aromaticity and electronic delocalization in all-metal clusters with single, double, and triple...

J. Poater, F. Feixas, E. Ma,to, M. Duran, M. Solà

Ins$tute of Computa$onal Chemistry

Universitat de Girona (Catalonia, Spain)

I. INTRODUCTION TO AROMATICITY

II. INDICES OF AROMATICITY IN CLASSICAL ORGANIC AROMATIC MOLECULES

III. INDICES OF AROMATICITY IN INORGANIC AROMATIC MOLECULES

IV. SINGLE, DOUBLE AND TRIPLE AROMATIC CHARACTER

V. CONCLUSIONS

The concept of “aroma,city” is oMen invoked in organic chemistry textbooks and research works to explain a number of chemical phenomena.

Terms appearing as ar,cle ,tle, keywords, or abstract

ISI (2000-‐2010)

In 2009, in every 2 hours appeared a paper in which benzene is in the ,tle, keywords or the abstract!


How to measure aroma,city?

Aroma,city is not an observable, then there is not a unique and generally accepted measure of aroma,city.

Many criteria have been used to develop indices of aroma,city: – Energe,c (ASEs, REs,…) – Structural or Geometrical (HOMA,…) – Magne,c (NICS, ring currents, 1H NMR…) – Electronic (hardness, ELF, DIs…)


Energe,c, structural, magne,c, and electronic criteria are easily measurable but unfortunately they do not always give consistent results among themselves → Mul,dimensional phenomenon.

It is your favorite index of aroma,city be`er than mine ?

Many authors recommend to perform aroma,city analyses using a set of aroma,city descriptors.

Different indices afford divergent orderings of aroma,city since one compound may be more aroma,c than other in one direc,on and less aroma,c in another.



When a new index is defined, usually the results obtained in a set of aroma,c compounds are correlated with previously defined indices of aroma,city.

The mul,dimensional character of aroma,city is some,mes used as a generic excuse to consider any local index of aroma,city defined a good descriptor irrespec,ve of the results obtained.

How can one differen,ate methods that provide essen,ally spurious informaIon from those that simply do not correlate because of the mul,dimensional character of aroma,city?



Fortunately, the accumulated experience provides several examples for which most chemists would agree about the expected aroma,city trends. S,ll most aroma,city descriptors fail to reproduce certain basic chemical situa,ons.

We propose to build a set of aroma,city tests using a series of such examples to assess the quality of the informaIon derived from the different indicators. The chosen tests must fulfill two requirements:

The size of the systems involved should be small

Controversial cases must be avoided


Indices of aroma,city analyzed

They are based on bond length equaliza,on between single and double bonds:

Ropt = 1.388 Å

α = 257.7

J. Kruszewski and T. M. Krygowski Tetrahedron Le>. 1972, 3839.

M. K. Cyranski, B. T. Stepien and T. M. Krygowski Tetrahedron 2000, 56, 9663.

Structural or Geometric criteria


Indices of aroma,city analyzed MagneIc criteria

Aroma,c rings have nega,ve NICS values at the center.

Aroma,c ring π-‐electrons are induced to circulate in a strong magne,c field (Ho) such that the induced magne,c field is aligned with the applied field in the vicinity of the aryl protons, but opposes the applied field causing shielding (upfield shiM) of protons above and below the ring.

z

R 0

H 0

O N *

R av

R av

MagneIc shielding tensor

P. v. R. Schleyer et al., J. Am. Chem. Soc. 1996, 118, 6317

Hind


Indices of aroma,city analyzed Electronic criteria

Symmetry Delocaliza,on

The sums are over occupied molecular orbitals. DIs measure the number of electrons shared between atoms A and B. QTAIM par,,on used.

The para-‐delocaliza,on index (PDI) is computed as an average of all possible DI between para-‐related carbons in a 6-‐MR.

The aroma,c fluctua,on index (FLU) is constructed considering the amount of electron delocaliza,on and also taking into account the similarity of electron delocaliza,on in adjacent atoms (symmetry).

They are based on the calcula,on of electronic delocaliza,on indices (DIs) computed for closed-‐shell HF or approximate DFT WFs as:


Indices of aroma,city analyzed Electronic criteria

MulIcenter delocalizaIon indices

For monodeterminantal closed-‐shell WFs:

M. Giambiagi, M. S. de Giambiagi, C. D. dos Santos and A. P. de Figuereido, Phys. Chem. Chem. Phys. 2000, 2, 3381

P. Bultinck, R. Ponec and S. van Damme, J. Phys. Org. Chem. 2005, 18, 706

A = {A1, A2, …, AN}


15 PROPOSED TESTS

F. Feixas, E. Matito, J. Poater and M. Solà J. Comput. Chem. 2008, 29, 1543


F. Feixas, E. Matito, J. Poater and M. Solà J. Comput. Chem. 2008, 29, 1543


The problem with the calcula,on of mul,center delocaliza,on indices is that they are quite expensive, especially for large rings. It would be convenient to have an electronic measure of aroma,city based on 2c-‐DIs. Something similar to PDI or FLU but more general and effec,ve.

First we looked at the total and total π electronic delocaliza,on taking into account the 4n+2 Hückel’s rule we should have:

+ 2 e- + 2 e-

+ 2 e- + 2 e-

F. Feixas, E. Matito, M. Solà, J. Poater, J. Phys. Chem. A 2008, 112, 13231


B3LYP/6-‐311G(d,p)

Δ1=P(N)-‐P(N-‐2) Δ2=P(N+2)-‐P(N) diff=Δ2-‐Δ1

F. Feixas, E. Matito, M. Solà, J. Poater, J. Phys. Chem. A 2008, 112, 13231


δ1-‐2

δ1-‐3 δ1-‐4

δ1-‐2

δ1-‐3

δ1-‐4 δ1-‐5

δ1-‐2

δ1-‐3

1

2

3

4

5

6

F. Feixas, E. Matito, M. Solà, J. Poater, Phys. Chem. Chem. Phys. 2010, 12, 7126


δ1-2 δ1-3 δ1-4 δ1-2 δ1-3 δ1-4 δ1-5

4,5-MR 6,7-MR 8,9-MR

δ1-2 Decrease Increase Decrease

δ1-3 Increase Decrease Increase

δ1-4 Increase Decrease

δ1-5 Increase

4,5-MR 6,7-MR 8,9-MR

δ1-2 Increase Decrease Increase

δ1-3 Decrease Increase Decrease

δ1-4 Decrease Increase

δ1-5 Decrease

AROMATIC 4N±2

ANTIAROMATIC 4N

AROMATIC 4N±2

ANTIAROMATIC 4N

C8H82-

C8H82+

C8H8

C6H62-

C6H62+

C6H6

F. Feixas, E. Matito, M. Solà, J. Poater, Phys. Chem. Chem. Phys. 2010, 12, 7126


F. Feixas, J. O. C. Jiménez-Halla, E. Matito, J. Poater and M. Solà J. Chem. Theory Comput. 2010, 6, 1118


F. Feixas, J. O. C. Jiménez-Halla, E. Matito, J. Poater and M. Solà J. Chem. Theory Comput. 2010, 6, 1118

The examples analyzed show that there is not yet a single indicator of aroma,city that works properly for all cases. It is important in this context to inves,gate the strong and weak points of the different indexes.

According to our results, the best indicators of aroma,city are the electronic indices based on the calcula,on of mul,center delocaliza,on indices.


Al42-‐, the all-‐metal aroma,c cluster

• Al42-‐ is the quitessen,al all-‐metal aroma,c cluster.


F. Feixas, E. Matito, M. Duran, J. Poater and M. Solà Theor. Chem. Acc. 2011, 128, 419

• Confirmed aroma,city.

• 1 pair of delocalized π-‐e and 2 pairs of σ-‐e (MOs with orthogonal radial and tangen,al direc,ons).

Al42-‐, the all-‐metal aroma,c cluster

• π delocaliza,on slightly larger than σ.



• Al44-: antiaromatic 4π-e system. • Al4: aromaticity depending on the orbital. • MCI does not provide information about antiaromaticity. • δα1,3 is computationally much cheaper.

C4v Al42-‐ + ca,on

• Aroma,city: Al42-‐ > LiAl4-‐ > NaAl4-‐ > CuAl4-‐


• Reduc,on more important for π than σ component due to par,al transfer of the 2π-‐e from Al42-‐ to the ca,on.

Al4 + ca,ons

• From Al44-‐ to Li2Al42-‐ there is an important decrease of the an,aroma,c π-‐character: par,al transfer from Al4 to Li+.


• Aroma,city: Li2Al42-‐ > Li3Al4-‐ = Li4Al4

Symmetry distor,on of Al42-‐

• Expected trend: Al42-‐ > Al3Ge-‐ ≥ Al2Ge2 ≤ AlGe3+ > Ge42+ (reduc,on of symmetry and subs,tu,on by more electronega,ve Ge).



Symmetry distor,on of Al42-‐ IV. SINGLE, DOUBLE AND TRIPLE AROMATIC CHARACTER


Transi,on-‐metal rings

• Cu3+ is σ-‐aroma,c.



• CunHn cannot be considered as aroma,c.

• Y3-‐ and La3-‐ are first reported transi,on-‐metal systems with double σ-‐ and π-‐aroma,city.

δ-‐aroma,city IV. SINGLE, DOUBLE AND TRIPLE AROMATIC CHARACTER


δ-‐aroma,city

• 5Ta3-‐: strong overlap between σ 2e’ and δ 3a1’.

• 3Hf3: Single occupa,on of e’’ orbitals.



Conclusions

• The quan,ta,ve evalua,on of aroma,city in inorganic clusters is cumbersome due to the lack of aroma,c inorganic systems that can be used as a reference.

V. CONCLUSIONS


• The aroma,city of these species can only be assessed by the use of the simple Hückel’s 4n + 2 rule and the calcula,on of the NICS and MCI descriptors.

• MCI of planar (or pseudo-‐planar) species can be separated into the σ-‐, π-‐, and δ-‐components. These MCIα (α = σ, π, and δ) indices provide quan,ta,ve valuable informa,on about the type of aroma,city that a certain aroma,c inorganic cluster has.

Conclusions

• The crossed term corresponding to the two farthest atoms in the ring (i.e., δπ1,3 in 4-‐MRs) decreases also in aroma,c inorganic species when two electrons are added or removed and that this crossed term is higher for the most aroma,c molecule in a series of same-‐membered rings.

V. CONCLUSIONS


• Consequently, this crossed term, which is less computa,onally demanding than MCI, is also a good descriptor of aroma,city in all-‐metal and semimetal clusters.

aromaticity and electronic delocalization in all-metal clusters with single, double, and triple...

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