Readme on ORBITAL for Windows

ORBITAL for Windows

Program ORBITAL shows coloured contour plots of functions which represent simple atomic or molecular orbitals. It is intended to be used by students learning about molecular orbital theory in chemistry courses at an elementary undergraduate level.

It was written by Dr. Bruce W. Tattershall, Lecturer in Chemistry at the University of Newcastle, England.

Platforms

ORBITAL for Windows has been tested under Windows 95, Windows 2000, Windows XP and 64-bit Windows 7.

Availability

ORBITAL for Windows may be downloaded as a compiled executable and used free of charge, subject to the Disclaimer shown below. The two .dll files supplied with the program are proprietary software, which the author of ORBITAL for Windows is licensed to distribute with it. If the program is installed as described below under Installation, there should be no conflict with different versions of these libraries which you may have received with other software. The source code for ORBITAL for Windows is not being offered.

Built-in Help

Compiled into ORBITAL for Windows there is extensive help on its use. This may be switched off during setup, if it not desired for classroom use. Here follows the entire contents of the built-in help, which serves here to describe the program.

Introduction

Contents

What is it for?
What does it do?
Realism
Recognising the AOs
Plane of the plot
Colour of the contours
Nodes
Making MOs
Coefficients
One overlap at a time
Distance between the atoms
Triatomic molecules
What are the molecules?
Animation
Other sources
History of ORBITAL

Other Sections

Using ORBITAL
Setup

What is it for?

ORBITAL is an aid to teaching and learning about molecular orbital theory in chemistry courses at an elementary undergraduate level

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What does it do?

ORBITAL shows Atomic Orbitals or Molecular Orbitals on a Windows PC screen, as coloured contour plots
It provides simplified mathematical functions which are of the same form as the space-dependent parts of some of the one-electron wavefunctions for an atom
Atomic functions can be shown, or functions can be added to make MOs for a diatomic or a linear triatomic molecule
The program is a tool for students to use

It was originally devised for use in a drylab situation in which students were taught interactively by a demonstrator while they carried out loosely specified exercises using ORBITAL
It can be used in private study by students, but probably should be accompanied by a tutorial or a quiz provided to fit in with the course they are studying, suggesting work to do using ORBITAL
Teachers possibly could show it as a lecture demonstration

The student controls what the program does

There is no tutorial or programmed learning nature to ORBITAL, beyond what is provided in this help facility

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Realism

Although the functions have been simplified by removal of almost all of the combinations of constants which look confusing in textbooks, the resulting plots are very similar to those obtained with properly calculated AOs
This emphasizes that understanding the algebraic form of AOs is within the grasp of almost all university chemistry students
Commercially available modelling packages may produce more accurate surfaces (or possibly contour plots) for orbitals, but the algebraic form of the functions used is generally hidden from the user

If used for teaching or learning, the learning objectives are different: these packages are not meant to promote understanding about how MO theory works, whereas ORBITAL sets out to do this

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Recognising the AOs

Students select the atomic wavefunctions by their algebraic form, rather than by their name

This exercises students' understanding of the algebraic nature of natural orbitals, nodes, etc.

Wavefunctions are given in the Cartesian coordinate system, rather than in polar coordinates

The author finds that students find it much easier to understand and assimilate these functions, and it is anticipated that they will be taught about them in this form
Molecular modelling using MO methods, as used by chemists, employs Cartesian coordinates
Polar coordinates were used in the middle years of the 20th century, before the computer era, when students learned to solve Schroedinger's Equation for the hydrogen atom by hand

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Plane of the plot

Atomic orbitals are plotted in the xy plane: thus 3d(xy) and 3d(x^2-y^2) orbitals are provided, but 3d(z^2) is not
The molecular axis must therefore be the x axis, not the z axis which is the convention
The x axis is horizontal across the screen, y is vertical down the screen (and z, which is not used, comes out of the screen towards the user)
The nuclei lie in the plane of the plot, and are represented by black dots

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Colour of the contours

The contour bands are coloured with warm colours green to purple to represent positive values of the functions, and with cold colours cyan to deep blue to represent negative values

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Nodes

Values near zero are coloured neutral mid grey, so nodal surfaces intersecting the plane of the plot are easily recognised
Students should exercise their knowledge of both AOs and MOs by identifying and counting the nodes in the plots
The idea that the wavefunction has zero value at a node is of infinitely little importance to chemistry, because the nodal surface is infinitely thin

What is of supreme importance is that the wavefunction changes sign at the node: see the help item on animation
Nodes are not shown as infinitely thin in ORBITAL, because the student needs to see them
The coloured bands represent equal ranges of the value of the wavefunction, and the grey band spans zero symmetrically (except in the 1s orbital), making it wide enough to see easily

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Making MOs

MOs can be made by adding one AO at a time from each atom
Sufficient AOs are provided to make sigma bonds from s or p orbitals, or pi bonds from p or d orbitals

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Coefficients

Students enter coefficients for each AO
By varying the signs of these coefficients, bonding or antibonding MOs can be made

Students thus learn to use the rule that the sign of the product of two coefficients must match the sign of the overlap integral of these two AOs, in order to produce a bonding contribution to the MO
They should set out to produce a bonding or antibonding combination in each case, and confirm by counting the nodes in the MO that they have obtained the intended outcome

By varying the magnitudes of the coefficients, polarised MOs can be produced

Students should decide in advance which nucleus in the plot is to represent which nucleus in the molecule
By examining the shape and colouring of the lobes, they should confirm that the polarisation shown agrees with their assumptions about relative electronegativity of the atoms, in both the bonding and the antibonding MOs
Antibonding MOs are polarised in the opposite direction to a corresponding bonding MO

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One overlap at a time

Because understanding bonding or antibonding contributions is a main learning objective in using the program, use of more than one AO at a time per atom, e.g. for s and p orbital mixing in sigma MOs, is not supported

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Distance between the atoms

The distance between the atoms can be varied, showing the progression from almost pure AOs to highly bonding or antibonding MOs, as the overlap integral becomes bigger in magnitude

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Triatomic molecules

The important ideas which can be explored with the linear triatomic molecule are:

sigma and pi MOs each delocalised over all three atoms
the non-mixing of s and p on the central atoms, because they require different combinations of signs of coefficients of the ligand orbitals
there are pi MOs which are neither bonding nor antibonding: they are non-bonding by symmetry

ORBITAL's triatomic molecule does not bend

Understanding what happens to MOs if the molecule bent is an interesting and important topic, but it is more advanced than is usually covered in courses at the level which ORBITAL is meant to support
As the symmetry is lowered, more mixing of AOs into MOs takes place, and the situation becomes rapidly more complicated
The simple approach of ORBITAL, in which only one orbital at a time per atom is considered, becomes too limiting

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What are the molecules?

Since ORBITAL does not set out to make a realistic plot for a particular molecule, this is a matter for the imagination of the student or their teacher
Diatomic molecules could be H2, F2, O2, NO, or HF
Triatomic molecules could be CO2 or N2O
The triatomic combination could be part of a larger molecule:

two trans ligands surrounding an octahedrally coordinated metal
the metal-carbon-oxygen sequence of carbonyl complex, in which the d-pi* pi-bonding can be depicted

While a 3p(x) orbital is provided to support learning about inner lobes, 2s is not provided

Because atoms do not approach sufficiently for major overlap of the inner lobes of their AOs, it is suggested that 1s and 2p AOs are used in constructing MOs, even where 2s, 3s, or 3p orbitals are involved in 'reality'
This gives MOs which are of the correct form in the bonding region, but which are oversimplified in the core regions near the nuclei
This approach is often taken in elementary textbooks to avoid unnecessary confusion

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Animation

Our ideas of sigma and pi bonding, or of bonding, non-bonding and antibonding orbitals, which have carried over from small inorganic molecules to the most symmetrical of organic molecules, are all about nodes, i.e. the sign of values of the wavefunctions at different points in space
Students often need to work hard to lose the concept of electrons in atoms as particles, which is very harmful to their understanding of chemistry, and to replace it with the concept of electrons as wave phenomena
What is being plotted in ORBITAL, and in elementary textbooks, is the space-dependent part of the wavefunction, i.e. a snapshot at some instant in time of a parameter which varies in a wavelike manner
Lobes on opposite sides of a nodal surface have opposite signs because the wave phenomenon is out of phase in these two regions
It does not matter which region contains positive and which contains negative values, because a snapshot at a different instant could have shown the signs reversed
This is illustrated by the animation provided in ORBITAL, in which the space-dependent wavefunction set up by the student is multiplied by a sinusoidal time-dependent function

This causes values of the total wavefunction, and hence the colours and extents of the contour bands to change periodically, from the maximum values shown in the static plot, down through zero, and up to the maximum values but with the opposite signs

Students are advised to turn down the speed of the animation until they fully understand what they are seeing
The animation may have some reality for single-electron atoms in a steady state: for polyelectronic atoms, the time-dependence is very much more complex

The animation is provided mostly to encourage students to think about the meaning of the static space-dependent plots, which are similar to those shown in most elementary textbooks on the subject, but which are frequently misunderstood by beginners
Teachers who have misgivings about showing the animations may install ORBITAL with the animation feature switched off: see the Help section on Setup

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Other sources

The ground-breaking book which showed how MO theory could be presented to most chemistry undergraduates in an understandable form was: H.B. Gray, 'Electrons and Chemical Bonding', Benjamin, NY 1964

This shows highlighted dot pictures to give a 3-D idea of wavefunction surfaces (i.e. the 3D equivalent of contours)

The present-day book recommended by the author of ORBITAL to his students is: M.J. Winter, 'Chemical Bonding', Oxford U.Press, Oxford, 1994

This uses similar illustrations, as well as dot-density pictures to give an idea of electron distribution, i.e. the square of the wavefunctions

For well-drawn contour plots, J.E. Huheey, E.A. Keiter and R.L. Keiter, 'Inorganic Chemistry', Harper Collins, NY, 1993 is recommended
There are many websites available which show (mostly atomic) orbitals

Many of these use the Chime plugin to show views of 3D models which can be rotated by the user
A deficiency of Chime/Rasmol is that it does not colour wavefunction surfaces according to their sign, so website authors tend to show electron-density surfaces instead, since they do not have a sign
Several sites show 3D dot-density models in which the dots are really Chime atoms: these can be a bit difficult to see
While rotatable models are attractive, they are usually showing only pre-made models equivalent to the wooden models which many of us have on our lecture benches: there is nothing for the student to do except to look at them

In the opinion of the present author, the best of these websites is the Sheffield Orbitron, by M.J. Winter, the author of the Oxford Primer cited above: http://www.shef.ac.uk/chemistry/orbitron/

This still shows essentially pre-made models of various kinds
References to several other websites are given

There are some attractive animations in the Sheffield Orbitron:

the change in the spatial extent of surfaces as the contour level selected is changed (somewhat similar to the effect of the ORBITAL animation)
the change in shapes of orbital lobes for a diatomic molecule as the internuclear distance is changed dynamically (which is done one step at a time by the student using ORBITAL)

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History of ORBITAL

The present author wrote the ancestor of ORBITAL in 1976 in Hewlett-Packard Basic

Students accessed a time-shared computer via a 10-characters per second teletype and a telephone linkage
The program printed different upper-case letters to represent contour values, with white paper in between to aid visibility
A plot took about 12 minutes to print
Students changed function definitions by editing the program before running it
The idea came from L.J. Soltzberg, J. Chem. Educ., 1972, 49, 357-361

By 1985 the program had been translated into various dialects of Pascal for use in stand-alone microcomputers, but was still being used in an edit-compile-run mode

Monochrome screen output still used letters to represent contour values, but was a lot faster than teletype output

In 1993, Dr. Chris M. Smith assisted in translating ORBITAL into Prospero Pascal, and used its colour graphics capability to produce coloured contours similar to the present version

A sequential output-input conversation was used to set up all required parameters
The general nature of the previous versions, in which students could enter any function (in Pascal), was sacrificed in favour of selection from a menu of predefined functions in a pre-compiled program

In 1999, the ProPascal version became unusable because of purchase of PCs with non-compatible graphics adapters
In 2003, a decision was made to translate to a stand-alone Windows application, rather than a Web-based application, because of the greater ease of implementing interactive controls and particularly user-determined animation

Introduction Contents

Using ORBITAL

ORBITAL loads with an atomic orbital already selected
This may be changed using the drop-down function list for atom 2, or the X Range may be changed
Any change except setting the Animation on (if it is enabled in Setup), results first of all in the plot being greyed, to show that it no longer corresponds to the selected settings

Most details of the plot can still be seen, to help judge what new settings, e.g. Range, are required
Once the plot has been greyed, the controls respond quickly, so that e.g. the type-in box for Range keeps up with movement of the slider below it
The small buttons at the side of the type-in boxes control 'spin wheels': if they are kept pressed with the left mouse button, the value is stepped by pre-set amounts
When the plot is greyed, the Redraw Plot button at the top right of the display is ungreyed
Press Redraw Plot to remake the plot using the new settings

X Range controls the square xy region to be plotted

A higher value makes the orbital seem further away
Beware of using too low a value, i.e. zooming in too far, as this could result in essential features of the orbital being outside of the field of view
The same units are used for Range as for the interatomic Separations, but because the supplied functions are simplified, these are arbitrary: they do not correspond to Angstrom units nor Bohr radii

Animation may be stopped by clicking the Stop button, which appears when it starts

Fast animation on a slow computer may leave insufficient time for a mouse click to be seen easily by the program: in that case, the animation may be stopped by pressing the keyboard key S
Because animation stops at an arbitrary magnitude, the plot is left greyed and Redraw Plot should be pressed

Atomic Orbitals

Atomic wavefunctions are plotted if any one of the three atoms has an algebraic function selected and the other two have None

The coefficient typein boxes are greyed, and even if they are set using the 'spin wheel' buttons, they have no effect
The interatomic Separations have no effect

Molecular Orbitals

Molecular wavefunctions are plotted if any two, or all three of the three atoms have algebraic functions selected
The bond direction is horizontal, i.e. along the X axis

Use 2p(x) for sigma bonding or antibonding functions and 2p(y) for pi bonding or antibonding functions

Left separation is between atoms 1 and 2, and right separation between 2 and 3

If functions are selected only for atoms 1 and 3, the sum of the two separations may be used to select a much larger interatomic distance: e.g. use a separation of at least 20 units, made in this way, to display sigma bonding using 3p(x) functions

Separations of 3 units may be suitable for pi bonds using p orbitals, or for bonds using the 1s orbital
A separation of 3 units is too short for sigma bonds using 2p orbitals: separation 5 units is suitable
The 3p(x) function is supplied mainly for display as an atomic orbital (use a large X range)
Remember to increase X Range to include the separation selected as well as enough range for the lobes themselves

Selecting too large an X Range can easily be corrected, but selection of a too small range may lead to wrong conclusions

Coefficients may be typed in, or the provided 'spin-wheels' may be used

Because of an apparent deficiency in the programming facility used, the range of these spin wheels is less than may be typed in to the boxes
For polarised bonds, if coefficients are set to above 1 for some atom(s) and below 1 for the other(s), the range of the spin wheels is sufficient to represent any reasonable degree of polarisation

Setup

This software will run in Windows95, WindowsNT or Windows2000 environments.

The screen resolution should be set to at least 800 by 600 pixels in Settings, Control Panel, Display. If the windows run off the bottom of your screen, you probably have the resolution set to 640 by 480.

If you install this program in a different PC, the library files SALFLIBC.DLL and FTN90.DLL need to be in the windows path or in the directory in which ORBITAL is started. These libraries are commercial products, but you are permitted to take copies of them without charge.

ORBITAL may be started from DOS, or by creating a shortcut for your desktop and possibly changing its Properties as follows.

Giving the command ORBITAL in DOS, or double-clicking an unchanged shortcut, gives a version with Animation and full Help enabled

Adding -A after a space after the program name gives a version in which the animation controls do not appear

Adding -H after a space gives a version in which only Help About ORBITAL appears

Disclaimer

This software is produced in good faith with the expectation that it will work well, but neither the author nor the University of Newcastle accepts any liability for any failure to do so, nor for any damage to other software or hardware which it might cause. It may not be sold to third parties nor distributed for financial gain. Any reports on its use should cite it as:
ORBITAL for Windows by B.W. Tattershall, University of Newcastle, Newcastle, England, 2013.

The author makes no commitment to remedy reported bugs or make suggested improvements, but nevertheless would welcome comments from users.

Installation

Use pkunzip or Winzip, or whatever, to unzip the file orbtalwe.zip into a directory of its own on your PC. Make a shortcut to the executable file orbtalw.exe, which should stay in the same directory as the two .dll files.

No further installation under Windows is required. The software may be uninstalled simply by deleting orbtalw.exe and the two .dll files.

Feedback

I should like to hear about your use of ORBITAL, and be sent suggestions, comments, etc. As I say in the conditions of use, I do not undertake to act on suggestions, but I certainly welcome them and will give them due consideration.

Thanks very much.

Bruce Tattershall
School of Chemistry
University of Newcastle
Newcastle upon Tyne
England

Email: Bruce.Tattershall@ncl.ac.uk
Website: http://www.staff.ncl.ac.uk/bruce.tattershall/