The ionization energy of KO2(X̃2A2) and dissociation energies of KO2 and KO2+

2 September 2002

Chemical Physics Letters 363 (2002) 139–144 www.elsevier.com/locate/cplett

~ 2A2Þ and dissociation The ionization energy of KO2ðX energies of KO2 and KOþ 2 Edmond P.F. Lee b

a,b

, Timothy G. Wright

c,*

a Department of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, UK Department of Applied Biology and Chemical Technology, Hong Kong Polytechnic University, Hung Hom, Hong Kong c School of Chemistry, Physics and Environmental Science, University of Sussex, Falmer, Brighton BN1 9QJ, UK

Received 21 June 2002; in final form 11 July 2002

Abstract RCCSD(T) calculations, with an effective core potential for the inner electrons of potassium, and large polarized valence basis sets, have been used to calculate ionization energies of KO2 . In addition, the binding energies of the ~ 2 A2 , and KOþ , X3 R , have been determined. Comparison with previous values is ground electronic states of KO2 , X 2 made, where possible, and an estimate made of the errors in our calculations. The binding energy of KOþ 2 is found to be very limited. It is concluded that the r^ ole of KOþ 2 in the upper atmosphere will be small. Ó 2002 Elsevier Science B.V. All rights reserved.

1. Introduction Recently, we have performed a number of calculations on alkali metal monoxide [1–5] and dioxide [6,7] species, concentrating our efforts in obtaining accurate adiabatic ionization energies (AIEs). In the process of obtaining these quantities we also obtained equilibrium geometries of the neutrals and cations, and as a simple extension, the dissociation energies and heats of formation of the neutrals and cations. These results have been used, in the case of sodium, to model the appearance of sporadic sodium layers in the upper atmosphere [8,9]. Potassium is also an important *

Corresponding author. Fax: +44-1273-677196. E-mail addresses: [email protected] (E.P.F. Lee), t.g.wright @sussex.ac.uk (T.G. Wright).

atmospheric metallic species [10], and sporadic potassium layers have been observed [11]. Since the MX species are generally largely ionic, they strongly resemble Mþ X in the neutral ground state, which is quite strongly bound, because of the Coulomb attraction. The lowest energy ionization process corresponds, essentially, to removal of the negative charge from X , and so the cation is fairly weakly bound, since now the Coulomb attraction is replaced by a charge/(induced-)dipole interaction. For the alkali metal monoxides, the Mþ  O structure of the neutral species leads to the presence of two low-lying states, corresponding to the two orientations of the ‘hole’ in the occupancy of the 2p orbitals on O (directed towards the closedshell Mþ , or perpendicular to it): these are the 2 Rþ and 2 P states, respectively. It is a well-known fact

0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 1 1 4 8 - X

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that the ground state of LiO and NaO is 2 P, but that of the heavier RbO, CsO and FrO is 2 Rþ ; the ground electronic state of KO is still controversial (see Introductions of [1–5]). For the alkali metal superoxides, MO2 , again, the ionic nature of the ground state leads to a Mþ  O 2 species, where again there is a ‘hole’ in the occupancy of the 2pp orbitals, which can be either in-plane, or out-of plane, giving rise to 2 B2 or 2 A2 states, respectively. Partridge and co-workers [12,13] and others [14,15] have demonstrated that, in contrast to the monoxides, the ground elec~ 2 A2 state for LiO2 –CsO2 . tronic state is the X Previously [6] we employed the CCSD(T) and B3LYP methods, making use of large polarized valence basis sets in combination with effective core potentials (ECPs) to study KO2 . Our most reliable geometry in that work indicated that KO2 had a bond angle of 32.3°, and was essentially a Kþ cation interacting with an O 2 moiety – this was in good agreement with the conclusions of Partridge et al. [12], who used a modified coupledelectron pair (MCPF) approach; and in fair agreement with some earlier UHF calculations by Plane et al. [16]. In the present work, we make use of our previously reported geometry [6] for KO2 , and in addition calculate the equilibrium geometry of KOþ 2 . We then use RCCSD(T) calculations with large basis sets to calculate the adiabatic ionization energy of KO2 , and the dissociation energy of KOþ 2 . We compare these calculated quantities with values derived previously in photoelectron studies [17], involving one of the authors.

2. Computational details and results 2.1. Geometries The geometry of KOþ 2 was optimized using both the (U)B3LYP and (U)QCISD methods (only the 1s orbitals on O was frozen) as implemented in the GA U S S I A N suite of programs [18]. The basis set employed for K was basis set B of [6], which consists of the LANL2 ECP [19], augmented with further basis functions; overall, this basis set is denoted LANL2[8s8p4d]. The ECP describes the 1s2 2s2 2p6 electrons. For O, the

standard 6-311+G(3d) basis set was employed. The results of the geometry optimizations and second derivative calculations are given in Table 1 for a few of the low-lying electronic states. The equilibrium geometry is a C1v structure. For the triplet states, hS 2 i was less than 2.05, showing that spin-contamination is minimal. These results will be discussed below. 2.2. Ionization energies Employing the UQCISD geometry from Table 3  1 for KOþ 2 ðX R ), and our best geometry from [6] ~ 2 A2 ), we then performed single-point for KO2 ðX calculations at the RCCSD(T) [20] level (only 1s orbitals on O frozen) with MO L P R O [21], using the following basis set. The ECP10MWB [22] ECP was used, and augmented with a large, flexible valence basis set, as follows. First a (20s15p) set of basis functions were obtained as an even-tempered set: s(ratio ¼ 1.7, centre ¼ 0.7); p(ratio ¼ 1.7, centre ¼ 1.1). These were contracted to a [1s1p] set with the coefficients coming from a Hartree–Fock calculation on Kþ . To this set were added the following uncontracted functions: seven s: f ¼ 1:0  0:004095, ratio ¼ 2.5; seven p: f ¼ 2:0  0:02048, ratio ¼ 2.5; four d: f ¼ 1:5  0:096, ratio ¼ 2.5; three f: f ¼ 1:3, 0.4333 and 0.1444; two g: f ¼ 0:55 and 0.15. In these calculations, the aug-cc-pVQZ basis set for O was employed. We denote all of the above 248 basis functions as ECP-1 in the below. Finally, for the first AIE and the dissociation energies, we also employed a slightly larger basis set to ascertain the level of basis set saturation, as follows: the same contracted [1s1p] set and ECP were employed, but now augmented with: nine s: f ¼ 3:31776  0:00301408, ratio ¼ 2.4; eight p: f ¼ 2:4  0:00523278, ratio ¼ 2.4; five d: f ¼ 2:0  0:02048, ratio ¼ 2.5; four f: f ¼ 1:5  0:096, ratio ¼ 2.5; three g: f ¼ 1:3; 0:4333; 0:1444. In these calculations, the aug-cc-pV5Z basis set for O was employed, omitting the h functions. We denote all of the above by ECP-2 in the below. The ionization energy of KO2 , as noted above, is essentially a removal of an electron from O 2,

E.P.F. Lee, T.G. Wright / Chemical Physics Letters 363 (2002) 139–144 Table 1  and °), vibrational Optimized geometrical parameters (in A frequencies (cm1 ) and the relative electronic energies (Erel in kcal mol1 with respect to the lowest 3 R state) of low-lying triplet and singlet states of KOþ 2 at the UB3LYP and UQCISD levels of calculationa Geometric parameter 2 3

(U)B3LYPb

(U)QCISDb

2.8298 1.2025 1653(r); 98(r); 32(p) 0.0

2.8306 1.2022 1646(r); 102(r); 42(p) 0.0

3.1997 1.2076 21.8 1625(a1 ); 68(a1 ); 84i (b2 ) 1.7

3.1859 1.2068 21.8 –

2.9226 1.2061 23.8 1616(a1 ); 114(a1 ); 95(b2 ) 36.9

– – – –



Linear,    p R ) RKO (A ) ROO (A Vib. Freqs. (cm1 ) Erel (kcal mol1 ) T-shaped    b2 1 a12 3 B1 ) RKO (A ) ROO (A hOKO (°) Vib. Freqs. (cm1 ) Erel (kcal mol1 )

1.4

   b22 a02 1 A1

T-shaped ) RKO (A ) ROO (A hOKO (°) Vib. Freqs. (cm1 ) Erel (kcal mol1 )

–

a

Employing the LANL2[8s8p4d] basis set for K – see text, and a 6-311+G(3d) basis set for O. b hS 2 i less than 2.05 for the triplet states.

since KO2 is very ionic. To ascertain how accurate our calculated ionization energy would be, we calculated the ionization energy of K in this work, and noted the calculated electron affinity (EA) of O2 , calculated in our previous work on NaO2 [5] – in both cases employing the corresponding basis sets from ECP-2. IE(K) was calculated to be 4.30 eV, which compares with the experimental value [23] of 4.34 eV. For EAðO2 Þ the value of 0.43 eV was obtained, which compares very favourably with the experimental value of 0.45 eV [24]. Given that KO2 contains very little K character, the error in the calculated KO2 AIE from the description of the charge changes on the K and O during the ionization process, is expected to be no more than 0.03 eV. Another source of error is basis set superposition error (BSSE). It is straightforward to account for this in an ionic species, by using the full counterpoise correction [25]. We do this for KO2

141

and KOþ 2 at the respective equilibrium geometries, and obtain the values in Table 2; as may be seen, the amount of BSSE is very small and can contribute no more than an error of 0.02 eV. Overall, we are confident our error in the calculated AIE can be no more than 0.05 eV. In Table 3 are given the calculated AIE and VIE at the RCCSD and RCCSD(T) levels of theory, both for ionization to the X3 R cationic state, as well as to the lowest singlet state. It may be seen that the effect of triples is small, increasing the AIE, but decreasing the VIEs. In addition, the enlargement of the basis set had little effect, indicating that we are close to basis set saturation. Our best value ~ 2 A2 ) is therefore 5:98  0:05 eV, for the first AIEðX with the VIE ¼ 6:94  0:05 eV, where we have increased the ECP-1 value by 0.02 eV in line with the AIE trend on going from ECP-1 to ECP-2. The second VIE, accessing the lowest singlet state – expected to be the 1 D state in a linear geometry – is 7:81  0:05 eV. If we correct the ionization energies for the zero-point vibrational energy (ZPVE), using the harmonic vibrational frequencies from [6] for KO2 and from Table 1 for KOþ 2 , we obtain the same values to two decimal places. Table 2 ~ 2 A2 Þ and KOþ (X3 R )a BSSE (kcal mol1 ) calculated for KO2 ðX 2 Species

Kþ ð1 SÞ

2 O 2 ðX PÞ

3  O 2 ðX Rg Þ

~ 2 A2 ) KO2 (X 3  KOþ ðX R Þ 2

0.15 0.07

0.09 –

– 0.03

a At the respective equilibrium bond lengths, employing the ECP-2 basis set.

Table 3 Calculated ionization energies (eV) – see text for details Process

RCCSD

RCCSD(T)

ECP-1 ECP-2 ECP-1 ECP-2 3  AIE KOþ 2 ðX R Þ 3  VIE KOþ 2 ðX R Þ f VIE KOþ 2 ðsingletÞ

~ 2 A2 ) 5.86a KO2 ðX ~ 2 A2 Þe 7.00 KO2 ðX ~ 2 A2 Þ 7.98 KO2 ðX

5.88b – –

5.96c 6.92 7.81

5.98d – –

Etot ðKOþ 2 Þ ¼ 178:317395 Eh ; Etot ðKO2 Þ ¼ 178:532927Eh . Etot ðKOþ 2 Þ ¼ 178:342069 Eh ; Etot ðKO2 Þ ¼ 178:558061Eh . c Etot ðKOþ 2 Þ ¼ 178:347348 Eh ; Etot ðKO2 Þ ¼ 178:566423Eh . d Etot ðKOþ 2 Þ ¼ 178:373649 Eh ; Etot ðKO2 Þ ¼ 178:593308Eh . e Strictly, the 3 R state is of 3 B1 symmetry in C2v symmetry. f This singlet state corresponds to the closed-shell    b22 state in C2v symmetry. a

b

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E.P.F. Lee, T.G. Wright / Chemical Physics Letters 363 (2002) 139–144

2.3. Dissociation energies

3. Discussion

It is straightforward to calculate the dissociation energies for the processes

3.1. Geometry and vibrational frequencies

þ 1 2 ~2 KOþ 2 ðX A2 Þ ! K ð SÞ þ O2 ðX Pg Þ

ð1Þ

and 1

3  KO2 ðX3 R Þ ! Kþ ð SÞ þ O 2 ðX Rg Þ

ð2Þ

We can then correct the dissociation energy from process (1) by IE(K) and EA(O) obtained from [23] and [24], respectively, to give the dissociation energy for the process ~ 2 A2 Þ ! Kð2 SÞ þ O ðX3 R Þ KO2 ðX ð3Þ 2

g

The expected errors in these values will be 0.02 eV, arising from the BSSE as discussed above, and an estimated 0.01 eV arising from the small amount of charge alteration in the process. Thus, we cite an error of 0.03 eV (0.7 kcal mol1 ) in our dissociation energy values, and the calculated values, corrected for BSSE, are shown in Table 4. Note the very small changes that occur upon enlarging the basis sets, which indicate that we are close to saturation. Our best values are therefore: ~ 2 A2 Þ ¼ 41:1  0:7 kcal mol1 ; De ½KO2 ðX and 1 3  De ½KOþ 2 ðX R Þ ¼ 3:2  0:7 kcal mol

corresponding to processes (3) and (2), respectively. These may be corrected for ZPVE to give D0 values as follows: ~ 2 A2 Þ ¼ 40:2  0:7 kcal mol1 D0 ½KO2 X 1 3  D0 ½KOþ 2 ðX R Þ ¼ 2:9  0:7 kcal mol :

Table 4 ~ 2 A2 Þ Calculated dissociation energies (kcal mol1 ) of KO2 ðX þ 3  and KO2 ðX R Þ using reactions (1)–(3) – see text for details

1 3 2

RCCSD

3.2. Ionization energy A photoelectron study [17] employed K and O3 to obtain KO2 from the following two reactions:

and

Reaction

To our knowledge, there have been no previous reports of the geometry nor vibrational frequencies 3  of KOþ 2 . The linear R state obtained is consistent with our previous findings for NaOþ 2 [7]. The bond length increases between KO2 and KOþ 2 – notwithstanding the change in symmetry from C2v : this is exactly as one to C1v – from 2.41 to 2.92 A would expect as the Coulomb attraction between Kþ and O 2 is lost, to be replaced only by the charge/induced-dipole interaction. This is further demonstrated in the binding energies (vide infra). 3  The O–O bond length in KOþ 2 ðX R Þ is expected 3  to be close to that of free O2 ðX Rg ), which has a  [26], and as may be seen, both value of 1.20752 A the B3LYP and QCISD values are in very good agreement with this. In addition, the highest r vibration has a harmonic frequency of ca. 1650 cm1 at these levels of theory, which compares well with the experimental value [26] of 1580 cm1 for xðO2 ). Note that optimizations in C2v symmetry led to a 3 B1 saddle point lying just above the linear 3 R state to which it correlates, with the imaginary frequency indicating that a breaking of the C2v symmetry was required in the direction of the minimum. There was also a closed-shell singlet state higher in energy, which was bent.

RCCSD(T)

ECP-1

ECP-2

ECP-1

ECP-2

130.9 41.2 3.1

131.2 41.5 3.2

131.4 41.7 3.2

131.8 42.1 3.2

K þ O3 ! KO þ O2

ð4Þ

KO þ O3 ! KO2 þ O2

ð5Þ

The onset of the lowest energy band assigned to KO2 was at 5:7  0:1 eV, and this was taken as AIE(KO2 ). We have noted in our earlier study on NaO2 [7] that the onset of the photoelectron band assigned to NaO2 in [17] was slightly lower in energy than the calculated AIE in that [7] work, which we attributed to internal excitation of the NaO2 from the equivalent of reaction (5). Again, we attribute the lower onset for KO2 than the AIE

E.P.F. Lee, T.G. Wright / Chemical Physics Letters 363 (2002) 139–144

calculated in the present work, 5:98  0:05 eV, to be attributable to the same cause. This is unsurprising as the photoelectron spectrum reported in [17] was obtained from a reaction cell, with relatively high partial pressures of K and O3 , with the in situ photoionization allowing no time for vibrational relaxation of the KO2 formed. The calculated VIE of 6:94  0:05 eV is very much higher than the maximum in the KO2 photoelectron band, which was reported [17] at 6:01  0:08 eV. Clearly, if the neutral KO2 has been vibrationally excited, then this will alter the appearance of the (unresolved) photoelectron band, since each vibrational level will have a different set of Franck–Condon factors for the ionization process. Also, given the change in geometry – which clearly leads to the AIE and VIE being quite different – and the very low-binding energy of the cation, then it is highly likely that the vertical ionization leads to the accessing of unbound levels in the cation: this will also have a pronounced effect on the appearance of the photoelectron band. We note that DSCF and DSCF + CI calculations were reported in [17], where the first VIE was reported as 6.30 eV when the Davidson correction had been included – this is significantly below the value obtained herein. Certainly the basis sets employed in the latter work were relatively small. Finally, we note that an approximate electrostatic model was set up in [17] to calculate the VIE of KO2 , and a value of 6.46 eV was obtained – this value is in fair agreement with the value obtained herein. This confirms the dominance of a change in electrostatic effects during the ionization process. 3.3. Dissociation energies Our best value for the dissociation energy, D0 , of KO2 is 40:2  0:7 kcal mol1 , which is in excellent agreement with the value from Partridge et al. of 40:6  2 kcal mol1 . We agree with their conclusions that the high values of P 48:5 kcal mol1 from [16], and 59  5 kcal mol1 from [27] (for which some support was given in [28]) are incorrect, and that the best experimental value appears to be that of Jensen [29], who obtained 40:6  7:2 kcal mol1 , but the error is quite large. We also note that Hastie et al. [30] obtained a value for

143

D0 ðKO2 ) at 1000 K, obtaining 36:7  3 kcal mol1 , which is also of good consistency compared with the present value, and that of Jensen. To the authors’ knowledge, the only estimate of the binding energy of KOþ 2 comes from the photoelectron work [17], where values of around 8 kcal mol1 were derived, assuming various values for D0 ðKO2 ) and using the photoelectron band onsets of KO and KO2 : the errors in these values, however were as large as 8 kcal mol1 . It is clear that the present value of 2:9  0:7 kcal mol1 is of much greater reliability than those derived values. The very small binding energy of the cation is expected, since the dominant force is expected to be a weak interaction between the Kþ and the induced dipole of O2 , with other terms, such as the induced-dipole/induced-dipole and quadrupolar interactions expected to be smaller. Interestingly, the binding energy of KOþ 2 is slightly smaller than that of NaOþ , which was calculated to be 4:6  0:3 2 kcal mol1 in [7]. This suggests that electron– electron repulsion may be playing a role. Another possibility is that the positive charge is spread out over a larger volume in Kþ than it would be in Naþ : this would serve to lessen the overlap with the O2 orbitals. 3.4. Atmospheric relevance As noted above, we recently investigated the r^ ole of sodium-containing cationic complexes in the formation of sporadic sodium layers [8,9], and showed that actual observations were very well modelled by the chemistry of such complexes. One of the complexes involved was NaOþ 2 , which may be thought of as Naþ  O2 . As noted in Section 1, potassium sporadic layers have also been observed [11], and it is reasonable to assume that a similar mechanism involving cationic potassium complexes is involved with their formation. Considering the very low-binding energy for Kþ  O2 found in the present work, we conclude that the involvement of this cation is unlikely to be significant, since it will be relatively unstable to collisional dissociation, and indeed the cross-section for its formation from processes such as: Kþ þ O2 þ M ! KOþ 2 þM

ð6Þ

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E.P.F. Lee, T.G. Wright / Chemical Physics Letters 363 (2002) 139–144

(where M is a third body, most likely N2 ) is unlikely to be very high, as there will not be many KOþ 2 energy states into which the Kþ þ O2 can become a stable entity. In addition, the direct photoionization of KO2 is most likely to access the repulsive wall in the cationic state, and so lead to Kþ þ O2 . 4. Conclusions High-level ab initio calculations have allowed the accurate calculation of ionization energies for KO2 and dissociation energies for both KO2 and KOþ 2 . The D0 value for the cation is very small, and suggests that upon ionization of KO2 , most of the KOþ 2 will be formed above the dissociation limit, and so lead to Kþ þ O2 . The D0 value for the neutral was in good agreement with the best previous theoretical calculations, and two previous experimental determinations; other experimental determinations were found to be in poor agreement. The low D0 value for KOþ 2 is expected to limit its r^ ole in atmospheric chemistry.

Acknowledgements The authors are grateful to the EPSRC for the award of computer time at the Rutherford Appleton Laboratories under the auspices of the Computational Chemistry Working Party (CCWP), which enabled these calculations to be performed. E.P.F.L. is grateful to the Research Grant Council (RGC) of the Hong Kong Special Administration Region for support. T.G.W. is grateful to the EPSRC for the award of an Advanced Fellowship. References [1] P. Sold an, E.P.F. Lee, T.G. Wright, J. Phys. Chem. A 102 (1998) 9040. [2] E.P.F. Lee, P. Sold an, T.G. Wright, Chem. Phys. Lett. 295 (1998) 354. [3] P. Sold an, E.P.F. Lee, S.D. Gamblin, T.G. Wright, Phys. Chem. Chem. Phys. 1 (1999) 4947. [4] E.P.F. Lee, J. Lozeille, P. Soldan, S.E. Daire, J.M. Dyke, T.G. Wright, Phys. Chem. Chem. Phys. 3 (2001) 4863. [5] E.P.F. Lee, P. Sold an, T.G. Wright, Chem. Phys. Lett. 347 (2001) 481.

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