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1.
J Chem Theory Comput ; 20(5): 1829-1837, 2024 Mar 12.
Artigo em Inglês | MEDLINE | ID: mdl-38354106

RESUMO

As the most abundant molecule in the universe, collisions involving H2 have important implications in astrochemistry. Collisions between hydrogen molecules also represent a prototype for assessing various dynamic methods for understanding fundamental few-body processes. In this work, we develop a new and highly accurate full-dimensional potential energy surface (PES) covering all reactive channels of the H2 + H2 system, which extends our previously reported H2 + H2 nonreactive PES [J. Chem. Theory Comput., 2021, 17, 6747] by adding 39,538 additional ab initio points calculated at the MRCI/AV5Z level in the reactive channels. The global PES is represented with high fidelity (RMSE = 0.6 meV for a total of 79,000 points) by a permutation invariant polynomial neural network (PIP-NN) and is suitable for studying collision-induced dissociation, single-exchange, as well as four-center exchange reactions. Preliminary quasi-classical trajectory studies on the new PIP-NN PES reveal strong vibrational enhancement of all reaction channels.

2.
Chem Commun (Camb) ; 60(10): 1239-1256, 2024 Jan 30.
Artigo em Inglês | MEDLINE | ID: mdl-38197484

RESUMO

Advances in quantum state preparations combined with molecular cooling and trapping technologies have enabled unprecedented control of molecular collision dynamics. This progress, achieved over the last two decades, has dramatically improved our understanding of molecular phenomena in the extreme quantum regime characterized by translational temperatures well below a kelvin. In this regime, collision outcomes are dominated by isolated partial waves, quantum threshold and quantum statistics effects, tiny energy splitting at the spin and hyperfine levels, and long-range forces. Collision outcomes are influenced not only by the quantum state preparation of the initial molecular states but also by the polarization of their rotational angular momentum, i.e., stereodynamics of molecular collisions. The Stark-induced adiabatic Raman passage technique developed in the last several years has become a versatile tool to study the stereodynamics of light molecular collisions in which alignment of the molecular bond axis relative to initial collision velocity can be fully controlled. Landmark experiments reported by Zare and coworkers have motivated new theoretical developments, including formalisms to describe four-vector correlations in molecular collisions that are revealed by the experiments. In this Feature article, we provide an overview of recent theoretical developments for the description of stereodynamics of cold molecular collisions and their implications to cold controlled chemistry.

3.
Chem Sci ; 14(38): 10547-10560, 2023 Oct 04.
Artigo em Inglês | MEDLINE | ID: mdl-37799987

RESUMO

Protein fold adaptation to novel enzymatic reactions is a fundamental evolutionary process. Cofactor-independent oxygenases degrading N-heteroaromatic substrates belong to the α/ß-hydrolase (ABH) fold superfamily that typically does not catalyze oxygenation reactions. Here, we have integrated crystallographic analyses under normoxic and hyperoxic conditions with molecular dynamics and quantum mechanical calculations to investigate its prototypic 1-H-3-hydroxy-4-oxoquinaldine 2,4-dioxygenase (HOD) member. O2 localization to the "oxyanion hole", where catalysis occurs, is an unfavorable event and the direct competition between dioxygen and water for this site is modulated by the "nucleophilic elbow" residue. A hydrophobic pocket that overlaps with the organic substrate binding site can act as a proximal dioxygen reservoir. Freeze-trap pressurization allowed the structure of the ternary complex with a substrate analogue and O2 bound at the oxyanion hole to be determined. Theoretical calculations reveal that O2 orientation is coupled to the charge of the bound organic ligand. When 1-H-3-hydroxy-4-oxoquinaldine is uncharged, O2 binds with its molecular axis along the ligand's C2-C4 direction in full agreement with the crystal structure. Substrate activation triggered by deprotonation of its 3-OH group by the His-Asp dyad, rotates O2 by approximately 60°. This geometry maximizes the charge transfer between the substrate and O2, thus weakening the double bond of the latter. Electron density transfer to the O2(π*) orbital promotes the formation of the peroxide intermediate via intersystem crossing that is rate-determining. Our work provides a detailed picture of how evolution has repurposed the ABH-fold architecture and its simple catalytic machinery to accomplish metal-independent oxygenation.

4.
J Phys Chem A ; 127(33): 6924-6944, 2023 Aug 24.
Artigo em Inglês | MEDLINE | ID: mdl-37579497

RESUMO

The Li + HF and Li + HCl reactions share some common features. They have the same kinematics, relatively small barrier heights, bent transition states, and are both exothermic when the zero point energy is considered. Nevertheless, the pioneering crossed beam experiments by Lee and co-workers in the 80s (Becker et al., J. Chem. Phys. 1980, 73, 2833) revealed that the dynamics of the two reactions differ significantly, especially at low collision energies. In this work, we present theoretical simulations of their results in the laboratory frame (LAB), based on quasiclassical trajectories and obtained using accurate potential energy surfaces. The calculated LAB angular distributions and time-of-flight spectra agree well with the raw experimental data, although our simulations do not reproduce the experimentally derived center-of-mass (CM) differential cross section and velocity distributions. The latter were derived by forward convolution fitting under the questionable assumption that the CM recoil velocity and scattering angle distribution were uncoupled, while our results show that the coupling between them is relevant. Some important insights into the reaction mechanism discussed in the article by Becker et al. had not been contrasted with those that can be extracted from the theoretical results. Among them, the correlation between the angular momenta involved in the reactions has also been examined. Given the kinematics of both systems, the reagent orbital angular momentum, l, is almost completely transformed into the rotation of the product diatom, j'. However, contrary to the coplanar mechanism proposed in the original paper, we find that the initial and final relative orbital angular momenta are not necessarily parallel. Both reactions are found to be essentially direct, although about 15% of the LiFH complexes live longer than 200 fs.

5.
Int J Mol Sci ; 24(8)2023 Apr 18.
Artigo em Inglês | MEDLINE | ID: mdl-37108586

RESUMO

The deprotonation of an organic substrate is a common preactivation step for the enzymatic cofactorless addition of O2 to this substrate, as it promotes charge-transfer between the two partners, inducing intersystem crossing between the triplet and singlet states involved in the process. Nevertheless, the spin-forbidden addition of O2 to uncharged ligands has also been observed in the laboratory, and the detailed mechanism of how the system circumvents the spin-forbiddenness of the reaction is still unknown. One of these examples is the cofactorless peroxidation of 2-methyl-3,4-dihydro-1-naphthol, which will be studied computationally using single and multi-reference electronic structure calculations. Our results show that the preferred mechanism is that in which O2 picks a proton from the substrate in the triplet state, and subsequently hops to the singlet state in which the product is stable. For this reaction, the formation of the radical pair is associated with a higher barrier than that associated with the intersystem crossing, even though the absence of the negative charge leads to relatively small values of the spin-orbit coupling.


Assuntos
Tetralonas , Descarboxilação , Oxigênio/química
6.
Pharmaceutics ; 15(3)2023 Mar 09.
Artigo em Inglês | MEDLINE | ID: mdl-36986749

RESUMO

New lignohydroquinone conjugates (L-HQs) were designed and synthesized using the hybridization strategy, and evaluated as cytotoxics against several cancer cell lines. The L-HQs were obtained from the natural product podophyllotoxin and some semisynthetic terpenylnaphthohydroquinones, prepared from natural terpenoids. Both entities of the conjugates were connected through different aliphatic or aromatic linkers. Among the evaluated hybrids, the L-HQ with the aromatic spacer clearly displayed the in vitro dual cytotoxic effect derived from each starting component, retaining the selectivity and showing a high cytotoxicity at short (24 h) and long (72 h) incubation times (4.12 and 0.0450 µM, respectively) against colorectal cancer cells. In addition, the cell cycle blockade observed by flow cytometry studies, molecular dynamics, and tubulin interaction studies demonstrated the interest of this kind of hybrids, which docked adequately into the colchicine binding site of tubulin despite their large size. These results prove the validity of the hybridization strategy and encourage further research on non-lactonic cyclolignans.

7.
J Phys Chem A ; 127(7): 1619-1627, 2023 Feb 23.
Artigo em Inglês | MEDLINE | ID: mdl-36787203

RESUMO

The H2 + H2 system has long been considered a benchmark system for ro-vibrational energy transfer in bimolecular collisions. However, most studies thus far have focused on collisions involving H2 molecules in the ground vibrational level or in the first excited vibrational state. While H2 + H2/HD collisions have received wide attention due to the important role they play in astrophysics, D2 + D2 collisions have received much less attention. Recently, Zhou et al. [ Nat. Chem. 2022, 14, 658-663, DOI: 10.1038/s41557-022-00926-z] examined stereodynamic aspects of rotational energy transfer in collisions of two aligned D2 molecules prepared in the v = 2 vibrational level and j = 2 rotational level. Here, we report quantum calculations of rotational and vibrational energy transfer in collisions of two D2 molecules prepared in vibrational levels up to v = 2 and identify key resonance features that contribute to the angular distribution in the experimental results of Zhou et al. The quantum scattering calculations were performed in full dimensionality and using the rigid-rotor approximation using a recently developed highly accurate six-dimensional potential energy surface for the H4 system that allows descriptions of collisions involving highly vibrationally excited H2 and its isotopologues.

8.
Phys Rev Lett ; 130(3): 033002, 2023 Jan 20.
Artigo em Inglês | MEDLINE | ID: mdl-36763383

RESUMO

Resonant scattering of optically state-prepared and aligned molecules in the cold regime allows the most detailed interrogation and control of bimolecular collisions. This technique has recently been applied to collisions of two aligned ortho-D_{2} molecules prepared in the j=2 rotational level of the v=2 vibrational manifold using the Stark-induced adiabatic Raman passage technique. Here, we develop the theoretical formalism for describing four-vector correlations in collisions of two aligned molecules and apply our approach to state-prepared D_{2}(v=2,j=2)+D_{2}(v=2,j=2)→D_{2}(v=2,j=2)+D_{2}(v=2,j=0) collisions, making possible the simulations of the experimental results from first principles. Key features of the experimental angular distributions are reproduced and attributed primarily to a partial wave resonance with orbital angular momentum ℓ=4.

9.
J Phys Chem Lett ; 13(18): 4064-4072, 2022 May 12.
Artigo em Inglês | MEDLINE | ID: mdl-35499484

RESUMO

In recent experiments using the Stark-induced adiabatic Raman passage technique, Zhou et al. ( J. Chem. Phys. 2021, 154, 104309; Science 2021, 374, 960-964) measured the product's angular distribution for the collisions between He and aligned D2 molecules at cold collision energies. The signatures of the angular distributions were attributed to an [Formula: see text] = 2 resonance that governs scattering at low energies. A first-principles quantum mechanical treatment of this problem is presented here using a highly accurate interaction potential for the He-H2 system. Our results predict a very intense [Formula: see text] = 1 resonance at low energies, leading to angular distributions that differ from those measured in the experiment. A good agreement with the experiment is achieved only when the [Formula: see text] = 1 resonance is artificially removed, for example, by excluding the lowest energies present in the experimental velocity distribution. Our analysis revealed that neither the position nor the intensity of the [Formula: see text] = 1 resonance significantly changes when the interaction potential is modified within its predicted uncertainties. Energy-resolved measurements may help to resolve the discrepancy.

10.
Phys Chem Chem Phys ; 23(35): 19364-19374, 2021 Sep 15.
Artigo em Inglês | MEDLINE | ID: mdl-34524308

RESUMO

Quantum control of molecular collision dynamics is an exciting emerging area of cold collisions. Co-expansion of collision partners in a supersonic molecular beam combined with precise control of their quantum states and alignment/orientation using Stark-induced Adiabatic Raman Passage allows exquisite stereodynamic control of the collision outcome. This approach has recently been demonstrated for rotational quenching of HD in collisions with H2, D2, and He and D2 by He. Here we illustrate this approach for HD(v = 0, j = 2) + CO(v = 0, j = 0) → HD(v' = 0, j') + CO(v' = 0, j') collisions through full-dimensional quantum scattering calculations at collision energies near 1 K. It is shown that the collision dynamics at energies between 0.01-1 K are controlled by an interplay of L = 1 and L = 2 partial wave resonances depending on the final rotational levels of the two molecules. Polarized cross sections resolved into magnetic sub-levels of the initial and final rotational quantum numbers of the two molecules also reveal a significant stereodynamic effect in the cold energy regime. Overall, the stereodynamic effect is controlled by both geometric and dynamical factors, with parity conservation playing an important role in modulating these contributions depending on the particular final state.

11.
Chemistry ; 27(5): 1700-1712, 2021 Jan 21.
Artigo em Inglês | MEDLINE | ID: mdl-32975323

RESUMO

Despite being a very strong oxidizing agent, most organic molecules are not oxidized in the presence of O2 at room temperature because O2 is a diradical whereas most organic molecules are closed-shell. Oxidation then requires a change in the spin state of the system, which is forbidden according to non-relativistic quantum theory. To overcome this limitation, oxygenases usually rely on metal or redox cofactors to catalyze the incorporation of, at least, one oxygen atom into an organic substrate. However, some oxygenases do not require any cofactor, and the detailed mechanism followed by these enzymes remains elusive. To fill this gap, here the mechanism for the enzymatic cofactor-independent oxidation of 3,5-dihydroxyphenylacetyl-CoA (DPA-CoA) is studied by combining multireference calculations on a model system with QM/MM calculations. Our results reveal that intersystem crossing takes place without requiring the previous protonation of molecular oxygen. The characterization of the electronic states reveals that electron transfer is concomitant with the triplet-singlet transition. The enzyme plays a passive role in promoting the intersystem crossing, although spontaneous reorganization of the water wire connecting the active site with the bulk presets the substrate for subsequent chemical transformations. The results show that the stabilization of the singlet radical-pair between dioxygen and enolate is enough to promote spin-forbidden reaction without the need for neither metal cofactors nor basic residues in the active site.


Assuntos
Biocatálise , Coenzima A/química , Coenzima A/metabolismo , Oxigenases/metabolismo , Transporte de Elétrons , Oxigenases/química , Teoria Quântica
12.
J Phys Chem Lett ; 12(1): 310-316, 2021 Jan 14.
Artigo em Inglês | MEDLINE | ID: mdl-33351625

RESUMO

The collision geometry, that is, the relative orientation of reactants before interaction, can have a large effect on how a collision or reaction proceeds. Certain geometries may prevent access to a given product channel, while others might enhance it. In this Letter, we demonstrate how the initial orientation of NO molecules relative to approaching Ar atoms determines the branching between the spin-orbit changing and the spin-orbit conserving rotational product channels. We use a recently developed quantum treatment to calculate differential and integral branching fractions, at any arbitrary orientation, from theoretical and experimental data points. Our results show that a substantial degree of control over the final spin-orbit state of the scattering products can be achieved by tuning the initial collision geometry.

13.
Phys Chem Chem Phys ; 22(39): 22289-22301, 2020 Oct 15.
Artigo em Inglês | MEDLINE | ID: mdl-33005915

RESUMO

Understanding the molecular forces that drive a reaction or scattering process lies at the heart of molecular dynamics. Here, we present a combined experimental and theoretical study of the spin-orbit changing scattering dynamics of oriented NO molecules with Ar atoms. Using our crossed molecular beam apparatus, we have recorded velocity-map ion images and extracted differential and integral cross sections of the scattering process in the side-on geometry. We observe an overall preference for collisions close to the N atom in the spin-orbit changing manifold, which is a direct consequence of the location of the unpaired electron on the potential energy surface. In addition, a prominent forward scattered feature is observed for intermediate, even rotational transitions when the atom approaches the molecule from the O-end. The appearance of this peak originates from an attractive well on the A' potential energy surface, which efficiently directs high impact parameter trajectories towards the region of high unpaired electron density near the N-end of the molecule. The ability to orient molecules prior to collision, both experimentally and theoretically, allows us to sample different regions of the potential energy surface(s) and unveil the associated collision pathways.

14.
Molecules ; 25(18)2020 Sep 17.
Artigo em Inglês | MEDLINE | ID: mdl-32957517

RESUMO

Natural products are the ideal basis for the design of novel efficient molecular entities. Podophyllotoxin, a naturally occurring cyclolignan, is an example of natural product which displays a high versatility from a biological activity point of view. Based on its unique chemical structure, different derivatives have been synthesized presenting the original antitumoral properties associated with the compound, i.e., the tubulin polymerization inhibition and arising anti-topoisomerase II activity from structural modifications on the cyclolignan skeleton. In this report, we present a novel conjugate or hybrid which chemically combines both biological activities in one single molecule. Chemical design has been planned based in our lead compound, podophyllic aldehyde, as an inhibitor of tubulin polymerization, and in etoposide, an approved antitumoral drug targeting topoisomerase II. The cytotoxicity and selectivity of the novel synthetized hybrid has been evaluated in several cell lines of different solid tumors. In addition, these dual functional effects of the novel compound have been also evaluated by molecular docking approaches.


Assuntos
Antineoplásicos Fitogênicos/química , Produtos Biológicos/química , DNA Topoisomerases Tipo II/metabolismo , Podofilotoxina/química , Moduladores de Tubulina/química , Aldeídos/química , Antineoplásicos Fitogênicos/farmacologia , Apoptose/efeitos dos fármacos , Linhagem Celular Tumoral , Ensaios de Seleção de Medicamentos Antitumorais , Etoposídeo/metabolismo , Humanos , Simulação de Acoplamento Molecular , Podofilotoxina/farmacologia , Relação Estrutura-Atividade , Tubulina (Proteína)/metabolismo , Moduladores de Tubulina/farmacologia
15.
Artigo em Inglês | MEDLINE | ID: mdl-31678841

RESUMO

Leishmania is the aethiological agent responsible for the visceral leishmaniasis, a serious parasite-borne disease widely spread all over the World. The emergence of resistant strains makes classical treatments less effective; therefore, new and better drugs are necessary. Naphthoquinones are interesting compounds for which many pharmacological properties have been described, including leishmanicidal activity. This work shows the antileishmanial effect of two series of terpenyl-1,4-naphthoquinones (NQ) and 1,4-anthraquinones (AQ) obtained from natural terpenoids, such as myrcene and myrceocommunic acid. They were evaluated both in vitro and ex vivo against the transgenic iRFP-Leishmania infantum strain and also tested on liver HepG2 cells to determine their selectivity indexes. The results indicated that NQ derivatives showed better antileishmanial activity than AQ analogues, and among them, compounds with a diacetylated hydroquinone moiety provided better results than their corresponding quinones. Regarding the terpenic precursor, compounds obtained from the monoterpenoid myrcene displayed good antiparasitic efficiency and low cytotoxicity for mammalian cells, whereas those derived from the diterpenoid showed better antileishmanial activity without selectivity. In order to explore their mechanism of action, all the compounds have been tested as potential inhibitors of Leishmania type IB DNA topoisomerases, but only some compounds that displayed the quinone ring were able to inhibit the recombinant enzyme in vitro. This fact together with the docking studies performed on LTopIB suggested the existence of another mechanism of action, alternative or complementary to LTopIB inhibition. In silico druglikeness and ADME evaluation of the best leishmanicidal compounds has shown good predictable druggability.


Assuntos
Antiprotozoários/farmacologia , DNA Topoisomerases/efeitos dos fármacos , Leishmania infantum/efeitos dos fármacos , Leishmania infantum/enzimologia , Quinonas/farmacologia , Animais , Antraquinonas/farmacologia , Camptotecina/química , Camptotecina/farmacologia , DNA Topoisomerases/química , DNA Topoisomerases/genética , Resistência a Medicamentos , Feminino , Células Hep G2/parasitologia , Humanos , Leishmaniose Visceral/tratamento farmacológico , Macrófagos/parasitologia , Camundongos , Camundongos Endogâmicos BALB C , Simulação de Acoplamento Molecular , Naftoquinonas/farmacologia , Quinonas/química , Baço/citologia , Inibidores da Topoisomerase/química , Inibidores da Topoisomerase/farmacologia
16.
J Chem Phys ; 151(9): 094307, 2019 Sep 07.
Artigo em Inglês | MEDLINE | ID: mdl-31492055

RESUMO

This paper presents two new adiabatic, global potential energy surfaces (PESs) for the two lowest 3A' and 3A″ electronic states of the O(3P) + H2 system. For each of these states, ab initio electronic energies were calculated for more than 5000 geometries using internally contracted multireference configuration interaction methods. The calculated points were then fitted using the ansatz by Aguado et al. [Comput. Phys. Commun. 108, 259 (1998)] leading to very accurate analytical potentials well adapted to perform reaction dynamics studies. Overall, the topographies of both PESs are in good agreement with the benchmark potentials of Rogers et al. [J. Phys. Chem. A 104, 2308 (2000)], but those presented in this work reproduce better the height and degeneracy of the two states at the saddle point. Moreover, the long range potential in the entrance channel does not require any cutoff. These features make the new PESs particularly suitable for a comparison of the dynamics on each of them. The new set of PESs was then used to perform quantum mechanics and quasiclassical trajectory calculations to determine differential and integral cross sections, which are compared to the experimental measurements by Garton et al. [J. Chem. Phys. 118, 1585 (2003)].

17.
Phys Rev Lett ; 123(4): 043401, 2019 Jul 26.
Artigo em Inglês | MEDLINE | ID: mdl-31491255

RESUMO

Cold collisions of light molecules are often dominated by a single partial wave resonance. For the rotational quenching of HD (v=1, j=2) by collisions with ground state para-H_{2}, the process is dominated by a single L=2 partial wave resonance centered around 0.1 K. Here, we show that this resonance can be switched on or off simply by appropriate alignment of the HD rotational angular momentum relative to the initial velocity vector, thereby enabling complete control of the collision outcome.

18.
J Phys Chem A ; 123(42): 9079-9088, 2019 Oct 24.
Artigo em Inglês | MEDLINE | ID: mdl-31549832

RESUMO

The dynamics of inelastic collisions between HF and H has been investigated in detail by means of time-independent quantum mechanical calculations on the LWA-78 potential energy surface ( Li , G. ; et al. J. Chem. Phys. 2007 , 127 , 174302 ). Reaction probabilities, differential cross sections, and three-vector correlations have been calculated and analyzed. Our results show that there are two competing collision mechanisms that correlate with low and high impact parameters and show very different stereodynamical preferences. The mechanism promoted by high impact parameters is the only one present at low collision energies. We also observe the presence of an apparent threshold in the inelastic cross section for relatively high initial HF rotational quantum numbers, which is associated with the larger energy difference between adjacent rotational quantum states with increasing rotation.

19.
J Phys Chem A ; 123(41): 8787-8806, 2019 Oct 17.
Artigo em Inglês | MEDLINE | ID: mdl-31513425

RESUMO

The rotationally inelastic collisions of NO(X) with Ar, in which the NO bond-axis is oriented side-on (i.e., perpendicular) to the incoming collision partner, are investigated experimentally and theoretically. The NO(X) molecules are selected in the |j = 0.5, Ω = 0.5, ε = -1, f⟩ state prior to bond-axis orientation in a static electric field. The scattered NO products are then state selectively detected using velocity-map ion imaging. The experimental bond-axis orientation resolved differential cross sections and integral steric asymmetries are compared with quantum mechanical calculations, and are shown to be in good agreement. The strength of the orientation field is shown to affect the structure observed in the differential cross sections, and to some extent also the steric preference, depending on the ratio of the initial e and f Λ-doublets in the superposition determined by the orientation field. Classical and quantum calculations are compared and used to rationalize the structures observed in the differential cross sections. It is found that these structures are due to quantum mechanical interference effects, which differ for the two possible orientations of the NO molecule due to the anisotropy of the potential energy surface probed in the side-on orientation. Side-on collisions are shown to maximize and afford a high degree of control over the scattering intensity at small scattering angles (θ < 90°), while end-on collisions are predicted to dominate in the backward scattered region (θ > 90°).

20.
J Phys Chem A ; 123(34): 7408-7419, 2019 Aug 29.
Artigo em Inglês | MEDLINE | ID: mdl-31373813

RESUMO

A quasiclassical trajectory study of the kinetics of the title astrochemical reaction in a range of temperatures varying from 5 to 1000 K (corresponding to both the outer and the inner regions of the protostar and the circumstellar envelopes) was carried out and a clear dependence of the rate coefficient on the temperature is given, in contrast with the constant value adopted in kinetics astrochemical databases. Levering the massive nature of the performed calculations and of the detailed dynamical investigation of the reactive process, a rationalization of the temperature dependence of the released translational energy and of the rovibrational population of the CH and H2 diatomic products is also provided. Furthermore, the effect of the initial rovibrational energy of CH2 on the state-specific rate coefficients and cross sections is analyzed in order to single out the role played by the different regions of the potential energy surface on the dynamical outcomes and on the modeling the temperature dependence of the reactive efficiency of the investigated process. This led to a parametrization of the computed rate in terms of the following double Arrhenius expression (in cm3 s-1), k(T) = 2.50 × 10-10 exp(- 1.67/T) + 5.98 × 10-11 exp(- 280.5/T), alternative to the piecewise formulation into the three subintervals of temperature in which the overall 5-1000 K interval can be divided.

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