Easily Broken Strong Bonds: a New Law of Thermodynamics - ACS

Chapter 7

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Easily Broken Strong Bonds: a New Law of Thermodynamics Konstantin B. Borisenko, Sarah L. Hinchley, and David W. H . Rankin School of Chemistry, University of Edinburgh, West Mains Road, Edinburgh, EH9 3JJ, United Kingdom

Determination of the molecular structures of tetrakis[bis(trimethylsilyl)methyl]diphosphine and its arsenic analog in the crystalline phase showed that the central P-P and As-As bonds were little longer than in other diphosphines and diarsines. Nevertheless, their vapors consisted entirely of the bis[bis(trimethylsilyl)methyl]phosphido and bis[bis(trimethyl— silyl)methyl]arsenido free radicals. This thermodynamic conundrum has been solved by series of ab initio calculations, which have shown that the energy needed to break the strong central bonds is stored in deformed ligands. Detailed analysis of the dissociation process, aided by a simple ball and spring model, has allowed the intrinsic energy of the central bond to be separatedfromthe overall dissociation energy. The intrinsic bond energies are consistent for a wide range of disphosphines, even though their dissociation energies are scattered over a range of hundreds of kJ mol . -1

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Lattman and Kemp; Modern Aspects of Main Group Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2005.

95 At first sight, the dissociation of a sterically crowded tetraalkyldiphosphine into two dialkyl phosphido radicals (Figure 1) was not unexpected, although unusual. Large substituents would naturally cause lengthening, and eventually breaking, of bonds. So the observation that tetrakis[bis(trimethylsilyl)methyl]diphosphine had an EPR spectrum, consistent with the formation of bis[bis(trimethylsilyl)-methyl]phosphido radicals in the liquid phase, was seen as a natural consequence of the size of the bis(trimethylsilyl)methyl (also known as disyl) ligands. The transition from crystalline to liquid and gaseous phases was associated with a change in colour from pale yellow to intense purple, so it appeared that the radical was predominant in these phases, but absent from the crystal. It was only when the structures, in crystalline and gaseous phases, were determined that it became clear that the situation is considerably more complex. 1


1

2

R

Figure 1. Dissociation of a tetra-alkyldiphosphine to give two dialkylphosphido radicals

Structures of solid and gaseous tetrakis(disyl)diphosphine and tetrakis(disyl)diarsine The structure of tetrakis(disyl)diphosphine, {P[CH(SiMe ) ]2}2» in the crystalline phase was straightforward to determine. There was one molecule per asymmetric unit, in which the four asymmetric groups were arranged so that they packed in an efficient way (Figure 2). The steric crowding was demonstrated by large deviations of bond lengths and inter-bond anglesfromthe standard values (Table I). Thus, for example, the PCSi angles ranged from 110.9 to 125.2°, while CSiC angles covered the range from 103 to 117°. However, the central P-P bond length was 231.0(7) pm, only about 8 pm longer than a typical value for an unstrained diphosphine. Thus it was clear that the packing of the four disyl groups in each molecule was enabled by their asymmetry, and that this allowed the central P-P bond to be relatively unstrained, although it did not avoid the need for considerable distortions of the packing ligands. 3 2

2,3



Figure 2. The structure of {P[CH(SiMe )2}2 in the crystalline phase 3

Table I. Selected geometrical parameters for crystalline {PfCH(SiMe ) l }2 3

2

2

Parameter Number of occurrences Range rP-C r(P)C-Si inst

£„„(Χ-Χ)

1f

f

Figure 5. Energetics of dissociation of a molecule X-X to give two X radi

Χ'-Χ'

χ

+

χ

Figure 6. Ball and spring model of dissociation


103 resemble the actual dissociation energy of the bond, because of the reorganisation of the radicals. This model is illustrated in Figure 6. In this model the two half-molecules (PR in the case of a diphosphine) are regarded as flexible balls, linked by a spring. We define a single force constant, f , which represents deformation of the ball along the direction of the connecting spring, which has a force constant^. At equilibrium (i.e. as in the structure of the dimer) the spring is strained and the balls are also distorted, and the total potential energy of the system is thus equal to the sum of the potential energies stored in the balls and the spring. Values of these two force constants were computed by calculating the derivative of the total energy with respect to the P-P internuclear distance, first keeping the structures of the two half-molecules unchanged, and secondly allowing them to relax. Using the method described earlier, ' the energies stored in the spring and the distorted balls (half-molecules) were calculated, and the energy relationships shown in Figure 7 then gave the intrinsic energy of the P-P bond (Equation 1). 7

2


b

5 6

D = 0

bEjiss

+

2aE rg re0

+ àE

(1)

spring

2Ε (Χ) Ψ

I f

\ξ 1 I I

Ï

2ΑΕ £Χ) κοη

2E (X)

i

i

opt

E (X~X) opt

r

1 2A£ .g(X) mw

1

spring

1f

Figure 7. Relationships between energies of dissociation of a sterically crowd X-X molecule and a hypothetical unstrained molecule. The results of these calculations for a series of diphosphines and disilanes are shown in Figure 8, and data are given in Table V. The heavy straight line represents equality of the intrinsic bond energy and the actual dissociation energy. The data for two diphosphines lie very close to this line. These are tetramethyldiphosphine and tetrasilyldiphosphine, both compounds with small substituents, for which steric effects should be minimal. The remaining diphosphines compounds all have larger substituents, and as a consequence of


104 the interactions between the groups the dissociation energies are smaller, and in the case of tetrakis(disyl)diphosphine, even negative. Nevertheless, the intrinsic dissociation energies of the P-P bonds are remarkably consistent, particularly so given the approximations of the methodology. The smallest intrinsic energy is about 140 kJ mol" , for tetrakis(disyl)diphosphine, but the calculations for this system were only done with the B3LYP/3-21G* method and basis set. Using the conditions that were applied to the other systems, we would expect to obtain a rather larger value, as indicated by the arrow in Figure 8. Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 23, 2017 | http://pubs.acs.org Publication Date: December 1, 2005 | doi: 10.1021/bk-2005-0917.ch007

1

+

A)(X-X) / kJ mo\' ]

300

Easily Broken Strong Bonds: a New Law of Thermodynamics - ACS

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