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Abstract

This study systematically investigated the influence of substituents (NH₂, CH₃, CF₃, and Cl) on the keto-enol tautomerism of 1,2-cyclodiones, focusing on reactivity and thermodynamic stability. Calculations were performed using the M06-2X/6-311G++** level of theory, with a solvation model through CPCM/M06-2X/6-311G++**. Results indicate ring-size dependent tautomerism, with three-, five-, and six-membered rings favouring the keto-enol form, while four- and seven-membered rings favour the diketo form. The NH₂ substituent uniquely stabilised the keto-enol form. Electron-donating groups generally stabilised the keto-enol form. Contrary to common expectations, a direct correlation between dipole moment and stability order was not universally observed within 1,2-cyclodione systems, with the NH₂ group demonstrating nuanced effects. Similarly, dipole moment and electrostatic potential variance did not exhibit consistent correlation under the influence of different substituents. The diketo tautomer was generally found to be more reactive than the keto-enol form, especially in non-polar solvents. Surprisingly, substituent groups decreased the reactivity of the diketo form relative to the unsubstituted compound.

Keywords

1,2 cyclodiones CPCM density functional theory electrostatic potential substituent effect

Introduction

The substituent effect is a crucial driver in the analysis of structure-reactivity relationships (SRRs). Several factors, including inductive, resonance (mesomeric), and polarisation effects (through-bond, through-space, and field effects), contribute to the impact of substituents on chemical reactivity.¹ Both the ‘through-bond’ and ‘through-space’ inductive effects exhibit a rapid decrease as the distance from the substituent increases.² The theory of substituent effects has its root in Robinson and Ingold’s foundational research. It primarily serves as a qualitative framework for elucidating and predicting experimental reactivity and stability.³ The fundamental question can be articulated as follows: ‘How do two components of a molecule exert influence upon each other?’. Investigating tautomerism in organic compounds is a central focus in theoretical studies, utilising diverse quantum-chemical approaches.⁴ Understanding the relative stability, particularly in the context of three- to seven-member 1,2-cyclodiones, and the subsequent conversions between tautomeric forms is crucial for both biologists and chemists.⁵ While extensive experimental and theoretical research has explored tautomerisation as a fundamental process in bioorganic chemistry with implications for condensation reactions,⁶ significant questions remain regarding the specific interactions between substituents and the 1,2-cyclodione ring system.

Cyclodiones, a class of organic compounds containing two ketone functional groups within a cyclic structure, have captivated chemists due to their unique reactivity and potential applications in organic synthesis.⁷ These fascinating molecules exhibit a distinct propensity for keto-enol tautomerism, a phenomenon that plays a pivotal role in their reactivity and synthetic utility. Studies have shown that the enols produced from unhindered, unconjugated ketones are present in minimal amounts at equilibrium.⁵ Gaining insight into the relative stabilities of tautomeric forms holds significance from a structural chemistry perspective.⁸ Moreover, understanding the variations in tautomerisation energies across different derivatives provides valuable insight into the impact of substituents on molecular reactivity and stability.

Substituent groups are generally characterised by electron-realising and electron-withdrawing and are classified in terms of their inductive effects as +I and −I, respectively, and +M and −M, respectively, for the case of their resonance effects.² For example, based on our study, substituent groups, NH₂ +I (inductive effect), CH₃ +I (inductive effect), CF₃ −I (inductive effect) and Cl −I (inductive effect). Our study substituent groups were selected in form strong and its corresponding weak in term of inductive effect.

Keto-enol tautomerisation (Figure 1) of 1,2-hexanedione (cyclohexane-1,2-dione) 1a, an enolizable 1,2-diketone has been studied experimentally and theoretically. The diketo tautomer 1a is reported to have a very low content, estimated at less than 1%, and is undetectable. This low population is attributed to significant lone pair repulsion in 1a, leading to unfavourable energetics, in such, the repulsion is estimated to be substantial, with a suggested value equivalent to Δlog KE ≈ 5 or greater. Results show that the keto-enol form 1b is more stable than the diketo form.⁹ Now, these questions arise: does the presence of substituent groups drive the dynamics of keto-enol tautomerism? How do these substitutions affect the electronic structure and reactivity of the 1,2-cyclodiones? To answer these questions, we calculated the thermodynamic properties of three- to seven-member 1,2-cyclodiones with their substitution derivatives, along with their chemical reactivity properties, using density functional theory (DFT) calculations. The 1,2-cyclodiones have gathered significant attention due to their diverse applications in medicinal chemistry, photochemistry,¹⁰ and various chemical reactions. Despite the extensive research on cyclic diketones, the effects of substituents on their keto-enol tautomerism still need to be explored in the literature. This study aims to address this gap by employing computational methods to investigate the interplay between these factors and the tautomeric behaviour of cyclodiones. This research holds immense potential for developing novel cyclodiones-based compounds with tailored properties for various applications in medicinal chemistry and other fields.

Figure 1.

Two-dimensional molecular structures tautomerism in cyclohexane-1,2-dione.

In this article, we investigated the influence of substituents on the 1,2-cyclodiones system, comprising rings ranging from three to seven members. Specifically, we computationally examined derivatives of 1,2-cyclopropanedione (3a and 3b), 1,2-cyclobutanedione (4a and 4b), 1,2-cyclopentanedione (5a and 5b), 1,2-cyclohexanedione (6a and 6b), and 1,2-cycloheptanedione (7a and 7b) (refer to Figure 2). Our analysis focuses on exploring their molecular reactivity and stability at the same level of theory, considering both gas and solution phases. We accounted for solvation effects using water (ε = 78), acetone (ε = 21), and cyclohexane (ε = 2) as solvents.¹¹ The substituent groups under study include NH₂, CH₃, CF₃, and Cl. These substituents were strategically selected for this study not only based on their inductive effects but also due their diverse electronic properties and relevance in the context of 1,2-cyclodiones. (1) Range of inductive effects is on the chosen substituents encompass a range of inductive effects, from the strongly electron-donating NH₂ group to the strongly electron-withdrawing CF₃ group. This allows for a systematic investigation of how the inductive effect influences keto-enol tautomerism and reactivity. (2) Resonance effects occurs to some of these substituents also exhibit significant resonance effects. For instance, the NH₂ group can donate electron density through resonance, while the Cl group can withdraw electron density through resonance. Including substituents with varying resonance capabilities allows for a more comprehensive exploration of electronic effects on tautomeric equilibria and reactivity, (3) Prevalence in related compounds to the selected substituents are commonly found in various organic compounds, including natural products and pharmaceuticals containing 1,2-diketone motifs. Therefore, understanding their influence on the tautomeric behaviour and reactivity of 1,2-cyclodiones has broader implications for the design and synthesis of novel compounds with tailored properties. (4) Mechanistic insights to the diverse electronic properties of the chosen substituents enables a deeper exploration of the mechanistic factors governing keto-enol tautomerism. For example, the unique ability of the NH₂ group to stabilise the keto-enol form, as observed in this study, prompts further investigation into potential resonance or hydrogen bonding interactions that might contribute to this stabilisation. In summary, the selection of NH₂, CH₃, CF₃, and Cl as substituents was motivated by their diverse electronic properties, prevalence in related compounds, and potential to provide mechanistic insights into the keto-enol tautomerism of 1,2-cyclodiones. This comprehensive approach allows for a more thorough and impactful investigation of substituent effects on the reactivity and stability of these intriguing molecules.

Figure 2.

The optimised geometrical structures in keto-enol tautomerisation process of substituted cyclic-1,2-diones of the three- to seven-membered rings.

Computational methods

All calculations were conducted using the Maestro Materials Science Suite.¹² For accuracy, the three-dimensional (3D) molecular geometries of the 1,2-cyclodiones system (Figure 2) were initially generated with the Maestro editor in the Schrödinger Materials Science Suite. We then searched for the lowest energy conformer for each compound using the OPLS4 force field on the MacroModel module.¹³ This step ensured the desired molecular symmetry and proximity to a minimum.¹⁴

The identified lowest energy conformers underwent further optimisation in the gas phase through DFT methods. Jaguar¹⁵ programme, as implemented in Schrödinger Materials Science Suite, was employed for DFT calculations, specifically for conducting geometry optimisations and vibrational frequency analyses. The calculations were carried out using the M06-2X/6-311G++** level of theory, focusing on the gas phase. The frontier molecular orbital properties, atomic electrostatic potential (ESP) charges, and dipole moments were also calculated at the same theoretical level.

DFT is based on the Hohenberg and Kohn¹⁶ theorem, which states that the ground-state energy of a many-electron system can be uniquely expressed as a functional of the electron density, allowing for efficient computational calculations of electronic properties. DFT is a vital method for predicting molecules’ chemical reactivity and thermodynamic properties.¹⁷ It has proven highly successful in establishing the theoretical foundations of well-known qualitative chemical concepts.

To assess the impact of the solvent environment, the geometries of the tautomers were re-optimised in three different solvents, that is, water, acetone, and cyclohexane, maintaining the same theoretical level. To assess solvent effects on the relative stability and geometry of the 1,2-cyclodiones system, we employed the self-consistent reaction field (SCRF) method. For this, we used the polarisable continuum model (PCM) with the conductor-like polarisable continuum model (C-PCM) variant. Studies have shown that the C-PCM variant is a reliable and efficient method for computing solvation energies, structures, and properties of molecules in solution.¹⁸

Results and discussion

Energy and thermodynamic parameters

The obtained energies difference, enthalpy change and Gibbs free energies difference for the two main possible 1,2-cyclodiones system (tautomer) are listed (see Table 1) calculated using M06-2X/6-311G++** and CPCM/ M06-2X/6-311G++** methods.

Table 1.

Calculated thermodynamic properties simulated with M06-2X/6-311G++** for a vacuum (gas) and different solvent (water, acetone, and cyclohexane) ΔH, $Δ G = G_{k e t o - e n o l} - G_{d i k e t o}$ in (kcal/mol), ΔE in (Hartree) at 298.15 K, 1 atm.

Ring system	Tautomers substituents (X)	ΔE	ΔG	ΔH	Ring system	Tautomers substituents (X)	ΔE	ΔG	ΔH
3	Gas				6	Gas
	–H	−0.0231	−12.0015	−12.7502		–H	−0.0077	−4.0139	−4.4748
	NH₂	−0.0423	−25.0491	−25.0544		NH₂	−0.0269	−16.0462	−17.0324
	CH₃	−0.0288	−15.7292	−17.1856		CH₃	−0.0116	−6.8112	−6.8880
	CF₃	−0.0199	−10.4828	−10.9251		CF₃	−0.0071	−3.6715	−4.0001
	Cl	−0.0248	−13.6053	−14.1138		Cl	−0.0125	−7.0303	−7.3165
	Water					Water
	–H	−0.0296	−15.9429	−16.7942		–H	−0.0021	−0.8644	−1.1730
	NH₂	−0.0499	−29.4202	−30.6028		NH₂	−0.0234	−14.8582	−14.6674
	CH₃	−0.0358	−20.1040	−21.5768		CH₃	−0.0067	−4.0970	−4.0516
	CF₃	−0.0266	−14.7522	−15.1854		CF₃	−0.0007	−0.0131	−0.2362
	Cl	−0.0320	−17.9514	−18.5698		Cl	−0.0062	−3.4980	−3.6708
	Acetone					Acetone
	–H	−0.0293	−15.7640	−16.6137		–H	−0.0024	−1.0274	−1.3421
	NH₂	−0.0496	−29.2156	−30.3937		NH₂	−0.0236	−15.0544	−14.7979
	CH₃	−0.0354	−19.9007	−21.3645		CH₃	−0.0069	−4.2344	−4.1959
	CF₃	−0.0263	−14.5635	−14.9974		CF₃	−0.0012	−0.2821	−0.5234
	Cl	−0.0316	−17.7266	−18.3392		Cl	−0.0066	−3.6886	−3.8669
	Cyclohexane					Cyclohexane
	–H	−0.0261	−13.8417	−14.6148		–H	−0.0055	−2.8024	−3.1964
	NH₂	−0.0459	−26.8908	−28.0110		NH₂	−0.0258	−15.4963	−15.9154
	CH₃	−0.0320	−17.7373	−19.2031		CH₃	−0.0095	−5.6891	−5.7127
	CF₃	−0.0230	−12.4536	−12.9048		CF₃	−0.0046	−2.2629	−2.5505
	Cl	−0.0280	−15.5261	−16.0879		Cl	−0.0099	−5.5931	−5.8403
4	Gas				7	Gas
	–H	0.0086	6.0708	6.1985		–H	0.0096	5.7241	6.7622
	NH₂	−0.0136	−8.2024	−8.5203		NH₂	−0.0151	−8.8752	−8.9453
	CH₃	0.0036	2.8631	2.3100		CH₃	−0.0034	−1.5437	−1.6181
	CF₃	0.0116	8.2785	7.4587		CF₃	0.0009	1.4197	1.0703
	Cl	0.0020	2.0327	2.0636		Cl	0.0017	1.6404	1.5200
	Water					Water
	–H	0.0096	6.4651	6.6690		–H	0.0090	5.3863	6.3730
	NH₂	−0.0178	−10.9700	−10.7109		NH₂	−0.0140	−8.9222	−8.5730
	CH₃	0.0038	2.7372	2.2776		CH₃	0.0014	0.9914	1.1230
	CF₃	0.0120	8.4385	7.5994		CF₃	0.0070	4.7638	4.5740
	Cl	0.0033	2.6285	2.7107		Cl	0.0037	2.6605	2.5310
	Acetone					Acetone
	–H	0.0095	6.4235	6.6222		–H	0.0090	5.3078	6.3152
	NH₂	−0.0176	−10.8460	−10.5891		NH₂	−0.0140	−8.8984	−8.5815
	CH₃	0.0038	2.7225	2.2618		CH₃	0.0012	0.8325	0.9548
	CF₃	0.0119	8.3548	7.5230		CF₃	0.0069	4.7988	4.5537
	Cl	0.0032	2.5804	2.6581		Cl	0.0036	2.6216	2.4836
	Cyclohexane					Cyclohexane
	–H	0.0088	6.1095	6.2597		–H	0.0093	5.4956	6.5226
	NH₂	−0.0156	−10.0066	−9.2862		NH₂	−0.0145	−8.6363	−8.6870
	CH₃	0.0035	2.7064	2.1782		CH₃	−0.0015	−0.4837	−0.5196
	CF₃	0.0116	8.2240	7.3850		CF₃	0.0035	2.8259	2.5376
	Cl	0.0023	2.1799	2.2183		Cl	0.0025	2.0287	1.9112
5	Gas
	–H	0.0007	0.6914	0.7705
	NH₂	−0.0253	−15.9159	−16.0670
	CH₃	−0.0019	−1.3514	−1.5718
	CF₃	−0.0062	−3.2649	−3.9973
	Cl	−0.0138	−8.3592	−8.1469
	Water
	–H	−0.0012	−0.4757	−0.4420
	NH₂	−0.0248	−16.0858	−15.4768
	CH₃	−0.0049	−3.2682	−3.5516
	CF₃	−0.0013	−0.9640	−0.5985
	Cl	−0.0084	−5.2192	−4.9533
	Acetone
	–H	−0.0011	−0.4191	−0.3821
	NH₂	−0.0249	−16.1443	−15.4899
	CH₃	−0.0047	−3.1691	−3.4483
	CF₃	−0.0016	−1.1087	−0.7493
	Cl	−0.0087	−5.3863	−5.1243
	Cyclohexane
	–H	−0.0001	0.1571	0.2207
	NH₂	−0.0252	−15.9541	−16.1606
	CH₃	−0.0031	−2.1794	−2.4148
	CF₃	−0.0043	−2.6636	−2.3319
	Cl	−0.0116	−7.0810	−6.8509

In the 1,2-cyclopropanedione system (3a and 3b), the enol form, 2-hydroxy-2-cyclopropen-1-one, is of considerable chemical interest. This interest stems from its role as a photochemical precursor to hydroxyacetylene, formed through the photodecarbonylation of hydroxycyclopropenone, this study confirms that the keto-enol form exhibits greater stability than the diketo form due to its enhanced aromatic character.^5,10 Calculated Gibbs free energies (Table 1) further demonstrate that substituent groups on the 1,2-cyclopropanedione system maintain the stability of the keto-enol form in both gas and solution environments. These energies (in kcal/mol) range from −12.0 to −15.9 (H), −25.0 to −29.4 (NH₂), −15.7 to −20.1 (CH₃), −10.4 to −14.7 (CF₃), and −13.6 to −17.9 (Cl) both in the gas phase and solution. The observed stability order (NH₂ > CH₃ > H > Cl > CF₃) highlights the stabilising effect of electron-donating substituents. Notably, the keto-enol form exhibits its highest stability in the water phase compared to other phases (i.e. gas, acetone, and cyclohexane phase).

The 1,2-cyclobutanedione system (4a and 4b), particularly the diketo form, 1,2-cyclobutanedione, holds particular interest in thermal decomposition studies because it adopts a locked cis configuration.¹⁹ The scientific literature confirms that the diketo form is more stable than the keto-enol form in this system. This stability difference is attributed to the increased angle strain in the keto-enol form. With three sp²-hybridised carbon atoms, the four-membered ring experiences more strain compared to the diketo form, which has only two sp²-hybridised carbons.⁵ Calculated Gibbs free energies (Table 1) show that diketo form derivatives (4a) are more stable than their keto-enol counterparts. Stability differences range from 6.07 to 6.46 kcal/mol (H), 2.70 to 2.86 kcal/mol (CH₃), 8.22 to 8.35 kcal/mol (CF₃), and 2.03 to 2.62 kcal/mol (Cl), both in gas phase and solution. Interestingly, the presence of an NH₂ substituent stabilised the keto-enol form by −10.07 to −10.97 kcal/mol in both gas and solution phases. These results indicate that electron-donating substituents increase the stability of the keto-enol form. The observed stability order (CF₃ > H > CH₃ > Cl > NH₂) highlights that electron-withdrawing substituents play a major role in substantially enhancing the preference for the diketo form (4a) over its keto-enol counterpart.

In contrast to smaller ring systems, the cyclopentane-1,2-dione system (5a and 5b), the keto-enol form derivatives (5b) demonstrate greater stability than their corresponding diketo forms. Stability differences (in kcal/mol) range from −0.48 to 0.68 (H), −15.91 to −16.14 (NH₂), −1.35 to −3.16 (CH₃), −0.96 to −3.26 (CF₃), and −5.21 to −8.14 (Cl), measured in both the gas phase and in solution. The observed stability order of the keto-enol form is as follows: NH₂ > Cl > CH₃ > CF₃ > H. Interestingly, the unsubstituted cyclopentane-1,2-dione from Table 1 suggests that the keto-enol form is favoured in polar solvents like water and acetone, while the diketo form gains prominence in non-polar solvents (cyclohexane) and the gas phase. This highlights the significant role solvent polarity plays in determining the stability of the unsubstituted five-ring system.

In the cyclohexane-1,2-dione system (6a and 6b), the keto-enol form (6b) demonstrates a thermodynamic preference over the diketo form (6a). Literature reports attribute this to unfavourable lone pair repulsion in the diketo form, leading to higher energy.⁹ This preference is observed even for the unsubstituted compound. Substituted keto-enol form derivatives (6b) further demonstrate greater stability than their diketo counterparts. Stability differences (in kcal/mol) range from −0.86 to −4.01 (H), −14.85 to −16.04 (NH₂), −4.09 to −6.81 (CH₃), −0.013 to −3.67 (CF₃), and −3.49 to −7.31 (Cl), measured in both the gas phase and in solution. The observed stability order of the keto-enol form is as follows: NH₂ > Cl > CH₃ > H > CF₃. Interestingly, the keto-enol form exhibits its highest stability in the gas phase compared to solvents, regardless of polarity (e.g. water, acetone, and cyclohexane). This gas-phase preference could be due to the lack of solvent interactions that might destabilise the keto-enol form. In cycloheptane-1,2-dione system (7a and 7b), theoretical reports suggest that the unsubstituted diketo form (7a) exists in a puckered conformation. This conformation offers greater stability compared to the corresponding keto-enol form (7b), which adopts an envelope-like structure and experiences increased ring strain.⁵ The stability of the diketo form is further enhanced by its two carbonyl groups being oriented opposite to each other, minimising lone pair repulsion. This stability trend holds true for most substituents, favouring the diketo form as visualised in Figure 3. Interestingly, the NH₂ substituent is an exception to this trend. Here, the keto-enol form is thermodynamically favoured, being approximately 8 kcal/mol more stable than the diketo form.

Figure 3.

Change in Gibbs free energy in (kcal/mol) of the 1,2-cyclodiones system (tautomer) in vacuum (gas) and different solvent (water, acetone, and cyclohexane).

The studied compounds exhibit ring-size-dependent tautomerism. Three-, five-, and six-membered ring systems favour the keto-enol form, whereas four- and seven-membered rings tend to exist in the diketo form. Notably, an NH₂ substituent stabilises the keto-enol tautomer exclusively. Figure 3 visually demonstrates how electron-withdrawing groups (EWGs) destabilise the keto-enol form. This destabilisation arises from the EWG weakening the crucial C=O double bond in the keto form and disrupting the favourable electron distribution in the enol form. In contrast, electron-donating groups (EDGs) stabilise the keto-enol form by strengthening the enol’s ability to accommodate a negative charge.

Influence of amino group to the keto-enol form

Depending on the molecule structure and environment, the −NH₂ (amino) substituent can stabilise the keto-enol tautomeric equilibrium through many methods. (a) The hydrogen bonding mechanism can uniquely stabilise the keto-enol form, whereby the NH₂ group can make hydrogen bonds with either the oxygen atom of the carbonyl group (in the keto form) or the hydroxyl group in the enol form. Within the enol form, the NH₂ group can establish intramolecular hydrogen bonds with the hydroxyl (−OH) group, thereby stabilising the enol form (b) electron donation: an NH₂ group donates electrons by resonance or inductive actions. In the enol form, a C=C bond and a −OH group allow the NH₂ group to contribute electron density to the system. By increasing the electron density on the carbon–carbon double bond, the stability of the enol form can be enhanced. (c) Resonance stabilisation: Under certain circumstances, the NH₂ group can resonate with the conjugated π-system of the enol form. The electron density delocalisation phenomenon between the NH₂ group and the enol conjugated system can enhance the enol form’s stability.

For instance, the compound 3-amino-2-hydroxycyclohept-2-en-1-one (Figure 4) consists of a cycloheptenone (a seven-membered ring with a keto group) that has both an amino (−NH₂) group and a hydroxyl (−OH) group. Because of both electrical and steric considerations, this particular structure enables the NH₂ group to stabilise the enol form uniquely. An NH₂ group might stabilise the enol form in this system as follows: the keto ester has a carbonyl group (C=O) at position 1, an amino group (−NH₂) at position 3, and a hydroxyl group (−OH) at position 2. The formation of the enol form occurs when a proton is transferred from the alpha-carbon to the carbonyl oxygen, forming a hydroxyl (−OH) group at position 1 and a C=C double bond between carbons 1 and 2. The stabilisation processes involving NH₂ in the enol form occur through the following pathways (1) intramolecular hydrogen bonding occurs when the −OH group at position 2 in the enol form forms a hydrogen bond with the NH₂ group. This hydrogen bond stabilises the enol form by decreasing the system’s total energy and (2) resonance stabilisation involves the donation of electron density by the NH₂ group through resonance. The lone pair on nitrogen in the enol formulation can resonate with the neighbouring C=C bond and the −OH group. This prolonged conjugation enhances the stability of the enol form by distributing electron density over the ring. (3) Electron donation and inductive effects: The NH₂ group functions as an EDG by means of both resonance and inductive influence. It raises the electron density on the neighbouring carbon; therefore, enhancing the electron-richness and stability of the C=C bond in the enol form as against the keto form, (4) Steric effects occur in the keto form when there is steric repulsion present between the NH₂ and the carbonyl group, which is caused by their close closeness. Reduction of this repulsion in the enol form raises the favorability of the enol form.

Figure 4.

Structure of 3-amino-2-hydroxycyclohept-2-en-1-one.

Based on the above example, the presence of the NH₂ group at position 3 enhances the stabilisation of the enol form compared to the keto form. Within this molecule, the stability of the enol tautomer is enhanced by the interaction of intramolecular hydrogen bonding and resonance between the amino and enol groups. Fundamentally, including the amino group at the third position in 3-amino-2-hydroxycyclohept-2-en-1-one promotes the stabilisation of the enol form mainly through intramolecular hydrogen bonding and resonance stabilisation.

Atomic ESP charges and dipole moments

Atomic ESP and dipole moment (μ) are fundamental physicochemical properties that offer valuable insights into molecular structure and reactivity.^20,21 Understanding dipole moments (μ) is crucial in the study of tautomerism because distinct tautomeric forms often exhibit differences in their electronic structures, leading to potentially significant variations in dipole moments.²² The ability to predict dipole moments facilitates the assessment of tautomer stability in polar environments.²³ ESP maps visualise the distribution of charge within a molecule, pinpointing regions of positive and negative potential that correspond to electrophilic and nucleophilic sites, respectively, and thereby influencing reactivity.

The $ESP (φ (r))$ at position ‘r’ $' r'$ due to a charge $Q_{j}$ located at position ‘ $r_{j}$ r_j’ is defined as²⁴

ESP (φ (r)) = \frac{1}{4 π ϵ_{0}} \frac{Q_{j}}{| | r - r_{j} | |}

(1)

where $ϵ_{0}$ is the permittivity of free space, a constant describing electric field behaviour in a vacuum. $| | r - r_{j} | |$ is the magnitude of the distance between the point of interest ( $r$ ) and the charge $(r_{j}),$ and $Q_{j}$ is the charge at position $r_{j}$ . In a molecule, the ESP arises from the distribution of both positive nuclear charges and the surrounding electron cloud. The total charge density $(ρ_{tot})$ at any point ‘r $r$ ’ is expressed as:

ρ_{tot} (r) = ρ_{protons} (r) - ρ_{electrons} (r)

(2)

To calculate the total charge density of a molecule, we consider the contributions from each atom:

ρ_{tot} (r) = \sum_{j} (Z_{j} δ (r - r_{j})) - ρ_{j} (r - r_{j})

(3)

where $Z_{j}$ is the atomic number (number of protons) of atom $j$ , $δ (r - r_{j})$ is the Dirac delta function, modelling the nuclear charge as concentrated at a single point $r_{j}$ . $ρ_{j} (r - r_{j})$ is the electron density distribution of atoms $j$ , cantered at $r_{j}$ .

The ESP of a molecular system is directly determined by its total charge density distribution. It can be calculated by integrating the contributions from all infinitesimal charge elements:

φ_{stat} (r) = \int \frac{ρ_{tot} (r^{'})}{| | r - r^{'} | |} d r^{'}

(4)

where $φ_{stat} (r)$ is the ESP at point $r$ due to the static charge distribution. $ρ_{tot} (r^{'})$ is the total charge density at position $r^{'}$ (the integration variable). $| | r - r^{'} | |$ is the distance between point $r$ and the charge element at $r^{'}$ .

To assess the overall variability of ESP across the molecular surface, we calculate the ESP total variance $σ_{total}^{2}$ :

σ_{total}^{2} = \frac{1}{N} \sum_{i = 1}^{N} {(E S P_{i} - \bar{E S P})}^{2}

(5)

where $N$ is the number of points on the molecular surface, $E S P_{i}$ is the ESP at point $i$ , and $\bar{E S P}$ is the mean ESP value

A high ESP total variance $σ_{total}^{2}$ indicates a wide range of ESPs, suggesting diverse chemical environments within the molecule.

The dipole moment (μ) provides insights into the overall charge separation within a molecule and how it might orient itself in a solvent environment. It is calculated as:

μ = \sum_{i} q_{i} \cdot r_{i}

(6)

where $q_{i}$ is the partial charge of atom $i$ , and $r_{i}$ is its position vector.

Theoretical calculations at the M06-2X/6-311G++** level of theory was employed to analyse both ESP and dipole moments in the study of keto-enol tautomerism within 1,2-cyclodiones of varying ring sizes. These analyses shed light on how substituents affect, the stability, and reactivity of different tautomeric forms. By examining ESP variance (ESP total variance $σ_{total}^{2}$ ) patterns in conjunction with dipole moment data, reactivity trends, the relative stabilities of distinct tautomers, and their potential interactions with solvents were predicted.

The calculated ESP variance and dipole moment data (see Table 2) reveal differences between keto-enol and diketo forms. Both ESP variance and dipole moment increase when transitioning from gas to solution, with the highest dipole moments observed in water, the most polar solvent. This trend holds true for both tautomers.

Table 2.

Calculated dipole moment (D), ESP variance in (kcal/mol)²), energies of the HOMO and LUMO orbitals in (a.u) and HOMO/LUMO energy band gaps (in eV).

Ring system	Tautomers substituents (X)	Diketo form (a)					Keto-enol form (b)				ESP $σ_{total}^{2}$
Ring system	Tautomers substituents (X)	HOMO	LUMO	ΔE (eV)	µ (D)	ESP $σ_{total}^{2}$	HOMO	LUMO	ΔE (eV)	$μ$ µ (D)	ESP $σ_{total}^{2}$
3	Gas phase
	–H	−0.3198	−0.0905	6.2401	2.7385	141.4527	−0.3162	−0.0180	8.1127	3.3579	416.7111
	NH₂	−0.3066	−0.0753	6.2952	4.3765	192.7958	−0.2919	−0.0199	7.4030	4.3153	511.8385
	CH₃	−0.3090	−0.0784	6.2760	3.3659	111.0758	−0.3048	−0.0179	7.8079	3.6617	353.9394
	CF₃	−0.3474	−0.1166	6.2794	2.1269	204.0229	−0.3412	−0.0299	8.4707	3.7883	431.0676
	Cl	−0.3309	−0.0986	6.3201	2.2855	190.8248	−0.3314	−0.0300	8.1991	5.0113	473.9535
	Water phase
	–H	−0.3146	−0.0838	6.2811	3.7238	215.2701	−0.3237	−0.0009	8.7816	4.7339	629.1679
	NH₂	−0.3067	−0.0710	6.4129	5.9116	334.0723	−0.2928	−0.0066	7.7870	6.1203	784.6071
	CH₃	−0.3071	−0.0743	6.3334	4.4701	169.9579	−0.3163	−0.0059	8.4470	5.1794	573.9600
	CF₃	−0.3370	−0.1022	6.3899	2.8675	332.0561	−0.3405	−0.0088	9.0255	5.0866	652.1041
	Cl	−0.3243	−0.0900	6.3743	3.0441	312.3472	−0.3362	−0.0058	8.9903	6.9512	795.4882
	Acetone phase
	–H	−0.3148	−0.0841	6.2795	3.6761	211.0355	−0.3232	−0.0015	8.7553	4.6642	620.3536
	NH₂	−0.3066	−0.0712	6.4074	5.8367	326.6947	−0.2927	−0.0070	7.7742	6.0268	768.8036
	CH₃	−0.3072	−0.0740	6.3450	4.4237	166.6281	−0.3157	−0.0063	8.4199	5.1019	562.2026
	CF₃	−0.3374	−0.1028	6.3857	2.8303	325.3239	−0.3405	−0.0092	9.0132	5.0208	640.8550
	Cl	−0.3245	−0.0904	6.3720	3.0084	306.0817	−0.3358	−0.0066	8.9587	6.8527	777.2683
	Cyclohexane phase
	–H	−0.3174	−0.08722	6.26337	3.1591	171.4692	−0.3192	−0.0090	8.4412	3.9219	506.0953
	NH₂	−0.3064	−0.07377	6.33103	5.0366	247.0145	−0.2922	−0.0129	7.5996	5.0729	621.9082
	CH₃	−0.3082	−0.07669	6.29904	3.8233	134.6855	−0.3096	−0.0116	8.1111	4.2838	442.2437
	CF₃	−0.3428	−0.11096	6.30856	2.4225	251.7554	−0.3405	−0.0166	8.8141	4.3193	524.1617
	Cl	−0.3277	−0.09438	6.34807	2.6110	240.1257	−0.3331	−0.0176	8.5834	5.7994	595.0154
4	Gas phase
	–H	−0.3179	−0.0670	6.8263	4.0751	112.0480	−0.3163	−0.0221	8.0067	1.7630	192.3114
	NH₂	−0.3184	−0.0685	6.8011	4.5011	134.5760	−0.2658	−0.0164	6.7876	4.6861	360.6354
	CH₃	−0.3128	−0.0654	6.7339	4.2574	111.6878	−0.3011	−0.0110	7.8932	2.6506	181.0349
	CF₃	−0.3403	−0.0883	6.8569	3.3920	174.9059	−0.3421	−0.0493	7.9680	1.2188	185.7479
	Cl	−0.3286	−0.0872	6.5693	3.4088	174.0080	−0.3129	−0.0256	7.8181	0.6637	206.2633
	Water phase
	–H	−0.3185	−0.0655	6.8839	5.4881	175.4517	−0.3117	−0.0214	7.8972	2.4733	255.5577
	NH₂	−0.3168	−0.0676	6.7798	6.3363	226.6511	−0.2641	−0.0033	7.0975	7.0408	601.7158
	CH₃	−0.3146	−0.0652	6.7866	5.7207	182.0165	−0.2984	−0.0131	7.7621	3.6661	259.0702
	CF₃	−0.3348	−0.0804	6.9209	4.6084	290.9675	−0.3307	−0.0420	7.8572	1.3853	245.3425
	Cl	−0.3260	−0.0814	6.6557	4.5928	285.4841	−0.3080	−0.0235	7.7396	0.9670	278.2775
	Acetone phase
	–H	−0.3184	−0.0655	6.8817	5.4189	171.9862	−0.3118	−0.0214	7.9025	2.4365	252.5489
	NH₂	−0.3170	−0.0676	6.7867	6.2337	220.9652	−0.2642	−0.0036	7.0906	6.9045	585.7136
	CH₃	−0.3145	−0.0652	6.7849	5.6478	177.8687	−0.2985	−0.0130	7.7687	3.6136	255.0230
	CF₃	−0.3348	−0.0807	6.9167	4.5452	284.1568	−0.3312	−0.0422	7.8622	1.3787	242.6314
	Cl	−0.3261	−0.0816	6.6520	4.5332	279.8989	−0.3082	−0.0236	7.7436	0.9504	274.9353
	Cyclohexane phase
	–H	−0.3178	−0.0659	6.8547	4.6800	138.0502	−0.3141	−0.0215	7.9617	2.0599	218.9269
	NH₂	−0.3187	−0.0679	6.8239	5.1991	169.6713	−0.2650	−0.0090	6.9635	5.5807	446.2337
	CH₃	−0.3133	−0.0648	6.7615	4.8679	139.0079	−0.2998	−0.0117	7.8396	3.0739	214.1613
	CF₃	−0.3373	−0.0843	6.8863	3.9129	222.2719	−0.3368	−0.0457	7.9206	1.3012	211.6135
	Cl	−0.3271	−0.0843	6.6090	3.9126	219.6680	−0.3105	−0.0245	7.7849	0.7866	238.2068
5	Gas phase
	–H	−0.3080	−0.0575	6.8160	5.1259	144.3907	−0.3077	−0.0143	7.9831	4.8423	295.5480
	NH₂	−0.3125	−0.0611	6.8418	4.9906	154.9541	−0.2584	−0.0138	6.6562	4.9745	270.5042
	CH₃	−0.3055	−0.0568	6.7686	5.0798	159.8427	−0.2955	−0.0141	7.6567	5.4692	272.6949
	CF₃	−0.3282	−0.0769	6.8382	4.9416	177.2344	−0.3311	−0.0463	7.7502	2.9450	102.2621
	Cl	−0.3214	−0.0736	6.7433	4.8598	188.2517	−0.3048	−0.0276	7.5432	2.5517	135.5353
	Water phase
	–H	−0.3137	−0.0593	6.9233	6.9212	244.2214	−0.3053	−0.0187	7.8005	6.8743	471.2303
	NH₂	−0.3150	−0.0616	6.8942	7.3902	277.3046	−0.2600	−0.0010	7.0470	7.5914	499.2218
	CH₃	−0.3116	−0.0589	6.8759	6.9491	279.4973	−0.2943	−0.0131	7.6533	7.8145	466.1089
	CF₃	−0.3272	−0.0715	6.9568	6.8425	317.0867	−0.3242	−0.0402	7.7289	3.7990	145.8919
	Cl	−0.3236	−0.0715	6.8578	6.6876	328.0579	−0.3040	−0.0260	7.5659	3.4597	197.6165
	Acetone phase
	–H	−0.3134	−0.0591	6.9187	6.8307	238.6955	−0.3054	−0.0184	7.8104	6.7655	461.4038
	NH₂	−0.3149	−0.0615	6.8950	7.2537	269.5351	−0.2599	−0.0013	7.0361	7.4375	483.7549
	CH₃	−0.3112	−0.0587	6.8718	6.8546	273.2684	−0.2943	−0.0126	7.6647	7.6882	454.6376
	CF₃	−0.3272	−0.0717	6.9521	6.7481	308.7817	−0.3245	−0.0404	7.7300	3.7571	143.3961
	Cl	−0.3234	−0.0715	6.8533	6.5960	319.7793	−0.3040	−0.0260	7.5653	3.4131	194.3065
	Cyclohexane phase
	–H	−0.3101	−0.0579	6.8633	5.8906	183.1112	−0.3065	−0.0157	7.9132	5.6777	365.5714
	NH₂	−0.3144	−0.0611	6.8916	5.8105	199.7700	−0.2590	−0.0070	6.8580	5.9919	351.0332
	CH₃	−0.3079	−0.0573	6.8175	5.8659	205.4090	−0.2947	−0.0087	7.7822	6.4271	350.3076
	CF₃	−0.3273	−0.0739	6.8942	5.7489	232.3071	−0.3277	−0.0431	7.7426	3.3165	119.5455
	Cl	−0.3220	−0.0722	6.7970	5.6331	243.4188	−0.3042	−0.0265	7.5559	2.9350	161.0368
6	Gas phase
	–H	−0.3108	−0.0361	7.4749	5.2786	137.0431	−0.2982	−0.0259	7.4108	3.2763	112.2292
	NH₂	−0.3126	−0.0312	7.6556	5.6013	130.3825	−0.2522	−0.0119	6.5402	4.9763	221.2796
	CH₃	−0.3082	−0.0311	7.5403	5.1010	155.7715	−0.2877	−0.0197	7.2913	3.4243	122.7757
	CF₃	−0.3282	−0.0511	7.5422	5.5527	142.6426	−0.3242	−0.0495	7.4740	3.9819	86.5013
	Cl	−0.3238	−0.0458	7.5643	5.4056	159.9195	−0.2978	−0.0336	7.1888	3.5582	113.1954
	Water phase
	–H	−0.3193	−0.0447	7.4720	7.1874	247.6539	−0.3000	−0.0277	7.4122	4.5260	163.9272
	NH₂	−0.3210	−0.0420	7.5932	8.5288	284.2970	−0.2563	−0.0048	6.8420	7.6323	427.0563
	CH₃	−0.3166	−0.0398	7.5326	7.0735	287.2647	−0.2900	−0.0226	7.2760	4.9577	186.2366
	CF₃	−0.3306	−0.0534	7.5430	7.6606	268.3564	−0.3200	−0.0442	7.5050	5.1481	126.6806
	Cl	−0.3294	−0.0518	7.5530	7.4930	280.2829	−0.3003	−0.0329	7.2757	4.8303	168.7285
	Acetone phase
	–H	−0.3189	−0.0442	7.4736	7.0924	241.7299	−0.2999	−0.0275	7.4129	4.4615	160.8925
	NH₂	−0.3205	−0.0414	7.5967	8.3796	274.9146	−0.2561	−0.0045	6.8446	7.4760	412.2660
	CH₃	−0.3162	−0.0393	7.5343	6.9722	279.7558	−0.2898	−0.0224	7.2776	4.8764	182.2331
	CF₃	−0.3303	−0.0521	7.5704	7.5310	258.4023	−0.3201	−0.0444	7.5043	5.0927	124.4467
	Cl	−0.3290	−0.0514	7.5541	7.3880	273.5982	−0.3001	−0.0329	7.2721	4.7672	165.7859
	Cyclohexane phase
	–H	−0.3142	−0.0391	7.4847	6.0983	177.8658	−0.2989	−0.0264	7.4153	3.8054	133.3254
	NH₂	−0.3157	−0.0354	7.6259	6.7541	179.2556	−0.2565	−0.0062	6.8116	5.7556	270.8828
	CH₃	−0.3115	−0.0336	7.5620	5.9224	202.5122	−0.2885	−0.0206	7.2896	4.0604	148.6006
	CF₃	−0.3286	−0.0504	7.5721	6.4219	189.0987	−0.3222	−0.0468	7.4930	4.4946	102.4996
	Cl	−0.3259	−0.0478	7.5675	6.2981	207.8225	−0.2986	−0.0329	7.2302	4.1086	135.7574
7	Gas phase
	–H	−0.3130	−0.0474	7.2280	5.5345	162.9080	−0.2980	−0.0173	7.6357	4.5655	280.3991
	NH₂	−0.3001	−0.0157	7.7391	5.1662	174.1479	−0.2516	−0.0118	6.5259	4.6916	185.3548
	CH₃	−0.3069	−0.0316	7.4908	5.1315	161.7982	−0.2837	−0.0205	7.1617	3.5233	118.0306
	CF₃	−0.3281	−0.0563	7.3944	6.1568	144.8821	−0.3198	−0.0496	7.3515	4.4197	76.8149
	Cl	−0.3191	−0.0387	7.6291	4.9738	154.6644	−0.2938	−0.0383	6.9516	4.3194	107.1983
	Water phase
	–H	−0.3217	−0.0518	7.3443	7.4830	281.7469	−0.2987	−0.0243	7.4658	6.6847	469.5029
	NH₂	−0.3097	−0.0273	7.6850	7.2980	300.1420	−0.2538	−0.0063	6.7336	7.5946	396.0068
	CH₃	−0.3181	−0.0447	7.4371	7.2971	312.7884	−0.2872	−0.0238	7.1668	5.1160	185.1531
	CF₃	−0.3322	−0.0586	7.4470	8.3820	275.9913	−0.3161	−0.0461	7.3459	5.8942	124.8401
	Cl	−0.3268	−0.0461	7.6390	6.7545	262.1566	−0.2995	−0.0384	7.1054	5.8309	157.3128
	Acetone phase
	–H	−0.3217	−0.0528	7.3193	7.4064	274.8481	−0.2986	−0.0239	7.4755	6.5688	459.7663
	NH₂	−0.3094	−0.0258	7.7170	7.1423	289.9096	−0.2537	−0.0062	6.7349	7.4135	378.1780
	CH₃	−0.3175	−0.0448	7.4227	7.2019	308.6862	−0.2870	−0.0236	7.1675	5.0310	181.1639
	CF₃	−0.3320	−0.0584	7.4445	8.2673	268.8527	−0.3173	−0.0455	7.3976	5.6479	114.5546
	Cl	−0.3263	−0.0448	7.6589	6.6632	254.2232	−0.2992	−0.0384	7.0990	5.7569	154.9369
	Cyclohexane phase
	–H	−0.3168	−0.0496	7.2707	6.3732	211.1160	−0.2980	−0.0197	7.5745	5.4068	351.9669
	NH₂	−0.3045	−0.0191	7.7666	5.9908	219.6739	−0.2537	−0.0070	6.7125	5.6674	243.9500
	CH₃	−0.3108	−0.0345	7.5204	5.9786	214.4061	−0.2849	−0.0215	7.1688	4.1768	143.5153
	CF₃	−0.3298	−0.0576	7.4060	7.0983	195.0387	−0.3184	−0.0473	7.3763	4.9989	92.3874
	Cl	−0.3220	−0.0408	7.6516	5.7270	197.8357	−0.2961	−0.0380	7.0238	4.9744	128.4861

Small rings (three- and four-membered): For three-membered rings in the gas phase, the keto-enol form exhibits a higher value of dipole moment compared to the diketo form, indicating that greater polarity is associated with a wider range of ESPs. Notably, the Cl-substituted keto-enol form displays a high dipole moment (5.0113 D) and a significantly elevated ESP variance (473.9535 (kcal/mol))² while the NH₂-substituted keto-enol form displays a high ESP variance (511.8385 (kcal/mol))² and a dipole moment (4.3153 D). Furthermore, the observed dipole moment order of the keto-enol form is Cl > NH₂ > CF₃ > CH₃ > H, while the ESP variance order is NH₂ > Cl > CF₃ > H > CH₃ (in both gas and solution phases). This suggests a lack of direct correlation between dipole moment and ESP variance order under the influence of different substituent groups. In the four-membered rings (gas phase), the diketo form tends to exhibit a higher dipole moment than its keto-enol counterpart. This trend runs counter to expectations since the keto-enol form typically displays higher ESP variance. EWGs like CF₃ and Cl in the diketo form display high ESP variances [174.9059 and 174.0080 (kcal/mol)², respectively]. Conversely, EDGs such as NH₂ and CH₃ exhibit high dipole moments (4.5011 D and 4.2574 D, respectively). The observed dipole moment trend order in the keto-enol form is NH₂ > CH₃ > H > Cl > CF₃, while the ESP variance order is CF₃ > Cl > NH₂ > H > CH₃. This pattern holds true in both gas and solution phases. This study suggests a direct correlation between dipole moment and stability order in these tautomers, a relationship that runs counter to the trend observed with ESP variance.

Intermediate rings (five- and six-membered), in five-membered rings, a distinct pattern emerges: EDGs induce a high dipole moment in the keto-enol form, whereas EWGs lead to a high dipole moment in the diketo form. In addition, the keto-enol form typically displays higher ESP variance. In six-membered rings, results demonstrate a greater dipole moment in the diketo form compared to its keto-enol counterpart. This observation extends to ESP variance, which also appears dominant in the diketo form. Notably, EDGs induce a high dipole moment, specifically within the diketo form. This study highlights a lack of direct correlation between dipole moment and order of stability in these tautomers. Surprisingly, the least stable tautomer (diketo form) exhibits the largest dipole moment in both gaseous and aqueous phases, a pattern is also mirrored in ESP variance. The findings are supported by the study conducted by Anandan et al.,²⁵ indicates that there is no direct correlation between dipole moment and order of stability under SCRF conditions among the studied tautomers.

In seven-membered rings, a direct correlation between dipole moment and order of stability generally exists within these tautomers. However, the NH₂ group stands out as a potent outlier. It exhibits a greater dipole moment in the keto-enol form (7.5946 D) within a water phase compared to its diketo counterpart. This pattern remains consistent in acetone but differs in cyclohexane and gas phases. Interestingly, unsubstituted seven-membered rings display the highest ESP variance, followed by those with EDGs. These findings reveal a complex interplay between ring size, substituent effects, and solvent polarity in determining dipole moments and ESP variances of diketo and keto-enol tautomers. Interestingly, a direct correlation between dipole moment (see Figure 5) and order of stability is not universally observed. This is particularly evident in the presence of potent outliers such as the NH₂ group, further highlighting the nuanced behaviour of these tautomeric systems.

Figure 5.

Dipole moments in (Debye) of the 1,2-cyclodiones system (tautomer) in vacuum (gas) and different solvent (water, acetone, and cyclohexane).

ESP maps were generated (see Figure 6) to visualise electron density distribution within molecular structures, elucidating their reactivity. In the gas phase, the NH₂-substituted diketo form within a four-membered ring presents an intriguing contradiction: it exhibits a high dipole moment but a surprisingly low ESP variance. This discordance highlights a potential disharmony between these properties. Comparisons between keto-enol forms in a three-membered ring, using NH₂ and Cl substituents, emphasise substituents’ profound impact on both dipole moments and ESP variances. Further investigations reveal that the Cl-substituted keto-enol form displays marked shifts in these properties across different solvent phases, underscoring the critical role of solvent environments in molecular behaviour. Similarly, explorations of the NH₂-substituted keto-enol form within a seven-membered ring showcase notable variations in dipole moment across various solvents, providing further insights into solvent effects. These analyses of ESP distributions yield valuable knowledge regarding the structural characteristics and reactivity of the molecules studied, advancing our chemical understanding.

Figure 6.

Electrostatic potential (ESP) maps of the optimised geometrical molecular structures.

Correlation matrix: HOMO-LUMO gap and ESP values

Theoretical calculations at the M06-2X/6-311G++** level of theory was employed to analyse HOMO and LUMO energies in the study of keto-enol tautomerism within 1,2-cyclodiones of varying ring sizes. These calculations provide insights into the reactivity and stability of both diketo and keto-enol tautomers across different phases. The data suggest that the diketo tautomer generally exhibits higher reactivity than the keto-enol form, primarily due to its increased electrophilicity, which arises from the presence of two conjugated carbonyl groups. For example, in the gas phase, the diketo form of cyclopropane-1,2-dione demonstrates a smaller HOMO-LUMO energy gap compared to the keto-enol form, indicating greater reactivity. This pattern persists across other phases, such as water, acetone, and cyclohexane, though the exact influence of the solvent environment varies.

In the gas phase, there is a strong negative correlation between the HOMO-LUMO gap of the diketo form and its ESP_max (r = −0.5869), as well as with ESP_min (r = −0.6948) (Figure 7). These relationships suggest that as the reactivity of the diketo tautomer increases (indicated by a smaller HOMO-LUMO gap), the ability of the molecule to accept or donate electron density also increases. Similarly, for the keto-enol form in the gas phase, the HOMO-LUMO gap correlates negatively with ESP_max (r = −0.8496) and more weakly with ESP_min (r = 0.2307), indicating that reactivity is still largely governed by electron distribution. However, the correlation with electron donation (ESP_min) is less pronounced.

Figure 7.

The correlation matrix: HOMO-LUMO gap and ESP values in vacuum (gas) and different solvents (water, acetone, and cyclohexane).

In water, acetone, and cyclohexane phases, the relationship between the HOMO-LUMO gap and ESP values follows a similar trend but with some variations (see Supplementary Table S3 for phase-specific data). In the water phase, the correlation between the HOMO-LUMO gap and ESP_max for the diketo form is less negative (r = −0.4985) compared to the gas phase, reflecting the stabilising influence of polar solvents, which can reduce reactivity. The same trend is observed in the acetone and cyclohexane phases, where the correlations are slightly less negative, again underscoring the impact of solvent polarity on molecular reactivity. For the keto-enol form, the HOMO-LUMO gap’s relationship with ESP values becomes even less pronounced in polar solvents like water and acetone, suggesting that these environments particularly stabilise the keto-enol form, likely through hydrogen bonding, thereby reducing its reactivity.

Overall, the diketo tautomer exhibits higher reactivity compared to the keto-enol tautomer, particularly in non-polar solvents and in the absence of electron-donating substituents. This finding aligns with the smaller HOMO-LUMO gaps observed for the diketo forms across all phases, indicating a consistent trend of increased reactivity. The solvent environment plays a significant role in modulating these relationships, with polar solvents stabilising the keto-enol form and decreasing its reactivity.

Frontier molecular orbitals

The highest occupied molecular orbital (HOMO) energy level significantly influences a molecule’s behaviour in chemical reactions. Specifically, the HOMO energy determines the molecule’s capacity to donate electrons; the higher the HOMO energy, the greater the molecule’s ability to act as an electron donor. Conversely, the lowest unoccupied molecular orbital (LUMO) energy indicates the ability to accept electrons.²⁶ The HOMO energy is directly correlated with ionisation potential, while the LUMO energy reflects electron affinity.²⁷ A larger energy gap between the HOMO and LUMO suggests higher kinetic stability and lower chemical reactivity.²⁸ This is because adding electrons to a high-lying LUMO or removing them from a low-lying HOMO becomes energetically less favourable. Therefore, the magnitude of the HOMO/LUMO gap offers valuable insight into a molecule’s reactivity patterns.

Theoretical calculations at the M06-2X/6-311G++** level of theory was employed to analyse HOMO and LUMO energies in the study of keto-enol tautomerism within 1,2-cyclodiones of varying ring sizes. Results indicate (see Table 2) that the diketo tautomer exhibits higher reactivity than the keto-enol form due to its increased electrophilicity, stemming from the presence of two conjugated carbonyl groups. For example, in the gas phase, cyclopropane-1,2-dione’s diketo form demonstrates a smaller HOMO-LUMO energy gap (ΔE) compared to the keto-enol form (6.240 vs 8.112 eV). This smaller gap indicates greater reactivity. However, some studies indicate that the keto-enol form is more thermodynamically stable, likely due to a degree of aromaticity that can be gained in the enol form.¹⁰ The solvent environment significantly influences reactivity; polar solvents stabilise the keto-enol form through hydrogen bonding, making it less reactive. This is seen in water where cyclopropane-1,2-dione’s keto-enol form has a wider energy gap than in the gas phase (8.782 vs 8.113 eV). While electron-donating substituents like alkyl groups increase electron density on the carbonyl carbon, they unexpectedly decrease the reactivity of the diketo form. This is evident in 3-methylcyclopropane-1,2-dione, which exhibits a slightly wider energy gap in the gas phase compared to the unsubstituted compound (6.276 vs 6.240 eV). Overall, the diketo tautomer demonstrates higher reactivity compared to the keto-enol tautomer, particularly in non-polar solvents and in the absence of substituents. This increased reactivity is attributed to the presence of two conjugated carbonyl groups in the diketo form, which enhances its electrophilicity. The diketo tautomer was generally found to be more reactive than the keto-enol form, especially in non-polar solvents. This increased reactivity is attributed to the presence of two conjugated carbonyl groups in the diketo form, which enhances its electrophilicity. The smaller HOMO-LUMO energy gap observed for diketo tautomers, particularly in non-polar solvents, further supports this conclusion. This work does not explicitly explore the potential applications or implications of this enhanced reactivity although the discussion could be expanded to include (1) synthetic applications where the increased electrophilicity of the diketo form in non-polar solvents could make it a useful substrate in various organic reactions, such as Diels-Alder cycloadditions or nucleophilic additions. Highlighting these potential synthetic applications would demonstrate the practical relevance of the findings (2) Biological implications is if 1,2-cyclodiones or related compounds are found in biological systems, the preferential reactivity of the diketo form in non-polar environments (e.g. lipid membranes or hydrophobic protein pockets) could have implications for their biological activity or metabolic transformations. Discussing such possibilities would broaden the impact of the research (3) further research directions to the observed reactivity trends could inspire future studies explore the use of diketo tautomers as reactive intermediates or catalysts in non-polar solvents. Suggesting these potential research directions would demonstrate the potential for further development based on the current findings.

Conclusion

This investigation into the effect of substituents on the 1,2-cyclodiones system revealed how substituent groups influence stability and reactivity. The studied compounds exhibit ring-size dependent tautomerism, with the NH₂ substituent uniquely stabilising the keto-enol form. Surprisingly, dipole moment does not always directly correlate with stability, demonstrating the complex interplay of ring size, substituent effects, and solvent polarity. Findings suggest the diketo tautomer is generally more reactive than the keto-enol form, especially in non-polar solvents and without the influence of substituents.

Supplemental Material

sj-docx-1-chl-10.1177_17475198241305254 – Supplemental material for A density functional theory study of keto-enol tautomerism in 1,2-cyclodiones: Substituent effects on reactivity and thermodynamic stability

Supplemental material, sj-docx-1-chl-10.1177_17475198241305254 for A density functional theory study of keto-enol tautomerism in 1,2-cyclodiones: Substituent effects on reactivity and thermodynamic stability by Luqman Idd Juma and Rene Costa in Journal of Chemical Research

Footnotes

Acknowledgements

The authors are gratefully acknowledging the support from Dr Joseph Kyobe of the chemistry department, at St. John’s University of Tanzania for technical assistance during this study.

Author contributions

All authors have participated in (a) conception and design or analysis and interpretation of the data, (b) drafting the article or revising it critically for important intellectual content, and (c) approval of the final version of the manuscript document.

Availability of data and materials

This is upon the request.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Ethics declarations

The authors declare that no violation of ethics conscious committed or will be intended.

Consent to participate

Not applicable – This study involved computational chemistry methods only, with no human subjects.

Consent for publication

Not applicable – This study contains no personal or identifiable data.

ORCID iDs

Luqman Idd Juma

Rene Costa

Supplemental material

Supplemental material for this article is available online.

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