Metal Transition in Hydrogen Under Pressure

INSULATOR TO METAL TRANSITION IN HYDROGEN UNDER PRESSURE 

We note that the four electrons problem, a cluster of four hydrogen atoms, is a prototype for testing correlation methods in electronic structure. McWeeny [2] had already addressed this problem in the context of a valence bond formalism and here we tackle the problem in a quite unusual range of intermolecular separations. 

We have applied Pauling s theory to the molecular hydrogen cluster as follows the nonmetallic cluster is well described by the usual Kekule structure (1-2 3-4) (Fig.2), where orbitals 1 and 2 are at one hydrogen molecule and 3 and 4 are at the other one. The synchronized resonance is the mechanism in which the system alternates between structures (1-2 3-4) and (1-4 2-3) (anti-Kekule) (Fig.2), breaking simultaneously the two original covalent bonds and forming two new ones. 

In the unsynchronized resonance, just one bond is broken, with the concomitant transfer of one electron from one molecule to another and the formation of a new bond (Fig.2). In order for this to occur, one atom has to lose an electron, say atom 4, becoming a positive ion, and another atom must have an extra orbital to receive the extra electron, say atom 2, becoming a negative ion. Thus we form the structure (1-2 2 -3), that we will call metallic structure, where 2 , the metallic orbital, is the extra atomic orbital on atom 2. In a molecular hydrogen crystal, the unsynchronized resonance would provide a mechanism for charge transport and confer metallic properties to the system. 

We investigate the possibility of metallic structures and charge fluctuations as two hydrogen molecules approach each other. To do so, we associate two atomic orbitals to each hydrogen atom and select 14 VB structures from a total of 266 that can be formed with the set of 8 orbitals. 

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