Thermochemistry of Uracil, Thymine, Cytosine, and Adenine - The

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Thermochemistry of Uracil, Thymine, Cytosine, and Adenine Adam Ganyecz, Mihaly Kallay, and Jozsef Csontos J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b02061 • Publication Date (Web): 12 Apr 2019 Downloaded from http://pubs.acs.org on April 12, 2019

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The Journal of Physical Chemistry

Thermochemistry of Uracil, Thymine, Cytosine, and Adenine ´ am Ganyecz,∗ Mihály Kállay, and József Csontos Ad´ Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, Budapest P.O.Box 91, H-1521 Hungary E-mail: [email protected]

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Abstract The goal of this study is to give reliable and accurate thermochemical data for uracil, thymine, cytosine, and adenine. The gas-phase heats of formation of these compounds were determined with the diet-HEAT-F12 protocol, which uses explicitly correlated coupled-cluster calculations along with anharmonic vibrational, scalar relativistic, and diagonal Born–Oppenheimer corrections. The thermochemically relevant tautomers of cytosine were also investigated. To derive heats of formation in the gas and solid phases as well as sublimation enthalpies, the thermochemical network approach was utilized, i.e., the available literature data were collected, reviewed, and combined with our theoretical calculations. Solvation free energies were also determined with various methods and compared to experimental data.

Introduction Unquestionably, nucleobases, the purine bases adenine and guanine and the pyrimidine bases thymine and cytosine play essential roles in many biological processes. They are the building blocks of nucleic acids, encoding the information of protein sequences needed for the living organism. In DNA the Watson–Crick base pairs, guanine-cytosine and adenine-thymine, stabilize the double helix structure through the hydrogen bonding of these nucleobases. The derivatives of adenine also have important role in cellular respiration (ATP, NAD, FAD). Because of their biological significance, it is also important to know how nucleobases formed before living organisms appeared on Earth. 1–3 To have accurate energetics of the processes involving nucleobases, and to improve our understanding of structure-property relationships, high-quality thermochemical data are crucial. Despite of these needs, the available experimental data are in disarray, especially the sublimation enthalpies. For example, in the case of adenine the sublimation enthalpy values are scattered in a 30 kJ/mol range. 4 Nevertheless, high-level ab initio calculations in the gas phase can help sorting out these discrepancies if the heat of formation values are 2


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well-established in the solid phase. However, there is also some uncertainty surrounding the combustion enthalpy values, which have been used to derive the heat of formation of the nucleobases. On the one hand, from a practical, thermochemical point of view, the main issue is the low vapor pressure of the nucleobases, which makes the measurement of the heat of sublimation difficult. On the other hand, the temperature correction to the sublimation enthalpy can also be problematic. The currently utilized method is based on the empirical correction of Chickos and Acree. 5,6 However, well-established heat capacities can be easily computed nowadays with quantum chemical methods. A decade ago, to obtain reliable enthalpies for the nucleobases, the available thermochemical data were revised by Dorofeeva and Vogt; 7 the results were also supported by Gaussian-3X (G3X) calculations. 8 Recently, Emel’yanenko and associates 4,9 measured the heat of combustion and sublimation of uracil, thymine, cytosine, and adenine. Gaussian-n 10 (G3 and G4) calculations were also performed to corroborate their results. Although their results seem to be consistent, the more sophisticated and more reliable Weizmann protocols, 11,12 namely W1-F12 and W2-F12, 13 yield results that lie outside of their error bars reported. We also highlight the fact that larger species can have various thermodynamically relevant tautomers. Therefore, if accurate data is needed one should account for possible isomers. Hobza and his coworkers extensively studied the tautomers of nucleobases in the gas phase 14–17 and found that uracil, thymine, and adenine have no other relevant form but the canonical structure. However, cytosine has five low-energy tautomers, and not even the canonical form is the most stable. Nevertheless, biological processes take place almost exclusively in aqueous phase, thus additional thermochemical data, such as solvation free energy, is also needed to properly describe and understand these phenomena. The effect of solvation can be treated in numerous ways, i.e., by implicit and explicit solvent models at various theoretical levels using

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molecular dynamics (MD) and hybrid quantum mechanics/molecular mechanics (QM/MM) approaches. Nonetheless, the accurate calculation of absolute solvation free energies is still challenging for biologically important molecules. One goal of this study to provide reliable gas-phase formation enthalpies for uracil, thymine, cytosine, and adenine using the diet-HEAT-F12 protocol 18 taking into account the possible isomers. Another goal is to give reliable and consistent thermochemical values by collecting the available heats of sublimation and formation and combining them with the diet-HEAT-F12 results in a thermochemical network (TN). Besides those, solvation free energies also will be investigated with various implicit and explicit solvation models, and compared with the results derived from experimental data.

Methods Quantum chemical calculations To determine the gas-phase heat of formation of the studied nucleobases (Fig. 1) the recently developed diet-HEAT-F12 18 protocol was utilized. A brief summary of the protocol follows while more details are given in ref 18. The equilibrium structures were obtained with the coupled-cluster singles, doubles and perturbative triples [CCSD(T)] method and the modified cc-pVTZ 19 basis set lacking f functions [cc-pVTZ(-f)]. The total energies, ETOT , were calculated as CABS ∞ ETOT =EHF + ∆ECCSD(T) + ∆ECCSDT + ∆ECCSDT(Q) +

+

∞ ∆Ecore

(1)

+ ∆EZPE + ∆EDBOC + ∆EREL + ∆ESO .

CABS In the above equation, (i) EHF is the complementary auxiliary basis set (CABS) corrected ∞ Hartree–Fock (HF) energy determined with the cc-pVQZ-F12 20 basis set, (ii) ∆ECCSD(T)

stands for the correlation energy evaluated by the explicitly correlated CCSD(F12*)(T) 21

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O

O

NH2

H3 C NH N H

NH O

N H

uracil NH2 N

O

adenine H N

NH2

N

N H

N

thymine

NH2

N

N

N

H N

NH

NH

H N H

O

cytosine 1

N

O

H cytosine 2a

N

O

cytosine 2b

N H

O

cytosine 3a

N H

O

cytosine 3b

Figure 1: The species studied in this work method and extrapolated to the basis set limit using cc-pVXZ-F12 20 (X=T,Q) results, (iii) ∆ECCSDT and ∆ECCSDT(Q) denote the correlation energy increment due to iterative triples (CCSDT) 22 and perturbative quadruple excitations [CCSDT(Q)] 23–25 obtained with the ccpVTZ(-f) and cc-pVDZ basis sets, respectively; in both cases, the cost of the calculations was too high, therefore the second-order Møller–Plesset (MP2) frozen natural orbital (NO) approach was utilized, 26 i.e., the virtual orbitals were transformed to MP2 NOs, and a threshold ∞ of 0.95 was employed for the cumulative occupation number of the NOs, (iv) ∆Ecore is the

core correlation contribution extrapolated from CCSD(T)/cc-pCVXZ 27 (X=D,T) energies, (v) the zero-point vibrational energy (ZPE), ∆EZPE , was calculated at the CCSD(T)/ccpVTZ(-f) level of theory using the harmonic oscillator (HO) approximation; anharmonic contribution were also investigated with the MP2 method with the cc-pVDZ basis set, (vi) the deficiencies of the Born–Oppenheimer (BO) approximation were corrected by adjusting the energy with the diagonal BO correction (DBOC) calculated at the HF/cc-pVTZ(-f) level (∆EDBOC ), (vii) the scalar relativistic contributions (∆EREL ) were collected from exact two-component CCSD(T)/cc-pVTZ-DK 28 calculations, and (viii) the spin-orbit correction 5



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for atoms, ∆ESO , were taken from ref 29. The explicitly correlated calculations were obtained with the Turbomole 7.1 package, 30,31 the CCSDT(Q) calculations were carried out with the Mrcc 32 program, while all other results were obtained with Cfour. 33 The thymine molecule has a large-amplitude low-frequency motion corresponding to the rotation of the −CH3 group, which phenomenon calls for the correction of the rigid rotorharmonic oscillator (RRHO) approximation invoked in our study. To alleviate the errors of the HO model for this internal coordinate the one-dimensional hindered rotor model was applied, 34,35 and the energy levels calculated were used to correct both the ZPE and the thermal correction values. The one-dimensional Schrödinger equation,

−

~2 d2 Ψ + V (ϑ)Ψ = EΨ, 2Ir dϑ2

(2)

was solved using the Fourier grid Hamiltonian method. 36,37 Ir and V (ϑ) are the reduced moment of inertia and the potential obtained from CCSD(T)/cc-pVTZ calculations, respectively. The geometries for the single-point CCSD(T) calculations were provided by systematically changing the C−CH3 torsional angle from 0 to 360◦ by 15◦ increments; the resulting structures were partially optimized keeping only the torsional angle fixed and utilizing the MP2/cc-pVTZ level of theory. 38,39 To get an analytical form of the potential V (ϑ) was expanded in Fourier series,

V (ϑ) =

V0 X + {an cos nϑ + bn sin nϑ}, 2 n

(3)

where V0 , an ’s, and bn ’s are fitted parameters. Ir was calculated at the equilibrium geometries using Pitzer’s approximation. 40,41 The enthalpies were calculated as

HT◦ =ETOT +

RT 2 ∂Ω × + RT, Ω ∂T 6


(4)

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where ETOT , Ω, R, and T denote the total electronic energy, the molecular partition function, the ideal gas constant, and the absolute temperature, respectively. Ω is calculated via the standard formulas of statistical thermodynamics within the ideal gas approximation and using the RRHO approximation. 42 The heats of formation were calculated using the elemental reaction approach. 38,43 For example, using the elemental reaction 4 C + O2 + N2 + 2 H2 −−→ C4 H4 N2 O2 ∆f HT◦ (uracil) can be calculated as ∆f HT◦ (uracil) = HT◦ (uracil) − 4HT◦ (Cgas ) − HT◦ (O2 )−

(5)

− HT◦ (N2 ) − 2HT◦ (H2 ) + 4∆f HT◦ (Cgas ).

The reference state of the elements H2 , O2 , and N2 was defined as it is standard in thermochemistry, whereas for carbon the gaseous atom was used as a reference. For ∆f H0◦ (Cgas ) the ab initio value of ref 44, 711.65 ± 0.32 kJ/mol was adopted and the thermal correction ◦ was obtained from the NIST-JANAF tables 45 resulting in ∆f H298 (Cgas ) = 717.13 ± 0.32

kJ/mol. The size-dependent uncertainties of our results are also given, the 95% confidence interval p 1st 2nd × 0.52 + Natoms × 1.0 kJ/mol, where can be obtained from the following formula 2× Natoms 1st 2nd Natoms and Natoms are the number of the first- and second-row atoms in the molecule. 18 This

formula is based on the root mean square deviation calculated, on a per atom basis, for 26 first- and 36 second-row species. The reliability of the formula was thoroughly tested in heat of formation calculations involving 149 molecules. For more details the reader is referred to ref 18. Cytosine have several thermodynamically relevant tautomers, therefore averaged properties are also given according to the Boltzmann distribution. For an explicit formula of the averaging see ref 38.

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Treatment of available thermochemical data ◦ (g), are not In the literature, firsthand experimental gas-phase heats of formation, ∆f H298 ◦ (cr), available, they are derived from combustion enthalpies of the crystalline compound, ∆c H298

with the help of sublimation enthalpies, ∆gcr H. ◦ ◦ The ∆c H298 (cr) values have been converted to heats of formation, ∆f H298 (cr), using ◦ ◦ auxiliary data, ∆f H298 (H2 O, l) = −285.83 ± 0.04 kJ/mol and ∆f H298 (CO2 ) = −393.522 ± ◦ ◦ 0.005 kJ/mol from NIST-JANAF; 45 ∆f H298 (O2 ) and ∆f H298 (N2 ) are zero by definition.

If it is not stated otherwise, the sublimation enthalpy data were taken from the compilation of Acree and Chickos. 6 To adjust the values to 298.15 K, temperature corrections are needed. Instead of the empirical formula of Chickos, 5 the differences of molar heat capacities, ◦ ◦ (cr)] · (298.15 K − T ), have been used, where ∆gcr HT is the (g) − Cp,m ∆gcr H298 − ∆gcr HT = [Cp,m ◦ (g) stands for the gas-phase heat capacity sublimation enthalpy at temperature T , and Cp,m ◦ obtained from quantum chemical calculations, while Cp,m (cr) is the solid phase heat capacity

taken from literature. Furthermore, where the individual p-T data points were provided, the sublimation enthalpies were recalculated according to the following equations: 46 b R · ln p = a + + ∆gcr Cp,m · ln T

∆gcr HT = −b + ∆gcr Cp,m · T,

T T0

(6) (7)

where a and b are fitting parameters, ∆gcr Cp,m is the difference of molar heat capacities, and ◦ T0 is an arbitrary reference temperature, taken to be 298.15 K. The following Cp,m (cr) data

were used in this work: 131.8, 47 163.0, 47 130.9, 4 and 145.5 4 J/mol· K for uracil, thymine, ◦ cytosine, and adenine, respectively. The corresponding Cp,m (g) values, 108.4, 133.1, 114.1,

and 129.2 J/mol· K, were derived from our calculations using statistical thermodynamics. The uncertainties of the sublimation enthalpies are mostly represented by the standard error of b, or the standard error of the slope of the fitted linear equation to ln(p)-1/T data. However, in the field of thermodynamics, according to IUPAC recommendations, 48 8


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the reported uncertainty should represent the 95% confidence interval. Therefore, assuming ◦ values have been normal distribution, all the original error bars reported for the ∆gcr H298

doubled in this study. To provide well-established and consistent formation and sublimation enthalpies for each species, the available and revised literature data were combined with diet-HEAT-F12 results in a TN. The approach used for obtaining the solution of the TN is reported in detail in ◦ refs 49 and 50. Three types of enthalpy differences can be found in the TN, ∆c H298 (cr), ◦ ◦ which connects the two regression variables, (g) from our calculations, and ∆gcr H298 ∆f H298 ◦ ◦ (cr) values. Details of the TN, i.e., list of reactions with (g) and ∆f H298 namely the ∆f H298

reaction heats, and original references can be found in the Supporting Information.

Solvation free energy Solvation free energy, ∆G◦sol , is defined as the energy required to move the solute from gas (1 M) to aqueous solution (1 M). Solvation free energies can be directly measured but, as detailed below, can also be estimated from experimental vapor pressure and solubility values or determined by various theoretical methods. In our theoretical calculations the CCSD(T)/cc-pVTZ(-f) geometries were used if otherwise not specified.

Vapor pressure and solubility ∆G◦sol can be derived if solubility, csol , and vapor pressure, p, are known: 51 ∆G◦sol = RT ln

p − RT ln csol , p◦

(8)

where p◦ denotes the pressure of an ideal gas at 1 M concentration, 24.45 atm. The solubility data were taken from ref 52, while the vapor pressures at 298 K were calculated from the available p − T data of sublimation enthalpy measurements (see later).

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Implicit solvation models From the family of the implicit solvation models, the Polarizable Continuum Model (PCM), 53 the Solvation Model based on Density (SMD), 54 and the Direct Conductor-like Screening Model for Realistic Solvation (DCOSMO-RS) 55–57 were considered. Furthermore, the conductor-like PCM (CPCM) solvation model was used with the B3LYP/6-31G(d,p) method, while in the SMD calculations the recommended M06-2X/6-31G(d) method was applied. The SMD and CPCM calculations were obtained with the Gaussian 09 program 58 using the default settings. The DCOSMO-RS results were determined at the BP86/TZVP level of theory using the default settings in TURBOMOLE 7.1 with a relative permittivity of 80.

Molecular dynamics The simulations were performed with the GROMACS 2018 software package. 59,60 Molecular dynamics were used to determine the solvation free energy with alchemical free energy calculations using explicit solvent. The second version of the general Amber force field (GAFF2) 61 and Austin-model 1-bond charge correction (AM1-BCC) 62,63 charges were used in the simulations in a dodecahedron with at least 1.2 nm from the solute to the nearest box edge using the TIP3P 64 model of water. After energy minimization, the whole system was equilibrated in the NPT ensemble at 298.15 K and 1 bar. During the 5 ns simulations 2 fs steps were used in combination with stochastic dynamics, 65 τ = 1 ps, and the Parrinello–Rahman pressure coupling, 66 τp = 1 ps, algorithm using the compressibility of water. The electrostatic interactions were calculated with the Particle-Mesh-Ewald (PME) method. 67 The PME-order was 6 with a cut-off radius of 1.2 nm, and a spacing of 0.1 nm. The van der Waals interactions were scaled to zero between 1.0 and 1.2 nm. The neighbor list was updated every 10 steps with the Verlet cutoff-scheme where the cut-off was set to 1.2 nm. All bonds were constrained with the Linear Constraint Solver (LINCS) algorithm 68 of order 12. The Gibbs free energy of hydration was then calculated from the equilibrated solvated systems with alchemical 10


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molecular dynamics simulations, as described above, where the intermolecular interactions between each solute and the solvent were switched off through a λ parameter using soft core potentials with values of σ = 0.3 and α = 0.5 and p = 1 originally proposed by Beutler et al. 69 First the electrostatic interactions were decoupled using the values of the λ parameter [0.00, 0.25, 0.50, 0.75, 1.00] followed by the van-der-Waals interaction at values of [0.00, 0.05, 0.10, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, 1.00]. The analysis of the free energy simulations was performed with the implemented Bennett acceptance ratio method. 70 Reference interaction site model (RISM) 3D-RISM is based on statistical mechanics and the Ornstein–Zernike type integral equation theory of molecular liquids. About the theory and possible implementations the reader is referred to the review of Ratkova et al. 71 In the current work, 3D-RISM was utilized with partial third order series of expansion of the hypernetted chain closure (PSE-3) 72 bridging function and pressure correction (PC+) as described in refs 73 and 74. The python script provided in ref 74 was utilized with the default options, except that the GAFF2 force field was used instead of GAFF with the AmberTools 17 program. 61 The main advantages of RISM are that (i) the results are almost as accurate, for a fraction of computational cost, as those provided by MD calculations, 73 (ii) solvent distribution data is also provided in contrast with the implicit models.

Results Heats of formation and sublimation enthalpies Quantum chemical calculations Table 1 lists the individual contributions of the diet-HEAT-F12 model chemistry to the CABS ∞ ∞ heats of formation at 0 K. The most dominant contributions are ∆EHF , δECCSD(T) , δEcore ,

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harm and δEZPE . The magnitude of the rest of the individual contributions are smaller than 10

kJ/mol. The δECCSDT and δECCSDT(Q) contributions are relatively small, except for adenine, where they are 5.5 and -3.7 kJ/mol, respectively. The sign of these terms is opposite for every species, and their sum falls between -0.5 and 1.8 kJ/mol. The relativistic correction, δErel , is in the range of 7-9 kJ/mol, while the δEDBOC term is practically constant at -0.8 kJ/mol. In the case of cytosine, five tautomers were considered, and the calculated contributions for them are fairly similar. Largest differences occur up to the CCSDT level. We also note that the δECCSDT contribution has even an effect on the stability order of the tautomers: without this term cytosine 2b would be more stable than cytosine 1. Thymine has a large amplitude motion due to the rotation of the -CH3 group, which is treated with the one-dimensional hindered rotor model. The energy barrier of the rotation is 6.2 kJ/mol at the MP2/cc-pVTZ level, which leads to an overall correction of 0.2 kJ/mol to the heat of formation of thymine at 298 K.

Comparison with literature Table 2 shows the available heats of combustion, sublimation enthalpies, gas-phase heats of formation, and the computational results of various model chemistries. The majority of the listed combustion and sublimation data along with our diet-HEAT-F12 result were used in a thermochemical network to provide consistent heats of formation and sublimation for these species. Particular values were excluded from the TN because of their large uncertainty or inconsistency with the other data. The results of de Barros et al. 75 were consistently dismissed, because they are obvious outliers with unrealistic uncertainties. The earlier values of Emel’yanenko 76 were only implicitly included in the TNs, because the authors’ more recent work is built on their previous results. 9 All the dismissed data are indicated with italic in the corresponding columns in Table 2, and the thermochemical networks for each species can be found in the Supporting Information. In the following we separately analyze the thermochemical data for each compound.

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Uracil The combustion enthalpies reported are consistent with each other, except the result of Wilson et al., 77 which differs by 5 kJ/mol from the other records. The ∆gcr H(298) values are more scattered, but most of the data are in the 125-135 kJ/mol range. Bardi et al., 78 Brunetti et al., 79 Szterner et al. 80 and Emel’yanenko et al. 9,76 provided the raw p-T data, which were used to recalculate the sublimation enthalpy at 298 K. Bardi studied the sublimation of uracil with torsion-effusion, thermogravimetry, and transpiration methods, but the results were inconsistent, therefore in this work the data were evaluated separately. The torsion-effusion results of Bardi, 78 146.0±5.2 kJ/mol, and the value of Nowak et al., 81 139.1±16.8 kJ/mol, were excluded from the TN. The reported gas-phase enthalpies of formation for uracil are in line with each other and with the data provided by quantum chemical calculations. Nabavian and associates 82 studied both the combustion and sublimation of the nucleobases and gave −303.1 ± 2.3 ◦ kJ/mol for ∆f H298 (g). This data hardly differs from that listed by Pedley. 83 Dorofeeva and ◦ Vogt, 7 with the help of G3X calculations and revised literature data, reported ∆f H298 (g) =

−301.5 ± 2.5 kJ/mol. Emel’yanenko et al. 9 also conducted experiments to determine the heats of combustion and sublimation, and their slightly higher sublimation enthalpy led them to −298.1 ± 0.6 kJ/mol for the enthalpy of formation of gaseous uracil. Our dietHEAT-F12 model suggests −302.1 ± 3.5 kJ/mol, which is lower than the most recent value of Emel’yanenko, and also lower than the other theoretical data. ◦ ◦ ◦ The TN yielded ∆f H298 (cr) = −429.6 ± 0.5, ∆gcr H298 = 130.5 ± 1.9, and ∆f H298 (g) =

−299.1 ± 2.0 kJ/mol. These results are all consistent with the available literature and our diet-HEAT-F12 calculations.

Thymine There are two preliminary data from 1904 for the heats of combustion of thymine by Fischer and Wrede, 84 and Lemoult, 85 -2369.0 and -2367.3 kJ/mol, respectively. The results of Nabavian et al., 82 Achrainer and coworkers 76 and Emel’yanenko and his associates 9 are in a 3 kJ/mol wide interval [−2362.2, −2359.3] kJ/mol), while the value of da Silva and

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coworkers 86 differs from these by 10 kJ/mol (-2371.2 kJ/mol). The ∆gcr H298 values are spread in an interval of 15 kJ/mol and can be grouped into two disjoint sets: (i) the range of 125–130 kJ/mol contains the results of Teplitsky et al., 87 Burkinshaw and Mortimer, 88 and Emel’yanenko et al.; 9,76 (ii) the range of 134–140kJ/mol includes the data of Nabavian et al., 82 134.1 kJ/mol, Ferro et al., 89 139.6 kJ/mol, and de Barros et ◦ al., 75 136.8 kJ/mol. If ∆gcr H298 was in the second range, then assuming ∆f H298 (cr) = −465 ◦ (g) would be higher than −331 kJ/mol, which contradicts all theoretical calkJ/mol, ∆f H298

culations ([−342.5, −336.7] kJ/mol). Also the higher enthalpy of formation of solid thymine suggested by refs 84–86 would lead to higher enthalpy of formation in the gas phase. The first enthalpy of formation of thymine in the gas phase is reported by Nabavian, 82 −328.7 ± 4.3 kJ/mol and also listed by Pedley. 83 Dorofeeva and Vogt revised this value and based on recent sublimation data got −338.0 ± 2.5 kJ/mol, which is similar to the results of Emel’yanenko et al. 9 (−337.6 ± 0.9 kJ/mol). The diet-HEAT-F12 result is −339.3 ± 3.9 kJ/mol, which is 1–2.5 kJ/mol lower than the values provided by other model chemistries. ◦ Using only those data in the TN, which generate ∆f H298 (cr) result in line with the ◦ (cr) = theoretical results, the solution of the TN provides the following values: ∆f H298 ◦ ◦ (g) = −338.2 ± 1.2 kJ/mol. = 127.4 ± 0.9, and ∆f H298 −465.6 ± 0.7, ∆gcr H298

Cytosine Three out of the four available heat of combustion values are consistent with each other being in the range of [−2067.3, −2064.8] kJ/mol, and the result of Sabbah et al., 90 -2053.2 kJ/mol, considerably deviates from their average. The available sublimation enthalpy data converted to 298 K are in the range of [149.5, 157.4] kJ/mol, the only exception is the 168.8 kJ/mol value of de Barros et al. 75 It is also worth noting that the originally reported uncertainty of Zielenkiewicz et al. 91 was too optimistic compared to the 95% confidence interval obtained from their data points. The most recent values of Emel’yanenko et al. 4 are slightly higher than the rest of the sublimation enthalpies. Nevertheless, these values were obtained independently by utilizing two different approaches

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and they support each other. ◦ (g) data for uracil was determined to be −59.4 ± 10 kJ/mol. 92 After The earliest ∆f H298

reconsidering the available literature data Dorofeeva and Vogt 7 suggested a −69.5 ± 3.5 kJ/mol value. The result of Emel’yanenko 4 is somewhat higher, −66.9 ± 2.1 because of their higher sublimation enthalpy value. Nonetheless, these are consistent with the theoretical calculations, including our diet-HEAT-F12 result, −68.8 ± 3.6 kJ/mol. ◦ ◦ The TN treatment of the available data gives ∆f H298 (cr) = −223.6 ± 1.0, ∆gcr H298 = ◦ (g) = −67.8 ± 2.7 kJ/mol. 155.7 ± 2.6, and ∆f H298

◦ Adenine For ∆c H298 (cr) Stiehler and Huffman 93 measured −2777.1 kJ/mol, which is sim-

ilar to the value of Kirklin and Domalski, 94 −2779.0 kJ/mol. The data of Emel’yanenko et al., 4 −2764.9 kJ/mol, differs from these by more than 10 kJ/mol. It is claimed in ref 4, that in the work of Stiehler and Huffman, during the combustion, carbon had formed, and although this had been corrected in the original work, it still could affect the reliability of the results of ref 93. Kirklin and Domalski used an aneroid vacuum-jacketed microcombustion calorimeter, and the authors of ref 4 also speculated that some amount of unburned carbon formed and could have gone undetected. To corroborate their data, Emel’yanenko and as◦ (cr) = −2765.0 ± 4.6 kJ/mol. sociates used some of the results of Kilday, 95 namely ∆c H298

However, the results of Kilday can be separated into two groups, (i) three of them are in the range of [−2776.7, −2773.5] kJ/mol, and fairly close to the results of Stiehler and Kirklin, (ii) the other three lie in the interval of [−2756.7, −2752.1] kJ/mol, and deviate by about 20 kJ/mol from the data in the first group. One possible explanation to the difference can be the state of the crystalline material. Stiehler and Huffman made two different preparations, one was apparently adenine·3H2 O, and the other is anhydrous adenine. The hydrous adenine after drying gave consistent results regardless of the type of drying, while the anhydrous crystals had lower combustion enthalpy, and also showed mass loss with more drastic heating treatment. After a combination of various drying procedures the heat of combustion of the

15



anhydrous adenine provided consistent results with those of dried hydrous adenine. This observation led the authors concluding that “it may be that on losing the water the ghosts retains the shape of the hydrated crystals but are actually made up of submicroscopic crystals” of anhydrous adenine. Kilday also experienced that different preparation of adenine could lead to different thermochemical values. Based on the solvation enthalpy measurements of recrystallized and vacuum sublimed samples, he found that the vacuum sublimed samples had 4-5 kJ/mol lower solution enthalpy than the others, but this difference decreased with time if the sample had not been protected from atmospheric H2 O. The microscopic images showed that these samples were a mixture of small and larger particles, the latter ones being an agglomerate of the smaller particles, rather than solid crystals. These results led him to conclude that sublimation either increases the amount of tautomers or decreases the crystallinity of the adenine sample, and atmospheric H2 O catalyzes the restoration of the adenine crystal. In a recent study, Stolar and coworkers found a polymorph of adenine, 96 but the lattice energy difference is only 3-4 kJ/mol, which solely does not explain the outlying data of Emel’yanenko. This uncertainty also occurs in sublimation enthalpies: the data are scattered from 128.7 to 146.2 kJ/mol at 298 K. The results of Yanson et al., 97 A. Zielenkiewicz et al., 98 and de Barros et al. 75 are around 130 kJ/mol, while the data of W. Zielenkiewicz 99 and Emel’yanenko et al. 4 are around 140 kJ/mol. Dorofeeva and Vogt, 7 and Emel’yanenko and coworkers 4 list 225.7 and 225.8 kJ/mol, respectively, as the heat of formation of adenine in the gas phase. The first value is based on the combustion calorimetry results of Kirklin and Domalski combined with the sublimation enthalpy of A. Zielenkiewicz et al., while the other is the original result of ref 4. G3X and G4 calculations agree well with these values, yielding 225.3 and 226.6 kJ/mol, respectively. Nev◦ ertheless, more sophisticated calculations suggest higher values for ∆f H298 (g), [228.2, 232.0]

kJ/mol. The difference between W2-F12 and diet-HEAT-F12 can be explained with the sum of the CCSDT and CCSDT(Q) contributions, 1.8 kJ/mol, which is neglected in the W2-F12

16


Page 16 of 38

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theory. Our diet-HEAT-F12 protocol gave 232.0 ± 3.9 kJ/mol, which considerably, by more than 6 kJ/mol differs from the results of Emel’yanenko et al. ◦ ◦ = (cr) = 94.9±3.2, ∆gcr H298 The solution of the thermochemical network resulted in ∆f H298 ◦ (g) = 234.7 ± 5.9 kJ/mol. These results are based on the available 139.8 ± 5.1, and ∆f H298

experimental data and our diet-HEAT-F12 calculations, however, the aforementioned uncertainty in the state of crystallinity of adenine questions the reliability of the values and further investigations are needed.

Solvation free energies Table 3 shows the solvation free energies obtained with various theoretical methods and compares them with results derived from experimental vapor pressures and solubility. At first glance it can be seen that the C-PCM results are consistently higher, while DCOSMORS gives lower value for ∆G◦sol compared to experimental data. Also MD and 3D-RISM results are within 2 kJ/mol, with the exception of cytosine 2a and 2b. For uracil the derived solvation free energy interval agrees well with the experimental result of −69.4 ± 1.1 kJ/mol from the SAMPL2 challenge. 100 The MD and 3D-RISM results, −68.8 and −71.0 kJ/mol, respectively, are closest to the reference ∆G◦sol , while SMD gives a value of almost 15 kJ/mol higher. Similar tendency can be seen for thymine, where both MD, −68.6, and 3D-RISM, −69.7 kJ/mol, data are close to the interval [−66.6, −67.2] kJ/mol derived from experiments, whereas the SMD value, −51.3 kJ/mol, is higher by more than 15 kJ/mol. However, for adenine the SMD result, −69.6 kJ/mol, is the closest to the derived interval, [−74.0, −70.9] kJ/mol, followed by the 3D-RISM and MD values, −67.4 and −64.5 kJ/mol, respectively. For cytosine, one can see that the canonical (1) tautomer has the lowest solvation free energy with every method, which indicates that this can be the most stable tautomer in aqueous solution. The performance of SMD is similar to that of MD and 3D-RISM, but each of them gives at least a 10 kJ/mol higher ∆G◦sol value than the derived interval, [−93.6, −88.9] kJ/mol. The relative solvation free energies of the tautomers qualitatively agree with the 17



results of Hobza et al. 14 For these species, among the methods investigated, MD and 3D-RISM give the most reliable solvation free energies, and without direct experimental data these provide our best estimates for thymine, cytosine, and adenine.

Conclusions This study provides reliable and consistent heats of formation and sublimation enthalpies for uracil, thymine, cytosine, and adenine. On the one hand, the diet-HEAT-F12 protocol ◦ was utilized to provide accurate theoretical ∆f H298 (g) data, by taking into account the

various tautomers of cytosine and the large amplitude motion for thymine. Although this is commonly overlooked, for cytosine the results corroborate previous reports, i.e., in the gas phase the 2a tautomer is the most stable form. On the other hand, the available combustion and sublimation data were revised and recalculated using reliable theoretical heat capacities. In addition, the uncertainties of sublimation enthalpy data were revised to correspond to the 95% confidence intervals. Furthermore, these data and other experimental values were utilized in a TN along with the diet-HEAT-F12 results, yielding our best estimates for the studied thermochemical quantities. In case of uracil, thymine, and cytosine the results are in accord with the reported values of Emel’yanenko. 4,9 However, their error bars might be too optimistic because (i) their uncertainty considered for the sublimation enthalpy does not correspond to the 95% confidence interval, (ii) the supporting literature data of Kilday 95 were not representative, and (iii) the utilized Gn calculations are not the most reliable model chemistries. The available data for adenine contradict each other, which can be attributed to the fact that different preparations of the sample lead to different degree of crystallinity. However, this question requires further investigation, which is out of scope of the present study. This uncertainty ◦ can also be seen in the network results, nevertheless, the ∆f H298 (g) value obtained from the

18


Page 18 of 38

Page 19 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TN agrees well with the diet-HEAT-F12 result. Solvation free energies were also investigated with various methods and compared to the data derived from experiments. Overall, MD and 3D-RISM provided the best performances, which also supports that 3D-RISM can be seen as a cost-effective alternative to MD calculations to determine solvation free energies. For thymine, cytosine, and adenine our study provides the best estimates for solvation free energies.

Acknowledgement The authors are grateful for the financial support from the National Research, Development, and Innovation Office (NKFIH, Grant No. KKP126451). This work was also supported by the BME-Biotechnology FIKP grant of EMMI (BME FIKP-BIO). Time consuming calculations were carried out on the Hungarian HPC infrastructure (NIIF Institute, Hungary).

Supporting Information Available Total energies, geometries, frequencies, anharmonicity constants, and thermochemical networks. This material is available free of charge via the Internet at http://pubs.acs.org.

19


−801.0 −801.5 −800.6

C4 H5 N3 O −2239.0 −2228.4 −2236.4

cytosine 2b

cytosine 3a

cytosine 3b


20 −3.7

−1.3

−1.4

−1.6

−28.7

−23.6

−23.5

−22.8

−22.9

−23.4

−28.5

−23.5

∞ δEcore

192.8

167.5

167.0

167.6

167.7

167.0

198.0

151.2

harm δEZPE

−2.9

−2.3

−2.3

−2.6

−2.6

−2.6

−2.8

−1.9 c

anharm δEZPE

−0.9

−0.8

−0.8

−0.8

−0.8

−0.8

−0.8

−0.8

δEDBOC

b

∆f H0◦

8.9

7.2

7.2

7.1

7.1

7.2

259.3 ± 3.9

−42.5 ± 3.6

−35.8 ± 3.6

−43.5 ± 3.6

−46.4 ± 3.6

−44.8 ± 3.6

8.3 −314.4 ± 3.9

7.1 −282.4 ± 3.5

δEREL

The spin-orbit contribution included.

Hindered rotor correction of 0.02 kJ/mol included, the contribution due to the harmonic frequency of 152.97 cm−1 was replaced.

c

∞ ∞ ∞ 5∆ECCSD(T) (Cgas ) − 52 ∆ECCSD(T) (H2 ) − 25 ∆ECCSD(T) (N2 )

∞ ∞ (adenine) − All values are in kJ/mol. δ denotes the difference of the differences, for instance, for adenine, δECCSD(T) = ∆ECCSD(T)

5.5

1.2

1.2

3.0

−1.6

−1.5

−2.1

−1.1

δECCSDT(Q)

b

a

−2452.6 −1017.3

−800.9

−2242.0

cytosine 2a

C 5 H5 N 5

1.9

−799.9

−2239.2

cytosine 1

adenine

1.6

C5 H6 N2 O2 −3046.4 −1000.0

thymine

3.0

1.2

−810.9

δECCSDT

C4 H4 N2 O2 −2450.1

∞ δECCSD(T)

uracil

CABS ∆EHF

Formula

Species

a

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 1: Contributions to the calculated heats of formation at 0 K.

The Journal of Physical Chemistry Page 20 of 38

-430.5±1.0

-429.4±0.9

-1715.2±1.0

-1716.3±0.9


21 this work

-465.8±1.0

-465.3±1.4

-465.6±0.7

-2359.3±1.0

-2359.8±1.4

Continued on Next Page. . .

ref 9

-453.9±1.0 ref 76

ref 86

ref 82

-2371.2±1.0

ref 85

-457.8

-462.9±0.8

-2367.3

ref 84

-456.1

this work

ref 9

ref 76

ref 77

ref 82

source

-2362.2±0.8

-2369.0

thymine

-424.4±2.2

-1721.3±2.2

-429.6±0.5

-429.6±0.3

◦ (cr) ∆f H298

-1716.1±0.3

uracil

◦ (cr) ∆c H298

ref 9

127.4±1.2d

123.3±0.3 (441 K)

this work

ref 76

125.6±4.0 d

123.2±1.2 (419 K)

127.4±0.9

ref 75

136.8±0.8

ref 88

135.8±0.4 (330 K)

129.1±7.2

127.6±2.6

137±1 (461 K) 124.4±1.3 (403 K) 125.7±3.6 (411 K)

ref 89

139.6±2.8 d

ref 87

ref 82

134.1±8.4

134.1±4.2 (298 K)

ref 9

128.7±0.5 (458 K) this work

ref 76

132.4±1.4d

128.7±0.7 (458 K)

130.5±1.9

ref 75

132.4±1.8 d

ref 80

ref 79

ref 78

128.3±1.0

131.1±10.4d

130.1±1.6d

134.7±15.6d

132.6±4.6d

ref 87

ref 102

ref 81

ref 82

ref 101

source

125.3±0.2 (425 K)

128.6±3.9 (405 K)

130.2±4.9 (405 K)

127.0±2.0 (441 K)

130.6±4.0 (520 K)

146.0±5.2 d

123.0±2.6

120.5±1.3 (403 K)

139.1±16.8

133.9±8.4 (523 K) 124.7

126.2

122.9 (440 K)

121.7 (425 K)

123.5±10.4

◦ c ∆gcr H298

120.5±5.2(426 K)

∆gcr HT b

-338.2±1.2

-337.6±0.9

-338.0±2.5

-328.7±4.2

-328.7±4.3

-299.1±2.0

-298.1±0.6

-301.5±2.5

-302.9±2.3

-303.1±2.3

◦ (g) ∆f H298

this work

ref 9

ref 7

ref 83

ref 82

this work

ref 9

ref 7

ref 83

ref 82

source

-339.3±3.9

-337.1

-336.7

-337.9

-338.1

-342.5

-302.1±3.5

-299.4

-298.9

-299.5

-299.2

-303.6

◦ (g) ∆f H298

a

this work

ref 13

ref 13

ref 9

ref 9

ref 7

this work

ref 13

ref 13

ref 9

ref 9

ref 7

source

diet-HEAT-F12

W2-F12

W1-F12

G4

G3

G3X

diet-HEAT-F12

W2-F12

W1-F12

G4

G3

G3X

method

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 2: Summary of thermochemical data for the studied species.

Page 21 of 38 The Journal of Physical Chemistry

-222.0±1.6

-223.9±0.6

-2066.7±1.6

-2064.8±0.6


22 this work

[−94 .5 , −91 .3 ]

[−74 .5 , −69 .9 ]

82.7±1.3

94.9±3.2

[−2776.7, −2773.5]

[−2756.7, −2752.1]

-2764.9±1.3

Continued on Next Page. . .

ref 4

96.8±1.3

-2779.0±1.3 ref 95

ref 94

94.9±0.9

ref 93

this work

ref 4

ref 103

ref 77

ref 90

source

-2777.1±0.9

adenine

-221.4±2.0

-2067.3±2.0

-223.6±1.0

-235.5±0.4

◦ (cr) ∆f H298

-2053.2±0.4

cytosine

◦ (cr) ∆c H298

157.4±2.4d 157.3±2.4d

155.3±1.1 (422 K) 153.7±0.9 (513 K)

130.6±4.0 142.3±1.8d 141.1±2.2d

130.6±2.0 (330 K) 139.4±0.7 (472 K) 140.1±1.1 (359 K)

139.8±5.1

ref 99

137.7±2.2 (417 K)

this work

ref 4

ref 75

ref 99

ref 98

ref 97

139.6±4.6d

129.2±1.9

128.7±2.8

ref 104

this work

ref 4

146.2±4.2d

144.2±2.0 (422 K)

127.2±3.8 (421 K)

126.4±1.3 (418 K)

100 – 109

168.8±1.0

167.7±0.5 (365 K)

155.7±2.6

ref 91

151.7±0.7 (515 K) ref 75

ref 88

ref 89

149.5±4.2d

155.4±11.6d

ref 92

152.6±5.6

◦ c ∆gcr H298

149.8±5.2

147.2±2.6 (453 K)

147±1 (507 K)

149.9±2.8 (457 K)

∆gcr HT b source

234.7±5.9

225.8±2.3

225.7±3.5

205.7±8.5

-67.8±2.7

-66.9±2.1

-69.5±3.5

-45.3±10.0

-59.4±10.0

◦ (g) ∆f H298

this work

ref 4

ref 7

ref 83

this work

ref 4

ref 7

ref 83

ref 92

source

232.0±3.9

229.8

228.2

226.6

225.3

-68.8±3.6

-68.1

-68.2

-67.7

-71.5

-65.1

◦ (g) ∆f H298

this work

ref 13

ref 13

ref 4

ref 7

this work

ref 13

ref 13

ref 4

ref 7

ref 103

ref

diet-HEAT-F12

W2-F12

W1-F12

G4

G3X

diet-HEAT-F12

W2-F12

W1-F12

G4

G3X

G3B3MP2

method

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Table 2 – Continued

The Journal of Physical Chemistry Page 22 of 38

source

∆gcr HT b

◦ c ∆gcr H298

source

◦ (g) ∆f H298

source

◦ (g) ∆f H298

ref

method

Available data recalculated using the R · ln p = a +

to correspond to 95% confidence limit. b T

+ ∆gcr Cp · ln

T 298.15K

expression, where ∆gcr Cp = Cp (cr) − Cp (g).

Temperature correction to 298 K from experimental heat capacity for solid phase, Cp (cr), and theoretical for gas phase, Cp (g). Uncertainties were doubled or recalculated

d

Originally reported values

c

presented in the last two columns, respectively.

All values are in kJ/mol. The values typesetted in italic are left out from the thermochemical network. Experimental and theoretical gas-phase heats of formation are

◦ (cr) ∆f H298

b

a

◦ (cr) ∆c H298

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Table 2 – Continued

Page 23 of 38 The Journal of Physical Chemistry


23


24

Values are derived from the available p-T data and extrapolated to 298.15 K

Experimental data from ref 52

d

e

[-74.0, -70.9]

Direct experimental value from ref 100

-67.4

[-93.6, -88.9]

[-67.2, -66.6]

[-75.8, -67.5]

c

-64.5

-65.8

-71.9

-58.0

-57.9

-78.0

-69.7

-71.0

Ranges of solvation free energies derived from the p and csol data

-92.0

-65.4

-72.8

-50.9

-51.7

-77.5

-68.6

-68.8

rangeb

b

-69.6

-92.6

-99.8

-76.4

-72.9

-112.0

-112.4

-89.8

3D-RISM

All values are in kJ/mol, unless otherwise noted.

-35.5

adenine

-57.3

-60.8

-60.4

-57.7

-79.0

-51.3

-54.0

MD

a

-37.4

cytosine 3b

-39.5

-30.4

cytosine 2a

cytosine 3a

-51.8

cytosine 1

-32.8

-36.3

thymine

cytosine 2b

-38.3

C-PCM SMD DCOSMO-RS

uracil

species -69.4±1.1c

experimental

csol (mol/l)e

[2.74E-2, 3.55E-2]

[2.28E-14, 5.08E-14] [5.48E-3, 8.69E-3]

[6.95E-17, 4.15E-16] [6.50E-2, 7.20E-2]

1.43E-12

[5.19E-14, 8.70E-13] [2.38E-2, 4.13E-2]

p (atm)d

Table 3: Solvation free energies obtained with various theoretical methods compared to experimental values derived from vapor pressure and solubility. a

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 The Journal of Physical Chemistry Page 24 of 38

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Figure 2: Table of Contents image

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Thermochemistry of Uracil, Thymine, Cytosine, and Adenine - The

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