J. Phys. Chem. 1991,95, 5455-5462
5455
Ab Initio Molecular Orbital Calculations on the Electronic Structure of Sodium Silicate Glasses Takashi Uchino,* Matae Iwasaki, Tetsuo Sakka, and Yukio Ogata Institute of Atomic Energy, Kyoto University, Uji, Kyoto-Fu 611. Japan (Received: November 21, 1990) Ab initio molecular orbital (MO)calculations have been performed on clusters H&i207Na, (x = 0, 1,2, and 4) modeling sodium silicate glasses. Geometries are optimized at the HartretFock/STO-3G level. The 3-21G and 3-21G + polarization d functions on Si basis sets are employed in single-point calculations using the STO-3G optimized geometries. On the basis of the MO diagrams obtained for the clusters, photoionization, X-ray emission, and UV excitation energies are calculated. The calculated energies are in good agreement with the experimental values reported previously. Furthermore, the addition of d orbitals on Si yields a realistic charge distribution in the clusters. The results show that Na atoms in the cluster affect the electron density not only on 0 atoms next to Na (i.e., nonbridging oxygens) but also on all 0 and Si atoms in the cluster. Consequently, it is found that Si-0 bonds are weakened totally by the introduction of Na into the glass structure. Also, reactivity of the S i 4 bonds in sodium silicate glasses are discussed in terms of charge distribution calculated for the clusters.
1. Introduction The structure of the Si-0-Si network in sodium silicate glasses is largely influenced by the amount of alkali metal oxide introduced in the glasses.lJ For example, the Si-0-Si bridges composed of ‘bridging” oxygens will be broken by the addition of N a 2 0 to form singly bonded oxygens called ‘nonbridging” oxygens. The reaction can be represented as follows:
ei-O-Sir
+ Na20
+
@i-O-Na’Na+-O-Si=
The positively charged Na ions are thus considered to be incorporated interstitially in the vicinity of the negatively charged nonbridging oxygens.’ These nonbridging oxygens are known to affect the physical and chemical properties of sodium silicate glasses such as density,” viscosity,’ refractive index? and resistance to water? For these reasons, the effect of alkali metal ions upon the glass structure has been studied experimentally in several ways.’*f7+ X-ray and neutron diffraction measurements have provided a number of pieces of information to characterize the structure of silica and silicate glasses. Warren and @workers1 have studied ~~
(1) (a) Warren, B. E.; B i m , J. J . Am. Cerum. Soc. 1983, 21, 259. (b) Wamn, 8 . E. J. Am. Cerum. Sm.1!341,24,256. (c) Moui, R. L.; Wamn, B. E. J . Appl. Crystallogr. 1969, 2, 164.
(2) (a) Sigel, G. H. J. Phys. Chem. Solids lWl,32, 2373. (b) Sigel, G. H. J . Non-Crysr. Solids 1973/1974, 13, 372. (3) (a) Shartis, L.; Spinner, S.;C a m , W. J. Am. Cerum. Soc. 1952,35, 155. (b) Shener, H. F. J. Nurl. Bur. Srund. 1956, 57, 97. (4) BocLrir, J. O’M.; Mackenzie, J. D.; Kitchner, J. A. Trans. Furuduy Soc. 1955, 51, 1734. (5) Faick, C. A.; Finn, A. N. J . Am. Cerum. Soc. 1931, 14. 518. (6) (a) Saden, D. M.; Penon, W. P.; Hench, L. L. Appl. Spccrrmc. 1974, 28, 247. (b) Scholze, H. J. Non-Crysr. Solids 1982, 52, 91. (7) Brawa, S. A.; White, W. B. J . Chem. Phys. 1975,63, 2421. (8) Hanna, R. J . Phys. Chem. 1%5,69, 3846. (9) Gudker, R.;Urns, S. Phys. Chem. Glosses 1973, 14, 21. (IO) Greaves, G. N.; Fontaine, A.; Lagarde, P.; Raoux, D.; Gurman, S. J. Nature 1981, 293,611. (1 1) Mkwa, M.;Price, D. L.; Suzuki, K. J . Non-Crysr.Solids 1980,37, 85. ( I 2) Nagel, S. R.; Tauc, J.; Baglcy, B. 0.Solid Srure Commun. 1976,20, 245. (13) (a) Bdckna, R.;Chun, H.-U.; Goretzki, H. Glusrech. Ber. 1978,51, 1. (b) BrOckner, R.; Chun, H.-U.; Goretzki, H.; Sammet, M. J . Non-Crysr. Solids 1980, 42, 49. (14) Smets, B. M. J.; Lommen, T. P. A. J . Non-Cryst. Solids 1981, 46, 21. ( I 5) Kaneko, Y. Yogyo-Kyokuishi 1978,86, 330. (16) Sakka, S.; Matsurhita, K. J. Non-Crysr. Solids 1976,22, 57. (17) Duffy, J. A.; Ingram, M. D. J . Am. Chem. Soc. 1971, 93, 6448. (18) Dupree, R.;Hollamd, D.; McMillan, P. W.; Pettifer, R. F. J . NonCrysr. Solids 1984,68, 399. (19) Schramm, C. M.; de Jon& B. H. W. S.; Parziale, V. E. J. Am. Chem. Soc. 1984, IW,4396. (20) Wicch, G.; Zopf, E.; Chun, H.; BrOckner, R. J. Non-Crysr. Solids 1976, 21, 251.
the structures of amorphous solids using the X-ray diffraction method extensively. They have found that the short-range order of glasses is almost similar to that of the corresponding crystalline phases. Besides, highly resolved neutron scattering experiments on sodium silicate glasses have shown that the S i 4 distance increases slightly (-0.02 A) with increasing N a 2 0 content from 0 to 33 mol%.” On the other hand, Dupree et a1.’* carried out an extensive study on sodium silicate glasses using “magic-angle spinning” NMR (MAS NMR) spectroscopy and extracted additional information about the structure of the glasses. They have found that (1) the introduction of Na20 into Si02structures causes the progressive replacement of SiO, tetrahedra containing four bridging oxygens by SiO, tetrahedra with three bridging oxygens and one nonbridging oxygen, (2) at 33.3 mol 7% N a 2 0 all SiO, tetrahedra consist of the latter type, and (3) on further addition of N a 2 0 they are pregressively replaced by SiO, tetrahedra with two nonbridging oxygens until complete replacement is achieved at 50 mol 3’6 Na20. X-ray photoelectron spectroscopy (XPS) is very useful for characterizing the electronic structure of sodium silicate glasses. Previous XPS studies have shown the following result^:^^-'^ (1) Two peaks are observed in 0 1s photoelectron spectra; the peak of the higher and lower energies can be attributed to the bridging ( o b ) and nonbridging ( o n b ) oxygen atoms. (2) The positions of the O b and O n b 1s photoelectron bands shift to lower binding energies with increasing N a 2 0 content. (3) The absolute shift of the O b peak is greater than that of the O n b peak; that is, the binding energy difference between O b 1s and O n b 1s electrons becomes smaller as the concentration of N a 2 0 increases. From these results, it has been concluded that Na ions in sodium silicate glasses affect the electron density of the bridging oxygens as well as that of nonbridging oxygens; in other words, Na ions affect the glass network nonlocally. This is known as a “nonlocalized effect”.13The effect of Na ions upon the glass structure has been also confirmed by X-ray emission16*20 analyses. In order to interpret these findings, in this work we have made ab initio molecular orbital (MO) calculations on small clusters such as H&3i207Nax (x = 0, 1,2, and 4) modeling sodium silicate glasses. These cluster calculations will provide useful information to evaluate the structure of sodium silicate glasses, because it has been demonstrated that in systems like silica and silicates, where the local-scale atomic structures of the glass and the corresponding crystalline phase are similar, local binding forces of bulk samples are not very different from those in small clusters consisting of the same atoms with the same coordination number^.^^-^' Although a lot of MO calculations on clusters modeling silica have (21) Newton, M.D.; Gibbs, G.V. Phys. Chem. Miner. 1980, 6, 221. (22) Gibbs, G.V. Am. Miner. 1982,67;421. (23) O’Kccffe, M.;Domenges, B.; Gibb, G. V. J. Phys. Chem. 1985,89, 2304.
0022-365419112095-5455SO2.5010 Q 1991 American Chemical Societv
5456 The Journal of Physical Chemistry, Vol. 95, No. 14, 19'91 left
a
05
center
rigM side
02
Uchino et al.
tZ paramu
x=o
x-2
x-1
Distances 1.627 1.588 1.565 1.680 1.680 1.663 1.663 1.663
Si141 Si241 Si142 Si143 Si144 Si245 Si246 Si247
1.596 1.596 1.656 1.656 1.656 1.656 1.656 1.656
Si4b Si4,b O,b-Na 0-0
Av Distances 1.641 1.652 1.565 1.839 2.631 2.642
x=4
1.612 1.612 1.584 1.689 1.689 1.584 1.689 1.689
1.629 1.629 1.725 1.606 1.606 1.725 1.606 1.606
1.663 1.584 1.846 2.653
1.677 1.606
1.815 2.654
Angles
Si2-01-Si1 av & S i 4
142.18 109.45
138.94 109.37
139.41 109.34
135.69 109.25
ODistances in angstroms; angles in degrees.
Figure 1. Ge4metries of model clusters: (a) H6Si207;(b) HsSi207Na; (c) HSi207Na2; (d) H#i207Na4.
been made up to n0w,21-31to our knowledge, this is the first ab initio MO study on small clusters modeling sodium silicate glasses. Recently, Murray and Ching'" also performed theoretical studies on the electronic states in sodium silicate glasses on the basis of the atomic models with periodic boundary conditions. Their models consisted of 162 atoms32band they used the orthogonalized linear combination of atomic orbitals (OLCAO) method.'& In general, their calculations succeeded in characterizing the electronic structure of sodium silicate glascs; however, they were partly at variance with the experimental results obtained by XPS. In this paper, we will demonstrate that our calculations reproduce the experimental results more satisfactorily. We further calculate the charge distribution in the model clusters. On the basis of the calculated atomic charges, we discuss the reactivity of the S i 4 bonds in silicate glasses. 2. Models and Calculational Procedure As mentioned above, we employ here small clusters H&3i207Na, to deduce bulk properties of sodium silicate glasses (see Figure 1). In these clusters, hydrogen atoms are used to
saturate the dangling bonds of ysurfaces oxygen atoms. This is a common way to eliminate the surface unsaturated bonds of small ~ l u s t e r s . ~Lopez ~ - ~ ~at a1.,29however, suggested that the method of hydrogen saturation is not suitable for materials consisting principally of r bonds such as silicates; nevertheless, our calculations using this method gave reasonable results as will be shown later. From this reason, we consider that the hydrogen terminators do not seem to affect the nature of the S i 4 bonds in silicates so severely; hence, we did not use other atoms or atomic groups to saturate the dangling bonds of the surface oxygens. The oxygen (24) Yip, K. L.;Fowler, W. E. Phys. Reu. B 1974, IO, 1400. (25) T d ,J. A,; Vaughan, D.J.; Johnaon, K.H. Chem. Phys. Leu. l!W3, 20,239. (26) Collins, G. A. D.;Cruicbhank, D.W. J.; Breeze,A. J . Chcm. Soc., Faraday Trans. 2 1972,68, 1189. (27) Ernst. C. A.; Allred, A. L.; Ratner, M. A,; Newton, M.D.;Gibbs, G. V.; Moskowitz, J. W.; Topiol, S . Chem. Phys. Lerr. 1981, 81, 424. (28) Grigoras, S.;Lane, T. H. 1. Compur. Chem. 1987,8, 84. (29) Lopez,J. P.; Yang, C. Y.; Helms, C. R.J. Compur. Chem. 1987,8, 198. (30) Bennett, A. J.; Roth, L. M. J . Phys. Chem. Solids 1971,32, 1251. (31) Murakami, M.; S a m , S.J . Non-Crysf. Solfds 1988, 101, 271. (32) (a) Murray, R.A.; Ching, W. Y .J . Nowcrysf.Solids 1987,94, 144. (b) Murray, R. A.; Song. L. W.; Ching, W. Y. 1.Non-Crysr. Solids 1987, 94, 133. (c) Ching, W.Y.; Lin, C. C. Phys. Rw. B 1975, 12, 5536.
atoms adjacent to Na were regarded as nonbridging oxygens. This is a simplistic model of Onb-Na bonds, because X-ray scattering" and absorptionlo studies have suggested that the coordination number of Na in sodium silicate glasses is 4. Bmckner et have proposed that the multiple coordination of Na is only possible with the help of both 0, and on, atoms. However, such an effect of the direct coordination between Ob and Na is not included in the model clusters. The rest of the oxygens in Figure 1 were esteemed to be bridging oxygens. All ab initio MO calculations were carried out by using the GAUSSIANEZ computer progE"3 Previous geometry optimizations for the cluster H&07 modeling s i l i ~ a ~at' - the ~ ~ Hartree-Fock (HF) level with the STO-3G basis setMhave yielded S i 4 bond lengths and Si-0-Si angles comparable with the experimental values of Si02glass. Hence we also optimized the geometries of the molecules H&ii2O7Na, at the same economical HF/STO-3G level by means of the gradient 1nethod.3~ The structures of the model clusters were completely optimized within the assumed symmetry constraints except for the molecule with x = 1, HSSi207.Na.Since this molecule has a very low symmetry, we optimized it under the following constraints: (1) The two dihedral angles between the planes 01-Si245 and 0 1 - S i 2 4 , and 0 1 - S i 2 4 5 and 01-Si2-07 in Figure 1 are fixed at 1 2 0 O . (2) The three S i 4 and &H bond lengths and the three Si+-H bond angles on the left side of the molecule are equal, respectively. On the basis of the results of MAS NMR18 spectroscopy mentioned in the Introduction, the structures of the model molecules with x = 0, 1, 2, and 4 can be compared with those of SO2, 20Naz0-80SiO2 (mol a), 33.3Naz0-66.7SiO2, and 50Na20-50Si02 glasses,respectively. The HF/STO-3G geometry was then used for single-point calculationswith the split-valence basis sets, the 3-21G and 3-21G polarization d functions on Si basis sets.% We will call the latter basis set 3-21G+d(Si) from now on. In later sections, we will mainly use the calculated results with such larger basis sets to evaluate the electronic structure of the model clusters. Because of computer time limitations we did not add d orbitals to 0 and Na atoms. However, this may not be a crucial disadvantage, because it has been confirmed that the polarization
+
(33) Binkley. J. S.;Frisch, M.J.; DeFrces, D. J.; Rahgavachari, K.; Whiteaide, R. A,; Schlegel, H. B.; Fluder, E.M.;Pople, J. A. GAUSSIAN82 Department of Chemistry, CarncgieMdlon University: Pittsburgh, PA,1982. (34) Hehre. W. J.; Ditchfield, R.; Stewart, R. W.;Pople, J. A. J. Chrm. Phys. 1970,52,2769 and rcfercncea therein. (35) Pulay, P. In Modern Theorerid Chemisrry;Schaefer, H. F., 111, Ed.; Plenum: New York, 1977; Vol. 4, p 153. (36) (a) Gordon, M. S.;Binldey, J. S.;Pople, J. A,; Pietro, W. J.; Hchrc, W.J. J . Am. Chcm. Soc. 1982,104,297 and reference thmin. (b) Pietro, W. J.; Franc], M.M.; Hehrc, W. J.; DeFrees, D.J.; Pople, J. A.; Binkley, J. S . J. Am. Chem. Soc. 1982, 104, 5039.
The Journal of Physical Chemistry, Vol. 95, No. 14, 1991 5457
Electronic Structure of Sodium Silicate Glasses ~~
S i 4
Si-0
~~
intcratomicdist, A Si-0.* SNa ThisWorP
bond angle, deg 0-Si-0 SiQSi
0-0
~~
~~~~
~
x = 0 (Si02) x = 1 (20N,2080Si02) x = 2 (33Na2067Si02) x = 4 (50Na20.50Si02)
1.641 1.652 1.663 1.677
1.565 1.584 1.606
2.631 2.642 2.653 2.654
1.839 1.846 1.815
109.45 109.37 109.34 109.25
142.18 138.94 139.41 135.69
X-ray Diffraction 1.62 1.62
2.65 2.65
2.35
1431
Neutron Diffraction 1.613 1.631
2.628 2.66
109.1 109.3
146h
2.62 2.62 2.62
109.4 109.4 109.4
152.8 151.8 150.5
2.61-2.68 2.62-2.71
107.54-1 13.20 103.06-1 16.89
138.93-160.04 133.72
M D Simulation 1.61 1.61 1.62 a-Na&Olf Na2Si03f
1.61-1.64 1.67-1.68
2.25 2.28 2.28 Crystals (X-ray Diffraction) 1.578 2.29-2.60 1.592 2.28-2.55
'Average values of Table I arc listed. bReferencc IC. CReferencela. dReference 11. .Reference 40. fReference 38. rReferena 37. *Reference 39.
functions of 0 have only a minor influence on the electronic properties of the siloxane bond.27-29
3. Rewlts 3.1. OptimiZea Geometry. Table I lists the optimized parameters of Hb$i207Na, molecules at the HF/STO-3G level. Also, the experimental values obtained by X-ray1J7.38and neutron scattering"f9 methods for sodium silicate systems and the results of molecular dynamics (MD) calculationsa simulating the structure of sodium silicate glasses are given in Table 11. We notice that the calculated Na-O bond lengths are particularly shorter (-0.5 A) than the corresponding observed bond lengths. These errors in lengths for the Na-O bonds are probably due to the minimal STO-3G basii set employed in this optimization procedure; it has been reported that for bonds between oxygen and electropositive elements such minimal basii sets generally yield bond lengths shorter than experimental values." In spite of this drawback, other optimized parameters are substantially in agreement with the experimental and calculated values of the glascs and crystals to which the model molecules correspond (see Table 11). Moreover, our calculations reproduce the experimental results that the S i 4 bond length of sodium silicate glasses increases with increasing Na20 content. We, therefore, consider that even the optimized geometries of such small clusters calculated with the STO-3G basis set can simulate the total structure of the corresponding sodium silicate systems. 3.2. Molecular Orbital Structure. Molecular orbital energies of the model clusters were calculated at three levels, STO-3G, 3-21G, and 3-21G+d(Si), using STO-3G optimized geometries. The results of these calculations have the same basic feature; that is, all energy levels in clusters He&O7Nax are destabilized as x increases. A typical energy diagram for the valence states of the clusters is illustrated in Figure 2; this is the result of the single-point calculation with the 3-21G+d(Si) basis set. The valence orbitals can be separated into the following sets. The highest energy valence orbitals (labeled A in Figure 2a) are best described as nonbonding 0 2ptype orbitals. The next set (labeled B in Figure 2a) are the main a-bonding orbitals with (37) Zmzycki, J. Verres Refrucr. 1957, 11, 3. (38) (a) Pant, A. K.; Cruiclrrhank, D. W. J. Acta Crysrullogr., Secr. B 1%8,24,13. (b) McDonald, W.S.;Cruicbhank, D. W. J. Acru Crysrullogr. 1967. - - - ., -22. -, -37. .. (39) Milligan, W. 0.;Levy, H.A.; Peterson, S.W. Phys. Rcu. 1951, 83,
226.
(40)Mitra, S.K.;Hockncy, R. W. Phil. Mug.B 1983,48, 151. (41) Hehre, W. J.; Radom, L.; Schleyer, P. V. R.;Poplc, J. A. Ab lnlrlo hfoleculur Orblrul Theory; Wilcy-Interscience: New York, 1986; p 140.
-6r
a
X=4
-1
- 10
-2f
iI
--
I -
-
-
J
-22L -
j
7 -31
llbo-
- I
- n
-
- -
-31
Figure 2. Occupied valence orbitals of model clusters at the 3-2lG+d(Si) level. STO-3G optimized geometries were used. (a) Higher energy region: The sets of the longest lines, second longest lines, and shortest lines indicate the regions A, B', and B, respectively. (b) Lower energy region: The orbitals localized at nonbridging oxygens arc labeled "nbo".
substantial Si 3s or 3p or 0 2p character. However, the boundary between these two sets, A and B, is obscure especially for the clusters containing Na atoms, because there are several orbitals with both nonbonding 0 2p and a-bonding characters in the intermediate region. These orbitals are labeled B' in Figure 2a. The lowest energy valence orbitals (labeled C in Figure 2b) are mostly nonbonding 0 2s in character. Each orbital in region C is nearly localized at a particular oxygen atom and has some Si 3s or 3p and Na 2p (for orbitals of nonbridging oxygens) character. As shown in Figure 1, the three oxygen atoms 01.02, and 0 5 and the two silicon atoms S1 and S2 are located on the same y-z plane. Hence, r-type bondings are formed by overlapping atomic orbitals of these atoms out of this plane. That is, the molecular
5458 The Journal of Physical Chemistry, Vol. 95, No. 14, 1991
Uchino et al.
TABLE 111: Mrllikca Atomic cbrrges, Si d PopuLtlonr, and Bond Overlap PopuhtioaS for &3i2@N8,
Clustem 011 STO-3C Optimized
Geometries' x=o
x = l
x=2
x=4
Atomic Charges -1.12 -0.84 -0.85 -0.85 -0.84 -0.85 -0.85 1.93
-0.80 -0.72 -0.73 -0.73 -0.72 -0.73 -0.73 +1.45
+
-1.11 -1.04 -0.86 -0.86 -0.85 -0.84 -0.84 +1.91 +0.76
-0.82 -0.876 -0.75 -0.75 -0.74 -0.73 -0.73 1 .42c 4-0.76
+
-1.12 -1.04 -0.85 -0.85 -1.04 -0.85 -0.85 +1.88 +0.73
-0.83 -0.8g6 -0.74 -0.74 -0.886 -0.74 -0.74 +1.40 +0.73
-1.10 -0.84 -1.04 -1.04 -0.84 -1.04 -1.04 +1.85 +0.66
-0.83 -0.75 -0.906 -0.906 -0.75 -0.906 -0.906 1.37 +0.65
+
Si d Populations 0.41
n(Si d)
0.42c
0.42
0.42
Bond Overlap Populations n(Si-Ob)d n(Si-Oab) n(O,b-Na)
0.48
0.70
0.45 0.63 0.29
0.67 0.90 0.29
0.42 0.61 0.30
0.63 0.86 0.30
0.40 0.53 0.33
0.60 0.78 0.33
'Left and right a l u m s for each x value are the results of single-point calculations with the 3-21G and 3-21G+d(Si) basis sets, respectively. *Nonbtidging oxygen. 'Average value of Si1 and Si2. dAverage value of all %-Ob bonds. TABLE I V Mulllken r Overlap Populltioas for Si+H~,.si&N8~M d C l w t e d n[Si(p)-O(p)], n[Si(d)-O(p)], tot.
x-0
x = l
x=2
0.0787 0.0502 0.1289
0.0788 0.0486 0.1274
0.0799 0.0477 0.1276
Bonds in x=4 0.0908 0.0410 0.1318
oCalculations were performed with the 3-21G+d(Si) basis set and optimized STO-3G geometries.
orbitals constructed mainly as a linear combination of the px, d,, and pxr orbitals of these atoms represent r-type bonding orbitals. However, molecular orbitals representing other T bondings, namely, ?r bondings between oxygen 0 3 , 0 4 , 0 6 , and 0 7 and silicon SI and S2 atoms, are not discerned by analyzing the linear weighting coefficients of the atomic orbitals, because the directions perpendicular to the local Si0 vectors do no coincide with the directions of the coordinate axes in Figure 1. The molecular orbitals describing r-type bondings out of the yz plane are marked by wedges in Figure 2a. In these orbitals, there was not any mixing of the 0 2px orbitals of 0 1 , 0 2 , and 05 atoms and the Si 2p,, 2p,, d d ,and d9 orbitals, but a considerable mixing of 0 2p, orbitab odhe oxygen atoms and Si 2p, d, and d, orbitals, which mixing indicates the overlap of the *-electrons in the Si-01, Si-02, and S i 4 5 bonds. The molecular orbitals with &onding character are mainly located in the region B', at the top of region B or at the bottom of region A. Other lower energy orbitals that are not shown in Figure 2 were found to be almost completely localized at the core levels of each atom. In spite of such localization, slight energy differences were seen among the core orbitals, in particular, the orbitals localized at the 0 1s level. As will be discussed later, the energy difference reflects different bonding environmentsof oxygens in each cluster. 3.3. Mullikm Population Analysis. An additional property of considerable interest for the model clusters is the charge distribution obtained from a Mulliken population analysis.42 As has been pointed out by several researcher^,'^ the charge on an atom in a molecule can never be defined uniquely and it is not subject to experimental measurement. Nevertheless, the Mulliken approach is widely used for qualitative discussions of bonding or for comparing electron distribution in a series of related molecules. Relevant Mulliken charges and overlap populations calculated with the 3-21G and 3-21G+d(Si) basis sets are collected in Tables 111 and IV. 3.4. Comparison with Experiments. 3.4.1. XPS Spectra. The frozen-structure approximation describes the remaining electrons (42) Mulliken, R. S.J. Chem. Phys. 1955, 23, 1833. (43) Reference 41, pp 25-29.
after an ionization by the same wave functions as in the initial state. Koopmans' theoreqU which equates binding energy to the negative of the one-electron energy of the corresponding orbital, is based on this concept. The 0 1s core binding energies calculated from Koopmans' theorem at the 3-21G+d(Si) level together with experimental values obtained by XPS are given in Table V. As we expect in view of our use of Koopmans' theorem, which neglects the electronic reorganization energy, there is a considerable discrepancy between calculated and experimental binding energies. However, it has been recognized that for atoms in the same molecule the relative energy shifts of the core levels can be estimated reliably by Koopmans' theorem," and split-valence basis sets tend to give better results for the chemical shift This is also true of our case. As shown in Table VI, the energy difference between bridging and nonbridging oxygens calculated with the STO-3G basis set only qualitatively agreed with experiment. On the other hand, calculated resultswith larger basis sets (3-21G and 3-21G+d(Si)) were in much better agreement; the energy differences between 0, and Onbwere calculated to be -2 eV and they decreased slightly with increasing x. 3.4.2. X-rayEmission Spectra. The K emission X-ray spectra of silica and silicate glasses have been interpreted in terms of molecular orbital theo~y;~'the Si Ka1,2 peak has been assigned to transitions from the Si 2p to the Si 1s levels and the main Si KB peak has been ascribed to transitions from the a-bonding orbitals to the Si Is levels. On the basis of these assignments, we calculated the Si Ka1,2 and KB peak energies. The energy of the transition was assumed to be the difference between the mean one-electron energies of the molecular orbitals involved in the transition, that is, the difference between the mean orbital energies in regions B and B' in Figure 2 and those of Si 1s levels. Thus, we ignored the changes in a wavefunction due to an ionization and a subsequent transition. The calculated values are given in Table VII. Sakka and MatsushitaI6 reported that the Si Ka1,2 peak energies of silica and silicate glasses are constant irrespective of the glass compositions, whereas the Si KB peak energy of sodium silicate glasses increases with increasing Na content. As shown in Table VII, our results are quantitatively in agreement with the experimental values. Furthermore, Dodd and Glen4' assumed that the high-energy shifts of the Si KB peak in silicate glasses are attributed to destabilization of the u-bonding orbitals. Their assumption is also supported by the MO calculationson our cluster models, because we have found that the molecular orbitals rep(44) Koopmans, T. Physica (Amsterdam) 1933, I , 104. (45) Meier, R. J. Chem. Phys. Lett. 1987, 138, 471. (46) Wyatt, J. F.; Hiller, I. H.; Saunders, V. R.;Conner, J. A,; Barber, M.J. Chem. Phys. 1971,54,5311. (47) Dodd,C. G.; Glen, G.L. J. Am. Ceram. Soc. 1970, 53, 322.
The Journal of Physical Chemistry, Vol. 95, No. 14, 1991 5459
Electronic Structure of Sodium Silicate Glasses
-
TABLE V: ClleULted 0 18 Core Bhdhg Eaugia (eV) Obtriaed by Kospmras’ Theorem at the 3-21C+d(Si) Lev# x
x = 1 (20Na2080Si02)
0 (SO2)
01 02,05 03, 04, 06, 0 7
556.38 556.60 556.65
av
556.60 540.0bc
03,04 01 06,07 05
02
x = 4 (50Na2O50SiO2)
x = 2 (33Na20.76Si02)
Bridging Oxygen 554.91 01 554.93 03, 04, 06, 0 7 555.70 555.81 555.33 536.ab
01 02, 0 5
553.77 554.38
551.30 552.44
554.26 534.46
Nonbridging Oxygen 553.02 02,05 534.66
552.06
552.28 532.46
03, 04, 06, 0 7
550.59
.STO-3G optimized geometries were used. Experimental XPS values (eV) are also shown. bReference 13, experimental value. eAn observed value for infrasil.
TABLE VI: Calculated a d Experimental Core Binding Energy Diffemcea (eV) between Bridging md NonbridOxygem‘ x = l x=2 (33Na20 (20Na20. 80Si02) 67Si02) Calculated Valuesb 5.57 4.52 2.35 2.01 2.31 1.98
STO-3G 3-21G 3-21G+d(Si)
x-4 (50Na205OSiO2) 4.34 1.46 1.41
XPS Results BrIlckner et al? Smets & Lommend
2.2 2.3
2.0 2.1
*Calculations were performed with STO-3G optimized geometries. b(Avcrage Ob 1s binding energy) ( 0 , b 1s binding energy). eReference 13. ‘Reference 14.
-
resenting the sigma bonding are destabilized more than those of the Si Is orbitals, and, as a result, the energy difference between the two types of orbitals (Le., Si KB peak energy) increases with increasing Na content. 3.4.3. UV spectra. The ultraviolet (UV) reflectance spectrum of Si02glass has been observed by a number of researcher^;^'^ it shows peaks at 10.3 eV, 11.5 eV, and higher energies. The 10.3-eV peak or the 11.5-eV peak has been assigned to a lowest interband transiti~n.Z’~”~On the other hand, DiStefano and Eastmans4 have found an interband gap of 9.0 eV in SiO, glass by photoconductivity measurements. These results indicate that the interband energy gap of amorphous silica lies between -9 and -1 1 eV. The band gap of the model clusters can be estimated as the eigenvalue difference between a highest occupied molecular orbital (HOMO) and a lowest unoccupied molecular orbital (LUMO). The HOMO and LUMO levels of the clusters along with the calculated values of each band gap are illustrated in Figure 3. The band gap for the cluster with x = 0 modeling silica was calculated to be 17.5 eV, which is considerably larger than the experimental value. This inamsistency probably lies in the LUMO at positive energy, which is the antibonding level of the S i 4 bond. Previously Tossell et al.25demonstrated that the calculation of the photoionization transition state of the cluster yields the LUMO at negative energy and, therefore, they obtained a reasonable band gap of IO eV. In this work, however, we did not try such a transition-state calculation for the cluster H6Si207. Besides, UV reflectance studies have shown that the 10.3-eV peak is broadened and a new absorption band arises at ca. 8 eV when alkali-metal oxide is incorporated into the SiO, structure.”’
- --
-
-
(48) Philip , H. R. Solid State Commun. 1966,4,73. (49) Loh, Solid State Commun. 1964, 2, 269. (50) PIatzodsr, K. Phys. Stat. Sol. 1968, 29, K63. (51) Pantelidcs, S. T.; H a r r h , W. A. Phys. Rcu. S 1976, 13, 2661. (52) Reilly, M.H. 1.Phys. Chem. Solids 1970, 31, 1041. (53) Ruffa, A. R. Phys. Status Solidi 1968, 29, 605. (54) DiStefano, T. H.; Eastman, D. E. Solid State Commun. 1971, 9, 2259.
8.
I 11.68
I
I
I
L L L ‘i A
Figure 3. HOMO-LUMO energy levels for model clusters at the 321G+d(Si) level. STO-3G optimized geometries were used. HOMOS are indicated by solid lines; LUMOs, by broken lines.
A similar trend has also been observed in the UV absorption spectra;, the transmission cutoff occurs at lower energies by several electronvolts upon further addition of Na into SiO, glass. These results demonstrate that the band gap of sodium silicate glasses d e m w as the concentration of NazO increases. Such decreasing of the band gap is indeed seen in Figure 3. Furthermore, we have found that the LUMOs in the clusters with x = 1,2, and 4 are mostly Na 3s in character. The presence of the Na 3s levels in the conduction band has been previously reported by Ellis et al.?5 who calculated the valence band structure of sodium disilicate, Na20-2Si02, using the extended Hiickel method. 4. Discussion 4.1. N d d z e d Effect of Na. As referred in section 3.4.2, Dodd and Glen47assumed that the high-energy shift of the Si K I ~ peak observed for silicate glasses is attributed to destabilization of the u-bonding orbitals. Furthermore, they proposed that the destabilization of the u-bonding orbitals results from progressive weakening of S i 4 bonds owing to the incorporation of alkalimetal oxides into the SiOz structure. Previous IR,8 Raman,’ and neutron scattering” studies have also suggested such overall weakening of S i 4 bonds owing to alkali-metal oxides in glasses. In general, alkali-metal ions in silicate glasses are considered to sit near the nonbridging oxygens in order to provide charge compensation; that is, the alkali-metal ions will be bonded to the nonbridging oxygens through Coulomb interaction. However, as has been pointed out by Bdckner et aI.,l33O the above experimental and calculated results intimate that the Na ions affect the electron density not only of the nonbridging oxygens but also of the bridging oxygens. In other words, the Na ions weaken the glass network not locally but collectively. The effect of Na ion is known as a “nonlocalized” effect.” The nonlocalized effect of Na can also be seen in the XPS spectra of sodium silicate glasses;1s15 the core binding energy of bridging oxygens is lowered as the concentrationof Na increases (see Table V). As shown in section 3.4.1, this phenomenon has (55) Ellis, E.; Johnson, D. W.; Breeze, A.; Magee, P. M.;Perkins, P. G. Phil. Mag.B 1979, 40, 105.
5460 The Journal of Physical Chemistry, Vol. 95, No.14, 1991
Uchino et al.
TABLE Vn: c.lcrhtcd ud okemd Si Et Jhi" lhergks (eV) x = 0 (SiO,)
3-21G 3-21G+d(Si) exptl
Kal,2 KO Kal,2 KB Ka 1,2
KB
1744.85 1844.6 1 1746.44 1845.30 1740.54c 1831.15c
x = 1 (20NaZO*80SiO2) x = 2 (33Na2067Si02) 1744.81 1744.81
1845.25 (Ab = 0.64) 1746.43 1845.89 (A = 0.59) A-Od A = 0.33d
1845.41 (A = 0.80) 1746.43 1846.03 ( A = 0.73) A-Od A = 0.77d
x = 4 (50Na2G50SiOz)
1744.82 1845.82 (A = 1.21) 1746.45 1846.41 (A = 1.11) A-Od A = lMd
"STO-3G equilibrium geometries were used for the calculations. b A is an absolute energy shift from the value for Si02. eReference 20. Reference 16. 'Reference 47.
-> ' A
v x.4 A X-2 0 x-1 x.0
6-
c)
5
c
-
: P 4 r
s
2-
1 4. Relative core binding energy shift of 0 and Si atom in clusters with x = 1.2, and 4 with reference to corresponding atom in the cluster with x = 1. The energies calculated at the 3-21G+d(Si) level are used. For symbols in this figure, see Figure 1.
been reproduced in our calculations. Then in order to evaluate the effect of Na upon the network-forming atoms (0and Si) in the clusters in more detail, we illustrate in Figure 4 the shift of core binding energy of the network-forming atoms in the clusters with x = 1, 2, and 4 relative to the corresponding atoms in the cluster with x = 0. The symbols with superscripts "center", "right", and "left" in Figure 4 correspond to the atoms in the center, right side, and left side of the clusters in Figure 1, respectively. Referring to the line for the cluster with x = 1, we see that the core binding energy of the nonbridging oxygen atom is affected most by the Na ion indeed, but we should note that the effect extends even Over the rest of atoms in the cluster. This figure thus shows the degree of energy destabilization of each atom caused by the Na atom in the cluster. As x increases further, the core electrons of 4 atoms are affected more by the newly introduced Na atoms. A d i n g l y , we see in Figure 4 that the energy shift of 0, lxa" larger, and the Ob and Onb atoms become energetically similar with increasing x. As referred to previously, this is consistent with the observed tendency shown in Table VI. Recently Murray and Ching'" have calculated the electronic structure of (NazO)x(Si02)l-xglasses (x = 0,0.018,0.111,0.222, and 0.333) based on models containing 162 atoms with riodic boundary conditions3zbusing the OLCAO m e t h ~ d . ' ~The structure of their models was built by using a combination of Keating and Lennard-Jones (LJ) types of potentials. Although their results showed the energy difference between Ob and Onb, the calculated difference increased with increasing Na20 content. Thii is a trend opposite to that of the experiments. They suggested that this discrepancy could be due to the use of a single effective oxygen potential to represent both the 0, and Onb atoms in their atomic models. In contrast to their results, our cluster calculations have reproduced the observed trend as shown above. Thus, we can conclude that the electronic structure of sodium silicate glasses can be given more exactly by MO calculations on small clusters whose geometries were optimized at the H F SCF level than those on larger clusters whose geometries were relaxed by using atomic potentials such as Keating and LJ potentials. In other words, in the case of silicate glasses precise calculations on small clusters tend to yield better results than rough calculations on much larger clusters. The conclusion is not surprising, because it has been demonstrated that the nature of the bonds in silica and silicates can be understood in terms of the electronic structure of the local-scale SiO, unit and Si-0-Si bridge in the glass networkeu
Briickner et once interpreted that the nonlocalized effect of Na ions is due to the direct coordination of the Na atoms not only with nonbridging oxygen but also with bridging oxygen atom on the basis of the concept of the multiple coordination of alkali-metal atoms. However, such direct interaction between Na and Ob atoms is not considered in the cluster calculations employed here. Nevertheless, our calculations have given comparable results with experiments and have reproduced the nonlocalized effect. This means that the nonlocalized effect is not necessarily due to the direct interaction of Na ions with bridging oxygens as s u g gated by Briickner et al., but it can also be explained by the simple cluster models in which alkali-metal atoms and nonbridging oxygens are singly attached and linked to the glass network rather like hydroxyl groups might be configured. In summary, our results show that the electronic states of network-forming atoms not adjacent to Na atoms are affected by the Na atoms, and we can interpret the nonlocalized effect in terms of such indirect interaction between the Na and network forming atoms. 4.2. Charge Distribution in Silicate Network. 4.2.1. Role of Si d (kbibla Numerous studies have established that core binding energy decreases approximately linearly with increasing charge on the test The most successful empirical comlation between core binding energy and atomic charge has been the pointcharge model presented by Siegbahn et aI.;% the core binding energy of the ith atom (EI)is given by or where ql is the atomic charge on the ith atom, V, is the molecular potential due to the surrounding atoms in the molecule
R , is the distance between nuclei i and j , and k, and I , are the constants determined empirically for the studied type of atom A. Later, Ellison and Larcoma demonstrated the theoretical grounds of this empirical formula. Since we have already shown that the calculated energy shift is satisfactorily compared with the experimental value, we can use this formula to estimate whether the calculated charges obtained here are realistic or not. Figure 5a,b shows plots of E, - VIversus q, at the 3-21G and 3-21G+d(Si) levels, respectively. The deviation from the linear relationship for the value at the 3-21G level is apparent. Moreover, calculated results at this level gave slightly more charged compared with Onb in the same cluster (see Table 111). This is inconsistent with the general concept of nonbridging oxygen bearing an increased negative charge. Hence, the atomic charges calculated with the basis set without Si d functions do not seem to represent a realistic charge distribution in the model clusters. (56) Slegbahn, K.; Nordliig, C.; Johanseon, G.; Hedmm, J.; Heden, P. F.; Hamnn, K.; Gelius, U.;Bergmark, T.; Werme, L. 0.;Manne, R.; Fhr, Y.ESCA Applied 10 Free Molecules; North-Holland: Amsterdam, 1969. (57) Baclch, H.; Snyder, L. C. Chem. Phys. Left, 1%9,3,333. ( 5 8 ) Hollander, J. M.;Henderickmn, D. N.;Jolly, W. L. J. Ch" Phys. 1968,19, 3315. (59) Schwartz, M.E. Chem. Phys. Lerr. 1910, 6, 631. (60) Ellison, F. 0.;Larcom, L.L. Chem. Phys. feu. 1911, IO, 580. Ellison, F. 0.; Larcom, L. L. Chem. Phys. k r r . 1972, 13, 399.
The Journal of Physical Chemistry, Vol. 95, No. 14, 1991 5461
Electronic Structure of Sodium Silicate Glasses
1 :::
5451
I
I
I
I
I
I
I
TABLE Vm: Compuirol of Atomic chrrga Obtriaed by Mereat Method#
a:0 X = l
M3
v
x=4
x x x x
-t
7 541
This WorP (Mulliken) +1.45 -0.74b +1.42 -0.75* +1.40 -0.76b +1.37 -0).78*
-0.87 -0.88 -0.90
+0.76 +0.73 +0.65
Pauling Procedure +1.27 -0.63 +1.25 -0.64 +1.23 -0.64 +1.20 -0.64
-0.96 -0.96 -0.96
+0.68 +0.68 +0.68
= 0 @ioz) = 1 (20NaZ0.80SiOz) = 2 (33Na20.67SiO2) = 4 (50Na20.50SiO2)
SiO; 20Na20.80SiOzd 33Naz0.67Si02d 50NaZ0.50SiOzd
‘Calculations pcrformed with the 3-21G+d(Si) basis set and optimum STO-3G geometries. Average values. c Reference 62. dReference 63.
*
-1.14
-1.06
-0.911
-0.90
-0.12
Atomic charge
results characterizing the electronic structure of sodium silicate are explained on the bask of the molecular orbital structure. In addition, it is known that the nature of the bonds can also be boX=O discussed in terms of the Mulliken population analysis, namely, atomic charge and bond overlap population?’” According to the consideration mentioned in section 4.2.1, one may approve that the result with the 3-21G+d(Si) basis set is the most appropriate OD for the estimation. A An intimate correlation between bond overlap population and bond strength has been well documented;z2,6sthe Si-0 covalent V bond strength is linearly correlated with the bond overlap population, while the ionic character of the Si-0 bond decreases with increasing the bond overlap population. Table 111shows that the 6 overlap population of the Si-Onbbond is larger than that of the S i a b bond in the same cluster. This indicates that for glasses 541 with the same composition Si-0,b bonds are stronger than Si+ bonds. We also see in Table 111 that the overlap populations of I I I I 1 I I I 1 the Si-Ob and Si-Onbbonds decrease with increasing x. At the -0.88 4.88 -0.80 4.12 -0.84 3-21G+d(Si) level the tendency is especially conspicuous for the Atomic charge Si-Onbbonds; accordingly, the overlap populations of the Figure 5. Correlation between atomic charge and calculated binding bonds draw near to those of the Si-Ob bonds. These results energy corrected for molecular potential: (a) 3-21G level; (b) 3-21G+demonstrate that both Si+ and Si-0,b bonds are weakened and d(Si) level. the nature of Ob and Onb electrons becomes energetically similar as the concentration of Na increases. As mentioned in sections Previous MO calculations for the cluster modeling silica have 3 and 4, this tendency is consistent with experiments. yielded a substantial population (0.4-0.6)of Si d electronsZ1”a*‘j1 ~ *-electron contribution to the Si-0 overlap populations but a negligibly small population (-lo wt %) amount of molecular water. Hence, we have proposed the following: (1) Molecular water present in glasses with low (- 10 wt %) water content interacts directly with Ob atoms in the silicate network and, as a result, the Si-Ob bonds are weakened severely. In general, the reactivity of the siloxane bond in the glass network is fairly low; then the Si-0-Si bridge in silica is not usually allowed to react with molecular water except for a strained S i U S i bond.74975However, our calculated results obtained here show that the electron density, in other words basicity, on 0, atoms increases with increasing Na content. This probably means that the reactivity of Ob atoms in sodium silicate glasses is intensified compared with that of silica. Moreover, the electrical conductivity measurements on hydrated sodium silicate glasses have shown that the mobility of Na ions increases as the concentration of water increases to over -3 wt %..la Such mobile Na ions will interact with the silicate network more extensively through the nonlocalized effect. Accordingly, the basicity of Ob atoms in hydrated sodium silicate glasses will be larger than that in dry glasses; the chemical reactivity of the Si-Obbond will be enhanced more. We hence believe that interaction between molecular water and Ob atoms in the silicate network begins to occur in the glasses containing a large amount (over 10 wt %) of water and the weakening of the S i U S i network observed in the spectra of the hydrated glasses is due to this interaction. 5. Conclusions Ab initio molecular orbital calculations on model clusters Hb$i207Nax (x = 0, 1, 2, and 4) have enabled us to obtain information on the electronic structure of sodium silicate glasses. Although the model clusters employed here are simple ones, calculated 0 1s core binding energies, Si Ka1,2 and yB peak energies, and UV excitation energies are in good agreement with the experiments. Our results clearly show that sodium ions affect the electronic state of network-forming atoms (Si and ob) not adjacent to the sodium ions. The nonlocalized effect of alkalimetal atoms observed experimentally for silicate glasses may be caused by such indirect interaction between alkali-metal atoms and network-forming atoms. In addition, we have shown that polarization d functions on Si are necessary to obtain realistic charge distributions in the clusters. Thus obtained atomic charges and overlap populations are also found to be useful for the discussion on the nature of the bonding in sodium silicate glasses.
Acknowledgment. We are grateful to the Data Processing Center of Kyoto University for providing the GAUSSIAN82 program and for the generous permission to use the FACOM M-780130 computer system. (74) Michalske, T. A,; Freiman, S.W. J. Am. Gram. Soc. 1983,66,284. (75) Morrow, B. A,; Cody, I. A. J. Phys. Chem. 1976,80, 1995. (76) Tahta, M.; Acocella, J.; Tomozawa, T.; Watson, E. B. J. Am. Ceram. Soc. 1981, 64, 719.
