J . Phys. Chem. 1993,97, 3116-3182
3176
Deformation Density Studies of Thiathiophthene. 3.t Theoretical Studies on 2,S-Dimethylthiathiophthene and 2,4-Diphenylthiathiopht hene Kuan-Jiub Lin and Yu Wang' Department of Chemistry, National Taiwan University, Taipei, Taiwan, Republic of China Received: August 31, 1992
Theoretical deformation density distributions of a symmetric 25dimethyl- and an unsymmetric 2,4diphenylthiathiophthene using an ab initio method with the 3-21G* basis set have been studied. There is a remarkable agreement of calculated values with the corresponding model deformation density distributions derived from the low-temperature X-ray diffraction data. The unusual properties of a linear S S S threecentered four-electron a-bond and a 10 r-electron aromatic system are illustrated in terms of molecular wave functions for both compounds. The differences between the symmetric and unsymmetric S S S bonds are discussed. The importance of the inclusion of d polarization functions on the sulfur atom is apparent in its bonding and hypervalency. A better understanding of the chemical bonding of thiathiophthenes is thus obtained. A linear relationship between the calculated ionization potential and the experimental observations from photoelectron spectroscopy provides the confidence in the ground-state calculation.
Introduction
6a-Thiathiophthene derivative^)-^ have attracted widespread interest because of their unusual S S bonding and possible aromatic properties of the two fused five-membered rings. Two types of linear S S S bonds, i.e. symmetric and unsymmetric, were found, which are dependent on substituents on the ring. Experimentally, there have been ESCA studies'&l2that attempt to resolve the symmetry problem of such compounds. Deformation density distributions based on low-temperature X-ray diffraction data were investigated on a symmetric 2,s-dimethylthiathiophthene (1)3-4and an unsymmetric 2,4-diphenylthiathiophthene (2).2-4 While EHMO calculations4 were also performed on these two compounds, the agreement between such calculated deformation density and the corresponding experimental deformation density distribution was unsatisfactory, especially along S S S regions. Apparently, more sophisticated molecular orbital calculations are needed to resolve the bonding type of such molecules.
functions to deal with the deformation density distributions. The addition of d polarization functions on the sulfur atom would introduce only a small reduction of the total energy, but it would introduce a large effect on the deformation density di~tributi0n.l.~~ Although the inclusion of electronic correlation, such as CI and MCSCF methods, or calculationsin large basis sets would perhaps result in further reduction of the total energy of the molecule, only a small effect would be expected in the deformation density distributions.14-i7 Static Model Deformation Density
There are many studies concerning both theoretical and experimental deformation denstiy distributions. 19*23-25 However, in theoreticalcalculations,they normally do not include the nuclear thermal motion. In order to compare directly and quantitatively the experimental and the theoretical deformation density distributions, the maps of the static multipole deformation density are produced for this comparison. The model deformation density distributions are generated by subtracting the spherical atomic electron density from the sum of the atomic electrondensity evaluated from a multipole model.I9 I
a
A priori contributions from various resonance structures, e.g., a and b for the thiathiophthene~,~,~~ may be considered. Hoffmani3proposed a 10 r-electron as well as a linear electron-rich three-centered bond scheme for the thiathiophthene ring. He also predicted a stable symmetric S S S type when 3d orbitals of sulfur atoms are included and an unsymmetric one when 3d orbitals are excluded. In order to clarify all these unusual types of bonding, we performed ab initio calculationson both symmetric 2,s-dimethylthiathiophthene(1) and unsymmetric 2,4-diphenylthiathiophthene (2). It was our hope that this would yield theoretical deformation density distributions in close agreement with the experimental results.2.3 Once the calculation and experimental data converge, the bonding character, e.g. u and T bonds, can be analyzed from the molecular orbital wave functions. The net atomic charges can be obtained from Mulliken populations. Our previous work1 on small molecules indicated that the split valence 3-21G* basis set is the most economic and adequate basis +
I
b
To whom correspondence should be addressed. Part I, ref 3; part 11, ref 4.
0022-3654/93/2091-3176504.00/0
t w+3
The first two terms are the spherical part ofthe atomicelectron density and the third term is the sum of multipole terms which are expressed as spherical harmonic functions (Yl,,,); R/(r)is the radial function, n, and { Iare the parameters of radial function, and K is theexpansion-contractionfactor of the radialdistribution. The coefficients (Pv,Pl,) of the multipole terms together with the atomic positions and thermal parameters are obtained from a least-squares fit on the X-ray diffraction data using the MOLLY program.I9 There are symmetry constraints imposed in the leastsquares refinement in addition to the crystallographic symmetry, Le., P,,P,, for all methyl H-atoms in 1 and those for all the phenyl C and H atoms in 2 are taken to be the same, respectively. The model deformation density distribution is generated by subtracting the spherical parts with P, fixed at the value of a neutral atom. The static model deformation density distributions ( A ~ M -is~the ) one which does not include the nuclear vibration 0 1993 American Chemical Society
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The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 3177
c /
Figure 1. Deformation density distributions of the 2,5-dimethylthiathiophthenemolecule: solid line positive, dash line zero, dotted line negative; (a) APM A of the thiathiophene plane, contour interval 0.1 e A-3; (b) A ~ M -ofA the plane perpendicular to a; contour interval 0.05 e A-]; (c) Ap\~,-~lc;* of the plane a, contour as a; (d) Apl
2 1 ~ .of
the plane b, contour as b; (e) Ap3.21~ of the plane a, contour as a.
and is based on Fourier summation up to the limiting sphere of Mo Ka radiation (sin(e)/A I 1.41 A-').
Computational Procedure It is beyond doubt that answers to chemical problems of an isolated molecule may be obtained from the solution of a timeindependent SchrBdinger equation. Currently, the ab initio calculation is believed to be the most reliable one and it becomes more and more popular because of the available software and the rapid improvements of computer hardware. Theoretical deformation density analyses of both molecules (1 and 2) were carried out at the RHF-SCF-MO level using 3-21G and 3-21G' (including d polarization functions for the sulfur atom only, Cartesian d functions (6d)were employed,the 6 d-type
functions provide further s-type functions (3s') as well as the conventional 5 d-orbitals (xy,xz,yz,x2 - y2.22)29)with the Gaussian90 program.20 The theoretical deformation den~ityl.1~ is defined as the difference between the total molecular electron density and the promolecular electron density. The total molecular electron density is calculated from a closed shell ground-state molecule at the R H F level; each occupied molecular orbital is assigned to have twoelectrons. The promolecular electron density is the sum of the superposition of the spherical atomic electron density with atoms at the same nuclear positions as in the equilibrium molecular geometry. Such geometry is taken from the X-ray diffraction data at 1 10K. The spherical atomic density is calculated at the ROHF/GVB level, each outer most valence orbital is assigned to have equal population, e.g. and 4 / 3 for porbitals of a carbon and a sulfur atom, respectively.
3178 The Journal of Physical Chemistry, Vol. 97,No. 13. 1993
Lin and Wang
Figure 2. Deformation-density distributions of the 2,4-diphenylthiathiophthene molecule: solid line positive, dotted line negative; (a) A ~ M - of A the thiathiophthene plane, contour as in Figure la; (b) APM-Aof the plane perpendicular to a; contour as in Figure 1b; (c) Ap3.21~. of the plane a, contour as in Figure la; (d) Ap3.21~. of the plane b, contour as in Figure lb. (1)----MuRipole (2)----3-210 (3)----3-2 1G*
All the electron density calculations are produced with a MOPLOT programls and the contour plotting of the deformationdensity maps or molecular wave functions were generated with a locally developed program.2’ All computations were performed on the Micro-Vax 3800 computer with a DEC-LN03+ laser jet plotter.
1
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Result The static model deformation density maps of two thiathiophthenes are illustrated in Figure la,b (1) and Figure 2a,b (2) for the thiathiophthene plane (a) and the plane perpendicular to (a) including the linear S S S region (b), respectively. The corresponding deformation density maps calculated from an ab initio method using 3-21G* basis set are shown in Figure lc,d and Figure 2c,d, respectively. The effect of d-polarization functions of sulfur atoms is illustrated in comparison of Figure I C and Figure le, where all the conditions of computations are kept constant except the inclusion of d-polarization functions of sulfur atoms for one (Figure IC)but not for the other (Figure le). The net atomic charges of both compounds derived from multipole refinements and a b initio molecular orbital calculations are displayed in Figure 3. In order to investigate the bonding further, the wave functions representing the *-orbitals of the molecular plane are shown in Figures 4 and 5 for 1 and 2, respectively. Wave functions of SS-S a-orbitals for 1 and 2 are given in Figures 6 and 7. In addition to the deformation-density distributions and the occupied u, r molecular orbital wave functions, the first six ionization potentials according to Koopman’s theorem are compared with those experimental values.Z2 The good linear relationship is illustrated in Figure 8. The values are listed in Table I, the linear equation for a least-squares fit is 1POb, = 0.62(4)1Pcalc+ 2.8(2) for 3-21G2 results.
Discussion
In both compounds (1 and 2), the agreements between the static deformation density maps (Figure l a and Figure 2a) and the theoretically calculated deformation-density maps (Figure
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Figure 3. Net atomic charges of (a) 2,5-dimethylthiathiophthene;(b) 2.4-diphenylthiathiophthene.
I C and Figure 2c) of the thiathiophthene plane are excellent ( l a vs 1c; 2a vs 2c). The agreementson the SSS part of the molecule are also very good except the region within 0.3 A around nucleij9 (see Figure 1b vs Id; Figure 2b vs 2d). This means that not only the density along the C-C and C-H bond can be reproduced by ab initio calculation with 3-21G* basis set, but also the part along S-SS region can be reasonably reproduced which was
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The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 31'19
,
1
.1 I
Figure 4. Wavefunctions of the five r-orbitals of 2$dimethylthiathiophthene; contour taken at 1.0 A above the thiathiophthene plane: (a) r l r 23a'(-14.5827 eV); (b) r 2 , 20a"(-12.0321 eV); (c) *I, 26a'(-10.5750 eV); (d) ~ 4 27a'(-9.9045 , eV); (e) *s, 21af'(HOM0,-7.9727 eV); (e') r5,same *-orbital as in e, at the plane perpendicular to Figure 4e including the linear S-S-S system. recognized previous1y.l The addition of d-polarization functions is apparently important for the sulfur related bonding. The effect is quite obvious by comparing the two deformation maps: one with thed-polarization functions(Figure IC)and the other without such functions (Figure le). The enhancement of the density accumulation along S-C bonds by the inclusion of sulfur d polarization functions is more prominent than the region around the sulfur atom. The improvements of the deformation density based on split valence level ab initio calculation in comparison with the one based on EHMO calculations4 (Figure 3 in ref 4) are far more significant. The more symmetric appearance in the theoretical density maps versus the experimental ones is probably due to the fact that thecalculation is doneon the isolated molecule but the experimental one is derived from the molecule in a crystal. Although two neighboring S S distances in 1 and in 2 are quitedifferent, the former (1) has twoexact1yequalS-Sdistances (2.35 10( 1) A), the latter has two significantly different distances (2.2125( 1) A/2.5087(4) A), somewhat unexpectedly the deformation-density maps of two compounds (Figure la and Figure
2a) are similar in all C-C, C-H, S-C, and S S regions. It indicates that the differences of the bonding between 1and 2 may not beobvious in thetotaleltctrondensitydistributions. Adetailed comparison of the net atomic charges and a comparison of the u- and *-bond molecular orbital wave functions between the two compounds were undertaken. The net atomic charges are displayed in Figure 3. The agreement between the charges obtained from multipole refinement and from ab initio calculation (3-21G') is very gaod for carbon atoms and reasonably good for the relative trend of the charges on sulfur atoms, e.g., in 1, S1 is more positive than S2. Apparently the inclusion of the d-polarization functions of sulfur atoms improves the agreement between thechargesobtained from the theoretical calculation (ab initio) and from the experimental multipole refinement. However, there are severe limitations of using the net atomic charges obtained from the Mulliken populati~n.~~J~J~ With respect to occupied *-orbital wave functions of both compounds (Figures 4 and 5 ) . there are five r-orbitals mainly
Lin and Wang
3180 The Journal of Physical Chemistry, Vol. 97, No. 13, 1993
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Figure 5. Wavefunctions of the five *-orbitals of 2,4-diphenylthiathiophthene;planes defined the same as Figure 4: (a) T I ,63a(-15.2369 eV); (b) eV); (c) r3, 74a(-10.9507 eV); (d) ~ 4 75a(-10.5731 , eV); (e) w5, 8la(HOMO, -7.7300 eV); (e') w5, same *-orbital as in e, at the plane perpendicular to Figure Se including the linear S-S-S system. *?,72a(-12.6509
contributed from the porbitals of carbon and sulfur atoms. The lowest energy level orbital (Figures 4a and Sa) contains no nodal plane and the highest (Figures 4e and Se) contains two nodal surfaces which are perpendicular to each other. They apparently confomto thearomaticity with lor-electronsdistributed among all eight atoms on the rings. The 10 r-electrons might be considered as a combined electron contribution, one from each of all the carbon atoms and the central sulfur atom, and two electrons each from the terminal sulfur atoms. A similar result was found in 2.5-diaza- 1,6-dio~a-6a-thiapentalene.2~.2~.*~ In comparison of the r-orbitals of two compounds (see Figures 4 and 51, there are no significant differences for the four lower energy orbitals (TI-4) except the probabilityaround two terminal sulfur atoms as well as the two five-membered rings in 1 are exactly the same because of the C,rsymmetry, but the probability
density in the two rings is slightly different in 2. The significant difference between the HOMO(w5) of the two compounds is quite apparent in Figure 4e,e' and Figure Se,e': In 1, one of the nodal plane coincides with the central S-C bond, but in 2, this nodal surface passes through the S 3 S 2 (the shorter S S bond). In other words, in this HOMO wave function there is some r-bond character along the long S 1 S 2 bond but no r-bond character or slight antibonding along the short S 2 S 3 bond (Figure Se,e'). In addition to thew-orbitals,theoccupied three-centered SSS u-bond orbitals were analyzed in order to understand difference of symmetric and unsymmetric S S S part in the ground state of thiathiophthene derivatives. There are two occupied u-bonds in each compound: the lower energy ones are roughly the same for both compounds (Figures 6a and 7a), this u-orbital is of p p p type; the other a-orbitals for 1 (Figure 6b) and 2 (Figure 7b) are
Studies of Thiathiophthene
The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 3181
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Figure 6. Wavefunctions of u-orbitals of the SS-S system for 1: (a) u l , 19a”(-12.4376 eV); (b) u2, 28a’(-8.2203 eV).
slightly different from each other. Again the density probability around the two terminal sulfur atoms is the same in 1, but the density probability around three sulfur atoms in 2 has the order of S1 > S3 > S2, this orbital is of p-d-p type. According to the two occupied a-bond orbitals, the a-electron density (+*(r))around S1 is greater than that around S3 and a-density around S3 is greater than that around S2. This is in accord with our previous observation4 and the earlier theoretical prediction^^^-^^^^^ of the fact that long SS bond length is associated with the greater a-electron density. One point worth mentioning is that in 2, the u-bond orbital (Figure 7b) shows an antibonding character along S 2 S 1 near thecentralS2atom (thenodalsurfacepassesthrough the S 2 S 1 bond, but very close to the S2 nucleus). Whereas in 1, there is no such antibonding character along either S-S bond (Figure 6a,b). This may also give rise to a long S1-S2 bond length. In summary, there is a slight a-antibonding character along the long S 1 S 2 bond near S1 in unsymmetric thiathiophthene such as 2; no a-antibonding character is found along the SS bond in the symmetric thiathiophthene such as 1. Theoverall r-bond character of the thiathiophthene ring represented by five r-orbital wavefunctions is roughly the same for both compounds; there is only a slight difference in the HOMO wavefunction. All the comparisons are made thus far on the electron density distributions and the orbital wave functions of the molecule in its ground state. In order to confirm that calculations in the present work do correspond to the ground-state properties, the calculated orbital energies are correlated with the ionization potentials obtained from photoelectron spectra**of 1. The result is quite satisfactory: the good linear relationship of the first six ionization potentials is shown in Figure 8. This gives some justification of the correctness in the ground-state calculation. The slope of less than 1.O is probably due to the limited size of basis sets and the lack of the electron correlation energy in this calculation. Similar phenomena were found e1~ewhere.I.~~ A calculation according to density functional theory is currently being undertaken.
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(a) Figure 7. Wavefunctions of u-orbitals of the S-S-S system for 2: (a) u l , 73a(-12.5943 eV); (b) u2, 80a(-8.2951 eV).
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An excellent r e v i e ~ 3has ~ summarized the role of the d polarization functions in sulfur hypervalency. The dominance of ionic bonding and negative hyper~onjugation35.3~ over actually d-orbital participation on chemical bonding in hypervalency molecules was manifested. It has been suggested that the Lewis rule of localized bonding pairs be modified to allow bonds of 50% or more ionic character, thus preserving the octet rule and circumventing the necessity of expanding the valence shell to include the d-orbitals. The three-centered four-electron bonding
3182 The Journal of Physical Chemistry, Vol. 97, No. 13, 1993
TABLE I: Assignment of the First Six IP Values (eV) for 1 3-21G 3-21G’ exp22 character 8.08 8.13 10.10 10.88 12.15
12.39
7.97 8.22 9.90 10.57 12.03 12.43
7.73 7.90 9.08 9.53 10.04 10.70
2 l a ” TC? C) 28a’as s 27a’ “SI CI TSZ C J 26a’ T C c c AS s s 20a“
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19a” U S ~ S - S
model shown in this work is in support of such a proposal, the total d-orbitals occupancies are very small (0.le-) and the d functions act primarily not as valence but as polarization function^,^^.^* or as acceptor orbitals for back-donation from the bonded atoms.35 The present study emphasizes the importance of the inclusion of d polarization functions in chemical bonding and hypervalency of sulfur compounds.
Conclusion The bonding character of the thiathiophthene ring consists of a 10 *-electron aromatic system around the ring and a threecentered four-electron u-bond along linear SS-S part. The symmetric and unsymmetric S S bond lengths correlated with the u-electron density around the sulfur atom which in turn is affected by positions and types of the s ~ b s t i t u e n t s . ~ The ~~J inclusion of d-polarization functions is apparently important for the sulfur-related chemical bonding and hypervalency.
Acknowledgment. The authors thank the National Science Council for financial support. References and Notes ( I ) Lin, K . J.; Wang,C. C.; Wang.Y. J. Chin. Chem.Soc. 1991,38,505. (2)Wang, Y.;Chen, M. J.; Wu,S. Y. AclaCrystallogr.,Sect. B Struct. Sci. 1988,844, 179. (3) Wang,Y.; Wu,S. Y.;Cheng,A.C. ActaCrystallogr.,Sect.B Struct. Sci. 1990,846, 850. (4) Wang, Y.; Yeh, S. K.; Wu, S. Y.; Pai, C. T.; Lee, C. R.; Lin, K. J. Acta Crystallogr., Sect. 8: Struct. Sci. 1991,847, 298. ( 5 ) Johnson, L. K.; Paul, I. C. J. Chem. Soc., Chem. Commun. 1969, 1014. (6)Dingwall, J. G.;Mckenzie, S.; Reid, D. H. J. Chem. Soc. C 1968, 2543. (7)Leung, F.;Nyburg, S. C. J . Chem.Soc.,Chem. Commun. 1969,137. (8) Hansen, L. K.: Hordvik, A. Acta. Chem. Scand. 1973,27, 41 I .
Lin and Wang (9)Shen. Q.;Hedberg, K. J. Am. Chem. Sot. 1974,96.289. ( I O ) Clark, D. T.; Kilcast, D. J. Chem. Soc.,Chem. Commun. 19719638639. ( 1 1 ) Saethre, L. J. Chem. Phys. 1977,20,431. ( 12) Saethre, L. J.; Malmquist, D. A.; Martensson,N.;Svensson,S..Gelius,
U . ; Siegbahn. K. Inorg. Chem. 1981,20,399. ( I 3) Gleiter, R.; Hoffman, R. Tetrahedron 1968, 24, 5899. (14) Kunze, K. L.; Hall, M. B. J . Am. Chem. Soc. 1987. 109,7617. (IS) Schwarz, W. H. E.; Ruedenberg, K.; Mensching, L. J . Am. Chem. Soc. 1989. I I I, 6926. (16)Mensching, L.; Niessen. W. V.; Valtazanos, P.; Schwarz, W. H. E.; Ruedenberg, K. J. Am. Chem. Soc. 1989,I l l , 6933. (17) Darakjian, 2.; Fink, W. H.; Hope,H. J . Mol. Struct. (Theochem) 1989,202, I 1 I. (18) Lichtenberger, D. L.; Fenske, R. F. MOPLOT. QCPE 1975. ( I 9) (a) Coppens, P.; Hall, M. 8.Electron Distribution and the Chemical Bond Plenum Press: New York, 1982. (b) Hansen, N.K.; Coppens, P. Acta Crystallogr.. Sect. A: Cryst. Phys. DiJfr., Theor. Gen. Crystallogr. 1978. A34, 909. (20)Pople, J. A.; Frish, M. J.; Head-Gordon, M.;Truch,G. W.; Foresman, J. B.;Schlegel,H.B.;Raghavachari,K.;Robb.M.A.;Binkley,J.S.;Gonzalez, C.; Defrecs, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, L. R.;Kahn, L.; Stewart, J. J. P.; Topiol, S.Gaussin 90, Inc., Pittsburgh, PA, 1990. (21) Tsai, C. J. Master thesis, National Taiwan Uni., Taiwan, 1987. (22)Gleiter. R.; Hornung, V.; Lindberg. B.; Hogberg, S.; Lozach. N. Chem. Phys. Lett. 1971,1 1 , 401. (23)Cohen-Addad, C.; Lehman, M. S.;Becker, P.; Parkanyi, L.; Kalman, A. J. Chem. Soc., Perkin Trans. 2 1984, I9I. (24) Becker, P.; Cohen-Addad, C.; Delly, B.; Hirshfed, F. H.; Lehman, M. S. Applied Quantum Chemistry; D. Reid Publishing Co.: Kluwer, 1986; p 361. (25) Fabius, B.; Cohen-Addad, C.; Larsen, F. K.; Lehman, M. S.;Becker, P. J. Am. Chem. Soc. 1989,1 1 1 , 5728. (26)Clark, D.T.; Kilcast, D. Tetrahedron 1971,27, 4367. (27) Palmer, M. H.; Findlay, R. H. Tetrahedron Lett. 1972,41, 4165. (28) Palmer, M. H.; Findlay. R. H.; Gaskell, A. J. J. Chem. Soc.,Perkin Trans. 2 1974,420. (29) Palmer, M. H.;Findlay, R. H. J. Chem. Soc., Perkin Trans. 2 1974, 1885. (30)Palmer, M. H.; Findlay, R. H. J. Mol. Struct. 1977,37, 229. (31) Mayer, 1. J. Mol. Struct. (Themhem) 1987, 149,81. (32) Mayer, I. Chem. Phys. Lett. 1983,97, 270. (33) Patterson, C. H.; Messmer, R. P.J. Am. Chem.Soc. 1989,111.8059. (34) Patterson,C. H.;Messmer, R.P. J. Am. Chrm.Soc. 1990,112.4138. (35) Reed, A. E.;Schleyer, P. v. R. J . Am. Chem. Soc. 1990,112,1434. (36) Kutzeluigg, W. Angew. Chem., Int. Ed. Engl. 1984,23, 272. (37)Schleyer, P. v. R.; Kos, A. J. Tetrahedron 1983,39, 1141. (38)Reed, A. E.;Weinhold. F.; Curtiss. L. A. Chem. Reu. 1988.88.899. (39) The contribution of u. .I is predominantly within about 0.3A from each nucleus, typically 0.25e at the nucleus, but is generally negligible elsewhere. See Rees, B. Acta Crystallogr., Sect. A: Cryst. Phys., Dvfr., Theor. Gen. Crystallogr. 1978,A34, 254.
