Mapping Electron Density in Molecules
The Journal of Physical Chemistry, Vol. 82,No. 12, 1978 1407
Mapping Electron Density in Molecules. 14. Nonbonded Contacts between Lone Pairs on Divalent Sulfursli2 Donald B. Boyd Lilly Research Laboratories, Eli Lilly and Company, Indianapolis, Indiana 46206 (Received December 2 1, 1977) Publication costs assisted by Hi Lilly and Company
As a prerequisite to molecular orbital studies of large, sulfur-containing molecules of biological interest, three frequently used semiempirical methods, EH, CNDOIB, and MIND0/3, are evaluated in regard to their ability to predict qualitatively reasonable potential energy curves for the process of moving two dimethyl sulfide molecules at each other such that the lone pair regions are forced to overlap in various ways. CND0/2 as usual underestimates nonbonded repulsions and therefore gives completely unreasonable results by indicating a very deep energy minimum a t an S.43 distance close to that for a covalent S-S bond. MIND0/3 performs better, but still indicates a shallow minimum at a somewhat longer S.43 distance. Extended Huckel is the only method to show the expected repulsive potential in the van der Waals contact region. The EH potential curve is not satisfactory at shorter distances. Semiempirical, ab initio, and experimental electron density maps of molecules containing divalent sulfur show that the 3p-type lone pair extends farther from the sulfur nucleus than the sp2-typelone pair. By allowing (CHJ2S models to approach each other in selected orientations with S . 4 contact, the EH calculations indicate that the dimeric arrangement of C a symmetry with the two C-S-C units coplanar, the C-S--S-C sequence roughly linear, and the sp2-typelone pairs antiparallel to each other, is significantly less unfavorable for close S-4contact than the others. Correlation diagrams and electron density maps of the (CH3)2Sdimers and monomers reveal a fundamental reason for this preference is that it affords the opportunity for favorable interactions between the frontier orbitals of the two sulfides. The conclusions provide a basis for understanding accumulating experimental evidence that the nonbonded contacts of sulfurs can be shorter than previously expected and display an orientational preference. Intramolecular nonbonded contacts of sulfur in methyl ethyl disulfide are examined by MINDO/3 calculations, and no hint of a stabilizing 1,4 carbon-sulfur interaction is found.
Introduction Traditionally, sulfur has been regarded as having a van der Waals r a d i ~ ofs ~about ~ ~ 1.85 A. There now seems to be accumulating evidence5-14that a shorter value may be more appropriate. For instance, crystallographic data for a thiourea5 show i n t e r m ~ l e c u l a rS-S ' ~ contact distances of 3.35 A between dicoordinated divalent sulfurs. An even shorter intermolecular S . 4 distance, the shortest found so far, occurs in neso-lanthionine 1.6 Here the two sulfurs HOOCCHCH,SCH,CHCOOH I
I
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are only 3.25 A apart. Distances almost this short have been observed in other molecules also."J2 In addition, nonbonded contact distances less than the sum of the usual van der Waals radii have been noted for C - H . 4 intera c t i o n ~ , ' ~ *N-H-.S ' ~ J ~ interaction^?^ and other situations.6*8 A reduction of 0.15-0.20 A in the accepted van der Waals radius for divalent sulfur has quite reasonably been proposed by Scheraga e t al.13 Parthasarathy et a1.8Johave more specifically suggested that the in-plane interatomic contacts, i.e., those in the C-S-C plane, are 0.2 A shorter than those normal to this plane. All these nonbonded contacts involve electron density on some atom penetrating (to an extent greater than previously thought possible) the electron density in the lone pair region around sulfur. Hence we are led to the question of what is the shape of the lone pair region on a divalent sulfur. Also, is the electron cloud more easily penetrable from certain directions than others, and why? This paper is addressed to obtaining qualitative answers to these questions. An equally important concern of this paper is a comparison of three semiempirical molecular orbital methods 0022-3654/78/2082-1407$0 1.OO/O
in regard to their ability to describe the interaction between the electron clouds of two nonbonded divalent sulfurs. The three methods are extended Huckel (EH)," complete-neglect-of-differential-overlap(CND0/2),l8 and modified-intermediate-neglect-of-differential-overlap (MIND0/3).19 EH, CNDOI2, and M I N D 0 / 3 are frequently used as demonstrated by perusal of the recent literature. EH usage is down from the previous decade, but seems t o have leveled off toward a plateau in the last several years. CNDO/2 usage continues strong, and MIND0/3 usage is increasing rapidly. When researchers turn t o the semiempirical MO methods to explain newly recognized chemical phenomena, careful selection of the appropriate method or methods to employ for a given type of problem is essential if misleading results are t o be avoided. Evaluation of these methods on simple model systems is imperative in order to learn what systematic errors might be expected. I t is of utmost importance t o known where and to what extent the methods may be deficient. Despite continuing advances in computer programs for ab initio treatments of larger and larger systems, the semiempirical methods will no doubt retain their role of probing the nature of molecules beyond the frontier of the ab initio studies. In the present case of nonbonded contacts between sulfurs, we are dealing with a phenomenon which is most likely or even exclusively to be observed in very large molecules or assemblages of molecules. If, in a theoretical study of such a large system, conformations involving short S - 4 contacts are encountered, then the investigator needs to interpret his results borne by an appreciation of the characteristics of his calculational method. On the other hand, if one were only interested in obtaining accurate potential curves of S-.S interactions, one would obviously perform ab initio calculations on some simplified model system with a large,
0 1978 American Chemical Society
1408
The Journal of Physical Chemistry, Vol. 82, No. 12, 1978
Donald
well-balanced basis set and some account of electron correlation, such as configuration interaction. In practice, the more readily available ab initio programs would employ a minimum basis set, and hence the results could be equivocal to some degree because of the basis set and because of the subtle nature of the interactions of interest in this paper. A dimer of H2S comes readily to mind as the simplest model, but this might not be adequate if, for instance, hyperconjugation through S-CH2R bonds is important in favoring close S-S contacts. It should be emphasized a t the outset that the semiempirical MO methods can, at best, give potential energy curves that are only suggestive. However, as is now well known, certain orbital interaction effects can be fundamental to a phenomenon and should then transcend any reasonable MO treatment. If such interactions pertain to the present case, semiempirical methods may disclose them. Moreover, recent work has established an interesting link between the semiempirical E H MO’s and those from ab initio theory.20 We shall be looking for the orbital interaction effects and for qualitative understanding in the calculations reported in this paper.
\\ EH
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0 2
the n(3p) MO is a t higher energy than the n(sp2) orbita1.21-23 Electron density maps provide a very direct way to see the shape of the lone pair region. Roughly speaking, the electron density on S is spherically symmetric on the side away from the A and B groups. However, careful examination of electron density maps from EH, CND0/2D (CND0/2 followed by a deorthogonalization stepz4),and a b initio MO calculations all show the cloud to be more extensive perpendicular to the A-S-B plane than in the plane.w30 Based on these results, it may be estimated that the outer, ~ize-deterrnining,~~ isodensity contour is 4-9% farther away from the S nucleus in the perpendicular direction than in the in-plane, nonbonded direction.32 Low temperature X-ray diffraction data for S8also reveal a slightly nonspherical distribution of density around divalent The experimental work shows that the cross section of density through sulfur bisecting the A-S-B bond angle is elliptical with the long axis perpendicular to the A-S-B plane. Because of this anisotropy, one would suppose that two divalent sulfurs could be forced into closer proximity if the nonbonded contact involves the n(sp2) orbitals. Note that in the system with the S-S distance of 3.25 A mentioned earlier,“ the two C-S-C units
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Anisotropy of the Sulfur Lone Pairs We begin with an elementary description of the lone pairs on sulfur and then describe what the electron density around sulfur looks like according to both theoretical and experimental studies. The lone pair region of a dicoordinated, divalent sulfur atom is described as the combination of an orbital with mainly S3p atomic orbital character normal to the A-S-B plane and another orbital in this plane with sp2 hybrid orbital character. These are depicted qualitatively in 2 for dimethyl sulfide. Typically,
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B. Boyd
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s .S Distance, A
Flgure 1. Relative energy of two (CH,),S
molecules approaching each other in a coplanar sp’.-sp’ mode. The energies are relative to that for two infinitely separated monomers as calculated by each of the three MO methods.
are nearly coplanar so that the contact does, indeed, involve the n(sp2) lone pairs mainly. Electron density maps give a necessarily static picture of charge distributions. Charge redistributions can be seen only with a series of “snapshots”. A way to obtain a deeper understanding of nonbonded contacts of sulfur would therefore be quantum mechanical calculations where the sulfurs of two molecules are brought into close contact and electron density on both molecules is free to adjust to the changing environment. These computer experiments are described next.
Nonbonded Interactions of Sulfur Comparison of the M O Methods. Descriptions and parameterizations for the three MO methods, E H , CNDO/2, and MIND0/3, are in the l i t e r a t ~ r e . ’ ~ -The ’~~~ S3d Slater-type orbitals are in the basis set for the first two methods, but not for MIND0/3. We allow two dimethyl sulfide molecules, each with a molecular geometry fixed as described el~ewhere?~ to approach each other such that the n(sp2) orbitals are forced to overlap. In this first set of calculations, the molecules are moved along an axis collinear with their C2symmetry axes, and the two C-S-C units are kept coplanar. This mode of approach will be labeled “coplanar sp2.-sp2”. Results are given in Figure 1.
Obvious from Figure 1 is the disturbing fact that the popular C N D 0 / 2 method gives an attractive potential which is completely unreasonable. The dimer is predicted by CNDO/2 to be 130 kcal/mol more stable than the infinitely separated monomers, and the equilibrium S-S distance of 2.0 A is essentially equal to that of a covalent S-S bond.36 Such misleading predictions stem from the known tendency of CNDO/2 to underestimate overlap repulsions with respect to nonbonded attraction^.^^*^^-^^ However, the seriousness of this tendency is not always fully appreciated. When an unexpected energy minimum is found by CNDO/2 which involves unusually short nonbonded contacts between two atoms in some molecular
The Journal of Physical Chemistry, Vol. 82, No. 12, 1978
Mapping Electron Density in Molecules
3P 3P
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s s Distance. A Figure 2. Relative EH energy of two (CH,),S molecules approaching each other in one of the five modes as shown in the inset. The energy is relative to that of the infinitely separated monomers and is obtained from half the sum (over electrons) of the eigenvalues of the occupied MO's. For the antiparallel (a.p.) mode, 0 was set at 85.5". The symmetry of the dimeric complexes are DPhfor coplanar sp2-.sp2, Dpd for perpendicular sp2-sp2, C,for sp2.43p, C2hfor 3 p - 3 ~ ; and C2,,for antiparallel.
association or conformation, it is important to recognize this as more likely an artifact of the method rather than the discovery of some new type of interaction. The problem encountered with CNDO/2 has been ascribed to a general tendency of the neglect-of-differential-overlap (NDO) methods to energetically favor structures with greater c o n n e ~ t i v i t y .The ~ ~ other NDO method tested in Figure 1, MIND0/3, also fails to show a repulsive potential until a t about 2.5 A. However, the energy minimum is shallow (6 kcal/mol) and occurs a t larger S.43 distance compared to CNDO/2. So even though M I N D 0 / 3 cannot be trusted to give reasonable representations of nonbonded contacts, it a t least does much better than CNDO/2 and might be worth trying for qualitative comparisons of different modes of approach. The E H method is the only method in Figure 1 to give the repulsive potential in the van der Waals contact region that one would expect to see. Thus, this method has the best chance of giving usable information on the relative ease of overlapping sulfur lone pairs in different modes of approach. The E H method does have the peculiarity, -6-7
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1409
previously known, of not showing a monotonically increasing repulsive potential as the two nonbonded atoms are shoved into severe overlap. The drop in energy between 2.2 and 1.5 A in the E H curve of Figure l can be traced to the crossing of energy levels in a correlation diagram (which is presented in the next section). The drop can be understood qualitatively in terms of the overlapping of the 3p, orbitals on two atoms approaching along the z axis. At long distances the overlap is small and negative. As the two atoms get closer the overlap becomes more negative and unfavorable (corresponding to a higher E H total energy9. At some point the + lobe of the 3p, orbital on one center will begin to overlap more with the distal + lobe of the 3p, orbital on the other center than with the latter's proximal - lobe.46 At this point, the energy, as approximated by EH theory, will become less unfavorable. Eventually, a t still shorter distances the unfavorable overlap of the other orbitals on each center will turn the energy curve back up. A comparable effect is not encountered with the E H potential energy curves of noble gas atoms47 because these atoms have all the basis set atomic orbitals filled; these systems showed repulsive potentials a t all distances examined. Returning to the dimethyl sulfide case, we may conclude that the EH method can be used with discretion for studying nonbonded contacts provided the S-43 distance is 2.5 A or greater and the results are given no more than qualitative significance. EH Results on the Modes of Approach. In the second set of computer experiments, the relative E H energy45of the system of two dimethyl sulfide molecules as a function of S-23 distance for five different modes of approach was calculated. The energy curves and the relative orientations of the two molecules are shown in Figure 2. Four of the modes of approach produce potential energy curves that are so similar that nothing definitive can be concluded because of the approximate nature of the MO method. However, the fifth curve stands out as distinctly different from the rest. This is the one labeled antiparallel (asp.). It is this mode of approach that involves the least expenditure of energy of those tested. The antiparallel mode with 0 = 85.5" (Figure 2) closely mimics that geometry present in crystalline rneso-lanthionine dihydrochloride where the S.43 interatomic distances of 3.25 A were observed.6 In that crystal the C-S-C bond angle is 103.7" and 0 (as defined in Figure 2) is near 83". Thus, the E H calculations indicate that the antiparallel mode is significantly less repulsive for permitting close nonbonded contacts between the sulfurs.
........,(,.. --bg.................................. -.............. ............... ....... S 3d __ S 3d ag .................... S 3d ......... --
0
S*-S Distance, A Figure 3. EH eigenvalues of the (CH,),S dimer as a function of S-43 distance for the coplanar sp2-.sp2, 3p--3p, and antiparallel (a.p.) modes of approach as depicted in Figure 2. The energy levels are correlated with the eigenvalues of the monomers at infinity. The empty orbitals are traced with dotted lines. Filled u MO's are below -14 eV in energy.
1410
Donald 6.Boyd
The Journal of Physical Chemistry, Vol. 82, No. 12, 1978
Insight into why the antiparallel mode should have a lower repulsive potential than the other modes of approach can be obtained from the correlation diagram in Figure 3. At infinite separation the higher energy lone pair is the n(3p) type as usual. The lowest empty MO by EH is one labeled S 3d.48 As the two dimethyl sulfide molecules approach each other in any one of the three modes depicted, the symmetric and antisymmetric combinations of the lone pair orbitals begin to split apart in energy due to the intermolecular interaction. In the coplanar sp2-.sp2 approach, the MO's with n(sp2) character show the largest perturbative splitting. The higher energy (antisymmetric) combination rises above the n(3p) lone pair combinations a t about 3.0 A and even becomes the lowest empty MO a t about 2.0 A. What was the lowest empty MO in the monomer becomes occupied below 2.0 A. This energy level crossing corresponds to a forbidden reaction in the Woodward-Hoffmann sense.49 In this coplanar sp2.-sp2 mode, the antisymmetric n(3p) combination also reaches quite high energy below 2.5 A. In the 3 p - 3 ~ approach, only one lone pair orbital combination rises to high energy a t short separations. This level is the antisymmetric combination of the n(3p) orbitals. Because the n(sp2)lone pairs are anti to each other in this dimer (see Figure 21, they are far enough apart to avoid much perturbation. In contrast to the first two cases, the correlation diagram for the antiparallel approach (Figure 3) shows no huge splittings even when the sulfurs are only 2.5 A apart. And even a t 2.0-A separation, the rise in energy of the antisymmetric n(3p) and n(sp2) combinations is small compared to the other two modes of approach. This finding explains the distinction in the potential energy curves in Figure 2, namely, that the dimeric complex with the two n(sp2) lone pairs antiparallel to each other as shown in 3
3
is favorable for close nonbonded S-.S contact. M I N D 0 / 3 Results on t h e Modes of Approach. A set of computer experiments on the dimethyl sulfide dimeric system was carried out using the MIND0/3 MO method. In the coplanar sp2-sp2 mode of approach, the MIND0/3 total energy of the dimer reaches a minimum (Figure 1) when the S.43 distance is 2.49 A. The heat of formation, AHf, a t this point is -15.5 kcal/mol, which can be compared to -9.6 kcal/mol for the two monomers separated by 10.0 A. Keeping the two C-S-C units coplanar and again holding all monomer bond lengths and angles constant, but optimizing the S-.S distance and the S.-S-C angle 0 yields 2.50 A and 106", respectively. This geometry with AHf = -15.9 kcal/mol does have 0 a little nearer 83" than in the coplanar sp2-esp2mode where 0 is held fixed at 130.565'. Thus, MINDO/3 has shown some preference for a dimeric structure somewhat like the antiparallel complex 3. However, if the monomers are allowed the additional degree of freedom of rotating about their axis of approach (which is collinear with their Cz symmetry axes), then M I N D 0 / 3 predicts the perpendicular sp2-sp2 mode (see Fi ure 2) to yield a still lower AHf. In this case, S-S is 2.41 and AHf = -17.2 kcal/mol. This structure turns out to be the most stable according to M I N D 0 / 3
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of any dimeric form of dimethyl sulfide such that the lone pairs are directed a t each other. MINDO/3 seems to predict the n(3p) lone pair orbital to occupy so much space that one molecule twists 90" with respect to the other (about the axis of approach) so that the two n(3p) lone pairs have minimum overlap with each other. Optimizing the S.-S distance in the n(3p)-n(3p) approach mode (as in Figure 2) yields a small AHf of -9.6 kcal/mol and an S-S distance of 6.97 A. This large distance arises because the potential energy curve for this mode of approach is quite flat according to MIND0/3. MINDO/3 appears to show no dipole-dipole stabilization in the n(3p)-(3p) dimer." The perpendicular sp2-.sp2 dimer of (CH,)2S-4(CH3)2 is reminiscent of the situation in disulfides. Dialkyl disulfides are known to exist with a CS-SC dihedral angle near 90°,26,27,51--54 and almost all MO methods do not have any trouble predicting this correctly. Force fields for molecular mechanics calculations have therefore been built to yield twofold barriers for rotation about the S-S bond.36v55In order to gain a better appreciation of the generality and limitations of MIND0/3, calculations were also carried out on methyl ethyl disulfide 4. The equiH,C-S
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librium CS-SC dihedral angle is predicted by M I N D 0 / 3 to be in the range 90-103" depending on the SS-CC dihedral angle. This prediction is in fair agreement with the 80-90" known to exist in unconstrained d i s ~ l f i d e s . ~ ~ * ~ ~ ~ Molecule 4 is also of considerable immediate interest in regard to the torsional potential about the S-C bond36and possible 1,4 carbon-sulfur interactions.% It has been hypothesizedM that there is a potential energy minimum near 30" in rotation about the SS-CC bond, in addition to the expected minima in the gauche and trans regions. However, all experimental evidence for the existence of a conformer with favorable C-H.4 interactions is indirect,56 and our previous molecular mechanics and a b initio STO-3G MO calculation^^^ indicated a normal threefold potential energy curve for rotation about the S-C bond, and not a four- or fivefold barrier. M I N D 0 / 3 predicts a threefold barrier also.57 The trans conformer (T) of 4 is calculated to be most stable with barriers of 1.1-1.3 kcal/mol separating it from the two possible gauche conformers (G and G'). G has an optimum SS-CC dihedral angle of 64" and is 0.9 kcal/mol less stable than T; G' has an optimum SS-CC dihedral angle of 300" and has a higher relative energy of 1.2 kcal/mol due to the proximity of the two terminal methyl groups. This cis (C) conformer with SS-CC = 0" is the least stable conformer (1.8 kcal/mol above T). The potential energy curve in the 0-64" range is smooth and sinusoidal with no hint of any minimum or shoulder near 30". M I N D 0 / 3 is knownlg to underestimate rotational barriers, so, in fact, the maxima on the potential energy curve for rotation about the S-C bond of 4 should probably be even higher. The 1-2 kcal/mol barriers that were obtained are somewhat lower than the 1-3 kcal/mol obtained by molecular mechanics and ab initio calculations.36 It seems unlikely that a stable conformer of 4 will be found in the 30" SS-CC dihedral angle range even with more sophisticated calculations because of the steepness of the gradient of the potential energy curve between the maximum a t 0"and the minimum near 60". Besides the high energy of the C conformer, the repulsive nature of the C-H.43 interaction also seems to be evident in the optimized C-C-S bond angle which opens up by about 15" in the C conformer compared
The Journal of Physical Chemistry, Vol. 82, No. 12, 1978 1411
Mapping Electron Density in Molecules
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to the T. Also, the most stable arrangement of the ethyl terminus in the C conformer has the terminal methyl hydrogens in a bifurcated arrangement with respect to the sulfur of the 1,4 interaction; the short C-He-S distances in this interaction are 3.3 and 3.4 A. Thus, the hydrogens have gotten as far away from sulfur as possible in the C conformer. Close nonbonded contacts between C-H units and sulfur do not seem to be especially stabilizing, and we may conclude that these C-H.4 contacts exist only a t the expense of structural constraints imposed other intra- or intermolecular interactions. Electron Density Maps and Charge Distributions. The EH wave function of the antiparallel complex 3 of dimethyl sulfide is analyzed further in Figures 4-9. The geometry of the complex is such that the S . 4 distance is 3.25 8, and 0 (Figure 2) is 85.5'. These numbers will be recognized as similar to the values observed in crystalline mesolanthionine.6 Thus, our electron density maps should give some idea of the charge distribution present in the experimentally relevant situation. The total valence-electron density maps (Figures 4 and 5) show considerable overlap of the electron clouds in the region between the sulfurs. Note that the density is 0.002 e/(bohr r a d i ~ s between )~ the "R" and "S" contours; the 0.002 value has been regarded3I as the size-determining contour of molecules. The n(sp2) and n(3p) lone pair regions can be discerned as the bulges in the "U" and "T" contours on the nonbonded sides of the sulfurs. The antiparallel alignment of the n(sp2)lone pair axes is apparent in Figure 4. The combination of the n(sp2) and n(3p) lone pairs to give roughly circular contours can be seen in Figure 5 . Note that the contours are slightly further from the nuclei in the perpendicular direction than in the C-S-C plane. This observation coincides with our previous statements about the n(3p) lone pair being more extensive in space than the n(sp2) type.
Figure 5. Total EH electron density calculated in a plane through dimeric dimethyl sulfide in the antiparallel geometry 3 which is perpendicular to the plane of Figure 4 and intersects the two sulfurs. The same notation as in Figure 4 is used.
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Figure 6. Difference electron density obtained by substracting from the total EH density of dimeric dimethyl sutfide in the antiparallel geometry 3 the EH total density of two isolated monomers positioned at the same atomic coordinates as the dimer. This view is analogous to that in Figure 4. Negative contours are labeled 9 for 0.125, 8 for 0.025, 7 for 0.005, 6 for 0.001, and 5 for 0.0002 e/(bohr radiusI3. Dotted contours denote zero difference. Some contours appear fused or discontinuous, but this is only an artifact of the limited resolution of the printer.
The difference maps in Figures 6 and 7 are also interesting because they highlight that part of the electron distribution which undergoes change upon formation of the dimer from the infinitely separated monomers. The charge redistribution in each n(sp2) region (Figure 6) is seen to be biphasic: electron density is lost from the side closest to the lone pair of the other molecule, and electron density is gained on the distal side of the lone pair. In other words, the lone pairs have, in effect, bent slightly away from each otherm when the sulfurs are 3.25 A apart. A small increase in density halfway between the sulfur nuclei remains despite the overlap repulsions. One could interpret this remnant in terms of a slight attractive force between the molecules. In the EH framework, electron
The Journal of Physical Chemisfry, Vol. 82, No. 12, 1978
1412
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Q(S) -0.081 -0.081 --0.077 -0.072 -0.060 -0.001 t0.087
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-0.122 -0.122 -0.124 -0.1 27 -0.146 -0.174
0.663 0.663 0.664 0.665 0.667 0.672 0.669
0.663 0.663 0.664 0.665 0.667 0.679 0.678
' I The terms distal and proximal refer to the carbons farthor or closer to the sulfur of the other (CH,),S molecule. The distal S-C bond is the one rough1 collinear with t h e The EH method line of approach shown in Figure 2. gives a less reliable description of events below 2.5-A separation.
density is shifted into the C-S u bonding regions, especially for the C-S bond which is roughly collinear with the line of approach in the antiparallel mode. The shift is apparent in Figure 7 as well as Figure 6. I t suggests that the C-S bonds are strengthened in the dimer a t the expense of electron density lost from the n(sp2) regions. The phenomenon of charge redistribution can also be monitored by a population analysis (Table I). The sulfurs become less negative59as they approach each other, the carbons become more negative, and the C-S bonds acquire more covalent bond strength. The strengthening of the C--S bonds in the antiparallel approach can be linked to a slight decrease in S3p character of the n(sp2)-typeMO's, so that more 3p character may become available in the other sp2hybrid orbitals for u bonding between sulfur and the carbons. However, these changes are dependent on the mode of approach and, probably, to some extent, on the MO method.60 Further insight into the interactions taking place in the dimeric arrangement can be obtained from looking at electron density maps of two of the individual MO's of monomeric dimethyl sulfide. The n(sp2)-typeMO (the next to the highest occupied one) is shown in Figure 8, and the lowest empty MO is shown in Figure 9. The n(sp2)
.........................
OYOOOUY..YR~RYR.RPYSSSSSS5RR~~~~~OO.....................
Figure 9. Electron density of the lowest empty MO from EH calculations on dimethyl sulfide. The densty IS computed as in Figure 8 assuming an occupation number of 2.
MO is mostly concentrated on the nonbonded side of sulfur, but it also has density between the carbons and sulfur and on the hydrogens. Two nodal surfaces divide the MO such that it has some S-C u bonding character. The lowest empty MO has a large amount of S3d character; the largest A 0 coefficients61 of this MO in the E H calculations are 4 . 5 3 S3px + 0.75 S3dXzfor the monomer. The CNDO/2 lowest empty MO is quite similar, except that the 3px contribution outweighs the 3d contribution: -0.69 S3p, 0.56 S3d,, before deorthogonalization, and -0.91 S3p, + 0.38 S3dXzafter the S-'I2 deorthogonalizat i ~ n This . ~ ~3d-type4*virtual orbital, whether produced by E H or CNDO/2 calculation, does not have S-C u* character; none of the three nodal surfaces dividing this MO cuts across the S-C axes. According to CNDO/2, S-C u* character appears in the next to the lowest empty MO.
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MIND0/3, which does not account for 3d orbitals, gives both lowest empty MO’s S-C u* character. In an arrangement such as 3, either type of virtual orbital will interact strongly with the n(sp2)-typeorbital. For instance, by mentally overlaying the plots in Figures 8 and 9, the excellent overlap between the filled and unfilled MO’s can be appreciated. (The perturbative mixing of these n(sp2)and 3d-type MO’s will strengthen the S-C bonds because both MO’s have S-C u bonding character.) A u* orbital typically has electron density extending a t both ends of the bond axis,n so that this orbital too can interact strongly with the n(sp2) MO. (The perturbative mixing of these n(sp2) and u* MO’s would have an equivocal effect on the S-C bond strength). It is not possible to state which type of virtual orbital is more appropriate for describing the electronic structure of sulfides, and, in fact, both appear to be relevant for conceptual purposes. The important point is that with a lowest empty MO either of 3d-type or of S-C u* character, attack of nucleophiles will, in general, be favored on the back side of the S-C bonds. For sake of completeness, we should a t least mention the possibility of Rydberg orbitals affecting the nonbonded contacts of sulfur. Both quantum mechanical calculation^^^^^^ and spectroscopy experiments62 point strongly toward the existence of 4s n and 4p n Rydberg states intermingled with the u* n and 3d n excited states of sulfides. Thus, energy-wise one can envision Rydberg orbitals in the same range as the other virtual orbitals that we have just considered. However, because of their spatial characteristics, the Rydberg orbitals would probably have no more than a minor influence on the specificity of interatomic interactions. The appropriateness of using Rydberg-type orbitals in orbital symmetry correlation diagrams is a topic that has received little attention in the literature. Rydberg-type atomic orbitals are typically not included in basis sets for semiempirical MO calculation^.^^ However, one recent example@which did include them for a model hydrocarbon reaction showed that the Rydberg levels had little decisive effect on the outcome of the reaction. It has been pointed out in an excellent discussion65of Rydberg orbitals that they are very diffuse and typically encompass an entire molecule. Hence the 4s- and 4p-type orbitals of sulfur probably contribute little, if anything, to an orientational preference for nonbonded S . 4 contacts. With our particular E H parameter^,'^ the occupancy of the 3d AO’s is quite low in the filled MO’s. For the dimethyl sulfide monomer, the total population of the S3d’s is negative and close to zero. For the antiparallel dimer a t 3.25 A, the population is still insignificant. The population increases to about 0.2 e a t 2.5 A and to about 0.7 e a t 2.0 A. The general question of the importance of d orbitals continues to be discussed frequently.66 For our case of understanding close S-.S contacts as observed experimentally, we conclude that the 3d AO’s are not highly important basis functions for the ground state; they act as polarization functions67and allow slight rehybridizations in the less stable dimers. However, the 3d AO’s do contribute in a more important way by providing low-lying excited states. These levels help make sulfur more polarizable than first-row atomse4 Electron density maps are especially useful because they can be used to detect chemically interesting charge redistributions not evident from a population analysis of a wave function. For instance, some time ago, it was found t h a t when a water molecule approaches a nucleophilic center, there is appreciate charge reorganization a t the oxygen a t a point rather early (3.25 A) in its approach to
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the second molecule.68 The reorganization was not very evident from the Mulliken populations. Likewise, in Table I it can be seen that most of the quantities have changed little at 3.25 A compared to infinite S . 4 separation. Only Q(S) has changed by as much as 0.01 e. Yet Figures 6 and 7 certainly testify to the fact that small, but noticeable, adjustments in the charge distribution have occurred a t a separation of 3.25 A. (In addition, the adjustments are consistent with the anticipated interaction.) Experience indicates that net atomic charges are not the best criterion for discerning the interactions of two approaching molecules. However our results do support the conclusion69 that significant charge reorganization, such as occurs in a drug-receptor interaction, develops in the vicinity of 3-A intermolecular separation.
Discussion In order to further delineate areas of applicability and inappropriateness, we have investigated three of the more frequently used valence-electron MO methods in regard to their ability to represent the repulsive potential between two molecules with divalent sulfur. The dimethyl sulfide molecules were moved toward each other in various orientations such that the lone pair regions were made to overlap. Two of the methods, E H and CNDO/2, did not include electron correlation, so that the attractive dispersion forces between the molecules will not come out of the calculations. The third method, MIND0/3, is parameterized to fit a base of diverse experimental data, so it is conceivable that some electron correlation effects may be partially accounted for implicitly. T h e C N D 0 / 2 method leads to obviously spurious results; the molecules are predicted to dimerize with a large exothermicity and with only 2.0-A separation between the sulfurs. One of the important points we wish to make in this paper is that CNDO/2 calculations cannot be trusted to yield reliable information about nonbonded interactions. The problem is apparent to some extent with first-row atoms,34i39*42 but becomes even more serious in the treatment of atoms such as sulfur as evidenced by the results here and else~ h e r e . ~ Although ~ , ~ ~ i ~the~ problem can be alleviated somewhat with other CNDO parameterizations,’O the same problem to a lesser extent plagues other NDO methods, such as INDO and MIND0/3. The MINDO/3 method predicts a slightly stable dimeric structure for the dimethyl sulfide system, but a t too short an S.43distance. Although M I N D 0 / 3 does well a t predicting intramolecular stretching f r e q ~ e n c i e sit, ~does ~ not seem to do as well for intermolecular forces. Structural predictions from MINDO/3 for sulfur-containing molecules, in general, do not seem to be as good as those for first-row molecules. Further refinement of MINDO/3 parameters for sulfur, or development of an approximate method a t a more sophisticated level, such as MND0,72may be necessary before the dimethyl sulfide complexes can be predicted with confidence. Nevertheless, MIND0/3 remains one of the better MO methods available for studying drug-receptor interactions because it can be employed to obtain useful information on the three-dimensional structures of transition state and transition intermediate species of first-row molecule^.^^*^^ The oldest and simplest of the three methods tested here, EH, is found to yield a qualitatively reasonable repulsive potential between the two dimethyl sulfide molecules in the van der Waals contact region (3-4 A). The foundation of this MO method on overlap integrals leads both to its ability to predict a repulsive potential curve a t long distances and to its breakdown a t shorter separations. However since the van der Waals contact
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region is the main concern to us, the EH method is useful. Other authors have also noted the ability of the E H method a t predicting potential energy curves between certain simple closed-shell species.47 Despite its simplicity and limitations, the EH method continues with proper use to provide insights to physical phenomena. We wish merely to point out that there remain areas where it can be utilized as a preliminary probe. Accurate potential energy curves can only be obtained with ab initio calculations including electron correlation. Such ab initio calculations would be a very useful follow-up to the work described in the present paper. The present study is obviously a model study because experimental conditions, such as are present in the crystalline systems where short nonbonded S-S contacts are actually observed, will complicate somewhat the situation. Nevertheless, the EH method does show that the dimeric structure with the n(sp2) lone pairs of divalent sulfur in an antiparallel arrangement (3) involves a significantly lower repulsive potential than the other modes that were tested. This arrangement is modeled after that observed in crystalline meso-lanthionine dihydrochloride> and its calculated relative stability is consistent with its existence. It is conceivable that ab initio calculations on a model system could reveal refinements on the detailed molecular geometry that we assumed and perhaps additional arrangements involving lone pair contacts also relatively less unstable. Rosenfield and P a r t h a ~ a r a t h y ~ have surveyed nonbonded S-S contacts in the crystalline state structures of many sulfur-containing compounds. They discovered that a majority of the close contacts occurred when one sulfur was nearly in the A-S-B plane of the second sulfur. This observation is consistent with the E H calculations and with the meso-lanthionine case, and implies that more refined calculations will not yield predictions greatly different than the present ones. The EH calculations indicate that the relatively low repulsion in the antiparallel approach is due to a propitious spatial arrangement in the one-electron energy levels. The shifts in energy levels are small relative to the other modes of approach; no filled MO rises sharply to correlate with an empty MO as occurs with other overlapping arrangements of the s ~ *and - 3p-type lone pairs. Electron density maps reveal that the n(sp2)orbitals bend away from each other in the antiparallel arrangement. One would suppose that, in analogy to the situation with bonding electron pairs, it is easier to bend the lone pairs than to change their spatial extent. In other words, just as it costs less energy to deform a bond angle than to stretch or shorten a bond length, it is easier to bend a lone pair out of the way rather than to squash it. Of course, in the coplanar and perpendicular n(sp2)-n(sp2) and in the n(3p).-n(3p) modes (Figure 2), the lone pairs move directly at each other, and the only way to reduce unfavorable overlap is to squash down. Molecular orbital correlation diagrams and electron density maps have given us some insight into why the divalent sulfurs align the way they do in lanthionine. It is also of interest to set forth the situation in terms of the language of force fields and molecular mechanics. Consider a pair of lanthionine molecules in the antiparallel arrangement. The existence of close nonbonded contacts between the divalent sulfurs means the attractive forces between sulfur and the atoms of the other molecule and among these other atoms with each other more than offset the repulsive forces between the two sulfurs at the older S - 8 van der Waals contact distance of 3.7 A. Thus, the molecules are drawn together until repulsions balance
Donald
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attractions. In addition to the dispersion forces, one would expect the interaction of the local dipoles of the n(sp2) lone pairs to contribute to the stabilization of the complex. This interaction should be quite favorable when the local dipoles are aligned head-to-tail as in the antiparallel geometry. We concur with the earlier recommendation^'^ that the van der Waals radius of sulfur needs to be reduced from the commonly accepted values of 1.831.90 A. In addition, our analysis shows that a divalent sulfur atom does not present a spheroidal face on its nonbonded side. The electron density is up to 0.2 A more extensive perpendicular to the A-S-B plane than in the plane. This anisotropy of sulfur is quite consistent with crystal structure data that have been accumulated.6-10~33 An important recent paper74has been pointed out that short nonbonded contacts between divalent sulfur and some other atom can be divided into two types: electrophilic atoms prefer approaches from a direction roughly perpendicular to the A-S-B plane, and nucleophilic atoms prefer approaches in this plane on the back side of the S-A or S-B bond. Thus, when the environment around sulfur is averaged over a great many structures, divalent sulfur appears to be hexacoordinated in a roughly octahedral arrangement. Not much difference is noticed between the in-plane nonbonded contact distances and those perpendicular to the A-S-B plane when the second nonbonded atom is other than sulfur. These author^'^ noted that nucleophiles interact strongly with the lowest empty MO, which they expected to be an S-C u* orbital. Electrophiles interact preferentially with the highest occupied MO, which is the n(3p)-type lone pair of sulfur. The crystal structures with nonbonded contacts less than the sum of the older van der Waals radii can be rationalized as showing early stages of chemical reaction.74 The rneso-lanthionine system would correspond to nucleophilic attack of one sulfur or another because the sulfurs approach in-plane. Although the semiempirical methods are not suited to establish the exact nature of the lowest empty MO, the calculations do show that this MO of dimethyl sulfide can have a shape suited for interaction with the n(sp2)orbital of another sulfur in the antiparallel approach. Whereas these orbital interactions are weak compared to other forces operating in a molecule, recognition of their existence should help in understanding of enzymatic reaction mechanisms and the elucidation of the conformation of sulfur-containing proteins. Although S - 8 interactions could conceivably be obscured by other, stronger forces involved, for instance, in crystal. packing, the orbital interaction effects do seem to be important enough to make certain trends apparent in a surveyg of many crystal structures.
Acknowledgment. The author expresses his deep appreciation to R. Parthasarathy for a preprint and helpful correspondence. M. M. Marsh, R. Hoffmann, and N. L. Allinger provided valuable consultations. References and Notes (1) This paper is dedicated to the memory of Howard Milton Boyd (1895-1976), chemist. (2) F. S. Richardson, C.-Y. Yeh, T. C. Troxell, and D. B. Boyd, Tetrawon, 33, 71 1 (1977), constituted paper 73 of the present series. (3) L. Pauling, "The Nature of the Chemical Bond", 3rd ed, Cornell University Ress, Ithaca, N.Y., 1960, p 260; A. Bondi, J. phys. Chem., 68, 441 (1964). (4) N. L. Allinger and M. J. Hickey, J. Am. Chem. Soc., 97, 5167 (1975), and N. L. Aliinger. Adv. Phys. Or Chem., 13, 1 (1976), suggest a "van der Waals radius" of 2.00 f ' f o r sulfur while pointing out that the sum of their "van der Waals radii" should be distinguished from the distance of closest approach in crystals. In the present paper, we use the term van der Waals contact distance to mean the distance of closest approach. (5) J. L. Flippen and I. L. Karle, J . Phys. Chem., 74, 769 (1970).
Mapping Electron Density in Molecules (6) R. E. Rosenfield, Jr., and R. Parthasarathy, J. Am. Chem. Soc., 96, 1925 (1974). (7) R. E. Rosenfield, Jr., and R. Parthasarathy, Acta Crystallogr., Sect. B . 31. 462 (1975). ( 8 ) R.'E. dosenfjeld, Ji., and R. Parthasarathy, Acta Crystallogr., Sect. B , 31, 816 (1975). (9) R. E. Rosenfield. Jr.. and R. Parthasarathy, Abstracts, 25th Meeting of the American Crystallographic Association, Charlottesville, Va, March 9-13. 1975. D 28. (10) C.4. Chen, d. Parthamrathy,and G. T. DeTitta, J. Am. Chem. Soc., 98, 4983 (1976). (11) . . W. L. Kehl and G. A. Jeffrey, Acfa Crystal/ogr., 11, 813 (1958); G. A. Jeffrey and R. Shiono, ibid., 12, 447 (1959). (12) D. B. Cosulich, N. R. Nelson, and J. H. van den Hende, J . Am. Chem. Soc., 90, 6519 (1968). (13) H. E. Van Wart, L. L. Shipman, and H. A. Scheraga, J. Phys. Chem., 79, 1436 (1975). (14) M. M. Kadooka. L. G. Warner, and K. Seff, J . Am. Chem. Soc., 98, 7569 (1976); N. V. Raghavan and K. Seff, Acta Crystalbgr., Sect. 6 , 33, 386 (1977). (15) The thiourea in ref 5 also shows intramolecular contact distances between formally nonbonded sulfurs of 2.9-3.0 A. However,, we are more interested in intermolecubrcontacts because the possibility of resonance structures Involving S-S bonding is rendered unlikely. Other molecules wM short intramolecuhr sub-sulfur contacts include thiothiophthene [R. Gleiter and R. Hoffmann, Tetrahedron,24, 5899 (1968); H.-B. Burgi, Angew. Chem., Int. Ed. Engl., 14, 460 (1975)] and tetranltrogen tetrasulfde (M. S.Gopinathan and M. A. WhRehead, Can. J. Chem., 53, 1343 (1975)]. Both of these molecules can be drawn with contributing resonance structures with covalent bonds between the sulfurs. (16) A case earlier claimed to have short C-H-S contacts may not, in fact; see J. D. Lee and M. W. R. Bryant, Acta Crystallogr., Sect. . 8 , 27, 2325 (1971), J. Donohue and J. P. Chesick, ibid., 31, 986 (1975). (17) D. B. Boyd, J. Am. Chem. Soc., 94, 6513 (1972), and references cited therein. (18) J. A. Pople and D. L. Beveridge, "Approximate Molecular Orbital Theory", McGraw-Hill, New York, N.Y., 1970; J. A. Pople and G. A. 1-, J. Chem. phys., 44,3289 (1966); D. P. Santry and G. A. %gal, ibid., 47, 158 (1967); the spd basis set is used. (19) R. C. Bingham, M. J. S.Dewar, and D. H. Lo, J . Am. Chem. Soc., 97, 1285, 1294, 1302, 1307 (1975); M. J. S.Dewar, D. H. Lo, and C. A. Ramsden, ibd.,97, 1311 (1975); M. J. S.Dewar, R. C. Haddon, W.-K. Li, W. Thiel, and P. K. Weiner, ibid., 97, 4540 (1975); M. J. S.Dewar, Chem. Brit., 11, 97 (1975). (20) P. K. Mehrotra and R. Hoffmann, Theor. Chim. Acta, in press. Some reasons for the success of EH theory in dealing with certain electronic problems are mentioned by J. H. Ammeter, H.B. Bikgi, J. C. ThibeauR, and R. Hoffmann, submitted for publication. (21) F. P. Boer and W. N. Lipscomb, J. Chem. Phys., 50, 989 (1969). (22) M. F. Guest and W. R. Rodwell, Mol. Phys., 32, 1075 (1976). (23) See, also, e.g., H. Sakai, T. Yamabe, H. Kato, S. Nagata, and K. Fukui, Bull. Chem. SOC. Jpn., 48, 33 (1975); P. D. Mollere and K. N. Houk, J. Am. Chem. Soc., 99, 3226 (1977). (24) D. B. Boyd, J. Am. Chem. Soc., 94, 64 (1972). See, also, H.-L. Hase, H. Meyer, and A. Schweig, Z. Naturforsch. A, 29, 361 (1974), who stress the importance of deorthogonalizing to get proper nodal character in electron density maps from neglectafdifferentiakverbp wave functions. (25) D. 8. Boyd, J . Chem. Phys., 52, 4846 (1970). (26) D. B. Boyd, Theor. Chim. Acta, 30, 137 (1973). (27) D. B. Boyd, J. Phys. Chem., 78, 1554 (1974). (28) D. B. Boyd, J . Phys. Chem., 78, 2604 (1974). (29) D. B. Boyd, Int. J. Quantum Chem., Quantum Bo/. Symp., No. 1, 13 (1974). Electron density difference maps from CNDO/2D wave functions fail to show any buildup of electrons in the A-S-B plane, and consequently are suggestive of a hybridization scheme where both lone pairs are in sp3-typeorbitals rather than as in 2 (see also ref 28). It should be noted that the individualCNDO/2 MO's of suifiies are analogous to those from EH and ab initio calculations in that the highest occupied MO's include one with S3p nonbonded character and a lower one with sp2 nonbonded character. Only the difference map from CNDO/2D gives the appearance of sp3 hybridization, and this arises because the renormalization process decreases the ratio of 3p to 3s A0 character in the n(sp2)MO. As a consequence, there is less density in the A-S-B plane in the molecule compared to the spherical reference atoms. (30) J. Bicerano, D. S. Marynick, and W. N. Lipscomb, J. Am. Chem. Soc., 100, 732 (1978). (31) R. F. W. Bader, W. H. Henneker, and P. E. Cade, J. Chem. Phys., 46, 3341 (1967); R. Daudel, R. F. W. Bader. M. E. Stephens, and D. S. Borrett, Can. J. Chem., 52, 1310 (1974), and references cited therein. For an alternative definition of orbltal size, see M. A. Robb, W. J. Haines, and I.G. Csizmadia, J. Am. Chem. Soc., 95,42 (1973). (32) A similar qualitative model for the oxygen lone pairs has been assumed; see J. Hine and P. D. Dalsin, J. Am. Chem. Soc., 94, 6998 (1972). (33) P. Coppens, Y. W. Yang, R. H. Blessing, W. F. Cooper, and F. K. Larsen, J . Am. Chem. Soc., 99, 760 (1977). It is of interest that
The Journal of Physical Chemistry, Vol. 82, No. 12, 1978 1415 an ab initio electron density map for H2S2in this paper bears some resemblances to EH (ref 26) and CNDO/2D (ref 27) ones, except that in the ab initio work the reference atomic wave function for H appears to be deficient compared to the molecular basis set that was used. (34) D. B. Boyd, R. B. Hermann, D. E. Presti, and M. M. Marsh, J . Med. Chem., 18, 408 (1975). (35) G. L. Bendazzoli, G. Gottarelli, and P. Palmieri, J . Am. Chem. Soc., 96, 11 (1974); see,also, H. Drebler and H. D. Ruddph, 2.Naturfwsch. A , 17, 712 (1962). (36) N. L. Ailinger, J. Kao, H.-M. Chang, and D.B. Boyd, Tetrahedron, 32, 2867 (1976), and references cited therein. (37) J. R. Sabin, J . Am. Chem. Soc., 93, 3613 (1971). (38) A. R. Gregory in "Chemical and Biochemical Reactivity", E. D. Bergmann and B. Pullman, Ed., Israel Academy of Sciences and Humanities, Jerusalem, 1974, p 23. (39) A. Grimison, Theor. Chim. Acta, 35, 169 (1974); M. Martin, R. Carbo, C. Petrongolo, and J. Tomasi, J . Am. Chem. Soc., 97, 1338 (1975); F. Jordan, ibid., 97, 3330 (1975); S.F. Abdulnur and R. L. Flurry, Jr., Chem. phys. Lett., 36, 586 (1975); J. C. Schug and K. A. Levinson, Theor. Chim. Acta, 37, 269 (1975); C. W. Eaker and J. Hinze, /bid., 40, 113 (1975); P. E. S.Wormer and A. van der Voird, J . Chem. Phys., 62, 3326 (1975). (40) H. E. Van Wart, L. L. Shipman, and H. A. Scheraga, J . phys. Chem., 79, 1428 (1975). (41) C. N. R. Rao, P. C. Dwivedi, A. Gupta, H. S.Randhawa, H. Ratajczak, M. M. Szczesniak, K. Romanowska, and W. J. Orville-Thomas, J . Mol. Struct., 30, 271 (1976). (42) A. R. Gregory and M. N. Paddon-Row, J. Am. Chem. Soc., 98, 7521 (1976). (43) P. Caramelb, K. N. Houk, and L. N. Dometsmith, J. Am. Chem. Soc., 99, 451 1 (1977); K. B. Lipkowitz and R. Larter, Tetrahedron Left., 33 (1978). (44) Related examples were encountered in the work of M. Froimowitz and P. J. Gans, J . Am. Chem. SOC.,94, 8020 (1972); J. J. Dannenberg, ibid., 98, 6261 (1976); L. L. Combs and M. Rossie, Spectrosc. Lett., 9, 495 (1976); M. V. Basilevsky, A. G. Shamov, and V. A. Tikhomirov, J. Am. Chem. Soc., 99, 1369 (1977). (45) For a discussion of different ways of obtaining total energies from EH theory which approximate ab initio values, see D. B. Boyd, J . Chem. Phys., 67, 1787 (1977). The EH relative energies of Figures 1 and 2 are based on using the best total energy approximation in this reference; this involves using 0.5& where the sum of the EH eigenvalues is over all electrons. (46) For two sulfurs along the zaxis, the magnitude of the overbp integral between the 3p, Slater-type orbitals on the two centers (using exponents described in ref 17) increases monotonically from 0.02 at 4-A separation to a maximum of 0.38 at 1.75 A and then drops sharply to 0.02 at 1.0 A. In contrast, the magnitude of the 3s, 3p, overlap integral increases monotonically from 0.01 at 4 A to 0.40 at 1.75 A and to 0.57 at 1.0 A. Simihrty, 3s, 3s and 3p,, 3p,overhps rise from 0.002 at 4 A to 0.26 and 0.21, respectively, at 1.75 A and to 0.64 and 0.59, respectively, at 1 A. (47) K. B. Hathaway and J. A. Krumhansl, J . Chem. Phys., 63, 4308 (1975). (48) A little over half of the electron population in this MO, if it were to be occupied, is in a linear combination of the 3d AO's. I n earlier work [D. B. Boyd, C.-Y. Yeh, and F. S.Richardson, J . Am. Chem. Soc.,98, 6100 (1976)], a distinction was noted between the EH and CNDO/2 methods regarding the low-lying empty MO's of sulfides and disulfides. The former method usually gave predominantly empty 3d character to these MO's, whereas CNDO/2 often gave S-C u* character (with some 3d contribution mixed in). (49) R. Hoffmann and R. B. Woodward, Acc. Chem. Res., 1, 17 (1968); R. B. Woodward and R. Hoffmann, Angew. Chem., 81, 797 (1969). (50) Lack of dipole-dipole effects is also apparent in the CND0/2 method. See, A. Veillard, Chem. Phys. Lett., 33, 15 (1975), and references cited therein. (51) D. B. Boyd, J . Am. Chem. Soc., 94, 8799 (1972); and references cited in ref 27. (52) J. P. Snyder and L. Carlsen, J . Am. Chem. Soc., 99, 2931 (1977). (53) J. A. Pappas, Chem. Phys., 12, 397 (1976). It should be noted that some misleading statements about the results and conclusions in ref 27 appear in this study of simple disulfides. One reason is that in this Chem. phys. paper Mullaten overlap populations betweenatoms are labeled and treated at "net charges on" atoms. This terminology is contrary to common usage; see, e.g., R. Hoffmann and W. N. Lipscomb, J . Chem. Phys., 36, 3489 (1962); W. J. Hehre and J. A. Pople. J . Am. Chem. Soc.. 92, 2191 (1970); D.Booth and J. N. Murrell, Mol. Phys., 24, 1117 (1972); S.FliszBr, A. Goursot, and H. Dugas, J. Am. Chem. Soc., 96, 4358 (1974). Nothing was stated in ref 27 regarding ionization potentials (IP's) correlating with S-R overlap populations, and, indeed, one would expect no such "cwebtion" to extend beyond the two molecules treated in the Chem. Phys. paper. Also, ref 27 did not conclude that induction of the R groups was unimportant in explaining 1P's of R2S2 compounds for alkyl groups R larger than CH,. Our conclusion regarding inductive effects of these R groups agrees with that of H. Bock and G. Wagner, Angew Chem., Int. Ed. Engl., 11, 150 (1972). See, also, J. A. Pappas, J . Am. Chem. Soc., 99, 2926 (1977).
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The Journal of Physical Chemistry, Vol. 82, No. 12, 1978
(54) H A . Mez, Cryst. Struct. Commun., 3, 657 (1974). This noteworthy X-ray diffraciion study showed that cycioi-cystine has a CS-SC dihedral angle of 91' in the crystalline state. This disulfide is very interesting because the M heiicity of the disulfide bridge is opposite the P helicity deduced from NMR, UV, and CD experiments; see, e.g., B. Donzel, B. Kamber, K. Wuthrich, and R. Schwyzer, Helv. Chim. Acta, 55, 947 (1972); M. Ottnad, P. Hartter, and G. Jung, Hoppe-Seyler's Z.Physiol. Chem., 356, 101 1 (1975). In fact, the latter reference reported an exceptionally high barrier of 15.8 kcal/moi for the P F! M interconversion. Such a barrier height seems difficult to surmount with the energy derivable from crystal packing forces. A final point of interest is that, in this molecule and others with a four-membered bridge across a diketopiperazine ring [see, e.g., M. Przybylska and E. M. Gopalakrishna, Acta Crystallogr., Sect. B., 30, 597 (1974)], each of the sulfurs in the middle of the bridge reside in positions proximal to amide nitrogens rather than proximal to the carbonyl carbons, unlike the situation with a twwmembered disulfide bridge [ref 27 and K. H. Michel, M. 0. Chaney, N. D. Jones, M. M. Hoehn, and R. Nagarajan, J . Antibiot., 27, 57 (1974)]. See, also, A. R. Gregory and M. Przybylska, J . Am. Chem. Soc., 100, 943 (1978), for an excellent, thorough discussion of this topic, and C . 4 . Chen, T. Srikrishnan, and R. Parthafarathy, Biochem. Bbphys. Acta, 538, 534 (1978), for additional references. N. L. Allinger, M. J. Hickey, and J. Kao, J . Am. Chem. SOC.,98, 2741 (1976); J. Kao and N. L. Allinger, rnorg. Chem., 16, 35 (1977). H. E. Van Wart and H. A. Scheraga, Proc. Natl. Acad. Sci. U.S.A ., 74, 13 (1977). See, also, ref 36 and 14, and F. R. Maxfield and H. A. Scheraga, Biochemistry, 16, 4443 (1977). The threefold barrier of methyl ethyl disulfide 4 was obtained with complete optimization of all geometrical variables, except for the SS-CC dihedral angle determining the various conformers. In preliminary work, we fwnd that with essentially fixed geometries during rotation about the S-C bond, no minimum was detected in the G' region (-300'). In another set of runs, ail geometrical variables were optimized, except the SS-CC and SS-CH (for H's on the methylene carbon) dihedral angles which were kept at exactly 120' intervals. In these runs only a single minimum at 180' was obtained for the potential energy curve; no minima were found for the G and G' conformers. These findings imply the importance of allowing free equilibration of all geometrical variables other than the one under consideration in the MIND013 procedure. I t should be mentioned that some of the MIND0/3 structural and energetic predictions for 4 are not totally satisfactory. For instance, compared to microwave and molecular mechanics results (which are essentklly in complete agreement with each other; see ref 36), MINDO/3 predicts C-C-S bond angles to be 5-10' higher or lower, S-S-C angles to be ca. 10' higher, S-C bond lengths to be 0.07 A shorter, C-C lengths to be 0.05 A shorter, and S-S lengths to be 0.06 A longer. Similar discrepancies in predicted bond length have been reported for (CH3),S2 (ref 19). An unusual S-C-H bond angle for the methylene group of 4 was also noted; in the G and G' conformers, the bond angle to the H trans to the second sulfur is predicted to be rather small (99') compared to the near tetrahedral angle for the gauche H. Regarding relative energies of the SS-CC conformers of 4, MIND013 predicts T to be roughly 1 kcal/moi more stqble than either G or G', which are of similar energy. On the other hand, molecular mechanics and the STO-3G calculations (ref 36) both indicated that G and T were of essentially equal stability and that G' was 0.6-0.7 kcal/mol less stable. The electron density in a lone pair region is somewhat analogous to an inflated balloon: if it is squeezed on one side it bulges out at another place. One also notices this characteristic property of lone pairs in the calculational results of W.-K. Li and T. C. W. Mak, J . Mol. Struct., 25, 309 (1975). Mulliken population analysis [R. S. Mulliken, J . Chem. Phys., 23, 1833 (1955)] gives sulfur net atomic charges (called partial charges by some) that are quite dependent on the MO method. For monomeric (CH,),S, CNDOI2 gives -0.07, CNDO/2D $0.05,EH -0.08, and MIND0/3 -0.19. The variability is not suprising consideringthe similar electronegativities of sulfur and carbon and the reversal of relative electronegativity among various scales [see, e.g., G. Simons, M. E. Zandler, and E. R. Talaty, J . Am, Chem. Soc ., 98, 7869 (1976)]. Ab initio calculations are no more decisive than the semiempirical ones in regard to the sign of the net atomic charge on sulfur. Generally, divalent sulfur bears a small positive charge in ab initio minimum basis set calculations, but becomes less positive or negative with improvement of the basis set, such as by inclusion of 3O'functions [see, e.g., ref 21; R. BoMccorsi, E.Scrocco, and J. Tomasi, J . Chem.
Donald B. Boyd Phys., 52, 5270 (1970); M. H. Palmer and R. H. Findlay, J . Chem.
S&., Perkin Trans. 2, 1223 (1975); and ref 531. Net atomic charges
(60)
(61)
(62) (63) (64) (65) (66)
(67) (68) (69) (70) (71) (72)
(73) (74)
for atoms in molecules with small charge separations, such as sulfdes and hydrocarbons, are capricious to the extent that they depend on the MO method, the basis set, and the population analysis scheme. Perhaps in molecules of this type, the charges are only meaningful enough to show trends between related structures, rather than being accurate indicators of electron density, such as for electrostatic energy calculations. Ifa choice of a suitable net atomic charge for divalent sulfur hadto be made for a semiempirical energy calculation, then consideration of the lone pairs on this atom would intuitively lead one to prefer a (small) negative value, rather than a positive one. According to the EH description, the only other modes of approach in Figure 2 to result in strengthening S-C bonds as the sulfurs get cioser together are those involving contact toward the n(3p) orbital. In all modes of approach the sulfurs become less negative as they get closer, except for the sp2-.3p case where the sulfur making nonbonded contact through its n(3p) orbital gains, rather than loses, electron population. The CNDO/2 and MINDO/3 calculations of Figwe 1 agree with EH in showing reduced populations on sulfurs as S.-S distance decreases. The bulk of the displaced population ends up on the carbons. For the quoted LCAO-MO coefficients, we use a coordinate system such that the C, symmetry axis of the monomer coincides with the z axis, the C-S-C atoms lie in the xz plane, and the carbons are in the + r direction from S. R. McDiarmid, J . Chem. Phys., 61, 274 (1974); J. D. Scott and B. R. Russell, /bid., 63, 3243 (1975). For a few exceptions, see, e.g., D. R. Sabhub and C.Sandorfy, T b r . Chim. Acta, 20, 227 (1971); D. R. Salahub, ibM., 22,325, 330 (1971); W. Haque, J . Chem. Phys., 67, 3629 (1977). K. Wittel, Tetrahedron, 33, 2687 (1977). K. Wittei and S. P. McGlynn, Chem. Rev., 77, 745 (1977). For recent examples where 30' orbitals (or basis functions) have been found to be important in MO calculations on some second-row molecules, but not in others, see A. Streitwieser, Jr., and J. E. WBiams, Jr., J . Am. Chem. SOC.,97, 191 (1975); J. E. Williams, Jr., and A. Streltwieser, Jr., ibid., 97, 2634 (1975); F. Bernardi, I.G. Cslzmadla, A. Mangini, H. B. Schlegel, M.-H. Whangbo, and S. Wolfe, lbM., 97, 2209 (1975); G. M. Schwenzer and H. F. Schaefer, 111, lbM., 97, 1393 (1975); M.-M. Rohmer and 8. Roos, bid., 97, 2025 (1975); F. Keii and W. Kutzelnigg, ibM., 97, 3623 (1975); C.C. Levin, ibM., 97, 5649 (1975); ref 22; K. Tatsumi, Y. Yoshioka, K. Yamaguchl, and T.Fueno, TetraMron, 32, 1705 (1976); J. B. Cdlins, P. v. R. Schleyer, J. S. Binkiey, and J. A. Pople, J . Chem. Phys., 84, 5142 (1976); M. P. S. Collins and 8. J. Duke, Chem. Phys. Lett., 42, 364 (1976); ref 48; N. D.Epiotis, R. L. Yates, F. Bernardl, and S. Wolfe, J . Am. Chem. Soc., 98, 5435 (1976); J.-M. Lehn, and G. Wipff, ibid., 98, 7498 (1976); R. Hoffmann, J. M. Howell, and A. R. Rossi, lbld., 98, 2484 (1976); H. Lischka, ibid., 99, 353 (1977); L. M. Loew and W. R. MacArthur, bid., 99, 1019 (1977); F. J. Marsh and M. S. Gordon, Chem. Phys. Lett., 45, 255 (1977); M. A. Ratner and J. R. Sabin, J . Am. Chem. Soc., 99, 3954 (1977); T. A. Halgren, L. D. Brown, D. A. Kleier, and W. N. Lipscomb, ibid., 99, 6793 (1977); and references cited in these papers. Although no statistical survey has been carried out,probably there have been as many literature r e m s concluding that 3d orbitals are of little or no importance as reports concluding significant participation. There seems to be a tendency among some authors to overgeneralize from cases where d orbitals are genuinely important, or unimportant, to untested situations. A few studies devoted to showing irrelevance of d orbitals have suggested that the unique properties of second-row atoms like sulfur derive from the polarizability of the electron clouds of these atoms; yet this is a property which is intimately connected with the contrbution of d orbitals to the excited states of these atoms. C. A. Coulson, Natwe(London), 221, 1106(1969); D. B. Boyd, Theor. Chem. Acta, 20, 273 (1971); R. S.Muliikenand B. Liu, J. Am. Chem. Soc., 93, 6738 (1971). D. B. Boyd, J . Am. Chem. SOC.,91, 1200 (1969). L. B. Kier and H.-D. Hokje, J . Theor. Biol., 49, 401 (1975); L. H. Hall and L. B. Kier, ibid., 58, 177 (1976). F. J. Marsh and M. S. Gordon, J . Mol. Struct., 31, 345 (1976). M. J. S.Dewar and G. P. Ford, J. Am. Chem. Sm.,99, 1685 (1977). M. J. S.Dewar and W. Thiel, J . Am. Chem. Soc., 99, 4899, 4907 (1977). D. B. Boyd, Proc. Natl. Acad. Sci. U.S.A., 74, 5239 (1977). R. E. Rosenfield,Jr., R. Parthasarathy, and J. D. Dunitz, J. Am. Chem. Soc., 99, 4860 (1977).
