Theoretical study of the spectroscopy of the alkali oxides LiO, NaO, and KO

ChemicalPhysics 153 (1991) l-12 North-Holland

Theoretical study of the spectroscopy of the alkali oxides LiO, NaO, and KO Stephen R. Langhoff, Harry Partridge and Charles W. Bauschlicher

Jr.

NASA Ames Research Center, Moffett Field, CA 94035, U.S.A. Received 24 August 1990

Theoretical calculations show that only three of the eleven doublet electronic states of LiO, NaO, and KO dissociating to the three lowest asymptotes are significantly bound. The only bound-bound transitions that occur in the visible and infrared spectral regions are from the C ‘II state to the lowest two ionic states (*lI and sZ+ ). The emission is dominated by the C *IT-X *lT transition, which has a very large transition moment near r, (C *lI). Although chemiluminescence observed for these alkali oxides has been correctly assigned to this transition, the vibrational assignments are incorrect, as the strongest transitions from the lower vibrationallevels of the C *lI state are into ratherhigh vibrational levels of the X *lI state. The radiative lifetimes for the C 211(u=O) level are 66.2, 90.7, and 315.5 ns for LiO, NaO, and KO, respectively: the C *l&A *Z+ channel contributes less than 1%to the radiative lifetimes. Emission spectra are presented for the C *lI-X *ll band systems of LiO, NaO, and KO. Except for very high vibrational temperatures, most of the emission occurs in the infrared region. The maxima in the spectra shift to longer wavelengths for the heavier alkali oxides, paralleling the decrease in the T,(C ‘TI) values.

1. Introduction

Spectroscopic data on the alkali monoxides are necessary for the in situ gas-phase monitoring of these species in gasification and combustion environments [ 1,2 1. Recently, spectra from the alkali monoxides in the red and near infrared have been assigned to a transition from a weakly bound covalent state [ 2,3]. Under multiple collision conditions the spectra exhibited a structure that was attributed to a progression in the vibrational levels of the low-lying ‘II and 2Z+ ionic states. This is the only electronic transition reported for the alkali oxides. Other experimental data, which includes both matrix isolation infrared [ 4 ] and microwave spectra [ 5 1, have been obtained exclusively for the lowest two ionic states. Previous theoretical studies [ 6-81 of the alkali oxides have focused on explaining the reversal of ground state symmetry from LiO ( 211) to CsO (‘C+ ). Both theory [6-lo] and experiment [4,5,11,12] agree that LiO and NaO have X 2H ground states and that RbO and CsO have X 2C+ ground states. Conflicting experimental [ 11,12 ] and theoretical [ 6,7 ] data exist for the identity of the ground state of KO. However, 0301-0104/91/$03.50

singles plus doubles configuration-interaction (SDCI ) calculations in a large Slater basis correlating both the valence and inner-shell potassium electrons demonstrate rather convincingly [ 71 that KO has a X 2E+ ground state. We have taken this into account in the state designations used in this work, except that we sometimes refer generically to the C 211-X ‘II transition when the statement applies to all three alkali oxides. In this work we consider the higher-lying states of LiO through KO, with emphasis on characterizing the emission from the relatively weakly bound C 211state. Potential energy curves for the X 211,A ‘C+, and C 211 states and the dipole-allowed transition moments are computed using the state-averaged (SA) completeactive-space selfconsistent-field (CASSCF) multireference configuration-interaction (MRCI ) method. Synthetic spectra are generated in a line-by-line fashion, with all of the rovibrational matrix elements computed numerically based on spline representations of the theoretical data. The ab initio calculations corroborate the experimental assignment [ 21 of the emitting state as C *II, but indicate that the tentative experimental band assignments (due to the

0 1991 - Elsevier Science Publishers B.V. (North-Holland)

2

limited spectral resolution)

S.R. LanghoJf et al. /Spectroscopy ofLt0,

are incorrect.

2. Methods The primitive sp basis sets for the alkali atoms are those optimized for the ‘S states by Partridge [ 131. These are augmented with a diffuse s function optimized [ 131 for the ‘S state of the negative ions, and for Na and K three diffuse p functions optimized [ 13 ] for the 2P state of the neutral. For Li, we used the 7p set from ref. [ 13 1. The basis sets are augmented with even-tempered d polarization sets chosen as c~=2.S@,, where O
NaO, and KO

tion. This active space includes the oxygen 2p and alkali valence s and p orbitals and electrons. The most weakly occupied o and A orbitals are primarily 0 d orbitals that provide angular correlation. The use of the (433) active space ensures that there are no important configurations in the subsequent MRCI calculations outside the reference space. Seven electrons were correlated in the MRCI treatment, which includes the oxygen 2s-like electrons in addition to the five electrons in the CASSCF active space. It was impossible to include all single and double replacements from the full CASSCF reference, as this resulted in prohibitively long configuration-statefunction (CSF) expansions. Thus occupations were selected based on their importance in the CASSCF wave function. The reference lists for the MRCI treatments included all occupations for which the absolute value of the coefficient of any one of the component spin couplings exceeded a threshold of 0.05 in the CASSCF wave function at any r value for any of the three states treated in the MRCI. CASSCF and exploratory MRCI calculations indicated that of the 11 doublet states dissociating to the three lowest asymptotes (e.g. K(2S)+O(3P), K(*S) +O(‘D), and K(‘P) +O(3P) for KO), only the X 211, A ‘C+ and C 211 states were significantly bound - see for example the CASSCF curves for KO in fig. 1. Thus to obtain the most accurate potentials for these three bound states in a common set of molecular orbitals, the state-averaging procedure was restricted to include just these states. The spectra shown in this work are generated from spline representations of the MRCI(0.05) potentials and transition moment functions (TMFs). One problem that arises when the (n- 1 )s and (n - 1 )p electrons are not included in the correlation treatment is that the correlation space can change as a function of r, as a result of arbitrary mixing between the oxygen 2s and alkali inner-shell orbitals. This does not occur for LiO and occurs only slightly for NaO. However, for KO the nearly equal 0 2s and K 3p orbital energies result in substantial mixing that affects not only the shape of the potentials, but the T, values as well. Thus for KO it was necessary to first localize the orbitals before carrying out the correlation treatment. This was accomplished by using a corresponding orbital procedure to constrain the predominantly potassium 3s and 3p orbitals in KO to

S.R. Lmghoffet al. /Spectroscopyof LiO, NaO, and KO

3

six principal branches contribute significantly to the spectra. All of the rovibrational line positions and line strengths were computed numerically using tinitedifference methods. Since the vibrational analysis is essentially exact given the above assumptions, we believe that the spectra reported here are limited in accuracy primarily only by the quality of the theoretical potentials.

3. Resultsand discussion 3.1. Qualitative description of the bonding

3

4

5

6

7

0

9

10

Bond Length, a, Fig. 1. SA-CASSCF(433) potential curves for the doublet states of KO that dissociate to K(%)+O(‘P), K(‘S)+O(‘D), and K(zP)+O(3P).

have maximal overlap with the potassium atomic orbitals. All calculations were performed on the NASA Ames CRAY Y-MP/832 using the MOLECULESWEDEN program system [ 16 1. Using the MRCI potential curves and TMFs, we constructed a synthetic spectrum for the C ‘II-X ‘II band system with the following assumptions in the vibrational analysis. The levels were assumed to be populated according to a Boltzmann distribution, although it is highly likely that the vibrational distribution is very nonBoltzmann under both single and multiple collision conditions. Separate rotational and vibrational temperatures were allowed, but both were set to 300 K unless otherwise stated. The spectra were generated assuming an optically thin gas, the intensity was taken to be proportional to the cube of the energy difference, and each line was assigned a Gaussian linewidth of 10 A. The Hiinl-London factors were taken to be those for intermediate coupling assuming a spin-orbit splitting of 120 and 60 cm-’ for the X 211and C ‘II states, respectively [ 2 1. Only the

Before discussing the spectroscopy of the alkali oxides, we first present a qualitative description of the bonding in the low-lying electronic states. The SACASSCF (433 ) potentials for KO shown in fig. 1 illustrate the nature of the states dissociating to the three lowest asymptotes. Only three of the states are significantly bound, while the remaining eight doublet states are either repulsive or very weakly bound. Including more extensive correlation (with a CASSCF/MRCI procedure) for LiO yielded potentials that were in very good agreement with the CASSCF potentials. Hence, an improved treatment of electron correlation is not expected to substantially change the nature of the essentially repulsive states for any of the alkali oxides. Although the bonding in the two lowest states is very ionic, the remaining states are more easily described from a covalent viewpoint. Thus, we first discuss the covalent bonding, and then discuss how the ionic contribution modifies it. The lowest asymptote arises from M 2S( s’ ) and 0 3P ( 2p4 ) . This generates a ‘II and a 2E- state corresponding to an oxygen 2pa’2pn3 and 2p022p7t2occupation, respectively. The 2C- state is repulsive, because the three o electrons preclude forming a chemical bond. A o bond is formed from the oxygen 2po’2prr3 occupation leading to a bound ‘II state. The M 2P-0 3P asymptote gives rise to six doublet states. The M po’ occupation with the 0 2p022prc2occupation yields the repulsive 2E- state due to the unfavorable repulsion in the o space, while the 2po’2px3 occupation leads to the formation of a o bond resulting in the bound C 211 state. The M prr’ occupation and 0 2p022p7c2occupation can also form a n bond, but the 211state de-

S.R. Langhoffet al /Spectroscopy of LlO, NaO, and KO

4

rived from this combination is only weakly bound for all three alkali oxides, perhaps as a result of the repulsive interaction with the lower two ‘II states. The interaction of the M px’ and 0 2po’2p7t3 occupations gives a 2C +, 2E- and 2A state. Of these, only the 2E+ state has a chemical bond. The M 2S-0 ‘D asymptote is not expected to yield bound states, and the SA-CASSCF potentials are repulsive for all three states. The ionization potentials ( IPs) of the alkali metal atoms are quite low, ranging from 5.39-4.34 eV [ 171. The low IPs and large ( 1.46 eV) EA of oxygen leads to a substantial ionic contribution (M+O- ) to the bonding. The ionic contribution to the X 211 and A 2E+ states is derived from the 2p5 occupation of O-, with the hole in the 2prr and 2po orbitals, respectively. The Mulliken population analyses, the dipole moments, and the dipole derivatives reflect the large ionic contribution to these two states. Although the two lowest states correlate diabatically to the M + + O- asymptote, they correlate adiabatically with the M+O asymptotes. For the 2C+ state, the ioniccovalent curve crossing occurs at large r, so this state is ionic except for very large r values, as can be seen from the fact that the dipole moment function of the A 2C+ state of LiO (fig. 2) is nearly linear with the form of - r. Two curve crossings occur between the 211states. The crossing of the C 211state with a higherlying 211state occurs at very large r values, and therefore has little impact on the spectroscopy. However, the avoided crossing between the C ‘II and X 211 states gives the C 211 state its unusual “square-well” shape (see fig. 3 ). While the crossing may not be completely apparent from the potentials, it is clearly visible in the dipole moment curves in fig. 2. At short r values the X 211 state is ionic like the A 2C+ state, while at large r the C ‘II state is ionic and similar to the A 2C+ state. However, the C ‘II state is predominantly covalent at least for r< r,, in agreement with earlier conjectures [ 2 1. 3.2. Core-valence correlation Probably calculations tion on the shortcoming, calculations,

the biggest shortcoming of the present is neglect of core-valence (CV) correlaalkali atoms. To assess this potential we performed core-valence CI (CVCI ) which correspond to MRCI calculations

6

6

4

2

4

Bond

6

8

Length,

a,

10

Fig. 2. MRCI dipole moment functions for the X *ll, A ‘I;‘, and C TI states of LiO.

with 15 electrons correlated, except that double excitations are not allowed from the alkali inner shell. Calibration calculations were carried out for NaO and KO to assess the importance of this contribution to the spectroscopic constants of the X ‘II, A 2I;+ and C ‘II states; the results for NaO are given in table 1. Although CV correlation had a significant bond shortening effect on ah three states of NaO, the T, and D, values were not greatly changed. While it would have been ideal to determine the entire potential curves with the CVCI procedure, this would be prohibitively expensive as the CI expansions contain nearly two million CSFs, even using a smaller [ (5+2)s(4+2)p(2+2)d] AN0 basis set for Na. The valence results in the CV basis set are not significantly different from those reported in table 1. It is also of interest to study the effect of CV correlation on the small A 2II-X ‘Z+ state separation in KO. In previous work [ 7 ] an SDCI calculation correlating 15 electrons and employing a Slater basis set,

S,R. Imghoffet

al. /Spectroscopy ofLi0, NaO, and KO

5

multireference treatment of valence correlation appears to reduce the separation by about 80 cm-‘, based on a comparison of the SDCI ( 7 ) and MRCI ( 7 ) state separations given in table 2. The separation is increased by inner-shell correlation. However, the CVCI( 15 ) results are somewhat surprising as the separation is very small at this level. This calculation is not invariant to a unitary transformation of the valence orbitals and may be biased by the fact that the corresponding orbital procedure does not perfectly localize the orbitals. Nevertheless, the present calculations that include only valence correlation are expected to yield suff~cie~ly accurate potentials to give quanti~tive predictions of the spectra. The actual KO C 2II-A 211spectrum may be slightly blue-shifted as core-valence correlation should slightly increase To, as observed for NaO. 3.3. LiO spectroscopy 2

4

6

8

10

12

Bond Length, a,, Fig. 3. SA-CASSCF(433)/MRCI(7) potential energy curves for the X ‘II, A ‘I;+, and C ‘II states of LiO.

which reproduced the numerical Hat-tree-Fock separation to within 24 cm-‘, gave a separation of 238 cm-’ - see last entry in table 2. The present MRCI ~lculations correlating 7 valence electrons give r, values that are about 0.2 & longer and o, values that are about 30-40 cm-’ smaller than previous results [ 7 J. Most of the difference is due to neglect of innershell correlation in the present treatment. Also, the A-X separation is only 46 cm-’ as compared with 238 cm-’ in the ST0 basis set. To assess whether this difference is due to basis set, inner-shell correlation, or to improvements in the valence treatment in the MRCI calculations, we performed some additional calculations at the single-reference level. First, it was necessary to uncontract the K basis set still further and to add tight d functions giving a [ ( 3 + 6 )s ( 3 + 5 )p6d2f] set in order to accurately account for inner-shell correlation. This basis produces an SCF A 21’I-X 2C+ separation that is within 61 cm-’ of the numerical Hartree-Fock value, Moreover, the separation at the SDCI ( 15 ) level is in excellent agreement with the Slater basis set result. The

The LiO spectrum resulting from single collision Li-N20 metathesis has been measured by Woodward et al. [ 21. The dominant emission region extends from 3950-6700 A, but substantial emission was observed for wavelengths approaching 9000 A. No structure was observed under single collision conditions. Even though under multiple collision conditions internal excitation hampered the precise evaluation of the band locations, the separations of the dorn~~t features were correlated with a ground-state frequency of 800 A 30 cm- ‘_ Thus the band system was assigned [ 21 to a transition from a relatively weakly bound, predominantly covalent state into the lower vibrational levels of the X ‘II ground state. Of all the doublet states dissociating to the three lowest asymptotes, only the X ‘II, A 2Z+, and C *II states are significantly bound at either the CASSCF and MRCI levels. Thus the LiO bound-bound transitions observed in the work of Woodward et al. [ 2 ] must involve either the C 2II-X ‘II or C 2II-A 2I;+ transition. To obtain our most accurate potentials for the three bound states, we carried out SA-CASSCF( 433)/ MRCI(O.05 ) calculations averaging for these three states in the SA-CASSCF procedure. The resulting potentials for LiO are shown in fig. 3 and the spectroscopic constants based on a parabolic fit in 1(r are given in table 1. The spectroscopic constants for the

6

S.R. Langhoff et al. /Spectroscopy qfLl0,

NaO, and KO

Table 1 Spectroscopic constants for the alkali oxides Molecule

State

Calc. ‘)

r, (a0)

W, (cm-‘)

T. (cm-‘)

LiO

x %I A%+ c Q

MRCI MRCI MRCI

3.247 3.057

6.101

801 826 132

2400 31165

x % x 2I-I A %+ A %+ C2I-I C211

MRCI CVCI MRCI CVCI MRCI CVCI

3.955 3.841 3.767 3.625 6.899 6.574

463 490 495 520 105 95

1902 1873 24201 24613

X2-Z+ A2I-I C211

MRCI MRCI MRCI

4.321 4.593 9.117

395 355 56

46 22670

NaO

KO

0. (eV) 3.41

2.62

2.44

‘) Seven electrons are correlated in the CASSCF(433)/MRCI calculations and 15 electrons are correlated in the CVCI calculations with the restriction that no double excitations are allowed from the alkali inner shell.

Table 2 Spectroscopic constants and A 211-X ‘Z+ energy separations in KO for various levels of treatment State

K Basis ‘)

Calc.b)

r, (a0)

W, (cm-‘)

x 3+

[ 8s7p4d2f] [ 8s7p4d2f] [ 9s8p6d2f] [ 9s8p6d2f] [ 9s8p6d2f] [ 9s8p6d2f] [ 9s8p6d2f] [ 9s8p6d2f] Slater ‘) Slater ‘)

MRCI(7) MRCI(7) SDCI(7) SDCI(7) 1ref-CVCI ( 15 ) 1ref-CVCI ( 15 ) SDCI( 15) SDCI( 15) SDCI( 15) SDCI( 15)

4.321 4.593 4.259 4.527 4.153 4.412 4.156 4.423 4.131 4.399

395 355 399 381 423 380 428 382 429 395

A2I-I x *z+ A 2I-I x %+ A2I-I x *c+ A% x aI;+ A2l-I

T, (cm-‘) 46 126 77 255 238

‘) The oxygen basis is the [ 5sSp2dlf] basis described in the text. b, Seven electrons are correlated in the MRCI calculations and 15 electrons are correlated in the CVCI calculations with the restriction that no double excitations are allowed from the alkali inner shell. ‘) Slater basis of ref. [ 71.

X ‘II and A ‘C+ states are in reasonably good agreement with our previous theoretical study that employed a large Slater basis [ 7 1. The De value for the X *II state is significantly underestimated in the present calculation, because the MRCI potential is ionic at r, but dissociates to neutral ground state atoms. Thus a substantial portion of the error in the electron affinity of oxygen [ 18 ] carries over into De. Our earlier calculations are therefore expected to be more accurate, especially for De since they were for-

mulated to avoid problems in describing the electron affinity of oxygen. The LiO A ‘x+-X ‘II separation is 2400 cm-‘, in good agreement with previous theoretical calculations [ 6,7,9]. The C *II-X *II T, value of 3 1 165 cm- ’ is probably a lower bound, as there is a larger correlation error in the X *II state. Also, considering that the De value is too small, further improvements in the theoretical calculations are likely to shift the calculated spectra to the blue. The maximum blue shift is expected to be less than the error

S.R. Lunghoff et al. /Spectroscopy of LiO. NaO, and KO

in the calculated 0, value (about 3000 cm- ’ for LiO and 2000 cm- ’ for NaO and KO ) . The C 211 state is observed to have a very distinctive “square-well” shaped potential in all three molecules. The unique shape of this potential derives from the strongly avoided crossing with the X 211 state. In contrast with the estimates of Woodward et al. -for the C ‘II state potential, we observe that T, (C 217) > D, (X 211). Also, the difference in r, values between the C ‘II and X 2H states is much larger than their estimates. Thus the strongest transitions from the low-lying vibrational levels of the C 211state involve relatively high vibrational levels of the X ‘II state. Electronic transition moment functions (TMFs) for the C ‘II-X 211 and C 211-A 2C+ transitions of LiO, NaO, and KO are compared in figs. 4 and 5, respectively. The C ‘II-X 211 transition moment reaches a maximum near r, of the C ‘II state. Thus despite the relatively small energy separation between the two states, the transition is moderately

7

0.6

0.5

0.4

0.3

0.2

0.1

2

4

6

8

10

12

14

Bond Length, a, Fig. 5. The C ‘II-A ‘Z+ transition moment for LiO, NaO and KO at the SA-CASSCF(433)/MRCI( 7) level.

2

4

6

8

10

12

14

BOND LENGTH, a, Fig. 4. The C %-X ‘iI transition moment for LiO, NaO and KO at the SA-CASSCF(433)/MRCI(7) level.

strong. In contrast, the C 2II-A 2Zc+ transition moment is relatively small in this region - see fig. 5. This, combined with smaller Franck-Condon factors for the C-A transition, results in the C-X transition dominating ( > 99%) the radiative lifetimes. The radiative lifetimes for the lowest 10 vibrational levels of the C ‘II state of LiO given in table 3 indicate that the C 2H-X ‘II band system is relatively strong. The emission spectrum for the C ‘II-X 2H transition of LiO corresponding to a temperature of 300 K and a resolution of 10 A is shown in fig. 6. The band system extends over the large wavelength region of z 3500-l 6000 A. Unlike the experimental multiple collision LiO spectrum shown in tig. 6 of ref. [ 2 ] that peaks near 5000 A, the theoretical spectrum peaks at about 9000 A. This difference cannot be attributed to the experimental phototube response, which is still very good at 9000 A. Instead, as we show next, the experimental spectrum reflects a high vibrational temperature, which shifts the maximum to shorter

S.R. Langhoffet al. /Spectroscopy ofL10, NaO, and KO

8

Table 3 Radtative lifetimes (ns) a)for the u’= O-9 levels of the C ‘IT state of the alkali oxides

0

1 2 3 4 5 6 7 8 9

LiO

NaO

KO

66.2 62.8 60.3 58.4 51.2 56.6 56.4 56.5 56.7 57.0

90.7 85.7 81.4 77.7 14.6 71.8 69.5 67.6 65.9 64.6

315.5 285.6 260.5 239.2 221.4 206.4 193.6 182.7 173.3 165.1

9 ‘0

%

‘) The radiative lifetimes include both the C *lT-X ‘fI and C *IIA ‘C+ channels, although the latter channel contributes less than 1% to the lifetimes in all cases.

2 0

4.0

6.0

6.0

10.0

12.0

14.0

Wovelength angstroms

16.0

16.0

20.0

lld

Fig. 7. Einstein coefficients (s- ’ ) for transitions from the v’ = 0 (-), v’=4 (---), andv’=8 (...) vibrationallevelsoftheC21T state into all lower vibrational levels of the X ‘IL state of LiO.

Wavelength,

angstroms

Fig. 6. The C 2lT-X *II band system of LiO at 10 A resolution corresponding to a rotational and vibrational temperature of 300 K.

wavelengths by populating higher vibrational levels of the C ‘II state. The emission intensity as a function of wavelength is very sensitive to the C 21T state vibrational quantum number and thus to the temperature. This is illustrated in fig. 7 where we have plotted the Einstein coefftcients as a function of wavelength for v‘ = 0, 4 and 8 to all Y”. The oscillatory nature of the curves reflects the Franck-Condon factors. Since the inten-

sity increases significantly at the shorter wavelengths with increasing v’, the entire emission spectrum shifts to the blue with increasing temperature. This is further illustrated in figs. 8a-c where we have plotted the emission spectrum for vibrational temperatures of 600, 1000, and 2000 K, respectively, with the rotational temperature fixed at 1000 K. These spectra should also be compared with the 300 K spectrum in fig. 6. The spectrum shifts significantly to the blue with increasing temperature, but there remains considerable intensity at the longer wavelengths. The fact that the higher-temperature spectra in fig. 8 look more like the experimental spectrum suggests a rather high vibrational temperature even in the multiple collision experiments [ 21. This is consistent with the fact

S.R. Lunghoff et al. /Spectroscopyof LiO, NaO, and KO

la) SOOK

I

9

that under multiple collision conditions one expects rotational relaxation, but not necessarily vibrational relaxation. 3.4. NaO spectroscopy

Fig. 8. The C *II-X *lI band system of LiO at 10 A resolution corresponding to a rotational temperature of IO00 K, and vibrational temperatures of (a) 600 K, (b ) 1000 K, and (c ) 2000 K.

The first experimentally reported electronic transition for an alkali oxide was the observation of the “6700 A” band system for NaO [ 3 1. Chemiluminescent emission spectra were obtained under both single and multiple collision conditions [ 2,3 1. Features observed between 6740-9830 A were assigned to a long progression in the lowest vibrational levels of the X ‘I-I state. On the basis of energy conservation and the known bond energy of NaO, it was thought unlikely that the 6740 A feature could be associated with ground vibrational levels U”> 2. This led to a prediction that the upper state of this transition was a relatively weakly bound predominantly “covalent” state at z 15000 cm-’ above the ground state. The upper state was predicted to have an r, value that was about 0.2 8, longer than that for the X *II or A 2Z+ states. Theoretical potentials for the X ‘l-I, A *C+, and C *l-I states, based on the three-state CASSCF(433)/ MRCI treatment, are given in fig. 9. The spectroscopic constants for NaO, computed at both the MRCI and CVCI levels of correlation, are summarized in table 1. It is clear from the results in table 1 that the difference in r, values of the C *II and X 211 states is not on the order of 0.4 ao, but is 3.0 and 2.7 a0 at the MRCI and CVCI levels, respectively. Also, the T, value is on the order of 24000-25000 cm-‘, much larger than the experimental estimate [2] of z 15000 cm-‘. As we will see next, these differences have a major impact on the assignment of the chemiluminescent spectra. The emission spectrum of NaO at 300 K is shown in fig. 10 at 10 A resolution. It is similar in appearance to that for LiO, except that the maximum is shifted from about 9000 A to about 11000 A, primarily as a result of the zs 7000 cm-’ larger T, value for LiO. This in turn reflects the larger 0, value of LiO. As for the case of LiO, the strongest bands involving the low vibrational levels of the C 211 state involve relatively high vibrational levels of the X *l-I state. For example, based on the MRCI potentials the O-42 transition is the strongest band involving u’ =O. Although this may change slightly with improvements

S.R. Langhqffet al. /Spectroscopy sf LtO, NaO, and KO

10

1.0 -

h 5 zri

$ 3 ce d P=

0.8 -

0.6 -

0.4 -

0.2 -

00

Wavelength, angstroms

2

4

6

0

10

12

Bond Length, a, Fig. 9. SA-CA!ZiCF(433)/MRCI( 7) potential energy curves for the X 2fI, A 2E+, and C *lI states of NaO.

in the potentials, the conclusion that relatively high vibrational levels of the X 211 state are involved is conclusive. Thus the assi~ment of the expe~mental spectrum cannot be correct. Woodward et al. [2] noted that at the shortest wavelengths only one progression was apparent, but that at wavelengths longer than 8200 A additional features are observed, which are shifted by ~265 cm-’ from the initial progression. These additional features cannot be associated with excited state vibrational excitation, considering that w: is z 100 cm-‘. However, it is not surprising that additional features are observed considering that the high degree of vibrational excitation results in a large number of overlapping bands. The C *II-A 2Z+ transition is expected to overlap signi~cantly with the C ‘II-X *II band system. Since the C-A band system is over two orders of magnitude weaker, we have not included its contribution to the NaO spectrum shown in fig. 10. However, we have included both channels in determining the lifetimes, even though the C-A contribution is less than 1% in

Fig. IO. The C 21LX ‘I1 band system of NaO at 10 8, resolution corresponding to a rotational and vibrational temperature of 300 K.

all cases. The C-A transition is much weaker primarily because of the much smaller TMF - compare figs. 4 and 5. Also, the Franck-Condon factors are even more unfavorable, as the r, value of the A 2C+ state is smaller than that for the X ‘II state. The radiative lifetimes decrease from 90.7 ns for U’= 0 to 64.6 ns for v’ = 9 - see table 3. Thus as for LiO, the emission is very strong, especially considering that most of the intensity falls into the infrared. Presumably, the failure to observe this band system of NaO at the longer wavelengths is due to the fact that the phototube quantum efficiency drops rapidly at A> 9200 A. (Note that in the NaO single collision spectra, the quantum efficiency drops rapidly for A> 7800 8, - see figure caption to fig. 3 of ref. [ 2 1.) It is also possible that most of the emission occurs from higher vibrational levels of the C *II state, thereby substantially decreasing the emission at shorter wavelengths. In any case, it would be very worthwhile to attempt an experimental characterization of this band system in the infrared either in emission or in absorption. 3.5. KO spectroscopy The ~hemiluminescent spectrum of KO in the region 7500-10~0 A has been observed under both

S.R. Langhoffet al. /Spectroscopyof LiO, NaO, and KO

single and multiple collision conditions [ 21. Although some spectral features were identified, it was not possible to assign the complicated pattern of spacings, which was attributed to overlapping transitions between the nearly degenerate C *II-X 2C+ and C 2II-A 2Z+ band systems. However, as can be seen from comparing the TMFs for the C ‘II-A ‘II and C ‘II-X ‘C+ band systems in figs. 4 and 5, respectively, the parallel transition is much stronger; the calculated Einstein coefficients for the C ‘II-A ‘II transition are between 2 and 3 orders of magnitude larger than for the C 211-X 2E+ transition. Thus the complicated spectral pattern cannot be due to the overlapping of two band systems. Potential curves for the X 2Z+, A 211, and C 211 states of KO plotted in fig. 11 illustrate that the X 2E+ and A 211states of KO are nearly degenerate. Spectroscopic constants for these three states of KO are summarized in table 1. The minimum of the C 211 state occurs near 9.1 a0 in our calculation. Although this is expected to decrease by several tenths of an a0

11

with the inclusion of core-valence correlation, it is clear that emission from the low-lying vibrational levels will occur preferentially into the high vibrational levels of the X 2Z+ and A 211states. Also, considering the small rotational constant and o: value of only 56 cm- ‘, the spectra is likely to appear nearly continuous without high resolution. The C ‘II-A ‘II spectrum expected for emission from a Boltzmann distribution at 300 K is given in fig. 12. In analogy with LiO and NaO, the emission extends over a large wavelength region, peaking in the infrared. The maxima in the spectra shift to longer wavelengths for the heavier alkali oxides, paralleling the decrease in the C 211 T, values and X 211bond energies. The strongest band involving C 211(v’ = 0 ) is to V”= 66. Again, this may change slightly with improvements in the potentials, but the fact that the higher vibrational levels of the A 211 state are involved is a direct consequence of the large difference (4.4 ao) in r, values - see table 1. Since the C ‘IIA 211 band system is much more intense than the C 211-X ‘I;+ band system, it is unlikely that emission from the C 211state could be used to deduce the A-X separation, even if sufficient spectral resolution could be achieved. Thus another experimental approach will

1.0 -

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-

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2

4

6

8

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Bond Length, a,, Fig. I 1. SA-CASSCF( 433 ) /MRCI ( 7) potential the A ‘II, X *Z+, and C ‘II states of KO.

10000

15000

20000

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14

energy curves for

Wavelength, angstroms Fig. 12. The C *II-A zII band system of KO at 10 8, resolution corresponding to a rotational and vibrational temperature of 300 K.

12

S.R. Langhoff et al. /Spectroscopy of LiO. NaO, and KO

probably be required to test the theoretical prediction of a X 2x+ ground state for KO. During the course of this work, Shen et al. [ 191 have reanalyzed their experimental results, and have shown that the chemiluminescent emissions can be reinterpreted in a manner consistent with our theoretical calculations. This requires a C ‘II population mechanism that involves the reaction of electronically excited 2P alkali atoms. The new experimental study employing laser induced excitation supports this reinterpretation and demonstrates the important role of excited alkali atoms in the excitation process.

4. Conclusions Theoretical SA-CASSCF/MRCI calculations are presented to characterize the bound-bound emission from the C ‘II state into the two lowest ionic states of LiO, NaO, and KO. This work corroborates the recent experimental assignment of the chemiluminescence of the alkali oxides to the C 2II-X *II band system [ 21, but requires a rather high excited state vibrational temperature to explain the observed spectra. Since re(C ‘II) B r,(X 211) the emission is found to extend over a large wavelength interval. The strongest emission from the low-lying vibrational levels of the C ‘II states occurs in the infrared. At the temperatures observed in flames a rotational analysis of the spectra is likely to be complicated by the overlapping of many rovibrational transitions. Thus it may prove difficult to probe for the alkali oxides using laser excitation in the red and near infrared. However, it may be possible to detect the alkali oxides in combustion streams using lasers operating in the ultraviolet [ 191. Recently, Shen et al. [ 191 have been able to populate rovibrational levels of the C 211 state of LiO using a dye laser through chemiluminescent reactions of excited 2P Li atoms and ozone. The results of this new experimental work are consistent with the shape and position of the theoretical C ‘II state potential.

References [ 1] J.L. Gole, Opt. Eng. 20 ( 198 1) 546; D.E. Jensen and G.A. Jones, Combustion Flame 4 1 ( 198 1) 7 1. [ 2 ] J.R. Woodward, J.S. Hayden and J.L. Gole, Chem. Phys. 134 (1989) 395. [3] J. Pfeifer and J.L. Gole, J. Chem. Phys. 80 ( 1984) 565. [4] D. White, K.S. Seshardi, D.F. Dever, D.E. Mann and M.J. Linevsky, J. Chem. Phys. 39 ( 1963) 2463; KS. Seshardri, D. White and D.E. Mann, J. Chem. Phys. 45 ( 1966) 4697; R.C. Spiker and L. Andrews, J. Chem. Phys. 58 ( 1973) 702, 713. [ 51 S.M. Freund, E. Herbst, R.P. Mariella and W. Klemperer, J. Chem. Phys. 56 (1972) 1467; R.A. Berg, L. Wharton, W. Klemperer, A. Buchler and J.L. Stauffer, J. Chem. Phys. 43 (1965) 2416. [6] J.N. Alhson and W.A. Goddard III, J. Chem. Phys. 77 ( 1982) 4259; J.N. Alhson, R.J. Cave and W.A. Goddard III, J. Phys. Chem. 88 (1984) 1262. [ 7 ] S.R. Langhoff, C.W. Bauschlicher and H. Partridge, J. Chem. Phys. 84 (1986) 4474. [ 81 S.P. So and W.G. Richards, Chem. Phys. Letters 32 ( 1975) 227. [ 91 M. Yoshimine, J. Chem. Phys. 57 ( 1972) 1108. [lo] P.A.G. O’Hare and A.C. Wahl, J. Chem. Phys. 56 (1972) 4516. [ 111 D.M. Lindsay, D.R. Herschbach and A.L. Kwiram, Mol. Phys. 32 ( 1976) 1199, D.M. Lindsay and D.R. Herschbach, J. Chem. Phys. 60 (1973) 315. [ 121 R.R. Herm and D.R. Herschbach, J. Chem. Phys. 52 ( 1970) 5783. [ 131 H. Partndge, J. Chem. Phys. 90 (1989) 1043; 87 (1987) 6643. [ 141 J. Almliifand P.R. Taylor, J. Chem. Phys. 86 (1987) 4070. [ 151 F.B. van Duijneveldt, IBM Research Report No. RJ 945 (1971). [ 161 MOLECULE-SWEDEN is an electromc structure program system written by J. Almliif, C.W. Bauschlicher, M.R.A. Blomberg, D.P. Chong, A. Heiberg, S.R. Langhoff, P.-A. Malmqvist, A.P. Rendell, B.O. Roos, P.E.M. Siegbahn and P.R. Taylor. [ 171 C.E. Moore, Atomic Energy Levels, Natl. Bur. Stand. (US) Cnc. 467 (1949). [ 181 C.W. Bauschlicher, S.R. Langhoff, H. Partridge and P.R. Taylor, J. Chem. Phys. 85 (1986) 3407. [ 19 ] K.K. Shen, X. Qi and J.L. Gole, submitted for publication.