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A density functional approach to the molecular structure, bonding and vibrational analysis of the SiOM (M = Na,K) molecules
THEO CHEM ELSEVIER
Journal of Molecular
Structure
(Theochem)
394 (1997) 25-31
A density functional approach to the molecular structure, bonding and vibrational analysis of the SiOM (M = Na,K) molecules M.E. Alikhani*, L.aboratoire
de Spectrochimie
MoltGxlaire
B. Tremblay
(URA 508). Universit&
‘, L. Manceron
P. et M. Curie, Boite 49, britiment
F74. 4 Place Jussieu.
Puris Cedex 05, France
Received 22 July 1996; accepted 23 October
1996
Abstract The structural properties and vibrational spectra of the SiO, SiO-, SiONa, and SiOK molecules have been calculated using density function@ theory. SiqNa and SiOK are calculated to have bent, L-shaped geometries, with fairly long O-M (M = Na,K) distance (2.17 A and 2.435 A, respectively) and Si-O-M bond angles close to 100”. The nature of the bonding within the different species has also been studied using Bader’s topological method. It appears that the interactions between the SiO molecule and Na (or K) atom result primarily from a charge transfer effect from the metal to the SiO subunit. The net transferred charge is essentially borne on the Si atom. The calculated moderately large red shift of the SiO stretching mode upon complexation agrees very well with the experimental result, and the positions of the yet unobserved low frequency stretching and bending modes are predicted. 0 1997 Elsevier Science B.V. Si OK molecule; Bonding analysis after Bader’s topological Density functional theory (B3LYP)
Keywords:
1. Introduction The study of silicon est both from
oxides
the scientific
is of considerable
inter-
of point of view and for
theoretical applications. In contrast to metal-monocarbonyl interactions [I- lo], there are still few experimental and theoretical investigations on the metal-silicon monoxide complexes. Recently Kiippe and coworkers recorded, for the first time, the infrared spectra of the Ag-SiO [I I. 121, Na-SiO, and K-SiO [ 131 complexes in solid
* Corresponding author. ’ Also at: LURE, Bit. 209D, LJniversitC Paris Sud, 91405 Orsay Cedex, France.
016 P/l
method; Vibrational
argon. They observed only the SiO stretching in the complexes. From a force-field analysis of the vibrational frequencies they had suggested a side-on coordination of SiO to Na and K atoms. On the other hand, from the IR spectra of isotopic effects, they interpreted the large red shift of the SiO vibrational frequency upon complexation as the consequence of the formation of ionic complexes (M’ (SiO)-, M = Ag, Na, and K). This bonding characterization had then been justified by comparison with the isolated anion (SiO)- properties. It is interesting to recall that for SiOAg the ESR observation [14] had indicated a 75% s spin density on the Ag atom. This result shows a small but still significant participation of the Ag p orbitals in the bonding, indicating a possible
I280/97/$17.00 Copyright 0 1997 Ekevier Science B.V. All rights reserved 166 1280(96)04925I
SO
analysis; Structural property:
M.E. Alikharzi et ul./Jorrmol
26
of M&cuiur
sideways bonding or bent structure. The linear structure calculated by Schaefer et al. [ 151 at the CISD level of theory is evidently inconsistent withe the ESR prediction, while the bent structure calculated by Tse [ 161 at the MP2 level of theory is in agreement with the experimental result. Nevertheless, in the latter work the calculated frequency shift of the SiO stretching mode, when complexed, is still twice smaller than the experimental value. It is now well known that the density functional theory (DFT) has become an accurate method to study the metal-ligand complexes [17-21 J. In this paper, the structural and vibrational properties of SiOM (M = Na and K) complexes have been studied using the DFT approach. Furthermore, in order to obtain a deeper understanding of the type of bond involved in these complexes, a topological study has been undertaken, using Bader’s method [22].
2. Methods of calculation Electronic calculations have been performed using the Gaussian 94/DFT quantum chemical package [23]. The DFT calculations have been carried out with the Becke’s three parameters functional (241 and the non-local transformed correction functional of Lee-Yang-Parr 1251. We have used the extended basis set of Bauschlicher et al. [26] for the potassium atom, and the 6-3 11 + G(2d) 6d basis set of Pople et al. [27] for the others. The study of the nature of bonding interactions of the systems undertaken in this paper has also been Table I Electronic
rs,-0
and geometrical
A
propenies
D, (kcal mol-‘)
P (D)
3. Results and discussion 3.1. Energetic and structural considerations Before performing calculations on the SiOM complexes, the subunits (sodium, potassium, and silicon monoxide) have been investigated at the same level of theory. The energies of the sodium and potassium are found to be -162.2885115 and atoms -599.9205809 a.u., respectively. The electronic properties and geometrical parameters are listed in Table 1. The calculated parameters of isolated SiO (bond length and dipole moment) are quite close to experimental values 1281, showing that the used basis set is well adapted. For the three other systems (SiO-, SiONa, and SiOK), there are no experimental data about the geometrical properties. From the calculated structural parameters (Table 2) two observations can be made. First, the alkali atom binds to the oxygen atom, carbonyl-like structures with attachment on the silicon end do not converge in our calculations. To give a quantitative idea of the relative instability of the Si-bonded structures, single-point calculations have been performed either with the same bond lengths and angle as those of the optimized geometries, or
SiOK
I.561
I .564
- 364.787261 - 3.65 0.32 6.9
2.170 2.919 101.6 - 527.095283 - 15.9 3.91 6.67
1.569 2.435 3.291 108.6 - 964.731276 - k8.4 6.54 6.44
(SiO).
1.514 (1.510) a
- 364.781441 h
0 I ‘ /SO(mdynA- )
performed using the Gaussian 94/DFT with the AIM = All keyword option. As it is still pointed out in the Gaussian 94 User’s Reference, the topological method sometimes fails, and the SiONa molecule represents such a case.
SiONa
SiO
(deg.1
E (au)
394 (1997) 25-31
of SiO, (SIO).. and SiOM (M = Na.K)
rM-0 rrv-s, ~+Ios,,
Srruc~urr (Throrhem)
3.23 (3.1) ’ 9.35
*The experimental value [28], is shown in parentheses. h Dissociation energies relative to SiO and M isolated fragments ’ SiO harmonic force constant.
M.E. Alikhani
Table 2 Bonding properties
et d/Journal
of Molecular
Sfrucrure
(Theochem)
21
394 (1997) 25-31
of SiO, (SiO)-, and SiOM (M = Na,K) a
Parameters
SiO
(SiO) -
SiONa h
SiOK
p(r,) o!LJ(r,) qs1 L 40
1.195 I.461 1.376 - 1.376
0.173 1.172 0.496 - 1.496
0.172 and 0.03 1 I. I63 and 0.208
I .456
1.461
0.168 and 0.033 1.139 and 0.159 0.795 - 1.522 0.727 1.296 0.320 0.276
qM
PC,-0 (1 PSI-M PO-M
a There are two bond critical points for SiOM complexes. h The AIM code fails in the case of SiONa, because the zero-flux surfaces are curved strongly enough to generate a very large number of rays. This job has failed with the message: too many interval subdivisions ’ qn indicates the atomic charges according to Bader [221. d P cl-8 indicates the covalent bond order [33]. a linear arrangement. The energies of both linear and bent structures M-SiO (M = Na, K) lie well above the dissociation energy by about 25 to 30 kcal mol-‘. The Si-0 bond lengths in SiONa and SiOK are longer than that of isolated SiO. Secondly, this lengthening (0.049 and 0.055 A for SiONa and SivK respectively) is similar to that of SiO- (0.047 A), maybe even a little greater. Moreover, the SiOM molecules are calculated to have strongly bent structures, with the Si-O-M bond angle close to 100”. This is unexpected in an entirely ionic picture, but may be not surprising, as other alkali-containing molecules had been found to have such bent structures: LiON [29] or Na and KCN 130,311. It is interesting to recall that carbon monoxide does not bind at the isolated pair level with either Na or K [7,32]. In contrast, silicon monoxide is calculated to form a stable adduct with both. The products are calculated here to be moderately strongly bound by - 15.9 and - 18.4 kcal mol-’ for SiONa and SiOK, respectively (values uncorrected for BSSE and ZPE effects). constraining
3.2. Bunding analysis The nature of bonding in SiO, SiO-, SiONa, and SiOK has been investigated with topological analysis of the electronic charge density, p, and its Laplacian, v*p [22]. In the topological electron density method developed by Bader, instead of partitioning the molecular
electron density via a spin-orbital occupation scheme (Hilbert space), as in the Mulliken procedure, the density is to be divided among the atoms based on the spatial distribution of the electron. The treatment of the bonding nature (polarity degree and bond order) by means of the topological theory of atoms in molecule may essentially be discussed using three independent observations. First, the positive values of the electron density Laplacian at the bond critical point (bcp) are usually associated with interactions between closed shell systems (ionic bonds, hydrogen bonds, and van der Waals molecules), whereas negative values usually indicate a dominance of shared interactions such as in covalent bonds. Secondly, a direct measure of the polarity or covalency of a bond is offered by the calculated covalent bond orders PAB and the Bader atomic charges of the atoms involved in the molecule. Finally, the study of the localized spin orbitals [33] provides, in addition, a possible interpretation about the bonding. 3.2.1. SiO molecule The topological study results are presented in Table 2. For the SiO free molecule, at the bond critical point (t-J, p(r,) is relatively small (0.195 e), and the value of V*p(r,) is positive. This observation indicates that the Si-0 bond already could be characterized with a high degree of ionicity. This conclusion is in line with the Bader atomic charges borne on the Si and 0 atoms ( 5 1.376 e), which are, furthermore, much larger than the charge density at bcp. The atomic populations of the localized orbitals
28
M.E. Alikhani et d/Journal
of Molecular Srructure (Theochem) 394 (1997) 25-31
offer an even more detailed picture of the Si-0 bonding (Table 3). This study clearly points out that, out of 11 occupied orbitals, three are mostly responsible for the bonding between the Si and 0 atoms, and that their ionic coefficients are quite large (78.9%, 74.6%, and 74.6%). Moreover, from the atomic occupancies of the localized orbitals corresponding to the Si-0 bonds, it can be shown that the atomic occupation is almost completely localized at the oxygen atom (89.5%, 87.3%, and 87.3%). Finally, in agreement with what is discussed above, the calculated covalent bond order, P s1o is small (1.456) compared to the expected value for a triple bond (3.0). This confirms the high degree ionicity of the Si-0 triple bond. 3.2.2. SiO- anion For the SiO- anion, the values of p(r,) is even slightly smaller than that of SiO, and V’p(r,) remains positive. This points out that the Si-0 bonding in SiO- is a closed-shell interaction in Bader’s sense. The Bader atomic charges (Table 2) indicate that the unpaired electron is completely borne on the Si atom. Furthermore, the spin orbital analysis in Table 3 shows that the triple bond of Si-0 is weakened upon electron attachment. The covalent bond order in SiO- presents a very slight increase with respect to that in SiO. Nevertheless, it still remains very small. 3.2.3. SiONa and SiOK molecules For each of these molecules there are two bond critical points. As Table 2 shows, the two values of p(r,) are very small. The p(r,) corresponding to the Table 3 Bond interpretation
O-M (M = Na and K) bond is five times smaller than that of the Si-0 bond, which is of comparable magnitude as in SiO-. The values of V2p(r,) are always positive, and the Laplacian values at O-M bcp are 0.2 1 or less, while those at Si-0 bcp are even slightly lower than in SiO-. One can readily conclude that the Si-0 bond remains largely polar, while the O-M bond (corresponding to the (SiO)-M bond) is even more ionic. This conclusion is largely corroborated by the atomic charge study (Table 2). Indeed, this indicates that a great proportion of the potassium valence electron (about 73%) is transferred to the SiO unit, and essentially borne on the Si atom. In addition, the covalent bond order of the Si-0 bond through the complexation is decreased relative to the P s,O in the SiO free molecule. The PslK and POK are actually very small, but nevertheless non-zero. The spin orbital analysis (Table 3) obviously points out that the SizO triple bond is reduced to a Si=O double bond from SiO to the SiOK adduct. Therefore, in agreement with the experimental interpretation, the bonding described by the topological analysis in the SiO-M adduct is mostly formed through a charge transfer interaction leading to a (SiO)- Mf pair. The parallel with the alkali metal cyanides, another family of ionic molecules, is quite striking. Na and KCN isolated molecules have been formed to have bent, L-shaped structures with an almost perpendicular bonding between the K-N and CrN coordinates [ 30,3 11. These unexpected structures have been reproduced by ab initio calculations [34,35], but the reasons for the departure from an isocyanide linear structure, expected for an ionic molecule purely held by coulombic interactions, are not yet clear. Here, as
after localized spin orbitals
SiO
(SiO)
SiOK
All electrons: Triple bond 0-Si (78.9% Ion.) 0-Si (74.6% Ion.) 0-Si (74.6% Ion.)
alpha electrons: Double bond 0-Si (77.9% Ion.) 0-Si (73.7% Ion.)
alpha electrons: Double bond 0-Si (79.1% Ion.) 0-Si (77.6% Ion.)
beta electrons: Triple bond 0-Si (77.7% Ion.) 0-Si (74. I % Ion.) 0-Si (73.8% Ion.)
beta electrons: Double bond 0-Si (78.8% Ion.) 0-Si (77.9% Ion.)
M.E. Alikhani et al/Journal of Molecular Structure (Theochem) 394 (1997) 25-31
for the cyanides, the potential energy is remarkably flat with respect to the bending coordinate (see the low value of the v-( mode calculated here for KOSi, or estimated for KNC [30]), and incipient covalency indicated here by the electronic charge densities and covalent bond orders could tip the scale in favor of the bent structure. Finally, the weakening of the Si-0 bond upon complexation may be appreciated by studying the SiO force constant variation. According to the calculated results, the SiO force constant is reduced from 9.35 mdyn A-’ in the SiO free molecule to 6.9, 6.67, and 6.44 mdyn I\-’ for SiO-, SiONa, and SiOK, respectively. Note that it decreases from SiO- to SiOK. 3.3. Vibrational analysis In Table 4 are collected the vibrational frequencies of the SiO and SiOM (M = Na and K) molecules. The calculated vibrational analysis has been performed in the harmonic approximation. Before comparing DFT frequencies with available experimental data, it must be recalled that the experimental frequencies are not Table 4 Vibrational Isotopes asi_
frequencies
29
corrected for anharmonicity, thus the comparison between calculated and experimental values may only be considered as indicative of the main trends. As Table 4 shows, the calculated SiO frequencies in the SiO, SiONa, and SiOK molecules are in very good agreement with the experimental data. The harmonic vibrational frequency in the SiO- anion has been calculated to be 1073.3 cm-‘. More significative is a comparison of the frequency shifts upon complexation, for which the absence of anharmonicity correction is negligible. The red shift of the SiO mode upon electron attachment (SiO-) or complexation (SiONa and SiOK) is moderately large, around 200 cm-‘. This is in good agreement with the experimental value (198 cm-‘). Furthermore, it is interesting to compare the SiO frequency shift between the isotopic species, because the correction for anharmonicities plays a very little role. In the case of the SiONa molecule, ‘60/‘80 substitution leads to an experimental red shift of the SiO stretching mode of 36.5 cm-’ to be compared to 37.1 cm-‘, the DFT value. For the SiOK the agreement between experimental molecule, isotopic shifts and calculated counterparts is very good. For example, for the 28Si’h0/29Si’80 isotopic
(cm-‘) and infrared intensities (km mol-‘) (shown in parantheses)
of SiO and SiOM (M = Na,K) a
SiO
SiO”Na
SiO”“K
Mode character
1249.0 (56) 1229.6
156.3 (19) 330.2 (22) 1041.3 (597) 1013.9
130.8 (10) 275.8 (13) 1024.1 (652) 1025.0
v1 SiOM bending Ye OM stretching I,, SiO stretching
153.8 (18) 320.5 (22) 1004.2 (549) 977.4
129.0 (9) 130.8 (IO) 987.5 (600) 987.7
1241.2 (55)
155.2 (18) 330.2 (21) 1034.6 (592)
129.7 (10) 275.7 (13) 1017.6 (645) 1018.7
1195.8 (51)
152.8 (18) 320.4 (21) 997.2 (543)
127.9 (9) 265.5 (12) 980.7 (594) 981.2
IhO
DFT DFT DFT Exp. h 2RSi_ “0 Dfl DFT DFT Exp. h XSi_ lb. DFT DFT DFT Exp. ’ ?qsi_ ‘X0 DFT DFT DFT Exp. ’
1204.0 (52)
* Dm frequencies are calculated at the harmonic level. h Ref. [ 131 for the SiOM complex in solid argon, and Ref. [28] for the stretching
frequency
VI
in the SiO free molecule.
30
ME. Alikhani et d/Journal
of Molecular Structure (Theochem) 394 (1997) 25-31
substitutions the calculated shift is 43.4 cm-‘, close to 43.8 cm-‘, the experimental value. The infrared intensities are reported in Table 4. The infrared intensity of the SiO stretching mode is remarkably increased (more than one order of magnitude) through the complexation. In addition, the calculated intensity ratios Iv~SiO~lv~NaO~ and I (in SiONa and SiOK, respectively) provide v(SiOljfv(KO) a clear response to why only the SiO stretching mode has been observed experimentally’.
References [I]
B. Silvi, 0. Ayed and W.B. Person, J. Am. Chem. Sot.. 108 (1986) 8148.
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4. Conclusions
Schaefer III, J. Chem. Phys., 104 (1996) 3672. [9] C. Adamo and F. Lelj, J. Chem. Phys., 103 (1995)
The geometries, electronic structure and vibrational properties of SiONa and SiOK have been calculated. The binding energy in SiONa and SiOK has been calculated around 16 kcal mol-’ with respect to SiO and metal separated fragments. The shapes of SiONa and SiOK are predicted to be bent by some 109”. The bonding between SiO and Na (or K) can be described as mostly ionic. The calculated SiO force constant in the complexes presents a 30% reduction with respect to that of the free SiO molecule. This weakening translates the lengthening of the Si-0 bond. The SizO triple bond (in free SiO) is reduced to a Si=O double bond upon complexation. The DFT frequencies and predicted isotopic shifts are in good agreement with the experimental ones. This study also predicts the position of the O-M stretching and SiOM bending modes (~2 and ~3, respectively), particularly sensitive to the bonding and molecular shape, and yet to be observed.
[IO] R.
Foumier
and 1. Papai,
in D.P.
Chong
10605.
(ed.),
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Advances in Density Functional Methods, Part I, World Scientilic. Singapore, 1995.
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[ 131 R.
Kiippe and H. Schnockel, Heteroatom
Chem., 3 (1992)
329. 1141 J.H.B. Chenier. J.A. Howard,
H.A. JoIy, B. Mile and P.L.
Timms, J. Chem. Sot.. Chem. Commun., (1990) 581.
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Goursot. I. Papai and D.R. Salahub. J. Am. Chem. Sot., I I4
(1992) 7452. [20] F. Sim, A. St-Amant, I. Papai and D.R. Salahub, J. Am. Chem. Sot.. I I4 (1992) 4391. ]?I]
D.R. Salahub and N. Russo (eds.), Metal-Ligand
Interactions:
From Atoms to Clusters to Surfaces, Kluwer,
Boston, MA,
1992.
Acknowledgements
]22] R.F.W.
Bader, Atoms in Molecules:
[23] Gausstan 94 (Revision A.I),
All calculations have been carried out on the computer CRAY 98 at Idris, Orsay, 91403, France, which is gratefully acknowledged.
Schlegel. P.M.W. reman, T.A.
Theory,
M.J. Frisch, G.W. Trucks, H.B.
Gill, B.G. Johnson, M.A. Robb, JR
Keith, G.A.
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Petersson, J.A. Montgomery,
Raghavachari, M.A. Al-Laham,
V.G. Zakrzewski,
K.
J.V. Orttz,
J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe,
xof us (BT and LM) have unsuccessfully attempted to observe the low fre uency Y? and Y? modes of SiOK isolated in argon matrix. The *9 Si/2?Si/‘oSi isotooic structure on Y, of SiOK was clearly observed, but the vz and Ye vibrations could not be detected even with samples where Y, had 1.0 or more of optical density. With their spectral signal to noise ratio, this meant that v2 and Ye are, at least, 40 times weaker than v ,, in good agreement with the DFT prediction.
A Quantum
Oxford University Press, Oxford, 1994.
C.Y.
Peng, P.Y. Ayalas, W. Chen, M.W.
Wong, J.L. Andre& ES.
Replogle,
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D.J. Fox.
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Bauschlicher Jr., S.R. Langhoff
Chem. Phys., 84
(1986)901.
and H. Partridge, J.
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et al.Noumal
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J.S. Binkley, R. Seeger and J.A. Pople, J. Chem. Phys., 72 (1980) 650; M.J. Frisch, J.A. Pople and J.S. Binkley, J. Chem. Phys., 80 (1984) 3265 [28] K.P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure Constant of Diatomic Molecules, van Nostrand Reinhold, New York, 1979. 1291 D.E. Tevault and L. Andrews, J. Phys. Chem., 77 (1973) 1640. [30] T. Thing.
J.P. Bekooy, W.L. Meerts, J. Hoeft, E. Tiemann and A. Dymanus. J. Chem. Phys., 73 (1980) 4875.
Structure
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394 (1997) 25-31
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Journal of Molecular
Structure
(Theochem)
394 (1997) 25-31
A density functional approach to the molecular structure, bonding and vibrational analysis of the SiOM (M = Na,K) molecules M.E. Alikhani*, L.aboratoire
de Spectrochimie
MoltGxlaire
B. Tremblay
(URA 508). Universit&
‘, L. Manceron
P. et M. Curie, Boite 49, britiment
F74. 4 Place Jussieu.
Puris Cedex 05, France
Received 22 July 1996; accepted 23 October
1996
Abstract The structural properties and vibrational spectra of the SiO, SiO-, SiONa, and SiOK molecules have been calculated using density function@ theory. SiqNa and SiOK are calculated to have bent, L-shaped geometries, with fairly long O-M (M = Na,K) distance (2.17 A and 2.435 A, respectively) and Si-O-M bond angles close to 100”. The nature of the bonding within the different species has also been studied using Bader’s topological method. It appears that the interactions between the SiO molecule and Na (or K) atom result primarily from a charge transfer effect from the metal to the SiO subunit. The net transferred charge is essentially borne on the Si atom. The calculated moderately large red shift of the SiO stretching mode upon complexation agrees very well with the experimental result, and the positions of the yet unobserved low frequency stretching and bending modes are predicted. 0 1997 Elsevier Science B.V. Si OK molecule; Bonding analysis after Bader’s topological Density functional theory (B3LYP)
Keywords:
1. Introduction The study of silicon est both from
oxides
the scientific
is of considerable
inter-
of point of view and for
theoretical applications. In contrast to metal-monocarbonyl interactions [I- lo], there are still few experimental and theoretical investigations on the metal-silicon monoxide complexes. Recently Kiippe and coworkers recorded, for the first time, the infrared spectra of the Ag-SiO [I I. 121, Na-SiO, and K-SiO [ 131 complexes in solid
* Corresponding author. ’ Also at: LURE, Bit. 209D, LJniversitC Paris Sud, 91405 Orsay Cedex, France.
016 P/l
method; Vibrational
argon. They observed only the SiO stretching in the complexes. From a force-field analysis of the vibrational frequencies they had suggested a side-on coordination of SiO to Na and K atoms. On the other hand, from the IR spectra of isotopic effects, they interpreted the large red shift of the SiO vibrational frequency upon complexation as the consequence of the formation of ionic complexes (M’ (SiO)-, M = Ag, Na, and K). This bonding characterization had then been justified by comparison with the isolated anion (SiO)- properties. It is interesting to recall that for SiOAg the ESR observation [14] had indicated a 75% s spin density on the Ag atom. This result shows a small but still significant participation of the Ag p orbitals in the bonding, indicating a possible
I280/97/$17.00 Copyright 0 1997 Ekevier Science B.V. All rights reserved 166 1280(96)04925I
SO
analysis; Structural property:
M.E. Alikharzi et ul./Jorrmol
26
of M&cuiur
sideways bonding or bent structure. The linear structure calculated by Schaefer et al. [ 151 at the CISD level of theory is evidently inconsistent withe the ESR prediction, while the bent structure calculated by Tse [ 161 at the MP2 level of theory is in agreement with the experimental result. Nevertheless, in the latter work the calculated frequency shift of the SiO stretching mode, when complexed, is still twice smaller than the experimental value. It is now well known that the density functional theory (DFT) has become an accurate method to study the metal-ligand complexes [17-21 J. In this paper, the structural and vibrational properties of SiOM (M = Na and K) complexes have been studied using the DFT approach. Furthermore, in order to obtain a deeper understanding of the type of bond involved in these complexes, a topological study has been undertaken, using Bader’s method [22].
2. Methods of calculation Electronic calculations have been performed using the Gaussian 94/DFT quantum chemical package [23]. The DFT calculations have been carried out with the Becke’s three parameters functional (241 and the non-local transformed correction functional of Lee-Yang-Parr 1251. We have used the extended basis set of Bauschlicher et al. [26] for the potassium atom, and the 6-3 11 + G(2d) 6d basis set of Pople et al. [27] for the others. The study of the nature of bonding interactions of the systems undertaken in this paper has also been Table I Electronic
rs,-0
and geometrical
A
propenies
D, (kcal mol-‘)
P (D)
3. Results and discussion 3.1. Energetic and structural considerations Before performing calculations on the SiOM complexes, the subunits (sodium, potassium, and silicon monoxide) have been investigated at the same level of theory. The energies of the sodium and potassium are found to be -162.2885115 and atoms -599.9205809 a.u., respectively. The electronic properties and geometrical parameters are listed in Table 1. The calculated parameters of isolated SiO (bond length and dipole moment) are quite close to experimental values 1281, showing that the used basis set is well adapted. For the three other systems (SiO-, SiONa, and SiOK), there are no experimental data about the geometrical properties. From the calculated structural parameters (Table 2) two observations can be made. First, the alkali atom binds to the oxygen atom, carbonyl-like structures with attachment on the silicon end do not converge in our calculations. To give a quantitative idea of the relative instability of the Si-bonded structures, single-point calculations have been performed either with the same bond lengths and angle as those of the optimized geometries, or
SiOK
I.561
I .564
- 364.787261 - 3.65 0.32 6.9
2.170 2.919 101.6 - 527.095283 - 15.9 3.91 6.67
1.569 2.435 3.291 108.6 - 964.731276 - k8.4 6.54 6.44
(SiO).
1.514 (1.510) a
- 364.781441 h
0 I ‘ /SO(mdynA- )
performed using the Gaussian 94/DFT with the AIM = All keyword option. As it is still pointed out in the Gaussian 94 User’s Reference, the topological method sometimes fails, and the SiONa molecule represents such a case.
SiONa
SiO
(deg.1
E (au)
394 (1997) 25-31
of SiO, (SIO).. and SiOM (M = Na.K)
rM-0 rrv-s, ~+Ios,,
Srruc~urr (Throrhem)
3.23 (3.1) ’ 9.35
*The experimental value [28], is shown in parentheses. h Dissociation energies relative to SiO and M isolated fragments ’ SiO harmonic force constant.
M.E. Alikhani
Table 2 Bonding properties
et d/Journal
of Molecular
Sfrucrure
(Theochem)
21
394 (1997) 25-31
of SiO, (SiO)-, and SiOM (M = Na,K) a
Parameters
SiO
(SiO) -
SiONa h
SiOK
p(r,) o!LJ(r,) qs1 L 40
1.195 I.461 1.376 - 1.376
0.173 1.172 0.496 - 1.496
0.172 and 0.03 1 I. I63 and 0.208
I .456
1.461
0.168 and 0.033 1.139 and 0.159 0.795 - 1.522 0.727 1.296 0.320 0.276
qM
PC,-0 (1 PSI-M PO-M
a There are two bond critical points for SiOM complexes. h The AIM code fails in the case of SiONa, because the zero-flux surfaces are curved strongly enough to generate a very large number of rays. This job has failed with the message: too many interval subdivisions ’ qn indicates the atomic charges according to Bader [221. d P cl-8 indicates the covalent bond order [33]. a linear arrangement. The energies of both linear and bent structures M-SiO (M = Na, K) lie well above the dissociation energy by about 25 to 30 kcal mol-‘. The Si-0 bond lengths in SiONa and SiOK are longer than that of isolated SiO. Secondly, this lengthening (0.049 and 0.055 A for SiONa and SivK respectively) is similar to that of SiO- (0.047 A), maybe even a little greater. Moreover, the SiOM molecules are calculated to have strongly bent structures, with the Si-O-M bond angle close to 100”. This is unexpected in an entirely ionic picture, but may be not surprising, as other alkali-containing molecules had been found to have such bent structures: LiON [29] or Na and KCN 130,311. It is interesting to recall that carbon monoxide does not bind at the isolated pair level with either Na or K [7,32]. In contrast, silicon monoxide is calculated to form a stable adduct with both. The products are calculated here to be moderately strongly bound by - 15.9 and - 18.4 kcal mol-’ for SiONa and SiOK, respectively (values uncorrected for BSSE and ZPE effects). constraining
3.2. Bunding analysis The nature of bonding in SiO, SiO-, SiONa, and SiOK has been investigated with topological analysis of the electronic charge density, p, and its Laplacian, v*p [22]. In the topological electron density method developed by Bader, instead of partitioning the molecular
electron density via a spin-orbital occupation scheme (Hilbert space), as in the Mulliken procedure, the density is to be divided among the atoms based on the spatial distribution of the electron. The treatment of the bonding nature (polarity degree and bond order) by means of the topological theory of atoms in molecule may essentially be discussed using three independent observations. First, the positive values of the electron density Laplacian at the bond critical point (bcp) are usually associated with interactions between closed shell systems (ionic bonds, hydrogen bonds, and van der Waals molecules), whereas negative values usually indicate a dominance of shared interactions such as in covalent bonds. Secondly, a direct measure of the polarity or covalency of a bond is offered by the calculated covalent bond orders PAB and the Bader atomic charges of the atoms involved in the molecule. Finally, the study of the localized spin orbitals [33] provides, in addition, a possible interpretation about the bonding. 3.2.1. SiO molecule The topological study results are presented in Table 2. For the SiO free molecule, at the bond critical point (t-J, p(r,) is relatively small (0.195 e), and the value of V*p(r,) is positive. This observation indicates that the Si-0 bond already could be characterized with a high degree of ionicity. This conclusion is in line with the Bader atomic charges borne on the Si and 0 atoms ( 5 1.376 e), which are, furthermore, much larger than the charge density at bcp. The atomic populations of the localized orbitals
28
M.E. Alikhani et d/Journal
of Molecular Srructure (Theochem) 394 (1997) 25-31
offer an even more detailed picture of the Si-0 bonding (Table 3). This study clearly points out that, out of 11 occupied orbitals, three are mostly responsible for the bonding between the Si and 0 atoms, and that their ionic coefficients are quite large (78.9%, 74.6%, and 74.6%). Moreover, from the atomic occupancies of the localized orbitals corresponding to the Si-0 bonds, it can be shown that the atomic occupation is almost completely localized at the oxygen atom (89.5%, 87.3%, and 87.3%). Finally, in agreement with what is discussed above, the calculated covalent bond order, P s1o is small (1.456) compared to the expected value for a triple bond (3.0). This confirms the high degree ionicity of the Si-0 triple bond. 3.2.2. SiO- anion For the SiO- anion, the values of p(r,) is even slightly smaller than that of SiO, and V’p(r,) remains positive. This points out that the Si-0 bonding in SiO- is a closed-shell interaction in Bader’s sense. The Bader atomic charges (Table 2) indicate that the unpaired electron is completely borne on the Si atom. Furthermore, the spin orbital analysis in Table 3 shows that the triple bond of Si-0 is weakened upon electron attachment. The covalent bond order in SiO- presents a very slight increase with respect to that in SiO. Nevertheless, it still remains very small. 3.2.3. SiONa and SiOK molecules For each of these molecules there are two bond critical points. As Table 2 shows, the two values of p(r,) are very small. The p(r,) corresponding to the Table 3 Bond interpretation
O-M (M = Na and K) bond is five times smaller than that of the Si-0 bond, which is of comparable magnitude as in SiO-. The values of V2p(r,) are always positive, and the Laplacian values at O-M bcp are 0.2 1 or less, while those at Si-0 bcp are even slightly lower than in SiO-. One can readily conclude that the Si-0 bond remains largely polar, while the O-M bond (corresponding to the (SiO)-M bond) is even more ionic. This conclusion is largely corroborated by the atomic charge study (Table 2). Indeed, this indicates that a great proportion of the potassium valence electron (about 73%) is transferred to the SiO unit, and essentially borne on the Si atom. In addition, the covalent bond order of the Si-0 bond through the complexation is decreased relative to the P s,O in the SiO free molecule. The PslK and POK are actually very small, but nevertheless non-zero. The spin orbital analysis (Table 3) obviously points out that the SizO triple bond is reduced to a Si=O double bond from SiO to the SiOK adduct. Therefore, in agreement with the experimental interpretation, the bonding described by the topological analysis in the SiO-M adduct is mostly formed through a charge transfer interaction leading to a (SiO)- Mf pair. The parallel with the alkali metal cyanides, another family of ionic molecules, is quite striking. Na and KCN isolated molecules have been formed to have bent, L-shaped structures with an almost perpendicular bonding between the K-N and CrN coordinates [ 30,3 11. These unexpected structures have been reproduced by ab initio calculations [34,35], but the reasons for the departure from an isocyanide linear structure, expected for an ionic molecule purely held by coulombic interactions, are not yet clear. Here, as
after localized spin orbitals
SiO
(SiO)
SiOK
All electrons: Triple bond 0-Si (78.9% Ion.) 0-Si (74.6% Ion.) 0-Si (74.6% Ion.)
alpha electrons: Double bond 0-Si (77.9% Ion.) 0-Si (73.7% Ion.)
alpha electrons: Double bond 0-Si (79.1% Ion.) 0-Si (77.6% Ion.)
beta electrons: Triple bond 0-Si (77.7% Ion.) 0-Si (74. I % Ion.) 0-Si (73.8% Ion.)
beta electrons: Double bond 0-Si (78.8% Ion.) 0-Si (77.9% Ion.)
M.E. Alikhani et al/Journal of Molecular Structure (Theochem) 394 (1997) 25-31
for the cyanides, the potential energy is remarkably flat with respect to the bending coordinate (see the low value of the v-( mode calculated here for KOSi, or estimated for KNC [30]), and incipient covalency indicated here by the electronic charge densities and covalent bond orders could tip the scale in favor of the bent structure. Finally, the weakening of the Si-0 bond upon complexation may be appreciated by studying the SiO force constant variation. According to the calculated results, the SiO force constant is reduced from 9.35 mdyn A-’ in the SiO free molecule to 6.9, 6.67, and 6.44 mdyn I\-’ for SiO-, SiONa, and SiOK, respectively. Note that it decreases from SiO- to SiOK. 3.3. Vibrational analysis In Table 4 are collected the vibrational frequencies of the SiO and SiOM (M = Na and K) molecules. The calculated vibrational analysis has been performed in the harmonic approximation. Before comparing DFT frequencies with available experimental data, it must be recalled that the experimental frequencies are not Table 4 Vibrational Isotopes asi_
frequencies
29
corrected for anharmonicity, thus the comparison between calculated and experimental values may only be considered as indicative of the main trends. As Table 4 shows, the calculated SiO frequencies in the SiO, SiONa, and SiOK molecules are in very good agreement with the experimental data. The harmonic vibrational frequency in the SiO- anion has been calculated to be 1073.3 cm-‘. More significative is a comparison of the frequency shifts upon complexation, for which the absence of anharmonicity correction is negligible. The red shift of the SiO mode upon electron attachment (SiO-) or complexation (SiONa and SiOK) is moderately large, around 200 cm-‘. This is in good agreement with the experimental value (198 cm-‘). Furthermore, it is interesting to compare the SiO frequency shift between the isotopic species, because the correction for anharmonicities plays a very little role. In the case of the SiONa molecule, ‘60/‘80 substitution leads to an experimental red shift of the SiO stretching mode of 36.5 cm-’ to be compared to 37.1 cm-‘, the DFT value. For the SiOK the agreement between experimental molecule, isotopic shifts and calculated counterparts is very good. For example, for the 28Si’h0/29Si’80 isotopic
(cm-‘) and infrared intensities (km mol-‘) (shown in parantheses)
of SiO and SiOM (M = Na,K) a
SiO
SiO”Na
SiO”“K
Mode character
1249.0 (56) 1229.6
156.3 (19) 330.2 (22) 1041.3 (597) 1013.9
130.8 (10) 275.8 (13) 1024.1 (652) 1025.0
v1 SiOM bending Ye OM stretching I,, SiO stretching
153.8 (18) 320.5 (22) 1004.2 (549) 977.4
129.0 (9) 130.8 (IO) 987.5 (600) 987.7
1241.2 (55)
155.2 (18) 330.2 (21) 1034.6 (592)
129.7 (10) 275.7 (13) 1017.6 (645) 1018.7
1195.8 (51)
152.8 (18) 320.4 (21) 997.2 (543)
127.9 (9) 265.5 (12) 980.7 (594) 981.2
IhO
DFT DFT DFT Exp. h 2RSi_ “0 Dfl DFT DFT Exp. h XSi_ lb. DFT DFT DFT Exp. ’ ?qsi_ ‘X0 DFT DFT DFT Exp. ’
1204.0 (52)
* Dm frequencies are calculated at the harmonic level. h Ref. [ 131 for the SiOM complex in solid argon, and Ref. [28] for the stretching
frequency
VI
in the SiO free molecule.
30
ME. Alikhani et d/Journal
of Molecular Structure (Theochem) 394 (1997) 25-31
substitutions the calculated shift is 43.4 cm-‘, close to 43.8 cm-‘, the experimental value. The infrared intensities are reported in Table 4. The infrared intensity of the SiO stretching mode is remarkably increased (more than one order of magnitude) through the complexation. In addition, the calculated intensity ratios Iv~SiO~lv~NaO~ and I (in SiONa and SiOK, respectively) provide v(SiOljfv(KO) a clear response to why only the SiO stretching mode has been observed experimentally’.
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The geometries, electronic structure and vibrational properties of SiONa and SiOK have been calculated. The binding energy in SiONa and SiOK has been calculated around 16 kcal mol-’ with respect to SiO and metal separated fragments. The shapes of SiONa and SiOK are predicted to be bent by some 109”. The bonding between SiO and Na (or K) can be described as mostly ionic. The calculated SiO force constant in the complexes presents a 30% reduction with respect to that of the free SiO molecule. This weakening translates the lengthening of the Si-0 bond. The SizO triple bond (in free SiO) is reduced to a Si=O double bond upon complexation. The DFT frequencies and predicted isotopic shifts are in good agreement with the experimental ones. This study also predicts the position of the O-M stretching and SiOM bending modes (~2 and ~3, respectively), particularly sensitive to the bonding and molecular shape, and yet to be observed.
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xof us (BT and LM) have unsuccessfully attempted to observe the low fre uency Y? and Y? modes of SiOK isolated in argon matrix. The *9 Si/2?Si/‘oSi isotooic structure on Y, of SiOK was clearly observed, but the vz and Ye vibrations could not be detected even with samples where Y, had 1.0 or more of optical density. With their spectral signal to noise ratio, this meant that v2 and Ye are, at least, 40 times weaker than v ,, in good agreement with the DFT prediction.
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