A theoretical study of gas-phase basicities and proton affinities of alkali metal oxides and hydroxides

Journal of Molecular Structure (Theochem) 638 (2003) 119–128 www.elsevier.com/locate/theochem

A theoretical study of gas-phase basicities and proton affinities of alkali metal oxides and hydroxides Peeter Burk*, Sven Tamp Institute of Chemical Physics, Tartu University, 2 Jakobi Street, Tartu 51014, Estonia Received 10 April 2003; revised 10 April 2003; accepted 5 July 2003

Abstract B3LYP and PBE0 density functional calculations with different effective core potentials (ECP) and basis sets were used to investigate gas-phase geometries, basicities, and proton affinities of alkali metal oxides M2O and hydroxides MOH (M ¼ K, Rb, Cs). The alkali metal oxides and hydroxides were all found to be linear. We suggest the gas phase proton affinities for Rb2O and Cs2O to be 331.9 and 324.4 kcal/mol, respectively. Our calculations show that the most accurate method for calculating geometries of potassium, rubidium and cesium oxides and hydroxides is PBE0 density functional with CRENBL ECP and basis set (augmented with Glendening’s polarization functions) on alkali metal, Dunning’s double-zeta basis augmented with set of polarization and diffuse functions on oxygen, and Dunning’s double-zeta plus polarization basis on hydrogen, while for proton affinities the B3LYP functional (with the same ECP/basis set combination) is marginally better. q 2003 Elsevier B.V. All rights reserved. Keywords: Gas-phase basicity; Proton affinity; Alkali metal oxides; Alkali metal hydroxides; DFT calculations

1. Introduction During the last decades an increased amount of data about the intrinsic properties of molecules has been published. This allows studying the direct influence of electronic structure on the chemical properties of molecules as well as reaction mechanisms without solvent effects. Proton transfer is one of the most important and thoroughly studied phenomena of chemical and biochemical reactions. Consequently, an accurate * Corresponding author. Tel.: þ 372-7375258; fax: þ 3727375264. E-mail address: [email protected] (P. Burk). 0166-1280/$ - see front matter q 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0166-1280(03)00540-2

data of the gas-phase acidities and basicities (GB) of neutral molecules must be available. Recently published GB scale by Lias [1] which is an updated edition of an absolute gas-phase basicity/proton affinity scale compiled by the same author in 1984 [2], now includes data for more than 2000 compounds. The average uncertainty of the scale is 1.9 kcal/mol in the central part. However, the situation is less certain at the upper end as there still seem to be discrepancies in the reported basicities of the strongest bases –alkali metal oxides [1]. Basicity is defined as the negative of the Gibbs free energy of the following hypothetical protonation reaction: þ BðgÞ þ Hþ ð1Þ ðgÞ ¼ BHðgÞ

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GB ¼ 2DG0ð1Þ ¼ Df G0 ðBÞ þ Df G0 ðHþ Þ 2 Df G0 ðBHþ Þ ð2Þ Parallel with basicities it is often more common to use proton affinities (PA) defined as the negative of the corresponding enthalpy change: PAB ¼ 2DH10 ¼ Df H 0 ðBÞ þ Df H 0 ðH þ Þ 2 Df H 0 ðBHþ Þ ð3Þ The reported experimentally determined gas-phase basicities and PA [1,3] of alkali metal oxides are based on the following ion-molecule equilibrium: þ M2 OHþ ðgÞ ¼ MðgÞ þ MOHðsÞ

ð4Þ

PA can be obtained by measuring the equilibrium constants of the earlier reaction and following use of thermodynamic cycle as: PAðM2 OÞ ¼ Df H 0 ðM2 O; gÞ þ Df H 0 ðH þ ; gÞ 2 Df H 0 ðMþ ; gÞ 2 Df H 0 ðMOH; sÞ þ DH4 ð5Þ The corresponding thermodynamic data is presented in Table 1. Comparison indicates that Lias et al. [1] have taken DH4 values from Butman

[3] but different enthalpies of formation used in thermodynamic cycle (5) result in different PA values and even basicity ordering. The biggest differences occur in the values of Df H 0 ðM2 O; gÞ for K2O and Cs2O (16.3 and 10.8 kcal/mol, respectively). The other Df H 0 values are quite consistent, with differences of 1.5 kcal/mol for Df H 0 ðMþ ; gÞ and practically the same values for Df H 0 (MOH,s). Butman et al. have used Df H 0 values taken from Glushko [4]. We do not know the origin of the Df H 0 (K2O,g) value used by Lias, but as it is about 18 kcal/mol off compared to other values found in literature as shown by Burk and Sillar [5], it should be considered highly suspicious. Yet another reason for different PA-s in Refs. [1,3] has been pointed out by Burk and Sillar [5]. It lies in the fact that Lias et al. have used DH4 values (mistakenly, we presume) with positive sign (9.1, 11.5, 9.1, and 9.3 kcal/mol for Li2O; Na2O; K2O and Cs2O, respectively), while they were in fact reported as 2DH4 ðLiÞ ¼ 9:1 kcal=mol; 2DH4 ðNaÞ ¼ 11:5 kcal=mol; 2DH4 ðKÞ ¼ 9:1 kcal=mol and 2DH4 ðCsÞ ¼ 9:3 kcal=mol: Also, Butman et al. [3] have used positive DH4 (Li) value (obtained from ab initio calculations and not experiment) while for other PA-s the DH4 values were taken as negative. The PA from

Table 1 The experimental data used by different authors for calculating the proton affinities (PA) of alkali metal oxides and the obtained PA (converted to kcal/mol) M

Li

Lias et al. [1] ðDf H 0 ðHþ ; gÞ ¼ 365:6 kcal=molÞ DfH 0 (M2O,g) 240.0 DfH 0 (MOH,s) 2115.9 9.1 DfH 0 (Mþ,g) DH4 PAorig 288.2 PArecalc 270.0

Na

26.0 2101.8 144.1 11.5 328.8 305.8

Butman et al. [3] ðDf H 0 ðHþ ; gÞ ¼ 365:6 kcal=molÞ 240.0 24.0 DfH 0 (M2O,g) DfH 0 (MOH,s) 2115.9 2101.8 DfH 0 (Mþ,g) 163.8 145.6 DH4 29.1 211.5 285.8 306.6 ^ 2.4 PAorig PArecalc 268.6 306.3 PA (M2O) [5] 285.1 315.2 PA (M2O) [9] 285.1 340.7

K

Rb

234.0 101.5 121.4 9.08 320.8 302.6 217.7 2101.5 122.8 29.1 318.2 ^ 4.7 318.2 328.3 370.2

Cs

222.0 299.6 108.0 9.3 344.8 325.9 226.0 2100.1 117.1 29.6 313.5 ^ 4.5

232.8 299.5 109.5 29.3 313.5 ^ 4.5

PAorig is the original PA given by the authors and PArecalc is the corresponding PA recalculated by Burk and Sillar [5], using the data used by authors of Refs. [1,3], respectively.

P. Burk, S. Tamp / Journal of Molecular Structure (Theochem) 638 (2003) 119–128

thermodynamic cycle (5), recalculated by Burk and Sillar [5] have also been included in Table 1. The reported gas-phase PA of alkali metal hydroxides [1,6] are based on the measurement of equilibrium constants of the following reaction by Kebarle [6]: Mþ þ H2 O ¼ ðMOH2 Þþ

ð6Þ

Here, DH6 is basically the hydration enthalpy of the alkali metal cation. The basicity/proton affinity from the hypothetical gas-phase protonation reaction MOH þ Hþ ¼ MOHþ 2

ð7Þ

and can be calculated from analogous (as compared to Eq. (5)) thermodynamic cycle: PAðMOHÞ ¼ Df H 0 ðMOH;gÞ2DH6 2Df H 0 ðMþ ;gÞ þDf H 0 ðH þ ;gÞ2Df H 0 ðH2 O;gÞ

ð8Þ

The PA of alkali metal hydroxides from Refs. [1,6] with associated Df H 0 values are presented in Table 2. Once again, the results reported by Hunter and Lias [1] differ from those of original measurements [6]. The biggest differences occur in the Df H 0 (MOH)

Table 2 The experimental data used by different authors for calculating the proton affinities (PA) of alkali metal hydroxides and the obtained PA-s in kcal/mol M

Li

Na

K

Cs

Lias et al. [1] ðDHf0 ðHþ ; gÞ ¼ 365:6 kcal=molÞ DH0f (MOH,g) 247.3 256.0 DH0f (Mþ,g) 144.1 121.4 257.8 257.8 DH0f (H2O,g) DH6 224.1 217.0 PA (MOH) 238.9 256.1 263.0 GB (MOH) 257.0

262.0 108.0 257.8 211.9 265.3 261.0

Kebarle et al. [6] ðDHf0 ðHþ ; gÞ ¼ 367 kcal=molÞ 255.0 256.0 257.6 DfH 0 (MOH,g) DfH 0(Mþ,g) 162.3 144.4 121.7

260.0 108.5

Kebarle et al. [6] DHf ðH2 O; gÞ ¼ 251:3 kcal=mol DH6 234.0 224.0 217.9 PA (MOH) 240.6 247.6 262.5 PA (MOH) [5] 234.7 256.0 265.1 GB (MOH) [5] 230.5 249.0 258.9 PA (MOH) [9] 250.4 272.5 287.0

2137.0 269.1

121

value for M ¼ Na (8.7 kcal/mol) and Df H 0 (H2O) (6.5 kcal/mol), while for other Df H 0 values the differences lie within 2 kcal/mol. Lias [1] has given two different PA values for CsOH based on slightly different DH6 values. Both of them are shown in Table 2. A number of papers investigating the reliability of different quantum chemical methods for predicting gas-phase basicities have been published. Smith and Radom [7] found that G2(MP2) method (being a more economic variant of the computationally more demanding G2 procedure) gave very good results with the average uncertainty of up to 2.4 kcal/mol for about 20 compounds studied. Burk and Koppel [8] have investigated the ability of DFT B3LYP hybrid method with various basis sets to reproduce experimental PA for a series of bases. A conclusion was drawn that the best bargain between accuracy and computational speed was achieved at the B3LYP/6-311 þ G** level with an average absolute error comparable to an experimental uncertainty. Two more theoretical studies of alkali metal oxides and corresponding hydroxides have been published by Burk and Koppel [5,9]. In their earlier study [9] at the RHF level with TZV*, SBK* and 3-21G* basis sets it was shown that empirical corrections should be applied to the calculated PA to get more acceptable results. In their most recent relatively high level computational study [5] PA of alkali metal oxides, M2O and hydroxides, MOH (M ¼ Li, Na, K) were investigated at the CCSD(T,Full)/6-311þ þ G(2df,2pd) and DFT B3LYP/6-311 þ G(3df,3pd) level. For alkali hydroxides the DFT B3LYP method gave an almost perfect match within 2.2 kcal/mol as compared to experimental values while the CCSD(T,Full) results were worse, overestimating the PA by up to 7.2 kcal/mol. The PA-s of alkali metal oxides were systematically overestimated by up to 21 kcal/mol with both methods. In our current report we have undertaken an extensive study of the basicities and PA of all alkali metal oxides and hydroxides from potassium to cesium. Our special interest is in the PA of Rb2O, Cs2O and corresponding hydroxides as we are not aware of any earlier computational studies of those compounds. The geometries of those molecules have also been investigated.

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2. Methods All calculations were performed using the 4.0 program package [10]. Density functional calculations were done using B3LYP [11] and PBE0 hybrid [12] functionals. As the number of inner shell electrons becomes greater for heavier alkali metals, we have tested various effective core potentials (ECP) on alkali metal atoms differing in the number of electrons replaced by the potential as well as in the size of the basis sets designed explicitly for those ECP-s. The core potentials and basis sets used on all atoms were LanL2DZ [13], SBKJC –VDZ [14], and CRENBL [15]. For alkali metal atoms we used also Stuttgart RLC [16], Stuttgart RSC [16,17], and Hay – Wadt MB ðn 2 1Þ [13d] core potentials and basis sets together with Dunnings double-zeta basis [18] on oxygen and hydrogen. We also investigated the effects of adding polarization and diffuse functions on the geometries and PA in case of two small-core ECP-s (Stuttgart RSC and CRENBL) by using Dunnings DZP and DZP þ Diffuse basis sets [13a] on hydrogen and/or oxygen atoms. We believe this should give a better description of the highly ionic character of the metal – oxygen bond and accordingly more accurate results. Glendening’s polarization functions [19] were used on alkali metal atoms in some of those calculations. The geometries of the neutral and protonated forms of molecules were optimized into a minimum (the number of imaginary frequencies NImag ¼ 0) at all investigated levels. Frequencies were calculated at the same levels to obtain enthalpies and Gibbs free energies. Gas-phase basicities and PA were calculated as defined by formulas (2) and (3). NWCHEM

3. Results and discussion 3.1. Geometries The geometries of K2O and KOH have been thoroughly investigated and reasonably determined already in earlier theoretical investigations [5,9]. In the current paper we concentrate on the geometries of Rb2O, Cs2O, and corresponding hydroxides. Calculated structures are given in Fig. 1 and corresponding

Fig. 1. Typical structures of calculated neutral and protonated alkali metal oxides and hydroxides.

geometry parameters presented in Tables 3 and 4 together with available experimental data. Spiker and Andrews [20] studied the IR and microwave spectra and established the bent ðC2v Þ structures for both Rb2O and Cs2O with the most probable valence angle, M –O –M, being 160 –1808. The idea of the linear structure of those compounds was not completely rejected, though. Our calculations indicate that the studied alkali metal oxides are linear, belonging to the D1h point group. Linear structures have been predicted for RbOH and CsOH in experimental measurements [21,22] as well as in theoretical calculations by Nemukhin [23]. Our calculations support this fact, indicating linear structures (C1h point group) for both hydroxides. We have compared the ability of different ECP and corresponding basis sets used in this study to predict the geometries of potassium, rubidium, and cesium oxides and hydroxides. The CRENBL ECP gives the closest match with experimentally determined metal – oxygen bond lengths in neutral bases with both density functionals (B3LYP and PBE0), usually ˚ . The O – H bond overestimating it by up to 0.13 A lengths are also systematically overestimated by all ˚ . It studied ECP-s, but the errors are within 0.02 A should be noted that the SBKJC – VDZ ECP gives unrealistic geometries for cesium compounds with ˚ ) and very short metal – oxygen bonds (1.1 – 1.4 A rubidium compounds have also considerably shorter metal – oxygen bonds as compared to other ˚ shorter). used ECP-s and experiment (ca. 0.3– 0.5 A Much better results are obtained when the use of ECP on alkali metal atoms is augmented with the use of double-zeta basis on oxygen and hydrogen and even better results can be obtained when polarization functions are added to all atoms and diffuse functions are added to oxygen. Addition of diffuse functions to

K2O

K2OH

H

r(M–O)

r(M–O)

r(O –H)

DZ DZ DZP DZP þ CRENBL DZP DZP þ

1.840 2.365 2.422 2.352 2.360 2.273 2.273 2.326 2.269 2.269

2.510 2.568 2.454 2.472 2.450 2.451 2.458 2.450 2.452 2.507 2.555 2.441 2.458 2.434 2.435 2.444 2.434 2.437

ECP/basis set used on each atom M

O

LanLDZ SBKJC-VDZ Stuttgart_RLC Hay –Wadt MB Stuttgart_RSC Stuttgart_RSC, P Stuttgart_RSC, P CRENBL CRENBL, P CRENBL, P LanLDZ SBKJC-VDZ Stuttgart_RLC Hay –Wadt MB Stuttgart_RSC Stuttgart_RSC, P Stuttgart_RSC, P CRENBL CRENBL, P CRENBL, P Experimental [24]

DZ DZ DZP þ DZP þ CRENBL DZP þ DZP þ

DZ DZ DZP þ DZP þ CRENBL DZP þ DZP þ

DZ DZ DZP DZP þ CRENBL DZP DZP þ

1.849 2.359 2.412 2.333 2.344 2.255 2.255 2.317 2.253 2.253 2.18

Rb2O

Rb2OH

a

r(M–O)

r(M–O)

r(O–H)

109.3 109.8 110.3 110.2 108.1 108.3 109.0 108.2 108.3

2.530 2.069 2.546 2.352 2.490 2.411 2.411 2.468 2.369 2.369

2.651

0.991 0.985 0.985 0.984 0.970 0.969 0.984 0.970 0.970 0.985 0.978 0.980 0.980 0.966 0.965 0.977 0.966 0.965

109.7 110.1 110.5 110.3 108.2 108.3 109.5 108.3 108.3

2.512 2.068 2.533 2.512 2.466 2.391 2.391 2.441 2.347 2.347 2.32

Cs2O

Cs2OH

a

r(M– O)

r(M–O)

r(O– H)

a

0.986

109.9

2.708 2.454 2.615 2.615 2.617 2.213 2.587 2.589

0.986 0.985 0.986 0.970 0.970 0.995 0.970 0.970

108.8 110.3 109.6 107.6 107.7 113.2 106.3 107.7

2.706 1.166 2.716 2.352 2.594 2.456 2.456 2.410 2.412 2.412

2.840 1.166 2.890 2.454 2.759 2.732 2.735 2.673 2.709 2.710

0.987 2.447 0.988 0.985 0.987 0.971 0.971 0.985 0.971 0.970

109.5 90.0 108.8 110.3 109.3 107.6 107.6 109.6 107.6 107.5

2.634 2.209 2.693 2.635 2.596 2.595 2.597 2.605 2.567 2.589

0.981 0.986 0.980 0.981 0.981 0.966 0.966 0.985 0.966 0.970

110.1 111.2 109.2 110.1 109.8 107.7 107.7 108.9 107.7 107.7

2.680 1.166 2.702 2.680 2.545 2.427 2.427 2.376 2.380 2.412 2.403

2.817 0.893 2.873 2.817 2.725 2.703 2.705 2.642 2.679 2.679

0.983 2.261 0.981 0.983 0.982 0.967 0.966 0.979 0.967 0.966

109.7 89.4 109.2 109.7 109.6 107.7 107.6 110.1 107.7 107.7

P. Burk, S. Tamp / Journal of Molecular Structure (Theochem) 638 (2003) 119–128

Table 3 Calculated structures of neutral and protonated forms of alkali metal oxides

Bond lengths ðrÞ are in angstroms and angles ðaÞ in degrees.

123

124

ECP/basis set used on each atom

KOH

M

H

r(M–O) r(O –H) r(M–O) r(O –H) a

r(M –O) r(O–H) r(M –O) r(O–H) a

r(M–O) r(O –H) r(M–O) r(O –H) a

DZ DZ DZP þ

DZ DZ DZP

1.527 2.255 2.351 2.252 2.273 2.242

0.984 0.982 0.976 0.973 0.975 0.963

2.188 2.684 2.691 2.592 2.599 2.625

0.981 0.984 0.977 0.978 0.978 0.970

126.5 125.8 125.5 125.8 125.6 127.7

2.442 1.933 2.471 2.442 2.402 2.387

0.977 0.982 0.978 0.977 0.976 0.964

2.799 2.284 2.851 2.800 2.770 2.814

0.978 0.986 0.977 0.978 0.978 0.970

125.7 126.6 125.5 125.7 125.6 127.7

2.615 1.347 2.640 2.615 2.514 2.476

0.978 1.030 0.980 0.978 0.977 0.966

3.022 1.363 3.039 3.023 2.971 3.002

0.978 1.018 0.977 0.978 0.978 0.970

125.7 146.1 125.5 125.7 125.6 127.7

DZP þ

DZP þ

2.244

0.962

2.629

0.970

127.7 2.391

0.964

2.819

0.970

127.7 2.480

0.965

3.009

0.970

127.7

CRENBL DZP þ DZP þ

CRENBL 2.255 DZP 2.240 DZP þ 2.245

0.974 0.963 0.963

2.589 2.623 2.629

0.976 0.970 0.970

125.9 2.392 127.7 2.354 127.7 2.357

0.977 0.964 0.964

2.755 2.794 2.800

0.976 0.970 0.970

125.9 2.407 127.7 2.448 127.7 2.448

0.978 0.966 0.966

2.892 2.987 2.994

0.977 0.970 0.970

125.8 127.7 127.7

0.978 0.976 0.970 0.969 0.971 0.959

2.182 2.681 2.677 2.582 2.589 2.613

0.976 0.978 0.971 0.974 0.974 0.966

126.5 125.6 125.3 125.7 125.6 127.7

2.430 1.934 2.460 2.430 2.384 2.371

0.972 0.976 0.972 0.972 0.972 0.960

2.785 2.287 2.833 2.785 2.754 2.798

0.974 0.981 0.971 0.974 0.974 0.966

125.6 126.5 125.3 125.6 125.5 127.7

2.587 1.353 2.629 2.597 2.484 2.451

0.974 1.016 0.974 0.974 0.972 0.962

3.000 1.368 3.020 3.000 2.944 2.972

0.974 1.005 0.971 0.974 0.974 0.966

125.6 145.6 125.3 125.6 125.5 127.7

O

LanLDZ SBKJC-VDZ Stuttgart_RLC Hay –Wadt MB Stuttgart_RSC Stuttgart_RSC, P Stuttgart_RSC, P CRENBL CRENBL, P CRENBL, P LanLDZ SBKJC-VDZ Stuttgart_RLC Hay –Wadt MB Stuttgart_RSC Stuttgart_RSC, P Stuttgart_RSC, P CRENBL CRENBL, P CRENBL, P Experimental [24]

KOH2

RbOH

RbOH2

CsOH

CsOH2

DZ DZ DZP þ

DZ DZ DZP

1.540 2.252 2.342 2.245 2.261 2.229

DZP þ

DZP þ

2.230

0.958

2.617

0.966

127.8 2.375

0.959

2.802

0.966

127.7 2.454

0.961

2.979

0.966

127.7

CRENBL DZP þ DZP þ

CRENBL 2.244 DZP 2.227 DZP þ 2.232 2.212

0.968 0.959 0.959 0.96

2.576 2.611 2.617

0.971 0.966 0.966

125.7 2.372 127.7 2.336 127.7 2.339 2.3

0.970 0.960 0.960 0.96

2.735 2.775 2.780

0.971 0.966 0.966

125.7 2.380 127.7 2.421 127.7 2.421 2.391

0.972 0.962 0.962 0.96

2.861 2.956 2.962

0.972 0.966 0.966

125.6 127.7 127.7

Bond lengths ðrÞ are in angstroms and angles ðaÞ in degrees.

P. Burk, S. Tamp / Journal of Molecular Structure (Theochem) 638 (2003) 119–128

Table 4 Calculated structures of neutral and protonated forms of alkali metal hydroxides

P. Burk, S. Tamp / Journal of Molecular Structure (Theochem) 638 (2003) 119–128

the hydrogen or alkali metal atoms does not affect the geometries noticeably. Comparison of two used density functionals (with the best ECP-basis set combinations) indicates that the bond lengths are somewhat shorter in case of PBE0 and thus usually closer to experimental values. Accordingly, our calculations show that the most accurate method for calculating geometries of potassium, rubidium and cesium oxides and hydroxides is PBE0 density functional with CRENBL ECP and basis set (augmented with Glendening’s polarization functions) on alkali metal, Dunning’s doublezeta basis augmented with set of polarization and diffuse functions on oxygen, and Dunning’s doublezeta plus polarization basis on hydrogen. It is interesting to note that while in case of early alkali metals (lithium, sodium, potassium) the M –O bond lengths in hydroxides are shorter than in corresponding oxides [5], they are equalized in case of rubidium and cesium both according experiment

125

[24] and our calculations. It has been suggested [5] that the linear structures for both M2O and MOH can be explained by the strong Coulombic repulsion between metal atoms (or hydrogen and a metal atom) which all bear considerable positive charge. Similarly, the M – O bond shortening in early alkali metal hydroxides as compared to oxides has been attributed to diminished electrostatic repulsion between M and H compared to that between two M in oxides. Apparently, the effect of smaller electronegativity of late alkali metals and thus greater ionicity of M– O bond is here compensated by the effect of bigger ionic radius of rubidium and cesium, and thus greater distance (and smaller electrostatic repulsion) between metal atoms or metal and hydrogen atoms. The protonated forms of K2O, Rb2O, Cs2O, and corresponding hydroxides were found to be planar, belonging to the C2v point group, with majority of used ECP-s and basis sets. The only exceptions were calculations of K2OHþ with LANLDZ ECP/basis and

Table 5 Calculated proton affinities (PA) and gas phase–phase basicities (GB, both in kcal/mol) of the alkali metal oxides M2O (M ¼ K, Rb, Cs) K2 O

ECP/basis set used on each atom M B3LYP LanLDZ SBKJC-VDZ Stuttgart_RLC Hay-Wadt MB Stuttgart_RSC Stuttgart_RSC,P Stuttgart_RSC,P CRENBL CRENBL, P CRENBL, P PBE0 LanLDZ SBKJC-VDZ Stuttgart_RLC Hay-Wadt MB Stuttgart_RSC Stuttgart_RSC,P Stuttgart_RSC,P CRENBL CRENBL, P CRENBL, P Exp. [1]6 Exp. [3]

O

DZ DZ DZP þ DZP þ CRENBL DZP þ DZP þ

DZ DZ DZP þ DZP þ CRENBL DZP þ . DZP þ

Rb2O

Cs2O

H

PA

GB

PA

GB

PA

GB

326.5 337.9 335.2 346.8 331.8 326.7 327.4 348.9 327.1 327.8

345.1 339.7 347.1 345.1 344.7 335.6 335.8 344.4 331.9 332.1

338.0 333.9 341.2 338.0 337.5 329.7 330.4 338.9 326.1 326.7

353.5

347.0

DZ DZ DZP DZP þ CRENBL DZP DZP þ

332.5 344.7 341.3 353.7 339.1 332.9 333.1 353.0 333.2 333.5

355.5 353.5 353.1 329.4 329.6 318.4 324.4 324.5

349.8 347.0 346.4 323.9 324.5 312.5 318.8 319.3

337.0 348.9 345.3 358.9 344.5 337.1 337.3 359.7 337.3 337.3 302.7 318.2

331.0 342.2 339.2 352.2 337.6 331.0 331.6 352.1 331.2 331.2

350.5 343.9 351.3 350.5 350.0 339.5 339.6 349.6 335.1 335.1

343.7 338.0 345.5 343.7 343.2 333.6 334.2 342.9 329.3 329.3

358.8

352.3

360.0 358.8 357.6 330.6 330.7 318.6 325.3 325.3 326.0 313.6

354.3 352.3 351.2 325.1 325.6 312.7 319.6 319.6

DZ DZ DZP DZP þ CRENBL DZP DZP þ

313.6

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Rb2OHþ with SBKJC VDZ ECP/basis (in both cases on all atoms), which resulted in planar Cs geometries, where the O –H bond was strongly bent towards one of M– O bonds (corresponding M –O – H angles were ca. 70– 808). The M –O –M angles in protonated oxides were ca. 208 larger than the M– O – H angles in hydroxides, a probable indication of the influence of molecular geometries by the electrostatic repulsion between ligands of oxygen. The geometries of protonated hydroxides are better described as those of complexes between water molecule and alkali metal cation (Fig. 1) as the geometries of H2O fragment are very close to that of individual water molecule. 3.2. Proton affinities The experimentally determined PA of alkali metal oxides are based on only one experiment

referring to the gas phase equilibrium (1) while those of hydroxides to the hydration equilibrium (6) of alkali metal cations Mþ. We would like to point out that the comparison of our calculated PA-s with those in literature is somewhat complicated as the experimental PA values are dependent on the used Df H 0 values for M2O and MOH assuming that Df H 0 values for H2O and Mþ are well established. The higher gas phase basicities and PA of alkali metal oxides over the corresponding hydroxides have been found by Butman et al. in their gas phase mass spectroscopic experiment [3] and later confirmed by Burk and Koppel in their theoretical studies [5,9]. Our results (Tables 5 and 6) on all investigated levels clearly support this. Indeed, the two electropositive, electron donating alkali metal atom ligands increase the negative charge on oxygen (and consequently the basicity) as compared to one metal atom in hydroxides.

Table 6 Calculated and experimental proton affinities (PA) and gas-phase basicities (GB, both in kcal/mol) of the alkali metal hydroxides ECP/basis set used on each atom M B3LYP LanLDZ SBKJC-VDZ Stuttgart_RLC Hay–Wadt MB Stuttgart_RSC Stuttgart_RSC Stuttgart_RSC,P CRENBL CRENBL, P CRENBL, P PBE0 LanLDZ SBKJC-VDZ Stuttgart_RLC Hay–Wadt MB Stuttgart_RSC Stuttgart_RSC,P Stuttgart_RSC,P CRENBL CRENBL, P CRENBL, P Exp. [1]6 Exp. [3]

O

DZ DZ DZP þ DZP þ CRENBL DZP þ DZP þ

DZ DZ DZP þ DZP þ CRENBL DZP þ . DZP þ

KOH

RbOH

CsOH

H

PA

GB

PA

GB

PA

GB

DZ DZ DZP DZP þ CRENBL DZP DZP þ

254.4 277.1 269.7 287.5 277.6 268.1 268.0 283.8 268.2 268.2

249.1 270.9 263.9 281.3 271.5 262.3 262.3 274.9 262.4 262.4

284.8 262.4 274.2 284.8 283.3 271.5 271.5 281.3 269.5 269.6

278.7 256.9 268.5 278.7 277.0 265.8 265.8 275.0 263.9 263.9

291.6 227.3 279.8 291.6 289.3 271.1 271.2 265.1 269.4 269.5

285.7 221.3 274.2 285.7 283.2 265.6 265.7 259.4 263.8 263.9

255.7 278.8 272.1 287.4 279.1 270.6 270.5 284.7 270.6 270.6 263 262.6

250.4 273.0 266.2 281.4 273.0 264.8 264.7 278.4 264.8 264.8 257

285.9 263.7 276.6 285.9 284.5 273.8 273.8 282.7 271.7 271.7

279.9 258.1 270.8 279.9 278.4 268.1 268.2 276.7 266.0 266.1

292.4 229.4 282.2 292.4 289.7 272.7 272.8 265.9 270.9 271.0 267.2 269.2

286.6 223.5 276.5 286.6 283.8 267.1 267.2 260.1 265.3 265.4 261

DZ DZ DZP DZP þ CRENBL DZP DZP þ

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As mentioned earlier, the PA of the alkali metal hydroxides are reasonably well established experimentally. We have used those PA values for evaluation of the reliability of different computational methods used. Unfortunately, the PA for rubidium hydroxide has not been experimentally measured, so we have to assume that the trends observed for potassium and cesium compounds are also valid for rubidium. Generally our calculated PA are more or less overestimated as compared to available experimental values. The results with B3LYP and PBE0 functionals are quite consistent with each other, the PBE0 calculated PA being on average greater by around 3.7 kcal/mol for oxides and 1.7 kcal/mol for hydroxides. Comparison of different ECP and corresponding basis sets used in this study for prediction of PA of alkali metal hydroxides indicates that from unmodified ECP-s/basis sets the best correspondence with experiment is obtained with Stuttgart RLC. Somewhat better results are obtained, as in case of geometries, when the use of Stuttgart RSC or CRENBL ECP on alkali metal atoms is augmented with the use of double-zeta plus polarization basis on oxygen and double-zeta basis hydrogen. Further addition of polarization functions on alkali metal atoms and diffuse functions on oxygen does not affect the PA noticeably. Based on aforementioned good agreement of our calculated results with experiment, we believe that the experimental gas phase PA, reported by Butman for Rb2O (313.6 kcal/mol) and Cs 2O (313.6 kcal/mol) are slightly underestimated. Our calculated PA values on all levels for K2O agree better with the experimental value of Butman. This indicates that Lias et al. have used an apparently erroneous Df H 0 value for K2O and his proposed proton affinity, 302.7 kcal/mol is underestimated at least by 15 kcal/mol. In the light of the current results, we suggest that the PA of Rb2O and Cs2O are 331.9 and 324.4 kcal/mol, respectively. Butman et al. interpreting their gas phase experimental proton affinity results for alkali metal oxides found that going in the group towards the heavier alkali metals, the proton affinity should gradually increase from Li2O to K2O, decreasing for Rb2O and staying constant for Cs2O. Our results indicate somewhat different pattern: the gas-phase

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proton affinity reaches its maximum value for Rb2O but falls off afterwards for Cs2O.

4. Conclusions The alkali metal oxides M2O and hydroxides MOH (M ¼ K, Rb, Cs) were all found to be linear although there is some controversy in the literature regarding the heavier alkali metal oxides in this matter. Also, there was generally a good agreement between our calculated structural information (bond lengths and angles) for Rb2O, Cs2O (and corresponding hydroxides) and available experimental information. The protonated forms of studied oxides and hydroxides were found to be planar. The calculated PA of alkali metal oxides and hydroxides generally overestimated the experimental values. It was concluded to be generally useful to add additional sets of polarization and diffuse functions on alkali metal and oxygen atoms, which markedly improved our calculated PA of studied alkali metal oxides and hydroxides. In the light of the current results, we suggest that the PA of Rb2O and Cs2O by Butman [3] are slightly underestimated. Considering a far better agreement of our calculated PA-s of Li2O, Na2O and K2O with the high level computational study by Burk and Sillar [5], as opposed to experimental values by Butman and Lias, we suggest the experimental values being slightly underestimated, too, and need further measurements. We suggest the gas phase PA for Li2O, Na2O and K2O to be 285, 315 and 328.3 kcal/mol, respectively, as reported by Burk and Sillar in their high level computational study [5] and 331.9 and 324.4 kcal/mol for Rb2O and Cs2O, respectively. Our calculations show that the most accurate method for calculating geometries of potassium, rubidium and cesium oxides and hydroxides is PBE0 density functional with CRENBL ECP and basis set (augmented with Glendening’s polarization functions) on alkali metal, Dunning’s double-zeta basis augmented with set of polarization and diffuse functions on oxygen, and Dunning’s double-zeta plus polarization basis on hydrogen, while for PA the B3LYP functional (with the same ECP/basis set combination) is marginally better.

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Acknowledgements Authors gratefully acknowledge the financial support of this research by the Estonian Science Foundation (grant No. 5196). NWCHEM Version 4.0, as developed and distributed by Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA, and funded by the US Department of Energy, was used to obtain some of these results.

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