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1.
Phys Chem Chem Phys ; 26(27): 18930-18942, 2024 Jul 10.
Artículo en Inglés | MEDLINE | ID: mdl-38952212

RESUMEN

Single crystal X-ray diffraction analysis of needle shaped riboflavin (RF) crystals revealed π-stacking of RF's isoalloxazine units (distance: 3.643-3.313 Å) with syn-orientated ribityl chains. In line with this, classical molecular dynamics (MD) (400 ns) using an isobaric-isothermal (NPT) ensemble of eight RF in a water box (〈V〉 ∼ 508.62 nm3, 〈p〉 = 1.11 bar) revealed anti-aligned aggregation of RF in water (COM-distance: 4 Å). Comparing umbrella sampling for the separation of two RF molecules to the separation of two lumichrome molecules, the similar mean potential force for the separation of RF and lumichrome (22.8 kJ mol-1; 24.4 kJ mol-1) proved dispersive interactions as the origin of RF's aggregation. Though stacking of RF is the major water-solubility limiting factor, the conformation of RF's ribityl chain may alter the solubility in water. Both, MD (in water) and COSMO-RS (in water continuum) predicted that conformations of RF with an extended ribityl chain are thermodynamically preferred over any conformations with internal hydrogen bonds between hydroxyl groups and nitrogen/oxygen atoms of the pyrimidine moiety of the flavin ring. Interestingly, COSMO-RS predicted the solubility of the extended conformation to be significantly lower than the latter leading to the very low average solubility of RF. Nuclear Overhauser effect measurements (NOESY) of the structurally related sodium riboflavin 5'-monophosphate (RF-PO4) in deuterium oxide confirmed π-stacking of the isoalloxazine rings. In conformity with the 350 times higher water-solubility of RF-PO4, NOESY also indicated a contorted conformation of the ribityl phosphate chain, whereas, for RF, indications for a contorted chain were not observed.

2.
Chem Sci ; 15(24): 9104-9111, 2024 Jun 19.
Artículo en Inglés | MEDLINE | ID: mdl-38903236

RESUMEN

N-Triflylphosphoramides (NTPAs) represent an important catalyst class in asymmetric catalysis due to their multiple hydrogen bond acceptor sites and acidity, which is increased by several orders of magnitude compared to conventional chiral phosphoric acids (CPAs). Thus, NTPAs allow for several challenging transformations, which are not accessible with CPAs. However, detailed evidence on their hydrogen bonding situation, complex structures and aggregation is still lacking. Therefore, this study covers the hydrogen bonding behavior and structural features of binary NTPA/imine complexes compared to their CPA counterparts. Deviating from the single-well potential hydrogen bonds commonly observed in CPA/imine complexes, the NTPA/imine complexes exhibit a tautomeric equilibrium between two proton positions. Low-temperature NMR at 180 K supported by computer simulations indicates a OHN hydrogen bond between the phosphoramide oxygen and the imine, instead of the mostly proposed NHN H-bond. Furthermore, this study finds no evidence for the existence of dimeric NTPA/NTPA/imine complexes as previously suggested for CPA systems, both synthetically and through NMR studies.

3.
Phys Chem Chem Phys ; 26(15): 11880-11892, 2024 Apr 17.
Artículo en Inglés | MEDLINE | ID: mdl-38568008

RESUMEN

Recent experiments have revealed that adenosine triphosphate (ATP) suppresses the fibrillation of amyloid peptides - a process closely linked to neurodegenerative diseases such as Alzheimer's and Parkinson's. Apart from the adsorption of ATP onto amyloid peptides, the molecular understanding is still limited, leaving the underlying mechanism for the fibrillation suppression by ATP largely unclear, especially in regards to the molecular energetics. Here we provide an explanation at the molecular scale by quantifying the free energies using all-atom molecular dynamics simulations. We found that the changes of the free energies due to the addition of ATP lead to a significant equilibrium shift towards monomeric peptides in agreement with experiments. Despite ATP being a highly charged species, the decomposition of the free energies reveals that the van der Waals interactions with the peptide are decisive in determining the relative stabilization of the monomeric state. While the phosphate moiety exhibits strong electrostatic interactions, the compensation by the water solvent results in a minor, overall Coulomb contribution. Our quantitative analysis of the free energies identifies which intermolecular interactions are responsible for the suppression of the amyloid fibril formation by ATP and offers a promising method to analyze the roles of similarly complex cosolvents in aggregation processes.


Asunto(s)
Amiloide , Péptidos , Amiloide/química , Péptidos/química , Agua/química , Entropía , Solventes/química , Simulación de Dinámica Molecular , Proteínas Amiloidogénicas , Péptidos beta-Amiloides/química , Fragmentos de Péptidos/química
4.
J Am Chem Soc ; 2023 Nov 01.
Artículo en Inglés | MEDLINE | ID: mdl-37909095

RESUMEN

In recent years it has been increasingly recognized that different classes of large ions with multiple valency have effects conceptually similar to weakly solvated ions in the Hofmeister series, also labeled by the term chaotropic. The term "superchaotropic effect" has been coined because these effects are much more strongly pronounced for nanometer-sized ions, whose adsorption properties often resemble typical surfactants. Despite this growing interest in these nanometer-sized ions, a simple conceptual extension of the Hofmeister series toward nanoions has not been achieved because an extrapolation of the one-dimensional surface charge density scale does not lead to the superchaotropic regime. In this work, we discuss a generic model that is broadly applicable to ions of nearly spherical shape and thus includes polyoxometalates and boron clusters. We present a qualitative classification scheme in which the ion size appears as a second dimension. Ions of different sizes but the same charge density differ in their bulk solvation free energy. As the ions grow bigger at constant surface charge density, they become more stable in solution, but the adsorption behavior is still governed by the surface charge density. A detailed molecular dynamics simulation study of large ions that is based on a shifted Lennard-Jones potential is presented that supports the presented classification scheme.

5.
Research (Wash D C) ; 6: 0026, 2023.
Artículo en Inglés | MEDLINE | ID: mdl-37040494

RESUMEN

Water/ethyl acetate/ethanol is widely used as a "green" extractant system. We show that 2 different types of phase separation can be induced upon centrifugation in this ternary system using ethanol as a cosolvent of water and ethyl acetate: centrifuge-induced criticality and centrifuge-induced emulsification. The expected composition profiles of samples after centrifugation can be represented by bent lines in a ternary phase diagram when gravitational energy is added to the free energy of mixing. The experimental equilibrium composition profiles behave qualitatively as expected and can be predicted using a phenomenological theory of mixing. The concentration gradients are small except near the critical point, as expected for small molecules. Nevertheless, they are usable when accompanied by temperature cycles. These findings open new possibilities of centrifugal separation, even if control is delicate during temperature cycles. These schemes are accessible even at relatively low centrifugation speed for molecules that float and sediment with apparent molar masses several hundred times larger than the molecular mass.

6.
Angew Chem Int Ed Engl ; 62(27): e202301183, 2023 Jul 03.
Artículo en Inglés | MEDLINE | ID: mdl-36994733

RESUMEN

Chiral phosphoric acids (CPA) have become a privileged catalyst type in organocatalysis, but the selection of the optimum catalyst is still challenging. So far hidden competing reaction pathways may limit the maximum stereoselectivities and the potential of prediction models. In CPA-catalyzed transfer hydrogenation of imines, we identified for many systems two reaction pathways with inverse stereoselectivity, featuring as active catalyst either one CPA or a hydrogen bond bridged dimer. NMR measurements and DFT calculations revealed the dimeric intermediate and a stronger substrate activation via cooperativity. Both pathways are separable: Low temperatures and high catalysts loadings favor the dimeric pathway (ee up to -98 %), while low temperatures with reduced catalyst loading favor the monomeric pathway and give significantly enhanced ee (92-99 % ee; prior 68-86 % at higher temperatures). Thus, a broad impact is expected on CPA catalysis regarding reaction optimization and prediction.

7.
Nat Commun ; 14(1): 813, 2023 Feb 13.
Artículo en Inglés | MEDLINE | ID: mdl-36781877

RESUMEN

Terpene cyclases catalyze one of the most powerful transformations with respect to efficiency and selectivity in natural product (bio)synthesis. In such polyene cyclizations, structurally highly complex carbon scaffolds are built by the controlled ring closure of linear polyenes. Thereby, multiple C,C bonds and stereocenters are simultaneously created with high precision. Structural pre-organization of the substrate carbon chain inside the active center of the enzyme is responsible for the product- and stereoselectivity of this cyclization. Here, we show that in-situ formed fluorinated-alcohol-amine supramolecular clusters serve as artificial cyclases by triggering enzyme-like reactivity and selectivity by controlling substrate conformation in solution. Because of the dynamic nature of these supramolecular assemblies, a broad range of terpenes can be produced diastereoselectively. Mechanistic studies reveal a finely balanced interplay of fluorinated solvent, catalyst, and substrate as key to establishing nature's concept of a shape-selective polyene cyclization in organic synthesis.

8.
Chem Sci ; 13(48): 14366-14372, 2022 Dec 14.
Artículo en Inglés | MEDLINE | ID: mdl-36545144

RESUMEN

BINOL derived chiral phosphoric acids (CPAs) are a prominent class of catalysts in the field of asymmetric organocatalysis, capable of transforming a wide selection of substrates with high stereoselectivities. Exploiting the Brønsted acidic and basic dual functionality of CPAs, substrates with both a hydrogen bond acceptor and donor functionality are frequently used as the resulting bidentate binding via two hydrogen bonds is expected to strongly confine the possible structural space and thus yield high stereoselectivities. Despite the huge success of CPAs and the popularity of a bidentate binding motif, experimental insights into their organization and origin of stereoinduction are scarce. Therefore, in this work the structural space and hydrogen bonding of CPAs and N-(ortho-hydroxyaryl) imines (19 CPA/imine combinations) was elucidated by low temperature NMR studies and corroborated by computations. The postulated bidentate binding of catalyst and substrate by two hydrogen bonds was experimentally validated by detection of trans-hydrogen bond scalar couplings. Counterintuitively, the resulting CPA/imine complexes showed a broad potential structural space and a strong preference towards the formation of [CPA/imine]2 dimers. Molecular dynamics simulations showed that in these dimers, the imines form each one hydrogen bond to two CPA molecules, effectively bridging them. By finetuning steric repulsion and noncovalent interactions, rigid and well-defined CPA/imine monomers could be obtained. NOESY studies corroborated by theoretical calculations revealed the structure of that complex, in which the imine is located in between the 3,3'-substituents of the catalyst and one site of the substrate is shielded by the catalyst, pinpointing the origin or stereoselectivity for downstream transformations.

9.
Angew Chem Int Ed Engl ; 61(49): e202208611, 2022 Dec 05.
Artículo en Inglés | MEDLINE | ID: mdl-36111586

RESUMEN

Chemical bond activations mediated by H-bond interactions involving highly electronegative elements such as nitrogen and oxygen are powerful tactics in modern catalysis research. On the contrary, kindred catalytic regimes in which heavier, less electronegative elements such as selenium engage in H-bond interactions to co-activate C-Se σ-bonds under oxidative conditions are elusive. Traditional strategies to enhance the nucleofugality of selenium residues predicate on the oxidative addition of electrophiles onto SeII -centers, which entails the elimination of the resulting SeIV moieties. Catalytic procedures in which SeIV nucleofuges are substituted rather than eliminated are very rare and, so far, not applicable to carbon-carbon bond formations. In this study, we introduce an unprecedented combination of O-H⋅⋅⋅Se H-bond interactions and single electron oxidation to catalytically generate SeIII nucleofuges that allow for the formation of new C-C σ-bonds by means of a type I semipinacol process in high yields and excellent selectivity.

10.
Phys Chem Chem Phys ; 24(18): 11353-11361, 2022 May 11.
Artículo en Inglés | MEDLINE | ID: mdl-35485971

RESUMEN

Surfactants aggregate in water into micelles, and these micelles incorporate organic substances to solubilize them. Hydrotropes are compounds that increase the solubility of hydrophobic substances in water without this form of aggregation. Decreasing the chain length of the classical surfactant Aerosol OT (AOT) from C8 to C5 results in a molecule with intermediate properties. Molecular dynamics simulations and surface tension measurements are performed on this short chain derivative of AOT. This compound shows high solubility and at the same time progressive weak aggregation. The hydration of head groups hinders significant plunging into a hydrophobic core, which leads to well defined liquid chain nanodomains. The transition to bicontinuous aggregates is in the concentration range of 1 mol L-1. The sulfonate group of the head groups (placed at the water interface of worm-like aggregates) rather than the aggregate-aggregate interaction is responsible for the unusual small angle X-ray scattering pattern.

11.
J Phys Chem B ; 125(43): 12054-12062, 2021 Nov 04.
Artículo en Inglés | MEDLINE | ID: mdl-34694817

RESUMEN

In this work, we developed a general theoretical description of ternary solutions of small molecules under a centrifugal field, from which we obtained the centrifugation map (CMap) as a general tool to understand observations or to predict composition profiles in centrifugal fields of arbitrary strength. The theoretical formalism is based on the classical density functional theory with established models for liquid mixtures. Thermodynamics also yields a general criterion for apparent aggregation. The strength of the CMap approach is illustrated for a ternary model system where ethanol is a co-solvent.

12.
Phys Chem Chem Phys ; 23(14): 8261-8272, 2021 Apr 14.
Artículo en Inglés | MEDLINE | ID: mdl-33527947

RESUMEN

We use the model system ethanol-dodecane to demonstrate that giant critical fluctuations induced by easily accessible weak centrifugal fields as low as 2000g can be observed above the miscibility gap of a binary liquid mixture. Moreover, several degrees above the phase transition, i.e. in the one-phase region, strong gradients of ethanol concentration occur upon centrifugation. In this case, the standard interpretation of sedimentation equilibrium in the analytical ultracentrifuge (AUC) yields an apparent molar mass of ethanol three orders of magnitude higher than the real value. Notably, these composition gradients have no influence on the distribution gradient of solutes such as dyes like Nile red. The thick opaque interphase formed upon centrifugation does not appear as the commonly observed sharp meniscus, but as a turbidity zone, similar to critical opalescence. This layer is a few millimeters thick and separates two fluids with low compositional gradients. All these effects can be qualitatively understood and explained using the Flory-Huggins solution model coupled to classical density functional theory (DFT). In this domain hetero-phase fluctuations can be triggered by gravity even far from the critical point. Taking into account Jean Perrin's approach to external fields in colloids, a self-consistent definition of the Flory effective volume and an explicit calculation of the total free energy per unit volume is possible.

13.
J Am Chem Soc ; 143(2): 724-735, 2021 01 20.
Artículo en Inglés | MEDLINE | ID: mdl-33423466

RESUMEN

Preorganization and aggregation in photoredox catalysis can significantly affect reactivities or selectivities but are often neglected in synthetic and mechanistic studies, since the averaging effect of flexible ensembles can effectively hide the key activation signatures. In addition, aggregation effects are often overlooked due to highly diluted samples used in many UV studies. One prominent example is Knowles's acceleration effect of thiophenol in proton-coupled electron transfer mediated hydroamidations, for which mainly radical properties were discussed. Here, cooperative reactivity enhancements of thiophenol/disulfide mixtures reveal the importance of H-bond networks. For the first time an in-depth NMR spectroscopic aggregation and H-bond analysis of donor and acceptor combined with MD simulations was performed revealing that thiophenol acts also as an acid. The formed phosphate-H+-phosphate dimers provide an extended H-bond network with amides allowing a productive regeneration of the photocatalyst to become effective. The radical and acidic properties of PhSH were substituted by Ph2S2 and phosphoric acid. This provides a handle for optimization of radical and ionic channels and yields accelerations up to 1 order of magnitude under synthetic conditions. Reaction profiles with different light intensities unveil photogenerated amidyl radical reservoirs lasting over minutes, substantiating the positive effect of the H-bond network prior to radical cyclization. We expect the presented concepts of effective activation via H-bond networks and the reactivity improvement via the separation of ionic and radical channels to be generally applicable in photoredox catalysis. In addition, this study shows that control of aggregates and ensembles will be a key to future photocatalysis.

14.
Langmuir ; 37(1): 469-477, 2021 01 12.
Artículo en Inglés | MEDLINE | ID: mdl-33356282

RESUMEN

It is widely recognized that solvation is one of the major factors determining structure and functionality of proteins and long peptides, however it is a formidable challenge to address it both experimentally and computationally. For this reason, simple peptides are used to study fundamental aspects of solvation. It is well established that alcohols can change the peptide conformation and tuning of the alcohol content in solution can dramatically affect folding and, as a consequence, the function of the peptide. In this work, we focus on the leucine and lysine based LKα14 peptide designed to adopt an α-helical conformation at an apolar-polar interface. We investigate LKα14 peptide's bulk and interfacial behavior in water/ethanol mixtures combining a suite of experimental techniques (namely, circular dichroism and nuclear magnetic resonance spectroscopy for the bulk solution, surface pressure measurements and vibrational sum frequency generation spectroscopy for the air-solution interface) with molecular dynamics simulations. We observe that ethanol highly affects both the peptide location and conformation. At low ethanol content LKα14 lacks a clear secondary structure in bulk and shows a clear preference to reside at the air-solution interface. When the ethanol content in solution increases, the peptide's interfacial affinity is markedly reduced and the peptide approaches a stable α-helical conformation in bulk facilitated by the amphiphilic nature of the ethanol molecules.

15.
Phys Chem Chem Phys ; 22(39): 22185-22189, 2020 Oct 15.
Artículo en Inglés | MEDLINE | ID: mdl-32812598

RESUMEN

Hydrophobe solubilization concepts rely on the shielding of solutes from water in nonpolar domains comprising traditional surfactants. We show how an octanol/ethanol/water surfactant-free microemulsion solvates hydrophobic propane in small octanol/ethanol aggregates similar to traditional micelles. These aggregates have the comparable solvent quality as bulk octanol/ethanol with the same composition.

16.
Biophys Chem ; 257: 106258, 2020 02.
Artículo en Inglés | MEDLINE | ID: mdl-31881504

RESUMEN

Recent methodological progress in quantum-chemical calculations using the "embedded cluster reference interaction site model" (EC-RISM) integral equation theory is reviewed in the context of applying it as a solvation model for calculating pressure-dependent thermodynamic and spectroscopic properties of molecules immersed in water. The methodology is based on self-consistent calculations of electronic and solvation structure around dissolved molecules where pressure enters the equations via an appropriately chosen solvent response function and the pure solvent density. Besides specification of a dispersion-repulsion force field for solute-solvent interactions, the EC-RISM approach derives the electrostatic interaction contributions directly from the wave function. We further develop and apply the method to a variety of benchmark cases for which computational or experimental reference data are either available in the literature or are generated specifically for this purpose in this work. Starting with an enhancement to predict hydration free energies at non-ambient pressures, which is the basis for pressure-dependent molecular population estimation, we demonstrate the performance on the calculation of the autoionization constant of water. Spectroscopic problems are addressed by studying the biologically relevant small osmolyte TMAO (trimethylamine N-oxide). Pressure-dependent NMR shifts are predicted and compared to experiments taking into account proper computational referencing methods that extend earlier work. The experimentally observed IR blue-shifts of certain vibrational bands of TMAO as well as of the cyanide anion are reproduced by novel methodology that allows for weighing equilibrium and non-equilibrium solvent relaxation effects. Taken together, the model systems investigated allow for an assessment of the reliability of the EC-RISM approach for studying pressure-dependent biophysical processes.


Asunto(s)
Modelos Químicos , Espectroscopía de Resonancia Magnética , Metilaminas/síntesis química , Metilaminas/química , Simulación de Dinámica Molecular , Presión , Teoría Cuántica
17.
J Chem Inf Model ; 60(2): 604-610, 2020 02 24.
Artículo en Inglés | MEDLINE | ID: mdl-31790243

RESUMEN

Specific ion effects in zwitterionic micelles, especially for anions, are evident in reaction kinetics, zeta potential, and critical micelle concentration measurements. However, anion adsorption to zwitterionic micelles does not produce significant changes in shape, aggregation number, or interfacial hydration. Here we used molecular dynamics simulation of systems containing sulfobetaine zwitterionic micelles of N-dodecyl-N,N-dimethyl-3-ammonio-1-propanesulfonate (DPS) and nine different salts to explore ion adsorption in terms of group dehydration. Our results, in line with those obtained for cationic micelles, showed that the adsorption degree of anions containing both hydrophobic and hydrophilic portions, i.e., hydrotropes, were correlated with the ion dehydration and were governed mainly by the hydrophobic portion dehydration upon adsorption.


Asunto(s)
Interacciones Hidrofóbicas e Hidrofílicas , Micelas , Simulación de Dinámica Molecular , Compuestos de Amonio Cuaternario/química , Agua/química , Adsorción , Conformación Molecular
18.
Cell Chem Biol ; 26(11): 1501-1514.e9, 2019 11 21.
Artículo en Inglés | MEDLINE | ID: mdl-31495713

RESUMEN

Imidazole glycerol phosphate synthase (ImGPS) is an allosteric bienzyme complex in which substrate binding to the synthase subunit HisF stimulates the glutaminase subunit HisH. To control this stimulation with light, we have incorporated the photo-responsive unnatural amino acids phenylalanine-4'-azobenzene (AzoF), o-nitropiperonyl-O-tyrosine (NPY), and methyl-o-nitropiperonyllysine (mNPK) at strategic positions of HisF. The light-mediated isomerization of AzoF at position 55 (fS55AzoFE ↔ fS55AzoFZ) resulted in a reversible 10-fold regulation of HisH activity. The light-mediated decaging of NPY at position 39 (fY39NPY → fY39) and of mNPK at position 99 (fK99mNPK → fK99) led to a 4- to 6-fold increase of HisH activity. Molecular dynamics simulations explained how the unnatural amino acids interfere with the allosteric machinery of ImGPS and revealed additional aspects of HisH stimulation in wild-type ImGPS. Our findings show that unnatural amino acids can be used as a powerful tool for the spatiotemporal control of a central metabolic enzyme complex by light.


Asunto(s)
Aminoácidos/química , Aminohidrolasas/metabolismo , Luz , Regulación Alostérica , Sitio Alostérico , Aminoácidos/síntesis química , Aminoácidos/metabolismo , Aminohidrolasas/química , Glutamina/química , Glutamina/metabolismo , Isomerismo , Cinética , Simulación de Dinámica Molecular , Subunidades de Proteína/química , Subunidades de Proteína/metabolismo
19.
Biophys Chem ; 254: 106260, 2019 11.
Artículo en Inglés | MEDLINE | ID: mdl-31522071

RESUMEN

Molecular simulations based on classical force fields are a powerful method for shedding light on the complex behavior of biomolecules in solution. When cosolutes are present in addition to water and biomolecules, subtle balances of weak intermolecular forces have to be accounted for. This imposes high demands on the quality of the underlying force fields, and therefore force field development for small cosolutes is still an active field. Here, we present the development of a new urea force field from studies of urea solutions at ambient and elevated hydrostatic pressures based on a combination of experimental and theoretical approaches. Experimental densities and solvation shell properties from ab initio molecular dynamics simulations at ambient conditions served as the target properties for the force field optimization. Since urea is present in many marine life forms, elevated hydrostatic pressure was rigorously addressed: densities at high pressure were measured by vibrating tube densitometry up to 500 bar and by X-ray absorption up to 5 kbar. Densities were determined by the perturbed-chain statistical associating fluid theory equation of state. Solvation properties were determined by embedded cluster integral equation theory and ab initio molecular dynamics. Our new force field is able to capture the properties of urea solutions at high pressures without further high-pressure adaption, unlike trimethylamine-N-oxide, for which a high-pressure adaption is necessary.


Asunto(s)
Simulación de Dinámica Molecular , Urea/química , Presión , Soluciones/química , Termodinámica , Agua/química
20.
Biophys Chem ; 253: 106222, 2019 10.
Artículo en Inglés | MEDLINE | ID: mdl-31421516

RESUMEN

We present measurements, molecular dynamics (MD) simulations, and predictions using Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) of the density of aqueous solutions in a pressure range from 1 bar to 5000 bar, a pressure regime that is highly relevant for both biochemical applications and the fundamental understanding of solvation. The accurate determination of density data of pressurized solutions remains challenging. We determined relative density changes from the variations in X-ray absorption through the sample and developed a new water parameter set for PC-SAFT modeling that is appropriate for high pressure conditions in the kilobar regime. As a showcase, we studied trimethylamine N-oxide (TMAO) solutions and demonstrated that their compressibility decreases with the TMAO content. This result is linked to the stabilizing effect of TMAO on the local H-bond network of water. Experiments and calculations, which represent two independent methods, are in very good agreement and are in accordance with results of force field molecular dynamics simulations of the same systems.


Asunto(s)
Metilaminas/química , Simulación de Dinámica Molecular , Enlace de Hidrógeno , Modelos Estadísticos , Soluciones
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