Ab initio infrared and Raman spectra of the H3SiO4− monomeric anionic species

Wwational Spctroscopy,

5 (1993) 325-335

325

Elsevier Science Publishers B.V., Amsterdam

Ab initio infrared and Raman spectra of the H,SiO; monomeric anionic species Wagner B. De Almeida and Patrick J. O’Malley Department of Chemistry, UMIST, P.O. Box 88, Manchester M60 IQD (UK)

(Received 12th October 1992)

Abstract Spectroscopic parameters for the stable minimum-energy structures on the potential energy surface for the HsSiOc monomeric silicate species are reported. Harmonic frequencies and infrared and Raman intensities of the vibrational normal modes are analytically calculated at the ab initio Hartree-Fock level. Calculations were carried out with the 6-31G * basis set and also including diffuse functions (3-21+ + G and 3-21+ + G* * basis sets) in order to assess their importance for the prediction of the vibrational spectrum of this anionic species. Comparisons with available experimental data are made. Keywords: Infrared spectrometry; Raman spectrometry; Ab initio calculations; Silicates; Zeolites

The exact role of soluble silicate species in the zeolite synthesis mechanism is still not well understood [l]. Silicate solutions are usually a complex mixture of monomeric and polymeric anions, the ratio of which has a complex dependence on pH and counter cation used [2-81. Raman spectroscopy provides a sensitive method for studying such species in aqueous solution 151. Dutta and Shieh [6-81 have reported laser Raman spectroscopic studies which revealed the existence of monomeric, dimeric, trimeric and tetrameric silicate species in alkali hydroxi solubilized silicates. Assignment of vibrational bands is generally made via comparison with experimental silicate and phosphate spectra. It is now, however, possible to use high-level ab initio methods to calculate the vibrational characteristics of smaller silicate species present, i.e. monomer and dimeric forms, and then put the assignment of vibrational spectra on a firmer theoretical footing. Correspondence to: W.B. De Almeida, Departamento de Quimica, ICEx, U.F.M.G., Pampulha, CP 702, Belo Horixonte, MG, 30.161 (Brazil) (permanent address).

This paper reports on the ab initio molecular orbital (MO) calculations of the infrared (IR) and Raman spectrum for the monomeric anionic species H,SiO; . Band assignments for the monomeric silicate species are compared with the experimental results previously reported by Dutta and Shieh [6-81.

CALCULATIONS

Four minimum-energy structures (implying that all eigenvalues of the Hessian matrix [9] are positive) have already been located on the potential energy surface (PES) for the H,SiO& species [lo] at the ab initio I-Iartree-Fock (HF) self consistent field (SCF) level of theory employing the 6-31G * basis set including d polarization functions on Si and 0 atoms [ll-141. In the present study we report harmonic frequencies and IR and Raman vibrational intensities calculated analytically with the 6-31G * basis set [ll-141. Also calculations with the 3-21G

0924~2031/93/$06.00 0 1993 - Elsevier Science Publishers B.V. Ah rights reserved

U?B. De Almeiab and P.J. O’Malley / Vl5. Spectrosc. 5 (1993) 325-335

326

basis set [15-171 with diffuse (sp> functions added to Si and 0 atoms and a diffuse s function to hydrogen [18] were performed in order to examine the effect of diffuse functions on the calculated spectroscopic parameters. This basis set is named 3-21+ + G and when polarization functions on all atoms are added it is called 3-21+ + G* *. Computational cost prohibits inclusion of electron correlation effects. All calculations were executed with the ab initio MO package Gaussian-86 [191 as implemented on the Amdahl VP1100 and VP1200 computers at the Manchester Computing Centre (MC0

RESULTS

AND DISCUSSIONS

The geometrical parameters and total energies for the four genuine minimum-energy structures previously located on the multidimensional PES for the H,SiO; anionic species [lo] are given in Table 1. The spatial arrangements are shown in Fig. 1 along with definition of the bond and dihedral angles. All structures are predicted to have C, symmetry. An apparent C, symmetric configuration (having a C, symmetry axis passing through the negative oxygen atom) was shown to be a transition state rather than a minirnum-energy structure [lo]. From Table 1 it can be seen that the energy difference between the minima on the PES is not higher than 4 kJ mole1 at the HF/6-31G* level, and when diffuse functions are introduced the energy difference is below 0.5 kJ mol-’ implying that structures I, II, III and IV are essentially degenerate and so, a unique global minimum cannot be assigned. Bond distances are practically unchanged within the four stable configurations and bond angles do not alter more than 7”, whether or not diffuse functions are employed. Also, a considerable deviation from a tetrahedral behaviour can be seen by comparing the calculated values for the geometrical parameters. It should be emphasized that inclusion of diffuse functions lead to a similar characterization of the stationary points on the PES, i.e. four minimum-energy structures,

TABLE

1

Fully optimized geometries (distances in pm a and angles in degrees), total energies, E, in Hartrees a, for the minimumenergy structures I, II, III and IV on the PES for the H,SiO; species. The dihedral angles are defined in Fig. 1 I-W/6-31G

* I

II

III

IV

Bond distances Si-O1 Si-0 O-H

153.1 168.8 94.61

153.1 168.7 94.61

153.7 168.3 94.62

153.1 168.7 94.62

;

116.8 99.72

119.8 106.4

113.1 99.72

112.4 99.21

: 6

120.3 106.5 108.6

116.2 101.0 109.1

107.8 119.9 107.6

105.3 120.9 108.9

77.63 98.20 71.61 86.32 - 96.00

76.58 93.87 3.861 - 167.0 - 126.1

Bond angles

Dihedral angles 71 72 73 74

75

E tot

74.73 94.12 - 158.5 - 151.3 - 127.9

- 590.29802

- 590.29789

- 590.29933

75.40 97.71 15.00 4.471 50.39 - 590.29785

HF/3-21++G I

II

III

Iv

Bond distances Si-O1 Si-0 O-H

160.8 170.8 95.96

160.8 170.8 95.96

160.8 170.8 95.%

160.8 170.8 95.96

;

118.9 103.2

116.4 104.8

112.5 98.55

112.5 98.56

: 9

117.4 104.3 122.2

118.8 103.8 122.0

118.1 104.5 122.2

117.4 103.8 122.3

77.25 95.22 - 142.5 - 109.8 - 124.9

75.60 96.16 36.73 66.54 - 100.9

79.58 99.46 - 11.15 153.4 - 149.6

80.54 100.4 11.08 - 30.35 26.73

- 587.25211

- 587.25219

- 587.25201

Bond angles

Dihedral an&s 71 72 73 74

75

Em

a 1 pm = lo-’

A; 1 Hartree = 2625.50 kJ mol-‘.

- 587.25201

W.B. De Almeida and P.J. O’iUalley/ Vib. Spectmsc. 5 (1993) 325-335

as when the extended 6-31G* basis set is used. However, the degeneracy of the four minima is definitively highlighted when the HF/3-21+ +G approach is used. The torsional angles connecting the hydroxyl groups to the Si centre (r3, r4 and TV)undergo a considerable change when diffuse functions are used leading to a somewhat distinct set of confor-

327

mations, however without affecting the nature of the stationary points. It has been pointed out that anomeric effects may be connected to the flexibility of silicate species [20] which has also been supported by the ab initio calculations reported in Ref. [lo]. From the present results it can be inferred that inclusion of diffuse functions have a direct effect on the orientation of the O-H DEFINITION OF THE -___-_ DIHEDRAL ANGLES. --__-

a)

I-

71 = [03,Si,X;,X31 7: = [04,Si,X2,X4] TV = [Hl,O2,Si,X;l 74 = [H:, OJ,Si,Xll 75 = [Hj,O,,Si,X:I

101

The X's are dummy and the positive

A-B C-D

in the around

centres sign of

direction the B-C

of line.

b)

Fig. 1. (a) Configuration space spanning the multidimensional PES. (b) The true minimum-energy structures I, II, III and IV calculated with the 6-31G* basis set. The view is equivalent to that of Fig. la, but rotated by 90” around the X,-X, axis.

W.B. De Almida and P.J. O’Malley / Kb. Spectrosc. 5 (1993) 325-335

328

dipoles in the H,SiOi species, which may explain the significant change in the dihedral angles r3, r4 and r5. Table 2 reports harmonic frequencies, IR and Raman intensities for minimum-energy structure I, using different levels of theory. Frequency and intensity data for structures II, III and IV were found to be virtually the same as for I [21] and therefore are not reported here. It is interesting to point out that structures I, II, III and IV are structurally quite distinct, but are spectroscopically indistinguishable. The effect of the basis set on the frequencies and intensities is quite noticeable. The HF/3-31G* frequencies are consistently higher than the HF/3-21+ + G ones, with the O-H stretching modes being increased by approximately 150 cm-‘. The effect on the lowfrequency modes is not so pronounced. The addition of polarization functions to the 3-21G basis set 117,181 followed by inclusion of (sp) diffuse functions on heavy atoms and s diffuse function on hydrogen atoms, i.e. the 3-21+ + G* * basis set, result in an increase of the O-H stretching frequencies by at least 100 cm-‘. In the light of the O-H stretching frequencies usually reported

TABLE

in the literature and bearing in mind that the 6-31G* basis set is well known to overestimate vibrational frequencies, we concluded that the 3-21+ + G basis set is the more adequate for the prediction of the normal mode frequencies of the H,SiO; anionic species. The effect of the basis set on the calculted vibrational intensities are not so apparent. It does not follow a regular pattern as does the harmonic frequencies. The vibrational spectrum of H,SiO; is represented in Figs. 2-4, which aim to facilitate a comparison between experimental and theoretical results. The complete spectrum as calculated using the 6-31G* and 3-21+ + G basis sets, showing all fundamental vibrational absorptions (0 < w, < 4700, in cm-‘), is displayed in Fig. 2. It is seen that the most rich features of both IR and Raman spectra are confined to the region O-1300 cm-i. Figure 3 gives a pictorial representation of the IR spectrum of the H,SiO; monomeric anionic species, in the O-1300 cm-i region, calculated using three different basis sets. The spectrum calculated with the 3-21+ + G basis set and using a similar basis set but adding polarization

2

Harmonic frequencies (we in cm-‘), IR intensities (A in km mol-‘) energy structure I on the PES for the H,SiOc species Mode

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

I-W/6-31G

*

HF/3-21+

and Raman intensity (A’ in A4 amu-‘)

+G

HF/3-21+

0,

A

A’

0,

A

A’

139 177 297 320 370 407 440 482 770 843 854 1002 1034 1044 1279 4132 4134 4138

34.3 118 14.8 5.80 11.3 50.2 114 176 20.5 265 246 124 294 178 352 51.4 30.8 40.8

2.21 1.74 0.80 1.16 1.78 1.75 1.15 1.03 6.53 0.78 1.17 3.06 1.27 3.23 2.95 65.3 63.6 73.5

122 162 255 327 336 358 406 457 757 799 815 846 932 938 1150 3983 3987 3988

187 18.1 87.6 22.9 36.8 70.5 179 275 53.8 373 419 105 137 181 378 50.8 90.5 13.5

1.92 1.91 2.49 1.48 1.31 2.10 2.32 2.02 15.3 0.63 3.24 1.88 1.16 3.71 9.13 94.3 23.4 191

for the minimum

+ G* *

we

A

A’

56.5 119 256 330 343 367 424 455 777 822 849 855 919 929 1221 4249 4251 4252

173 24.6 87.1 32.6 42.8 47.4 124 193 30.0 348 157 443 167 157 460 83.8 78.9 48.4

0.78 1.15 1.20 0.64 1.01 1.13 1.14 1.37 7.79 0.23 1.52 2.05 1.02 2.98 10.5 57.9 56.6 103

W?. De Aheida

a)

and P.J. O’iUalley/ VI. Spectrosc. 5 (1993) 325-335

HF/6-31G*

I.R. spectrum.

1)

HF/3-21++G

I.R. spectrum.

cl

HF/6-31G*

Raman spectrum.

HF/3-21++G

Raman spectrum.

329

420

195

4700

0

d) 195

4700

0 Fig. 2. IR and Raman spectrum for the H&O<,

structure I. (a) I-W/6-31G * IR spectrum; (b)HF/3-21++ G IR spectrum; (c)

HF/6-31G* Raman spectrum;(d) HF/3-21++G Rsman spectrum.

330

WB. De Almekia and P.J. O’MaUey/ Vii. S’ctrosc. 5 (I 993) 325-335

functions on H, Si and 0 atoms (3-21+ + G* * basis set) exhibits a very similar pattern. Nevertheless the latter basis set increases frequency and intensity of the higher-frequency modes and decreases the respective values for the lower vibrational modes, when compared to the 3-21+ + G basis set. The IR spectrum calculated with the 6-31G* basis set is significantly different from the 3-21+ + G one. The HF/6-31G * harmonic frequencies are systematically shifted towards higher values. Also, some strong absorption present in the HF/3-21+ + G spectrum are

a)

considerably attenuated when the 6-31G* basis set is employed. The Raman spectrum calculated with the three aforementioned basis sets is depicted in Fig. 4. Three distinct profiles are promptly seen. The Raman intensities are found to be very sensitive to the basis set used for their calculation. This result was not unexpected since the Raman intensity depends on the molecular polarizability derivative which is known to be a very sensitive quantity to calculate. Assignments of the fundamental bands are also

HF/6-31G*

1300

0 b)

HF/3-21++G

520 1 H 0 d \ *

0

I

II

I 13;o

1

c)

HF/3-21++G**

1

0 Fig. 3. IR spectrum for structure I. (a) HF/6-31G

*; (b) HF/3-21+

+ G; (c) ~~/3-21+

+ G* *.

W.B. De Almeida and P.J. O’iUalley/ Vii. Spectrosc. 5 (1993) 325-335

included in Fig. 4 and the respective normal modes are displayed in Figs. 5-9. The normal modes plots are represented by arrows indicating normal coordinate displacements that come about as a given normal vibration takes place. In order to make clear the assignment of the normal modes the X-Y, X-Z and Y-Z projections are shown in Figs. 5-9. It can be seen from Figs. 5, 7 and 8 that the O-H bending modes are unequivocally identified and are uncoupled to the stretching normal modes. However, for the Si-OH (Fig. 6) and Si-O- (Fig. 9) stretching modes a consider-

17 ;I

331

able coupling with the Si-O-H bending modes is observed. It should be stated that our band assignments and harmonic frequencies for the most active Raman vibrations correspond to a gas phase system while the experimental investigations were conducted in solution. Among the three spectra presented in Fig. 4 the profile predicted by the 3-21+ + G basis set fits the experimental spectra reported in Ref. 181 much better than the other two basis sets, with the calculated Si-OH stretching frequency differing from the experimental value reported by only

HF/6-3lG*

,

_(

2

3

str.

si-OH (777)

; Si-01-l

\ O-H O-H

k

O-H

0 300 h)

I

str.

band

band

III

bend

II

I 770

407

HF/3-21++G

; Expt.

I looa

854

value

from

ref.

1044

[a]

1279

in

1300

parenthesis.

Si-oH str. (777)

O-H O-H

III 00

17

cl

O-H

bend

bend

bend

I

I

358 406457

1 757

I

815

938

1300

1150

HF/3-21++G’* si-01-1 str. Si-oH Str.

$

(777)

; \ O-H

bend

k O-H

0 300

III

bsr,d

II 4a4

777

a55

Fk. 4. Raman Wectrumfor structure I. (a) HF/6-31G*; (c) HF/3-21+ +G**.

I 1211

929

(b) HF/3-21++G,

1300 experimentalvalue from Ref. [8] in parenthesis;

332

W.B. De Almeidn and P.J. O’MaUey/ VI. Spectrosc. 5 (1993) 32S-335

20 cm-‘. It is also found [21] that both 6-31G* and 3-21+ + G* * basis sets failed to predict correctly the relative positions of the two strong

b) b)

Fig. 5. HF/3-21++G projections of the O-H normal bending mode (vibrational mode no. 7; o, = 406 cm-‘). (a) X-Y, (b) X-Z; Cc) Y-Z.

Fig. 6. HF/3-21++G projections of the SCOH normal stretching mode (vibrational mode no. 9; o__= 757 cm-‘) (a) X-Y, (b) X-Z, Cc) Y-Z.

W.B. De Aimeida and PJ. O'Mahky/Vii.

Spectnxc. 5 (1993) 325-335

absorption peaks cmrespo@ing to the SCOH and Si-O-stretching modes of the H,SiOispecies reported in Ref. [31.

333

It is worthwhile to say that the Si-O- absorption band of the H,SiO; anionic species has not been assigned by Dutta and Shieh [81.The correz r

b)

b)

Fig. 7. W/3-21++G projections of the O-H normal bending mode (vibrational mode no. 11; o, = 815 cm-‘). (a) X-Y, 6) x-z; (cl Y-Z.

Fig. 8. HF/3-21++G projections of the O-H normal bending mode (vibrational mode no. 14; O, = 938 cm-l). (a) X-y! (b) X-z; (c) Y-Z.

334

WB. De Almeti

sponding absorption band for the H,SiOispecies is observed at 925 cm-’ [8]. Such a peak, which the authors [81 expected around 930 cm-’

b)

i-P@ cl

H

\/

k

cl’” Sr

b’\ @

Fig. 9. HF/3-21++G projections of the Si-Onormal stretching mode (vibrational mode no. 15; w, = 1150 cm-‘). (a) X-Y; (b) X-Z; (c) Y-Z.

and P.J. O’MaUey/ Vib. Spectrosc. 5 (1993) 325-335

is not found in the H,SiOi spectrum where a relatively strong absorption at 1015 cm-’ was observed and assigned to SiO, stretch vibration of the dimeric silicate species [8]. We have performed Hartree-Fock calculations of the Raman spectra for the H,SiOispecies as well [21] and have confirmed that there is a strong absorption band at 914 cm-’ due to the Si-Ostretch vibration, which is in agreement with the Raman results reported in Ref. [8]. However, what we found analyzing the calculated HF/3-21+ +G Raman spectra is that the Si-O- band has been shifted from 914 cm-’ (H,SiOi-) to 1150 cm-’ (H,SiO;). Dutta and Shieh [8] have implicitly assumed that the shift for the Si-O- stretching mode would be of similar magnitude as that for the Si-OH stretching vibration on going from the H,SiOito HsSiO;. Our HF/3-21+ + G results [21] revealed that this shift is rather large. This could be the reason why Dutta and Shieh [8] did not assign the Si-O- band of the H,SiO; anionic species. It has also been found [21] that the strong Si-O- absorption band in the HSiOispecies occur at a lower frequency than the corresponding absorption of the H,SiOispecies. So, there is a considerable shift in the Si-O- stretching mode such that the respective harmonic frequencies decrease in the following order: HSiOi- < H,SiOi- < H,SiO;. These results indicate that the Raman band observed at 1015 cm-’ by Dutta and Shieh [8] could well be the Si-Ostretching vibrational mode of the H,SiO; species. In the light of the comparisons with available experimental Raman data it is seen that the inclusion of diffuse functions is crucial for an adequate description of the spectra of silicate species. The present study shows that a moderate basis set with addition of diffuse (sp) functions on heavy atoms (diffuse s function on hydrogen atoms have been reported to be more important for the calculation of H- and hydride affinities [22] and so can be neglected) can yield satisfactory results for the calculation of the Raman most active vibrational modes of the silicate species. Thus the ab initio calculations can be used to confirm assignments for such species. Of course the use of a higher polarized basis

335

WB. De Almeida and P.J. O’Malley / vib. Spectrosc. 5 (1993) 325-335

set including more diffuse functions and also an adequate treatment of electron correlation would be highly desirable. However, our present computer resources preclude such calculations to be carried out for molecular systems of the size of the silicate species investigated in this paper. Conclusions The IR and Raman spectra for the H, SiO;anionic species were calculated at the Hartree-Fock level of theory employing three distinct basis sets: 6-31G *, 3-21+ + G and 3-21 + + G* *. The experimental spectra reported for the silicates in solution (containing both H,SiO; and H,SiOiforms) exhibit a profile which is well reproduced by the 3-21+ + G basis set. Additionally our theoretical assignments of the normal vibrational modes match the experimental band assignments for the Si-OH stretching modes [8] made by comparisons with the Raman spectra of phosphates and crystalline silicate minerals, and also provide some evidence for the stretching Si-O- band which has not been assigned by Dutta and Shieh [8]. Therefore we conclude that the 3-21+ +G basis set appears to give a satisfactory description of the vibrational characteristics of silicate species and so it may be used in further theoretical investigations of dimeric and higher multimeric silicate structures. Clearly indentifying the silicate species present in zeolite synthesis media is a prerequisite to an understanding of the synthesis mechanism. Here we illustrate how high-level ab initio molecular orbital methods can aid in the assignment of species present in such a system. P.J. O’Malley thanks the Manchester ing Centre (MCC) for support.

Comput-

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