, ±1, and –2 sequences, and of thered�extended Δv = +2 sequence. In his extensivepaper [1], he mentioned that the bands of the Δv = +1sequence superpose each other and appear as a singlestrong band. Mulliken’s observations are in agreementgenerally with our calculated pattern of the bandarrangement of the B–A system.

In addition, the reliability of our computation wastested by comparison of our computed band originwavenumbers from the spectroscopic constants andthose derived from band head positions measured byMulliken, listed also in table (fifth entries). It is readilyseen that both sets of values are very close. Differencesof about 3–5 cm–1 are reasonable, bearing in mindthat Mulliken’s measurements were not of high accu�racy, and that some B–A bands overlap each other orare masked by A–X band structure.

Unfortunately, the lack of corresponding intensitymeasurements of B–A bands prevents a direct com�parison of simulated and experimentally observedband intensities. There are only Mulliken’s visual esti�mates of B–A band head intensities, which are quiteuncertain, and cannot be used for comparison. Hisestimates of those intensities for all observed bandswere only either 0 or 1. For this reason, the quality ofour simulated intensities of B–A bands was tested by asimilar simulation of the well known A–X bands of BObased on our computed RKR�based FC factors andband origin wavenumbers. The computed relativeintensities of the A–X bands, approximated by the

products of , were normalized to 10 for the1–1 band. Figure 2 compares our simulated intensitiesfor the A–X bands with the experimentally measuredintensities reported in [23].

The differences between the simulated and mea�sured relative intensities of the A–X bands are reason�able, and not unexpected due to the approximationand simplifying assumptions made for the relativeband intensity calculation. Our simulated A–X bandintensities herein do not include the ETMF derived byRobinson and Nicholls [23] for this band system. Onthe other side, the comparison of their calculatedintensities at infinite temperature, I

∞v'v'', and experi�mentally measured intensities, I

v'v'' (Table 4 in [23]),show differences of the same order as those betweenour simulated and measured intensities. Such resultsindicate that the population of the upper vibrationallevels cannot be considered equal under the physicalconditions of the given source of emitting molecules.

Using ratios between Iv'v'' and I∞v'v'' listed in [23],

we found the mean relative density numbers for theupper vibronic levels v' = 0, 1, 2, 3, and 4. They are

qv'v''νv'v''

4

approximately 1.8, 1.1, 0.70, 0.35, and 0.25, respec�tively. Taking into account these values in calculationof the relative band intensities as the products

, the differences between the two sets ofvalues (our simulated and the measured) become sig�nificantly smaller. Nevertheless, as seen in Fig. 2, thesimulated intensity pattern matches well with theexperimental intensity distribution, and thus offersgood support for the viability of our calculated FC fac�tors and simulated band intensities of the lesser�stud�ied B–A band system of 11BO.

CONCLUSION

Using improved molecular constants and RKRpotentials, FC factors and band origins are computedfor the B–A combination band system of 11BO, andthen used to simulate their band intensities. The reli�ability of the applied method was tested by comparisonof the observed and simulated A–X spectrum of thismolecule. Our simulated B–A bands of the 11BO mol�ecule provide new information about this electronic�vibrartional transition, which will be very useful infuture theoretical and experimental studies.

ACKNOWLEDGMENTS

This work was supported by the Ministry of Educa�tion and Science of the Republic of Serbia, projectno. 172019. R.R.L is grateful for support from NASA’sSpitzer Science Center.

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5. A. Lagerqvist, N. E. L. Nilsson, and K. Wigartz, Ark.Fys. 13, 379 (1958).

Nv'qv'v''νv'v''

4

10

2

5

0Rel

. in

ten

sity

514

03

16967

~ ~ ~ ~ ~ ~

18734 20526 21721 24178

24

13

03

23

Wavenumber, cm−1

v'v''

12

01

~ ~

33

11

00

21

10

22

10

5

0 ~ ~ ~ ~

(a)

(b)

Fig. 2. Comparison of (a) measured and (b) simulated rel�ative intensities of the A–X bands of 11B16O.

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