Explicit inclusion of electronic correlation effects in molecular dynamics

We design a quantum molecular dynamics method for strongly correlated electron metals. The strong electronic correlation effects are treated within a real-space version of the Gutzwiller variational approximation (GA), which is suitable for the inhomogeneity inherent in the process of quantum molecular dynamics (MD) simulations. We also propose an efficient algorithm based on the second-moment approximation to the electronic density of states for the search of the optimal variation parameters, from which the renormalized interatomic MD potentials are fully determined. By considering a minimal one-correlated-orbital Anderson model with parameterized spatial dependence of tight-binding hopping integrals, this fast GA-MD method is benchmarked with that using exact diagonalization to solve the GA variational parameters. The efficiency and accuracy are illustrated. We have demonstrated the effect of temperature coupled with electronic correlation on structural properties simulated with MD. This method will open up an unprecedented opportunity enabling large-scale quantum MD simulations of strongly correlated electronic materials.

Figure 1

The exact (full line) and approximate (dashed line) $\partial \sqrt{q_{i\sigma }}/\partial d_i$ as a function of $d_i$.

Figure 2

Total energy (in eV) vs interatomic distance (in units of $r_0$) for the dimer calculated with exact diagonalization (solid line) and with the second-moment approximation (dashed line) in uncorrelated case ($U=0$).

Figure 3

Equilibrium interatomic distance vs $U$ for the dimer calculated with the Gutzwiller method in the SMA.

Figure 4

Total energy (a) and force (b) vs interatomic distance for the dimer calculated with the Gutzwiller method in the SMA for $U=4t$.

Figure 5

Snapshot of atomic positions obtained from exact diagonalization (a) and the SMA (b) for a cluster of 1600 atoms, with open boundary conditions, after 100 000 MD steps from ordered initial conditions (see text).

Figure 6

Dependence of the interatomic equilibrium distance on $U$ from the GA-MD simulations with the SMA on a $40\times 40$-atom cluster with MIC.

Figure 7

For a given interaction $U=2\text{eV}$, radial pair distribution function $g\left(r\right)$ for different temperatures: $T=300$ (full line), 600 (thick dashed line), 1500 (thin dashed line), 3000 (dotted line), and $6000\text{K}$ (dotted-dashed line).

Figure 8

For a given temperature $T=300\text{K}$, radial pair distribution function $g(r/r_0)$ for different Coulomb interactions: $U=0$ (full line), 1 (thick dashed line), 2 (thin dashed line), and $4\text{eV}$ (dotted line).