Output structure in multilevel MCTDHX computations

For the case that atoms with internal structure are treated (Multi_Level = .T.), the column structure of the ASCII output files is described in the following tables 18,19.

The structure of the output files described in tables 12,13,15, is identical for multilevel computations.

Table 18: NO_PR.out file structure for computations with Multi_Level=.T..

Column $1$	Column $2$ to $(1+M)$	Column $(2+M)$	Column $(3+M)$ to $3+M+N_l$
Time $t$	Natural orbital occupations $\rho^{(NO)}_M(t)$ to $\rho^{(NO)}_1(t)$	Energy $E(t)$	State populations (density) for all levels

This table explains the column structure of the NO_PR.out file. $M$ stands for the number of orbitals in the computation and $N_l$ is the number of internal states considered.

Table 19: <time>orbs.dat file structure for multilevel computations.

Column $1$ to $3$	Column $4$	Column $5$to $4+N_l+N_{CI}$	Column $5+N_l+N_{CI}$ & $6+N_l+N_{CI}$ to $3+3N_l+N_{CI}$ & $4+3N_l+N_{CI}$	Column $5+3N_l+N_{CI}$ & $6+3N_l+N_{CI}$ to $3+5N_l+N_{CI}$ & $4+5N_l+N_{CI}$
$x,y,z$	DVR weight	$V^i(x,y,z,t)$ and $V^i_{CI}(x,y,z,t)$	$\rho^i_w(x,y,z;t)$	$\rho^i_{(NO)}(x,y,z;t)$

Column $5+5N_l+N_{CI}$ & $6+5N_l+N_{CI}$ to $3+5N_l+N_{CI}+2 M N_l$ & $4+5N_l+N_{CI}+ 2 M N_l$	Column $5+5N_l+N_{CI}+2 M N_l$ & $6+5N_l+N_{CI}+ 2 M N_l$ to $3+5N_l+N_{CI}+4 M N_l$ & $4+5N_l+N_{CI}+ 4 M N_l$
$\phi^i_k(x,y,z;t)$ for $i=1,..,N_l$ and $k=1,..,M$	$\phi^{(NO),i}_k(x,y,z;t)$ for $i=1,..,N_l$ and $k=M,..,1$

This table explains the column structure of the <time>orbs.dat output files of the main or analysis program for the case that Multi_Level=.T. was set. $N_l$ is the number of internal states and $N_{CI}$ is the number of conical intersections ($N_{CI}=0$ if Conical_Intersection=.F.). Please note, that the index of the internal state is always running first before the orbitals' index. $x,y,z$ are the spatial coordinates, $V^i(x,y,z,t)$ is the one-body potential of internal state $i$, $V^i_{CI}(x,y,z,t)$ is the coupling of the $i-$th conical interaction, $\rho^i_w(x,y,z;t)$ is the density in working orbitals for internal stat $i$, $\rho^i_{(NO)}(x,y,z;t)$ is the density in natural orbitals for state $i$, $\phi^i_1(x,y,z;t)$ to $\phi^M_1(x,y,z;t)$ are the working orbitals in internal state $i$, and $\phi^{(NO),i}_M(x,y,z;t)$ to $\phi^{(NO),i}_1(x,y,z;t)$ are the natural orbitals in state $i$. Please note, that some of the quantities are complex numbers which then are output decomposed in their real and imaginary parts in two columns (as specified by the column numbers).