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Ab initio molecular orbital calculated stationary points on the potential energy surface of H4AlO4−—similarities with H4SiO4
Journal of Molecular Structure (Theo&m), 257 (1992) 305-312 Elsevier Science Publishers B.V., Amsterdam
305
Ab initio molecular orbital calculated stationary points on the potential energy surface of H,AlO, - similarities with H,SiO, Wagner B. De Almeida’ and Patrick J. O’Malley Department
of Chemistry,
UMIST, PO Box 88, Manchester M60 1QD (UK)
(Received 4 September 1991)
Abstract Ab initio calculations of the stationary points on the potential energy surface for the H,AlO, species were carried out at the Hartree-Fock level with the ST0/6-31G* basis set. Full geometry optimisation with no symmetry constraint followed by harmonic frequency analysis predicted the existence of three minimum-energy structures. Self-consistent-field (SCF) calculations using diffuse functions were also performed in order to assess the importance of such functions for an adequate description of the anionic species HIA . The rich conformational flexibility observed is thought to be due to anomeric effects involving Al-O u* orbit& and vicinal oxygen lone pair pn orbit.&. It is shown that the conformational space occupied by H&O, is similar to that occupied by H,SiO,. This provides a good explanation of the ease of substitution of aluminium for silicon atoms in aluminosilicate frameworks and, in particular, it provides a ready explanation for the ease of insertion of aluminium atoms into xeolite silicate frameworks during synthesis.
INTRODUCTION
Silicates and aluminosilicates, the most abundant chemical compounds on earth, are an important subject of basic research in mineralogy and solid-state chemistry [ 11. Zeolites, the microporous three-dimensional aluminosilicate frameworks [ 21 have found wide industrial application as ion exchangers, molecular sieves and catalysts [ 3-61. The TO4 tetrahedra (T = Si, Al, etc. ) , where T is tetrahedrally coordinated by oxygen atoms, are the primary building units of these complex structures. The key to the acidic nature of zeolites lies in the presence of isomorphous substitution of AlO; into the silicate framework. This gives rise to a negative Correspondence to: P.J. O’Malley, Department of Chemistry, UMIST, PO Box 88, Manchester M60 lQD, UK. ‘Permanent address: Departamento de Qufmica - ICEx, UFMG - Pampulha - CP 702, Belo Horizonte - MG, 30.161, Brazil.
0166-1269/92/$05.96
0 1992 Elsevier Science Publishers B.V. All rights reserved.
charge on the framework which must be balanced by a charge balancing cation for neutrality of the framework to be obtained. To generate Briinsted acid zeolite catalysts this cation is H +. The substitution of AlO, tetrahedra into the framework generally occurs during the synthesis stage. Over the pH range usually employed in zeolite synthesis, the principal aluminium species present has been shown to be H,AlOc [ 31. This, therefore, is likely to be the form in which isomorphous substitution takes place. In essence, H,AlO; successfully competes with silicate species such as H4Si04 and H,SiO, for vacant sites on the developing framework. To accomplish this the properties of the species (i.e. the volume occupied and the charge distribution) must be similar. In the present study we examined the conformational space available for the H,AlO; species by examining the conformers generated by rotation around the AlOH bonds. Comparison with H4Si04 indicates that the conformational preferences of both molecules are very similar and can principally be attributed to the anomeric effect. We suggest that this is an explanation for the ease of substitution of H,AlO; into silicate frameworks. CALCULATIONS
The configuration space which spans the multidimensional potential energy surface (PES ) for the H,AlO; species is shown in Fig. 1. The procedure used to locate the many stationary points on the PES is described in ref. 7. The PES were calculated point wise using a small basis set and then each stationary point was located by looking at several different three-dimensional representations of the PES which was further fully optimised using an extended basis set. The whole procedure is not described here. The stationary points previously located for the H,SiO, molecule [ 71 were taken as the starting point for the geometry optimisation procedure for the H,AlO; . The dihedral angles re-
Dihedral
Angles
71 =
[03,A1,X2,X31
72
[OI,Al,XZ,XI]
=
[HI,OI,A~,X~I T4 = [H2,02,Al,Xll 7s = IH3,03rAlrXll 76 = [H1,01,AlrX21 73
Fig. 1. Definition of the configuration space 1R.
=
307
quired for the definition of the torsional PES are given in Fig. 1. Five distinct stationary points corresponding to five different combinations of the dihedral angles ri, z,, 5, r,, z5 and r6 have been located in ref. 7, and these are given in Table 1. In the present study the dihedral angles given in Table 1 were used as the starting point for the geometry optimisation of the five probable stationary points on the PES of the H,AlO, species. By analogy to the case of the H,SiO, molecule, full symmetry-unconstrained geometry optimisation was carried out followed by analytic calculation of the harmonic vibrational frequencies using the ab initio quantum-mechanical package GAUSSIAN aa [8] as implemented on the Amdahl VP1100 computer at the Manchester Computing Centre (MCC). TABLE 1 SCF/6-31G’ geometries and total energies for the stationary points I-V” on the PES of the HISi04 molecule taken from ref. 11. The dihedral angles Tare as defined in Fig. 1 I (M) Ci (near&) Bond length (pm)b R(Si-0) R(O-H) Bond angle (deg.) (r(Ol-Si-02) or cY(O3-Si-04) B(Ol-Si-03) @(02-Si-04) B(H-0-Si) Dihedral angle (deg.)’ ‘51
IV (TS) C,
V (‘I’S) D2d
162.9 94.69
162.9 94.69
163.0 94.66
162.9 94.65
106.4
106.5
115.8
104.4
103.3
115.8 115.8 117.0
106.3 106.3 117.1
106.4 106.4 117.5
112.0 112.0 117.3
112.6 112.6 117.3
76
Et (hartree)d AE (kJ mol-I)’
- 590.891687 0.0
73
4 rs
III(M) C,
162.9 94.69
83.16 83.20 - 146.6 - 157.2 - 146.6 - 157.3
r2
II W) C1
(90.0) (90.0) (180.0) (180.0) (180.0) (180.0)
96.89
89.99
96.90
90.01 95.09 - 85.00 -95.10 84.93
146.3 156.3 -23.90 - 33.70 -590.891685 0.0
- 590.891687 0.0
90.08
90.0
90.02
90.0
- 23.37 - 156.8 180.0 180.1
0.0 180.0 0.0 180.0
- 590.887623 - 590.886434 10.6700
13.7917
“M, minimum energy structure: TS, transition state structure. bl pm=lO-* A. “Dihedral angles are defined in Fig. 1. Values in parentheses are dihedral angles for a typical S, configuration. dTotai energies; 1 hartreeE2625.50 kJ mol-‘. ‘AE= (Ei- E,), where i indicates points I-V.
308
The calculationswere executed with the ST0/6-31G* basis set (including polarisationfunctions on oxygen and silicon atoms) [9-121 and also usingthe ST0/3-21G basis set [ 13-151 with added diffuse functions for hydrogen,aluminiumand oxygen atoms [ 161. Electron correlation effects were not taken into account due to computational limitations.However, it has been shown that inclusion of electron correlation at the MP2/6-31G* (second-order Mraller-Plessetperturbationtheory [ 171) level of theory have little effect on the values of the geometrical parametersof the H,SiO; anionic species [ 181. RESULTS AND DISCUSSION
The resultsof the Hartree-Fock calculationsof the five stationarypoints on the PES for the H,AlO, species, carried out as described in the calculations section, are listed in Table 2. The geometryof each stationarypoint was fully optimisedand the eigenvaluesof the Hessianmatrix [ 191 werethen evaluated in order to characterisethe stationarypoints as minimum-energystructures (all eigenvaluespositive) or transition states (TS) (negative eigenvalues). The occurrence of one, two, etc., imaginaryfrequenciescharacterisesa firstorder, second-order,etc., TS structure,respectively. Three minimum-energystructures (I, II and III) and two first-ordertransition states (structuresIV and V) wereidentifiedand these are shown in Fig. 2. All conformations,except structureV are predictedto have C, symmetry.A considerabledeviationfrom any possible symmetricstructuralarrangementis noticed. StructuresI, II and III have the same energyto five significantdecimal figures which precludes the assignment of a unique global-minimum configuration. The bond distances AI-O and O-H and the bond angles (Yand 8 do not change significantlywithin the five stationarypoints (I-V) except in structure III wherecyis increasedby approximately10” (at the SCF/6-31G* level). It can be seen from Fig. 2 that the reason for this may well be the proximity of the hydrogenatoms Hl and H4. In order to minimisethe hydrogen-hydrogen repulsionthe angle a! must widen. The deviation of (Yfrom the normal tetrahedral angle is approximately3.5 ’ in structuresI, II, IV and V and approximately 7” in structureIII at the SCF/6-31G* level of theory. StructureIII exhibits the most pronounced deviation from tetrahedralsymmetry. The inclusion of diffuse functions is generallythought to be important for the correct descriptionof anionic species.We haveexaminedthe effect of using diffuse functions on the results obtained for the geometricalparametersand relativeenergiesof the five stationarypoints located on the PES for H,AlO, (Table 2 ) . Computationalresourcesenabled us to add diffuse functions only to an ST0/3-21G basis set. The energydifferencesas calculatedusing diffuse (sp) functions follow the
309 TABLE 2 Geometries and total energies for the stationary points I-V” on the PES of the H&O,
Symmetry
I (M)
n 04)
III (M)
C1
C*
C1
SCF/6-31G* Bond length (pmjb R(Al-0) R(O-H) Bond angle (deg.) (~(01-Al-02) (03-Al-04) /3(01-Al-03) $(02-Al-04) @H-O-Al)
IV (TS) C,
species V (TS) DZd
177.0 94.60
177.0 94.60
177.0 94.60
177.1 94.60
177.1 94.62
105.9
106.0
116.7
106.2
106.3
116.7 116.6 110.3
106.0 106.0 110.3
106.0 106.0 110.3
111.1 111.1 111.1
111.1 111.1 110.9
82.25 82.30 157.2 148.0 157.3 148.0
97.80 97.77 156.9 147.7 - 32.40 - 23.30
Dihedral angle (deg.) 71
72 73
-
74
-
75
-
76
-
ET (a.u.)d AE” (kJ mol-‘)
- 543.90900 0.0
SCF/3-21G+ (sp) diffuse functions Bond length @mJb R(Al-0) 177.5 R(O-H) 95.71
90.00 90.00
90.00
85.46 - 94.60 -85.30 94.64
- 34.54 - 145.5 180.0 180.0
- 543.90900
- 543.90900
0.0
0.0
90.00
90.00 90.00 0.0 180.0 0.0 180.0
- 543.90594 8.0340
- 543.90470 11.2897
177.5 95.71
177.5 95.71
177.4 95.61
177.4 95.58
107.0
107.0
114.4
109.5
107.1
114.4 114.4 129.8
107.1 107.1 129.8
107.0 107.0 129.8
109.5 109.5 132.3
110.6 110.7 132.7
84.67 84.66 154.8 148.4 154.7 148.3
95.31 95.31 155.1 148.7 -31.30 - 25.02
90.02 90.03 86.92 - 93.05 - 87.01 93.53
89.99 90.01 - 79.58 - 100.4 180.0 180.0
90.00 90.00 0.0 180.0 0.0 180.0
-541.11181 0.0
-541.11181 0.0
Bond angle (deg.) a(Ol-Al-02) (03-Al-04) g(Ol-Al-03) @(02-Al-04) @H-O-Al)
Dihedral angle (deg.y 71 72 73
-
74
-
75
-
7,
-
ET (a.u.)d AE (kJ mol-I)’
-541.11181 0.0
Y&e footnotes a-c to Table 1. dTot.al energies 1 a.u.=2625.50 kJ mol-‘. ‘See footnote e to Table 1.
-541.10987 5.0964
-541.10585 15.6472
,02kH2 01 -Al
//
/
I II
Cl(near-SO
Cl
02.
*.
62
Hl 1 01
-Al
/ / /
/ _H 03
?3
H;
ir,
III
IV
Cl
Cl 02 ‘82
/ 01
’
HI
/i.’ /
I
/
\
1’
04
Pa
83 V
&d Fig. 2. The “true” minimum energy structures I, II and III and the transition states IV and V, as calculated using the ST0/6-31G* basis set.
same trend as those evaluated with the extended basis set ST0/6-31G*, with three degenerate minimum-energy structures being predicted. The geometrical parameters, principally the H-O-Al bond angles, calculated with the inclusion of diffuse functions are different from the values calculated at the HF/6-31G* level of theory. In addition, the dihedral angles 5 and r4 of the transition state structure IV are very different from the SCF/G-
311
31G* values.When diffuse functions are addedthe hydrogenatoms Hl and H2
are twisted by approximately 45” in order to minimize hydrogen-hydrogen repulsions.The other dihedral angles do not change significantlywhen diffusion functions are included. At the HF/3-21G + diffusion functions level of theory the bond angle a! is closer to the normal tetrahedral angle (109.5”) than the HF/6-31G* value, and for structureIV cr is equal to the tetrahedralvalue. The most noticeable effect of including diffuse functions in the calculation of the geometricalparameters for the H,AlO, species is, therefore, that the aluminiumatom approaches tetrahedralsymmetry. The previouslyreported [ 71 SCF/6-31G* geometricalparametersand energies for the stable configurationsof the H4Si04 molecule are given in Table 1, for comparison with the present results for the H*AlOc anionic species. The similaritiesbetween the spatial arrangementsof H4Si04 and H,AlO; can be easily seen. The good agreementbetween the two sets of dihedral angles (z, Tables 1 and 2) is of interest.It indicatesthat the silicon atom can be replaced by aluminiumwith very little conformationalchange,and very little change in the relative energies.We believe that this minimal perturbation on substitution is a major reason for the ease of substitutionof silicon by aluminiumin aluminosilicateframeworks. A previous analysis of silicon compounds suggestedthe important contribution of anomeric effects in the stabilisationof the conformations [ 201. The H4Si04 conformations in which the O-H bonds are almost perpendicularto the vicinal Si-0 bond are stabiliseddue to the negativehyperconjugationbetween the pn oxygen atom and the c* Si-0 orbital. This study suggeststhat aluminiumbased compounds also exhibit such effects. Indeed,the importance of anomericeffects in the stabilisationof silicatesand aluminosilicatesin general needs to be addressedmore carefully.
CONCLUSIONS
The ab initio investigationat the Hartree-Fock level of theory of the stationary points on the PES of the H,AlO, anionic species, without symmetry constraints,located three degenerateminimum-energystructuresbelongingto the C1symmetrypoint group. The main effect of including diffuse functions in the calculation of the geometricalparameters was that the configuration approachedtetrahedralsymmetry.Comparisonswith the HF/6-31G* results previously reported for the H4Si0, molecule reveal that the silicon atom can be replacedby an aluminiumatom with very little change in the conformation or energy.
312 ACKNOWLEDGMENTS
W.B. De Almeida wishes to thank the Departamento de Quimica, U.F.M.G., Brazil for granting leave of absence. P.J. O’Malley thanks the Manchester Computing Centre (MCC ) for support.
REFERENCES 1
2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17 18 19 20
R.K. Ller, The Chemistry of Silica. Solubility, Polymerization, Colloid and Surface Properties, and Biochemistry, Wiley, New York, 1979. F. Liebau, Structural Chemistry of Silicates. Bonding and Classification, Springer-Verlag, Berlin, 1985. D.W. Breck, Zeolite Molecular Sieves. Structure, Chemistry and Use, Wiley-Interscience, New York, 1974. R.M. Barrer, Zeolites and Clay Minerals as Sorbents and Molecular Seives, Academic Press, London, 1978. Y. Murakami, A. Iijima and J.W. Ward, New Developments in Zeolite Science and Technology, Kodansha, Tokyo, 1986. P.J. Grobet, W.J. Mortier, E.F. Vansant and G. Schulz-Ekloff (Eds.), Studies in Surface Science and Catalysis, Vol. 37, Elsevier, Amsterdam, 1988. W.B. De Almeida and P.J. O’Malley, Chem. Phys. Lett., 178 (1991) 483. M.J. Frisch, J.S. Binkley, H.B. Schlegel, K. Raghavachari, C.F. Melius, R.L. Martin, J.J.P. Stewart, F.W. Bobrowicz, C.M. Rohlfmg, L.R. Kahn, D.J. DeFrees, R. Seeger, R.A. Whiteside, D.J. Fox, E.M. Fleuder, E.M. and J.A. Pople, GAUSSIAN 88, Carnegie-Mellon Quantum Chemistry Publishing Unit, Pittsburgh, PA, 1984. W.J. Hehre, R. Ditchfield and J.A. Pople, J. Chem. Phys., 56 (1972) 2257. P.C. Hariharan and J.A. Pople, Theor. Chim. Acta, 28 (1973) 213. MS. Gordon, Chem. Phys. Lett., 76 (1980) 163. M.J. Frisch, J.A. Pople and J.S. Binkley, J. Chem. Phys., 80 (1984) 3265. J.S. Binkley, J.A. Pople and W.J. Hehre, J. Am. Chem. Sot., 102 (1980) 939. M.S. Gordon, J.S. Binkley, J.A. Pople, W.J. Pietro and W.J. Hehre, J. Am. Chem. Sot., 104 (1982) 2797. W.J. Pietro, M.M. Francl, W.J. Hehre, D.J. DeFrees, J.A. Pople and J.S. Binkley, J. Am. Chem. Sot., 104 (1982) 5039. W.J. Hehre, L. Radom, P.v.R. Schleyer and J.A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1986, p. 87. C. Meller and M.S. Plesset, Phys. Rev., 46 (1934) 618. W.B. De Almeida and P.J. O’Malley, J. Mol. Struct. (Theochem), in press. P.G. Mezey, Studies in Physical and Theoretical Chemistry, Vol. 53, Potential Energy Hypersurfaces, Elsevier, Amsterdam, 1987. A.E. Reed, C. Shade, P.v.R. Schleyer, P.V. Kamath and J. Chandrasekhar, J. Chem. Sot. Chem. Commun., (1988) 67.
305
Ab initio molecular orbital calculated stationary points on the potential energy surface of H,AlO, - similarities with H,SiO, Wagner B. De Almeida’ and Patrick J. O’Malley Department
of Chemistry,
UMIST, PO Box 88, Manchester M60 1QD (UK)
(Received 4 September 1991)
Abstract Ab initio calculations of the stationary points on the potential energy surface for the H,AlO, species were carried out at the Hartree-Fock level with the ST0/6-31G* basis set. Full geometry optimisation with no symmetry constraint followed by harmonic frequency analysis predicted the existence of three minimum-energy structures. Self-consistent-field (SCF) calculations using diffuse functions were also performed in order to assess the importance of such functions for an adequate description of the anionic species HIA . The rich conformational flexibility observed is thought to be due to anomeric effects involving Al-O u* orbit& and vicinal oxygen lone pair pn orbit.&. It is shown that the conformational space occupied by H&O, is similar to that occupied by H,SiO,. This provides a good explanation of the ease of substitution of aluminium for silicon atoms in aluminosilicate frameworks and, in particular, it provides a ready explanation for the ease of insertion of aluminium atoms into xeolite silicate frameworks during synthesis.
INTRODUCTION
Silicates and aluminosilicates, the most abundant chemical compounds on earth, are an important subject of basic research in mineralogy and solid-state chemistry [ 11. Zeolites, the microporous three-dimensional aluminosilicate frameworks [ 21 have found wide industrial application as ion exchangers, molecular sieves and catalysts [ 3-61. The TO4 tetrahedra (T = Si, Al, etc. ) , where T is tetrahedrally coordinated by oxygen atoms, are the primary building units of these complex structures. The key to the acidic nature of zeolites lies in the presence of isomorphous substitution of AlO; into the silicate framework. This gives rise to a negative Correspondence to: P.J. O’Malley, Department of Chemistry, UMIST, PO Box 88, Manchester M60 lQD, UK. ‘Permanent address: Departamento de Qufmica - ICEx, UFMG - Pampulha - CP 702, Belo Horizonte - MG, 30.161, Brazil.
0166-1269/92/$05.96
0 1992 Elsevier Science Publishers B.V. All rights reserved.
charge on the framework which must be balanced by a charge balancing cation for neutrality of the framework to be obtained. To generate Briinsted acid zeolite catalysts this cation is H +. The substitution of AlO, tetrahedra into the framework generally occurs during the synthesis stage. Over the pH range usually employed in zeolite synthesis, the principal aluminium species present has been shown to be H,AlOc [ 31. This, therefore, is likely to be the form in which isomorphous substitution takes place. In essence, H,AlO; successfully competes with silicate species such as H4Si04 and H,SiO, for vacant sites on the developing framework. To accomplish this the properties of the species (i.e. the volume occupied and the charge distribution) must be similar. In the present study we examined the conformational space available for the H,AlO; species by examining the conformers generated by rotation around the AlOH bonds. Comparison with H4Si04 indicates that the conformational preferences of both molecules are very similar and can principally be attributed to the anomeric effect. We suggest that this is an explanation for the ease of substitution of H,AlO; into silicate frameworks. CALCULATIONS
The configuration space which spans the multidimensional potential energy surface (PES ) for the H,AlO; species is shown in Fig. 1. The procedure used to locate the many stationary points on the PES is described in ref. 7. The PES were calculated point wise using a small basis set and then each stationary point was located by looking at several different three-dimensional representations of the PES which was further fully optimised using an extended basis set. The whole procedure is not described here. The stationary points previously located for the H,SiO, molecule [ 71 were taken as the starting point for the geometry optimisation procedure for the H,AlO; . The dihedral angles re-
Dihedral
Angles
71 =
[03,A1,X2,X31
72
[OI,Al,XZ,XI]
=
[HI,OI,A~,X~I T4 = [H2,02,Al,Xll 7s = IH3,03rAlrXll 76 = [H1,01,AlrX21 73
Fig. 1. Definition of the configuration space 1R.
=
307
quired for the definition of the torsional PES are given in Fig. 1. Five distinct stationary points corresponding to five different combinations of the dihedral angles ri, z,, 5, r,, z5 and r6 have been located in ref. 7, and these are given in Table 1. In the present study the dihedral angles given in Table 1 were used as the starting point for the geometry optimisation of the five probable stationary points on the PES of the H,AlO, species. By analogy to the case of the H,SiO, molecule, full symmetry-unconstrained geometry optimisation was carried out followed by analytic calculation of the harmonic vibrational frequencies using the ab initio quantum-mechanical package GAUSSIAN aa [8] as implemented on the Amdahl VP1100 computer at the Manchester Computing Centre (MCC). TABLE 1 SCF/6-31G’ geometries and total energies for the stationary points I-V” on the PES of the HISi04 molecule taken from ref. 11. The dihedral angles Tare as defined in Fig. 1 I (M) Ci (near&) Bond length (pm)b R(Si-0) R(O-H) Bond angle (deg.) (r(Ol-Si-02) or cY(O3-Si-04) B(Ol-Si-03) @(02-Si-04) B(H-0-Si) Dihedral angle (deg.)’ ‘51
IV (TS) C,
V (‘I’S) D2d
162.9 94.69
162.9 94.69
163.0 94.66
162.9 94.65
106.4
106.5
115.8
104.4
103.3
115.8 115.8 117.0
106.3 106.3 117.1
106.4 106.4 117.5
112.0 112.0 117.3
112.6 112.6 117.3
76
Et (hartree)d AE (kJ mol-I)’
- 590.891687 0.0
73
4 rs
III(M) C,
162.9 94.69
83.16 83.20 - 146.6 - 157.2 - 146.6 - 157.3
r2
II W) C1
(90.0) (90.0) (180.0) (180.0) (180.0) (180.0)
96.89
89.99
96.90
90.01 95.09 - 85.00 -95.10 84.93
146.3 156.3 -23.90 - 33.70 -590.891685 0.0
- 590.891687 0.0
90.08
90.0
90.02
90.0
- 23.37 - 156.8 180.0 180.1
0.0 180.0 0.0 180.0
- 590.887623 - 590.886434 10.6700
13.7917
“M, minimum energy structure: TS, transition state structure. bl pm=lO-* A. “Dihedral angles are defined in Fig. 1. Values in parentheses are dihedral angles for a typical S, configuration. dTotai energies; 1 hartreeE2625.50 kJ mol-‘. ‘AE= (Ei- E,), where i indicates points I-V.
308
The calculationswere executed with the ST0/6-31G* basis set (including polarisationfunctions on oxygen and silicon atoms) [9-121 and also usingthe ST0/3-21G basis set [ 13-151 with added diffuse functions for hydrogen,aluminiumand oxygen atoms [ 161. Electron correlation effects were not taken into account due to computational limitations.However, it has been shown that inclusion of electron correlation at the MP2/6-31G* (second-order Mraller-Plessetperturbationtheory [ 171) level of theory have little effect on the values of the geometrical parametersof the H,SiO; anionic species [ 181. RESULTS AND DISCUSSION
The resultsof the Hartree-Fock calculationsof the five stationarypoints on the PES for the H,AlO, species, carried out as described in the calculations section, are listed in Table 2. The geometryof each stationarypoint was fully optimisedand the eigenvaluesof the Hessianmatrix [ 191 werethen evaluated in order to characterisethe stationarypoints as minimum-energystructures (all eigenvaluespositive) or transition states (TS) (negative eigenvalues). The occurrence of one, two, etc., imaginaryfrequenciescharacterisesa firstorder, second-order,etc., TS structure,respectively. Three minimum-energystructures (I, II and III) and two first-ordertransition states (structuresIV and V) wereidentifiedand these are shown in Fig. 2. All conformations,except structureV are predictedto have C, symmetry.A considerabledeviationfrom any possible symmetricstructuralarrangementis noticed. StructuresI, II and III have the same energyto five significantdecimal figures which precludes the assignment of a unique global-minimum configuration. The bond distances AI-O and O-H and the bond angles (Yand 8 do not change significantlywithin the five stationarypoints (I-V) except in structure III wherecyis increasedby approximately10” (at the SCF/6-31G* level). It can be seen from Fig. 2 that the reason for this may well be the proximity of the hydrogenatoms Hl and H4. In order to minimisethe hydrogen-hydrogen repulsionthe angle a! must widen. The deviation of (Yfrom the normal tetrahedral angle is approximately3.5 ’ in structuresI, II, IV and V and approximately 7” in structureIII at the SCF/6-31G* level of theory. StructureIII exhibits the most pronounced deviation from tetrahedralsymmetry. The inclusion of diffuse functions is generallythought to be important for the correct descriptionof anionic species.We haveexaminedthe effect of using diffuse functions on the results obtained for the geometricalparametersand relativeenergiesof the five stationarypoints located on the PES for H,AlO, (Table 2 ) . Computationalresourcesenabled us to add diffuse functions only to an ST0/3-21G basis set. The energydifferencesas calculatedusing diffuse (sp) functions follow the
309 TABLE 2 Geometries and total energies for the stationary points I-V” on the PES of the H&O,
Symmetry
I (M)
n 04)
III (M)
C1
C*
C1
SCF/6-31G* Bond length (pmjb R(Al-0) R(O-H) Bond angle (deg.) (~(01-Al-02) (03-Al-04) /3(01-Al-03) $(02-Al-04) @H-O-Al)
IV (TS) C,
species V (TS) DZd
177.0 94.60
177.0 94.60
177.0 94.60
177.1 94.60
177.1 94.62
105.9
106.0
116.7
106.2
106.3
116.7 116.6 110.3
106.0 106.0 110.3
106.0 106.0 110.3
111.1 111.1 111.1
111.1 111.1 110.9
82.25 82.30 157.2 148.0 157.3 148.0
97.80 97.77 156.9 147.7 - 32.40 - 23.30
Dihedral angle (deg.) 71
72 73
-
74
-
75
-
76
-
ET (a.u.)d AE” (kJ mol-‘)
- 543.90900 0.0
SCF/3-21G+ (sp) diffuse functions Bond length @mJb R(Al-0) 177.5 R(O-H) 95.71
90.00 90.00
90.00
85.46 - 94.60 -85.30 94.64
- 34.54 - 145.5 180.0 180.0
- 543.90900
- 543.90900
0.0
0.0
90.00
90.00 90.00 0.0 180.0 0.0 180.0
- 543.90594 8.0340
- 543.90470 11.2897
177.5 95.71
177.5 95.71
177.4 95.61
177.4 95.58
107.0
107.0
114.4
109.5
107.1
114.4 114.4 129.8
107.1 107.1 129.8
107.0 107.0 129.8
109.5 109.5 132.3
110.6 110.7 132.7
84.67 84.66 154.8 148.4 154.7 148.3
95.31 95.31 155.1 148.7 -31.30 - 25.02
90.02 90.03 86.92 - 93.05 - 87.01 93.53
89.99 90.01 - 79.58 - 100.4 180.0 180.0
90.00 90.00 0.0 180.0 0.0 180.0
-541.11181 0.0
-541.11181 0.0
Bond angle (deg.) a(Ol-Al-02) (03-Al-04) g(Ol-Al-03) @(02-Al-04) @H-O-Al)
Dihedral angle (deg.y 71 72 73
-
74
-
75
-
7,
-
ET (a.u.)d AE (kJ mol-I)’
-541.11181 0.0
Y&e footnotes a-c to Table 1. dTot.al energies 1 a.u.=2625.50 kJ mol-‘. ‘See footnote e to Table 1.
-541.10987 5.0964
-541.10585 15.6472
,02kH2 01 -Al
//
/
I II
Cl(near-SO
Cl
02.
*.
62
Hl 1 01
-Al
/ / /
/ _H 03
?3
H;
ir,
III
IV
Cl
Cl 02 ‘82
/ 01
’
HI
/i.’ /
I
/
\
1’
04
Pa
83 V
&d Fig. 2. The “true” minimum energy structures I, II and III and the transition states IV and V, as calculated using the ST0/6-31G* basis set.
same trend as those evaluated with the extended basis set ST0/6-31G*, with three degenerate minimum-energy structures being predicted. The geometrical parameters, principally the H-O-Al bond angles, calculated with the inclusion of diffuse functions are different from the values calculated at the HF/6-31G* level of theory. In addition, the dihedral angles 5 and r4 of the transition state structure IV are very different from the SCF/G-
311
31G* values.When diffuse functions are addedthe hydrogenatoms Hl and H2
are twisted by approximately 45” in order to minimize hydrogen-hydrogen repulsions.The other dihedral angles do not change significantlywhen diffusion functions are included. At the HF/3-21G + diffusion functions level of theory the bond angle a! is closer to the normal tetrahedral angle (109.5”) than the HF/6-31G* value, and for structureIV cr is equal to the tetrahedralvalue. The most noticeable effect of including diffuse functions in the calculation of the geometricalparameters for the H,AlO, species is, therefore, that the aluminiumatom approaches tetrahedralsymmetry. The previouslyreported [ 71 SCF/6-31G* geometricalparametersand energies for the stable configurationsof the H4Si04 molecule are given in Table 1, for comparison with the present results for the H*AlOc anionic species. The similaritiesbetween the spatial arrangementsof H4Si04 and H,AlO; can be easily seen. The good agreementbetween the two sets of dihedral angles (z, Tables 1 and 2) is of interest.It indicatesthat the silicon atom can be replaced by aluminiumwith very little conformationalchange,and very little change in the relative energies.We believe that this minimal perturbation on substitution is a major reason for the ease of substitutionof silicon by aluminiumin aluminosilicateframeworks. A previous analysis of silicon compounds suggestedthe important contribution of anomeric effects in the stabilisationof the conformations [ 201. The H4Si04 conformations in which the O-H bonds are almost perpendicularto the vicinal Si-0 bond are stabiliseddue to the negativehyperconjugationbetween the pn oxygen atom and the c* Si-0 orbital. This study suggeststhat aluminiumbased compounds also exhibit such effects. Indeed,the importance of anomericeffects in the stabilisationof silicatesand aluminosilicatesin general needs to be addressedmore carefully.
CONCLUSIONS
The ab initio investigationat the Hartree-Fock level of theory of the stationary points on the PES of the H,AlO, anionic species, without symmetry constraints,located three degenerateminimum-energystructuresbelongingto the C1symmetrypoint group. The main effect of including diffuse functions in the calculation of the geometricalparameters was that the configuration approachedtetrahedralsymmetry.Comparisonswith the HF/6-31G* results previously reported for the H4Si0, molecule reveal that the silicon atom can be replacedby an aluminiumatom with very little change in the conformation or energy.
312 ACKNOWLEDGMENTS
W.B. De Almeida wishes to thank the Departamento de Quimica, U.F.M.G., Brazil for granting leave of absence. P.J. O’Malley thanks the Manchester Computing Centre (MCC ) for support.
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2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17 18 19 20
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