Discontinuous transition of molecular-hydrogen chain to the quasiatomic state: Combined exact diagonalization and ab initio approach

We obtain in a direct and rigorous manner a transition from a stable molecular-hydrogen $n{\text{H}}_2$ single chain to the quasiatomic two-chain $2n\text{H}$ state. We devise a method composed of an exact diagonalization in the Fock space combined with an ab initio adjustment of the single-particle wave function in the correlated state. In this approach the well-known problem of double counting the interparticle interaction does not arise at all. The transition is strongly discontinuous, and appears even for relatively short chains that are possible to tackle, $n=3–6$. The signature of the transition as a function of applied force is a discontinuous change of the equilibrium intramolecular distance. The corresponding change of the Hubbard ratio $U/W$ reflects the Mott-Hubbard transition aspect of atomization. A universal feature of the transition relation to the Mott criterion for the insulator-metal transition is also noted. The role of electron correlations is thus shown to be of fundamental significance in this case. The long-range nature of Coulomb interactions is included.

Figure 1

Schematic representation of a ${\text{H}}_2$ molecular chain with possible nearest-neighbor and next-nearest-neighbor hoppings ${\left\{t_i\right\}}_{i=0,1,2}$ marked. The labeling of the sites $i=1,2,3,\cdots$ is specified, as well as the bond length $R$ at an intermolecular distance $a$. The radius of the included intersite Coulomb interaction is equal to $250a$ in the atomic representation (see the main text).

Figure 2

Phase diagram encompassing quasiatomic and molecular states for the $n{\text{H}}_2$ chain as a function of exerted force along the chain. Inset: Effective bond length $R_{\text{eff}}$ vs the intermolecular distance $a$.

Figure 3

Electron density projected onto the plane of ${\text{H}}_2$ molecules near the molecular→atomic transition: (a) for the molecular state; (b) for the quasiatomic state. In (a) the density is very small in the space in between molecules (vertical line joining the atoms). The critical intermolecular distance $a$ and the effective bond length $R_{\text{eff}}$ are also specified in each of the states. The corresponding critical force is $f_C=25.705$ nN for the $3{\text{H}}_2$ system.

Figure 4

Equilibrium intermolecular distance $a$ vs exerted force $f$ for the case of the $3{\text{H}}_2$ system. The transition is of first order, as marked. Inset: $U/W$ ratio vs $a$ showing that in the quasiatomic state $U/W\sim 0.8$, signaling the onset of a correlated metallic state.

Figure 5

Evolution of the intra- and intermolecular hopping parameters $t_0$ and $t_1$ respectively, vs intermolecular distance $a$. Note the jump of $a$ at the transition molecular→quasiatomic configurations, as marked by the arrows. Inset: Hopping probabilities, intra- and intermolecular, $C_0$ and $C_1$, respectively. For a discussion, see the main text.