deletions | additions       diff --git a/section_Method_In_this_work__.tex b/section_Method_In_this_work__.tex  index 2f5831e..8121fa5 100644  --- a/section_Method_In_this_work__.tex  +++ b/section_Method_In_this_work__.tex 
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\end{aligned}  \end{equation}  where the external potential is $V_\text{ext}[\{\mathbf{R}_J(t)\}_J](\mathbf{r}, t)$ due to ionic core potential (with ions at positions $\mathbf R_J(t)$), $V_\text{H}(\mathbf{r}, $V_\text{H}[n](\mathbf{r},  t)$ is the Hartree potential comprising the classical electrostatic interactions between electrons and $V_\text{XC}[n](\mathbf{r}, t)$ denotes the exchange-correlation (XC) potential. The spatial and time coordinates are represented by $\mathbf{r}$ and $t$ respectively.   At time $t$ the instantaneous density is given by the sum of individual electron probabilities  $n(\mathbf{r}, t) = \sum_i |\psi_i(\mathbf{r}, t)|^2$. The XC potential used in this study is due to Perdew-Burke-Ernzerhof (PBE) ~\cite{Perdew_1992,Perdew_1996}, using a norm-conserving Troullier-Martins pseudopotential, with $17$ explicit electrons per $\mathrm{Cu}$ atom (not necessarily all 17 electrons participate in the process as we will discuss later).