Molecular dynamics method

1: Initialization: $\delta t:=t_0$ ; $\overline{v}:=0$ ; ${\overline{\omega }}^{\text{*}}:={\overline{\omega }}_0$ ; $F^{\text{*}}:=F_0$

2: while stopping criteria are not met do

3: Calculating force $\overline{f}$ and updating $\overline{\omega }$ and $\overline{v}$ , Equation (12); calculating F, Equations (1)-(3);

4: if $F<F^{\text{*}}-\epsilon$ then

5: $F^{\text{*}}:=F$ ; ${\overline{\omega }}^{\text{*}}:=\overline{\omega }$

6: else if $F<F^{\text{*}}$ then

7: $F^{\text{*}}:=F$ ; ${\overline{\omega }}^{\text{*}}:=\overline{\omega }$ ; Heating the system by setting the desired temperature $T_d=\beta T_0$ ;

8: else

9: Heating the system by setting the desired temperature $T_d=\beta T_0$ ;

10: end if

11: Damping the system by setting the atom j, if $v_j\left(t\right)f_j\left(t\right)<0$ ; $v_j\left(t\right)=\lambda v_j\left(t\right)$ ;

12: Checking the physical constraint, set $v_j\left(t\right)=-v_j\left(t\right)$ , when ${\omega }_j\left(t\right)<0$ ,

14: end while

15: return ( ${\overline{\omega }}^{\text{*}}$ ) as optimal solution