Supporting Information 

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Response to “Comment on "Restricted Geometry Optimization: A Different Way to Estimate Stabilization Energies for Aromatic Molecules of Various Types"”

   Firstly, we would not like to make comment whether the uses of the words “simple fact” and “measures” in the comment are professional or not. The commenter should know our method is based on the principle of the Morokuma’s energy decomposition.² The modified Fock (density) matrix, obtained from partly deleting the elements of the matrix, has been widely used in the various fields of organic chemistry,³ which have made the great contributions to developing theoretical chemistry. The Kollmar,^3a Jug^3b and Morokuma² procedures are all based on the modified Fock matrix and have played an important role in developing the methods of calculating (aromatic) resonance energy (including - energy partition). Emphatically, our - energy partition can be used in any conjugated molecule no matter whether it is planar or nonplanar.⁴ Therefore, our title and related papers⁴ have been positively cited and commented.⁵  We wonder whether the commenter has concluded that all such related research and computations, reported in literature, are completely meaningless. However, as shown by an inspection of the list of the commenter’s papers, he seems not professional enough to be able to comment on the energy decomposition method.

            

Figure 1-jpca. The G ( Ground state geometry) , GL ( Geometry having Localized double bonds), and GE-n ( the nth particular GEometry ) geometries of hexatriene were obtained from the full and restricted geometry optimizations at the B3LYP/6-31G* level; In a specific geometry, the thick and thin lines indicate that all the  orbital interactions between the double bonds have been set equal to zero except for those between the double bonds denoted by the thick lines ( yellow Color).

Figure 3-jpca. The procedure for calculating the extra stabilization energy (ESE) of benzene. the G, GL and GE-1 geometries, as indicated by the thin ( green color) and thick lines (yellow color), were obtained from the full and restricted geometry optimizations at the B3LYP/6-31G* level. The thin lines indicate that all the  orbital interactions between the double bonds have been set equal to zero except for those between the double bonds denoted by the thick lines. Molecular energy of the GL geometry was denoted as E^T(GL) in the title paper, and it is writen as  E(GL) in this response manuscript )

In our title paper, as shown by the Figure 1 ( Figure 1-jpca in this manuscript) and Figure 2  in the title paper, it was confirmed first that the energy differences [E(GE-n) - E(GL)] between the corresponding GE-n and GL geometries are additive in each acyclic polyene, i. e. [E(G) - E(GL)]  [E(GE-n) - E(GL)], and [E(G) - E(GL)] – [E(GE-n) - E(GL)]  0 ( Figure 1-jpca in this manuscript). In the case of benzene, the molecular energy difference E^A1= [E(GE-1) - E(GL)] between the GE-1 and GL geometries is 9.4 kcal/mol ( Figure 3-jpca in this paper). If these three energy differences E^An ( n = 1, 2, 3, and E^A1 = E^A2 = DE^A3 ) were additive, the expected geometry of the ground state of benzene would be similar to the FG (cyclohexatriene) geometry in which the lengths of the single and double bonds would be equal to those of the C2-C3 and C1=C2 bonds in the GE-1 geometry. Correspondingly, the molecular energy difference [E(FG) - E(GL)] between the expected ground state (FG geometry) and GL geometry would be about 3*E^A1(28.2 kcal/mol), i.e. [E(FG) - E(GL)]  3*[E(GE-1) - E(GL)]. In fact, cyclohexatriene is not a real molecule, the energy difference [E(G) - E(GL)] between the G (ground state) and GL geometries of benzene is -10.8 kcal/mol. In this case, ([E(G) - E (GL)] - 3 * [E(GE-1) - E(GL)]) = [E(G) - E(GL)] - [E(FG) - E(GL)] = E(G) - E(FG) = -10.8 - 28.2 = -39.0  0, indicating –39 kcal/mole deviation from the additivity was found in the benzene molecule (this detail derivation is meant to help the commenter to understand the principle of our procedure).  In our title work, the quantity -39.0 kcal/mol is defined as ESE of benzene with respect to its reference structure FG, and it is the molecular energy difference [E(G) - E(FG)] between the G and FG states of benzene. Emphatically, therefore, it is misunderstanding of definition of aromatic resonance energy for the commenter to say: “The fully optimized benzene structure Gb is now more stable than the artificial system GLb, but only by 10.8 kcal mol-1. This would correspond to the aromatic stabilization, although the number is much lower than any of the estimates in the literature”.
    Accordingly, there are no differences, in the use of additive principle and in the supposing of the fictitious geometry (FG), between the Kistiakowsky’s procedures and ours. The fundamental difference between the two procedures is in the choosing and constructing of the reference structure (s) as well as in the type of physical quantity satisfying additivity. 

Then, we would like to interpret why it is reasonable that the energy difference, such as [E(GE-1) – E(GL)] > 0, is destabilizing.  According to the data presented in Figures 1, 2 and 3 of the supporting information as well as according to those in our related papers,⁴ the energy difference, such as E^A1 = [E(GE-1) – E(GL)] between the GE-1 and GL geometries of benzene, can be partitioned into various components using the following general expressions (1) to (7):

where E_e and E_N are total electron and nuclear repulsion energy differences, respectively.

       

where E_H and E_two are one and two electron energy differences, respectively.

       

where E_e and E_e are the and  components of total electron energy difference,^3k respectively

               

where E_N and E_N are the  and  components of nuclear repulsion difference,^3k respectively                                                

where E and Eare the  and  components of molecular energy difference, respectively.

       

where E_e-n and E_e-mn are the energy effects associated with FMO interactions occurring, respectively, in the double bonds such as C1=C2 (subscript “e-n”, n = 1) and C3=C4 (subscript “e-n”, n = 2) and occurring between the double bonds C1=C2 and C3=C4 (subscript “e-mn”, n = 1 and m = 2), et. al.

 

where E_mn-CT and E_mn-EX are the charge transfer and exchange energy differences, respectively.

     

         

 At ab initio and DFT ( density function theory) theory levels, therefore, the components of the energy difference, such as E^A1 = [E(GE-1) – E(GL)], are complex. Particularly, as shown by the data in Figures 1 and 2 of the supporting information, the -interactions between the double bonds has a great effect on the  framework, and the size and sign of the energy difference (vertical resonance energy) E^V depend upon which components, abs(E_e^V-) or abs(E_e^V-), is greater.

On the contrary, the one of earliest resonance energy calculations was based on the Hückel theory (1931), and the resonance energy for benzene is -2,^11a~c indicating the resonance energy (about -120 ~ -140 kcal/mol,  = 60 ~ 70 kcal/mol^11d or 64.5 kcal/mol^11e) for benzene is stabilizing. As indicated by Jug, Hibertyand Shaik (2001)^3e, “The contemporary theories of electronic structure of that time were unable to describe benzene in a satisfactory manner. The Hückel method gave a beautifully simple solution of the dilemma”…….. “In this way, a stabilizing delocalization energy of -2 was obtained. This led to the conclusion that delocalization of electrons was a stabilizing factor which in turn is responsible for the D_6h structure of benzene. Since it was believed that in benzene there is a resonance interaction between two Kekule´ structures,  the delocalization energy was also called resonance energy”. Accordingly, the earliest conclusion that π-electron delocalization is stabilization came from the Hückel method. In the Hückel method, however, only  electrons are involved and the coulomb and resonance integrals, _i and _ij are constant in benzene and its reference molecule ethylene. As a result, the effect of the -interactions between the double bonds on the  system, denoted as (E_e), has been artificially excluded. Hence, it is certain that the value (-21.2 kcal/mol in Figure 2 of supporting information) of the energy difference E^V(G) is greatly different from that of HRE (Hückel resonance energy, -120 ~ -140 kcal/mol) although the two energy effects both arise from the -electron delocalization.

Particularly, as shown by our practical calculations (including our previous works^4c) and by literature,¹² the exchange energy effect E_mn-EX is more destabilizing than the charge transfer energy effect E_mn-CT is stabilizing , i. e. E_mn-EX > abs(E_mn-CT).  In the case of the GE-1 geometry of benzene, as a result, the energy differences of E_e^A1 and E^A1 are always destabilizing (Figures 3c~3d), leading to the following results: the length of the bond C2-C3 in the GE-1 geometry being longer than that in the GL geometry, and molecular energy for the GE-1 geometry being higher than that for the GL geometry. Emphatically, GE-n and GL are the fictitious geometries, and the GL geometry resulted from GE-1 geometry via the way to artificially exclude the destabilizing components from the GE-1 geometry. At ab initio and DFT theory levels, therefore, the size and sign of resonance energy depend upon whether the exchange interaction between double bonds is artificially excluded from the localized system (a fictitious geometry) or not.

In our program as well as in Kollmar and Jug procedures, on the contrary, all the charge transfer and exchange interactions between the double bonds are artificially excluded from the localized geometry. The -electron delocalization results from the charge transfer and exchange interactions between double bonds rather than only from the charge transfer interaction according to the following Morokuma’s words (1976):^2b “We now define the components of the interaction on the following principles which are based on traditional viewpoints and physical meanings (Fig.1): (i) Electrostatic: the classical electrostatic interaction between occupied MO’Swhich does not cause any mixing of MO’S. (ii) Polarization: the interaction which causes the mixing between the occupied and vacant MO’Swithin each molecule. (iii) Exchange: the interaction between occupied MO’Swhich causes electron exchange and delocalization between molecules. (iv) Charge Transfer: the interaction which causes intermolecular delocalization by mixing the occupied MO’Sof one molecule with the vacant MO’Sof the other and vice versa.”

         

We wonder once more whether the commenter knows the great controversy^13g,14,3e, taken place from 1980’s to 1990’s, on -distortive propensity. The controversy was arisen by Shaik and Hiberty in 1980’s.   Shaik and his collaborators said:^14d “the -electrons of allyl radical (1) and benzene (2) prefer to distort to their localized -components, much like the -electrons of singlet cyclobutadiene (3). These distortive propensities in 1 and 2 are, however, quenched by the -frames that strongly prefer regular geometries with uniform C-C bond lengths. Consequently, -electronic delocalization in 1 and 2 turns out to be a byproduct of a geometric constraint and occurs despite the opposite inherent tendency of the -electrons. This result touches a key question of chemical epistemology: is electronic delocalization a driving force of stability and geometric shape?”Epiotis criticized the concept of resonance stabilization vividly to support Shaik’s viewpoint.^15a  Recently, as shown by a quantum chemical analysis of -substituent effects on alkyl and vinyl cations, delocalization does not always stabilize.^15b

  

Figure 8-jpca. bond lengths ( green color) in the PG geometries. The PG geometries of the molecules were obtained from the restricted geometry optimization at B3LYP/6-31G*,  In each PG geometry, the  systems of the four rings I, II, III and IV have been artificially isolated each other. The data (yellow color) in the parentheses are the bond lengths in the ground state geometries)

 In our title paper, the shaik’s conclusion was supported. In strained aromatic compounds C₆X₃ (tris-benzocyclobutenobenzene, X = -C₆H₄-), C₆X₃ (triscyclobutenobenzene-like species,X = -CH=CH-, -BH=BH-, -NH=NH-) and C₆X₃(tris-cyclopropenobenzene-like species, X = -BH- and -NH-), as shown by the geometrical data obtained from the restricted geometry optimizations (Figure 8-jpca in this paper), it is the  interactions between the central phenyl ring and annelating groups X, rather than SIBL (strained-induced bond localization), which distort the central phenyl ring away from equal bond lengths. Besides, as shown by the geometrical data presented in the GE-7 and G geometries of substituted benzenes (Figure 7 in our title paper), it is resonance interaction between substituent group and  phenyl ring to distort phenyl ring.

In a way similar to the commenter’s way, at last, we conclude our response also with the Schleyer’s comments (2001)^1b on Shaik’s works: “The related review by S. Shaik, A. Shurki, D. Danovich, and P. C. Hiberty emphasizes the duality of the -component of benzene.…..The basis for the conclusion that the D_6h structure of benzene is due to the  framework, now widely accepted, is applied instructively to interpret a number of related aromatic, antiaromatic, and strained systems.”

Supporting Information Available: The following information were detailed:(i)- Energy Partition; (ii) The Physical Meaning of Destabilizing Energy Differences; (iii)The Difference, in the Way to Change Nuclear Repulsion, between Benzene and Hexatriene is compared in order to search for the potentialcorrelation between energetic and geometrical criteria.

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Supporting Information 

 Our Title Paper

Response Manuscript