4 Induced Current Density Programs 4.2 BOCUST - Bond current strength 4.4 MOLGRA - Molecular Graph

4.3 STAGRA - Stagnation graph

To obtain a stagnation graph (GS) for each orientation of the perturbing magnetic fields, the program STAGRA can be used either interactively (suggested way)

prompt> STAGRA [ options ]

or redirecting the input from a file (less frequently)

prompt> STAGRA [ options ] < somefile.txt

The easiest way to use the program is to type the command indicating the magnetic field components by means of the option -B comp ${}_{x}$ comp ${}_{y}$ comp ${}_{z}$ (by default the magnetic field is set to -B 0 0 1). The program starts searching for singularities of the current density over planes perpendicular to the magnetic field in steps set by the option -step_B some_value_in_au (by default some_value_in_au is equal to 0.2 au). The dimensions of the searching field is determined automatically by the program on the basis of the atomic coordinates. However, the searching field can be changed using the options -x $x_{min}\ x_{max}$ , -y $y_{min}\ y_{max}$ , and -z $z_{min}\ z_{max}$ (the order is not mandatory). For every singularity found, the program writes a line having the following format

| SP X Y Z ( $r$ , $s$ ) $\xi_{1}$ $\xi_{2}$ $\xi_{3}$

where the stagnation point SP can be either Para, Dia, or Sel, which stand for paratropic center, diatropic center, or saddle point, respectively; X Y Z are the coordinates (in au) of the singularity; ( $r$ , $s$ ) are rank and signature of the singularity; $\xi_{1}$ $\xi_{2}$ $\xi_{3}$ are the eigenvalues of $\left(\nabla_{\beta}J_{\alpha}^{\bf B}\right)_{{\bf r}_{0}}$ , i.e., the Jacobian of the induced current density calculated in the stagnation point ${\bf r}_{0}$ . A file GS.3d is generated containing the meta-graphic of the stagnation, which can be visualized using the v3d program 4.8.

For a list of options type:

prompt> STAGRA -h
-o STRING graphic file name, do not add .3d
-f FAT molecular model scale factor
-g GX GY GZ gauge origin (a.u.)
-B BX BY BZ magnetic field components
-j TOT | ROT/PARA | TRA/DIA
-m CO|DZx|PZx|GRRO|GPRO|GRLN|CSGT|BS|BCP
-A GRRO/GPRO variable
-GRLN_N GRLN_N variable
-GRLN_Z GRLN_Z variable
-q +-N O1 O2 ... ON: +add,-del MOs from the sum
-qf file reads +-N O1 O2 ...ON from file
-h this help
------------------------------------
-2D set J parallel to B to zero (pseudo-SG)
-x XMIN XMAX  window size along x
-y YMIN YMAX  window size along y
-z ZMIN ZMAX  window size along z
-hx XSTP  exploration step for x
-hy YSTP  exploration step for y
-hz ZSTP  exploration step for z
-stepB VAL updates ZSTP along B direction
-eps EPSI Newton-Raphson minimum criterion
-itm ITMAX Newton-Raphson max iterations
-pgm SPMAX Stagnation Graphic max points
-drd DMIN minimum distance among singulatities
-sgs STRING stagnation graph saving file (XX=nosave)
-lgs S1-S2-...Sn: stag-graph reading files (XX=noread)
-crc S T size and thickness saddle crosses (S<0 dots)
-rgp R dots-radius for centers (and saddles)
-por D saddle connection graph d=SP-trajectory dist.
-v set verbose printing to 0(min), 1(SG-point), 2(max)

Up to -h, options are the same as for the JBMAP program 4.1. In particular the CTOCD details are described in 4.12.
Other options can be used to change: SG to pseudo-SG (-2D); dimension of the searching field (-x, -y, -z); steps of search (-hx, -hy, -hz, -stepB); Newton-Raphson criterion and maximum number of iterations (-eps, -itm); maximum number of stagnation points (-pgm) and their inter-distance (-drd); file name for saving the stagnation graph (-sgs); file name for reading the stagnation graph (-lgs); size and thickness of the crosses indicating the saddle positions (-crc); radius of the dots indicating the center positions (-rgp); saddle connection graph calculation from off to on (-por); type of output (-v).

Further hints.

•

When using the -lgs option the stagnation graph is not calculated, it is read from the specified file (or list of files).
•

different portions of a stagnation graph can be searched separately and eventually written on a file, let say fnp1, fnp2,...fnpn for file-name-portion-1, file-name-portion-2 and so on.
•

All different files can be read together using -lgs fnp1-fnp2-...-fnpn to obtain the full stagnation graph.
•

To calculate a true SG, it is suggested to perform first a pseudo-SG calculation using STAGRA -2D -sgs psdfn (to save the pseudo-SG on the psdfn file); then run STAGRA -lgs psdfn (note the absence of the -2D option in the second run).
•

When using the -por option to calculate a saddle connection graph (SCG), let say STAGRA -por 0.1, note that the value (0.1 au) sets the distance between the saddle position and the starting point of the induced current density trajectory; at the same time it sets also the distance for a connection with another saddle (which may also be a different arm of the same starting saddle).
•

Whit the -por option the program prompts once to change the vertices of the molecular space in which to confine the trajectory (by default these are the same of the searching field and are good almost always), twice to change many subtle technicalities such as the trajectory integration method (by default a 4th order Runge-Kutta is used), the possibility to show a small direction arrow along the trajectory and many other things, which is better to skip over in many occasions.

Examples for the benzene molecule are provided here in the following. Instructions and commands to generate the examples can be found here.

Two views of the same pseudo-stagnation graph.

Two views of the same saddle connection graph.