HAlO system

Volume 208, number 1.2

CHEMICAL PHYSICS LETTERS

Ab initio study on the AlOH/HAlO

4 June 1993

system

F. Hirota, M. Tanimoto DepartmentofChemistry,Shizuoka University,Shizuoka422, Japan

and H. Tokiwa Departmentof Materials Science, Shizuoka Instituteofscience and Technology,Fukuroi 437, Japan Received 2 December 1992; in tinat form 19 March 1993

The structure of the AIOH molecule is investigated by the ab initio SCF and MP3 methods. The 6-311G and well-tempered Gaussian-type basis seta are supplemented by triple polarization functions. The most stable geometry is a bent form, with an AlOH angle of 163”, The potential energy curve for H rearrangement from HA10 to AlOH is calculated along with the vibrational frequencies and intensities. The stabilization energy due to bending of the AlOH angle is small in comparison with the zero-point vibrational energy of the bending mode. The experimental average structure of AlOH is expected to be linear.

1. Introduction

Simple metal-bearing diatomics have been observed recently in an astronomical source. Refractory metal halides, NaCl, KCI, AlCl, and possibly also AIF, have been detected in the envelope of the evolved carbon star IRC + 102 16 [ I]. AlOH species is taken into consideration in some of the theoretical calculations on molecules in model stellar atmospheres [ 2-51. However, there seems to be no experimental information available from the high-resolution spectroscopy of polyatomic aluminum species. The spectroscopic detection of such transient molecules will be aided greatly by the availability of their theoretical constants. Recent successful detection in the laboratory and structure determination of HBO [ 61, which is valence isoelectronic with HAlO, has stimulated our interest in the AlOH/HAlO system. Xie and Schaefer studied theoretically the silaformyl radical HSiO and its isomer SiOH [ 71. The latter species was found to be more stable. Jin et al. [ 8 ] considered AlCH and found that it is linear. The first ab initio theoretical study of the AlOH/ HA10 system was reported by Zyubina et al. using Elsevier Science Publishers B.V.

a double zeta plus d basis set and self-consistent electron pair theory [ 91. Yet their data seem to be insufficient for future spectroscopic detection. In order to prompt an experimental effort to observe the AlOH/HAlO system, we have attempted to obtain more detailed structural data on this system.

2. Method The primary basis set used in this study was the 63 11G set of Krishnan et al. [ lo]. This basis was supplemented by (2df, 2pd) polarization functions, where 2df was applied for the Al and 0 atoms and 2pd for the H atom. The used levels of theory are SCF, MP3 (the Mlaller-Plesset perturbation theory of the third order [ 111) and CISD (configuration interaction including single and double excitation). In order to test the dependence on basis set, the well-tempered GTF basis set of Huzinaga et al. [ 121 was also used. The primitive (16~1 lp) set for Al and the ( 14~9~) set for 0 were contracted to (9~8~) and (7~6~) respectively. For H, the (8s) set was contracted to (4s). This basis set is designated simply as W-T in later discussion. Polarization functions of 115

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CHEMICAL PHYSICS LETTERS

(3d2f, 3p2d) type were used for the W-T set. In this case, the SCF and MP3 level calculations were performed only for stable states. Table 1 lists geometries of three simple molecules calculated at the present levels of theory. Here, AIF is isoelectronic with AIOH. These results give an approximate estimate of the accuracy of the present calculation. For three molecules listed, the results at the MP3 and CISD levels gave almost the same geometries. All molecular geometries were fully optimized using the analytical gradient method [ 151 at the SCF level of theory. At the MP3 and CISD levels, the Fletcher-Powell method [ 161 was applied to the frozen core system. In the region near the global minimum of the AlOH geometry, the bond distances were optimized with the fixed bond angles at the MP3 level. The reason for this is that the potential hypersurface is too flat to converge effectively to the stationary state. The optimization was performed with 1’ steps of the AIOH angle. All the calculations were carried out using the GAUSSIAN 88 program package [ 171 and the GAMESS package (North Dakota version) [ 18 1, on the Convex Cl at Shizuoka University and the C3J at Shizuoka Institute of Science and Technology, Computer Center.

4 June 1993

3. Results and discussion 3.1. Energy and stable geometries Two minima exist in the AlOH/HAlO system; one is at a linear HAlO form and the other is at a bent form of AIOH. The optimized geometries at the two minima and one transition state are given in table 2 together with the relative energies at the SCF, MP3 and CISD levels. The total energies of the bent form of AIOH, used as references in table 2, are listed in table 3. The ground electronic states are ‘A for AIOH and IX+ for HAIO. In the linear form of AIOH, the highest occupied orbital is 70 and the second highest orbital is 2~. In HA10 these two orbitals are in the reverse order. The lowest unoccupied orbital is the 3rr orbital in both molecules. A calculation at the 631 lG(2df, 2pd) SCF level gave the result that the triplet state was higher than the singlet state by more than 2 eV. Consequently, no further study was attempted on the triplet state. As shown in table 2, the bent form of AlOH is more stable than the linear form of HA10 by about 2 eV. This is contrary to the case of the HBO/BOH system, which is valence isoelectronic with HAlO/ AIOH. In the case of HBO/BOH, HBO is more stable than BOH by 2.1 eV at the 6-31lG(2df, 2pd) MP3 level, and HBO has been observed experimentally [ 61. On the other hand, in the SiOH/HSiO system the bent SiOH has been predicted to be the most stable [ 7 1. The energy difference between SiOH and

Table 1 The geometries (in A and deg) of AIF, NaOH and SiOH Ref.

6-311G(2df, 2pd) SCF

W-T(3df)

MP3

CISD

SCF

MP3 1.652

AlF

r(AI-F)

1.65437 ”

1.645

1.655

1.656

1.638

NaOH b,

r(Na-0) r(O-H)

1.95 c, 0.96 d,

1.925 0.933

1.937 0.945

1.937 0.945

-

SiOH

r(Si-0) r(O-H) f SiOH

1.628 0.940 120.4

1.643 0.954 117.7

1.642 0.952 117.9

-

1.652e, 0.953 118.8”

a) Observed value, ref. [ 131. b, Linear molecule. ElObserved value, ref. [ 141. d, Assumed value. e, Calculated at CISD level, ref. [ 7 1.

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4 June 1993

Table 2 Relative energies (AE) and geometries of the AlOH/HAlO system AE (eV)

LA~OH (deg)

r(Al-0) (A)

r(O-H)/r(Ai-H)

0.0002 0 4.84 ‘) 2.30

180 166 53.6 0

1.656 1.659 1.604 1.563

0.93 1 0.931 1.911 1.554 b’

MP3 MP3 MP3 MP3

0.0003 0 3.95 a’ 2.12

180 163 53.5 0

1.664 1.669 1.627 1.581

0.943 0.943 1.914 1.559 b’

CISD CISD CISD CISD

0.0002 0 4.05 a) 1.97

180 163 53.5 0

1.665 1.669 1.625 1.586

0.941 0.942 1.906 1.557 b,

0 2.29

180 0

1.659 1.565

0.931 1.553 b’

0.0003 0 2.05

180 163 0

1.671 1.675 1.583

0.944 0.945 1.557 b,

Level of theory

6-3llG(Zdf,2pd) SCF SCF SCF SCF

W-T( 3d2f, 3p2d) SCF SCF MP3 MP3 MP3 a) Transition state.

bJ r(Al-H).

Table 3 Total energies at the global minimum of AlOH in hartree a) 6-31 lG(Zdf, 2pd) SCF MP3 CISD

-317.438212 -311.743322 - 317.726039

W-T (3d2f, 3p2d) SCF MP3

-317.458270 -317.778196

a1 1 hartree=27.21 eV.

HSiO is 0.5 eV, much smaller than that of the AlOH system. 3.2. Bent angle ofAlOH The bent angle of AlOH is calculated to be rather small. In the 6-3 11G SCF level, the optimized angle is 14” and the stabilization energy is only 10 cm-‘. In the W-T SCF calculation, the linear form is the most stable. On the other hand, both basis set calculations at the MP3 level predict the bent form to

be the most stable. A bent angle of 17’ was obtained. The 6-311G CISD level calculation also gave the same result. The potential curves for the H rearrangement from HA10 to AlOH are given in fig. 1 at the SCF and MP3 levels. The energies are almost the same between 120” and 180” of the AlOH angle. The bending potential curves near the linear AIOH are plotted in the enlarged energy scale in fig. 2, where the angle of AlOH is drawn symmetrically to emphasize the double-minimum feature. The stabilization due to the bending of the AlOH angle is only of the order of 10 cm-‘. Such a small stabilization is rarely seen in other molecules. This feature is remarkably different from that of BOH, where the stabilization due to the bending is about 1200 cm-’ in our 6-311G MP3 level calculation. Many XOH-type molecules are bent. The LBOH in BOH is predicted to be 122” at the 6-31 lG( 2df, 2pd) MP3 level. The L SiOH in SiOH is also about 122’ [ 71. In SiOH, the energy difference between the linear and bent forms reaches about 2700 cm-‘. In HzO, the corresponding value is about 11000 117

Volume 208, number 1,2

CHEMICAL PHYSICS LETTERS

4 June 1993

tween metal and oxygen, the electron distribution is like X+0’-H+. In these molecules, bonding between 0 and H is so strongly ionic that it shows little directivity. As discussed below, the stabilization energy of AlOH due to bending is smaller than the zero-point vibration energy of the bending mode. Thus AlOH is a typical quasilinear molecule. 3.3. Vibrational frequencies

0

l-i-(I-0Al/H\ - 0

90"

180’ Al-O-H

Fig. 1.Potential energy curves of the H rearrangement from HAIO to AIOH. The energy (in eV) relative to the global minimum is plotted as a function of the angle HALO (in deg) at the 63 I 1G (2df, 2pd) SCF and MP3 levels,

cm -l d

150’

180’

-150”

Fig. 2. Potential energy curves near the linear form of AIOH. The energyis in cm- ’ at the 6-3 11G ( 2df, 2pd ) SCF and MP3 levels.

cm-‘. In comparison with these cases, the corresponding energy of AlOH is small. On the other hand, Kuijpers et al. [ 141 reported that NaOH is linear. In NaOH, the 6-3 1lG( 2df, 2pd) MP3 calculation gives a fairly small bending frequency of 265 cm- ’ and a potential curve along L NaOH is flat between 180’ and 120”, being similar to the case of AlOH. One reason for the flat potential may be as follows. Since both NaOH and AIOH have strong ionic bonds be118

Calculation of harmonic vibrational frequencies at several stationary points at the SCF and MP3 levels gave the results shown in table 4. The values corresponding to the transition states are given in the imaginary unit, i. The frequencies calculated at the MP3 level are smaller than those at the SCF level, as is often the case. Yet the frequencies predicted at the MP3 level can be overestimated by 3-10% in comparison with the observed values. In AlF, the frequency is predicted to be 837 cm-’ at the 631 lG(2df, 2pd) MP3 level, while the observed frequency is 802 cm-’ [ 131. The most remarkable feature is the low frequency of the bending mode for the AlOH system. The force constant of the bending mode in AlOH is about & of that in HAlO, where the bending mode has a usual frequency ( -440 cm-‘). Hence the estimation of the zero-point vibrational energy is difftcult. It is expected to be between 20 and 100 cm-‘. This value is larger than the calculated stabilization energy due to the AlOH bending. Consequently, we predict the linear form as an average structure. The root mean square amplitude of the AlOH angle is about 24”. The other two frequencies are predicted to lie near 880 and 4100 cm-‘, which correspond to the AI-O and O-H stretching modes in AlOH, respectively. In HAlO, these frequencies are about 1160 and 2050 cm- ‘. Hauge et al. [ 191 measured the infrared spectrum of the photolysis product of the condensate of aluminum atom with water in excess argon at 15 K. They assigned two absorption peaks at 3790 and 8 10 cm- ’ to the OH and AI-OH stretching fundamentals, respectively, of the AlOH species isolated in an Ar matrix. These two peaks may correspond to the present 4100 and 880 cm-‘. They found no peak corresponding to a bending frequency in the region higher than 400 cm-‘. This agrees with the present

4 June 1993

CHEMICAL PHYSICS LETTERS

Volume 208, number I,2

Table 4 Vibrational frequencies (in cm-‘) and force constants (md/A)

Levelof theory

in parentheses

LAIOH

Vibrational mode

(deg)

bending

V(AI-O)

v (O-H)

6-3llG(Zdf,Zpd) W-T( 3d2f, 3pd)

SCF SCF

166 180

98 (0.007) 52 (0.002)

899 ( 5.00) 886 ( 5.13)

4325 (11.8) 4310 (11.7)

6-3llG(Zdf,2pd)

MP3

163

101 (0.007)

887 ( 4.80)

4145 (10.8)

L HAlO

6 (HAlO)

u (HAl-0)

v (H-AlO)

6-311G(2df, 2pd) W-T( 3d2f, 3pd)

SCF SCF

0 0

491 (0.17) 488 (0.17)

1209 (10.9) 1199 (10.9)

2113 ( 2.78) 2115 ( 2.79)

6-31 lG(Zdf, 2pd)

MP3

0

446 (0.14)

1168 (10.2)

2058 ( 2.64)

result that the bending frequency is 20% 100 cm-‘. The intensities of IR absorption are calculated at the SCF level. All three modes are IR active. In AlOH, the bending mode has the largest intensity of 196 km/mol and the two other modes have intensities of about 140 km/mol. In HA10 as well, the bending mode has the largest intensity of 156 km/ mol. The two other modes have smaller intensities of about 60 km/mol. On the other hand, the calculated dipole moment of AlOH is about 1.4 D, while that of the less stable HA10 is about 5.3 D. The smaller dipole moment of the more stable isomer will make the detection slightly more difficult.

References [ 1 ] J. Cemicharo and M. Guelin, Astron. Astrophys. 183 ( 1987) LIO. [2] T. Tsuji, Astron. Astrophys. 23 ( 1973) 411. [3] H.R. Johnson and A.J. Sauval, Astron. Astrophys. Suppl. Ser. 49 (1982) 77. [4] J.M. Brett, Mon. Not. R. Astron. Sot. 241 (1989) 247. [S] A.W. Irwin, Astron. Astrophys. Suppl. Ser. 74 (1988) 145. [6] Y. Kawashima, Y. Endo and E. Hirota, J. Mol. Spectry. 133 (1989) 116.

[ 7 ] Y. Xie and H. Schaefer III, J. Chem. Phys. 93 ( 1990) I 196. [8] S.Q. Jin, Y. Xie and H. Schaefer III, J. Chem. Phys. 95 (1991) 1834. [ 91 T.S. Zyubina, A.S. Zyubin, A.A. Gorbik and O.P. Charkin, Zh. Neorg. Khim. 30 (1985) 2739. [ 101 R. Krishnan, J.S. Binkley, R. Seeger and J.A. Pople, J. Chem. Phys. 72 ( 1980) 650. [ 111J.A. Pople, R. Seeger and R. Krishnan, Intern. J. Quantum Chem. Symp. 11 ( 1977) 149. [ 121 S. Huzinaga, M. Klobukowski and H. Tatewaki, Can. J. Chem.63 (1985) 1812. [ 131 IC_P. Huber and G. Her-&erg, Molecular spectra and molecular structure, Vol. 4. Constants of diatomic molecules (Van Nostrand Reinhold, New York, 1979). [ 141P. Kuijpers, T. T&ring and A. Dymanus, Chem. Phys. 15 (1976) 457. [ 151 H.B. Schlegel, J. Comput. Chem. 3 ( 1982) 214. [ 161 R. Fletcher and M.J.D. Powell, Comput. J. 6 (1963) 163. [ 171 M.J. Frisch, M. Head-Gordon, H.B. Schlegel, K. Raghavachari, J.S. Binkley, C. Gonzalez, D.J. DeFrees, D.J. Fox, R.A. Whiteside, R. Seeger, CF. Melius, J. Baker, R. Martin, L.R. Kahn, J.J.P. Stewart, EM. Fluder, S. Topiol and J.A. Pople, GAUSSIAN 88 (Gaussian, Inc., Pittsburgh, PA, 1988). [ 181M.W. Schmidt, KK Baldridge, J.A. Boatz, J.H. Jensen, S. Koseki, M.S. Gordon, K.A. Nguyen, T.L. Windus and ST. Elbert, QCPE Bull. 10 ( 1990) 52. [ 191 R.H. Hauge, J.W. Kauffman and J.L. Margrave, J. Am. Chem. Sot. 102 (1980) 6005.

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