Interpretation of the Tanabe Sugano diagram

[Kenji Liew]

We can estimate the value of Δ and B from Tanabe Sugano diagram. For example Ni2+ which is has the electronic configuration of d8. So, by referring the d8 Tanabe Sugano diagram, we can can noticed that there are 3 types of transition. The transitions are observed as V1=8500cm-1, V2=13800cm-1 and v3=25300cm-1. We can take the ratio V2/V1=1.624. But the problem is, from the ratio ,how can we determine value of the vertical axis, that is Δ /B? Due to this problem, I find the difficulty to estimate the value of Δ and B.
In addition, how can we explain the further splitting of the spectrum? Thanks.

 

[GCT]

We can estimate the value of Δ and B from Tanabe Sugano diagram. For example Ni2+ which is has the electronic configuration of d8. So, by referring the d8 Tanabe Sugano diagram, we can can noticed that there are 3 types of transition. The transitions are observed as V1=8500cm-1, V2=13800cm-1 and v3=25300cm-1. We can take the ratio V2/V1=1.624. But the problem is, from the ratio ,how can we determine value of the vertical axis, that is Δ /B? Due to this problem, I find the difficulty to estimate the value of Δ and B.
In addition, how can we explain the further splitting of the spectrum? Thanks.

You need to find the proper diagram - d3 , d6 , etc...

Then deduce all of the transitions

Then find the point on the x-axis where the ratio of values between the transitions equals your ratio for the wavelenghts.

Visit my link to find some applets on Tanabe-Sugano diagrams.

 

[Kenji Liew]

Hi, thanks for your explanation. But you still don't explain how to find the point on the x-axis where the ratio of values between the transitions equals with the ratio for the wavelengths.Try and error? or got suitable method? From the URL you provide, I notice that the point on the x-axis is given after ratio is known.It don't explain how we get the x-axis point Thanks!

 

[GCT]

Hi, thanks for your explanation. But you still don't explain how to find the point on the x-axis where the ratio of values between the transitions equals with the ratio for the wavelengths.Try and error? or got suitable method? From the URL you provide, I notice that the point on the x-axis is given after ratio is known.It don't explain how we get the x-axis point Thanks!

Once you find the proper diagram as well as the right two lines you are able to skim across to find the point that corresponds to your ratio , this may be done manually which would be an approximation or use a software such as that provided on the directed website.

 

[GCT]

Hi, thanks for your explanation. But you still don't explain how to find the point on the x-axis where the ratio of values between the transitions equals with the ratio for the wavelengths.Try and error? or got suitable method? From the URL you provide, I notice that the point on the x-axis is given after ratio is known.It don't explain how we get the x-axis point Thanks!

One other thing , if you are able to know of the equation of the two lines then there is a mathematical way of getting an exact answer ... if you are in need of it reply to this message.

 

[Kenji Liew]

I think to make life easy,solving two mathematical equations and then get the point of x-axis is the better way. The answer may more accurate. If I use the method of skim across, this may take some time to do this. So, can you show me an example or a guidance to do this by solving two mathematical equations? Really thanks for your help.

 

[GCT]

If you used that software that was included in that link that I mentioned then it would only take seconds ... I don't have the time to give you an example , it's actually been a while since I came across this topic.

equation 1 - y1 = x1c1 + b1

equation 2 - y2 = x2c2 + b2

v2 / v1 = C

C = ( x2c2 + b2 ) / ( x1c1 + b1 )

x2 = x1

C = ( xc2 + b2 ) / ( xc1 + b1 )

Solve for x

 

[RusLatviaScie]

In case anybody is looking for the issue of X axis again here it is:
Example:
The complex [Co(H₂O)₆]⁺ has two d-d absorption bands at 16,600 cm^-1 and 24,800 cm^-1

Looking at the Tanabe-Sugano diagram specifically for d⁶ (Co³⁺ is d⁶) we can see that the transitions are ¹T_1g <-- ¹A_1g and ¹T_2g <-- ¹A_1g transitions (right hand side because there are 2 transitions and it is low spin).

Then we find the ratio of the peaks 24,800/16,600 = 1.49, the next step is to find the D/B on the X axis:
You may have to try several values in order to find the ratio that is closest to 1.49.
In this situation you look at the height (Y axis) of ¹T_1g and ¹T_2g (this is where the 2 of your transitions will end up, look above) and find the ratio of these heights. To make things easier, look for the 'good-looking' values of D/B, like 40, 30, 25 etc, not random 11 or 26. In this example the right ratio is of 41/27 = 1.51, where D/B=30.

Then you do the rest of the calculations if you need to find D. (by substitution of E/B=27 - the value on the Y-axis where X-axis = 30; then E=16600 cm^-1 and blaaaa)

Took me some time to figure things out, so I decided to share with people who are struggling. :)