[AdiDex]

My question is How to calculate the Resonance energy of Thiophene?
I know how to calculate the resonance energy of Benzene.I am applying same procedure for thiophene too.
Source:https://en.wikipedia.org/wiki/Resonance_(chemistry)#Resonance_energy
Here is the Data from http://webbook.nist.gov/.(Heat of formations are in Kcal/mol)

Thiophene    Tetrahydrothiophene     2,5-Dihydrothiophene
27.82              -8.03                        20.86

So from moving Tetrahydrothiophene to 2,5-Dihydrothiophene, there is a change of 28.89 Kcal/ mol, so Ideally thiophene should have 28.89*2 (=57.78) Kcal/mol more energy of formation, But it has only 35.85 Kcal/mol more. This difference should be called Resonance energy i.e. 35.85-57.78=-21.93.

But in literature, it is given -29.1 Kcal/mol .

I applied the same method on furan, I got an error of only 0.1 Kcal/mol but in case of Thiophene I am getting an error of about 7 Kcal/mol.
Why?

[pgk]

This kind of calculations is a simplified and not error-free, point of view for resonance energy that apart its educational value, it was used by the pioneers of the issue, in order to prove that aromaticity is more than a simple sequence of simple and double bonds. However, more adequate and exact calculations of resonance energy are based on quantum equations.
Anyway and roughly, aromaticity is not only a question of (4n+2)π electrons but it also a question of a planar structure. Thus, sulfur as being more electron rich and more bulky, needs more energy to keep to molecule planar at the “1,2-3,4-5-carbanion/sulfonium” hybridization structure, which cannot be estimated by the hydrogenation enthalpy method.

[AdiDex]

sulfur as being more electron rich and bulkier needs more energy to keep to molecule planar at the “1,2-3,4-5-carbanion/sulfonium” hybridization structure, which cannot be estimated by the hydrogenation enthalpy method.

So according to this, The resonance energy calculated by hydrogenation method should be more than the actual resonance energy. As I didn't consider the energy required to make the structure planar from it's more stable conformation. But resonance energy I calculated is less than the literature value!

[pgk]

1). Attention because you have negative values!
Although lower in absolute value, -21.93 is higher than -29.1 in negative scale.
2). Furthermore, take care when adding negative and positive numbers:
 -8.03 + 20.86 = 12.83 and not 28.89
3). Also, the formation enthalpy of 2,5-dihydrothiophene significantly differs than the one of 2,3-dihydrothiophene, due to the conjugation of the vinyl sulfide moiety in the latter.
4). Besides, the formation enthalpy is not constant but it may vary, depending on the formation reaction that is calculated from. In other words, comparison of the formation enthalpies between dehydro-/dihydro- derivatives does not always coincide with the corresponding hydrogenation enthalpy.
etc…

[Mitch]

Also, make sure you are using the heat of formation enthalpies for the gas state. That way molecule-molecule interactions won't contribute to an error.

[AdiDex]

1). Attention because you have negative values!
Although lower in absolute value, -21.93 is higher than -29.1 in negative scale.

1. Resonance is generally stabilizing in nature, that's why I used a negative sign. I said that I didn't consider the destabilizing effect of the planarity (as you said "needs more energy to keep to molecule planar ").

Let's consider due to the resonance of pi electrons there is an energy change of -100 Kcal/mol but it has also +20 Kcal/mol (destabilizing) energy change. So Actual Resonance energy should be -80 Kcal/mol (lower absolute value).

Since I've only considered that -100 Kcal/ mol, didn't consider that destabilizing effect, my calculation should have higher absolute value.
but it isn't!! So according to me, that error in case of Thiophene should be from another reason.

2.

So from moving Tetrahydrothiophene to 2,5-Dihydrothiophene, there is a change of 28.89 Kcal/ mol,

I took the difference, so 20.86-(-8.03)= 28.89 Kcal/mol

3. I've tried to use that also. Resonance energy was found out to be -23.5 Kcal/mol (using 2,3-dihydrothiophene, i.e. more accurate). But I tried to avoid it because it already has some resonance energy associated with it.

[pgk]

1). You are right!
Your calculations are correct. I was wrong and strict. So, I fully apologize for this.
2). Coming to the point:
Imagine that you have a combustible that has a theoretical combustion heat = -21.93 kcal/mole. But during combustion an endothermic reactions occurs, which consumes +10.00 kcal/mole but the reaction product is also combustible with combustion heat = -17.17 kcal/mole.
Neglecting their molar ratio for simplicity reasons, the overall combustion heat is:
-21.93 + 10.00 - 17.17 kcal/mole = -29.10 Kcal/mol
Thus and in terms of thermal yield: |29.10| > |21.93|
But in terms of Hess law: -21.93 > -29.10
3). Something similar happens hereby:
On the one hand, sulfur consumes (unknown?) energy, in order to keep a planar molecule but on the other hand, the planar structure contributes to the stabilization of the hybridization and the aromaticity of thiophene.
4). Restarting from the beginning:
The hydrogenation enthalpy is an approximate method for the calculation of aromatic energy, which has a high scientific and educational value. This method may work with benzene but it tends to be inaccurate with heteroaromatics, fused and polynuclear aromatics, aromatic ions, as well as with aromatics that have a number of members that is different than 6 because it does not take into account the size of the heteroatom, neither the difference of ring strain between the aromatic rings and their perhydro-derivatives (note that 6 members rings have ring strain ≈ 0).
More accurate results can be taken by using specific quantum equations, which are specially invented for.

[AdiDex]

Can you please refer to some literature, So that I can show it to my teacher? What are other ways? If you can write them in a nutshell, I want to know them.
By the way, Thanks for writing. 

[pgk]

Although, quantum chemistry is out of my expertise area, please take a look to indicative links, below:
On the top, are cited general methods of aromaticity estimation by molecular orbitals (MO) calculations.
On the bottom, are listed articles about the role the size and the electronegativity of the heteroatom in aromaticity, as well as the role of the empty d-orbitals of sulfur.
The last one refers on the influence of the double bond in the ring strain.
https://link.springer.com/content/pdf/10.1007/s00214-010-0793-8.pdf
https://onlinelibrary.wiley.com/doi/pdf/10.1002/qua.560010622
https://onlinelibrary.wiley.com/doi/pdf/10.1002/qua.560382482
https://www.sciencedirect.com/topics/chemistry/resonance-energy
https://link.springer.com/article/10.1007%2Fs00894-013-1877-x
http://pubs.rsc.org/-/content/articlelanding/1949/tf/tf9494500173#!divAbstract
https://pubs.acs.org/doi/abs/10.1021/cr60293a004?journalCode=chreay
http://fulir.irb.hr/2136/1/resonance.pdf
https://pdfs.semanticscholar.org/60f1/2eb7d20abfc6c613539e9a8a5c14e7d232b3.pdf
https://www.hindawi.com/journals/jchem/2015/456961/
http://aether.cmi.ua.ac.be/artikels/Comprehensive_Heterocyclic_Chemistry/HET2v2Ch09.pdf
http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1516-89132016000300400
https://aip.scitation.org/doi/full/10.1063/1.4933191
https://pubs.acs.org/doi/abs/10.1021/jo401319k
https://onlinelibrary.wiley.com/doi/pdf/10.1002/poc.610050203
https://www.sciencedirect.com/science/article/pii/0166128081850592
https://link.springer.com/article/10.1007/s10947-008-0169-2
https://nparc.nrc-cnrc.gc.ca/eng/view/accepted/?id=1aab8dc4-66ed-475b-8269-de15c5793885
https://hungary.pure.elsevier.com/en/publications/d-orbital-participation-in-bonding-in-thiophene-comparison-of-cnd
https://onlinelibrary.wiley.com/doi/pdf/10.1002/jhet.5570330414
https://www.nature.com/articles/s41598-017-01903-0
http://agris.fao.org/agris-search/search.do?recordID=US201800039407
http://info.phys.tsinghua.edu.cn/henucl/ning/18.pdf
https://quod.lib.umich.edu/a/ark/5550190.0010.730?rgn=main;view=fulltext
https://www.arkat-usa.org/get-file/28734/
http://www.nrcresearchpress.com/doi/pdfplus/10.1139/v65-208
https://www.ias.ac.in/article/fulltext/jcsc/128/02/0311-0324
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.041801
https://www.diva-portal.org/smash/get/diva2:516605/FULLTEXT01.pdf
https://authors.library.caltech.edu/25034/13/BPOCchapter12.pdf