BO: Low-lying electronic states obtained by configuration-interaction studies

JOURNAL OF MOLECULAR SPECTROSCOPY

122,356-364 (1987)

BO: Low-Lying Electronic States Obtained by Configuration-Interaction Studies S.

P.

KARNAAND

F. GREIN

Department of Chemistry, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 6E.2 Configuration-interaction studies were performed on low-lying ‘Z+, ‘2-, ‘II, *A, ‘Z+, ‘Z-, 411, and *A states of BO. Sixteen stable states have been found, among them four 3sa Rydberg states. Spectroscopic constants are compared with tbosc of the four observed states and with theoretical results obtained by others. Particular attentiolp is given to the observed perturbations in the C’II state, which can be explained by interaction with l*A, 122-, 32Z+, and other states. Comparison with isoelectronic molecules CN and CO+ reveals many similarities. 8 1987 AcademicPBS, hc. 1. INTRODUCTION

Following recent suggestions (I, 2) about possible lasing action of the A’II-X*Z+ transition of BO, there has been renewed interest in the reaction dynamics of formation of BO in electronically excited states from various sources (3-5) and more generally in the electronic spectrum of this molecule (6-8). Historically, boron monoxide, BO, played an important role in the early development of quantum theory. In 1925 Mulliken (9) obtained from low-resolution spectra of ‘“B160 and “B160 the first experimental verification of the vibrational isotope effect, and definitely established the existence of the zero-point vibrational energy in molecules. The electronic spectrum of BO was first observed in 19 14 by Jevons (10) who identified the cr(A*II-X*Z+) and /3(B*Z+-X*8+) systems. Subsequently, very detailed analyses of the (Yand j3 systems were reported, respectively, by Jenkins and McKellar (II) and Lagerqvist et al. (12). The y band system of BO was first observed by Chritien (13). A definite assignment as the C’II-X*Z+ system of BO was made by Mal’tsev et al. (14). More recently Dubois and his group (15) also analyzed the C-X transitions. Several perturbations in the A-X and C-X systems have been observed. In the case of the A-X system, perturbations of u’ = 4 have been attributed to u” = 17 (II), and recently of v’ = 8 by 2)”= 20 (7). For the C-X system most of the observed vibrational levels of the upper state [up to o’ = 5 in Ref. (14) and up to 2)’= 8 in Ref. (15)] have been found to be perturbed, but the nature and the number of the perturbing states have not been clearly established. The present study has been undertaken to complement the experimental information on the electronic spectrum, especially to help understand the experimentally observed perturbations, and to provide reliable information on hitherto unobserved states of BO. In a theoretical study made by Botschwina (16) only the X*Z’ and the A*II states have been considered. Several states of BO have been studied by AlmlSf et al. (I 7) 0022-2852187 $3.00 cowrisht@ 1987 by Academic Ress,

Inc. AU rightsof w.productionin my form resewed.

356

ELECTRONIC

STATES

OF BO

357

and Nemukhin et al. (18). However, their potential curves and spectroscopic constants are of low accuracy due to their use of a small orbital space available for excitations, and the averaging method for higher states. 2. BASIS SET AND

THEORETICAL

METHODS

The Huzinaga-Dunning (9sQ/5s3p) contracted Gaussian functions (19, 20) with dpolarization functions (CQ= 0.70, (~0= 0.85) and diffuse 3s (w-, = 0.019, cxo= 0.032) and 3p ((in = 0.015, a0 = 0.028) functions (21) were used. In view of the ionic nature of BO, 2p negative ion functions with (Yg= 0.024 and (~0 = 0.059 (21) were also included in the basis set. The negative ion function @_B was changed from the value given in Ref. (21) in order to avoid linear dependency problems. The multireference single and double excitation configuration-interaction (MRDCI) method of Buenker and Peyerimhoff (22-25) based on configuration selection and extrapolation was used. The final calculations were performed at the energy selection threshold T = 5 ph. Calculations were performed at internuclear distances R from 1.86 to 3.44 in intervals of O.lu,,, and at 3.6, 4.0, 5.0, and lO.O&. Initially, SCF molecular orbitals (MO) for the 2Z+ ground state, resulting from the ( lu-4a)21~45a electronic configuration, were used. However, due to SCF convergence problems at larger distances, all the final CI results were obtained from 4Z+ MOs with the electronic configuration (1 a-4a)* 1r35a2?r. All calculations were performed in the lower symmetry group C,, . The two lowest MOs, la1 and 2a,, corresponding to the 1s core orbitals of B and 0, were kept frozen while the two highest MOs of al symmetry were excluded from any excitations. This left a total of 9 electrons to be distributed over a space of 50 MOs. Two to four roots for each symmetry species were calculated. All configurations with C* 3 0.01 were included in the set of reference configurations, which numbered from 25 to 4 1 depending upon the states considered. About 600 000 symmetry adapted functions (SAFs) were generated and about 5000 to 18 000 selected for CI diagonalization. Extrapolated energies (T = 0) have been used throughout. Energies calculated at 10.04 have been taken for establishing dissociation limits. The correlation of lowlying molecular states with states of the separated atoms is given in Table I, Experimental (26) and theoretical energies for the low-lying dissociation products are included. 3. RESULTS

AND

DISCUSSION

Potential energy curves for all states calculated are shown in Figs. 1 and 2. Table II gives the dominant configurations found for the various excited states. At the same time, it shows the effective energy ordering of excited electronic configurations. By far the most states result from lu + 27r. Here, a possible 2*Z:- state was not included in the calculations. Its potential energy curve should be close to that of 2*A. At larger internuclear distances several avoided crossings are seen. The 4*2+ state has Rydberg character resulting from the 5u + 6u excitation up to 2.7&, beyond which it changes to the l?r --* 27r valence configuration. At small R, 6u is composed mainly of the B(3s) Rydberg orbital, and switches at large R to the B(2p,) valence orbital. The 3*II, 4*II, and 2411 states, resulting from the l?r + 6u excitation, also show Rydberg features in their equilibrium region.

358

KARNA

AND

GREIN

TABLE I Low-Lying

Molecular States of BO and Their Dissociation

Limits Au_&

Molecular States

Atomic states Bxpt'La

Theor.

B(*P) + O(lD)

1.97

1.91

B(*P) + OC3P)

0.0

0.0

2*2+, 3*x+, 3*2-, 3%. 4*n, 5*n, 228, 32A. 1%

1*x+, 14x+, 1*z-, 2%. 142_. 24z-, 1%.

2%.

1"Il.2411.12A,14A

%f.

26.

The 2*II state derives from two competing configurations, 5a --t 2?r and 4a --, 2a. Near equilibrium, the contributions are about 46 and 41%, respectively. Beyond 3.66, 2*II switches to lu* --t 5~2~. As seen from Fig. 2, the section of the 3*II potential curve between 3.2 and 3.6u,, also derives from l?r’ --* 5a27r, whereas it becomes 5u + 2a beyond 3.6ac,. After its Rydberg section, the 4*II state changes into ls* --, 5u2?r (which gives rise to two *II states). A similar situation applies to the 411 states. At about 3.5&, 1411 changes from 4u + 2a to lx* + 5u27r. The 2411 state has a short section of l?r* --* 5u27r between 3.1 and 3.4uo, thereafter changing into 4ul7r + 5~6~. It might be added that at large distances 5u correlates with 0(2p,), 17rx with 0(2p,), 27r, with B(2p,), and 6u with B(2p,).

E(eV) IO.0 9.0

0.0

7.0 6.0 5.0 4.0 3.0 2.0 I.0 0.0 2.0 2.4 2.6 3.2 3.6 4.0

R(a,)

nG. I. Potential curves for Z+ and Z- states of BO.

359

ELECTRONIC STATES OF BO

E(eV)

I

’

I

I

’

’

’

2.0 1 ’

’

’

’

’

’

1

2.0 2.4 2.0 3.2 3.6 4.0

No,,)

FIG.2. Potential curves for II and A states of BO.

Despite the appearance of a hump for l*A and a wiggle for 2*A, no changes of configurations could be observed. These particular features of the potential curves are found in both the A, and the A2 calculations of *A states. The calculated spectroscopic constants (Table III) are in good agreement with the available experimental values and with previous theoretical values for the X and A states as reported by Botschwina (16). However, the theoretical results obtained by AlmlSf and co-workers (I 7, 18) differ significantly. Spectroscopic constants were also TABLE II Dominant Configurations for Excited States of BO Configuration 40 )

Molecular

2n

1411, . . .

In + 60

32”,

50 -* ba

4*2+

5a + 2n

2%

In e 2n

3*x+, **A,

40 + 5a

2*x+

In )

12Il

50

(lo-4a)21n450

aAt b

Not

larger

States

1%’

R.

calculated.

42n.

24ll

(42E+),a 14Z+,

14E-,

12Z-, 14A

(22E-),b

l*A,

360

KARNA

AND

GREIN

TABLE III Calculated Spectroscopic

Molecular State

Te(eVja

0

PC+(x) b

Exp .

0

Constants of BO and Comparison and Other Theoretical Results

with Experimental

W,x,(cm-1)

Be(cm-‘)

a,(cm-1)

D,(eV)

R,(A)

we(cm -11

8.14

1.211

1870.1

15.5

1.763

0.0064

1.205

1885.3

11.7

1.781

0.0165

1.210

1873

11.8

8.32f0.05=

0.017

Bot.d

0

Alm.e

0

7.97

1.22

1909

2.81

5.33

1.357

1284.0

14.7

1.405

0.0264

2.96

1.353

1260.8

11.2

1.411

0.0185

Bot.d

2.71

1.356

1289

11.8

Alm.e

3.15

4.80

1.38

1238

5.35

4.69

1.308

1289.6

3.3

1.511

0.0267

5.35

1.305

1283.3

11.6

1.516

0.0220

6.32

1.41

1425 3.6

1.324

0.0132

15.5

1.294

0.0152

14.5

1.262

0.0148

1211(A) Exp .

b

22C+(B) Exp .

b

Ahe 14X+

5.49

2.64

1.397

1237.6

5.79

2.04

1.36

1279

5.90

2.24

1.413

1246.0

6.55

1.38

1.44

1140

6.55

1.20

1.431

1185.3

6.88

0.83

1.55

1231

12x-

6.55

1.59

1.434

1179.5

6.8

1.257

0.0130

14C-

6.57

1.57

1.428

1184.7

20.2

1.268

0.0219

22lI(C)

7.06

1.08

1.326

1306.4

14.0

1.442

0.0200

11.1

1.483

0.018

Nem.

f

14A NWI.

f

12A Nem .

f

ExP.~

6.86

1.320

1315.3

Alm.e

7.49

1.42

1539

1.356

1540.9

20.0

1.406

0.0109

14.8

1.397

0.0185

6.3

1.249

0.0052

2.12

32c+

7.92

1411

8.53

1.360

1266.0

7.03

1.30

1558

1.439

1140.0

Nem. 22A

f

8.85

1.20

ELECTRONIC

361

STATES OF BO

TABLE III-Continued 42Cf

9.62

1.204

(2126jh

(200.2jh

1.786

2411

10.06

1.315

1345.6

-20.1

1.498

0.0027

3211

10.30

1.303

1428.2

-36.5

1.525

-0.0012

4211

10.56

1.275

1437.0

41.7

1.588

0.0465

%(X2Z+) eRef.

17.

= -99.8038 fRef.

hartree 18.

at R e’ gRef. 14.

bRef. h

7.

‘Ref.

Approximate

31.

%ef.

16.

values.

calculated from the full-C1 estimates of the potential energies. The results are very similar, and have not been included in Table III. Five of the seven states resulting from 1?r + 2a he within an energy range of 1.08 eV. Consistent with this con&uration, their R, increases by 0.20 to 0.22 A while w, decreases by about 700 cm-’ relative to x=z+. Similarly an increase of about 0.15 A in & results from the 1?r + 50 excitation leading to the 1‘II state. This can be understood from the nature of the MOs involved. The 17~and 27r MOs are, respectively, of bonding and antibonding character, while 5a is a nonbonding MO located mainly on B. The same consideration explains why, in spite of 4a being an antibonding O(2s + 2p,) - B(2s - 2pz) MO, there is an increase in R, of about 0.1 A for the 4a --, 5a excitation resulting in the 2=2+ state. For the 4=2+ state the excitation takes place from the 5a nonbonding MO to the 3sB Rydberg orbital, so that & remains more or less unchanged. Using this argument, one would expect the ground state of BO+ to have spectroscopic constants similar to those of the ground state of the neutral molecule. The experimental results (27) on BO+ are in agreement with this expectation. A similar situation is seen in the isoelectronic molecule CN (27). The neutral molecule and the positive ion have similar R, and w, values in their respective ground states. Calculated dissociation energies, as well as experimental and theoretical values, are listed in Table III. Other experimental dissociation energies for the ground state range from 7.8 to 8.32 eV (28-31). Values obtained by Lippincott et al. by semiempirical methods (32) are 7.24 and 7.45 eV. The dipole moment of the X22’ state at its equilibrium geometry has been calculated to be -2.46 D (B+O-). The corresponding values for the A’II and the &I states at their respective & were found to be 0.3 1 D (B-O+) and -2.40 D (B+O-), respectively. The reversal of polarity in going from the X22+ to the A’II state is consistent with the excitation l?r + 5a, where l?r is mainly located on 0, and 5u on B. C211 arises from the excitation 5u + 2a, where both orbitals are located on B. Therefore, only a small change in the dipole moment relative to X’Z’ is expected. 4. PERTURBATIONS

OF THE A-X

AND

C-X

SYSTEMS

In Fig. 3, we show the calculated potential curves for the A and X states, including some of their vibrational levels. It is seen that the u’ = 4 and tY’= 17 levels for which

362

KARNA AND GREIN

perturbations were observed (II) are very close in energy. The best match using the calculated spectroscopic constants is obtained for the pair o’ = 5 and tY’= 18. Using experimental spectroscopic constants (see Table III), the energies for 2)’ = 4 and u” = 17 lie within 0.01 eV, and so do the energies for u’ = 8 and 0” = 20. This latter perturbation has also been observed (7). It is obvious that even relatively good calculated values for w, and o& are incapable of reproducing high vibrational energy levels with sufficient accuracy. On the other hand, a purely theoretical prediction of perturbation in the v’ = 5, u” = 18 (or nearby) vibrational levels is considered to be useful. To understand and help interpret the observed perturbations of the vibrational levels of C*II, its calculated potential curve as well as the potential curves of nearby states are shown in Fig. 4. The 2211(C) state is crossed by the 14A state at small R, and by three (overlapping) states 12A, 1*X-, and 142- in the equilibrium region. It is quite possible that all the states shown in Fig. 3 participate in the perturbation of the 2*II vibrational levels. However, the most pronounced effect would be expected from l*A, l*Z-, and 3*Zf. For 2*II, 12A, 1*2-, and 3*2+ low-lying vibrational levels are shown. It is seen that the 2)= 4 and 2)= 5 levels of l*A and 12Z- are almost isoenergetic with the u = 0 and 2, = 1 levels of the C*II state. The lowest level of 322+ coincides with the 2) = 6 level of the C*II state. Thus while the I.J= 0 to 8 = 5 levels of the C state will be perturbed by the upper levels (v > 3) of the l*A and 122- states, the higher (u > 5) levels of the C state will be perturbed by the lower levels of the 32Z+ state. None of these perturbing states have been observed so far. 5. COMPARISON WITH OTHER ISOELECTRONIC MOLECULES Although many experimental observations of the electronic spectra of CN and CO+, both being isoelectronic with BO, have been reported, only few of the low-lying states of these molecules are known with certainty. In Table IV spectroscopic constants of BO are compared with those of the known states of CN and CO+ (27).

E(eV) 4.0

3.0

2.0

1.0

0.0

2.0

2.4

2.8

Rk

FIG. 3. Perturbation in the A-X system.

ELECTRONIC

STATES

363

OF BO

2.0 2.4 2.8 3.2 3.6 4.0

R (a,)

FIG. 4. Perturbation in the C-X system.

The overall features of BO show more similarity with CO+ than with CN. Due to the more covalent nature of CN and CO+ compared to BO, R, of the ground state of CN and CO+ is smaller than that of BO. The o, values are correspondingly higher. An increase in R, of about 0.06 A in CN and about 0.13 A in CO+ is seen in going from the X state to the 1‘II state, the corresponding increase in BO being 0.15 A. The w, values decrease accordingly. Except for the 2*II state of CN and the 2*Zf state of CO+, the calculated & values for BO are, in general, about 0.1 A larger than the corresponding values in CN and CO+. The T, values for the BO molecule are, in general, higher by about 0.6 to 2.2 eV than the corresponding values in CN and, except for the l*II state, lower by 0.4 to 1.3 eV than in CO+. The most striking difference is noted for the 2*X+ state, deriving from a 4a + 5a excitation. For an antibonding 40 and a bonding 50 MO, this excitation should lead to a decrease in R, and a corresponding increase in the w, value. This is seen to be the case in CN. In BO, as discussed earlier, 5a is a nonbonding MO situated on B. At the same time 4a is not as strongly antibonding. Consequently, contrary to CN, a 4a --* 5u excitation leads to a lengthening of the bond and a corresponding decrease in w,. CO+ shows behavior similar to that of BO. TABLE IV

Comparison of BO with Isoelectronic Molecules CN and CO+” MCTlLXlllar

state 122+

w&m-l)

R,(A)

Te(eV) Configuration BO ln45a

0

CN

CO+

0

0

BO

CN

1.211

1.172 1.115 1870.1 2068.6 2214.2

CO+

Bo

CN

co+

12,

In + 50

2.81

1.15 2.57

1.357 1.233 1.244 1284.0 1812.5 1562.0

222+

40 + 50

5.35

3.19

5.69

1.308 1.150 1.169 1289.6 2163.9

1734.1

12A

In + 2n

6.55

7.45

7.81

1.431 1.373 1.34

1185.3 1239

1144

22n

50 + 2n

7.06

6.75

8.09

1.326 1.498

1306.4 1004.7

322+

In + 2n

7.92

7.33

1.356 1.324

1540.9 1681.4

226

In + 2n

8.85

8.09

1.439 1.413

1140.0 1121.8

=%or CN and CO+ experimental spectroscopic constants from Ref. 27 have been taken.

364

KARNA AND GRFJN ACKNOWLEDGMENTS

This work was supported by an operating grant from the Natural Sciences and Engineering Research Council of Canada. Discussions with Dr. P. J. Bruna and support by the University of New Brunswick in the form of computer time are gratefully acknowledged. RECEIVED:

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