This TUI guides the user towards the objective indicated in the title by offering a sequence of menus, each of which is displayed individually on the screen. In each menu the user must choose the most appropriate option, which in turn can request additional input.
Three different flowcharts show how to obtain three different types of electron density profile along a given direction.
PAMoC-TUI isn't a visualization program, so that it doesn't provide any
graphical output directly. Its results are printed in tabular form on the
output file and saved on a CUBE file.[L1CUBE
(PAMoC Manual)] Eventually, the TUI can launch a suitable visualization program which is able to read the CUBE file.[L1CUBE File Format
The radial electron density at a given radius is the number of electrons in a infinitesimally thin spherical shell at that radius. Its units are e⋅bohr−1.
To obtain the profile of this density along the radius we'll proceed as shown below in Flowchart 1:
It is clear from the asympotic value of the electron count function G(r) in Figure 1, as well as from the numerical results reported in the print-output file (see Section 4), that the presence of cusps at the nuclear centres destroys the accuracy of the numerical procedure used. In the example of Figure 1, the number of electrons in benzene is overestimated by 4.31 e (about 10%).
The error is even higher if the center of the spherical shell is located at a nuclear centre (screen 7, option 1, Flowchart 1), like a carbon atom (Figure 2a, error = 15.41 e or 36.7%) or an hydrogen atom (Figure 2b, error = 54.42 e or 130%).
From the examples above (Figures 1 and 2), it appears that the radial electron density of a molecular system is strongly dependent on the origin of the spherical shell, and can be of some interest only if the origin is placed in some special point, like a center of symmetry (Figure 2). On the other hand, it is particularly suited to describe the electron density of an isolated atom.
The planar electron density at a given point on a line is the number of electrons in a plane perpendicular to that line in that point. Its units are e⋅bohr−1.
To obtain the profile of this density along the line we'll follow the steps outlined in Flowchart 1 up to the screen number 6, where we will choose the option number 3 and proceed as shown below in Flowchart 2:
On the other hand, choosing option number 1 or 2 on screen number 7 in Flowchart 2, yields the following graph
The error in the electron count is still influenced by the presence of cusps on nuclear centres, but to a lesser extent than the integration on the unit sphere. In fact, it is underestimated by 0.5 electrons (1.20%) in the case of Figure 3, and by 3.4 electrons (8.12%) in the case of Figure 4, respectively.
The position electron density at a given point in 3-D space is the number of electrons contained in an infinitesimally small volume at that point. Its units are e⋅bohr−3.
The electron density values at a number of points along a line in 3-D space provide an electron density profile along that line. It can be obtained by selecting the option number 1 on the screen number 5 in Flowchart 1, and going through the steps shown in Flowchart 3:
The profiles in Figures 3 and 5 have some analogies as well as significant differences. Both figures describe the trend of the electron density along a given direction, but the values shown in Figure 5 refer to the electron density at each point of the space along that direction, while those shown in Figure 3 give the value of the total electron density in the plane perpendicular to the given direction.
The graphs of Figures 1-5 are not produced directly by the PAMoC-TUI.
Instead the latter provides numerical results in the form of a block data,
which is part of the print-output file. The block data (shown in the box below)
can be extracted from the print-output file and then read by
GRACE.[L2"Grace (plotting tool)",
Wikipedia, The Free Encyclopedia, L3GRACE website], a free 2D graph plotting tool, for visualization. All Figures 1-5 have been obtained using GRACE. The block data reported in the box below was used to generate Figure 1.
Using GRACE allows the user to change visualization of data as desired.
However, as indicated by the last line in the box extracted from the
print-output file (see above), the PAMoC-TUI also generates a
CUBE file,[L1CUBE File Format
(PAMoC Manual)] which contains the 1-D electron density profile. The default name of the CUBE file, is pamoc.g1d, but the user is allowed to change it by entering a new filename at the prompt in the following screen:
which is always presented as soon as calculation of the 1-D electron density profile is done.