Application of Hammett Equation to Dissociation Equilibriums of 1,3-Cyclohexadiene-1-Carboxylic Acids (Dihydro Benzoic Acid-The Benzane System)

Application of Hammett Equation to Dissociation Equilibriums of 1,3-Cyclohexadiene-1-Carboxylic Acids (Dihydro Benzoic Acid-The Benzane System) | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Application of Hammett Equation to Dissociation Equilibriums of 1,3-Cyclohexadiene-1-Carboxylic Acids (Dihydro Benzoic Acid-The Benzane System) Sanjeev Rachuru, Jagannadham Vandanapu, Adam A. Skelton This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5243403/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract The DFT computed p K a s of dissociation equilibriums of 1,3-cyclohexadiene-1-carboxylic acids (dihydro benzoic acid) were successfully found to obey Hammett equation. This is a new observation in Chemistry Literature applied to the benzane system - a six membered cyclic diene. Like in benzoic acids the correlation and the trend is the same but with higher Hammett r of 1.86 when compared to 1.00 of benzoic acid dissociation equilibriums. Suitable explanations are given. Hammett Equation Dissociation Equilibriums Dihydro Benzoic Acid The Benzane Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction Hammett equation is a very useful tool in Physical-Organic Chemistry [ 1 ]. It has been applied to benzene systems [ 1 ], and five membered heterocycles [ 2 ]. Now it is the turn that we have tried to apply the Hammett equation to dissociation equilibriums of 1,3-cyclohexadiene-1-carboxylic acids having the same carbon framework as benzoic acids and with two additional hydrogens. 1,3-Cyclohexadiene-1-carboxylic acids are also known as 2,3-dihydrobenzoic acids [ 3 ]. The importance and the necessity of the present work is whether the application of Hammett equation to such systems as 1,3-Cyclohexadiene-1-carboxylic acids is successful, if so we will be the first to see such observation and it will be a new addition to Physical-Organic Chemistry. 2. Methods Linear correlation is done using the KaleidaGraph software, Reading, PA, USA. The chemical structures are drawn using ChemDraw software. Guissian 09 [ 4 ] software was used to carry out quantum mechanical calculations. The p K a values of deprotonation equilibriums of 1,3-cyclohexadiene-1-carboxylic acids were determined using SMD sSAS (scaled solvent-accessible surface) model and the geometries were optimized at the M06-2X/6–31++(d,p) level [ 4 ] like that done by Lian et. al [ 5 ]. Please refer to reference [ 5 ] for all the calculations. In references [ 6 , 7 ] p K a was determined using DFT calculations i) B3LYP functional with 6- 311+(d,p) basis set ii) wB97XD functional 6-311+(d,p) basis set, iii) SMD continuum model at M06-2X/6–31+(d,p) level, and iv) SMDsSAS continuum model at m06-2X/6–31+(d, p) level. The relation used was p K a = ΔG/1.364. The free energies were determined implicitly in water; by doing this one could circumvent the thermodynamic cycle method and as a consequence the need for gas phase calculations. Of the four preceding methods i, ii, iii and iv the best method turned out to be SMD sSAS continuum model at M06-2X/6–31+(d, p) level. Hence, we have adopted this method to determine the p K a s of all the compounds in question (Table 1 and Table 2). One of the important factors in the SMD sSAS continuum model is the choice of α value. None of the p K a s of 1,3-Cyclohexadiene-1-carboxylic acid and its substituted compounds (Table 1 , 4th column) are available in the literature; hence choosing the accurate α values become very difficult. Benzoic acid has p K a value of 4.20 [ 8 ]. We found the p K a of benzoic acid with the help of SMD sSAS continuum model at M06-2X/6–31+(d, p) level and the p K a turned out to be 4.24 (experimental determined value is 4.20); the crucial α value used for this determination of p K a was 0.480. It can be seen from Scheme 1 that benzoic acid and 1,3-Cyclohexadiene-1-carboxylic acid have similar deprotonation sites. Hence, we have taken benzoic acid as reference compound and determined the p K a s of 1,3-Cyclohexadiene-1-carboxylic acid and its substituted compounds. As stated in article [ 7 ] the strategy is similar to the use of a reference molecule with an experimentally known p K a [ 9 , 10 , 11 , 12 , 13 ]. Hence, we have taken the same α value of 0.480 which we had used to determine the benzoic acid to determine the p K a of 1,3-Cyclohexadiene-1-carboxylic acid. In fact, Ping Lein et al [ 5 ] had taken an α value 0.485 for the atoms H, C, N, O, F, S and Cl. Since we have the same atoms in benzoic acid and 1,3-Cyclohexadiene-1-carboxylic acid, substituted compounds of Cyclohexadiene-1-carboxylic acid (except Br substituent) and 2-X-1,3-Cyclohexadiene (Scheme 4) the α value of 0.480 appears to be reasonable. Thus, the p K a s determined for the compounds in question might (Table 1 & Table 2) not be accurate but reasonably correct. Since experimentally determined p K a s for the compounds in question are not available, one cannot estimate the percentage of errors in the determination of these p K a s. The p K a values of benzoic acids are from reference [ 8 ]. Using the option pop = nbo (natural bond orbital) Second Order Perturbation Analysis was carried out. 3. Results and Discussion 1,3-Cyclohexadiene-1-carboxylic acid is also commonly known as 2,3-dihydrobenzoic acid (scheme 1). The only difference between 1,3-cyclohexadiene-1-carboxylic acid (A) and benzoic acid (B) is two hydrogens. The first one is non-planar with four sp 2 carbons and two sp 3 carbons, and the latter is planar with six sp 2 carbons. The four sp 2 carbons of 1,3-cyclohexadiene-1-carboxylic acid (A) are not in one plane and the two sp3 carbons are tetrahedral and out of plane. DFT optimized structure is given in Figure 1. The dihedral angle of carbon atoms 9, 7 and 4, 2 is 31.91 o reflecting that the carbon atoms 9, 7 (sp 2 carbons) & carbon atoms 4, 2 (sp 3 carbons) are not in the same plane. Similarly, the dihedral angle of carbon atoms 5, 3 and 2, 4 is 31.71 o reflecting that the carbon atoms 5, 3 (sp 2 carbons) & carbon atoms 2, 4 (sp 3 carbons) are not in the same plane. The dihedral angle between carbon atoms 7, 9 and 5, 3 (all sp 2 carbons) is 15.33 pointing towards 7, 9 and 5, 3 are not occupying the same plane. Yet their continuous conjugation is intact. Benzoic acid is planar and having continuous conjugation [14] and obeying Hammett equation [1], and 1,3-cyclohexadiene-1-carboxylic acid (A) with its four sp 2 carbons though not in one plane but with continuous conjugation is also assumed to obey Hammett equation (figure 1A). In benzoic acid all six planar sp 2 carbons will facilitate the smooth transmittance of substituent effect on to the carboxyl group from the ring using its less dense delocalized p-electron cloud over 6 sp 2 carbons in the benzene ring compared to that of denser delocalized p-electron cloud of 4 sp 2 carbons of 1,3-cyclohexadiene-1-carboxylic acid leading to higher Hammett r (1.86, figure 1B) for 1,3-cyclohexadiene-1-carboxylic acid dissociation than that of benzoic acids (1.00). The resonance structures of benzoate ion with electron withdrawing and electron donating substituents are shown in Scheme 2. In the same way we thought 1,3-cyclohexadiene-1-carboxylic acid with its four sp 2 carbons, at least in part from one side will facilitate the smooth transmittance of substituent effect on to the carboxyl group from the ring using its denser p-electron cloud than in benzoic acid confined to only 4 sp 2 carbons (scheme 3). To our expectation 1,3-cyclohexadiene-1-carboxylic acids are obeying Hammett equation with a correlation coefficient of 0.9268 and a higher Hammett r of 2.46 (Table 1, figure 1A) compared to 1.00 of benzoic acid dissociation equilibriums (Table 1, Figure 2). From table 1 one can see that the benzoic acids are stronger acids than the 1,3-cyclohexadiene-1-carboxylic acids as reflected from their p K a s. Therefore, the conjugate bases of benzoic acids, that is the benzoate ions are more stable than the corresponding conjugate bases of 1,3-cyclohexadiene-1-carboxylic acids that is 1,3-cyclohexadiene-1-carboxylate ions. From the Hammett r values obtained for both the dissociation equilibriums of 1,3-cyclohexadiene-1-carboxylic acids (2.46) and benzoic acids (1.00) reflects that the transition state of dissociation equilibrium leading to less stable conjugate base is effected by substituents and leading to more stable conjugate base is less effected. p K a values some of the of benzoic acids obtained by experiments and by DFT are well close to each other (table 1) indicating that the DFT calculated p K a s of 1,3-cyclohexadiene-1-carboxylic acids in the present work are reasonably correct. We could not get the DFT calculated p K a values of all the benzoic acids used by the literature. Though Hammett correlation is known for benzoic acids, it is presented here for comparison purpose (figure 2). Both experimental (in blue) and DFT (in red) calculated p K a s gave similar correlation with same Hammett r (figure 2). The Hammett correlation (figure 1A) with R = 0.9268 is a little poor. We thought it worthwhile to replot the data using Hammett s + values for electron donating groups 4-NH 2 , 4-CH 3 O, 4-CH 3 and 4-Cl. As the electron withdrawing substituents like 4-NO 2 and 4-CN did not deviate from the correlation, the Hammett s - values were not used for them in the replotting. In fact, the correlation improved very much with R = 0.9765 (figure 1B) from 0.9268 (figure 1A) with a Hammett r = 1.86. Why the Hammett r of the dissociation equilibriums of 1,3-cyclohexadiene-1-carboxylic acids is almost twice (1.86, figure 1B) that of benzoic acids (1.00, figure 2)? Looking at scheme 1, it is clear that 1,3-cyclohexadiene-1-carboxylic acid system is having two sp 2 carbons (carbons 2 and 3), baring carbons 1 and 4 which are common in both 1,3-cyclohexadiene-1-carboxylic acid and benzoic acid, benzoic acid is having four sp 2 carbons (carbons 2, 3 and 5, 6). If one unit of charge either positive or negative has to be transmitted from the substituent to the ionization site or vice versa, the same will be carried by four sp 2 carbons in benzoic acid with less dense p-electron delocalization cloud spread over four sp 2 carbons compared to that of two sp2 carbons in 1,3-cyclohexadiene-1-carboxylic acid. Therefore, it could be understood that this effect is reflected in Hammett r values. With almost twice the p-electron delocalization cloud density in 1,3-cyclohexadiene-1-carboxylic acid dissociation equilibriums will have Hammett r (1.86) twice that of Hammett r (1.00) of benzoic acid dissociation equilibriums. In the prototropic tautomeric isomerization of four 1,3-cyclohexadienes apparently the carbons 3, 4 and 5 are involved as reaction sites (scheme 4). First it was difficult to decide what type of substituent effect correlation to be adopted. Therefore, it was thought worthwhile to apply Hammett equation using meta and para substituent constants separately and also Taft correlation. Though not with experimentally determined data [15], the thermodynamic free energy change of prototropic tautomeric isomerization of four 1,3-cyclohexadienes (scheme 4) and four DFT calculated 1,3-cyclohexadienes (table 2) are plotted against Hammett s m (Table 2, figure 3A) taking carbon 4 as prime reaction site and as it is away by one sp 2 carbon 3 from the substituent X. The correlation is poor (R = 0.8642). Then it was thought to replot the data using carbon 5 as reaction site and substituents at 2 position of 1,3-cyclohexadienes are taken as para substituents because both are separated by two sp 2 carbons at position 3 and 4. And also the prototropic migration is taking place from carbon 5. Similar species like A # (scheme 4) is proposed as intermediate in the iodine catalyzed intramolecular 5,3-prototropic tautomeric isomerization of some cyclohexenes [16, 17]. A good Hammett plot is obtained with much improved correlation coefficient of 0.9628 (figure 3B). Therefore, the involvement of carbon 5 as reaction site is predominant with a proton shifting from it to carbon 3. The possibility of any involvement of carbon 3 alone as reaction site is eliminated by non-correlation of the data with Taft s * values (figure 3C). When four experimentally determined [15] and four DFT calculated (present work) thermodynamic free energy change of prototropic intramolecular tautomeric isomerization of 2-X-1,3-cyclohexadienes to 2-X-1,4-cyclohexadienes together follow Hammett correlation (figure 3B), there is no surprise that a similar system with same carbon framework, DFT calculated p K a s of 1,3-cyclohexadiene-1-carboxylic acids followed Hammett equation (figure 1A and 1B). This is yet another promising evidence that DFT calculated p K a s of 1,3-cyclohexadiene-1-carboxylic acids for following the Hammett correlation. It is a well-known fact that Second Order Perturbation Analysis provides the stabilization energy associated with donor acceptance process. It reflects how effectively electron transfer takes place. In the present subject p K a values 1,3-Cyclohexadiene-1-carboxylic acid is conforming to Hammett’s relation similar to substituted benzoic acids. Thus, reflecting effective transmittance of substituent effect in both substituted 1,3-Cyclohexadiene-1-carboxylic acids and substituted Benzoic acids. From Table 3, it can be clearly observed that the Second Order Perturbation Analysis data of both the series reflect effective transmittance of substituent effect. Further, the Bond length alternations (BLA) were recorded using py.Aroma 4 (ver. 4.1.0, Z. Wang , see https://wongzit.github.io/program/pyaroma) 18,19 . BLA is defined 18 by the equation BLA = R even – R odd which is the difference between average lengths of even bonds and odd bonds. A smaller value of BLA reflects better electron conjugation along the selected path. It can be clearly observed from Table 3 that BLA’s of both substituted 1,3-Cyclohexadiene-1-carboxylic acids and substituted benzoic acids are small and hence an effective conjugation. Thus, the Second Order Perturbation Analysis and BLA’s bolster the effective transmittance of substituent effect and conjugation respectively, which in turn is theoretical evidence for reason behind conformity to Hammett’s relation. Conclusion 1,3-Cyclohexadiene-1-carboxylic acid is commonly known as 2,3-dihydrobenzoic acid. 1,3-Cyclohexadiene-1-carboxylic acid is its IUPAC name. The only difference between 1,3-cyclohexadiene-1-carboxylic acid and benzoic acid is two hydrogens. Still the acid dissociation equilibriums of 1,3-Cyclohexadiene-1-carboxylic acids successfully obeys the Hammett equation with the same trends as benzoic acids. Theoretical rational (Second Order Perturbation and Bond Length Alternation) is provided for the conformity to Hammett’s relation. Declarations Conflict of interest: The authors don’t have any conflict of “interest”. Acknowledgment: The authors are grateful to the Centre for High Performance Computing (CHPC), Cape Town, South Africa, for their generous allocation of supercomputer time. References (a) Hammett Louis P 1937 The Effect of Structure upon the Reactions of Organic Compounds. Benzene Derivatives J. Am. Chem. Soc . 59 96 (b) Hammett Louis P 1935 Some Relations Between Reaction Rates and Equilibrium Constants J. Am. Chem. 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J Am Chem Soc 2021; 143(19): 7426–7439. doi:10.1021/jacs.1c01329 Wang Z. py.Aroma : an intuitive graphical user interface for diverse aromaticity analyses. ChemRxiv 2024. [Preprint, uploaded 21 June 2024] doi:10.26434/chemrxiv-2024-mjmj8 Schemes Schemes 1 to 4 are available in the Supplementary Files section. Tables Tables 1 to 3 are available in the Supplementary Files section. Supplementary Files Scheme1.jpg Scheme 1 Scheme2.jpg Scheme 2 Scheme3.jpg Scheme 3 Scheme4.jpg Scheme 4 Tables.docx Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 29 Mar, 2025 Reviewers invited by journal 27 Mar, 2025 Editor assigned by journal 20 Mar, 2025 First submitted to journal 19 Mar, 2025 Editorial decision: Major revisions 20 Jan, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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06:14:52","extension":"jpg","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":43257,"visible":true,"origin":"","legend":"\u003cp\u003eScheme 2\u003c/p\u003e","description":"","filename":"Scheme2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5243403/v1/32b3843d34dc7909b4e7d590.jpg"},{"id":79548558,"identity":"841cf4b6-ed8b-4921-86bc-ce693ccc8118","added_by":"auto","created_at":"2025-03-31 06:21:39","extension":"jpg","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":43093,"visible":true,"origin":"","legend":"\u003cp\u003eScheme 3\u003c/p\u003e","description":"","filename":"Scheme3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5243403/v1/0131c66d79a553572df3367b.jpg"},{"id":79548567,"identity":"ba6d8c94-a813-4b39-8d27-84de7b11ed55","added_by":"auto","created_at":"2025-03-31 06:21:43","extension":"jpg","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":31802,"visible":true,"origin":"","legend":"\u003cp\u003eScheme 4\u003c/p\u003e","description":"","filename":"Scheme4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5243403/v1/7df6cfb1bbd6d0800259e760.jpg"},{"id":79547751,"identity":"48b3afb3-6b51-4f98-a9c3-12507c891404","added_by":"auto","created_at":"2025-03-31 06:13:40","extension":"docx","order_by":5,"title":"","display":"","copyAsset":false,"role":"supplement","size":2901805,"visible":true,"origin":"","legend":"","description":"","filename":"Tables.docx","url":"https://assets-eu.researchsquare.com/files/rs-5243403/v1/d60be54ab89ed4336817e35d.docx"}],"financialInterests":"","formattedTitle":"Application of Hammett Equation to Dissociation Equilibriums of 1,3-Cyclohexadiene-1-Carboxylic Acids (Dihydro Benzoic Acid-The Benzane System)","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eHammett equation is a very useful tool in Physical-Organic Chemistry [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. It has been applied to benzene systems [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], and five membered heterocycles [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Now it is the turn that we have tried to apply the Hammett equation to dissociation equilibriums of 1,3-cyclohexadiene-1-carboxylic acids having the same carbon framework as benzoic acids and with two additional hydrogens. 1,3-Cyclohexadiene-1-carboxylic acids are also known as 2,3-dihydrobenzoic acids [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. The importance and the necessity of the present work is whether the application of Hammett equation to such systems as 1,3-Cyclohexadiene-1-carboxylic acids is successful, if so we will be the first to see such observation and it will be a new addition to Physical-Organic Chemistry.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cp\u003eLinear correlation is done using the KaleidaGraph software, Reading, PA, USA. The chemical structures are drawn using ChemDraw software. Guissian 09 [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] software was used to carry out quantum mechanical calculations. The p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e values of deprotonation equilibriums of 1,3-cyclohexadiene-1-carboxylic acids were determined using SMD\u003csub\u003esSAS\u003c/sub\u003e (scaled solvent-accessible surface) model and the geometries were optimized at the M06-2X/6\u0026ndash;31++(d,p) level [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] like that done by Lian et. al [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Please refer to reference [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] for all the calculations. In references [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e was determined using DFT calculations i) B3LYP functional with 6- 311+(d,p) basis set ii) wB97XD functional 6-311+(d,p) basis set, iii) SMD continuum model at M06-2X/6\u0026ndash;31+(d,p) level, and iv) SMDsSAS continuum model at m06-2X/6\u0026ndash;31+(d, p) level. The relation used was p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;ΔG/1.364. The free energies were determined implicitly in water; by doing this one could circumvent the thermodynamic cycle method and as a consequence the need for gas phase calculations. Of the four preceding methods i, ii, iii and iv the best method turned out to be SMD\u003csub\u003esSAS\u003c/sub\u003e continuum model at M06-2X/6\u0026ndash;31+(d, p) level. Hence, we have adopted this method to determine the p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003es of all the compounds in question (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Table\u0026nbsp;2). One of the important factors in the SMD\u003csub\u003esSAS\u003c/sub\u003e continuum model is the choice of α value. None of the p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003es of 1,3-Cyclohexadiene-1-carboxylic acid and its substituted compounds (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, 4th column) are available in the literature; hence choosing the accurate α values become very difficult. Benzoic acid has p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e value of 4.20 [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. We found the p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e of benzoic acid with the help of SMD\u003csub\u003esSAS\u003c/sub\u003e continuum model at M06-2X/6\u0026ndash;31+(d, p) level and the p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e turned out to be 4.24 (experimental determined value is 4.20); the crucial α value used for this determination of p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e was 0.480. It can be seen from Scheme 1 that benzoic acid and 1,3-Cyclohexadiene-1-carboxylic acid have similar deprotonation sites. Hence, we have taken benzoic acid as reference compound and determined the p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003es of 1,3-Cyclohexadiene-1-carboxylic acid and its substituted compounds. As stated in article [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] the strategy is similar to the use of a reference molecule with an experimentally known p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Hence, we have taken the same α value of 0.480 which we had used to determine the benzoic acid to determine the p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e of 1,3-Cyclohexadiene-1-carboxylic acid. In fact, Ping Lein et al [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] had taken an α value 0.485 for the atoms H, C, N, O, F, S and Cl. Since we have the same atoms in benzoic acid and 1,3-Cyclohexadiene-1-carboxylic acid, substituted compounds of Cyclohexadiene-1-carboxylic acid (except Br substituent) and 2-X-1,3-Cyclohexadiene (Scheme 4) the α value of 0.480 appears to be reasonable. Thus, the p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003es determined for the compounds in question might (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e \u0026amp; Table\u0026nbsp;2) not be accurate but reasonably correct. Since experimentally determined p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003es for the compounds in question are not available, one cannot estimate the percentage of errors in the determination of these p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003es. The p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e values of benzoic acids are from reference [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Using the option pop\u0026thinsp;=\u0026thinsp;nbo (natural bond orbital) Second Order Perturbation Analysis was carried out.\u003c/p\u003e"},{"header":"3. Results and Discussion","content":"\u003cp\u003e1,3-Cyclohexadiene-1-carboxylic acid is also commonly known as 2,3-dihydrobenzoic acid (scheme 1).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe only difference between 1,3-cyclohexadiene-1-carboxylic acid \u003cstrong\u003e(A)\u0026nbsp;\u003c/strong\u003eand benzoic acid \u003cstrong\u003e(B)\u0026nbsp;\u003c/strong\u003eis two hydrogens. The first one is non-planar with four sp\u003csup\u003e2\u003c/sup\u003e carbons and two sp\u003csup\u003e3\u003c/sup\u003e carbons, and the latter is planar with six sp\u003csup\u003e2\u003c/sup\u003e carbons. The four sp\u003csup\u003e2\u003c/sup\u003e carbons of 1,3-cyclohexadiene-1-carboxylic acid \u003cstrong\u003e(A)\u003c/strong\u003e are not in one plane and the two sp3 carbons are tetrahedral and out of plane. DFT optimized structure is given in Figure 1.\u003c/p\u003e\n\u003cp\u003eThe dihedral angle of carbon atoms 9, 7 and 4, 2 is 31.91\u003csup\u003eo\u003c/sup\u003e reflecting that the carbon atoms 9, 7 (sp\u003csup\u003e2\u003c/sup\u003e carbons) \u0026amp; carbon atoms 4, 2 \u0026nbsp;(sp\u003csup\u003e3\u003c/sup\u003e carbons) are not in the same plane. \u0026nbsp;Similarly, the dihedral angle of carbon atoms 5, 3 and 2, 4 is 31.71\u003csup\u003eo\u003c/sup\u003e reflecting that the carbon atoms 5, 3 (sp\u003csup\u003e2\u003c/sup\u003e carbons) \u0026amp; carbon atoms 2, 4 (sp\u003csup\u003e3\u003c/sup\u003e carbons) are not in the same plane. \u0026nbsp;The dihedral angle between carbon atoms 7, 9 and 5, 3 (all sp\u003csup\u003e2\u003c/sup\u003e carbons) is 15.33 pointing towards 7, 9 and 5, 3 are not occupying the same plane. Yet their continuous conjugation is intact. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBenzoic acid is planar and having continuous conjugation [14] and obeying Hammett equation [1], and 1,3-cyclohexadiene-1-carboxylic acid \u003cstrong\u003e(A)\u0026nbsp;\u003c/strong\u003ewith its\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003efour sp\u003csup\u003e2\u003c/sup\u003e carbons though not in one plane but with continuous conjugation is \u003cem\u003ealso\u003c/em\u003e assumed to obey Hammett equation (figure 1A). In benzoic acid all six planar sp\u003csup\u003e2\u003c/sup\u003e carbons will facilitate the smooth transmittance of substituent effect on to the carboxyl group from the ring using its less dense delocalized p-electron cloud over 6 sp\u003csup\u003e2\u003c/sup\u003e carbons in the benzene ring compared to that of denser delocalized p-electron cloud of 4 sp\u003csup\u003e2\u003c/sup\u003e carbons of 1,3-cyclohexadiene-1-carboxylic acid leading to higher Hammett r (1.86, figure 1B) for 1,3-cyclohexadiene-1-carboxylic acid dissociation than that of benzoic acids (1.00). The resonance structures of benzoate ion with electron withdrawing and electron donating substituents are shown in Scheme 2.\u003c/p\u003e\n\u003cp\u003eIn the same way we thought 1,3-cyclohexadiene-1-carboxylic acid with its four sp\u003csup\u003e2\u003c/sup\u003e carbons, at least in part from one side will facilitate the smooth transmittance of substituent effect on to the carboxyl group from the ring using its denser p-electron cloud than in benzoic acid confined to only 4 sp\u003csup\u003e2\u003c/sup\u003e carbons (scheme 3).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo our expectation 1,3-cyclohexadiene-1-carboxylic acids are obeying Hammett equation with a correlation coefficient of 0.9268 and a higher Hammett\u0026nbsp;r\u0026nbsp;of 2.46 (Table 1, figure 1A) compared to 1.00 of benzoic acid dissociation equilibriums (Table 1, Figure 2). From table 1 one can see that the benzoic acids are stronger acids than the 1,3-cyclohexadiene-1-carboxylic acids as reflected from their p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003es. Therefore, the conjugate bases of benzoic acids, that is the benzoate ions are more stable than the corresponding conjugate bases of 1,3-cyclohexadiene-1-carboxylic acids that is 1,3-cyclohexadiene-1-carboxylate ions. From the Hammett r values obtained for both the dissociation equilibriums of 1,3-cyclohexadiene-1-carboxylic acids (2.46) and benzoic acids (1.00) reflects that the transition state of dissociation equilibrium leading to less stable conjugate base is effected by substituents and leading to more stable conjugate base is less effected.\u003c/p\u003e\n\u003cp\u003ep\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e values some of the of benzoic acids obtained by experiments and by DFT are well close to each other (table 1) indicating that the DFT calculated p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003es of 1,3-cyclohexadiene-1-carboxylic acids in the present work are reasonably correct. We could not get the DFT calculated p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e values of all the benzoic acids used by the literature. Though Hammett correlation is known for benzoic acids, it is presented here for comparison purpose (figure 2). Both experimental (in blue) and DFT (in red) calculated p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003es gave similar correlation with same Hammett\u0026nbsp;r\u0026nbsp;(figure 2).\u003c/p\u003e\n\u003cp\u003eThe Hammett correlation (figure 1A) with R = 0.9268 is a little poor. We thought it worthwhile to replot the data using Hammett\u0026nbsp;s\u003csup\u003e+\u003c/sup\u003e values for electron donating groups 4-NH\u003csub\u003e2\u003c/sub\u003e, 4-CH\u003csub\u003e3\u003c/sub\u003eO, 4-CH\u003csub\u003e3\u003c/sub\u003e and 4-Cl. As the electron withdrawing substituents like 4-NO\u003csub\u003e2\u003c/sub\u003e and 4-CN did not deviate from the correlation, the Hammett s\u003csup\u003e-\u003c/sup\u003e values were not used for them in the replotting. In fact, the correlation improved very much with R = 0.9765 (figure 1B) from 0.9268 (figure 1A) with a Hammett r = 1.86.\u003c/p\u003e\n\u003cp\u003eWhy the Hammett\u0026nbsp;r\u0026nbsp;of the dissociation equilibriums of 1,3-cyclohexadiene-1-carboxylic acids is almost twice (1.86, figure 1B) that of benzoic acids (1.00, figure 2)? Looking at scheme 1, it is clear that 1,3-cyclohexadiene-1-carboxylic acid system is having two sp\u003csup\u003e2\u003c/sup\u003e carbons (carbons 2 and 3), baring carbons 1 and 4 which are common in both 1,3-cyclohexadiene-1-carboxylic acid and benzoic acid, benzoic acid is having four sp\u003csup\u003e2\u003c/sup\u003e carbons (carbons 2, 3 and 5, 6). If one unit of charge either positive or negative has to be transmitted from the substituent to the ionization site or vice versa, the same will be carried by four sp\u003csup\u003e2\u003c/sup\u003e carbons in benzoic acid with less dense\u0026nbsp;p-electron delocalization cloud spread over four sp\u003csup\u003e2\u003c/sup\u003e carbons compared to that of two sp2 carbons in 1,3-cyclohexadiene-1-carboxylic acid. Therefore, it could be understood that this effect is reflected in Hammett\u0026nbsp;r\u0026nbsp;values. With almost twice the\u0026nbsp;p-electron delocalization cloud density in 1,3-cyclohexadiene-1-carboxylic acid dissociation equilibriums will have Hammett\u0026nbsp;r\u0026nbsp;(1.86) twice that of Hammett\u0026nbsp;r\u0026nbsp;(1.00) of benzoic acid dissociation equilibriums.\u003c/p\u003e\n\u003cp\u003eIn the prototropic tautomeric isomerization of four 1,3-cyclohexadienes apparently the carbons 3, 4 and 5 are involved as reaction sites (scheme 4). First it was difficult to decide what type of substituent effect correlation to be adopted. Therefore, it was thought worthwhile to apply Hammett equation using \u003cem\u003emeta\u003c/em\u003e and \u003cem\u003epara\u003c/em\u003e substituent constants separately and also Taft correlation. Though not with experimentally determined data [15], the thermodynamic free energy change of prototropic tautomeric isomerization of four 1,3-cyclohexadienes (scheme 4) and four DFT calculated 1,3-cyclohexadienes (table 2) are plotted against Hammett\u0026nbsp;s\u003csub\u003em\u003c/sub\u003e (Table 2, figure 3A) taking carbon 4 as prime reaction site and as it is away by one sp\u003csup\u003e2\u003c/sup\u003e carbon 3 from the substituent X. \u0026nbsp;The correlation is poor (R = 0.8642). Then it was thought to replot the data using carbon 5 as reaction site and substituents at 2 position of 1,3-cyclohexadienes are taken as \u003cem\u003epara\u003c/em\u003e substituents because both are separated by two sp\u003csup\u003e2\u003c/sup\u003e carbons at position 3 and 4. And also the prototropic migration is taking place from carbon 5. Similar species like\u0026nbsp;\u003cstrong\u003eA\u003csup\u003e#\u003c/sup\u003e\u003c/strong\u003e (scheme 4) is proposed as intermediate in the iodine catalyzed intramolecular 5,3-prototropic tautomeric isomerization of some cyclohexenes [16, 17]. A good Hammett plot is obtained with much improved correlation coefficient of 0.9628 (figure 3B). Therefore, the involvement of carbon 5 as reaction site is predominant with a proton shifting from it to carbon 3. The possibility of any involvement of carbon 3 alone as reaction site is eliminated by non-correlation of the data with Taft\u0026nbsp;s\u003csup\u003e*\u003c/sup\u003e values (figure 3C).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWhen four experimentally determined [15] and four DFT calculated (present work) thermodynamic free energy change of prototropic intramolecular tautomeric isomerization of 2-X-1,3-cyclohexadienes to 2-X-1,4-cyclohexadienes together follow Hammett correlation (figure 3B), there is no surprise that a similar system with same carbon framework, DFT calculated p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003es of 1,3-cyclohexadiene-1-carboxylic acids followed Hammett equation (figure 1A and 1B). This is yet another promising evidence that DFT calculated p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003es of 1,3-cyclohexadiene-1-carboxylic acids for following the Hammett correlation.\u003c/p\u003e\n\u003cp\u003eIt is a well-known fact that Second Order Perturbation Analysis provides the stabilization energy associated with donor acceptance process. It reflects how effectively electron transfer takes place. \u0026nbsp; In the present subject p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e values 1,3-Cyclohexadiene-1-carboxylic acid is conforming to Hammett\u0026rsquo;s relation similar to substituted benzoic acids. Thus, reflecting effective transmittance of substituent effect in both substituted 1,3-Cyclohexadiene-1-carboxylic acids and substituted Benzoic acids. From Table 3, it can be clearly observed that the Second Order Perturbation Analysis data of both the series reflect effective transmittance of substituent effect.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFurther, the Bond length alternations (BLA) were recorded using py.Aroma 4 (ver. 4.1.0, Z. Wang , see https://wongzit.github.io/program/pyaroma)\u003csup\u003e18,19\u003c/sup\u003e. BLA is defined\u003csup\u003e18\u003c/sup\u003e by the equation BLA = R\u003csub\u003eeven\u003c/sub\u003e \u0026ndash; R\u003csub\u003eodd\u0026nbsp;\u003c/sub\u003ewhich is the difference between average lengths of even bonds and odd bonds. A smaller value of BLA reflects better electron conjugation along the selected path. It can be clearly observed from Table 3 that BLA\u0026rsquo;s of both substituted 1,3-Cyclohexadiene-1-carboxylic acids and substituted benzoic acids are small and hence an effective conjugation.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThus, the Second Order Perturbation Analysis and BLA\u0026rsquo;s bolster the effective transmittance of substituent effect and conjugation respectively, which in turn is theoretical evidence for reason behind conformity to Hammett\u0026rsquo;s relation.\u0026nbsp;\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003e1,3-Cyclohexadiene-1-carboxylic acid is commonly known as 2,3-dihydrobenzoic acid. 1,3-Cyclohexadiene-1-carboxylic acid \u0026nbsp;is its IUPAC name. The only difference between 1,3-cyclohexadiene-1-carboxylic acid\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eand benzoic acid\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eis two hydrogens. Still the acid dissociation equilibriums of 1,3-Cyclohexadiene-1-carboxylic acids successfully obeys the Hammett equation with the same trends as benzoic acids. Theoretical rational (Second Order Perturbation and Bond Length Alternation) is provided for the conformity to Hammett\u0026rsquo;s relation.\u0026nbsp;\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eConflict of interest:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors don’t have any conflict of “interest”.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgment:\u0026nbsp;\u003c/strong\u003eThe authors are grateful to the Centre for High Performance Computing\u003c/p\u003e\n\u003cp\u003e(CHPC), Cape Town, South Africa, for their generous allocation of supercomputer time.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003e(a) Hammett Louis P 1937 The Effect of Structure upon the Reactions of Organic Compounds. Benzene Derivatives \u003cem\u003eJ. 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[Preprint, uploaded 21 June 2024] doi:10.26434/chemrxiv-2024-mjmj8\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Schemes","content":"\u003cp\u003eSchemes 1 to 4 are available in the Supplementary Files section.\u003c/p\u003e"},{"header":"Tables","content":"\u003cp\u003eTables 1 to 3 are available in the Supplementary Files section.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"chemical-papers","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"chpa","sideBox":"Learn more about [Chemical Papers](http://link.springer.com/journal/11696)","snPcode":"11696","submissionUrl":"https://www.editorialmanager.com/CHPA/default.aspx","title":"Chemical Papers","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Hammett Equation, Dissociation Equilibriums, Dihydro Benzoic Acid, The Benzane","lastPublishedDoi":"10.21203/rs.3.rs-5243403/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5243403/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe DFT computed p\u003cem\u003eK\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003es of dissociation equilibriums of 1,3-cyclohexadiene-1-carboxylic acids (dihydro benzoic acid) were successfully found to obey Hammett equation. This is a new observation in Chemistry Literature applied to the \u003cem\u003e\u003cstrong\u003ebenzane\u003c/strong\u003e\u003c/em\u003e system - a six membered cyclic diene. Like in benzoic acids the correlation and the trend is the same but with higher Hammett r of 1.86 when compared to 1.00 of benzoic acid dissociation equilibriums. Suitable explanations are given.\u003c/p\u003e","manuscriptTitle":"Application of Hammett Equation to Dissociation Equilibriums of 1,3-Cyclohexadiene-1-Carboxylic Acids (Dihydro Benzoic Acid-The Benzane System)","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-31 06:13:31","doi":"10.21203/rs.3.rs-5243403/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2025-03-29T18:34:39+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-03-27T23:21:21+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-03-20T12:07:55+00:00","index":"","fulltext":""},{"type":"submitted","content":"Chemical Papers","date":"2025-03-20T00:29:21+00:00","index":"","fulltext":""},{"type":"decision","content":"Major revisions","date":"2025-01-20T17:40:09+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"chemical-papers","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"chpa","sideBox":"Learn more about [Chemical Papers](http://link.springer.com/journal/11696)","snPcode":"11696","submissionUrl":"https://www.editorialmanager.com/CHPA/default.aspx","title":"Chemical Papers","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"fc12fbdf-856a-4e24-9866-de3e49bb09fd","owner":[],"postedDate":"March 31st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-08-13T21:18:49+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-31 06:13:31","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5243403","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5243403","identity":"rs-5243403","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}