Density Functional B3LYP Method Research Articles

Adsorption of Cytarabine on the Surface of Fullerene C20: A Comprehensive DFT Study

In this study ، Cytarabine anticancer drug approached fullerene C20 and variations in the chemical properties and reactivity of Cytarabine (anti-cancer drug) the thermodynamic parameters of the formation of nano-derivatives of the Cytarabine with the fullerene C20 nanostructure were calculated. For this purpose, seven states proposed for the formation of nano-derivatives ، all compounds were geometric optimization. Then, the calculations for determining the thermodynamic parameters at a temperature range of 298.15° K to 103.10° K (every one degree) and at a constant pressure of 1 atm and gas phase as well as the aqueous solvent phase is done. All calculations were performed using the B3LYP density functional theory method and the 31G-6* base series using Gaussian, Nanotube Modeler, Gauss view and Spartan software. It was found the optimal temperature for the synthesis of both water and gas phase is 298° K. According to the calculations carried out in the gas phase, the adsorption of V isomer is more likely, but in the aqueous solvent phase, the adsorption of the VI isomer is more probable.

Exploring Cage‐warped Rotation Isomers of C20 Fullerene: MP2 and Density Functional Calculations

Using the density functional methods B3LYP, M06‐2X, PBE1PBE, B3LYP D3, M06‐2X D3, and PBE1PBE D3, and the ab initio MP2 calculations, the optimized atomic structures and energies of C20 cage rotation isomers without a constraint were obtained. The reaction path between the two rotational isomers was then studied, in which there are three local stable atomic structures. One is the most stable fullerene structure with the D2h point group staggered between the upper and bottom pentagons (ST) and the other is the second lowest energy rotational isomer with the Cs point group eclipsed between the upper and bottom pentagons (EC) with a torn fullerene structure (M1) between ST and EC. The first transition structure T1 between the ST and the M1, and the second transition structure T2 between the M1 and the EC were then obtained along the reaction coordinate between these three structures. Vibration analysis of all optimized structures including the transition structures without a constraint was carried out. For each of the rotational isomers obtained by our calculations, thermodynamic stability was explained with the relative energy difference, and then the kinetic stability was analyzed as the HOMO–LUMO energy difference.

Electronic Absorption Spectra and Third-Order Nonlinear Optical Property of Dinaphtho[2,3-b:2’,3’-d]Thiophene-5,7,12,13- Tetraone (DNTTRA) and Its Phenyldiazenyl Derivatives: DFT Calculations

Third-order nonlinear optical (NLO) materials have broad application prospects in high-density data storage, optical computer, modern laser technology, and other high-tech industries. The structures and frequencies of Dinaphtho[2,3-b:2’,3’-d]thiophene-5,7,12,13-tetraone (DNTTRA) and its 36 derivatives containing azobenzene were calculated by using density functional theory B3LYP and M06-2X methods at 6-311++g(d, p) level, respectively. Besides, the atomic charges of natural bond orbitals (NBO) were analyzed. The frontier orbitals and electron absorption spectra of A-G5 molecule were calculated by TD-DFT (TD-B3LYP/6-311++g(d, p) and TD-M06-2X/6-311++g(d, p)). The NLO properties were calculated by effective finite field FF method and self-compiled program. The results show that 36 molecules of these six series are D-π-A-π-D structures. The third-order NLO coefficients γ (second-order hyperpolarizability) of the D series molecules are the largest among the six series, reaching 107 atomic units (10-33 esu) of order of magnitude, showing good third-order NLO properties. Last, the third-order NLO properties of the azobenzene ring can be improved by introducing strong electron donor groups (e.g. -N(CH3)2 or -NHCH3) in the azobenzene ring, so that the third-order NLO materials with good performance can be obtained.

Computational studies on nonenzymatic pyroglutamylation mechanism of N-terminal glutamic acid residues in aqueous conditions*

Spontaneous cyclisation of glutamic acid (Glu) residues located at N-termini in peptides and proteins is called ‘pyroglutamylation’ and is assumed to be involved in several neurodegenerative diseases. Although it has long been believed that N-terminal Glu residues undergo pyroglutamylation enzymatically, it has recently been experimentally confirmed that nonenzymatic pyroglutamylation can proceed in some types of aqueous buffer. However, the detailed mechanism has not been proposed or investigated, and even whether some small-molecule catalysts are required for pyroglutamylation has not been clarified. Therefore, we investigated three types of pyroglutamylation mechanism of N-terminal Glu residues using quantum chemical calculations: in the absence of any catalysts, catalysed by one water molecule, and catalysed by two water molecules. All calculations were performed using N-terminal Glu residues capped with a methylamino group on the C-terminal as a model compound. Optimised energy minima and transition state geometries were obtained using the B3LYP density functional method. The pyroglutamylation mechanism is roughly divided into two steps: cyclisation and dehydration, and the calculated activation barrier was 108 and 107 kJ mol−1 in the two- and three-water-assisted pathways, respectively. The results of computational analysis suggest that water molecules can act as catalysts for pyroglutamylation. The calculated activation barrier of two-water-assisted pyroglutamylation was 108 kJ mol−1, and the results of computational analysis indicate that water molecules can act as catalysts for pyroglutamylation.

Theoretical investigation of the self-association of antitumor drug imexon

The dimers resulting from self-association of oxo-imino, oxo-amino, and hydroxyl-imino tautomers of imexon, that present two hydrogen bonds, were fully optimized with the density functional methods B3LYP, M06-2X in conjunction with 6-311++G(d,p) basis set. Additionally, second-order Moller-Plesset (MP2) level in combination with 6-311++G(d,p) basis set was employed for comparison purpose. The thermodynamic stability of the self assembled structures in gaseous phase has been obtained according to the analyses of total electronic energies and hydrogen bonding interactions. The bulk water environment has been simulated using the universal solvation model based on solute electron density (SMD). Stability and structure of homochiral and heterochiral imexon dimers resulting from the three imexon tautomers have been carried out to investigate the chiral discrimination. The imexon dimer with heterochiral configuration resulting from self-assembling oxo-amino tautomer is found to be thermodynamically most stable in both gas and aqueous phases. The interaction energies for these self assembled structures were further evaluated with the basis set superposition error corrections. The so-called seven-point interaction energy which includes corrections for BSSE and deformation was calculated. The intermolecular interactions of the selected dimers have been analyzed by calculation of electron density (ρ) and Laplacian (∇2ρ) at the bond critical points (BCPs) using atoms-in-molecule (AIM) theory.

Supramolecular interaction of modificated nanodiamonds, biomolecules and drugs: molecular modeling

Using molecular modeling by the density functional theory B3LYP method with 6-31 G(d) basic set, we analyse the hydrogen bonds formation and their influence on IR-spectra and structure of molecular complexes which is formed due to interaction between nanodiamonds with COOH- surface functionalization and highly toxic drugs on example of doxorubicin and mitoxantrone. Molecular modeling of modificated nanodiamonds and drugs interaction is based on nanodiamond representation by a diamond-like nanoparticle with simpler structure. As a result of calculations the combined IR spectrum is obtained as imposing of IR spectra for molecular complexes of drugs and nanodiamonds in various interaction positions. Combined IR spectra demonstrate a good agreement with experimental data. Received results demonstrate that there can be strong supramolecular interaction between drugs and modificated detonation nanodiamonds. Formed hydrogen bonds can be considered as one of the main mechanisms for targeted drug delivery and for drug retention in cells and, thus, for enhancement of anti-cancer therapeutic efficacy.

Synthesis, structural characterization, thermal behaviour and antimicrobial activity of copper, cadmium and zinc chelates of traizole-thiole ligand in comparison with theoretical molecular orbital calculations

This research involved structural and molecular behaviour of the ligand HL, 4-amino-5-(2,2-dichloro-1-methylcyclopropyl)-4H-1,2,4-triazole-3-thiol toward the transition metal ions namely Cu (II), Cd(II) and Zn (II) had been studied using elemental analyses, magnetic, electronic, FT- IR, 1H-NMR, XRD and Thermal analyses (TGA and DTA). The interpretation of practical data obtained had been evaluated and confirmed by theoretical molecular modelling. The computations had been done by software of Gaussian 09W package. The geometries of traizole-thiole ligand and its metal chelates were fully optimized using density functional theory B3LYP method. There are no symmetry constrains had been applied during geometry optimization. (DFT)/GENECP level by implementing Def2TZVP basis set was used for Cu, Cd and Zn-atoms; and basis set 6-311++G (d, p) was used for other atoms. The mixed basis set had been selected due to its flexibility. HOMO and LUMO energy values for chelates, chemical hardness and electronegativity had been calculated. NBO calculations had been done at the same level using (NBO 3.1) program involved in the software of Gaussian 09W for measuring the intra-molecular delocalization in systems under investigation qualitatively. TD-DFT approximation at the same level of theory was used to calculate the electronic absorption spectra of the studied chelates. Their structures were confirmed via correlation between experimental and theoretical calculations. The ligand and its metal chelates biological activities had been tested against Gram-positive (Staphylococcus aureus ATTC 12600), Gram-negative (Escherichia coli ATTC 11775 and) bacteria, two fungus (Aspergillus flavus and Candida albicans).. These biological activities are tested and give the order Zn-HL˃ Cd-HL˃ Cu-HL ˃˃ HL as a general trend in relation to transition metal cation present in chelate entity. This trend is also correlated to theoretical calculations of chelates electronegativity (X), polarizability and HOMO and LUMO values. Also this trend is correlated to theoretical calculations of energy gap values eV (Zn- HL = 5.19, Cd-HL = 4.32 and Cu-HL = 2.08) and in reverse order to electronegativity (X) values. The variation of electronegativity (X) values is supported by electrostatic potential, for any two molecules, where electron will be partially transferred from one of low X to that of high X. The results show that the order of decreasing X (increasing CT within the molecules) is: Cu-HL > Cd-HL > Zn-HL >> HL. Some of them have the order of magnitude effect like standard Amoxicillin.

Thermal analysis, structure, spectroscopy and DFT calculations of a pharmaceutical cocrystal of salicylic acid and salicylamide

The pharmaceutical cocrystal of salicylic acid (C7H6O3 or H2Sal) and salicylamide (C7H7NO2 or SAM) was synthesized and characterized by various techniques. The differential scanning calorimetry results confirmed the eutectic fusion showing the characteristic of the endothermic sharp peak of the solidus temperature at 108 °C. X-ray crystal structure of cocrystal is orthorhombic with space group Pna2(1). Cocrystal consists of H2Sal and a distorted phenolic group of SAM. The packing diagram of cocrystal H2Sal·SAM clearly confirmed the $$R_{8}^{2}$$ acid–amide dimer heterosynthons and other inter- and intramolecular interaction bonds to stabilize the structure. In addition, the strength of the hydrogen bonds is studied using the vibrational spectral measurements, confirming the band shifting due to the intermolecular interactions. The identity of compounds by matching the absorbance spectrum was confirmed by ultraviolet spectroscopy technique. Furthermore, the experimental studies were supported by calculation results using density functional B3LYP methods with the standard 6-311++G(d,p) basis set level. The parameters such as bond lengths, bond angles and Mulliken atomic charges values have been calculated and compared, confirmed the interactions and charge transfers. The frontier molecular orbitals (HOMO–LUMO) illustrated the lower band-gap value suggesting the possible pharmaceutical activity of this as obtained H2Sal·SAM cocrystal.

A Novel Immunosensing Method Based on the Capture and Enzymatic Release of Sandwich-Type Covalently Conjugated Thionine-Gold Nanoparticles as a New Fluorescence Label Used for Ultrasensitive Detection of Hepatitis B Virus Surface Antigen.

A novel ultrasensitive and simple amplified immunosensing strategy is designed based on a surface-enhanced fluorescence (SEF) nanohybrid made from covalently conjugated thionine–gold nanoparticles (GNP–Th), as a novel amplified fluorescence label, and magnetic nanoparticles (MNPs), as a biological carrier, used for hepatitis B virus surface antigen (HBsAg) detection. This immunosensing strategy operates on the basis of the capture and then release of the amplified fluorescence label. Capturing of the antiHBs-antibody (Ab)-modified GNP–thionine hybrid (GNP–Th-Ab) is carried out through the formation of a two-dimensional (sandwich) probe between this amplified label and antiHBs-antibody-modified magnetic nanoparticles (MNP-Ab), in the presence of a target antigen and using an external magnetic force. Afterward, releasing of the captured fluorescence label is performed using a protease enzyme (pepsin) by a digestion mechanism of grafted antibodies on the GNP–thionine hybrid. As a result of antibody digestion, the amplified fluorescent hybrids (labels) are released into the solution. To understand the mechanism of enhanced fluorescence, the nature of the interaction between thionine and gold nanoparticles is studied using the B3LYP density functional method. In such a methodology, several new mechanisms and structures are used simultaneously, including a SEF-based metal nanoparticle–organic dye hybrid, dual signal amplification in a two-dimensional probe between the GNP–thionine hybrid and MNPs, and a novel releasing method using protease enzymes. These factors improve the sensitivity and speed, along with the simplicity of the procedure. Under optimal conditions, the fluorescence signal increases with the increment of HBs antigen concentration in the linear dynamic range of 4.6 × 10–9 to 0.012 ng/mL with a detection limit (LOD) of 4.6 × 10–9 ng/mL. The proposed immunosensor has great potential in developing ultrasensitive and rapid diagnostic platforms.

Biomolecules of 2-Thiouracil, 4-Thiouracil and 2,4-Dithiouracil: A DFT Study of the Hydration, Molecular Docking and Effect in DNA:RNAMicrohelixes.

The molecular structure of 2-thiouracil, 4-thiouracil and 2,4-dithiouracil was analyzed under the effect of the first and second hydration shell by using the B3LYP density functional (DFT) method, and the results were compared to those obtained for the uracil molecule. A slight difference in the water distribution appears in these molecules. On the hydration of these molecules several trends in bond lengths and atomic charges were established. The ring in uracil molecule appears easier to be deformed and adapted to different environments as compared to that when it is thio-substituted. Molecular docking calculations of 2-thiouracil against three different pathogens: Bacillus subtilis, Escherichia coli and Candida albicans were carried out. Docking calculations of 2,4-dithiouracil ligand with various targeted proteins were also performed. Different DNA: RNA hybrid microhelixes with uridine, 2-thiouridine, 4-thiouridine and 2,4-dithiouridine nucleosides were optimized in a simple model with three nucleotide base pairs. Two main types of microhelixes were analyzed in detail depending on the intramolecular H-bond of the 2′-OH group. The weaker Watson–Crick (WC) base pair formed with thio-substituted uracil than with unsubstituted ones slightly deforms the helical and backbone parameters, especially with 2,4-dithiouridine. However, the thio-substitution significantly increases the dipole moment of the A-type microhelixes, as well as the rise and propeller twist parameters.

Theoretical investigation of the molecular structure, vibrational spectra, and molecular docking of tramadol using density functional theory

AbstractThe optimized molecular structures, harmonic vibrational wavenumbers, and the corresponding vibrational assignments of (1S,2S)‐tramadol and (1R,2R)‐tramadol are computationally examined using the B3LYP density functional theory method together with the standard 6–311++G(d,p) and def2‐TVZP basis sets. The optimized structures show that phenolic rings of both 1R,2R and 1S,2S tramadol adopt planar geometry, which are slightly distorted due to the substitution at the meta‐position; and the six‐membered cyclohexane adopts a slightly distorted chair conformation. The 1S,2S enantiomer is energetically more favorable than 1R,2R with the energy differences of 1.32 and 1.03 kcal/mol obtained at B3LYP/6–311++G(d,p) and B3LYP/Def2‐TVZP levels, respectively. The analysis of the binding pocket in the silico molecular docking with the m‐opioid receptor shows that it originated two clusters with the 1S,2S enantiomer and one cluster with the 1R,2R enantiomer of tramadol. The results point to a more stable complex of the m‐opioid receptor with the 1R,2R enantiomer of tramadol.

Quantum chemical calculations of the vibrational spectrum of aliphatic nitro compounds. Cluster analysis of torsion oscillations

The data of theoretical analysis of vibrational spectra in the long-wave range of different isomers of methyl nitrite, methyl, ethyl, n-propyl nitrate, as well as the electron density distribution obtained within the B3LYP Density Functional Theory method with the 6 - 31G(d) basis set are presented. The cluster analysis of charge distribution on carbon, oxygen, nitrogen atoms and torsion oscillation frequencies in the range of 10-400 cm-1 is carried out.

Structural, spectroscopic, molecular docking, thermal and DFT studies on metal complexes of bidentate orthoquinone ligand

4‐Triphenylmethyl‐1,2‐benzoquinone (TPMBQ) reacted with some metal ions and the structure of the new compounds had been identified. The metal to ligand ratio was 1:2 which was revealed by elemental analysis. The complexes were found to have octahedral geometry and their thermal stability was studied using thermogravimetric analysis technique. The molar conductance measurements revealed the electrolytic nature of the synthesized chelates. The IR spectra concluded the bidentate nature of the TPMBQ ligand while the 1H NMR revealed the presence of water molecules. The XRD spectra of Mn (II) and Fe (III) complexes concluded their crystalline structure while Co (II) and Cu (II) chelates refer to amorphous structures. The geometries of the TPMBQ ligand were optimized using Gaussian 09 W; density functional theory B3LYP method. (DFT)/basis set 6–311++G (d, p). HOMO and LUMO energy values for chelates, chemical hardness and electro‐negativity had been calculated. The ligand and its metal complexes had been examined against different kinds of bacteria such as Proteus vulgaris, Escherichia coli, Staphylococcus aurous and Bacillus subtitles to examine their antimicrobial activity. Molecular docking using Auto Dock tools were utilized.

Computational Studies on Water-Catalyzed Mechanisms for Stereoinversion of Glutarimide Intermediates Formed from Glutamic Acid Residues in Aqueous Phase.

Aspartic acid (Asp) residues are prone to non-enzymatic stereoinversion, and Asp-residue stereoinversion is believed to be mediated via a succinimide (SI) intermediate. The stereoinverted Asp residues are believed to cause several age-related diseases. However, in peptides and proteins, few studies have reported the stereoinversion of glutamic acid (Glu) residues whose structures are similar to that of Asp. We previously presumed that Glu-residue stereoinversion proceeds via a glutarimide (GI) intermediate and showed that the calculated activation barriers of SI- and GI-intermediate stereoinversion are almost equivalent in the gas phase. In this study, we investigated the stereoinversion pathways of the l-GI intermediate in the aqueous phase using B3LYP density functional methods. The calculated activation barrier of l-GI-intermediate stereoinversion in the aqueous phase was approximately 36 kcal·mol−1, which was much higher than that in the gas phase. Additionally, as this activation barrier exceeded that of Asp-residue stereoinversion, it is presumed that Glu-residue stereoinversion has a lower probability of proceeding under physiological conditions than Asp-residue stereoinversion.

Possible Mechanisms of Nonenzymatic Formation of Dehydroalanine Residue Catalyzed by Dihydrogen Phosphate Ion.

Uncommon crosslinked amino acids have been identified in several aging tissues and are suspected to trigger various age-related diseases. Several uncommon residues are formed when the dehydroalanine (Dha) residue undergoes a nucleophilic attack by surrounding residues. Dha residues are considered to be formed by posttranslational modification of serine (Ser) and cysteine residues. In the present study, we investigated the Dha residue formation mechanism catalyzed by dihydrogen phosphate ion (H2PO4-) using quantum chemical calculations. We obtained optimized geometries using the B3LYP density functional method and carried out single-point energy calculations using the second-order Møller-Plesset perturbation method. All calculations were performed using Ace-Ser-Nme (Ace = acetyl, Nme = methylamino) as a model compound. Results of the computational analysis suggest that the mechanism underlying the Dha residue formation from Ser consists of two steps: enolization and 1,3-elimination. The H2PO4- catalyzed both reactions as a proton-relay mediator. The calculated activation barrier for Dha residue formation was estimated as 30.4 kcal mol-1. In this pathway, the catalytic H2PO4- interacts with the Ser residue α-proton, carbonyl oxygen of Ser, and C-terminal side adjacent residues, and the calculated activation energy produced was the same as the experimentally reported value for nonenzymatic modifications of amino acid residues. Therefore, our calculation suggests that H2PO4--catalyzed Ser residue dehydration can proceed nonenzymatically.

Spectroscopic characterization, thermogravimetry, density functional theory and biological studies of some mixed‐ligand complexes of meloxicam and 2,2′‐bipyridine with some transition metals

The mixed‐ligand Mn(II), Fe(III), Ni(II), Cu(II), Zn(II) and Zr(IV) complexes of meloxicam (H2mel) and 2,2′‐bipyridine (Bipy) were prepared and characterized. For all complexes, the analytical and spectroscopic results revealed that H2mel acts in a monobasic bidentate manner through the oxygen of the amide and nitrogen of the thiazole groups, whereas Bipy coordinates through the two nitrogen atoms with slightly distorted octahedral geometry. Thermodynamic parameters (E, ΔS*, ΔH* and ΔG*) were calculated using Coats–Redfern and Horowitz–Metzger methods. The geometries of H2mel and the complexes were carefully studied using density functional theory to predict the properties of materials performed using the hybrid density functional method B3LYP. All studied complexes are soft with respect to H2mel where η varies from 0.096 for Zn(II) complex to 0.067 for Fe(III) complex and σ varies from 10.42 to 14.93 eV, while η and σ for H2mel are 0.14 and 7.14 eV, respectively. The antibacterial activities of the ligands and metal complexes were investigated and the data show that the complexes are active against some bacterial species compared with H2mel.

Experimental FTIR and theoretical investigation of the molecular structure and vibrational spectra of acetanilide using DFT and dispersion correction to DFT

The FTIR spectrum of acetanilide (ACN) is recorded and analyzed. The optimized molecular structures, harmonic vibrational wavenumbers and corresponding vibrational assignments of the ACN are computationally examined by using the B3LYP density functional theory method together with the standard 6-311[Formula: see text]G([Formula: see text],[Formula: see text]) basis set. From the calculations, the ACN is predicted to exist predominantly in trans configuration with the relative energy, rotational barrier, and population of 2.8[Formula: see text]kcal/mol, 14.8[Formula: see text]kcal/mol, and 99.5%, respectively. The optimized structure shows that the amide group (CO–NH) of trans-ACN adopts a planar peptide-like conformation. The effect of the incorporation of dispersion correction to the B3LYP on the calculated equilibrium structure and vibrational spectra of ACN is investigated. The highest occupied and the lowest unoccupied molecular orbitals, IR intensities and molecular electrostatic potential results are reported. In addition, reliable vibrational assignments have been made on the basis of Potential Energy Distribution (PED) using VEDA4 program. Simulated IR spectrum are compared with the experimental FTIR and FT-Raman spectra. Energy decomposition analysis (EDA) revealed that Pauli repulsion is responsible for the increased stability of the trans over the cis isomer.

Thermal and spectroscopic study of zinc, manganese, copper, cobalt and nickel 2,3-pyrazinedicarboxylate

In the frame of this work complexes of selected 3d transition metals with 2,3-pyrazinedicarboxylic acid were synthesized and characterized by spectroscopic (IR, Raman) and thermal (TGA, DSC) methods. FT-IR and FT-Raman spectra of 3d metal 2,3-pyrazinedicarboxylates were recorded and analyzed in the region of 4000–400 cm−1. The structures of the three 2,3-pyridazinecarboxylic acid conformers were calculated using density functional (DFT) hybrid method B3LYP with non-local correlation provided by Lee–Young–Parr expression. All calculations were carried out with functional base 6–311++G(d,p) in Gaussian 09 package. The aromaticity indices HOMA and I6 (Bird) for diffraction structures of 2,3-pyrazinedicarboxylates and the theoretical structures of the acid conformers were calculated.Thermal properties of the complexes were studied in the temperature range of 30–900 °C. Measurements were carried out in the atmosphere of oxygen and argon. The products of dehydration and decomposition processes were determined based on TG and DSC curves. Thermal studies revealed that 2,3-pyrazinedicarboxylic acid complexes are hydrated, and upon heating decompose to metal oxides.

Correlations of computational ionization energy with experimental oxidation potential and with antioxidant efficiencies in catechins

Ionization energies of catechins were calculated by using B3LYP density functional method with 6-31G** basis set. Then, conformations of catechins were extensively explored. Geometry optimizations starting from the explored conformers were made not only for the neutral species but also for the radical cation. The ionization energy of each catechin was estimated as the energy difference between the most stable geometries obtained for the neutral species and radical cation. Tendency of experimental oxidation potential in catechins is well reproduced by this calculation, and the ionization energy correlates well with the singlet-oxygen quenching efficiency in case that stereochemistry of attachment at the 3-position is common. Electron transfer from catechins plays an important role in the singlet-oxygen quenching, free-radical scavenging and recycling from vitamin E radical to vitamin E. The reason for discrepancy among antioxidant efficiencies with regard to the ionization energy dependence is explained.

A new theoretical calculation of the equilibrium constant and temperature for the carbon isotope exchange reaction between CH4 and CO2

The equilibrium isotope fractionations among COH gases in a variety of geological settings are commonly used as isotope geothermometers to evaluate the temperatures of geothermal fluids at depth, subsurface fluid-rock interactions, volcanic-hydrothermal systems and natural gas pools. However, due to limited experimental data and sophisticated theoretical calculations, applications of these geothermometers have been restricted. This study uses the carbon isotope exchange reaction between CH4 and CO2 as a case study to develop theoretical methods that can improve accuracies in calculating harmonic vibrational frequencies for CH4 and CO2, the equilibrium constants and temperatures for the carbon isotope exchange reaction between CH4 and CO2. Results suggest that the Bigeleisen-Mayer equation is sufficient to calculate the equilibrium constants and temperatures associated with the isotope exchange reaction between CH4 and CO2 with an accurate estimation of molecular harmonic vibrational frequencies. Calculations of the harmonic frequencies of CH4 and CO2 are achieved using the B3LYP density functional method with the 6-311+G(d) basis set, and the calculated harmonic frequencies are highly consistent with experimental values. The frequency correction factor is taken as 1.022 which puts the calculated fractionation factors in good agreement with experimental values. The calculated equilibrium constants are comparable to experimental data and a theoretical data set. They are highly consistent. In order to improve the accuracy and efficiency of solving for equilibrium temperatures using the Bigeleisen-Mayer equation, symbol operation and iterative algorithm in the MatLab software have been applied to compute the temperatures instead of using limited theoretical data sets or empirical fit equations. Our calculated results suggest that this algorithm can rapidly and conveniently yield relatively precise equilibrium temperatures. This algorithm can thus provide an important tool to evaluate whether the carbon isotope exchange reaction for CH4 and CO2 has attained equilibrium and estimate the formation temperature of CH4 and CO2 in high temperature geothermal systems.