Research: Science and Education
Should Gaseous BF3 and SiF4 Be Described as Ionic Compounds? Arne Haaland,* Trygve U. Helgaker, Kenneth Ruud, and D. J. Shorokhov Department of Chemistry, University of Oslo, PB 1033 Blindern, N-0315 Oslo, Norway; *
[email protected] In a thought-provoking article in the July 1998 issue of this Journal, R. J. Gillespie discussed the nature of the chemical bonds in binary fluorides of main group elements in the second and third periods (1). His discussion was based on net atomic charges calculated by the so-called Atoms In Molecules (AIM) approach: the total electron densities are calculated by ab initio methods, boundary surfaces between the atoms are drawn by invoking the “zero flux” criterion of Bader (2), and atomic charges are computed by integration of charge over the space allotted to each atom. The atomic charges thus obtained are listed in Table 1 (3). On the basis of the large atomic charges calculated for BF3 and SiF4, Gillespie suggested that these molecules are “much more ionic than has hitherto been supposed”, that “the fully ionic model is a much better description of the bonding than the fully covalent model”, and that “it provides a simple explanation of the bond lengths and bond energies”. Questions concerning the mean bond energies, the bond distances, or the most stable modification of the binary fluorides of the second and third period elements at standard temperature and pressure are scientific questions to which there are definite answers, though these will always be accompanied by some experimental uncertainty. The question of whether gaseous BF3 or SiF4 should be described as ionic or polar covalent compounds concerns our choice of words and the answer will depend on what we want to communicate to students or colleagues. We believe most chemists would use the term “ionic” to describe a molecule that (i) consists of more or less spherical ions carrying net charges approaching an integer number of elementary charges and (ii) for which the major contribution to the bonding energy is due to Coulomb attraction between these net charges. In the following we (i) use a spherical ion model to estimate the bond energies in these compounds for comparison with their experimental counterparts, (ii) estimate the bond dipole moments from the polarizabilities of the constituent ions for comparison with those calculated for spherical ions, (iii) calculate an alternative set of net atomic charges from the atomic polar tensors, (iv) compare the experimental bond distances with those obtained from a modified Schomaker– Stevensen rule, and (v) suggest that BF3 or SiF4 would, if they were ionic substances, aggregate to dimeric or polymeric species. The Spherical Ion Model and Mean Bond Energies In the following we use the simple spherical ion model, which is commonly and successfully used to calculate the energy of formation of an ionic solid from the gaseous neutral atoms (6, 7 ) A(g) + k X(g) → (A+k)(X 1)k(s) to calculate the energies of formation, ∆Ee, of the gaseous ion clusters A(g) + kF(g) → (A+k)(F 1)k(g)
1076
Mean bond energies may then be calculated from MBEe = ∆Ee /k (1) The formation of a gaseous ionic molecule (or ion cluster), AFk or (A+k)(F )k, from the gaseous neutral atoms may be divided into two steps: formation of the gaseous ions and formation of the ion cluster from the separated ions. Formation of the gaseous ions requires the energy Σ IEi (A) – k EA(F) where IEi is the ith ionization energy of the atom A and the sum extends from i = 1 to k, and EA(F) is the electron affinity of fluorine. Formation of the ion cluster from the separated Table 1. Net Atomic Charges and Bond Distances for Molecular Fluorides AFk in the Gas Phase A
k
Li
AIM a
APT b
Bond Distance/pm
q(F)/au
q(A)/au
q(F)/au
q(A)/au
Rexptlc
Rcalcd
1
0.94
0.94
0.86
0.86
156
165
Be
2
0.90
1.81
0.66
1.32
137
141
B
3
0.86
2.58
0.57
1.70
131
132
C
4
0.74
2.96
0.52
2.06
132
137
N
3
0.36
1.09
0.39
1.17
136
138
O
2
0.12
0.23
0.22
0.44
141
142
F
1
0.00
0.00
0.00
0.00
142
148
Na
1
0.94
0.94
0.88
0.88
193
199
Mg
2
0.91
1.83
0.75
1.50
177
183
Al
3
0.88
2.65
0.64
1.90
163
167
Si
4
0.86
3.42
0.60
2.39
155
161
P
3
0.84
2.51
0.59
1.78
156
160
S
2
0.71
1.43
0.47
0.95
159
160
Cl
1
0.50
0.50
0.28
0.28
163
163
aReference
1. bRuud, K.; Haaland, A.; Shorokhov, D. J.; Helgaker, T. U.; unpublished. cBond distances for LiF(g), NaF(g) and ClF(g) from ref 4, other bond distances from ref 5.
Table 2. Bond Energy and Polarity Data for Molecular Fluorides AFk in the Gas Phase MBE298/ kJ mol 1
MBEe / kmol 1
µ°/ D
µ*/µ°
1
608
7.51
0.16
1.75
594
6.59
0.42
2.42
351
6.28
0.68
3.08
310
6.31
0.85
1
482
9.25
0.09
513
1.75
470
8.50
0.20
3
589
2.42
474
7.83
0.35
4
593
3.08
320
7.47
0.51
A
k
Li
1
577
Be
2
636
B
3
642
C
4
489
Na
1
474
Mg
2
Al Si
Mk
NOTE: Experimental mean bond energies at 298 K (MBE298) were calculated from standard energies of formation listed in ref 8. “Molecular Madelung constants” ( M k), mean bond energies (MBE e), and bond polarities (µ°) were calculated from a spherical ion model. In the ratio µ */µ°, µ * is the induced dipole moment on the F anion (eq 7).
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ions is accompanied by an energy change k(+ke)(e)/(4πεoR) + [k(k – 1)/2] (e) /(4πεoRFF) + kB/(R) (2) 2
n
The first term in eq 2 represents the energy of Coulomb attraction between A+k and F ions, the second the Coulomb repulsion between F ions, and the third the Born repulsion between A+k and F ions. R is the A–F distance, RFF is the distance between the fluoride ions, εo is the permittivity of vacuum, and B is the Born constant. For calculations on solid alkali metal halides the exponent n is usually given a value between 6 and 11 (7); we shall use 10. In the case of a linear difluoride (BeF2 or MgF2) the first two terms in eq 2 may be combined to 1.75 (ke2/4πεoR) If we define a “molecular Madelung constant”, Mk = M2 = 1.75, the total energy of the ion cluster relative to the gaseous atoms may be written as E(R) = Σ IEi (A) – kEA(F) – Mk (ke2/4πεoR) + kB/R n The equilibrium bond distance satisfies the condition (dE /dR) = 0 or Mk(ke2/4πεoRe2) – nkB/Ren+1 = 0 This yields kB/Ren = Mk (ke2/4πεoRe) (1/n) and the energy of the ion cluster is given by Ee = Σ IEi (A) – kEA(F) – Mk (ke2/4πεoRe)(1 – 1/n) (3) Similar relationships are easily derived for trigonal planar AF3, M3 = 2.423, for tetrahedral AF4 clusters, M4 = 3.083, or for the gaseous ion pair AF, M1 = 1. The mean bond energies calculated from eq 1 are listed in Table 2. Comparison with experimental bond energies shows that these calculations based on a simple ionic model reproduce the bond energies of LiF(g) and NaF(g) to within 5%. Both bond energies are actually overestimated and the fit could be improved by including the vibrational energies of the AF molecules in the calculations. The bond energies of BeF2(g) and MgF2(g) are underestimated by 7 to 8%; the bond energy of AlF3(g), by 20%. The bond energies of BF3(g) and SiF4(g), however, are underestimated by about 45%. Inclusion of the vibrational energies of the molecules would increase the disparity between calculations and experiment. Finally, even though the computed AIM charges for the C and F atoms in CF4 are +2.96 and 0.74, respectively, the calculated MBEe turns out to be negative; the ion cluster is calculated to be thermodynamically less stable than the separated atoms. z− = −R z+ = 0 −e
+e
z
µο = e R −e
+e µ −*
−e
+e µ +*
Figure 1. Above: The electric dipole moment of the ion pair A+F . Below: Polarization of the anion (left) and of the cation (right). The directions of the dipole moments are indicated by vectors pointing from the negative to the positive pole.
The Polarizable Ion Model and Bond Polarities The spherical ion model is unphysical because it assumes that the cations and anions remain spherical when they are brought close together. In reality each ion will be deformed by the other. In this section we shall use the polarizable ion model (9) to estimate the polarity of the A–F bonds. If we assume that gaseous LiF or NaF consists of two spherical ions with net charges ±e and that the metal atom is situated at the origin and the F ion on the negative z-axis, the electric dipole moment of the ion pair is given by µ° = e z+ + ( e) z = ( e) z = eR
(4)
where R is the bond distance. See Figure 1. When an atom or monatomic ion is placed in an electric field, the nucleus and the electrons are pulled in opposite directions and the atom or ion is deformed. The center of gravity of the electron cloud no longer coincides with the nucleus, and the atom acquires an electronic dipole moment. If the strength of the electric field E is constant over the entire atom, the induced atomic dipole moment is given by µ* = αE + βE 2 + …
(5)
where α is the polarizability and β is the hyperpolarizability of the atom or ion (10). The polarizability is thus a measure of how easily the electron cloud is deformed by the electric field. Atomic polarizabilities decrease from left to right across the periodic table and increase with atomic number down a group. The polarizability of an atomic anion is significantly larger than that of the neutral atom, which in turn is significantly larger than that of the atomic cation. In Figure 1 we indicate how the cations and anions of a gaseous alkali metal halide polarize each other. The M+ cation generates an electric field at the nucleus of the anion: E = e/4πεoR 2
(6)
If we assume this field to be constant over the anion and if we omit higher-order terms in eq 5, the induced dipole moment on the anion is given by µ * = α E = α e/4πεoR 2 = α ′e/R 2
(7)
where α is the polarizability and α ′ = α /4πεo is the so-called polarizability volume of the anion (10). Similarly, the field generated by the anion will induce an atomic dipole moment on the cation: µ +* = α +′ e/R 2 and the total dipole moment of the ion pair is given by µ = µ° + µ* + µ +*
Note that while µ° (eq 4) is positive, the induced atomic or ionic dipoles are both negative. Their net effect is thus to reduce the magnitude of the overall dipole moment (see Fig. 1). Note also that polarization of the anion moves electron density into the overlap region; when polarization becomes sufficiently large, the polarizable ion model merges with a polar covalent bonding model. The experimental dipole moment of LiF is µexptl = 6.28 D as compared to µ° = eR = 7.41 D. Since the polarizability of the F ion is known to be much larger that the polarizability of the Li+ cation (9) we may write µ* = µexptl – eR
JChemEd.chem.wisc.edu • Vol. 77 No. 8 August 2000 • Journal of Chemical Education
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Research: Science and Education
The polarizability volume of the F ion depends on the environment; its value in a crystal or in a molecule will differ from that of the isolated ion (11). It may, however, be estimated by combining eqs 7 and 8; α′(F ) = 0.627 × 1030 m3
(9)
Because of their high symmetry, linear AF2, trigonal planar AF3, or tetrahedral AF4 molecules have molecular electric dipole moments equal to zero. We may, however, use the polarizable ion model to estimate bond dipoles. If we assume both cations and anions to be spherical, the central atom (A) to be placed at the origin of the coordinate system, and the F ion to be on the negative z-axis, the bond dipole moment may be defined as µ°(A–F) = k e z+ + ( e)z = ( e)z = eR
(10)
The electric fields generated by the F ligands will cancel at the nucleus of the central atom. The induced dipole moment of the cation will therefore be zero, while the induced dipole moment on the F ion is given by µ* = α′ Mk e/R 2
Figure 2. Constant electron density contour map in the molecular plane of the BF3 molecule. Lines perpendicular to the contours are lines along which the interatomic (zero flux) surfaces that separate one atom from another cut the molecular plane. Reproduced with permission from ref 1.
1.00
(11)
AIM
and the bond dipole is given by where Mk is the “molecular Madelung constant” defined in the preceding section. In Table 2, we list the bond dipole moments, µ°(A–F), calculated from eq 10 as well as the ratio µ*/µ°, where µ* is calculated from eq 11. It is seen that while the induced atomic dipoles in LiF or NaF reduce the overall bond dipole by 16 and 9%, respectively, the bond dipole moments of BF3, CF4, and SiF4 are reduced by 68, 85, and 51%, respectively. To put it simply: the induced dipole moments suggest that the electron transferred from A to F is moved halfway back to A—that is, into the overlap region. In this connection it may be useful to make comparisons with gaseous HF. In this molecule, which most chemists would describe as polar covalent rather than ionic, the experimental dipole moment is 58% smaller than calculated from eq 10. The calculations based on the spherical ion model thus indicate that the purported F anions in BF3 or SiF4 would be significantly distorted in the direction of polar covalency.1 Atomic Charges Calculated by the Atomic Polar Tensor Approach In Figure 2 we reproduce the constant electron density contours in the molecular plane of the BF3 molecule, and the lines separating the atoms indicated by the “zero flux” criterion (1, 3). It is noteworthy that the space allotted to the B atom is very small. The figure suggests that the allotted space includes only the K shell of the atom; electrons in the 2s or 2p atomic orbitals on B would presumably be found in those regions of space assigned to the F atoms. Such a division of space may have led to overestimation of the negative charges assigned to the F atoms and of the positive charge assigned to B. Perrin has offered convincing arguments that the zeroflux criterion generally will lead to exaggerated negative charges on the smaller and more electronegative of the bonded atoms (12 ). 1078
−Q (F )/e
(12)
0.50
APT
0.25
0.00 Li
Be
B
C
N
O
F
1.0
AIM 0.8
−Q (F )/e
µ(A–F) = µ°(A–F) + µ*
0.75
0.6
APT
0.4
0.2 Na
Mg
Al
Si
P
S
Cl
Figure 3. Comparison of net atomic charges on F atoms/ions in the gaseous fluorides of second- and third-period elements calculated by the AIM and ATP approaches.
We decided therefore to calculate the net atomic charges in these molecules by an alternative procedure, namely from the Atomic Polar Tensor (APT) (13). In the APT approach the net charge on each atom is determined by calculating the change of the electric dipole moment of the molecule when the atom is displaced from its equilibrium position. The physical basis for the calculations is easily understood by considering a diatomic molecule AB with net atomic charges equal to ±Q. The electric dipole moment is given by µAB = QR + µA* + µB*
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Research: Science and Education
The derivative of µAB with respect to the bond distance is determined numerically by increasing the bond distance by dR and calculating the change of the dipole moment dµAB. From eq 13 it follows that
170
R / pm
160
dµAB/dR = Q + R (dQ/dR) + (dµA*/dR ) + (dµB*/dR ) If the variation of Q and the atomic dipoles with bond distance may be neglected, the net atomic charge is given simply by (14)
High-level quantum chemical calculations on the binary fluorides of the second- and third-period elements yield the APT atomic charges listed in Table 1 (4 ). In Figure 3 we compare the net charges on the F atoms obtained by the two methods. It is seen that with the exception of NF3 and OF2, the APT approach yields smaller negative charges on the F atoms than the AIM; in most of the molecules studied (BeF2, BF3, CF4, and all the third-period compounds from AlF3 to ClF) the difference exceeds 0.2 au. The difference between the positive charges on the central atoms (A) depends on the number of F substituents; for BF3 the positive charge on the central atom is calculated to be 0.88 au smaller by APT; for CF4, 0.90 au smaller; and for SiF4, 1.03 au smaller. Most chemists would probably describe a molecule as consisting of approximately spherical, overlapping atoms or ions. If the choice is made to describe a molecule as consisting of sharply delineated, non-interpenetrating atoms, the zero-flux criterion provides a quantum-mechanically sound procedure for drawing the boundary surfaces (14 ). The shapes of the central atoms in BF3 or SiF4 thus obtained, are, however, far from spherical, and the net atomic charges are much higher than obtained by the APT approach. At the present time there is, in our view, no compelling reason for preferring one set of atomic charges over the other. Calculations by either approach may yield reliable information about the relative magnitude of atomic charges in related molecules, say CF4 and SiF4, but the absolute magnitudes of the atomic charges thus obtained should probably be regarded as less meaningful. A–F Bond Distances We now turn our attention to the A–F bond distances (see Table 1 and Fig. 4). Gillespie and coworkers noted that the bond distances in each of the two periods decrease from group 1 to group 13 or 14, and then increase slowly to group 17. They found that the bond distances up to BF3 in the second period and to SiF4 in the third are in better agreement with the sum of the ionic radii of the bonded atoms than with the sum of the covalent radii, and concluded that the bond distances in these compounds “are more consistent with an ionic than with a covalent model” (3). It is, however, well known that polar bonds tend to be shorter than the sum of the covalent radii (15 ), and some years ago we suggested a Modified Schomaker–Stevensen (MSS) rule for the prediction of polar covalent bond distances between atoms in groups 13 through 17: R(A – B) = rA + rB – c| χ A – χ B| n
Calc 140
(15)
where r and χ denote the bonding radii and electronegativity coefficients of the two bonded atoms, the constant c = 8.5 pm, and n = 1.4 (16 ). In combination with the associated bonding radii, this simple expression reproduces bond distances in
Exp 130 Li
Be
B
C
N
O
F
Si
P
S
Cl
200
190
Calc
R / pm
Q = dµAB/dR
150
180
170
Exp
160
150 Na
Mg
Al
Figure 4. Comparison of experimental and calculated (modified Schomaker–Stevensen rule, eq 15) bond distances in the gaseous fluorides of second- and third-period elements.
F
F
F
B
F F
B
B
B
F
B
F
F F
F F
F F
F F
B
A
D
C Sn
F
F F
F Sn
F
Sn
F
Sn Sn
F Sn
F
F
Sn
Sn F
F F
Figure 5. (A) A schematic representation of a possible polymeric chain form of BF3. (B) The structure of a dimer similar to that observed for AlCl3 in the gas phase (5 ) and for AlF3 in argon matrices (18, 19 ). (C) A possible layered structure of SiF4 similar to that of crystalline SnF4 (21). (D) A possible polymeric chain form of SiF4.
simple, gaseous compounds of elements in groups 13 through 17 with an average deviation of 2 pm (16 ). Use of the MSS rule yields the calculated A–F bond distances listed in Table 1 and displayed in Figure 4.2 The purely empirical relationship, eq 15, derived for polar bonds between elements in groups 13 through 17 is seen to reproduce the trends across the second and third period noted by Gillespie and coworkers. It reproduces the bond distance in BF3 to the nearest pm, while the Si–F bond distance in SiF4 is overestimated by 6 pm. We note, however, that the calculated bond distance reproduces the experimental Si–F bond distance in
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H3SiF, 159 pm (5 ), to within 2 pm. The shortening of the bond in SiF4 relative to H3SiF is commonly attributed to an increase of atomic charge on Si, hence increasing polarity of the Si–F bonds with increasing number of electronegative substituents (17). The MSS rule reproduces bond distances across the entire polarity range from nonpolar covalent to ionic bonds. There is no breakdown for the elements in groups 14, 13, or 2 signaling a transition to ionic bonding. We conclude that the observed bond distances in BF3 or SiF4 are equally consistent with descriptions in terms of ionic or polar covalent bonding. Physical States at Standard Temperature and Pressure Ionic compounds tend to form solids at room temperature. Thus the melting points of LiF, NaF and MgF2 are 845, 993, and 1261 °C, respectively, while solid BeF2 and AlF3 sublime at 800 and 1291 °C. Both BF3 and SiF4, however, are gaseous at room temperature. Crystalline AlF3 forms a three-dimensional network in which each Al atom/ion is surrounded by six F atoms/ions. In his article Gillespie suggests that formation of solid BF3 of similar structure is precluded because the B3+ ion is too small to be surrounded by six F (1). We find this suggestion reasonable, but since the B3+ ion is large enough to accommodate four F to form [BF4], we see no obvious reason why BF3, if it were ionic, should not form halogen-bridged polymers as indicated in Figure 5A—or at least dimers like those found in gaseous AlCl3 or in matrix isolated AlF3 (5, 18, 19) (see Fig. 5B). Gaseous BF3 under a pressure of 1 atm condenses to a liquid at 100 °C and freezes to a solid at 127 °C. The crystalline material contains molecular BF3 units with a B–F bond distance that is indistinguishable from that determined for the gaseous molecule, while the shortest distance between B and F atoms in different molecules is more than twice as long (20). Similarly we would expect SiF4, if it were ionic, to form a layered structure similar to that of solid SnF4 (21 ) (see Fig. 5C), or a polymeric chain structure as shown in Figure 5D. Conclusions Both AIM and APT calculations indicate that the B–F bonds in BF3 and the Si–F bonds in SiF4 are very polar, though the net atomic charges on the central atoms obtained by the APT approach are nearly a full elementary charge smaller than those obtained by the AIM method. The mean bond energies of BF3 and SiF4 calculated from the spherical ion model are less than 60% of the experimental value, and calculations on the polarizable ion model indicate that the F anions are strongly polarized in a manner indicating significant covalent bonding contributions. Finally, these compounds form monomeric gases at room temperature, whereas ionic compounds generally form oligomeric or polymeric aggregates that are stabilized through Coulomb attractions between oppositely charged ions. We believe that if the term “ionic compound” is taken to mean that it consists of nearly spherical ions carrying net charges approaching an integer number of elementary charges, and that the major contribution to the bonding energy is due to Coulomb attraction between these charges, then it would be misleading to refer to BF3 and SiF4 as ionic compounds. 1080
Acknowledgments We are grateful to R. J. Gillespie and R. DeKock for stimulating discussions and helpful comments. Notes 1. The electron densities at the bond critical points (ρ0) in BF3 and SiF4 also indicate significant covalent bonding contributions. In the second period ρ 0 increases from 0.075 au in LiF to 0.217 au in BF3 to 0.288 in F2; in the third period from 0.051 in NaF to 0.154 in SiF4 to 0.187 au in ClF (3). We are grateful to R. J. Gillespie for bringing this point to our attention. 2. The bonding radii of the elements in groups 13 to 17 are listed in ref 16. The bonding radii of Li, Na, Be, and Mg atoms were calculated using the MSS rule, the bonding radius of C, and the experimental bond distances in gaseous LiCH3 and NaCH3 (Grotjahn, D. B.; Pesch, T. C.; Xin, J.; Ziurys, L. M. J. Am. Chem. Soc. 1997, 119, 12368). In Be(CH3)2 and Mg[CH2C(CH3)3]2 (6 ) rLi = 165.1, rNa = 165.8, rBe = 99.9 and rMg = 145.8 pm.
Literature Cited 1. Gillespie, R. J. J. Chem. Educ. 1998, 75, 923. 2. Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Clarendon: Oxford, 1990. 3. Gillespie, R. J.; Johnson, S. A.; Tang, T.-H.; Robinson, E. A. Inorg. Chem. 1997, 36, 3022. 4. Huber, K. P.; Herzberg G. Molecular Spectra and Molecular Structure, IV, Constants of Diatomic Molecules; van Nostrand: New York, 1979. 5. Landolt–Börnstein, Numerical Data and Functional Relationships in Science and Technology, New Series, Group II; Atomic and Molecular Physics; Springer: Berlin; Vol. 7, 1976; Vol. 15, 1987; Vol. 21, 1992; Vol. 23, 1995. 6. Such calculations are described in many introductory or intermediate level textbooks in inorganic chemistry. See, for example, Cotton, F. A.; Wilkinson, G.; Gaus, P. L. Basic Inorganic Chemistry; Wiley: New York, 1996. 7. For a thorough discussion with extensive references see Sherman, J. Chem. Rev. 1932, 11, 93. 8. Thermochemical mean bond energies at 298 K were calculated from standard energies of formation listed in Barin, I. Thermochemical Data of Pure Substances; VCH: Weinheim, 1993. 9. Rittner, E. S. J. Chem. Phys. 1951, 19, 1030. 10. Atkins, P. W. Physical Chemistry, 6th ed.; Oxford University Press: Oxford, 1998; p 653. 11. Hati, S.; Datta, B.; Datta, D. J. Phys. Chem. 1996, 100, 19808. 12. Perrin, C. L. J. Am. Chem. Soc. 1991, 113, 2865. 13. Cioslowski, J. J. Am. Chem. Soc. 1989, 111, 8333. 14. Bader, R. F. W. Can. J. Chem. 1999, 77, 86. 15. Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Cornell University Press: Ithaca, NY, 1960; pp 228 ff. 16. Blom, R.; Haaland, A. J. Mol. Struct. 1985, 128, 21. 17. Rempfer, B.; Oberhammer, H.; Auner, N. J. Am. Chem. Soc. 1986, 108, 3893. 18. Snelson, A. J. Phys. Chem. 1967, 71, 3202. 19. Curtiss, L. A. Int. J. Quant. Chem. 1978, 14, 709. 20. Antipin, M. Yu.; Éllern, A. M.; Sukhoverkhov, V. F.; Struchkov, Yu. T.; Buslaev, Yu. A. Dokl. Akad. Nauk. SSSR 1984, 279, 892 (in Russian); Bull. Acad. Sci. USSR 1984, 33, 435 (in English). 21. Bork, M.; Hoppe, R. Z. anorg. allg. Chem. 1996, 622, 1557.
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