4.5 FIELD - Density functions

A number of density functions related to the current density tensor can be calculated using the program FIELD. A list of the available densities can be obtained issuing the command

prompt> FIELD -h
usage: FIELD [verbo] P1 [para-opz]
verbo makes a verbose output
P1 is mandatory and must be one of the following:
EXTERNAL FLNMPRL : load binary grid from file FLNMPRL
JBMOD : module of the CD vector induced by B
JB_ab : JB tensor component ab=xx,..,av,tr
NIMS_ab FILE : NIMS cmp ab=xx,..,av,tr at pnt in FILE
RHO : electron density
SRHO : spin electron density
GRADRHO : module(grad RHO)
LAPLRHO : Laplacian of RHO
RHOE_i  : 1st-ord-cor to RHO due to ele-fld i=1,2,3
ACID  : Current Density Tensor (T) anisotropy Herges
VARt  : variance Var(t)=sigma^2(t),  t=eigenvalues(T)
SIGt  : std deviation sigma(t)
PVART : pseudo-variance: pVar(T)=tau(T)
VARTS : variance of the symmetric part Var(TS)
SIGTS : std deviation symmetric part sigma(TS)
VARTA : variance of the anti-symmetric part Var(TA)
SIGTA : std deviation anti-symmetric part sigma(TA)
M12T  : Third moment alpha_12 of CDT
M30T  : Third moment alpha_30 of CDT
TRT   : trace(T)
DETT  : CDT determinant
IIT   : isotropic invariant of CDT: <T^2>
SORPden : Specific Optica Rotatory Power density
ORden   : Optical Rotatory density
AVT   : anisotropy of Vorticity Tensor (V) Pel.Laz.
VARv  : variance Var(v)=sigma^2(v),  v=eigenvalues(V)
SIGv  : std deviation sigma(v)
PVARV : pseudo-variance: pVar(V)=tau(V)
VARVS : variance of the symmetric part Var(VS)
SIGVS : std deviation symmetric part sigma(VS)
VARVA : variance of the anti-symmetric part Var(VA)
SIGVA : std deviation anti-symmetric part sigma(VA)
M12V  : Third moment alpha_12 of VT
M30V  : Third moment alpha_30 of VT
TVCD  : trace of vorticity tensor (Barquera-Lozada)
DETV  : Vorticity Tensor determinant
IIV   : Vorticity Tensor isotropic invariant <V^2>
MO    : molecular orbital value
DIAL: divergence of the isotropically averaged Lorenz force density
DIV_JB  : Div of current density induced by static B
DVSOCC  : Div of Spin-orbit-coupling current
DVNC    : Div of Nuclear-Larmor      current
CONTEQ  : CONTinuity EQuation div.JEP+dROE/dt
DIV_JN2 : IC divergence numerical by 2-pnts formula
DIV_JN4 : IC divergence numerical by 4-pnts formula
a_rR_ab : ele-pol density     r,R comp ab=xx,..,av,tr
a_pR_ab : ele-pol density mix p,R comp ab=xx,..,av,tr
a_rP_ab : ele-pol density mix r,P comp ab=xx,..,av,tr
a_pP_ab : ele-pol density     p,P comp ab=xx,..,av,tr
k_rL_ab : MEMDP density r,L component ab=xx,..,av,tr
k_pL_ab : MEMDP density p,L component ab=xx,..,av,tr
k_lR_ab : MEMDP density l,R component ab=xx,..,av,tr
k_lP_ab : MEMDP density l,P component ab=xx,..,av,tr
ENSD_ab : ele shielding den cmp ab=xx,..,av,tr at R_I
MSD_ab  : mag shielding den cmp ab=xx,..,av,tr at R_I

Actualizing the first parameter P1 with one of the listed keywords, the corresponding density function will be calculated and ready to be displayed. The main result is a graphic representation of the selected density. By default a 3D isosurface will be produced, but also 2D representations by means of contour levels or divergent color maps can be obtained. Different choices can be tuned using the optional parameters listed below.

 Optional pameters - to change defaults type:
-o STRING    : graphic file name with no extention
-f FAT       : molecular model scale
-g GX GY GZ  : gauge origin (a.u.)
-B  BX BY BZ : static magnetic field components
-BU BX BY BZ : static mag-field comps made unitary
-E  EX EY EZ : ele-field amplitude components
-EU EX EY EZ : ele-field amplitude comps made unitary
-j TOT | ROT/PARA | TRA/DIA
-m CO|DZx|PZx|GRRO,GPRO|CSGT|BS|BCP ...
-A CONST : GRRO/GPRO variable=CONST
-GRLN_N CONST : GRLN_N variable=CONST
-GRLN_Z CONST : GRLN_Z variable=CONST
-q +-N O1 O2 ... ON : +add,-del MOs from the sum
-qf FILE : reads +-N O1 O2 ...ON from FILE
-vjr : verbose printing loading data
-DM : using density matrices (default MOs)
-svcb FLNMPRL : save cube to a file called FLNMPRL
-h this help
-v VAL iso-surface value
-p DELTA grid step (a.u.)
-s TYPE surface type:0-curliv;1-cloud;2-cloud;3-curliv
-x XMIN XMAX  window size along x (au)
-y YMIN YMAX  window size along y (au)
-z ZMIN ZMAX  window size along z (au)
-c COLOR of the surface (26-32)
-t THICKNESS of contour levels
-l SCALING of contour levels (if 0 no contours)
-e EPSI minimum contour level value
-% PERC max/min percentage for the first contour
-DCM MIN MAX Diverging Color Map (0 0 for cube_minmax)
-Rot a,b,g grid rotational angles about x,y,z DCM only
-Tra a,b,g grid translation steps along x,y,z DCM only
-quote mark the grid DCM only
-sidebar add a sidebar DCM only
-topbar add a topbar DCM only
-R_I X Y Z coord magnetic shielding density reference

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 the isosurface value (-v VAL), or the exploration space size (-x XMIN XMAX, -y YMIN YMAX, -z ZMIN ZMAX). In particular, when the space is restricted to be a plane, i.e., when one of the MIN’s is equal to the corresponding MAX, the program produces a 2D graph on that plane instead of the default 3D isosurface. The 2D graph can be produced as a contour levels or a divergent color map or both. Contour levels are switched on using -l with a SCALING not equal zero. Divergent color maps can be obtained using the -DCM option.

Further hints.

• •

  Sometime the calculation of the grid of values can be very time consuming and even an apparently simple change of some of the parameters could result in a boring repetition of a long calculation. Therefore, at the end of the grid calculation, the program prints the actual values of the parameters controlling the graphic and prompts for their change. Before to exit pressing <q> on the keyboard, it is convenient to open the graphic file using the v3d program and check the result. If necessary, it is possible to modify some parameters and review the graph until a satisfactory result is obtained.

• •

  Writing a cube file before exiting enables the possibility to adopt a different graphics software to visualize the field, as for example, Gauss-view, Avogadro, Chimera, etc. This is asked along with the change of parameters.

• •

  For field having both positive and negative regions, FIELD does not use the isosurface value set by the -v option, instead it prompts in real-time for two new values.

• •

  The grid grade can be changed using -p where DELTA is the grid step in a.u..

• •

  A color for the isosurface can be set using -c followed by 26=red, 27=green, 28=blue, 29=cyan, 30=magenta, 31=yellow. The default value is 32=black. When a field can have both positive and negative values, two complementary colors will be used.

• •

  Contour level THICKNESS can be changed using the -t option.

• •

  Contour level SCALING can be changed using -l, where SCALING is the ratio between successive contour values, starting from a percentage (PERC) of the field maximum value, scaled up to a minimum value set by -e EPSI.

• •

  The magnetic field (see -B BX BY BZ) is used only to compute the divergence of the induced current density.

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