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Response to “Comment on "Restricted Geometry Optimization: A Different Way to Es
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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, People’s Republic of China.
Tel: 86-10-62564822 Fax: 86-10-62559373 Email: yuzh@iccas.ac.cn
Abstract: It 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.
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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.
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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 [E(GL) – E(G)] and [E(GE-1) –E(G)]
6. About Controversy on Resonance Stabilization.
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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 [E(GL) – E(G)] and [E(GE-1) –E(G)]
6. About Controversy on Resonance Stabilization.
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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. “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 don’t think it cannot be done forever, which is why so many efforts have been made to develop experimental and theoretical methods in literature1a. The commenter denoted that his conclusion was from Schleyer’s paper (ref. 1b in this response). It is misleading according to the following Schleyer’s words1b: “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 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 Jug3b 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 
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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.
- 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.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 places7a 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 distance7e and bond length7f (the unit in Å) were given in four decimal places and the energies (unit in hartree7g and kcal/mol7h) 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 ao = 0.52918 Å, and gas constant7j R = 8.314472 J·K-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 commenter’s 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 don’t think that such expressions are standard.
Besides, the use of the words “silly” and “scientific illiteracy“ in the paper6 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 commenter’s 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 too3. Consequently, they constructed the third fictitious structure FG5. 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 π-electron delocalization obviously "destabilizes" the π-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 Kistiakowsky’s 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 π 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.
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Scheme 1. Kistiakowsky’s procedure for experimentally determining aromatic stabilization energy of benzene.
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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 chemistry10 and related literature such as refs.1a and 7a, Kistiakowsky’s procedure was schemed and described (Scheme 1).
Kistiakowsky’s 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 the Figures 1 and 3 in our title paper, and these two Figures were 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 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).
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 ET(GL) in the title paper, and it is writen as E(GL) in this response manuscript )
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 ET(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 
EA1= [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 EAn ( n = 1, 2, 3, and EA1 = EA2 = DEA3 ) 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*EA1(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.
[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 EA1= [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 EAn ( n = 1, 2, 3, and EA1 = EA2 = DEA3 ) 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*EA1(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.
5. About the Signs of the Energy Differences [E(GL) – E(G)] and [E(GE-1) –E(G)]
The commenter wrote: “these calculations is that the bond length between two "localized" bonds in GL (1.447 Å) is shorter than that in the corresponding conjugated bond C2-C3 both in GE-1 (1.456 Å) and G (1.450 Å). 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 π-electron conjugation destabilizes π-system, is unacceptable”. ( in the lines from 31 to 43 of page 2)
Firstly, we would refute the commenter’s argument using the following Kollmar’s words (1979):3a “The π energy of the reference state is obtained from a Hückel calculation using a model Hückel 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: [E(GL) – E(G)] and [E(GE-1) – E(G)] ( 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 [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 EA1 = [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):
EA1 = [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 Ee and EN are total electron and nuclear repulsion energy differences, respectively.
Ee and EN are total electron and nuclear repulsion energy differences, respectively.
where EH and Etwo are one and two electron energy differences, respectively.
EH and Etwo are one and two electron energy differences, respectively.
where Ee and E
e are the and components of total electron energy difference,3k respectively
Ee and Ee are the and components of total electron energy difference,3k respectively
where EN and EN are the and components of nuclear repulsion difference,3k respectively 
EN and EN are the and components of nuclear repulsion difference,3k respectively where E and Eare the and components of molecular energy difference, respectively.
E and Eare the and components of molecular energy difference, respectively.the following partitions are available only at ab intino theory level:
where Ee-n and Ee-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.
Ee-n and Ee-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 Emn-CT and Emn-EX are the charge transfer and exchange energy differences, respectively.
Emn-CT and Emn-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 EA1 = [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) EV depend upon which components, abs(EeV-) or abs(EeV-), is greater.
EA1 = [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) EV depend upon which components, abs(EeV-) or abs(EeV-), 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/mol11d or 64.5 kcal/mol11e) 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 D6h 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 (Ee), 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 EV(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.
,11a~c indicating the resonance energy (about -120 ~ -140 kcal/mol, = 60 ~ 70 kcal/mol11d or 64.5 kcal/mol11e) 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 D6h 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 (Ee), 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 EV(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 works4c) and by literature,12 the exchange energy effect Emn-EX is more destabilizing than the charge transfer energy effect Emn-CT is stabilizing , i. e. Emn-EX > abs(Emn-CT). In the case of the GE-1 geometry of benzene, as a result, the energy differences of EeA1 and EA1 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.
Emn-EX is more destabilizing than the charge transfer energy effect Emn-CT is stabilizing , i. e. Emn-EX > abs(Emn-CT). In the case of the GE-1 geometry of benzene, as a result, the energy differences of EeA1 and EA1 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 200613e, is greater than that (74.3 kcal/mol13f, 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/mol3a) 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 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.”
-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.”
(here, Figure 1 is referred to as the original Figure 1 of Morokuma’s paper (ref. 2b))
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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 can’t 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 Yu3analyses 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 controversy13g,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
-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(The follwong Figure, denoted as Figure 8-jpca, is the Figure 8 in our title paper, and this Figure was 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)
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.
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. 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 geometry is longer than that of the corresponding bond in the GL geometry no matter whether molecule is aromatic (benzene) or not (hexatriene) also support Shaik’s viewpoint.
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 D6h 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.”
-component of benzene.…..The basis for the conclusion that the D6h 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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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.
- 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. References
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