261

Three Electron Bonds. I. The H2SSH; Radical Cation

Timothy Clark Institut fur Organische Chemie der Friedrich- Alexander- Uniuersitat Erlangen-Niirnberg, 0-8520 Erlangen, Federal Republic of Germany Received 30 October 1980; accepted 19 December 1980

Ab initio molecular orbital calculations are reported for HZS, its radical cation, and the HzSSH; radi- cal cation. At the MP2/4-31G level the S-S three-electron bond is 2.85 a long, and has a dissociation energy of 31.2 kcal mole-'. The performance of MNDO semiempirical molecular orbital theory is com- pared with the ab initio results.

INTRODUCTION

Three-electron two-center bonds in which one electron occupies a (r* orbital have been observed for a variety of elements, notably between two sulfur14 or two nitrogen5 atoms. These species are particularly important as models for the interac- tion of electrophilic radicals with bases, especially as they appear to be very sensitive to ring strain and electronic effect^.^-^ As a first step toward a wider investigation of three-electron bonded species we have used ab initio molecular orbital theory to investigate the simplest ion involving an S-S three-electron bond: H2SSH;. Our purpose was twofold: to assess the strength of the three- electron bond and to test the performance of MNDO semiempir ical molecular orbital theory for such systems so that the simpler and less expensive method may be applied to larger, experimentally accessible systems.

METHOD AND RESULTS

All ab initio calculations used the GAUSSIAN 76 series of programs6 using the 4-31G (44-31G for ~ u l f u r ) ~ basis set. Optimizations at the restricted and unrestricted Hartree-Fock levels (RHF and UHF, respectively) used analytically evaluated atomic forces* in a Davidon-Fletcher-Powell multiparameter search r ~ u t i n e . ~ Geometry opti-

mization in calculations including a correction for electron correlation by second-order M#ller- Plesset perturbation theory1° (MP2) were per- formed by cyclic variation of all parameters (MP2 calculations included the sulfur core orbitals).

MNDO calculations used the standard MNDO programll with modifications to allow the calcu- lation of radical excited states.12 The hydrogen13 and sulfur14 parameters used are as published. All radical calculations a t MNDO used the half-elec- tron method.15

The molecular orbital plots used Jorgensen's program16 using the UHF/STO-3G//MP2/4-31G wavefunction. The plots show the cy orbitals as if they were doubly occupied.

Table I shows the HF/4-31G, MP2/4-31G, and MNDO optimum geometries for H2S, the *B1 and 2A1 states of H2S+, and for the syn and anti con- formations of the H2SSH; ion. These two high- symmetry conformations have been chosen to allow MP2/4-31G optimization of H2SSH: and to simplify interpretation.

Table I1 shows the HF/4-31G and MP2/4-31G total energies and the MNDO heats of formation for the species shown in Table I. Also shown are the calculated ionization potentials for H2S and the S-S bond dissociation energies for H2SSHt.

* The analytical force routines8 were incorporated into the earlier DFP program by Chandrasekhar.9

cJournal of Computational Chemistry, Vol. 2, No. 3, 261-265 (1981) 0 1981 by John Wiley & Sons, Inc. CCC 0192-8651/81/030261-05$01.00

262 Clark

Table I. HF/4-31G. MP2/4-31G. and MNDO oDtimized geometriesa for H& and related radical cations.

SH HSH

I! + ss H\ : SH

HSH s-s, SSHze

L "H H

SSHae

1.366 98.5

1.360 131.2

2.826 1.355 97.4 96.8

2.842 1.356 97.4 104.9

1.373 94.3

1.384 97.2

1.372 130.3

2.850 1.375 96.1 94.4

1.302 1.328c 96.4 92.2c

1.322 1.358d 96.6 92.gd

1.355 136.5 ca. 127d

2.165 1.319 107.6 101.5

2.164 1.318 96.8 118.6

a Angles in deg, bond lengths in A. Reference 17. Reference 18. Reference 19. The angle between the S-S bond and the HSH bisector.

DISCUSSION values of 92.9' and ca. 127', respectively. The MP2/4-31G optimum angles of 97.2' and 130.3" are comparable to the HF/STO-% values. MNDO appears to overestimate the bond angle of the 2A1 state and also gives a significant lengthening of the SH bonds relative to those in the 2B1 ion. This bond lengthening is not reproduced at either the

HzS+

Sakai et a1.22 have previously considered H2S+ a t the minimal STO-3G basis set level. They ob- tained HSH angles for the 2B1 and 2A1 states of 97.4' and 126.1', compared with the experimental

Table 11. dissociation energies (kcal mole-') for hydrogen sulfide and related radical cations.

Total energies (a.u.), MNDO heats of formation (kcal mole-'), H2S ionization potentials (eV), and S-S bond

H F/4-3 1G MP2/4-31G MNDO ExDerimental

H2S Energy" -398.20395 -398.27076 1.7 -4.48 f 0.15" HzS+ ("1) Energya -397.85908 - 397.9 16 1 1 245.7

H2S+ (2A1) Energya -397.78760 -397.84080 299.3 IPH,s 9.38 9.65 10.58 10.48"

IPHzS 11.33 11.70 12.90 12.78c

B H\ : +

Energya -796.10068 -796.23656 208.2 H ' Dssd 23.8 31.2 39.2

s-s i-.

H\-;,H ? f I + Energya -796.09520 - 211.0 3.4 - 2.8

* Total energies for ab initio calculations, for MNDO and experimental values. Reference 20. Reference 21. Calculated energy for the reaction H2SSHl- HzS+ (2B1) + H2S. Rotation barrier for H2SSH2+ (C2h + C2").

Three Electron Bonds. I 263

H

5 a ~

Figure 1. HOMO ( 5 a l ) and SOMO (261) of 2B1 H$Y.

HF/4-31G or MP2/'4-31G levels. Sakai et a1.22 did not optimize the bond lengths.

The excitation energy (0-0) from 2B1 to 2A1 H2S+ was 2.63 eV at ST0-3G,22 slightly larger than the experimental value of 2.30 eV.19y21 HF/4-31G (1.95 eV) and MP5!/4-31G (2.05 eV) both slightly underestimate this energy, whereas MNDO repro- duces the experimental ionization potentials within 0.12 eV and the 0-0 excitation energy (2.30 eV) perfectly.

H2SSH;

The calculated length of the S-S three-electron bond varies from 2.17 A at MNDO to 2.85 A at MP2/4-31G. The effect of correlation is to lengthen the bond by 0.024 A at 4-31G. Calculated S-S bond dissociation energies vary from 23.8 kcal mole-' at HF/4-31G to 39.2 kcal mole-' at MNDO. The MP2/4:-31G bond dissociation energy is midway between the two at 31.2 kcal mole-l. The ab initio bond energies are likely to be too low because of the fact that H2S is calculated a t the RHF level and therefore the dissociation equation

is somewhat inconsistent. The MNDO bond dis- sociation energy of 39.2 kcal molep1 is therefore not unreasonably high. The length of the S-S three-electron bond is, however, severely under- estimated by MNDO. For comparison the S-S two-electron bond in HSSH is 2.24 8, long a t HF/4-31G.23

H2SSH; prefers the anti conformation by 3.4 kcal molep1 at HF/4-31G, and by 2.8 kcal mole-l at MNDO. The syn conformation was not investi- gated at MP2/4-31G. The preferred conformation around the S-S bond may be important for some bicyclic disulfide radical cations, such as those observed by Muskerl and by Asmus et al.2-5 as these species are constrained to the syn confor- mation, or close to it. The low barrier, comparable to that in ethane,24a and much lower than that expected of a molecule with adjacent lone pair,24b is a consequence of the long S-S bond.

ORBITAL INTERACTIONS IN H2SSHi

The HOMO and SOMO of 2B1 H2S+ are shown in Figure 1. The bond angles in H2SSH; are such that the SOMO of H2S+ approaches the HOMO of H2S

Figure 2. (a) First-order interaction diagram for complex formation between H2S and its radical cation. Strong mixing of the two adajacent ag orbitals leads to the orbital pattern shown in (b).

264 Clark

9 ULTRAVIOLET/VISIBLE ABSORPTION

Figure 3. The SOMO (76,) and the three highest doubly occupied molecular orbitals of C Z ~ HZSSH;.

(also a pure p orbital) directly, forming uss and cr; orbitals. The two doubly occupied a1 lone pairs (the HOMO of H2S+ and the HOMO-1 of H2S) form bonding and antibonding combinations of lone pairs (n+ and n-), although the splitting is not large because of the long S-S bond. Figure 2(a) shows the first-order interaction diagram. This results in two ug orbitals close to one another in energy, however (uss and n-). These two orbitals therefore interact strongly with each other to form the two new a, orbitals (uss + n- and uss - n-) as shown in Figure 2(b). Note that in syn H2SSH; the n+ orbital is of the correct symmetry to inter- act with the uSs, but that otherwise the situation is identical.

The result is that the two highest b, orbitals (u; and n+) are clearly discernible as being derived from the H$3/H2S+ a1 and bl orbitals, but that the two a, orbitals both show some u and some lone- pair character. The relevant orbitals are shown in Figure 3.

IN DISULFIDE RADICAL CATIONS

Asmus et al.24 have observed ultraviolet/visible spectra of a series of R2SSR:- radical cations. The A,,, values lie between 400 and 650 nm and cor- relate well with MNDO calculated S-S bond dis- sociation energies.25 The transition responsible for this absorption has been interpreted as a u - u* on the basis of these facts and because of the re- markable dependence of A,,, on geometrical and electronic factor^.^-^ Figure 3, however, shows that there is no clearly defined css orbital in H2SSH;, but rather two combination u,,/n- orbitals (or in the case of the syn conformation uss/n+). The observed transition is therefore most likely to be from the upper of the ug orbitals (uss - n- in Fig. 3) to the uss. The calculated vertical transition energy for this process at MP2/4-31G is 3.25 eV (380 nm), compared with the typical A,,, of 480 nm for R2SSR: ions.4 The fact that the excitation occurs from an essentially nonbonding orbital is reflected in the slope of the D, vs. A,, plot, which is slightly less than unity.25 After this article was submitted Chaudri and Asmus26 were able to ob- serve H2SSH; itself. The observed A,, is 370 nm, in excellent agreement with the value predicted in this work.

CONCLUSIONS

The S-S three-electron bond approaches the optimum conditions outlined by Baird27 (ener- getically equivalent interacting orbitals and low overlap), and has a dissociation energy of ap- proximately 30 kcal mole-I, half that of an S-S two-electron bond.28

The MP2/4-31G calculated S-S+ bond length is 2.85 A. Correlation appears to be important in calculations for three-electron bonds. MNDO un- derestimates the length of the S-S+ bond and gives a dissociation energy that is too large when compared with MP2/4-31G. The observed ultra- violet absorption in R2SSR: ions is due to a tran- sition from a nonbonding orbital, which has both sigma and lone-pair character, to the ais.

Three Electron Bonds. I 265

The author would like to thank Professor K.-D. Asmus for bringing this problem to his attention, for helpful dis- cussions, and for communication of his results prior to publication. Thanks are also due Dr. J. Chandrasekhar for stimulating discussions, Professor P. v. R. Schleyer for support and encouragement, the staff of the Regionales Rechenzentrum for their cooperation, and Professor J. A. Pople and his group for their hospitality during a visit to Pittsburgh, where this work was completed.

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