Prof. George C Schatz Editor-in-Chief The Journal of Physical Chemistry, Dr. Zhong-Heng YU Department of Chemistry Institute of Chemistry Northwestern University Chinese Academy of Sciences 2145 Sheridan Road, Evanston, Beijing 100080 IL602083113 P.R.China Oct. 1, 2008 yuzh@iccas.ac.cn Dear Editor and Prof. Schatz: According to the 30-Sep-2008 E-mail from the office of Prof. and Senior Editor Michael Duncan, we would submit the following manuscript (reply paper)， Response to Comment on Restricted Geometry Optimization: A Different Way to Estimate Stabilization Energies for Aromatic Molecules of Various Types ，to J. phys. Chem. A. Two authors are presented in this manuscript. Dr. Zhong-Heng Yu is the corresponding author. Dr. Peng Bao's contact information is the same as the corresponding author. Whether pi-electron delocalization is stabilization or not have been a subject of controversy for several decades. Therefore, we hope that the comment and our response can be published in J. Phys. Chem. A . Due to conflict of interest, I don't hope the following researchersare the reviewers: (i) P. v. R. Schleyer; (ii) xxxxxxx. (iii) xxxxxx. We would like to open the source codes of our calculation program to the researchers who are interested in our program. We have to get authorization from Prof. Granovsky first, though the revised version of PC-Gamess program is being developed in our research group. Thank you very much and Sincerely Yours Zhong-Heng YU Professor and Ph. D. of Physical Organic Chemistry
The PDF versions of the Response Manuscript , and its Supporting Informationare enclosed as the attachments. So Reader can downloadthe followingPDF files first, and then open and readthem ( It is impossible to directly open the PDF file on the net). Response Manuscript Supporting Information A readeris provided with an option todirectly read the following txt version of the Response Manuscript ====================================================== Response to Comment on Restricted Geometry Optimization: A Different Way to Estimate Stabilization Energies for Aromatic Molecules of Various Types Zhong-Heng Yu* and Peng Bao Beijing National Laboratory for Molecular Sciences (BNLMS), State Key Laboratory for Structural Chemistry of Unstable Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, Peoples Republic of China. Tel: 86-10-62564822Fax: 86-10-62559373Email : yuzh@iccas.ac.cn Abstract : I t is unprofessional to make comments out of personal feeling. The most of the comments are incorrect, and the some of those are rude. Our detail responses are presented . . ------------------------------------------ Names for Google Search: Zhong-Heng Yu and Zvonimir B. Maksic. Key Words for Google Search: Zvonimir B. Maksic's Comment, and Response to Zvonimir B; Maksic's Comment. ****** Contents 1. About the Possibility of Exactly Defining Aromaticity 2. About the Comment on Our Calculation Method 3. About the Number of Decimal Places 4. About Definition of Aromatic Resonance Energy and about Use of the FG (cyclohexatriene) Geometry in the Measurement and Calculation of Aromatic Resonance Energy for Benzene. 5. About the Signs of the Energy Differences and 6. About Controversy on Resonance Stabilization . *********** Annotations of the words, phrases and acronyms often used in this response manuscript 1. Commenter: Zvonimir B. Maksic. 2.Comment Paper by Zvonimir B. Maksic: Comment on Restricted Geometry Optimization: A Different Way to Estimate Stabilization Energies for Aromatic Molecules of Various Types (Its PDF file is enclosed as an attachment at the end of this manuscript). 3. Our title paper: Restricted Geometry Optimization: A Different Way to Estimate Stabilization Energies for Aromatic Molecules of Various Types published in J. Phys. Chem. A 2007, 111, 5304-5313. (Its PDF file is enclosed as an attachment at the end of this manuscript) 4. Figure (s): referring to as Figure (s) of the supporting information. (The support information for this response manuscript is enclosed as an attachment). 5. FG: Fictitious geometry (cyclohexatriene) of benzene. 6. Charge transfer interactions: the inter-double bond (fragment) interactions between the corresponding pair of vacant and occupied (fragment) molecular orbitals. 7. Exchange interactions: the inter-double bond (fragment) interactions between the corresponding pairs of occupied (fragment) molecular orbitals, and those between the corresponding pairs of vacant (fragment) molecular orbitals. 1. About the Possibility of Exactly Defining Aromaticity In the comment paper, the commenter wrote : Aromaticity is important concept in chemistry, which cannot be exactly defined. 1,2 . It is really difficult to exactly define aromaticity, but we dont think it cannot be done forever, which is why so many efforts have been made to develop experimental and theoretical methods in literature 1a . The commenter denoted that his conclusion was from Schleyers paper (ref. 1b in this response). It is misleading according to the following Schleyers words 1b : The failure to find correlations between aromaticity criteria may only reflect deficiencies in the procedures currently used to devise and to evaluate such indexes. I am not convinced that the search for a global aromaticity index has to be abandoned . This challenge may be met by the development of more highly refined methods to dissect aromaticity effects from other influences. I hope that some clever scientist will find a direct or indirect way to employ an easily determinable quantity, like HOMA or NICS in modified form, to deduce accurate stabilization energies due to cyclic electron delocalization in all kinds of complex systems. 2. About the Comment on Our Calculation Method. The commenter wrote: Aromaticity is important concept in chemistry, which cannot be exactly defined. This simple fact has two consequences: (1) there are many measures of aromaticity and (2) some of them are completely meaningless. The method recommended by Bao and Yu belongs to the second category . 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 Morokumas 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 Morokuma 2 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 papers 4 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 commenters papers, he seems not professional enough to be able to comment on the energy decomposition method. 3. About the Number of Decimal Places The commenter said: The first eyecatching detail is that the bond distances and total molecular energies are given in four and seven decimal places, respectively. This is unrealistic! Too many decimal places are unphysical and are generally considered silly . ( in the lines from 48 to 53 of page 1) An appeal of Hoffmann, Schleyer and Schaefer, 6 published one year after the publication of our title paper , meant itself that there were no unionized regulations for the use of decimal places in the physical quantities such as bond length and energy. In the papers published in the journals Science, J. Am. Chem. Soc. and Chem. Rev. and the Table of conversion factors et. al., it is not difficult to find that the thermal energies (energy unit in kcal/mol) of chemical bonds were given in two decimal places 7a and energies (energy unit in ev) were given in from four to six decimal places. 3i Similarly, X-ray crystallographic measurement data for bond length , except for the data for C-H bond, were given in four decimal places in the some professional papers, 7b~d,5n and the bond length is expressed as five decimal places in the software Gauss View.In the field of theoretical calculations, it is easy to find that the distance 7e and bond length 7f (the unit in ) were given in four decimal places and the energies (unit in hartree 7g and kcal/mol 7h ) were, respectively, given in 7 and 2 decimal places.In the Table of conversion factors and physical constant , 7i,j particularly, the numbers of decimal places in various units are mostly greater than those suggested by Hoffmann, Schleyer and Schaefer. Typically, for example, Bohr radius a o = 0.52918 , and gas constant 7j R = 8.314472 JK -1 .mol -1 , which are well known. In a word, there are too many such examples if the commenter can carefully read the literatures. Interestingly, the energies (unit in kcal/mol) were presented as integer in the commenters paper. 7k In the same paper of the commenter, 7l especially, the some of the energies (unit in kcal/mol) were presented as integer but others were given in one decimal place. We dont think that such expressions are standard. Besides, the use of the words silly and scientific illiteracy in the paper 6 is different from in the comments.In the latter case, it is the comment on the specific researchers.Therefore, it is very rude and unprofessional that these two words appeared in the comment, which violates the ACS (American Chemical Society) ethical obligations of reviewers . 8 In our title paper, molecular energies, as the intermediate data, were directly obtained from the output file of PC- Gamess program ( Granovsky, A. A. www http://classic.chem.msu.su/gran/gamess/index.html ) , and these were given in ten decimal places in the output data file. Emphatically, the ESEs (energy unit in kcal/mol), as the eventual energy data, were given in one decimal place, indicating the number of decimal places in the value of ESE was correctly quoted. Anyway, we have accepted the commenters suggestions in the supporting information of our response . 4. About Definition of Aromatic Resonance Energy and about Use of the FG (cyclohexatriene) Geometry in the Measurement and Calculation of Aromatic Resonance Energy for Benzene. Commenter said: 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 . Bao and Yu found it unsatisfactory too 3 . Consequently, they constructed the third fictitious structure FG 5 . It is composed of three double bond lengths C1=C2 of the structure GEb-1 separated by three conjugated bonds C2-C3 from the same artificial structure. The line of thoughts was as follows. Since the -electron delocalization obviously destabilizes the -system, the fictitious structure FG possessing three cis-1,3-butadiene substructures should be three times less stable than GLb, i.e. by 28.2 kcal mol-1. If this values is added to the difference between E(GLb) E(Gb) = 10.8 kcal mol-1, then the extra stabilization energy ESE of benzene is as large as 39 kcal mol-1. Bao and Yu found this number beautiful enough to be recommended as the aromatic stabilization of benzene. Needless to say, this is completely arbitrary. (in the lines from 4 to 54 of page 3) We really wonder whether the commenter knows the Kistiakowskys procedure and whether he understands the prerequisites to the determination of aromatic resonance energy . Aromaticity is referred to as the phenomenon that the thermodynamic stability of the system is enhanced with respect to a structurally analogous model system (reference structure) as far as the energetic criterion is concerned. 1a Therefore , aromatic resonance energy of an aromatic molecule (such as benzene) is referred to as an extra stabilization energy with respect to its reference structure (such as cyclohexatriene) having a deloczlized system , and the two prerequisites for determining aromatic resonance energy are as follows: the choosing of reference structure and the finding a physical quantity satisfying the additivity condition. . Scheme 1. Kistiakowskys procedure for experimentally determining aromatic stabilization energy of benzene . . In as early as 1936, thus, Kistiakowsky developed an experimental procedure for measuring aromatic resonance energy of benzene, 9 which is well known in the field of organic chemistry.In any standard textbook of organic chemistry 10 and related literature such as refs.1a and 7a, Kistiakowskys procedure was schemed and described (Scheme 1). Kistiakowskys procedure is based on the fact that heat (55.4 kcal/mole) of hydrogenation of cyclohexadiene is almost exactly twice the heat (28.6 kcal/mole) of hydrogenation of cyclohexene . Thus, as expected by Scheme 1, the heat of hydrogenation of the cyclohexatriene ( it was named FG geometry in our title paper ) should be 3 x 28.6 = 85.8 kcal/mol if heats of hydrogenation of three carbon-carbon double bonds were still additive in the case of cyclohexatriene . In fact, cyclohexatriene is not a real molecule, and heat of hydrogenation for benzene is 49.8 kcal/mol. Therefore, 36 kcal/mol (85.8 49.8 = 36) deviation from the additivity was found in the benzene molecule, and it was suggested as aromatic resonance energy of benzene. Certainly, this amount can be considered as the molecular energy (or enthalpy) difference between the FG and ground states of benzene, and it can also be named the extra stabilization energy (ESE) of benzene with respect to its reference structure (cyclohexatriene). (The follwong two Figures, denoted as Figure 1-jpca and Figure 3-jpca,are theFigures 1 and3 in our title paper, andthese two Figureswere not presented in the original response paper Figure 1-jpca. The G ( Ground state geometry) , GL ( Geometry having Localized double bonds), and GE-n ( the n th 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 between the corresponding GE-n and GL geometries are additive in each acyclic polyene, i. e. , and 0 ( Figure 1-jpca in this manuscript) . In the case of benzene, the molecular energy difference E A1 = 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 = D E 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 between the expected ground state (FG geometry) and GL geometry would be about 3* E A1 (28.2 kcal/mol), i.e. 3* . In fact, cyclohexatriene is not a real molecule, the energy difference between the G (ground state) and GL geometries of benzene is -10.8 kcal/mol. In this case , ( - 3 * ) = - = 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 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 Kistiakowskys 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. 5. About the Signs of the Energy Differences and The commenter wrote: these calculations is that the bond length between two localized bonds in GL (1.447 ) is shorter than that in the corresponding conjugated bond C2-C3 both in GE-1 (1.456 ) and G (1.450 ). If conjugation were operative, then the opposite should be the case. The most striking result, however, is that the ground state G is unstable relative to artificial structures GL and GE-1. The difference in energies E(GL) E(G) = -6.8 and E(G-1) E(G) = -3.9 (in kcal mol-1). This is obviously wrong and the subsequent discussion is unscientific. It is, therefore, not surprising that conjecture following these computations, namely, that -electron conjugation destabilizes -system, is unacceptable . ( in the lines from 31 to 43 of page 2) Firstly, we would refute the commenters argument using the following Kollmars words (1979): 3a The energy of the reference state is obtained from a Hckel calculation using a model Hckel operator with all those matrix elements set to zero which correspond to interactions between atomic orbitals separated by a single bond. and Energies obtained by this procedure can in principle be lower or higher than the energy of the actual system. In addition, the calculated energy is not a real physical quantity since it does not correspond to any state of any real physical system . Therefore, it is unprofessional to question the signs of the following energy differences : and ( In the comment, the symbol E (GE-1) was wrong written as E (G-1)). Then, we would like to interpret why it is reasonable that the energy difference, such as 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 = 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 E are the and components of molecular energy difference, respectively. the following partitions are available only at ab intino theory level: 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. The following partitions are available only at ab intino theory level, and related Fock and overlap integral matrices over AO ( atomic orbital) basis set should be transferred into those over FMO (fragment molecular orbitals): 4a~c 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 = , 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 H ckel 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, Hiberty and Shaik (2001) 3e , The contemporary theories of electronic structure of that time were unable to describe benzene in a satisfactory manner. The Hckel 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 -electron delocalization is stabilization came from the Hckel method. In the Hckel 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 ( H ckel 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 some calculation methods such as BLW (block-localized wavefunction) method, 13 as emphasized by Mo, Lin, Wu and Zhang, 13d the exchange interactions are not artificially excluded from the localized (reference) geometry . As a result, resonance energy, obtained from BLW method, is always stabilizing.It may be one of the reasons why 91.6 kcal/mol value ( 6-311 + G** ) of vertical resonance (VRE) for benzene, obtained from BLW method by Mo in 2006 13e , is greater than that (74.3 kcal/mol 13f , STO-6G) reported by Mo in 1994. Particularly, as emphasized by Mo, 74.3 value of VRE for benzene is quite near to the value (77 kcal/mol 3a ) by Kollmar (in addition, value of VRE for benzene, reported by Shak, 13g is 65 kcal/mol at VBSCF/6-31G level). 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 Morokumas 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 MOSwhich does not cause any mixing of MOS . (ii) Polarization: the interaction which causes the mixing between the occupied and vacant MOSwithin each molecule. (iii) Exchange: the interaction between occupied MOSwhich causes electron exchange and delocalization between molecules. (iv) Charge Transfer: the interaction which causes intermolecular delocalization by mixing the occupied MOSof one molecule with the vacant MOSof the other and vice versa. (here, Figure 1 is referred to as the original Figure 1 of Morokumas paper (ref. 2b)) . We would like to publish a paper to show the effects of the exchange interactions on the size and sign of resonance energy through comparison of our calculation results with those from BLW method if necessary. Facing the incessant developments of calculation theory and method, we cant really understand why the commenter, as a quantum chemist, stiffly keeps his feeling (so called classic viewpoint) unchanged. The commenter should read a great number of literatures before making the comments. 6 . About Controversy on Resonance Stabilization . The commenter wrote: Bao and Yu continue to discuss ESE of benzene heteroanalogues like pyridine, pyrazine, pyrimidine, 1,2,5-triazine, pyridazineand tetrazine, furan-like species, monosubstituted benzenes, benzenes fused to small rings including heteroatoms and biphenylenes. All conclusions obtained by Bao and Yu 3 analyses are unscientific and meaningless ( from line 56 of page 3 to line 7 of page 4) . We wonder once more whether the commenter knows the great controversy 13g,14,3e , taken place from 1980s to 1990s, on - distortive propensity . The controversy was arisen by Shaik and Hiberty in 1980s. 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 Shaiks viewpoint. 15a Recently, as shown by a quantum chemical analysis of -substituent effects on alkyl and vinyl cations, delocalization does not always stabilize . 15b (The follwong Figure, denoted as Figure 8-jpca,is theFigure8 in our title paper, andthis Figurewas not presented in the original response paper 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 shaiks conclusion was supported. In strained aromatic compounds C 6 X 3 (tris-benzocyclobutenobenzene, X = - C 6 H 4 - ), C 6 X 3 ( triscyclobutenobenzene-like species, X = - CH=CH - , - BH=BH - , - NH=NH - ) and C 6 X 3 (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 betweensubstituent group and phenyl ring to distort phenyl ring. Therefore, the calculaton results that the length of single bond C2-C3 between two double bonds C1=C2 and C3=C4 in the GE-1 geometryis longer than that of the corresponding bond in the GL geometry no matter whether molecule is aromatic (benzene) or not (hexatriene) also support Shaiks viewpoint . In a way similar to the commenters way , at last, we conclude our response also with the Schleyers comments (2001) 1b on Shaiks 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 . . Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grants 20472088 and 20672119). . 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