Real-Time Visualization of the Quantum Mechanical Atomic Orbitals The orbital images on this page represent the shape of the atomic orbitals. The clouds you see are the probability distribution of an electron bound to a Hydrogen nucleus. These images were created using Atom in a Box, a scientific and educational program that aids in visualizing the Hydrogenic atomic orbitals, a prime and otherwise unwieldy example of quantum mechanics. |
Orbital Ballistics by mandarancio The classic ballistics game but in the solar system! The player planets colony has to destroy the enemy planets with inter-planetary nukes! The program runs on both OS 9 and OS X. System requirements are fairly moderate – you need a G3 (333 MHz for OS 9, 600 MHz for OS X, OS X 10.7 and newer not supported) and you must have a video card that handles QuickTime RAVE (OS 9) or OpenGL (OS X). Linux and Mac OS X USERS MUST READ 1. See Section 2.1.2 and 2.1.3 on how to install Linux and Mac OS X versions of Multiwfn, respectively. I cannot guarantee that Linux and Mac OS X versions are as robust as Windows version, since all of my developments and most debugging are performed in Windows environment. Runs on: Mac OS X 10.4 or later. Chrono Trigger Quiz v.1.0. Illustrates and solves mathematical problems related to spherical trigonometry, orbital ballistics, conic sections, cartography and walks over the square Illustrates and solves mathematical problems related to spherical trigonometry, orbital ballistics, conic sections, cartography. If you're planning on running the treasures of the past you'll find here on real old Macintosh hardware from the 90's, you sir/madame, deserve to win an Internet! For others, there's SheepShaver, a PowerPC emulator capable of running Mac OS 9.0.4 down to Mac OS 7.5.2 and there's Basilisk II, a 68k emulator, capable of running Mac OS (8.1 to 7.0).
| Mac | iPhone | iPad |
Atom in a Box on the Mac App Store for both Apple Silicon and Intel Macs running macOS 'Big Sur' 11.2 or later See below for additional Mac versions. | Atom in a Box for the iPod Touch and iPhone is part of the debut of the App Store. |
NOTE: First announced at the 1998 Conference on Computational Physics held in Granada, Spain, I am a student winner in Computers In Physics' Ninth Annual Software Contest with Atom in a Box. Full descriptions of the prize winners are in CIP's Nov/Dec 1998 issue. This now makes me the only person to have been a student winner twice in a row in CIP's Software Contest. In addition, Apple has been kind enough to write an article about Atom in a Box in their inaugural issue of Apple University Arts. Do you speak Dutch? Prata svenska? Sprechen Sie Deutsch? Habla español? Parlez-vous Français? Parlate italiano? Also, this program appears in a 12-minute streaming RealVideo clip at the UCLA Department of Design. In addition to the many kind individuals who have registered, I thank all those who registered from institutions such as: Massachusetts Institute of Technology, Pacific Lutheran University, U. C. Davis, Georgia Institute of Technology, Pennsylvania State University, University of Houston, Wesleyan University, University of Missouri - St. Louis, Purdue University, Millikin University, West Virginia University, Karl-Franzens-Universität Graz, Universität Bern, Washington State University, Southwest Missouri State University, Douglas High School, San Joaquin Delta College, Maine Maritime Academy, Kalamazoo College, Southwestern University - Georgetown, Texas, Haverford College, Florida A&M University, Nagoya University, Miami University, Virginia Tech, Yale University, Bob Jones University, Cornell University, Kyoto University, Utah State, Institute for Advanced Study at Princeton, Snow College, Hammond High School, Reed College, University of Washington, Wooster College, Colorado School of Mines, the Wellington School, the University of Southern Mississippi, Harvey Mudd College. Many people have registered from outside the United States: Japan, United Kingdom, Canada, Austria, Switzerland, Belgium, Germany, and Italy. Through word of mouth, I have heard of my program in use at Caltech, U. C. Santa Cruz, Stanford, Harvard, and others. |
Unlike other tools in this category, this program raytraces through a three-dimensional cloud density that represents the wavefunction's probability density and presents its results in real-time (up to 48 frames per second on Mac G3s; even faster on the latest hardware). The user interface is very interactive and provides a wide degree of flexibility.
It contains all 140 eigenstates up to the n=7 energy level and the allowed spectral transitions between those eigenstates. The Mac version also allows a state formed by a superposition (see below) of up to eight of those eigenstates allowing for over 3 trillion possible states and can display a wavefunction as a picture of a cloud, use color as phase, plot in red-cyan left/right for 3D glasses, and slice the wavefunction.
You can see more example images at the bottom of the page.
What is Quantum Mechanics?
One of the great advances in human knowledge of the twentieth century is the birth of the theory of Quantum mechanics. It has led to some of the most common technologies used today, including the little transistors that make up the computers you're using to read this. One of the mysteries it revealed was the structure of the atom. Classical mechanics could not properly explain the existence of the atom. Because there was nothing to stop electrons from spiralling in to the nucleus, it predicted that all atoms would immediately destroy themselves in a spectacular high-energy blast of radiation.
Well, that obviously doesn't happen. Quantum mechanics describes that the electron (and all of the universe for that matter) exists in any of a multitude of states. The particular physical situation determines what and how many states there are. Borrowing from some of the techniques in mathematics, physicists organize these states into a particular set of mathematically convenient states called 'eigenstates'. Eigenstates are good to use because what makes one eigenstate different from another usually has a physical meaning. They also can make an horribly difficult problem managable. These and other phenomena in Quantum mechanics predict that possiblities in physical phenomena have distinct separations (e.g., 'quantum leaps') and that energy transport exists as indivisible packets, called 'quanta'. Hence the name: Quantum Mechanics.
What are Orbitals?
By applying these techniques to the hydrogen atom, physicists are able to precisely predict all of its properties. The electron eigenstates around the nucleus are called 'orbitals', in a rough correspondence with how the Moon orbits the Earth. We find that these states do not allow the electron to crash into the nucleus, but instead find themselves in any combination of these orbital eigenstates. These orbitals' physical structure describe effects from how atoms bond to form compounds, magnetism, the size of atoms, the structure of crystals, to the structure of matter that we see around us.
Visualizing these states has been a challenge, because the mathematics that describe the eigenfunctions are not simple and the states are a three-dimensional structures. The standard convention has the orbital eigenstates indexed by three interrelated integer indicies, called n, l, and m. Their range and interdependence comes out of the math in deriving the eigenstates. n can range from 1 to infinity. l can range from 0 to n-1. m can range from -l to +l. They also have physical meaning. The energy of the state, which is negative because the electron is bound to the nucleus, depends only on n and increases as n increases. l refers to the amount of angular momentum the electron has due to its 'orbit' around the nucleus. l is not equal to the amount of angular momentum but goes up as angular momentum goes up. m determines how much of the angular momentum is in the z direction. (However, the rest of the angular momentum is not l minus m or anything that simple. That's a long story that I can't fit here. Look in a Quantum textbook (a good one is A Modern Approach to Quantum Mechanics by John S. Townsend), take a course, or talk to a physics professor.)
What's here for me?
I have written a Macintosh application that displays atomic orbitals in real-time. Rather than just a plot of the spherical harmonics, as is shown in many Quantum mechanics textbooks, this program displays the electron orbital as a cloud. The cloud's density is determined by the orbital's probability density for the electron. There are three examples on this web page: The one at the top is the n=3, l=2, m=0 state; the screenshot above has n=7, l=4, m=0; the first example below is n=6, l=4, m=1. (The quality is poor so that they wouldn't take too long to download over the Internet. They'll look even worse if you are not using Millions of colors to view it. The program looks quite a bit better, trust me.) With the program, you can rotate the orbital around in real time. If you have red-cyan 3-D glasses, you can see it in 3-D too. The program has all the orbital eigenstates up to n=7, which is the highest occupied shell for the ground states of the heaviest elements, e.g., Uranium, Plutonium, etc.
You can download the application from the links below and have a look. The program is computation intensive. For individual users, the v1.x Mac application is US $20 shareware. Pricing of the later versions are on the App Store. You can read the details in the about box or the Read Me. Also supplied are example orbital files.
Platform Availability| Mac | iPhone and iPod Touch | iPad | |||||
Rewritten from the ground up, v2 of Atom in a Box uses SwiftUI 2.0 and multicore to reach new capabilities the previous code could never do.
After Mojave, Apple ended support for the Carbon API this app uses. If you're not sure if it'll run on your macOS, you may download it so you can test. This code base will receive no further updates. In 2006, the Universal Binary version included the following enhancements: QuickTime export of the orbital animation, in addition to PICS. Endian conversions for file and disk access. Adapted source to Xcode. OS X-compliant application and file icons and plst data. Correction of an issue with sound buffers for the orbital sound. New recognition of horizontal and vertical scroll wheels, so now you can use the Mighty Mouse's scroll ball to rotate the orbital. Known issue in the Universal version: On most Macs, OS X 10.4.x places a 60 fps governor on QDFlushPortBuffer, consequently limiting the speed with which AiB can display its animation. One should be aware of that before making speed comparisons. Hint: increase the Samples setting to make the calculations more challenging. For OS 9 and pre-OS X 10.3.9, we also provide a Carbon CFM version of AiB 1.1 (324 kB). v1.0.6 will run on both OS 9 (with CarbonLib) and OS X. The latest pre-Carbon version of Atom in a Box, v1.0.4 is no longer supported. See the READ ME for more details. |
See the App Store for pricing and availability for your country. |
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See the Atom in a Box iOS Online FAQ for Version History. Reviewers: Please email your request and your background info (e.g., your web site) to feedback @ daugerresearch.com to obtain a review copy. | |||||||
A Short Gallery of Animated Orbitals
This is the quantum state where n=6, l=4, and m=1: | Orbital Animation' src='Orbital.641.small.gif' width=192 align=center> |
This is an equal superposition of the 3,2,1> and 3,1,-1> eigenstates: | + 3,1,-1> Orbital Animation' src='Orbital.321+31-1.gif' width=192 align=center> |
This is an equal superposition of the 3,2,2> and 3,1,-1> eigenstates: | + 3,1,-1> Orbital Animation' src='Orbital.322+31-1.gif' width=192 align=center> |
This is an equal superposition of the 4,3,3> and 4,1,0> eigenstates: | + 4,3,3> Orbital Animation' src='Orbital.410+433.gif' width=192 align=center> |
The Lewis Structure approach provides an extremely simple method for determining the electronic structure of many molecules. It is a bit simplistic, however, and does have trouble predicting structures for a few molecules. Nevertheless, it gives a reasonable structure for many molecules and its simplicity to use makes it a very useful tool for chemists.
A more general, but slightly more complicated approach is the Molecular Orbital Theory. This theory builds on the electron wave functions of Quantum Mechanics to describe chemical bonding. To understand MO Theory let's first review constructive and destructive interference of standing waves starting with the full constructive and destructive interference that occurs when standing waves overlap completely.
When standing waves only partially overlap we get partial constructive and destructive interference.
To see how we use these concepts in Molecular Orbital Theory, let's start with H2, the simplest of all molecules. The 1s orbitals of the H-atom are standing waves of the electron wavefunction. In Molecular Orbital Theory we view the bonding of the two H-atoms as partial constructive interference between standing wavefunctions of the 1s orbitals.
We can also have partial destructive interference.
The energy of the H2 molecule with the two electrons in the bonding orbital is lower by 435 kJ/mole than the combined energy of the two seperate H-atoms. On the other hand, the energy of the H2 molecule with two electrons in the antibonding orbital is higher than two separate H-atoms. To show the relative energies we use diagrams like this:
In the H2 molecule, the bonding and anti-bonding orbitals are called sigma orbitals (σ).
- Sigma Orbital: A bonding molecular orbital with cylindrical symmetry about an internuclear axis.
When atomic orbitals are combined to give molecular orbitals, the number of molecular orbitals formed equals the number of atomic orbitals used. So the two 1s orbitals of H combine to give the σ orbitals of the H2 molecule. A molecular orbital (like an atomic orbital) can contain no more than two electrons (Pauli Exclusion Principle), and are filled starting with the lowest energy orbital first. In general, the energy difference between a bonding and anti-bonding orbital pair becomes larger as the overlap of the atomic orbitals increase. Now let's look at some examples:
The H2+ molecule has only one valence electron.
The H2 molecule has two valence electrons.
Mac Os Catalina
The He2+ molecule has three valence electrons.
The He2 molecule has four valence electrons.
In the Lewis Structure Theory we had single, double, and triple bonds, in the Molecular Orbital Theory we similarly define the bond order.
Bond order = 1/2 (# of electrons in bonding orbitals - # of electrons in anti-bonding orbitals).
The bond order in our four examples above are given in the table below.
| Bond | Bond Order |
|---|---|
| H2+ | 1/2 |
| H2 | 1 |
| He2+ | 1/2 |
| He2 | 0 |
The bond order must be positive non-zero for a bond to be stable. He2 has a bond order of zero and that is why the He2 molecule is not observed.
We can also form bonding orbitals using other atomic orbitals. To a first approximation only orbitals with similar energies can combine. For example, we can combine two p orbitals to form a sigma bond:
Using p orbitals a second type of orbital called a π orbital can also be formed.
Let's look at some examples where we have bonds forming between the s and p orbitals of two atoms bonding together.
For example, e.g. O2 has 6 + 6 = 12 valence electrons which can be placed in bonding and anti-bonding orbitals.
Notice that Molecular Orbital Theory predicts that O2 has unpaired electrons, so it will be paramagnetic.
Demo:- Show that iron metal is paramagnetic - is attracted to a magnet.
- Show chalk is not paramagnetic - is not attracted to a magnet.
- Show that liquid nitrogen is not paramagnetic - passes through pole faces of a magnet - shown on overhead projector.
- Show that liquid oxygen is paramagnetic - sticks to pole faces of a magnet - shown on overhead projector.
Another example is F2. It has 14 electrons which are placed in the bonding and anti-bonding orbitals starting with the lowest energy orbital first.
Mac Os Versions
In the case of B2, C2, and N2 there is a slightly different ordering in orbital energies.
For example, B2 has 3 + 3 = 6 valence electrons.
Orbital Ballistics Mac Os Pro
For much nicer three-dimensional renderings of all the bonding orbitals visit Mark Winter's Orbitron site .
Homework from Chemisty, The Central Science, 10th Ed.
Orbital Ballistics Mac Os Download
9.49, 9.53, 9.57, 9.59, 9.61, 9.63, 9.65, 9.67, 9.69, 9.71