Diamond: An Electronic Ground State of Carbon
Wojciech Grochala
University of Warsaw, CENT, Zwirki i Wigury 93, 02089 Warsaw Poland
The purpose of this contribution is to assess various contributions to relative stability of diverse forms of
carbon, and especially diamond (D) and graphite (G), from the first principles. The theoretical methods
used in this study encompass the hybrid functional density theory and particularly the HSE06/PBEsol
correlation–exchange functional [1,2], which has been successfully applied for description of crystal
structure, stability, lattice dynamics and electronic properties of extended solids. Our calculations lead to
excellent reproduction of the direct band gap as well as the lowest-frequency Raman-active E2g mode of G,
which governs such properties as energy of dissociation of graphite to free graphene sheets, and directly
influences the zero-point energy, vibrational entropy, and heat capacity of G, and in consequence the
predicted free Gibbs energy difference between D and G. Our calculations suggest that the electronic
energy of diamond is computed to be more negative by 1.1 kJ mol–1 than that of graphite at T=0 K and in
the absence of external pressure [3]. Graphite gains thermodynamic stability over diamond at 298 K only
because of the differences in the zero-point energy, specific heat, and entropy terms for both polymorphs.
These theoretical results may be critically compared to diverse sets of experimental data from the literature.
Our analysis indicates that the diamond-graphite equilibrium line should fall at smaller pressures than those
suggested by previous experiments which were carried out at temperatures of 1400-1500 K (i.e. when the
allotropic transformation is sluggish due to high energy barriers).
These findings are discussed on a broader background of the Maximum Hardness Principle (from Pearson
[4]) and the so-called diagonal line – separating metals from nonmetals in the Periodic Table – is revisited.
References
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[2] J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, K.
Burke, Phys. Rev. Lett. 2008, 100, 136406.
[3] W. Grochala, Angew. Chem. Int. Ed. Engl. 2014, 53, 3680.
[4] R. G. Pearson, J. Chem. Educ. 1987, 64, 561.