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I ran some vertical excitation energy calculations, and I'm a little confused about the results. Would someone be able to help me to understand?

Here are my results: enter image description here

I'm trying to understand the significance of the numbers associated with the orbitals in the following text:

Excited State 7:

149 -> 151 0.69645

I am unclear about what this value in front of transitions means. My labmate mentioned that I should choose the orbitals associated with the highest value to run some CASSCF calculations.

Additionally, when selecting the orbitals, should I look at the absolute values of these numbers or not? For instance, in Excited State 6, I am unsure whether I should select the transition:

Excited State 6:

140 -> 151 0.21876 Positive, but not the higher

or

142 -> 151 -0.40946 Negative, but the higher

Any guidance would be appreciated!

1 Answer 1

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TLDR;

Those numbers you’re seeing next to each orbital transition are basically showing you how strongly that particular “jump” (from one orbital to another) contributes to the overall excited state. In other words, they’re coefficients that tell you which transitions matter most. When you’re picking orbitals for follow-up calculations (like a CASSCF), you generally want to focus on the transitions with the largest absolute values. Don’t get too hung up on whether a coefficient is positive or negative—what really counts is how big it is.

More Detailed Explanation:

In many quantum chemistry methods, an excited state is described as a combination of different orbital-to-orbital excitations. Each of these excitations—like “149 → 151”—comes with a coefficient (that number you see). The larger the absolute value of that coefficient, the more that particular excitation shapes the character of the excited state you’re studying.

If you think of it like a “recipe” for the excited state, each excitation is an ingredient. The ones with big coefficients are the main ingredients; the smaller ones are more like a pinch of salt or a dash of pepper. The sign (positive or negative) doesn’t usually carry much physical meaning—it’s more about how the math shakes out in the calculation. What you really want to do is pick the orbitals linked to the biggest absolute coefficients for your next steps (like setting up a good active space in CASSCF), because that ensures you’re capturing the key features of the state.

So, if you see something like “149 → 151: 0.69645,” that’s a pretty big deal. You’d probably want orbitals 149 and 151 in your active space. On the other hand, if you compare something like “140 → 151: 0.21876” and “142 → 151: -0.40946,” the second one, despite being negative, has a larger magnitude. That means the 142 to 151 transition is more important than the 140 to 151 one, so you’d likely choose to include orbitals 142 and 151.

Bottom Line: Focus on the size of these coefficients, not the sign. The biggest numbers highlight the most important orbital transitions to include in your next calculation.

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