Hueckel calc. problems with resonance systems

Hi,





the problem about Hueckel calculations on the two resonance structures for enolates, discussed in another topic seems to be solved !


Now both resonance structures give the same result for the pi energy (6.2165 beta) and the same pi electon density, see screenshot.





I will test it for other mesomeric pi-systems.





But what are the HMO parameters? I must evaluate it, using my own HMO program, simply by fitting alfa-O and beta-CO to the results. To say it once more: These simple parameters must be documented in a list.





Regards, Hans-Ulrich





Addition Nov 27, 2008:


Now there are tests showing the problems are not solved. See the next posts.

Hi,


the problems about Hueckel calculations for mesomeric systems are not solved.





In this post and the next, there are two cationic examples involving hydroxy-carbenium-ions.


In both huckel calculations the two resonance structures show different results. That's wrong.


For the enolat-ion above the resonance handling is solved, for these cations not.





BTW: The option View - lone pairs is a super feature of MarvinSketch





Regards, Hans-Ulrich

Here are the different results for the hydroxy-allyl cation. Obviously the calcultion for the structure at left uses different = wrong parameters for the pi-system.





In all resonance structures the oxygen has two neighbors and so it must be handled as an -O- group.





Once more it is a problem of the "hidden" parameters.





Regards, Hans-Ulrich

Hi,








I fixed these bugs.


We are going to do a release on Dec. 15.








Jozsi

Hi Jozsi,





OK. That's a good information.





But now the problems should be solved for all elements for which HMO calculations make sense.


And this leads me to the questions:





1) Does Marvin block elements for which HMO calculations are not designed ?


I have done some simple example calculations for elements which are not in the usual list of HMO parameters.


(I don't know if the Te-ring or the Po-ring really exist, but a HMO calculation for these rings is useless in any case. And, is Se really a better donor than S ?).





2) For which elements is the HMO calculation allowed ? I tried K, Ca, Sc ... it calculates ...





A HMO calculation must be restricted to the elements B C O N S F Cl Br ,


as listed in the basic book of Streitwieser and in other books on HMO calculations.





A test showed me, Marvin does not use the models for CH3-groups, and that's good.





And in this context another comment:


To offer more than 3 decimals for the HMO results is very bad, at least in the GUI.


Streitwieser uses 2 or 3 decimals in his book.


For me even 3 decimals are dubious because the parameters have only 1 digit, and these are the basis for the calculations.


(And there is the option to have "infinite" decimals. It only produces 10).





There are also to much decimals in other Marvin tools.





Regards, Hans-Ulrich

Hi Jozsi,


I must revise my comment on CH3-groups, given above.





I calculated in another context the N-Methyl-pyridinium ion and I found charge densities at the CH3-group. So I must analyse this situation. Some results are in the attached screenshot.





1) The CH3-groups of Methyl- and Dimethyl-anilin are not included in the HMO calculation.


2) For N-Methyl-pyridinium the CH3-group is included as conjugated model (Hyperconjugation). Comparison with the unsubstituted pyridium shows, the CH3-group is modeled as a rather strong donor substituent: The alpha and para positions are negatively charged, in the unsubstituted pyridinium these positions are positively charged.





The HMO-model is a very simple model. To simulate hyperconjugation is very arbitrary.





Regards, Hans-Ulrich

Hi Jozsi,





here comes the context for which I found the inconsistency.





The color of the merocyanine in the picture is discussed using these two mesomeric resonance formulas. The Marvin HMO calculation using the unpolar mesomeric resonance formula (left) shows the expected high polarisation. But the calculation with the dipolar mesomeric resonance formula (right) gives a different result. Here obviously because of the inclusion of the CH3-group.





Regards, Hans-Ulrich

Hi,





I fixed this problem.





Is this molecule aromatic that can be proved with any experimental evidence?








Jozsi

Hi Jozsi,


first the answer to your question ":


Is this molecule aromatic that can be proved with any experimental evidence? ":





It is once more a mesomeric resonance system (I use intentionally this tautology).


It's "Brooker's Merocyanine" and there are a lot of papers which discuss the coefficient in this qualitative combination of two valence bond wave functions.


F.e. the paper John O. Morley et. al., J.Am.Chem.Soc. 1998, 120, 11479-11488.





Regards, Hans-Ulrich

And then once more my suggestions:





1) Restrict the tool HMO calculation to the elements for which it is designed.





2) Use only the topology of the molecule and not the casual valence bond representation.





3) Do not use the hyperconjugation model.


How to do for benzylalcohole having a hydroxymethyl group? Is there a conjugation to both sides of the -CH2- group?


How to manage the dication Di-pyrylium-methylen C([N+]1=CC=CC=C1)[N+]1=CC=CC=C1 ?


If someone want's to use the simple HMO model to simulate hyperconjugation then there should be used a dedicated HMO program, where one knows the exact paramaters.


It is not the function of MarvinSketch to simulate hyperconjugation by default.





And once more: Restrict the display to maximal 3 decimals.


(This concerns to other "tools" of MarvinSketch also.)





Regards, Hans-Ulrich

Hi,








I agree with all of your suggestions. And hyperconjugation is really a "very arbitrary" in the HMO method.





Thanks for the reference about "Brooker's Merocyanine"

Quote:

It is once more a mesomeric resonance system (I use intentionally this tautology).

When you use the expression mesomeric resonance system do you mean a resonance hybrid?











Here is one more reference:


http://pubs.acs.org/doi/abs/10.1021/ja971477m





I qouted this sentence from this reference:





"1H and 13C NMR evidence in a range of solvents suggests that the merocyanine exists as a resonance hybrid which is weighted toward the zwitterion even in solvents of low dielectric constants."





According to this the resonance hybrid must be aromatic because the zwitterionic form as major resonance contributor satisfy the 4n+2 rule in both rings.








Jozsi

Hi Jozsi, thank you for the reference.





1) Yes, I mean "resonance hybrid". It is really a language problem in English. In German we call it "Mesomerie" and "Grenzstrukturen", so no one can get the idea, these "structures" really exist.


AFAIK: L. Pauling used the word "resonance" and C.K. Ingold used „Mesomerie“. In my opinion "Mesomerie" is better, it means "meso = about in the middle".





2) The sentence "1H and 13C NMR evidence in a range of solvents suggests that the merocyanine exists as a resonance hybrid which is weighted toward the zwitterion even in solvents of low dielectric constants." is still misleading, since the "merocyanine exists as a resonance hybrid, with or without the NMR evidence. The conclusion should be: The coefficient for the resonance hybrid with formal charges is large.





3) "According to this the resonance hybrid must be aromatic because the zwitterionic form as major resonance contributor satisfy the 4n+2 rule in both rings. Yes, this is one reason why this resonance hybrid has a large coefficient at all.





These days I have a very hot discussion with a colleague who is producing dyes going in the infra red reagion. But also in our chemistry campus there is always a discussion about teaching the resonance = mesomery formalism.





Regards, Hans-Ulrich

Hi Jozsi,


doing a HMO calculculation for Betanin, or Beetroot Red, I found another bug in the Marvin-HMO-calculator.





The HMO results for the isolated carboxylat-group and the carboxylic-acid-group are both OK.





But position 3 in the 2,3-dihydro-indol ring has a pi-charge. Obviously this methylen-CH2-group attached to the pi-ring is included in the Marvin-HMO-calculation, see red arrow in the screenshot bf0393.





The other sp3-C-groups are not included, green arrows. That's OK.








In the posts above, there was the decision not to include "hyperconjugation".





The bug is also found in the Marvin-HMO-calculation for 2,3-dihydro-indole, see bf0397.





Regards, Hans-Ulrich

Hi,


getting no answer I will post one example more on Marvin Hueckel calculations including sp3-hybridized carbon centers.





The sp3-hybridized carbon center in the middle of Triphenylmethane bf0459 gets nearly the same positive charge +0.29 as


the sp2-hybridized carbenium center in the middle of the Triphenylcarbenium ion bf0460 having +0.31.





Simple Hueckel calculation should not include hyperconjugation.





Regards, Hans-Ulrich

Quote:

Simple Hueckel calculation should not include hyperconjugation.

    


We will fix this in Marvin 5.3.





Regards,


Zsolt

Hi,





there is one example more which shows that this type of calculating alkylsubstituted benzene derivatives is problematic, see attached screenshot. The number of the C-H bonds of the alkylgroup going from methyl to tert-butyl makes no difference in the pi-charge distribution.





And there is also problematic hyperconjugation between the phenyl ring and the bromine atom.





Regards, Hans-Ulrich

Hi, further analyses of Marvin Huckel calculations give the following results:





1) Hyperconjugation is only programmed for alkylgroups attached to "aromatic" systems, see the methyl-tropylium example bf0486. For methyl-cycloheptatriene the Marvin Huckel calculation gives no hyperconjugation, neither for the CH2-group nor for the CH3-group. Obviously the attribute "aromatic" is included in the input for the Marvin Huckel calculation.





2) The calculation of the charge densities (and other properties) shows that for "aza" (N2) nitrogen  pi-orbitals and for "amino" (N3) nitrogen pi-orbitals the Coulomb Integrals (0.5) and the Resonance Integrals (1.0) are the same. The screenshots bf0502 and bf0498 show the comparison of the Marvin results with the results using the SHMO program www.chem.ucalgary.ca/SHMO/





3) By analogous comparing the parameters for other heteroatoms the result is:


3a) The parameter for F, Cl and Br are exactly the same as "recommended" in the basic literature.


3b) The Coulomb Integral parameters for "carbonyl" (O1) oxygen and "ether" (O2) oxygen are both 0.5 units higher than in the literature. Why?





Literature: Streitwieser, Molecular Orbital Theory, Wiley 1961, page 135, and Heilbronner/Bock, Das HMO-Modell und seine Anwendung , 1970, page III 218. (I don't have Isaacs book anymore, it's back in the library). Of course there are now optimised parameters in the literature (f.e. in the SHMO program), but these are often optimised for special tasks and the optimisation should be documented.





In the next post, I will present suggestions for a new HMO implementation.


Regards, Hans-Ulrich

Hi, here my suggestions for a new HMO implementation in Marvin:




An HMO calculations needs as input only


a) the topology of pi-orbitals,


b) parameters for hetero atoms other than "normal" C-pi-orbitals and


c) the total number of pi electrons.




It does not use "bond" information as input or other attributes of the molecules/ions, f.e. "aromatic rings".






In the following the hetero parameters for Coulomb Integrals are called "h(X)" and for the Bond Integrals "k(X-Y)"(changed Feb 4, 2009 according to the paper F. A. Van-Catledge, J. Org. Chem. 1980, 45, 4801-4802).




I have programmed a FORTRAN program which uses the following algorithm:


1) The molecules/ions are read in 3D-xyz-coordinates. The topology is determined by analysing the geometry and finding the neighbors of an atom: The neighbors are in a distance shorter than the normal bondlengths plus a tolerance of 0.3 Angstrom.


2) The further analysis is restricted to the elements B C O N S F Si P Cl and also Br.


3) Corresponding to this nomenclature there are (here only the most important pi-orbital types):


C-atoms with 3 neighbors: C pi-orbital with 1 default electron and h(C)=0.00


N-atoms with 2 neighbors: N1 pi-orbital with 1 default electron and h(N1)=0.51


N-atoms with 3 neighbors: N2 pi-orbital with 2 default electrons and h(N2)=1.37


O-atoms with 1 neighbor: O1 pi-orbital with 1 default electron and h(O1)=0.97


O-atoms with 2 neighbors: O2 pi-orbital with 2 default electrons and h(O2)=2.09


Cl-atoms with 1 neighbor: Cl1 pi-orbital with 2 default electrons and h(Cl)=1.48


4) The bonds are parametrised using the recommended values,


f.e. k(C-C)=1.00,k(C-N1)=1.09, k(C-N2)=0.98, k(C-O1)=1.26, k(C-O2)=0.95 and so on.


5) The total number of pi-electrons must eventually corrected by a total charge of the ion, given in the title line of the input.




Acetylene- and nitrile groups are handled like the corresponding double bond groups. The orthogonal pi-bond is neglected.




There is no special procedure for "twisted" pi-orbitals, but this can be corrected giving special parameters for twisted locations in the molecules/ions.




That's all.No special bond information or other properties of the molecules/ions.




This procedure is also applicable for the Marvin format of compounds. The topology of the compound is defined and as well the heteroatoms and the total charge. A MO calculation needs no VB information.




Regards, Hans-Ulrich

Hi, one post more: MarvinSketch can be a very helpful program !


I opened a Gaussian-log-file coming from a DFT/B3LYB calculation,


added the double bonds to the non planar 3D structure (saved then as mrv and xyz)


and then used "Tool - Huckel calculation".


As seen in the screenshot the charge distribution corresponds exactly to the C2 symmetry,


especially the positive charges (+0.52) at the two nitrogen atoms are equal (green arrows),


and there are relatively high negative charges (-0.74) at the oxygens with red arrows.


Of course, this is a very crude MO calculation for a molecule which is not planar,


but the twisted substructures are not so heavily twisted to destroy pi-overlap (cosinus function),


and the HMO method overestimates charges, but the result shows:


One resonance formula cannot show those properties.


Regards, Hans-Ulrich

Hi, I changed the nomenclature according to the paper F. A. Van-Catledge, J. Org. Chem. 1980, 45, 4801-4802.



as shown in an earlier post of this topic the Marvin Huckel calculation tool uses for




N1: aza-nitrogen contributing 1 pi-electron to the pi-system and for




N2: amino-ntrogen contributing 2 pi-electrons




the same Coulomb Integrals and the same Bond Intergrals.




This is wrong and should be corrected immediately.




In Streitwieser's book there are the sentences: "Clearly, alfa for a heteroatom that contributes 2 electrons  should be considerably more negative than alfa for the same heteroatom in a pi-system to which it contributes one electron; ... We might expect the difference to have ... about 1.0 to 1.5".






In the literature mentioned above the parameters are: k(N1)=0.51 and k(N2)=1.37




and the bond integrals are h(C-N1)=1.09 and k(C-N2)=0.98.










In the screenshot there is the analysis of the Marvin results using the SHMO2 program which is also available in the internet as an applet.






Regards, Hans-Ulrich

Hi, further evaluting Marvins Hueckel tool for practical use, I found more problems with HMO parameters.






I am using the nomenclature of the posts before taken from the paper F. A. Van-Catledge, J. Org. Chem. 1980, 45, 4801-4802






As shown in the screenshot pyrane4on the difference between the Coulomb integral parameters h(O1)=1.5  and h(O2)=2.0 is relatively small and does not correspond to the analysis of Streitwieser (see the post before). Most implementations of the HMO model have differences of about 1.0 beta-units. In the well documented table of F. A. Van-Catledge the values are h(O1)=0.97 and h(O2)=2.09.




In the case of sulfur (see f.e. thiopyrane4thion) there is once more the same situation as for nitrogen (see the post before).




Both types of sulfur pi orbitals have the same parameters: h(S1) = h(S2) = 1.50 and k(C-S1) = k(C-S2) = 0.90.




That's wrong and must be corrected before Marvin 5.3.




And the absolut sulfur values h(S1)/h(S2) are too high relative to the oxygen values. These give the result that the negative charges a the exocyclic atom is higher in the thiopyranethione than in the pyranone pi-system (see screenshots). According to Streitwieser's book the Coulomb integral values should correspond to Pauling's electronegativity values and here oxygen is much more electronegative than sulfur.






The Van-Catledge parameters are: h(S1)=0.46 / h(S2) =1.11 and k(C-S1)=0.81 /k(C-S2)=0.69.






I would suggest to use Van-Catledge's parameters. These seem to be a complete set of HMO parameters "determined in an unambigious fashion". (SHMO is using these as default).




Regards, Hans-Ulrich

Hi, there are more problems in Marvins Hueckel calculations.





As shown in the screenshot there are negative Electrophilic Localisation Energies L(+).





The definition of L(+) is the energy difference (PE = Pi Energy):





L(+) = (PE total pi system) - (PE localized cationic pi system)





Having a negative L(+) means the localized cationic pi system is more stable than the total pi system.





There must be failures in the calculation.





For the definition of L(+) for systems with heteroatoms I refer to Streitwieser's book, chapter 11.7 and the book





Arvi Rauk, Orbital Interaction Theory of Organic Chemistry, Wiley 2001, chapter 11.





In the next two posts there are evaluations of the L(+) calculations for phenol and benzaldehyde.

In the screenshots there are the energy values for phenol and the ortho, meta and para localized pi-systems.





The values in red show the results using the Marvin Hueckel tool. The L(+) values for ortho, meta and para are much too low compared to the values for benzene (L(+)=2.54).





Calculating the energy differences between total and the localized pi-systems showed: Marvin Hueckel uses different parameters for the total and the localized cationic systems. This does not correspond to the definition of L(+) as a model for the transition state of electrophilic aromatic substitution reactions.





The values in blue show the results for calculations with the same parameters for the total and the localized pi-system.





Now the L(+) are in the expected reagion. The low L(+) values for ortho and para are in qualitative agreement with experiment. Substitution in meta position is not favoured relative to benzene.

In the screenshots there are the energy values for benzaldehyde and the ortho, meta and para localized pi-systems.





The values in red show the results using the Marvin Hueckel tool. The L(+) values for


ortho, meta and para for this acceptor substituted ring are much too low compared to the values for


benzene (L(+)=2.54).





Calculating the energy differences between total and the localized pi-systems showed: Marvin Hueckel uses different parameters for the total and the localized cationic systems. This does not correspond to the definition of L(+) as a model for the transition state of electrophilic aromatic substitution reactions.





The values in blue show the results for calculations with the same parameters for the total and the localized pi-system.





Now the L(+) are in the expected reagion. The L(+) values show electrophilic substitution reactions are not favoured relative to benzene.

Hi,




the last posts show the Marvin Hueckel calculation tool is now able to handle different resonance formulas describing the same pi-system: The result is the same, as it must be.




But the handling of heteroatomic pi-systems is wrong. It must be corrected.






I suggest to use the well defined heteroparameters: F. A. Van-Catledge, J. Org. Chem. 1980, 45, 4801-4802




and to restrict the HMO calculations for the "organic" elements of these tables: C N O F Si P S Cl




and to define the parameter exactly to the no. of electrons given at this atom-pi-orbital.







Regards, Hans-Ulrich