Analysis of Conformer Stability for 1, 3, 8-Trihydroxynaphthalene

1,3,8-Trihydroxynaphthalene is one of the substrates in the fungal melanin biosynthesis .... of the choices for the theory levels and solvation models...
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J. Phys. Chem. B 2007, 111, 8314-8320

Analysis of Conformer Stability for 1,3,8-Trihydroxynaphthalene: Natural Substrate of Fungal Trihydroxynaphthalene Reductase Michal Rostkowski and Piotr Paneth* Institute of Applied Radiation Chemistry, Technical UniVersity of Lodz, Zeromskiego 116, 90-924 Lodz, Poland ReceiVed: March 19, 2007; In Final Form: April 25, 2007

1,3,8-Trihydroxynaphthalene is one of the substrates in the fungal melanin biosynthesis pathway. We present theoretical studies on energies of its tautomeric forms and their rotamers. Several theory levels and solvent models have been tested using experimental results obtained in water-acetone mixtures as the reference point. Our results indicate that the best agreement with these data is obtained with density functional theory levels when the continuum solvation model uses the united atom topological cavity. We also noticed a fairly good performance of the semiempirical AM1 method that makes it a promising alternative for studies of large systems.

Introduction Melanin plays crucial role in the microbial world.1 It can act as a shield against unfavorable environmental conditions like high temperature, irradiation, oxidative and hazardous compounds, or even enzymatic lysis. It can also protect fungi mechanically by stiffening cell walls. On the other hand, it has been proved that melanin has effects in pathogenesis and in the fungal infection cycle. It can be involved in functionalization of the appressorium, a special apparatus that serves as a penetration structure enabling the transfer of the infection material into the host plant. Moreover, byproducts of melanin biosynthetic pathways can be cytotoxic. These features make melanin a very important factor in the development of plant diseases all over the world. Melanin is a pigment, which has no exact chemical definition, because it is a mixture of polymeric compounds. They are identified on the basis of their physical and chemical properties, as suggested by Nicolaus,2 rather than on accurate chemical analysis. Melanin structure is difficult to unambiguously describe because it depends on its source and even on the chemical treatment used for obtaining the pure compound. It is more reasonable to classify melanins on the basis of the chemical species that serves as the monomer unit in the polymerization process. The most important of these are dihydroxyphenylalanine (DOPA) and dihydroxynaphthalene (DHN) type melanins. The precursor of the former type is L-3,4dihydroxyphenylalanine, and that of the latter is 1,8-dihydroxynaphthalene. The most characterized fungal melanin is of DHN type. Its precursor is formed in two successive cycles of enzymatic reduction and dehydration processes starting from 1,3,6,8tetrahydroxynaphthalene (Figure 1).3 This compound is transformed into 1,3,8-trihydroxynaphthalene after one cycle of enzymatic reactions and, then, to the precursor 1,8-dihydroxynaphthalene in the second cycle. Both dehydration steps are probably catalyzed by the same enzymesscytalone dehydratase. Two remaining reductions are catalyzed by NADPH-dependent tetra- and trihydroxynaphthalene reductases. The most important * Corresponding author: Phone: +4842 631-3199. Fax: +4842 6365008. E-mail: [email protected].

step is the hydride transfer from the nicotynamide ring to the carbon atom of the substrate. Because reactants for these reductions have multiple hydroxyl groups attached to aromatic rings, there is increased probability of their tautomerization. This phenomenon leads to a large number of possible substrate forms, which can be initial structures for the hydride transfer process in the enzymes active site. Up to date, there were only a few experimental attempts to explore tautomerism of tetra- and trihydroxynaphthalenes, but to the best of our knowledge, there were not any approaches to compare their stabilities using computational methods. Experimental data indicate that in pure acetone4 1,3,8trihydroxynapthtalene exists only as tri-enolic tautomer. (We use the “enol” and “keto” terms to refer to the tautomeric forms of trihydroxynaphthalene. For example, tri-enol describes tautomer that contains three hydroxyl groups. Analogously, the term tri-keto refers to the tautomer with three carbonyl groups.) However, Simpson and Weerasooriya identified keto groups in acetone-water buffered solutions.5 They also showed the dependence of the enol-keto equilibrium on pH. In neutral solution, the all-enolic 1,3,8-trihydroxynapthtalene form was preferred by the ratio 2:1 over the keto tautomers, while this ratio was inverted at pH ) 8. Under acidic conditions (pH equal to 6), they obtained a much larger change in the enol-keto equilibrium resulting in the ratio of 10 to 1 toward the tri-enolic compound. In this paper, we present theoretical studies on tautomerism of 1,3,8-trihydroxynaphthalene, which is the reactant for the second and the last cycle of the enzymatic reduction and dehydration reactions leading to the precursor of DHN type melanins. We compare energetic stabilities of tautomers and their rotamers using semiempirical,6 Hartree-Fock7 (HF), and density functional theory8 (DFT) theory levels. All structures were optimized in the gas phase and in the presence of solvents, such as water, diethyl ether, and acetone represented by the conductor-like polarized continuum solvation model (CPCM).9 Calculations that include solvent models are much more demanding than calculations of isolated molecules in the gas phase. Thus, application of solvent models may pose problems for large systems, like biological ones. In order to circumvent these problems, a special group of continuum solvent models

10.1021/jp072177m CCC: $37.00 © 2007 American Chemical Society Published on Web 06/23/2007

Stability of 1,3,8-Trihydroxynaphthalene Conformers

J. Phys. Chem. B, Vol. 111, No. 28, 2007 8315

Figure 1. DHN type melanin biosynthetic pathway.

has been developed that uses gas-phase geometries for which only energies in solution are calculated without further reoptimalization. These models are referred to as “rigid” solvation models, as they neglect the change in geometry introduced upon solvation of a molecule. We have tested the performance of these models. For these calculations, different approaches to cavity representation and solvents were also incorporated. Moreover, solute energies were investigated with utilization of different solvation models, like the integral-equation-formalism polarizable continuum model (IEFPCM),10 the self-consistently isodensity polarized continuum model (SCIPCM),11 and solvation models SM5.4312 and SM6.13 Results and Discussion In order to gain better understanding of the chemical process that participates in the hydride transfer to trihydroxynaphthalene, it is necessary to learn detailed description of each factor determining the course of this reaction. One of the basic questions is which of the tautomeric forms is the most probable substrate for the reaction in the active site of the enzyme. We have approached this problem using computational tools. In order to decide which theory levels are suitable for the system in question, we have adopted the following strategy. First, we have optimized geometries of all possible tautomers at several theory levels using solvent models with parameters for acetone and water. These calculations allowed us to identify results that are in agreement with the experimentally determined preference found in acetone-water solutions. For the theory levels and solvent representations that yielded acceptable results, we have also compared results for rigid solvent models. Subsequently, chosen theory levels were used with solvent model of diethyl ether and in the gas phase since it is expected that the apparent polarity of the active site is substantially lowered compared to the bulk solution. These calculations allowed us to find tautomeric forms that should be most abundant in the enzyme active site. Because 1,3,8-trihydroxynaphthalene has three groups that can undergo tautomerization, there is a versatile set of structures that had to be examined. All tautomeric structures are depicted in Table 1. These structures were classified due to the number of enol groups in a given structure. Tautomers and their rotamers are identified by two numbers. The first one indicates the number of hydroxyl groups. The second is the running number of the structure. All calculations were carried out in the Gaussian 03 package, version C01.14 When the environment was represented by the Minnesota solvation models SM5.43 and SM6 (SMx), calculations were performed using the Minnesota Gaussian solvation module (MN-GSM), version 6.015 that incorporates SMx solvation features into the Gaussian 03 code. A detailed description

of the choices for the theory levels and solvation models used is given below. Because experimental results for tautomerization equilibrium were obtained in the mixture of acetone and water, we have optimized structures of all conformers in the presence of both solvents, modeled by the implicit CPCM solvation model using semiempirical AM116 and PM3,17 Hartree-Fock, and MPW1PW9118 and B3LYP19 DFT theory levels. All non-semiempirical calculations were carried out using the 6-31+G(d,p) basis set.20 Moreover, for each of these calculations, three different types of cavity models were considered, which differ in the atomic radii definition. These were the following: the united atom topological model,21 which is based on atomic radii from the UFF force field22 (UA0) and the default model in Gaussian; the Merz-Kollman23 (MK) model; and the united atom topological model with atomic radii parametrized in the Hartree-Fock theory level with the 6-31G(d) basis set, referred to as UAHF.24 Results for these calculations are collected in Table 2, where relative energies for conformers with respect to the structure denoted as 3-1, for the same choice of the theory level, solvent, and cavity type, are given. For AM1 calculations, when acetone is taken as the solvent modeled by the CPCM model with the UA0 cavity, the most stable is the fully aromatic tautomer denoted as 3-1. Slightly less stable are the following: di-keto structure 1-1 and remaining tri-enol rotamers, namely 3-2 to 3-6. It is worth noticing that energy differences between these conformers do not exceed 0.9 kcal/mol. In the case of the water solvation model, the situation is different: structure 3-5 becomes the most stable, and the energy difference between this structure and the next stable ones increases to 1.5 kcal/mol. For the MK cavity type, in acetone and water, the two most stable conformers have two keto groups in the first ring and differ by the presence of the hydrogen bond between groups attached to the first and eighth carbon atom in the naphthalene ring (C1 and C8 groups), respectively. Atom numbering is given in Figure 1. These structures are 1-1 and 1-2. The difference between the most stable 1-1 and the next stable all-enolic compound is larger than 3 kcal/mol. When the UAHF cavity model is applied, the lowering of the relative stability of structures that were most stable in calculations with the MK cavity model is observed. Nevertheless, this change in the acetone solvent model conserves the highest preference toward the di-keto 1-1 form, but only by about 1.4 kcal/mol, with respect to the second most stable tri-enolic compound 3-5. In water, in the same cavity model, a further increase in the relative stability of the fully enolic tautomers occurs, which leads to equal energies of these structures. It is worth noticing that the UAHF and UA0 cavity models do not show preference to the structure 1-2, which is the case in the MK model. When the PM3 method is studied, it can be seen that results are more

8316 J. Phys. Chem. B, Vol. 111, No. 28, 2007

Rostkowski and Paneth

TABLE 1: Studied Structures of 1,3,8-Trihydroxynaphthalenea

a The first number in the name of the structure describes the number of hydroxyl groups in the molecule. The second one is the running number of the structure.

Stability of 1,3,8-Trihydroxynaphthalene Conformers

J. Phys. Chem. B, Vol. 111, No. 28, 2007 8317

TABLE 2: Relative Energies of 1,3,8-Trihydroxynaphthalene Structures Optimized Using the Continuum Solvation Model CPCM theory level AM1

PM3

HFc

B3LYPc

MPW1PW91c

theory level AM1

PM3

HFc

B3LYPc

MPW1PW91c

cavity model

solvent

3-2 a

UA0 UA0 MK MK UAHF UAHF UA0 UA0 MK MK UAHF UAHF UA0 UA0 MK MK UAHF UAHF UA0 UA0 MK MK UAHF UAHF UA0 UA0 MK MK UAHF UAHF

acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water

0.68 0.83 b -0.09 0.14 0.63 -0.27 -0.22 -0.25 -0.24 -0.34 -0.23 -0.46 -0.44 -0.67 -0.32 -0.87 -0.41 -0.35 -0.39 -0.41 -0.30 -0.65 -0.34 -0.35 -0.39 -0.41 -0.29 -0.79 -0.36

cavity model

solvent

2-10

UA0 UA0 MK MK UAHF UAHF UA0 UA0 MK MK UAHF UAHF UA0 UA0 MK MK UAHF UAHF UA0 UA0 MK MK UAHF UAHF UA0 UA0 MK MK UAHF

acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone water acetone

20.29 20.07 15.63 14.57 20.98 19.19 20.72 20.49 16.57 15.61 22.09 20.10 25.01 24.61 18.70 17.04 26.38 22.68 23.42 22.99 18.97 17.80 24.73 21.16 24.93 24.56 20.56 19.42 26.11

3-3

3-4

3-5

3-6

2-1

0.85 0.67 -0.42 -0.65 1.65 0.95 2.42 2.21 2.14 1.95 3.63 2.65 1.73 1.42 2.83 2.86 4.48 2.26 2.32 2.00 3.89 3.74 5.15 2.91 2.36 2.04 3.96 3.80 5.17 2.92

0.48 0.64 -0.39 -0.97 0.02 -0.24 -0.32 -0.23 -0.30 -0.17 -0.26 -0.23 -0.73 -0.70 -0.81 -0.50 -1.15 -0.66 -0.53 -0.49 -0.41 -0.34 -0.76 -0.48 -0.54 -0.51 -0.43 -0.34 -0.79 -0.50

0.47 -0.33 -0.21 -0.03 0.44 -0.47 -0.45 -0.62 -0.42 -0.46 -0.45 -0.95 -0.92 -0.94 -0.56 -1.50 -0.89 -0.74 -0.71 -0.47 -0.54 -1.11 -0.66 -0.76 -0.72 -0.51 -0.40 -1.26 -0.69

0.58 0.44 -0.67 -0.80 1.40 0.75 2.15 2.01 1.96 1.79 3.43 2.45 1.11 0.75 2.27 2.30 3.60 1.65 1.87 1.52 3.47 3.38 4.48 2.47 1.89 1.53 3.53 3.41 4.48 2.48

4.83 4.95 1.55 1.37 3.01 3.63 1.93 2.19 -0.73 -0.81 0.98 1.01 3.07 3.41 -3.35 -3.75 -0.72 -0.04 4.61 5.01 -0.87 -1.10 0.41 1.34 5.34 5.75 0.20 -0.21 0.93 1.95

2-11

2-12

2-13

2-14

1-1

5.32 5.34 2.72 2.47 5.82 5.02 4.45 4.40 2.47 2.20 5.57 4.21 5.20 5.13 1.05 0.33 6.03 3.80 9.67 9.69 6.73 6.07 10.37 8.20 10.67 10.70 7.77 7.32 11.20

5.35 0.66 1.76 17.74 17.93 15.80 18.18 15.88 17.21 16.25 5.36 1.12 1.94 18.09 18.06 16.34 18.25 15.90 17.30 16.53 2.75 -3.72 -3.12 12.94 10.54 12.44 10.56 11.53 9.00 2.56 -4.25 -3.39 12.36 11.73 9.81 10.63 8.08 5.80 -1.41 1.49 16.15 17.91 13.57 18.04 16.41 17.46 15.38 5.06 -0.28 0.97 16.31 17.01 14.33 16.43 15.06 15.74 14.39 4.28 -4.38 -1.81 11.94 14.82 11.17 15.53 13.74 14.26 9.53 4.48 -3.98 -1.60 12.21 15.10 11.57 16.09 13.71 14.67 9.57 2.68 -8.80 6.82 10.29 6.14 10.81 9.57 4.49 2.36 -9.23 -6.46 6.28 9.68 5.83 9.81 8.04 8.53 3.26 5.63 -5.65 -1.40 11.18 16.14 10.04 16.97 15.11 15.78 9.63 4.31 -5.22 -2.24 10.92 14.76 10.20 15.00 13.48 13.82 10.67 5.26 -2.25 1.54 16.73 19.81 13.79 20.02 17.55 19.38 19.02 5.17 -1.55 1.71 17.15 19.86 14.41 20.01 17.34 19.14 17.76 1.11 -13.53 2.90 1.24 8.68 6.74 2.92 0.40 -14.17 -8.99 1.55 6.84 -0.05 6.76 4.71 5.76 -0.92 6.14 -8.22 -0.32 11.87 18.94 8.26 18.52 17.30 18.54 15.04 3.85 -6.99 -2.20 11.68 16.05 8.88 15.12 13.90 14.79 10.52 9.74 3.48 8.62 20.48 25.68 17.56 25.46 23.60 24.88 30.20 9.73 4.31 8.87 21.04 25.81 18.33 25.50 23.47 24.80 30.64 6.80 -6.35 8.53 16.63 6.59 15.01 16.00 15.99 6.16 -6.88 0.28 7.36 15.27 5.53 14.89 13.38 14.10 13.84 10.51 -3.33 6.22 14.84 24.40 11.11 23.38 22.90 23.57 25.25 8.26 -1.57 4.79 14.92 21.61 12.14 20.38 19.68 20.13 22.73 10.75 4.50 9.91 22.34 27.81 19.20 27.65 25.73 27.07 32.74 10.73 5.36 10.18 22.93 27.98 20.02 27.71 25.60 26.98 33.23 8.03 -4.97 10.91 19.03 8.57 18.97 17.53 19.35 7.48 -5.40 1.96 9.87 17.97 7.84 17.73 16.07 16.78 17.20 11.34 -2.58 7.27 16.40 26.13 12.42 25.29 24.77 25.47 27.46

4.27 4.63 1.77 2.53 3.30 0.68 0.96 -1.12 -1.11 -0.25 0.10 0.59 1.03 -4.97 -5.33 -2.86 -1.79 3.16 3.67 -1.80 -2.00 -0.66 0.53 3.83 4.36 -0.70 -0.97 -0.20

4.24 4.39 1.85 2.40 3.32 0.73 1.05 -1.03 -0.91 -0.29 0.16 0.45 0.95 -5.13 -5.36 -3.03 -1.87 3.06 3.67 -1.79 -2.00 -0.77 0.48 3.71 4.34 -0.82 -1.00 -0.34

2-2 3.41 0.73 1.94 2.76 0.90 1.22 -1.22 -1.17 0.22 0.53 0.97 1.37 -4.77 -4.98 -2.40 -1.29 2.95 3.40 -1.78 -2.15 -0.76 0.49 3.60 4.08 -0.93 -1.16 -0.29 1.06 1-2

2-3

2-4

2-5

2-6

2-7

2-8

2-9

5.90 4.54 4.39 20.42 5.07 18.59 5.01 5.85 4.55 4.50 20.30 5.16 18.75 4.99 2.49 1.78 14.62 2.47 2.16 1.46 1.97 15.39 14.20 2.14 6.20 5.14 4.06 20.35 4.88 18.04 5.64 5.15 4.42 4.23 19.02 4.88 18.06 5.05 5.52 4.56 2.48 19.45 2.74 17.15 -1.72 5.41 4.00 2.65 19.40 2.83 17.23 4.78 2.78 2.46 0.67 13.57 2.72 2.42 2.00 0.38 14.16 0.45 12.96 2.48 6.47 5.24 2.59 19.73 3.08 17.26 6.24 5.12 2.57 18.50 16.99 5.18 7.10 5.14 2.39 2.94 21.57 3.93 6.87 4.93 2.54 25.51 2.97 21.54 3.72 2.31 -3.64 17.57 -3.57 14.16 -0.73 1.48 0.31 -4.16 15.75 -4.09 13.01 -1.42 7.42 5.90 0.76 24.32 1.39 20.12 5.24 5.00 3.82 0.96 22.59 1.44 19.67 3.09 10.39 8.90 5.13 23.40 5.09 20.13 6.88 10.18 8.70 5.30 23.26 5.17 20.10 6.68 6.84 5.98 0.16 3.65 6.27 5.44 -0.51 15.39 -0.87 13.08 2.99 10.53 9.53 3.46 21.89 3.34 18.66 8.20 8.31 7.56 3.55 20.35 3.50 18.18 6.00 11.43 9.86 6.05 24.99 6.04 21.54 7.85 11.22 9.68 6.24 24.88 6.15 21.54 7.69 8.27 7.13 1.28 18.52 15.64 4.74 7.49 6.62 0.73 17.14 0.40 14.74 4.23 11.39 10.34 4.06 23.36 4.16 19.95 9.00 9.27 8.46 4.44 21.85 4.40 19.53 6.92 1-3

1-4

1-5

1-6

1-7

1-8

0-1

a All energies refer to the energy of the structure denoted as 3-1 for the same choice of the method and representation of the environment used. Energies are given in kilocalories per mole. b Geometries not converged. c In the 6-31+G(d,p) basis set.

similar throughout the solvent methods used. The most stable are di-keto 1-1 and 1-2 C8 hydroxyl rotamers. When MK radii are being used for the cavity definition, in addition to the most stable di-keto form, mono-keto compounds 2-2, 2-12, and 2-11 also become fairly stable unlike the results obtained with the

UAHF model. As a result, in acetone, energies for 2-11 and 2-12 rotamers are comparable to those for structures denoted as 3-(2,4,5). Tautomer 2-2 is not as stable as in the case of the MK cavity model, but it is still more stable than tri-enolic tautomers. The UA0 cavity does increase energies for structures

8318 J. Phys. Chem. B, Vol. 111, No. 28, 2007

Figure 2. Dependence of the energy (with mean error bars) on the mean HOMA index for sets of structures having the same number of hydroxyl groups.

2-11, 2-12, and 3-4 in contrast to the remaining models. For all PM3 results, it is worth pointing out that rotamers with three enolic groups 3-(2,4,5) have similar relative energies compared to the conformer 3-1, regardless of the solvent and its cavity model used. Besides, for this theory level, stabilization of diketo rotamers 1-1 and 1-2 is more important than for AM1. For Hartree-Fock calculations, again di-keto structure 1-1 is of the lowest energy. Nevertheless, with the UA0 cavity model, the energetic preference for this tautomeric form is not very strong. Its energy, compared to the second stable tautomer in the same solvation model, is lower by about 1.3 and just 0.6 kcal/mol for acetone and water, respectively. In contrast, remaining cavity models show higher stabilization for the diketo structure 1-1, C1-keto 2-2, and C8-ketos 2-11 and 2-12. Use of the MK model leads to an odd preference of C3-keto rotamers denoted as 2-5, 2-9, and 2-7 and di-keto tautomer 1-2 for both solvents, as well as tri-keto tautomer 0-1 in water. In the UAHF model, the energy preference of the most stable structures over the remaining ones is decreased. DFT methods are the most reliable among the presented theory levels, and when used with the UA0 cavity model, they show good agreement with experimental results. When cavity models other than UA0 are applied, the order of tautomer stabilities in MPW1PW91 and B3LYP looks similar to that obtained in Hartree-Fock calculations, although the preference toward 2-11, 2-12, 1-2, and 3-1 tautomers is less pronounced. Stabilization of keto moieties is considerably lower with the UAHF cavity model than with the MK model. This trend is noticeable mostly for water parameters, where, except for 1-1, keto forms have higher energies than tri-enolic ones when the B3LYP functional is used. In MPW1PW91 calculations, these keto structures further increase their energies, which makes the energy of the structure 1-1 equal to all-enol rotamers 3-4 and 3-5. The most important observation that can be made is the fact that in DFT calculations no preference for di-keto structures is seen with the standard Gaussian cavity (UA0) model for either solvent. The most stable in these cases are fully enol rotamers 3-5, 3-4, and 3-2 listed in order of their increasing energy. We have estimated aromaticity for all studied structures, in acetone with the UA0 cavity model at the MPW1PW91 theory level. We used the harmonic oscillator model of aromaticity (HOMA)25 to describe π-electron delocalization in naphthalene rings. This index estimates aromaticity from the deviation of geometry from the optimum structure of an aromatic system. The dependence of mean energies on the mean HOMA index for each group of structures collected by the criterion of the same number of hydroxyl groups is presented in Figure 2. It can be observed that change of the hydroxyl moiety into the

Rostkowski and Paneth keto group decreases the aromaticity of the system and increases the averaged energy by about 10 kcal/mol. Thus, structures with all hydroxyl groups are most stable. Three exceptions from this trend are structures 2-(6,8,10) where large energetic destabilization is observed compared to other isomers containing two hydroxyl groups. The common feature of these structures is the presence of a hydroxyl attached to C1 and the aliphatic group in the second position. It thus appears that such an arrangement is responsible for the lowered stability of these structures. Using the MPW1PW91 functional, we have also optimized geometries using the SM5.43 and SM6 solvation models to represent acetone and water. Results for these calculations are collected in Table 3. Both of the Minnesota models point out to structures 2-11, 2-12, and 2-2 as well as di-keto 1-1 as the most stable ones. Differences in their relative energies are small. In general, considering the water model as a solvent increases energies of fully enolic compounds slightly less in comparison to other tautomers. The conclusion from the comparison of the stabilities of tautomers in solution is that for all tested theory levels in the least stable compounds the keto group is attached to the third carbon atom in the naphthalene ring and the aliphatic carbon atom in the second instead of the fourth position, namely rotamers 2-10 and 2-6. Unfavorable configuration also characterizes structures having all three or two (in positions 1 and 8) carbonyl groups; i.e., structures 0-1, 1-5, and 1-4. As one could expect, conformers having hydroxyl groups attached to carbon atoms in positions 1 and 8 without hydrogen bonding between them are not stable either. The only exception to this observation is tautomer 1-2 in PM3 calculations. In general, differences in energies between the third and the second most stable tautomeric forms are much smaller than differences between the first and the second ones. It also seems that the solvation model and theory level have greater influence on the relative energies of the keto compounds than on those of the fully enolic ones. Solvent models with MK and UAHF cavities show higher preference toward keto tautomers, rather than to the fully enolic ones, than in case of the UA0 cavity model. Combinations of the theory level with the solvent representation that give agreement with experimental results, i.e., higher stabilization of enolic tautomers than keto forms, are obtained only for AM1 and DFT methods when the UA0 cavity model is incorporated. From the three tested models of cavity, the UAHF model is sensitive to connectivity and hybridization and has been optimized for the HF level. Since hybridization changes significantly among studied structures, this model may be expected to have larger errors than the other two cavity models that are insensitive to both hybridization and connectivity. Out of these two UA0 has been optimized for the DFT levels and thus is performing better for these levels. Among the tested DFT functionals, MPW1PW91 performs better for reaction barriers than B3LYP. Good performance of the semiempirical AM1 Hamiltonian is not surprising since similar systems have been used in its parametrization. Therefore, we have chosen AM1 and MPW1PW91 theories with the CPCM solvation model that uses the UA0 cavity type for further studies of 1,3,8-trihydroxynaphthalene. Inclusion of solvents in calculations facilitates getting closer to real systems although some simplifications regarding the surrounding environment are necessary. Such improvement of calculations, on the other hand, leads inevitably to the increase in the time of calculations. For complex systems, this can make theoretical investigation impractical. We have, therefore, carried calculations with solvation models referred to as rigid models,

Stability of 1,3,8-Trihydroxynaphthalene Conformers

J. Phys. Chem. B, Vol. 111, No. 28, 2007 8319

TABLE 3: Relative Energies of 1,3,8-Trihydroxynaphthalene Structures Optimized Using the SM5.43 and SM6 Solvent Models at the MPW1PW91/6-31+G(d,p) Theory Level solvent model

solvent

3-2

3-3

3-4

3-5

3-6

2-1

2-2

2-3

2-4

2-5

2-6

2-7

2-8

2-9

SM5.43

acetone water water

-0.99a -0.92 -0.97

4.77 4.91 5.12

-1.17 -1.12 -1.19

-1.36 -1.30 -1.49

3.89 4.04 4.10

-1.66 b -1.49

-3.08 -2.17 -2.80

9.14 9.76 9.23

8.11 8.78 8.17

3.49 4.19 3.54

22.81 23.31 22.25

3.97 4.69 3.40

20.21 20.96 19.67

8.09 8.90 8.58

solvent model

solvent

2-10

2-11

2-12

2-13

2-14

0-1

SM5.43

acetone water water

25.18 26.08 25.55

-3.15 -2.29 -3.05

-3.29 -2.36 -2.90

8.83 9.43 8.74

9.29 9.91

SM6

SM6

1-1

1-2

1-3

1-4

1-5

1-6

1-7

1-8

-3.55 -5.22

5.04 6.01 4.69

12.92 14.01 11.69

23.45 24.54 22.99

10.86 12.51 10.77

23.60 24.83 23.50

19.53 20.18

20.24 20.90

a

All energies refer to the energy of the structure denoted as 3-1 for the same choice of the method and representation of the environment used. Energies are given in kilocalories per mole. b Geometries not converged

TABLE 4: Relative Energies of 1,3,8-Trihydroxynaphthalene Structures, in Calculations with the Rigid Continuum Solvation Models at the MPW1PW91/6-31+G(d,p) Theory Levela solvent model solvent CPCM CPCM IEF IEF SCI SCI SM5.43 SM5.43 SM6

acetone water acetone water acetone water acetone water water

3-2

3-3

3-4

3-5

3-6

2-1

2-2

-1.68b

6.14 2.33 1.99 2.57 2.07 5.10 5.00 4.72 4.83 5.06

-1.56 -0.56 -0.53 -0.61 -0.54 -0.69 -0.60 -1.22 -1.14 -1.15

-1.84 -0.79 -0.78 -0.83 -0.79 -0.95 -0.87 -1.38 -1.28 -1.44

4.95 1.86 1.52 2.07 1.58 4.48 4.44 3.82 3.98 4.10

-0.90 5.11 5.52 4.81 5.43 1.26 1.47 -1.35 -0.55 -1.15

-2.75 3.31 3.79 3.01 3.70 -0.03 0.23 -2.79 -1.90 -2.46

-0.38 -0.41 -0.43 -0.43 -0.57 -0.47 -1.07 -0.97 -1.03

2-3

2-4

2-5

2-7

2-9

2-11

2-12

12.53 11.18 3.55 4.92 10.11 -1.87 -2.49 11.45 9.82 6.20 6.22 8.02 3.57 3.45 11.28 9.68 6.46 6.37 7.91 4.09 4.06 11.45 9.84 5.94 5.97 8.00 3.30 3.15 11.29 9.69 6.38 6.30 7.91 4.01 3.97 11.11 9.97 3.85 3.93 8.61 0.37 0.25 11.05 9.92 3.96 3.97 8.57 0.59 0.51 9.30 8.28 3.52 4.05 8.16 -2.74 -3.01 9.85 8.93 4.19 4.73 8.87 -1.93 -2.14 9.31 8.32 3.47 3.40 8.50 -2.62 -2.63

2-13

2-14

1-1

1-2

12.73 10.65 10.68 10.69 10.69 11.06 10.96 9.06 9.62 8.94

13.25 10.72 10.80 10.79 10.81 11.22 11.10 9.51 10.07 9.56

-5.69 3.98 4.81 3.50 4.67 -2.51 -2.20 -4.78 -3.39 -4.93

7.68 9.69 9.97 9.52 9.92 6.76 6.77 5.19 6.31 4.94

a Calculations were performed for the gas-phase optimized structures at the same theory level. b All energies refer to the energy of the structure denoted as 3-1 for the same choice of method and representation of environment used. Energies are given in kilocalories per mole.

TABLE 5: Relative Energies of 1,3,8-Trihydroxynaphthalene Structures Optimized in the Gas Phase and Diethyl Ether Represented by the Continuum Solvation Model CPCM for the UA0 Cavity Type theory level solvent AM1 ether DFTb ether

3-2 -0.72a 0.34 -1.68 -0.78

3-3

3-4

3-5

3-6

2-1

2-2

2-3

2-4 2-5 2-7 2-9

2.25 -0.70 -0.58 1.76 2.16 0.48 7.42 5.95 3.83 1.07 0.17 0.24 0.71 4.24 2.75 6.27 4.89 4.34 6.14 -1.56 -1.84 4.95 -0.90 -2.75 12.53 11.18 3.55 3.14 -0.85 -1.05 2.46 3.94 2.15 11.77 10.25 5.61

2-11 2-12 2-13 2-14

1-1

1-2

5.59 6.58 1.66 1.11 7.08 7.18 -2.80 2.37 5.31 5.34 3.73 3.53 5.80 5.86 0.06 1.98 4.92 10.11 -1.87 -2.49 12.73 13.25 -5.69 7.68 5.98 8.44 2.66 2.29 11.24 11.44 2.25 9.57

a

All energies refer to the energy of the structure denoted as 3-1 for the same choice of the method and representation of the environment used. Energies are given in kilocalories per mole. b MPW1PW91/6-31+G(d,p).

in which the solvation energy is evaluated using the gas-phaseoptimized geometry. This approach dramatically reduces the costs of calculations but may fail if large geometry changes are expected on the transition from the gas phase to the solution. Because semiempirical methods are much less time consuming than DFT, we have tested several rigid models using gas-phase geometries obtained at the MPW1PW91 DFT level (with the 6-31+G(d,p) basis set). Energy calculations with solvent models were performed at the same theory level. Table 4 lists results obtained for the gas phase, acetone, and water represented by the CPCM model with the UA0 cavity and for the comparison by the IEFPCM, SCIPCM, and Minnesota solvation models SM5.43 and SM6. For all energy calculations, tight convergence criteria were applied. The least stable structures have been removed from Table 4. They can be found, together with analogical results for Hartree-Fock and B3LYP levels in the Supporting Information. Comparison of rigid models to results of geometry optimizations with the solvent indicates that the contribution from the system geometry relaxation is minor, especially for tautomers with the lowest energies. The differences are too small to change the qualitatively obtained order of stabilities of tautomers and their rotamers. IEFCPCM has slightly higher influence on energies, especially on keto moieties

than the CPCM. Incorporating acetone and water using Minnesota solvation models leads to high preferences for keto moieties, higher than those found with the SCICPCM. Tautomers 1-1, 2-2, 2-12, and 2-11 are the most stable. It is interesting to note that comparison of conformer stabilities in water, modeled by the new model SM6, which is parametrized so far only for this solvent, reveals similarity to acetone represented by the previous SM5.43 model rather than to water. We can conclude that rigid solvation models are almost as good as those which involve reoptimization with a solvent model, but they are much less CPU-demanding. Thus, rigid solvation models can be considered a valuable theoretical tool for studying the tautomeric equilibrium of different trihydroxynaphthalene forms. Viviani et al.,4 noticed that chemical reduction of 1,3,8trihydroxynaphthalene does not occur in acetone, because the only stable forms are nonreactive enols. They justified this conclusion by showing the reduction of tetrahydroxynaphthalene, which exists in keto tautomer forms, under the same conditions. One of the goals of the present work is to identify tautomeric forms of 1,3,8-trihydroxynaphthalene dominant in the active site of the trihydroxynaphthalene reductase. Active sites of enzymes are believed to provide an environment of polarity lower than the bulk solution. An apparent dielectric

8320 J. Phys. Chem. B, Vol. 111, No. 28, 2007 constant of between 2 and 12 is usually assumed for an active site.26 We have, therefore, carried out calculations in the gas phase and in diethyl ether, modeled by the CPCM, which exhibits an apparent dielectric constant of 4.2. Calculations in the gas phase and in the presence of diethyl ether were performed at theory levels and with the cavity model that proved to reproduce experimental results as discussed above. Moreover, the least stable structures have been removed from considerations. The results are collected in Table 5. A complete set of data for the other theory levels, remaining cavity types, and structures is given in the Supporting Information. In general, the behavior of systems in diethyl ether is similar to that previously described for the other solvents. For the semiempirical AM1 and MPW1PW91 DFT levels of theory, in the presence of solvent with the UA0 cavity model, the lowest energies were obtained for tri-enolic tautomers of trihydroxynaphthalene. DFT calculations point to 3-5, 3-4, 3-2, and 3-1 structures as the most stable, while the results of AM1 calculations yield 3-1 as the most stable and the di-keto 1-1 as the second most stable. The next stable compounds are the same as for higher theory levels. In the case of AM1, the calculated energy difference between the most stable structures is small. Gas-phase calculations, as well as the remaining cavity models, show strong preference for the keto forms, especially for the di-keto 1-1. Conclusions The obtained results lead to the rather worrying observation that most of the methods incorporating a liquid environment are inconsistent with the experimental results of tautomerism of 1,3,8-trihydroxynaphthalene. In fact, the only methods giving qualitative agreement with experiments are AM1, MPW1PW91, and B3LYP but only when the UA0 cavity model is chosen. They evaluate tautomerization equilibrium to be shifted toward fully aromatic structures. Other theories in combination with studied solvent cavities give preference to the keto tautomers, especially to the di-keto structure, having both carbonyl groups in the first ring, that were not detected experimentally in solutions. Unfortunately, even for methods that point to tri-enolic forms as the most stable, the most stable among keto tautomers was di-keto 1-1. Although it has been shown that only a supplement of water in solution causes the appearance of carbonyl moieties in NMR spectra for trihydroxynaphthalene, in fact water in the presented simulations was destabilizing keto moieties by about 0.8 kcal/mol instead of stabilizing them. We have chosen the MPW1PW91 DFT functional as being more reliable than B3LYP for description of trihydroxynaphthalene because of its better performance for the theoretical description of the reaction barriers. It was also shown that relaxation of the systems does not play the crucial role in the stabilization for given systems. It is important to keep in mind that, in general, AM1 results give lower differences in energies between the most stable enolic structures and stable ones possessing keto groups, what is in agreement with the experimental data. Moreover, good performance of this semiempirical method suggests that it can be applied for complex calculations, e.g., for considering a biological environment of the studied system within a quantum mechanics/molecular mechanics (QM/MM) or ONIOM scheme. Acknowledgment. Access to the Supercomputer and Networking Center (PCSS), Poznan, Poland, and the Minnesota Supercomputer Institute (MSI), Minneapolis, MN, is greatly appreciated. This work was supported by the Grant 3 T09A 076 28 from the Ministry of Science and Higher Education, Poland.

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