Plotting Orbitals: Easy Formulas for Non-Physicists

[ghostanime2001]

My question is that is there any formula for non-physicists like me that can we can use to plot and graph the orbitals of atoms. I know the orbitals arise from solving the Schrödinger equation and solving them but are there already known equations that we can just plug into graphing program that graphs relations (because of the cut-away of the orbitals is the only information i need to visualize, the rest can be made 3D in my head)

 

[Civilized]

Yes, there are equations, they are called spherical harmonics. They are given here (look at equations 18 through 33):

http://mathworld.wolfram.com/SphericalHarmonic.html

In my opinion, if you are not interested in the math of QM it isn't worth dealing with them, it would be better to print out a piece of paper with the pictures on it. If you learn about spherical coordinates (for example in a multivariable calculus course) the functions are easy to visualize from the equations alone, no graphing calculator required.

 

[Fenn]

If you know about gnuplot, there's a great site that gives instructions how to plot spherical harmonics at http://t16web.lanl.gov/Kawano/gnuplot/spherical_harmonics/index-e.html

I've used this to render some nice orbital plots and generic P state chargeclouds, and exported the results to TikZ, a graphics rendering tool for LaTeX. I can provide more details if any of this sounds interesting to you,

 

[mccoy1]

Yes, there are equations, they are called spherical harmonics. They are given here (look at equations 18 through 33):

http://mathworld.wolfram.com/SphericalHarmonic.html

In my opinion, if you are not interested in the math of QM it isn't worth dealing with them, it would be better to print out a piece of paper with the pictures on it. If you learn about spherical coordinates (for example in a multivariable calculus course) the functions are easy to visualize from the equations alone, no graphing calculator required.

He was just asking if there were equations that describe the shapes of orbitals..he didn't say he was scared of the math behind QM.You guys here seem to think that anyone who's non-physicist is a dummy who can't understand QM math as if qm math was created by physicists.the qm math is just the differential equation that everyone knows,so when one asked a question,just be kind to give him the answer he want and he'll decide for himself whether he'll understand its content or not.giving someone a warning like you did belittle him n is an underestimation of his knowledge .

 

[Civilized]

He was just asking if there were equations that describe the shapes of orbitals..he didn't say he was scared of the math behind QM.You guys here seem to think that anyone who's non-physicist is a dummy who can't understand QM math as if qm math was created by physicists.the qm math is just the differential equation that everyone knows,so when one asked a question,just be kind to give him the answer he want and he'll decide for himself whether he'll understand its content or not.giving someone a warning like you did belittle him n is an underestimation of his knowledge .

No need to lecture me, I was offering the OP a tip, not trying to belittle them. Personally, I think it is merely busy work to deal with the expressions for spherical harmonics in the year 2009, whether or not someone is a physicist. Perhaps I should have said that if I, as a professional physicist or as a student, wanted to view the shapes of orbitals than I would not bother with the formulas on the page I linked. I don't think spherical harmonics are "too difficult", I think they are trivial busy work that I wouldn't recommend anyone bothering with, but obviously that is just an opinion, and is not the point of this thread, just a response to your lecture.

 

[ghostanime2001]

QM math does look rather difficult to solve and Understand it too for me, but I'm so interested in calculating the probability of finding an electron of a given distance from the nucleus I just thought that maybe for somebody inexperienced as I am would just be given somekind of formula together with a introductory tutorial explaining the physics behind the formula---made easy for me to understand withought all the technical terms. I am just interested in the qualitative understanding behind orbital shapes and calculating the probability of finding electrons at a given distance from the nucleus (if there is a formula(s) for that). That's pretty much the idea behind my post.

I want an understanding in simple bunny-easy terms. LOL i know i sound like an idiot but i just completed Grade 12 and with no knowledge or familiarity of what is harmonics or whatever I deserve an explanation in very simple terms. I remember my chem teacher in class saying, "the electron dematerializes into radiation and then rematerializes back into matter just like star treck"

I was so overwhelmed by that i spent endless days trying to picture how electrons show complimentarity of waves and particles. That's the whole reason why i wanted to learn orbitals and all that neat stuff... if there are any resources available like courses or online tutorials or pretty much ANYTHING out there that can help me understand princples and dynamics of orbitals I'd be filled with delight.

 

[Fenn]

One resource I found which may be helpful for what you're asking is at http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html. Give that a shot and see if any of that is of any help.

 

[ghostanime2001]

One question: Whenever i think about wave-particle duality is it reasonable to picture it like this?

a wave packet that has energy concentrated in one fraction of space-time but that's only if picturing a hypothetical "eye" close-up view. Now, take the eye away from the "wave-packet" has to increase the dimension of space-time and the "wave-packet" pictures so concentrated in space-time that to us now, in the new "zoomed-out" view of the dimension the wave packet seems like a localized particle but is actually a small little wave concentrate and tightly packed with energy----some sort of energy i do not know what to call it appropriately but some form of energy indeed... Am i correctly picturing wave-particle duality in my sense? or is there another view which is more correct but translates into the same picture as mine?

 

[ghostanime2001]

Is the virial theorem true for atoms and molecules ?

It says:
The total energy (kinetic + potential) of an electron in an atom or a molecule is always one-half its potential energy. Thus, for example, when an electron is shifted from a 1s to a 2s orbital, its potential energy increases by 3.27 aJ. At the same time the electron slows down and its kinetic energy drops by half this quantity, namely, 1.635 aJ. The net result is that the total energy (kinetic + potential) increases by exactly half the increase in potential energy alone; i.e., it increases by 1.635 aJ. A similar statement can he made for any change inflicted on any electron in any atomic or molecular system. This result is known as the virial theorem. Because of this theorem we can, if we want, ignore the kinetic energy of an electron and concentrate exclusively on its potential energy.

from: http://wiki.chemeddl.org/index.php/5.4_The_Potential_Energy_of_Electrons

 

[ghostanime2001]

Do atomic orbitals ever touch each other and if they do or are very close to other atomic orbitals what will happen?
What would an atom with all orbitals filled look like? all the way from 1s to 4f orbitals?

My chemistry teacher once told me that each orbital "interlocks" with another orbital so that they do not touch and the distance between them minimizes electron repulsion (is it called screening effect... sort of?) IS that true?

 

[jtbell]

Look at the electron probability distributions for various orbitals at

http://hyperphysics.phy-astr.gsu.edu/hbase/hydwf.html#c1

You'll see that they not only touch, they overlap in space.

 

[ghostanime2001]

Now that is just weird. I always thought that atomic orbitals are independent of each other. I don't understand why they partially overlap with the next higher energy orbital(s). If this truly happens then shouldn't let's say an electron in 2p orbital have an energy similar to the next 3s orbital? That's considering the case where atomic orbitals overlap. Why do they overlap anyway? In all chemistry textbooks they never show an atom with multiple orbitals illustrated.What would an atom REALLY look like if all the orbitals were filled and a physical model were made in real life considering the overlap as well of orbitals. I know orbitals are non-physical entities but just to give me a general idea?

and btw that site is just for hydrogen what about for multi-electron atoms?