Problem in basic equalities for Huckel energy

In summary, the conversation discusses the proof of the equation Sij = Sji and its relation to the complex functions f_i and f_j. The speaker is asking for a proof starting from the definition of complex functions and showing that the left side of equation (I) is equal to the right side. The link provided introduces this equation as <f_i|f_j>, but it may not be reliable and the equation only holds if the functions are real.
  • #1
georg gill
153
6
http://vallance.chem.ox.ac.uk/pdfs/VariationPrincipleNotes.pdf

In the proof above I need to understand why: $$S_{ij}=S_{ji}$$. Which is the same as proving

$$\int f_i f_j dg=\int f_j f_i dg$$ (I)
Not sure about what I should call the variable for so I called it g. Can someone prove this from the basics? From starting from defintion of complex functions and start from left of (I) and get to the right of (I). I know that complex times complex conjugate gives probability. Thank you!In the link this is introduced at page 2 as $$<f_i|f_j>$$
 
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Related to Problem in basic equalities for Huckel energy

1. What is a "problem in basic equalities" for Huckel energy?

The problem in basic equalities for Huckel energy refers to a discrepancy between the theoretical predictions of Huckel's rule and the experimental results for certain molecules. According to Huckel's rule, the total Huckel energy of a molecule should be equal to the sum of its individual atomic Huckel energies. However, in some cases, this is not observed, leading to a "problem" or inconsistency in the theory.

2. Can you explain Huckel's rule in simple terms?

Huckel's rule is a theoretical concept developed by Erich Huckel in 1931 to predict the stability and electronic structure of conjugated organic molecules. It states that molecules with a fully conjugated system of pi electrons (i.e. alternating single and double bonds) will have enhanced stability and delocalized electronic energy, resulting in lower total energy for the molecule.

3. What are some examples of molecules that exhibit a problem in basic equalities for Huckel energy?

Some common examples of molecules that show a discrepancy between theoretical and experimental Huckel energies include cyclobutadiene, cycloheptatriene, and benzene. These molecules have fully conjugated pi systems, but their experimental Huckel energies are lower than the sum of their individual atomic Huckel energies, violating Huckel's rule.

4. How do scientists explain the problem in basic equalities for Huckel energy?

The discrepancy between theoretical and experimental Huckel energies is often attributed to the presence of non-bonding electrons and other factors that are not considered in the basic Huckel theory. These additional electronic interactions can affect the total energy of the molecule and lead to inconsistencies with Huckel's rule.

5. What are the implications of the problem in basic equalities for Huckel energy in chemistry?

The problem in basic equalities for Huckel energy highlights the limitations of the Huckel theory and the need for more advanced models to accurately predict the properties of conjugated molecules. It also emphasizes the importance of considering all electronic interactions in understanding the stability and reactivity of organic compounds.

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