Web Models for Teaching and Learning Chemistry

Web Pages for Teaching and Learning Chemistry

by Dr. Bruce W. Tattershall, Chemistry, Newcastle University, England

This is a list of web pages designed for undergraduate students of Inorganic or Structural Chemistry

They provide interactive computer models of orbitals, molecules, reaction paths, or vibrations

Note about Popups

Most of the pages in this list show calculated models in popup browser windows or tabs, so that the user can compare two models
Most browsers block popups, so when you click on a chart or button to select a model, you will see a warning box rather than the desired model
There is no need to reduce the security of your browser, because a green Continue button will also appear on the web page, near to the chart or button which you clicked

If you are working in a small window, you may need to scroll a bit to find this green button

Click the green Continue button. This should satisfy the browser that you are not malware, and the popup should open, showing the desired model

Molecular Orbitals

Web Application Orbital

This is a two-dimensional contour plotting program intended for students following an introductory course about atomic and molecular orbitals

The student selects from a list of simplified functions expressed in Cartesian coordinates, which serve to represent natural atomic orbitals
The program plots coloured bands on the screen, to represent either one atomic wavefunction, or two or three of these wavefunctions added together to make a molecular orbital
The student appreciates the idea of a wavefunction, and learns about nodes in AOs and in MOs, and hence about π versus σ MOs and antibonding versus bonding MOs
LCAO coefficients and nuclear separations (on arbitrary scales) can be set at will as experiments
The program is best used in a classroom situation with a script designed by the instructor to fit the course being given, but the original online tutorial script used in Newcastle with the Orbital application has now been updated and is available online

Pre-calculated Molecular Orbitals for Simple Molecules

This series of web pages provide on-screen rotatable molecular models, with their valence-shell molecular orbitals, taken from real ab initio calculations. Species range from homonuclear diatomics, e.g. peroxide ion, to PF₃, a trigonal pyramidal molecule with π-bonded ligands

All of these pages work in the same way, using the same or similar web application software
Each has a schematic molecular orbital energy level correlation diagram, and when the student clicks on a MO, a new window pops up to show a JSmol/Jmol model of a surface of the selected orbital
The models come up as a ball and stick model of the geometry, with a surface at ψ = ±0.04 for the selected orbital, coloured blue and red to show relative signs of the wavefunction
A radio button is provided to switch on a contour plot in the plane of the screen in the initial view. For each orbital the direction of view is selected so that some useful contour plot is visible if the contours are switched on
What is different between these pages are the notes provided, which point up the principles illustrated by the particular species

Molecular Orbitals of Peroxide Ion [O₂]^2–

This a rather more familiar example of a formally singly bonded homonuclear diatomic species, than the isoelectronic fluorine molecule, F₂

From a Natural Bond Orbital analysis of the calculated MOs, tables of LCAO coefficients of natural atomic orbitals in the MOs, and of contributions of their overlaps to bonding, are provided and discussed
Orthogonality of the σ and π systems with each other, and between the π orbitals, is introduced
sp mixing in the σ system of peroxide is compared with the N₂ case, where it is much more important and, in contrast to peroxide, it results in crossover in energy of the σN(2p)N(2p) and the bonding π levels
For peroxide it is pointed out that although the σO(2s)O(2s) MO contains only 5.6% p character, 2s — 2p_z overlaps in it still provide 30.3% of the total bonding
The unusual situation that the HOMOs are antibonding, and that their negative contribution to bonding exactly cancels the positive contribution of the π-bonding orbitals, is dealt with

Molecular Orbitals of Nitrogen, N₂

For this molecule, the subject of sp mixing is explored in more depth

The ab initio calculations were done at the same level as for peroxide ion or for CO (see below), so the tables of LCAO coefficients etc. may be compared directly, between these web pages for diatomic species
A button is provided to switch on an additional explanation of sp mixing in terms of stepwise LCAO to make σ_g(s) and σ_u(s), etc., followed by mixing of σ_g(s) with σ_g(p) to produce the calculated overall coefficients. This follows the approach in some introductory textbooks
The competing requirements of different natural atomic orbitals, in determining the equilibrium bond length, is discussed. The dominant π bonding in N₂ needs a shorter bond length, so it is too short for optimum N(2_{p_z}) - N(2_{p_z}) overlap

Molecular Orbitals of Carbon Monoxide, CO

Polarisation of molecular orbitals is the chief new topic for this heteronuclear molecule

The percentage compositions of most MOs, in terms of the contributions of natural atomic orbitals, are shown against the correlation lines of the energy level diagram
All of the valence shell NAO contributions to the σ MOs are shown in the Table of Coefficients, so the student can assess the effect of polarisation, particularly in comparison with the isoelectronic N₂
Although the MO names are retained from the N₂ case for the sake of comparison, the HOMO σC(2p)O(2p), illustrated here, has 56% s character, and is 90% composed of carbon NAOs
The LUMO π^* orbitals are seen to be polarised towards carbon, with 71% C_2p character, and the concept of synergic bonding as a π-acceptor ligand to a transition metal is mentioned
A switch is provided to select either a high level of calculation for comparison with N₂, or a lower level of calculation for comparison with CO₂ (see below). Both the JSmol/Jmol models available, and the tables and notes, change appropriately on clicking this switch, but the student may see relatively little difference in either

Molecular Orbitals of Carbon Dioxide, CO₂

For this larger molecule, there are much less detailed notes. The topics to be introduced for CO₂ are as follows

Both σ and π MOs are each delocalised over all three atoms
s and p orbitals on the central atom do not mix with each other, because they require different combinations of signs of coefficients of the ligand orbitals. Correlation lines and orbital symbols on the energy level correlation diagram are colour coded accordingly
There are delocalised π MOs which are neither bonding nor antibonding, but are non-bonding by symmetry
The LUMO π^* orbitals are strongly polarised towards carbon, corresponding to the Lewis acidity which is an essential property of CO₂

Molecular Orbitals of Boron Trifluoride, BF₃

This web page is meant for a course at a slightly higher level than is the page on CO₂, so while a similar colour coding of the energy level correlation diagram is used as in the CO₂ case, optional group theory symbols and a character table are given as well

These may be turned off using a provided switch, if a suitable group theory course has not yet been taken
As in the CO₂ case, the 2s orbital on the central atom does not mix with any of its 2p orbitals, because they have different symmetries relative to the molecular symmetry
There are five delocalised MOs which are fluorine 2p combinations that are non-bonding by symmetry
The LUMO π^* orbital is even more strongly polarised towards boron than the antibonding LUMOs are towards carbon in CO₂, and BF₃ is a strong Lewis acid

Molecular Orbitals of Phosphorus Trifluoride, PF₃

How do molecular orbitals change, in going from the trigonal planar molecule BF₃ to the trigonal pyramidal molecule PF₃? A simple answer might be "surprisingly little" part of comparison table

Corresponding MOs are sufficiently similar in appearance, between the two molecules, that the names devised for BF₃ MOs have been carried over to those of PF₃
The web page shows optional group theory labels for the MOs in the same way that the BF₃ page does
The point group for PF₃ is a subgroup of that for BF₃
With the loss of the planar symmetry of BF₃, the phosphorus 3s orbital belongs to the same symmetry representation as the phosphorus 3p_z orbital, so they do mix
While the π-bonding orbital of PF₃ looks similar to that of BF₃, though with the π nodal surface bent to accommodate the pyramidal group of atoms, the π-antibonding orbital might be better labelled as σ^*, and is the HOMO 'lone pair' of PF₃
It is noted that the doubly degenerate LUMO pair of σ^*P(3p)F(2p) orbitals resemble, when seen down the z axis, the LUMO pair of π^* MOs of carbon monoxide, and reference is made to the somewhat parallel chemistry of PF₃ and CO as π-acceptor ligands

Pairwise Comparison of MOs of PF₃ and BF₃

Rather than the student selecting corresponding MOs on the two separate web pages and seeing them in two separate pop-up windows, this web page allows a pair of models to be selected by means of a single click on a line of a graphical comparison table. The selected rotatable JSmol models then come up side by side at the bottom of the table, on the same web page

Thus, as in the part of the table illustrated here, the HOMO of PF₃ may be shown alongside the LUMO of BF₃
In contrast to the separate pages for the molecules, where Java Jmol may be selected if the student's browser is Java-enabled, only HTML5.0 JavaScript JSmol models are provided in the comparison page, and no contour plot option is available for the models
A fast, modern browser should be used (at the time of writing this, 2019, this could be Chrome in a PC, or Safari)

Molecular Orbitals of Diborane, B₂H₆

Learning about LCAO MO theory is usually done in the context of small molecules, e.g. N₂, CO or CO₂. People doing wavemechanical calculations on larger molecules most often seek molecular geometries or energies of reaction or of activation, or perhaps other observables such as NMR shieldings. They are comparatively unlikely to look at details of the delocalised molecular orbitals involved in these calculations

So what is the biggest molecule in which it is worthwhile to learn in depth about the makeup of its MOs, as an aid to understanding MO theory?

I should say it is B₂H₆, with 14 valence shell atomic orbitals and hence 14 valence shell MOs
This is because it is a beautiful example of the application of group theory to the understanding of orbitals: many of the nodal surfaces of the MOs are planes of asymmetry in their group theory representation
To make most use of this web page, a student should have a working ability to set up a representation of a set of atomic orbitals in the molecule, given the character table for the point group, and to reduce this representation, at least using a publicly-available web page to do the reduction arithmetic
The discussion provided does use symmetry representation labelling, on the assumption that this will be familiar to the student

Interesting Molecules

The point of providing JSmol/Jmol rotatable models of molecular structure for teaching and learning inorganic or organic chemistry is usually so that the student may explore molecular shape, conformation, chirality, or symmetry. Physical ball and stick models, which the student may hold and manipulate, are possibly best, but ready-made computer graphics models have the advantage of speed and ease

Main Groups Inorganic Ring and Cage Molecules

This web page was developed to support a course which taught about synthesis, structure and bonding, symmetry and chirality in non-metal ring and cage chemistry, particularly that of sulfur and of phosphorus, where it is quite a dominant feature

The course was a vehicle for teaching principles of bonding and electron counting, aromaticity, and exercising the students' ability to spot symmetry elements and hence assign point groups
It introduced the idea of molecular chirality and its connection with symmetry operations, beyond the introductory organic chemistry idea of chiral centres
Most of the examples are of academic interest only, though some have a long history

The web page takes the form of a table with a line for each example
Most lines contain one or two questions, telling the student what to look for, and providing reinforcement of points made in the lecture course
Each line has a Model button, which replaces the table page with a page showing the JSmol/Jmol model. The student uses the back button to return to the table
All model pages have buttons to control the appearance of the model, and some have extra, customised controls, e.g. to set particular viewpoints helpful to the student in their exploration
Each model page has an Answers or Comments button which produces a half-width popup page, usually answering the original questions and often giving further guidance about looking at the model. Where the model might provide a useful example for assigning the point group symmetry, this answer is usually given, so as to provide a self-study tool for the student

Reaction Pathways

Traditionally, reaction pathways have been represented in illustrations by structural formulae of initial and final states, connected by reaction arrows via transition states or intermediates. Lecturers may demonstrate the well-practised manipulation of lecture-room-sized ball and stick models, but it is difficult for students to make adequate notes, and, when bond making and breaking is involved, the task of delivering a good demonstration approaches the superhuman. Smooth graphical animations, going from one recognisable state to another, are an excellent teaching and learning replacement for physical models. Alternative representations, e.g. spacefilling versus ball and stick, can be provided easily if desired, and the student may rotate the model on their screen so as to see the animation from any viewpoint

Ring-Flipping of Cyclohexane

This is probably one of the first fluxional molecules that chemistry undergraduates meet, as well as being an historical starting place for conformational analysis

The default JSmol mode works adequately in a fast browser such as Chrome in a PC or in Safari, but students with a Java-enabled browser may select the Java_Jmol mode to obtain faster animations and response to mouse rotations etc.
Like the MO web pages above, this Cyclohexane web page has a clickable schematic energy level diagram, but this time showing the end conformations, intermediates, and transition states in the inversion of the cyclohexane ring

Clicking on any of these structures produces a JSmol/Jmol rotatable model in a popup window
Up to two such windows are allowed, so that two different structures may be compared
The models come up as stick models and in profile so that e.g. the chair shape of the end conformations may be seen
The student may turn them around or select the more exciting representations Ball and Stick or Spacefill
Axial and equatorial hydrogen atoms are colour-coded so that the student may follow them during the animation
When all is ready, radio buttons allow the animation to be switched on or off, and further buttons allow a quick move to the beginning or end of the reaction pathway, or to nudge backwards or forwards
A frame counter allows the student to keep track of where the animation has got to, and this shows also the name of each of the clickable structures if and as they are passed
Quite a lot of notes are given on the calling web page, suggesting experiments for the student to do and explaining how to find the symmetry elements

Besides the simple reaction path via a Twist-Boat intermediate, given in most introductory textbooks, this web page shows also a 'Route B', going from one Twist-Boat intermediate to its enantiomer, via an untwisted boat transition state

The clickable models came from ab initio optimisations, and many of the intermediate frames from ab initio IRC calculations. A few were interpolated by hand

Rearrangement of a Chiral Main Groups Cage Molecule

This is one of the 'Interesting Molecules' referred to above. It is an obscure phosphorus-selenium cage molecule which undergoes a racemisation equilibrium reaction on the dynamic ³¹P NMR timescale at room temperature. This involves breaking and making of cage bonds

To see the animation of the reaction path, click on the Animation Model button
This animation always starts at the transition state, since the student needs to come to terms with that first
Now click the Start animation radio button
As in the cyclohexane case above, when the end of the reaction path is reached, the animation reverses and goes backwards
All of the points were from an ab initio IRC calculation
For ease of the ab initio calculations, the model used for the animation was P₃Se₄Br rather than P₃Se₄I. The bromide undergoes a similar exchange reaction but at a slower rate than does the iodide

Substitution Reactions in Metal Complexes

Each of the four following web pages deals with a substitution mechanism in transition metal complexes which goes via an intermediate. As in the cyclohexane web page above, there is a clickable reaction scheme, but in this case it is the reaction arrows which are clickable, rather than the end states of the reaction steps

Each page contains a reaction scheme with reaction arrows leading to or from one or more intermediates. Clicking on a reaction arrow produces a JSmol/Jmol model positioned beneath the reaction scheme
One or two models side by side are allowed: the left model is for a reaction leading from the starting material to the intermediate, while the right model is for the step going from the intermediate to the product

When an arrow is clicked, a red hand symbol indicates which step has been switched on
Clicking the provided Animate button switches the program to animate mode: starting with the leftmost model, a series of animation frames are shown, representing the course of the reaction. If two models have been selected, then when the left model ends at the intermediate, the right model starts automatically, carrying on from the intermediate to the product
The models come up with their own Pause and Play and positioning buttons, so the student can stop and reposition the models at any point in the sequence
Fuller introductory notes and instructions are given on the calling page, as well as buttons for selecting Java Jmol models instead of HTML JSmol, or for selecting a background colour, and on the individual pages there are Help buttons
The models are anonymous in terms of the identity of the metal or of the attacking or the leaving groups. In fact, the starting and end points were semi-empirical PM3 models of imaginary zinc complexes, and the leaving and attacking groups were bromide and chloride respectively
Animation steps were from Gaussian geometry optimisations going towards the stable molecules, and the reverse sequence for dissociation steps. This is explained more fully in an About.. page giving the history of these web pages

The four constituent web pages are as follows

S_N1 Mechanism for Substitution in an Octahedral Complex

This goes through a square pyramidal intermediate

Enantiomers in a S_N1 Mechanism for a Bis-chelate Octahedral Complex

This goes through a trigonal bipyramidal intermediate

Associative Substitution Mechanism for a Square Planar Diethylenetriamine Complex
Associative Substitution Mechanism for Square Planar Complexes with Monodentate Ligands

This shows retention of configuration, even in the absence of a constraining tridentate ligand

Molecular Vibrations

Some molecular modelling packages can calculate the vibrational modes of molecules, which give rise to infrared and/or Raman spectroscopic absorptions. To understand these, it is very desirable to see animated models which can be rotated so as to show the most informative view

A traditional chemical application of Group Theory, taught in undergraduate chemistry courses, is the calculation of the number, symmetry and nature of the vibrational modes of symmetrical small molecules. Possibly the most difficult part of this is visualising what the molecular motions 'look' like, particularly for symmetry representations which are doubly or triply degenerate. Several pages on the Web show JSmol models of vibrations, to support such courses

Vibrations of Some Phosphorus Chloride Species

This page shows animated JSmol models of the vibrational modes for some phosphorus chlorides which have molecular geometries common in Inorganic Chemistry

The models are from wavemechanical modelling, though at a very low level
The calculated vibration frequencies are not intended to approximate to experimental spectroscopic values, but serve to show the calculated order the vibrations, and which are degenerate with which
There is no tutorial content in this page: it just shows the models resulting from calculations, without comment
Users may find it useful in conjunction with learning or teaching the application of Group Theory to molecular vibrations