J. Phys. Chem. 1985,89, 5476-5480
5476
first monolayer and the bulk polymer are small. However, the sensitivity of the Raman difference spectroscopic technique allows us to detect some small shifts in the Raman lines. For example, the oxidation-state and core-size marker line vl0 for the surface layer of poly(Cu(ProtoP)) is shifted by 0.6 cm-’ relative to the bulk polymer. Some small-intensity differences are also observed in these high-frequency Raman lines.
Conclusions Raman spectroscopy clearly demonstrates that polymerization occurs via oxidative saturation of the vinyl substituents of the porphyrin in a manner that is very similar to polymerization of M(ProtoP)DME.1,2 Changes in the absorption spectrum and Raman spectra of the porphyrin in the films are a result of (1) saturation of the vinyls, (2) exciton coupling, and (3) T-s aggregation of the porphyrin rings. Neither axial ligation of Ni and
Cu nor distortion from D4,,symmetry by packing forces occurs in the polymer films. Strong surface enhancement of the Raman spectra is observed on Ag, and slight differences between these spectra and those for bulk films are observable. The RDS technique has been applied to the study of adsorbed surface species for the first time. RDS will be required for detailed investigation of large aromatic molecules on surfaces because of the relatively small Raman shifts The SERS effect provides anticipated to occur upon ad~orption.’~ a powerful probe of submonolayer amounts of adsorbed metalloporphyrins and their structural and electronic properties.
Acknowledgment. This work was performed at Sandia National Laboratories and supported by the United States Department of Energy Contract DE-AC04-76DP00789 and the Gas Research Institute Contract 5082-260-0767.
Bonding in Silicon Nitrides Maureen M. Julian* and G . V. Gibbs Department of Geological Sciences, Virginia Polytechnic Institute and State University, Blacksburg. Virgina 24061 (Received: June 10, 1985)
The SiN bond lengths found in Si,N4 framework structures and isolated molecular species range between 1.70 and 1.78 A. Bond lengths calculated for silicon nitride molecules with molecular orbital methods fall in this range, provided the local connectedness and net effects of long-range coulomb fields are modeled. An energy surface is constructed for the disilazane group of HI3SiZN7and its total electron density as well as several deformation maps are calculated. A correlation is made between experimental bond lengths and percent s character for the SiN bond. The bond lengths and angles for framework Si3N4act as if they are determined by short-range forces.
Introduction Static properties, like geometries and charge density distribution, and dynamical properties, like force constants and vibrational frequencies, for the silica polymorphs can be modeled and generated by careful consideration of short-range structural parameters.’ Overall molecular shape is preserved when such molecules as disiloxane condense from a gas to a solid.* Furthermore, properties found in framework structures with disiloxane units have been traced to short-range effects. For example, the shapes and sizes of the SiOSi and SiSSi groups in gas-phase siloxane and silicon sulfide molecules are close to those of the solid silicates and t h i o ~ i l i c a t e s . ~Also ~ ~ the bond lengths and angles of boron polyanionsS and phosphate molecules6 agree with those found experimentally in the borate minerals and phosphate crystals, respectively. Bonding in nitrides is of theoretical interest.’ All three forms of Si3N4(a? 0: and amorphouslo) have tetrahedrally coordinated
TABLE I: Mean Bond Lengths and Ranges Found in Framework and
(1) Gibbs, G. V. Am. Mineral. 1982, 67, 421. (2) Barrow, M. J.; Ebsworth, E. A. V. J. Chem. Soc., Dalton Trans. 1982, 21 1. (3) Geisinger, K. L.; Gibbs. G . V. Phys. Chem. Miner. 1981, 7, 204. Newton, M. D.; Gibbs, G. V. Ibid. 1980, 6, 221. (4) Geisinger, K. L.; Gibbs, G. V.; Navrotsky, A. Phys. Chem. Miner. 1985, 11, 266. Navrotsky, A.; Geisinger, K. L.; McMillan, P.; Gibbs, G. V. Phys. Chem. Miner. 1985, 1 1 , 284. ( 5 ) Zheng-Gang, Z.; Boisen, M. B.; Finger, L. W.; Gibbs, G . V. Am.
silicon atoms bonded to trigonally coordinated nitrogen atoms. Figure 1 shows two unit cells of the crystal structure of /3-Si3N4. In this paper, molecular moieties, such as the entity shown exploded out of the unit cells, were conceptually snipped out of this structure and protonated to achieve neutrality. Then, the geometries of these moieties were optimized and the calculated results compared with the observed molecular and framework structures.
Mineral., in press. (6) O’Keeffe, M.; Domenges, B.; Gibbs, G. V. J . Phys. Chem. 1985.89, 2304. (7) Morgan, P. E. D. Proc. NATO Ado. Study Inst. Nitrogen Ceramics 1977, 23-40. (8) Kato, K.; Inoue, Z.; Kijima, K.; Kawad, A,; Tanaka, H.; Yamane, T. J . Am. Ceram. SOC.1975, 58, 90.
0022-3654/85/2089-5476$01.50/0
Molecular Compounds Containing B N Moieties”
no. of
framework a-SipN4 fi-Si3N4 LiSiON-a
independent bond lengths
(R(SiN)),
A
range,
A
ref 8 9 14
1.743 1.732 1.749 (R(SiN)),
1.715 to 1.759 1.704 to 1.767
molecular comDd unconstrained 18 8-membered ring 2
1.723
6-membered ring
8
1.732
1.688 to 1.759 15-32 1.722 to 1.73 33-34 1.695 to 1.749 28, 33,
5-membered ring 4-membered ring
2
1.747 1.744
1.732 to 1.762 41-42 1.742 t o 1.747 28, 43-44
8 4 3 no. of
A
1.725
1.729 to 1.781 range.
A
ref
35-40 3
“Note that cu-Si,N4 can be considered as a framework of 6-membered rings and the 6 form as a framework of 8-membered rings.
(9) Grun, R.Acta Crystallogr., Sect. B 1979, 35, 800. (10) Stein, H. J.; Wells, V. A,; Hampy, R. W. J . Electrochem. SOC.1979, 126, 1750. Taylor, J. A. Science 1981, 7, 116. Jack, K. H. Chem. Ind. Chichester 1982, 271. Messier, D. R.; Schioler, L. J.; Quinn, G. D.; Napier, J. C. Ceram. Eng. Sci. Proc. 1981, 561.
0 1985 American Chemical Society
Bonding in Silicon Nitrides
The Journal of Physical Chemistry, Vol. 89, No. 25, 1985 5477 ometries found in silicon nitride framework structures are comparable with those found in molecules. Thus, we believe that molecular orbital calculations on representative moieties can provide insights into the forces that govern bond lengths and angle variations in silicon nitride crystals. From Table I, the weighted average SIN bond lengths in the framework structures is 1.741 A and in the molecular structures is 1.729 A. Despite the variety, all the molecular (R(SiN)) agree to within 0.01 with the framework structures.
Figure 1. Two unit cells of /3-Si3N4 shown with a representative Si2N7 unit extracted from the framework structure.
These comparisons involved bond lengths and angles, energy considerations, percentage s character, barriers to linearity, and various electron density maps, including total and deformation densities. The molecular orbital calculations were made with a version of the Brinkley et al." GAUSSIAN 80 program. Most calculations used a minimal STO-3G basis set, where each Slater type orbital is represented by linear combinations of three Gaussian functions.12 The HartreeFock procedure of Roothaan13 was used to calculate total molecular energies. The optimized configuration was reached by doing closely spaced, single-point calculations for various geometries. The minimum energy configuration was found by a least-squares fitting of the single point energies with a Morse curve. For some calculations a gradient optimization procedure or more robust bases, such as 6-31G* and 4-31GS*, were used. The program DENMAP, written by R. Stevens and modified by J. A. Tossell and L. W. Finger, was used to compute the electron density maps. Experimental values compiled in Table 18,9J444 show that ge(1 l ) Binkley, J. S.; Whiteside, R. A.; Krishnan, R.; Seeger, R.; De Frees, D. J.; Schlegel, H. B.; Topiol, S.;Kahn, L. R.; Pople, J. A. GAUSSIAN 80 Department of Chemistry, Carnegie-Mellon University, Pittsburg, PA, 1980. (12) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1969, 51, 2657. (13) Roothaan, C. C. J. Reu. Mod. Phys. 1951, 23, 69. (14) Laurent, Y.; Guyader, J.; Roult, G. Acta Crystallogr., Sect. B 1981, 37, 911. (15) Bradley, D. C.; Hursthouse, M. B.; Newing, C. W.; Welch, A. J. Chem. Commun. 1972, 567. (16) Sheldrick, G. M.; Taylor, R. J . Organomet. Chem. 1975, 87, 145. (17) Srinivasa, S. R.; Cartz, L.; Jorgensen, J. D.; Worlton, T. G.; Beyerlein, R. A.; Billy, M. J. Appl. Crystallogr. 1977, 10, 167. (18) Alcock, N. W.; Pierce-Butler, M. J . Chem. Soc.,Dalton Trans. 1975, 2469. (19) Clegg, W.; Noltemeyer, M.; Sheldrick, G. M.; Vater, N. Acta Crystallogr., Sect. B 1980, 36, 2461. (20) Clegg, W. Acra Crystallogr., Sect. C 1983, 39, 387. (21) Glidewell, C.; Holden, H. D. Acta Crystallogr., Sect. B 1981, 37,754. (22) Fjeldberg, T.; Lappert, M. F.; Thome, A. J. J. Mol. Struct. 1984,125, 265. (23) Jones, P. G. Acta Crystallogr., Sect. B 1979, 35, 1737. (24) Hursthouse, M. B.; Rodesiler, P. F. J. Chem. SOC.,Dalton Trans. 1972, 2100. (25) Sheldrick, G. M.; Taylor, R. J . Organomet. Chem. 1975, 101, 19. (26) Chioccola, G.; Daly, J. J. J . Chem. SOC.1968, 1658. (27) Clegg, W. Acra Crystallogr., Sect. B 1980, 36, 2830. (28) Engelhardt, U.; Metter, H.-P. Acta Crystallogr., Sect. B 1980, 36, 2086.
Molecular Orbital Calculations In this section, molecular orbital calculations will be given for six molecules. The goal is to find a few simple moieties that will successfully mimic the local geometry of a Si3N4crystal. H,SiN. In the crystal structure of Si3N4, each silicon atom is 4-coordinate and each nitrogen atom is 3-coordinate. For the molecule, we start with the isolated SIN entity. When three protons are attached to the silicon atom and two protons are attached to the nitrogen atom, the resulting configuration is the silylamine molecule, H3SiNH2. For this molecule, the optimized R(SiN) = 1.738 A, R ( N H ) = 1.003 A, LHNSi = 122.4', and R(SiH) = 1.424 A. However, unlike the planar configuration about the nitrogen atom in the crystal, the HzNSi group in the molecule is out of the plane by about 10'. Luke et al.45used a 3-21G* (d functions on silicon atom) basis on this molecule and found that the energies are virtually identical for either a staggered or a planar configuration about the nitrogen atom. Their R(SiN) is 1.710 A. The addition of d-type polarization functions on the silicon atoms decreases the SiN bond length by 0.03 A. Thus while the length of the SiN bond itself in the crystal is well mimicked by the optimized configuration of the H3SiNH2 molecule, the neighborhood of the nitrogen atom is not. Larger moieties of the Si3N4are needed. The next two sections focus on the tetrahedral configuration about the silicon atom found in H8N4Si and the trigonal configuration about the nitrogen atom found in H9Si3N. H8N4Si. To check the tetrahedral configuration about the silicon, silyltetraamine, Si(NH2)4,was constructed by placing four amine groups tetrahedrally around a silicon atom. The 6-31G* optimization gives R(SiN) = 1.722 A. This moiety is represented in the molecule18 Si(N=CPh3)4. There are two independent molecules to the asymmetric unit with an average SiN bond length = 1.707 A and an average NSiN angle = 109.53'. H9Si3N. Molecular orbital calculations were done on this molecule to test the planarity of the bonds surrounding the nitrogen atom. The nitrogen atom was displaced from the plane and the energy was calculated. The minimum energy with an STO-3G basis occurred when the configuration about the nitrogen atom was planar with R(SiN) = 1.740 A and LSiNSi = 120°, in agreement with the experimental data32of R(SiN) = 1.738 A, (29) Sheldrick, G. M.; Sheldrick, W. S.Inorg. Phys. Theor. 1969, 2279. (30) Clegg, W. Acra Crystallogr., Sect. C 1984, 40, 529. (31) Clegg, W.; Noltemeyer, M.; Sheldrick, G. M.; Vater, N. Acta. Crystallogr., Sect. B 1981, 37, 986. (32) Hedberg, J. K. J . Am. Chem. SOC.1955, 77, 6491. (33) Ertl, G.; Weiss, J. Z . Narurforsch. B 1974, 29, 803. (34) Shklover, V. E.; Bokii, N. G.; Struchkov, Y. T.; Andriano, K. A.; Zachernyuk, A. B.; Zhdanova, E. A. Zh. Struk. Khim. 1975, I S , 850. (35) Clegg, W.; Sheldrick, G. M.; Stalke, D. Acta Crystallogr., Sect. C 1984, 40, 816. (36) Clegg, W.; Sheldrick, G. M.; Stalke, D. Acta Crystallogr., Sect. C 1984, 40, 433. (37) Adamson, G. W.; Daly, J. J. J. Chem. SOC.1970, 2724. (38) Engelhardt, U.; Bunger, T.; Stromburg. B. Acta Crystallogr., Sect. B 1982, 38, 1173. (39) Engelhardt, U.; Metter, H.-P. Acta Crystallogr., Sect. B 1980, 36, 2086. (40) Daly, J. J.; Fink, W. Chem. Ber. 1964, 4958. (41) Clegg, W.; Noltemeyer, M.; Sheldrick, G. M. Acta Crystallogr., Sect. B 1979, 35, 2243. (42) Wheatley, P. J. J . Chem. SOC.1962, 1721. (43) Clegg, W.; Hasse, M.; Sheldrick, G. M.; Vater, N. Acta Crystallogr., Sect. C 1984, 40, 871. (44) Klebe, G.; Qui, D. T. Acta Crystallogr., Sect. C 1984, 40, 476. (45) Luke, B. T.; Pople, J. A,; Krogh-Jespersen, M. B.; Apeloig, Y.; Chandrasekhar, J.; Schleyer, P. v. R., to be submitted for publication.
5478 The Journal of Physical Chemistry, Vol. 89, No. 25, 1985 I 79 I
Julian and Gibbs method and the Morse curve method converge on the same optimized values. The values of the second derivatives with respect to r = R(SiN) and O = LSiNSi-that is the Hessian matrix-were ~ a l c u l a t e d . At ~ ~ the minimum of the energy the first derivative with respect to energy is zero. Thus we may use a Taylor expansion and write the energy difference equation as:
77
73
#E AE = '/2a2E(Ar)2 dr2 + =(Ar)(AO) 69
110
I20
I30
140
150
L S i NSi Figure 2. Potential energy surface for H,,Si2N7plotted as a function of its bridging length, R(SiN), and SiNSi angle. The energy represented by the contours corresponds to increments of 0.001 hartree (1 hartree = J). The data points plotted on the energy surfaces are 4.36 X appropriateexperimental data from ref 8 , 9 , and 14-49. The dashed line is the second-order energy ellipse of HI3Si2N7plotted at 0.0015 hartree above its minimum energy, and the dotted line is the second-order energy ellipse of H7SiiNalso plotted at 0.0015 hartree above its minimum energy. The data points were calculated by using a STO-3G basis.
LSiNSi = 119.6', and R(SiH) = 1.54 A. When the molecule was optimized with a 6-31G* basis on both N and Si and a 4-31G* basis on the H atoms, R(SiN) = 1.746 8, and R(SiH) = 1.475
A.
H7Si2N. Next we wished to see whether a simpler molecule with only two silicons and one hydrogen around the nitrogen atom maintains planarity about the nitrogen atom. Calculations for disilylamine, (H3Si)2NH,gave a planar configuration about the nitrogen atom with R(SiN) = 1.723 8, and LSiNSi = 128.3'. This angle is about 1' larger than the largest similar angle (127.36') observed in cu-Si3N4. When the proton is removed to form the ion N(SiH3)2-, the LSiNSi contracts to 113.72O which is about equal to the minimum similar angle found in both the a and p forms. Later, gradient optimization was used with a more robust basis of 6-31G* on both N and Si atoms and 4-31G** on the H atoms. Here R(SiN) = 1.735 8, and LSiNSi = 180', R (SiH) = 1.477 A. Thus H7Si2N is the smallest molecule that mimics the geometry of the Si3N4framework structures. HI3Si2N7.A larger molecule was constructed in which a nitrogen atom formed a bridge between two silicon atoms that in turn were tetrahedrally coordinated by nitrogen atoms. After protonation, HN(Si(NH )3)2 was optimized with a 6-31G* basis to give R(SiN) = 1.737 and LSiNSi = 134.2' for the bridging nitrogen. This moiety (without the protons) is shown exploded out of the P-Si3N4structure in Figure 1. Of the five molecules, for which the geometries were calculated in this section, only HJSiN did not exhibit the planar configuration found in the Si3N, framework structures. Energy Surface for H13Si2N7 Figure 2 shows the potential energy surface for H13Si2N7.More than 100 separate calculations were done for different pairs of bridging bond lengths and angles. The resulting total energies were plotted as a function of R(SiN) and LSiNSi and contoured. A study of the surface generated shows that the potential energy of this molecule varies slowly with angle and bridging distance in the vicinity of the minimum. However, the surface becomes much steeper if the bridging angle is less than 120'. Plotted on the energy surface are the experimental bond lengths and angles from all the compounds mentioned in this paper8~9J"40that have the appropriate SiNSi moiety and occur as unconstrained or in 6- or 8-membered rings. Notice that the experimental data points have LSiNSi bonds ranging from 110 to 145' and that the R(SiN) vary from about 1.69 to 1.79 8, or 1 8, with (R(SiN)) = 1.733 8,. The data follow the general trend of the surface even though the surface was calculated at 0 K and 0 pressure and the experimental data include lattice vibrations at room temperatures. After the calculations for the surface were completed, optimization programs became available. Both the gradient optimized
d2E + '/2-(AO)2 a02
The minimum occurs a t -955.1085 hartrees, thus the -955.1 100-hartree level is 0.0015 hartree above the minimum in the surface. In units of radians and bohrs the values substituted into the above equation give the following: 0.0015 =
Y2(0.9175 1)(Ar)2 + (-0.00643)( Ar)( AO)
+ y2(0.1654)(A8)2
This second-order equation is plotted as the dotted lines in Figure 2. Notice how closely this curve approximates the -955.1 10-hartree line in the same figure. Thus the shape of the well as far out as 7.7' and 0.030 A on either side of the energy minimum approximates an ellipse tilted at about an angle of 1.96'. Note that the cross term has a negative sign and is also relatively small, implying a weak correlation between r and 0. The main idea of this work is that the shapes of the molecules and therefore the shapes of the energy curves are similar for many different silicon nitrides. In the next section we will look at the deformation maps for H,Si2N. We were limited in our computations, or we would have used the HI3Si2N7molecule having the two adjacent tetrahedra. The second-order derivatives which make up the Hessian matrix were calculated for H7Si2Nin a 6-31G* basis. The minimum energy for this molecule is -636.3833 hartrees. If we choose a change in energy of 0.0015 hartree as before, then the second-order energy equation becomes as above: 0.0015 = '/2(0.60859)(Ar)2
+ 0.0138(Ar)(AO) + l/2(0.1238)(AR)2
This quadratic is plotted as dashed lines on Figure 2. The range of R(SiN) covers f0.037 %, and i ~ 8 . 9on~ either side of the minimum energy value. The dashed line falls just outside, but close to, the -955.1 100-hartree line even though the calculations are for another molecule calculated in a different basis with a different energy minimum. Note that the second ellipse tilts 6.5O in the opposite direction of the first. Again the cross term is relatively small, indicating a weak correlation between r and 0. For both ellipses the tilt is so close to zero that it is difficult to assign any meaning to the change in sign of the cross term. However, the dominant effect is that the two energy calculations fall so close to each other that we conclude that the short-range energy forces dominate the geometry. On Figure 2, experimental bond lengths and angles are overlaid on the energy map. A rough trend can be detected linking a longer bond length with a narrower LSiNSi. Hybridization is related to bond angle.6i4749 If only s and p orbitals are considered, then the fraction of the s character,& = 1/(1 - sec (LSiNSi)). Figure 3 shows the plot off, vs. bond length for both unconstrained and for 6- and 8-membered ring occurrences of the moiety SiNSi. When these two populations were plotted separately, the regression line did not shift significantly. This was expected since, as described earlier, 6- and 8-membered rings are present in Si3N4 framework structures. Admittedly the correlation is weak; nevertheless the trend is that the greatest percentage of s character indicates a shorter bond length. (46) Carsky, P.; Urban, M. "Ab initio Calculations"; Springer-Verlag: West Berlin, 1980. (47) Huheey, J. E. "Inorganic Chemistry"; Harper and Row: New York, 1978; 2nd ed, p 194. (48) Coulson, C. A. "Valence"; Oxford University Press: Oxford, U.K., 1961; 2nd ed. (49) Bingel, W. A,; Luttke, W. Angew. Chem., Inr. Ed. Engl. 1981, 20, 899.
The Journal of Physical Chemistry, Vol. 89, No. 25, 1985 5479
Bonding in Silicon Nitrides
0
0
= l I 1 7 4 Ic3 e
8
0
e
z
w
.
e
.
e
-J
0
n
5
. 0.
0
1 7 22 -
e
m
e e
1
0
I7Ot 0 28
e
0 32
0 36
0 40
0 44
fs Figure 3. Comparison of experimental SiN bond lengths vs. fraction of s character,f, = 1/(1 - sec (LSiNSi)).
Figure 5. Static deformation map of H,Si2N- through the N(SiH)2
moiety. isotropic shape of the nitrogen atom, which has its electron density directed along the SiN bonds and the N H bond. The minimum between the nitrogen and the silicon atoms indicates a bonded radius of 0.70 A for the silicon atom and of 1.03 8,for the nitrogen as measured along that bond. However, along the N H direction, the minimum for the nitrogen atom occurs at 0.70 A. Thus, the trigonal nitrogen atom is both elongated along the SiN directions and foreshortened along the N H direction. This compound also contains two different kinds of hydrogen atoms. When the hydrogen is an anion, its bonded radius is 0.79 A; and when the hydrogen is a cation, its radius shrinks to 0.30 A. Static Deformation Density Maps. In this case the electron density of the promolecule, pP(r),is subtracted from the total molecular density of the (bonded) molecule, p M ( r ) . The promolecule is a set of “unconnected” spherically averaged atoms in the same molecular configuration as the original molecule. Thus
W r ) = p M ( r )- pP(r) Note that the electron migration is an order of magnitude less than the total number of electrons in the molecule. Thus, the difference maps can exhibit such details as bonding densities, lone pair orbitals, and different polarizations of the SiH and N H hydrogen atoms. Note that the electron migration, while small, is the only contribution to the polarity of the molecule. In each deformation map, notice not only the buildup of electron density between the bonding atoms but also the decrease in the electron density in both positions directly behind the bond. Berlin5’ suggested a distinction between binding and bonding. Binding relates to forces acting on the nuclei in molecular formation, and bonding refers to the energy change occurring in molecular formation. Application of the Hellman-Feynman5* electrostatic theorem separates the force field into a binding region between the nuclei and an antibinding region behind the nuclei away from ’ , , . .... _‘ u :l--p_.J the. bond.53 Thus contributions to the binding can be made both Ib) by increasing the electron density between the bonding atoms and Figure 4. The molecule H7Si2Nthrough the planar HN(SiH), moiety. by decreasing the electron density in the antibinding region. (a) Total electron density map. The contours increase by factors of 2 Figure 4b is the deformation map of the same section shown beginning with e/A3. (b) Static deformation map. The contours for in the total electron density map in Figure 4a. Notice that the this and the following figures are plotted at 0.05 e/A3 where the zero line SiN bond has a buildup of 0.38 e/A3 between the atoms in the is a dashed line. Positive electron density is indicated by the solid lines binding region and two holes of 0.14 e/A3 on either side of the and negative electron density by the dashed lines. bond in the antibinding region. Thus, the nitrogen atom is surrounded by three electron density peaks and three holes. Electron Density Maps The peak position on the SiN bond is also about 0.66 8, away In this section we discuss a total electron density map and from the nitrogen atom. This distance is exactly the crystal radius several deformation mapsSofor H7Si2Ncalculated with a 6-31G* given by Slater.54 The direction of the shift, that is in the pobasis. Included also is a deformation map of the ion, H6Si2N, larization of the bond, is as expected from electronegativity to show what happens when the nitrogen is deprotonated. considerations, since nitrogen has a greater affinity for electrons Total Electron Density Map. Figure 4a shows the total electron density map in the plane of the HN(SiH), moiety of the H7Si2N molecule at the optimized configuration. The neighborhood of (51) Berlin, T. J . Chem. Phys. 1951, 19, 208. the silicon atom is essentially spherical compared with the an(52) Epstein, S. T. “The Force Concept in Chemistry”, Deb, B. M., Ed.; Van NosGand Reinhold: New York, 1981; p 1. (53) Spackman, M. A,; Maslen, E. N. Acta. Crysra//ogr.,Sect. A 1985, la)
I
(50) Coppens, P. “Electron Distributions and the Chemical Bond”; Plenum Press: New York, 1982; p 61.
41, 341. (54) Slater, J. J . Chem. Phys. 1964, 41, 3199.
5480 The Journal of Physical Chemistry, Vol. 89, No. 25, 1985
Julian and Gibbs
; < ' \ > > ,
- _ , I
~
I
,..'.......
..........
Figure 6. Static deformation map of H7Si2Nperpendicular to the plane of Figure 4 (a) through the SiN bond and (b) through the NH bond.
than silicon. The radius of the nitrogen atom along the SiN bond from Figure 4a (that is, at the minimum in the electron density along the SiN bond) is very close to the zero line in the difference map. When the hydrogen atom acts as an anion, as in the SiH bond, the electron density peak of 0.55 e/A3 is very close (about 0.06 A) to the hydrogen atom. On the other hand, when the hydrogen acts as a cation, as in the N H bond, the electron density peak of 0.60 e/A3 is about 0.24 A from the hydrogen atom. The map clearly shows that the electron-drawing ability of the anionic hydrogen is greater than that of the cationic hydrogen. Notice that the maximum of the electron density for the SiN bond lies on the line connecting the two bonded atoms. In Figure 5 , the cationic hydrogen was removed from the nitrogen and the deformation map of H6Si2N-was calculated for the plane of the N(SiH)2 moiety. The SiNSi angle is kept at the optimized value for the H7Si2N molecule. In this case, the maximum of the electron density is no longer on a line connecting the two bonded atoms but instead lies inside the SiNSi angle. The cationic hydrogen appears to attract this electron density peak and pull it onto the line connecting the silicon and nitrogen atoms. When this hydrogen io removed, the configuration relaxes and the peaks collapse inward. However when the H6Si2N-moiety is optimized with a 6-31G* basis, the SiNSi angle becomes 180'. Figure 6 shows the SiN and H N bonds through planes perpendicular to the plane of Figure 4. The nitrogen lone pair has symmetric maxima occurring at 0.20 8, above and below the nitrogen atom. The value of the electron density peak, 0.75 e/A3, is the largest peak observed on the deformation density map for this compound. Note that, for the SiN bond, the nitrogen lone
\,
I
I
'
I
\
,
,
I
\ - - , , '' , , #
Figure 7. Static deformation map of H7Si2Nat 0.2 A above (and parallel to) the plane of Figure 4 through the maximum in the lone pair above the nitrogen atom.
pair density appears to be shifted away from the anionic hydrogen. Experimental static deformation maps for diformohydrazide, H4C202N2,in the N N plane perpendicular to the approximate molecular plane show a similar accumulation above and below the trigonal nitrogen atoms.55 In this case the two lone pairs repel each other. Figure 7 shows the deformation plane at 0.20 A above and parallel to the plane of Figure 4. Thus, this section goes through the maximum in the nitrogen lone pair. The silicon atoms have disappeared. Also the lone pair of the nitrogen remains distinct from the peak maximums associated with the NH and SiN bonds.
Summary The SiN bond lengths found in Si3N4framework structures range from 1.70 to 1.78 A. The bond distances in small molecules lie within the bond distances found in framework Si,N4 structures. Furthermore, molecular orbital calculations give appropriate bond lengths as, for example, the optimized R(SiN) is 1.738 for silylamine, H3SiNH2. A larger moiety, such as disilyamine, HN(SiHJ2, is needed to model the planar trigonal configuration about the nitrogen atom. An energy surface for HI3Si2N7was generated and experimental data were superimposed upon this map. The data followed the general trend of the energy surface. Energy data from two different molecules, calculated in two different basis sets, fell close to one another on the energy surface, indicating that short-range forces dominate the geometry. A greater percentage of s character is associated with shorter bond lengths. Electron density and static deformation maps of the (H,Si),NH molecule with a 6-31G* basis exhibit bonding densities, lone pair orbitals, different polarizations of the SiH and N H bonds, and holes in the antibinding region. Acknowledgment. The National Science Foundation has supported this study with Grant EAR 82 18743 as has Virginia Polytechnic Institute and State University. We thank Dr. J. V. Silverton, Laboratory of Chemistry, National Heart, Lung and Blood Institute, National Institutes of Health for help in part of the literature search of compounds containing SiN bonds. We thank Prof. M. OKeeffe of the Chemistry Department of Arizona State University, Tempe, A Z for reading an earlier version of this paper and for his comments. We also thank Dr. Larry Finger of the Geophysical Laboratory of the Carnegie Institute for reviewing the manuscript and making several useful comments. Registry No. Si,N,, 12033-89-5; H13Si2N,,98799-79-2; Si, 7440-21-3; N2, 7727-37-9. ( 5 5 ) Eisenstein, M . Acta Crystallogr., S e a . B 1979, 35, 2614.
