J. Phys. Chem. A 2010, 114, 9349–9358
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Structures and Heats of Formation of Simple Alkaline Earth Metal Compounds: Fluorides, Chlorides, Oxides, and Hydroxides for Be, Mg, and Ca Monica Vasiliu,† David Feller,‡ James L. Gole,§ and David A. Dixon*,† Chemistry Department, Shelby Hall, The UniVersity of Alabama, Shelby Hall, Box 870336, Tuscaloosa, Alabama 35487-0336, Department of Chemistry, Washington State UniVersity, Pullman, Washington 99164-4630, and Schools of Physics and Mechanical Engineering, Georgia Institute of Technology, 837 State Street, NW, Atlanta, Georgia 30332-0430 ReceiVed: June 2, 2010; ReVised Manuscript ReceiVed: July 15, 2010
Geometry parameters, frequencies, heats of formation, and bond dissociation energies are predicted for the simple alkaline earth (Be, Mg and Ca) fluorides, chlorides, oxides, and hydroxides at the coupled cluster theory [CCSD(T)] level including core-valence correlation with the aug-cc-pwCVnZ basis sets up to n ) 5 in some cases. Additional corrections (scalar relativistic effects, vibrational zero-point energies, and atomic spin-orbit effects) were necessary to accurately calculate the total atomization energies and heats of formation. The calculated geometry parameters, frequencies, heats of formation, and bond dissociation energies are compared with the available experimental data. For a number of these alkaline earth compounds, the experimental geometries and energies are not reliable. MgF2 and BeF2 are predicted to be linear and CaF2 is predicted to be bent. BeOH is predicted to be bent, whereas MgOH and CaOH are linear. The OBeO angle in Be(OH)2 is not linear, and the molecule has C2 symmetry. The heat of formation at 298 K for MgO is calculated to be 32.3 kcal/mol, and the bond dissociation energy at 0 K is predicted to be 61.5 kcal/mol. Introduction Compounds containing the alkaline earth metals are commonly occurring substances in nature (calcium and magnesium are the fifth and eighth most abundant elements in the Earth’s crust) and are used on a daily basis as part of the chemical industry. We are particularly interested in the thermochemical properties of the chlorides, fluorides, oxides, and hydroxides of Be, Mg, and Ca. Magnesium hydroxide is the main component of milk of magnesia. Magnesium oxide is used for lining furnaces, and calcium hydroxide (slaked lime) is the principal ingredient in plaster and mortar. Calcium chloride absorbs water from the air, and it is used in the prevention of dust on roads, coal, and tennis courts and also as a drying agent in the laboratory. The alkaline earth monoxides play an important role in flame chemistry,1 in fuels (MgO),2 and possibly in stellar atmospheres.3 These are just a few examples of the importance of the alkaline earth compounds under study. The gas phase alkaline earth compounds are highly reactive species, and the composition of the vapors is very complex, especially for the oxides and hydroxides. Computational chemistry provides a useful alternative for the prediction of reliable structural, spectroscopic, and thermodynamic information about the alkaline earth compounds. To predict the thermodynamic properties of molecules, we have developed a composite approach4,5 based principally on molecular orbital theory using coupled cluster methods at the CCSD(T) level.6,7 In addition, the development of the correlation consistent basis sets which allows the extrapolation of the electronic energy to the complete basis set (CBS) limit8 provides chemical accuracy in the calculated energetics. In selected cases * To whom correspondence should be addressed. Email: dadixon@ bama.ua.edu. † The University of Alabama. ‡ Washington State University. § Georgia Institute of Technology.
the n-particle expansion has been extended to provide for the explicit inclusion of iterative triple and quadruple excitations.9,10 For most of the elements in the periodic table, the recent design of systematically convergent, correlation consistent basis sets for the third, fourth, and fifth row main group and transition elements using relativistic effective core potentials (RECPs)11 has been essential to the application of highly accurate correlation methods. With the new basis sets developed by Prascher et al.12 for the alkaline earth metals, we can expand our predictions to halides (chlorides and fluorides), oxides, and hydroxides of these alkaline earth metals. These authors reported the properties of MF, MO, MH2, and MF2 for M ) Be and Mg. There are a number of additional previous high level calculations for the alkaline earths hydroxides and oxides.13-18 We especially note the work of Martin and co-workers18 who emphasized the need to include the core electrons in the correlation calculations. Our goal is to expand on the previous work to provide accurate geometry parameters and heats of formation for these alkaline earth compounds. This data can be used in predicting a consistent, reliable set of bond dissociation energies. In addition, the monomer heats of formation can be used to develop reliable heats of formation of nanoclusters of the alkaline earth compounds using normalized clustering energies, for example, for model catalyst studies, following our prior work on the prediction of the heats of formation of transition metal oxide clusters.19 Computational Methods We used coupled-cluster methods at the CCSD(T) level including core-valence (CV) correlation corrections with the aug-cc-pwCVnZ basis set for n ) D, T, Q and 5 (abbreviated as awCVnZ) to predict the structural characteristics and thermodynamic properties of the alkaline earth compounds, including fluorides, chlorides, oxides and hydroxides, for Be, Mg and Ca. Equilibrium geometries were optimized at the
10.1021/jp1050657 2010 American Chemical Society Published on Web 08/06/2010
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CCSD(T)(CV)/awCVnZ level with n ) D and T except for the diatomic compounds, which were optimized for n ) D, T, and Q. Tight d functions were included for chlorine and magnesium, the second row elements.20 For Ca, Mg, and Cl, the outer core (3s and 3p for Ca and 2s and 2p for Mg and Cl) electrons are included in the correlation calculations because they may be higher in energy than the valence s orbitals of the F- or O-bonded atoms. The 1s orbitals on Be, F, and O were also correlated. The 1s orbitals of O and F are lower in energy than the 2p of Ca, so they were rotated into the correlation space in order to correlate the 1s for O and F. The harmonic frequencies (ωe) and anharmonic constants (ωeχe) of the diatomic compounds were obtained at the CCSD(T)/awCVQZ level using a Dunham expansion.21 Harmonic vibrational frequencies for the rest of the alkaline earth compounds were calculated with an all-electron basis set at the CCSD(T)/awCVTZ level. The CCSD(T) energies were extrapolated to the CBS limit by fitting to a mixed Gaussian/exponential (eq 1):22
E(n) ) ECBS + A exp[-(n - 1)] + B exp[-(n - 1)2] (1) where n ) 2, 3, and 4 (awCVDZ through awCVQZ). Values obtained from this procedure will be denoted as CBS-DTQ. The CBS estimates were also obtained by extrapolating the total energy from basis sets through n ) 5 using eq 2:23,24
E(lmax) ) ECBS +
3 B/lmax
(2)
with an lmax ) n. We label the values obtained from eq 2 as CBS-Q5. Total atomization energies (TAEs) at 0 K were calculated from the following expression (eq 3) with delta referring to the difference between the molecule (reactant) and the atomic products for each energy component:25
∑ D0 ) ∆ECBS + ∆Erel + ∆EZPE + ∆ESO
(3)
Additional corrections to the CBS energy (∆ECBS) are necessary to reach chemical accuracy ((1 kcal/mol). Scalar relativistic corrections were calculated at the CCSD(T)/second order Douglas-Kroll-Hess (DK) level with the all-electron aug-cc-pwCVTZ-DK basis set (abbreviated as awCVTZ-DK).12,26 The difference between ∆EawCVTZ-DK (the electronic energy calculated at the CCSD(T)/awCVTZ-DK level where the latter basis set is identical to awCVTZ but employs DK contraction coefficients) and ∆EawCVTZ (the electronic energy calculated at the CCSD(T)/awCVTZ level) is ∆Erel. The atomic spin-orbit corrections (SO) were calculated from the experimental values for the ground states of the atoms using Moore’s tables27 (∆ESO(O) ) -0.22, ∆ESO(F) ) -0.39, ∆ESO(Cl) ) -0.84 and 0 kcal/mol for H, Be, Mg, and Ca). For a few diatomics, we were able to perform CCSDT and CCSDTQ calculations to explore the effects of higher order correlation. For BeO, BeF, BeCl, and MgO, the CCSDT calculations were done with the cc-pVTZ basis set and the CCSDTQ calculations used the cc-pVDZ basis set. Heats of formation at 0 K were calculated by combining our computed ΣD0 values with the known enthalpies of formation at 0 K for the elements (∆Hf,0K(O) ) 58.98 ( 0.02, ∆Hf,0K(F) ) 18.47 ( 0.07, ∆Hf,0K(Cl) ) 28.59, ∆Hf,0K(H) ) 51.63, ∆Hf,0K(Be) ) 76.48 ( 0.2, ∆Hf,0K(Mg) ) 34.87 ( 0.2, and
TABLE 1: Calculated and Experimental Bond Distances for the Alkaline Earth Oxides, Monochlorides and Monofluorides M-A (Å) compound (spin/symmetry) 1 +
BeO ( Σ , C∞V) MgO (1Σ+, C∞V) CaO (1Σ+, C∞V) BeF (2Σ+, C∞V) MgF (2Σ+, C∞V) CaF (2Σ+, C∞V) BeCl (2Σ+, C∞V) MgCl (2Σ+,C∞V) CaCl (2Σ+, C∞V)
CCSD(T)/ awCVQZ c
1.334 1.740 1.826 1.365i 1.752 1.956 1.798m 2.200 2.446
other calculateda 1.3308, 1.7413, 1.8307, 1.3617 1.7536 1.9595, 1.7989 2.2025 2.4501,
d
1.333 1.742d 1.831,d 1.828g 1.959g 2.451g
experimentb 1.3309 1.749, 1.7482e,f 1.8221b,h 1.3610b, j 1.7500b, k 1.967, 1.9516l 1.7971 2.1991, 2.196n 2.4390, 2.4367o
a Values calculated at CCSD(T,all)CVQZ with the exception of BeO and BeF calculated at CCSD(T,all)CV5Z; ref 18. b Reference 33 unless otherwise specified. c Includes a correction of 0.003 Å from ∆r(r(CCSDT) - r(CCSD(T)) ) -0.00017 Å and ∆r(r(CCSDTQ) - r(CCSDT)) ) 0.00296 Å. d CCSD(T)/ aug′-cc-pwCVQZ; ref 17a. e Reference 40. f Reference 34. g CCSD(T)/aug-cc-pwCVQ+dZ; ref 14a. h Reference 35. i Includes a correction of 0.003 Å from ∆r(r(CCSDT) - r(CCSD(T)) ) 0.00010 Å and ∆r(r(CCSDTQ) - r(CCSDT)) ) 0.00296 Å. j Reference 36. k Reference 37. l Reference 39. m No correction from ∆r(r(CCSDT) - r(CCSD(T)) ) 0.00024 Å and ∆r(r(CCSDTQ) r(CCSDT)) ) 0.00018 Å. n Reference 38. o Reference 42.
∆Hf,0K(Ca) ) 42.38 ( 0.2 kcal/mol).28 Heats of formation at 298 K were calculated by following the procedures outlined by Curtiss et al.29 The CCSD(T) calculations were performed with the MOLPRO 2008.1 program package.30 The open-shell calculations were done with the R/UCCSD(T) approach where a restricted open shell Hartree-Fock (ROHF) calculation was initially performed and the spin constraint was then relaxed in the coupled cluster calculation.6c,31 The CCSDT and CCSDTQ calculations were done with the MRCC program of Ka´llay and co-workers32 interfaced to MOLPRO. The calculations were performed on Linux clusters at The University of Alabama and at Washington State University. Results and Discussion Geometries. The optimized geometries of the diatomic alkaline earth compounds are reported in Table 1 and compared to the experimental values and other high level calculated values. The M-A bond distances of the diatomics where M ) alkaline earth metal and A ) O, Cl or F are in good agreement with the experimental and other calculated values. The bond distances of the diatomics are generally larger by up to 0.004 Å as compared to the experimental values.33-38 The more recent experimental value39 for the CaF bond length is in better agreement with our calculated value than the value reported in Huber and Herzberg,33 which is too long. The Mg-O bond distance is predicted to be 0.009 (0.008) Å shorter than the experimental values.33,40 One reason for this difference could be the presence of low-lying 1Π and 3Π excited states that complicate the analysis of the experimental rotational-vibrational spectrum of the 1Σ+ ground state.40,41 The effect of the higher order correction for MgO is +0.0117 Å, mostly from the full T correction, which makes the calculated value slightly longer than experiment and substantially improves the agreement. The Ca-Cl distance is predicted to be 0.00733 to 0.00942 Å longer than the experimental values. The higher order correlation corrections increase the bond length in BeO and BeF by 0.003
Heats of Formation of Alkaline Earth Metal Compounds TABLE 2: Calculated and Experimental Geometry Parameters for the Alkaline Earth Halides (Fluorides and Chlorides) method
M-X (Å)
∠XMX (deg)
CCSD(T)/awCVTZ experiment CCSD(T)/awCVTZ experiment (C2V) CCSD(T)/awCVTZ other calculated experiment CCSD(T)/awCVTZ experiment CCSD(T)/awCVTZ experiment CCSD(T)/awCVTZ other calculated experiment
1.377 1.40 ( 0.03,a 1.373b 1.742 1.77 ( 0.02c 2.013 2.017d 2.1e 1.796 1.77,g 1.791h 2.170 2.185i 2.476 2.469d 2.51,j 2.483k
180 180 180 158c 157 157.6d 135 ( 7f 180 180 180 180 180 180 180
compound (spin/symmetry) BeF2 (1Σg+, D∞h) MgF2 (1Σg+, D∞h) CaF2 (1A1, C2V) BeCl2 (1Σg+, D∞h) MgCl2 (1Σg+, D∞h) CaCl2 (1Σg+, D∞h)
a Electron diffraction data for the vapor; ref 28. Linearity was confirmed by electric-deflection studies (ref 43) of the vapor and by infrared studies of matrix (ref 44). b Infrared spectroscopy; ref 46. c References 28 and 49. d CCSD(T)/aug-cc-pwCVQ+dZ; ref 14a. e Electron diffraction data; refs 28 and 51. f Matrix isolation spectroscopy and isotopically enriched materials; ref 28. g Electron diffraction data; refs 28 and 47. Linearity was confirmed by the electric deflection experiments; ref 45. h Electron diffraction; ref 48. i Electron diffraction data; ref 51. j Electron diffraction data; refs 28 and 51. Linear structure was determined by matrix-infraredspectrometric studies; refs 28 and 55. k Reference 56.
Å moving them further from experiment. For BeCl, the effect of the higher order corrections on the bond distance is negligible. The optimized and experimental geometry parameters for the alkaline earth difluorides and dichlorides are shown in Table 2. BeF2 and BeCl2 are linear molecules43-45 with Be-F and Be-Cl bond lengths in good agreement with the experimental values to within 0.01 Å.28,46-48 MgF2 at the CCSD(T)/awCVTZ level is calculated to be linear, which is not consistent with some of the experimental data. Infrared spectroscopy measurements in
J. Phys. Chem. A, Vol. 114, No. 34, 2010 9351 a krypton matrix indicate that the molecule is bent with an ∠FMgF angle of 158°,49,50 whereas electron diffraction,51 beam deflection measurements,52 and lower level theoretical calculations53 suggest a linear structure. Configuration interaction calculations with a polarized double-ζ basis set also predicted MgF2 to be linear.54 Our results suggest that the matrix is playing a role in the deviation of the molecule from linearity. MgCl2 and CaCl2 are calculated to be linear molecules in agreement with experiment.28,55 The Mg-Cl bond length is calculated to be 0.015 Å shorter than experiment51 and the Ca-Cl bond length is calculated to be 0.00756 and 0.03451 Å shorter than the experimental values. The fact that MgF2 has a very low frequency bending mode suggests that CaF2 may be bent, and this is indeed what we predict. Experimentally, CaF2 was found to have a permanent electric dipole moment consistent with a bent structure.57 Our calculated Ca-F bond length is almost 0.1 Å shorter than the experimental value from high temperature electron diffraction which employed a linear geometry28,51 and the ∠FCaF angle is larger by 15° than the experimental value derived from a matrix isolation experiment.50 Our high level calculated geometry parameters for CaF2 are consistent with previous calculations, which suggest the need for revising the experimental parameters.13,14a,54 The calculated and experimental geometry parameters for the alkaline earth hydroxides are reported in Table 3. At the CCSD(T)/awCVTZ level, MgOH and CaOH are predicted to be linear and BeOH to be bent. There has been some debate over whether MgOH and BeOH are linear or bent. Electron spin resonance data has been interpreted in terms of a linear molecule for BeOH.58 High level CCSD(T)/cc-pVQZ calculations16a for BeOH predict a quasilinear molecule with a bent structure (∠BeOH ) 140.9°) consistent with our predicted structure and with a barrier of only 136 cm-1 to linearity. Our calculated geometry parameters for MgOH are in good agreement with previous calculations which show the molecule to be linear.16b Our calculated Ca-O and O-H bond distances are in good agreement with experiment59 and other high level calculated values14a,16c to within
