Product Markovian Quantization of a Diffusion Process with Applications to Finance

Methodology and Computing in Applied Probability - We introduce a new methodology for the quantization of the Euler scheme for a d-dimensional diffusion process. This method is based on a Markovian...     

Direct Derivation of Free Energies of Membrane Deformation and Other Solvent Density Variations From Enhanced Sampling Molecular Dynamics

We report a methodology to calculate the free energy of a shape transformation in a lipid membrane directly from a molecular dynamics simulation. The bilayer need not be homogeneous or symmetric and can be atomically detailed or coarse grained. The method is based on a collective variable that quantifies the similarity between the membrane and a set of predefined density distributions. Enhanced sampling of this “Multi-Map” variable re-shapes the bilayer and permits the derivation of the corresponding potential of mean force. Calculated energies thus reflect the dynamic interplay of atoms and molecules, rather than postulated effects. Evaluation of deformations of different shape, amplitude, and range demonstrates that the macroscopic bending modulus assumed by the Helfrich–Canham model is increasingly unsuitable below the 100-Å scale. In this range of major biological significance, direct free-energy calculations reveal a much greater plasticity. We also quantify the stiffening effect of cholesterol on bilayers of different composition and compare with experiments. Lastly, we illustrate how this approach facilitates analysis of other solvent reorganization processes, such as hydrophobic hydration. Published 2019. This article is a U.S. Government work and is in the public domain in the USA.     

Surface products and coverage dependence of dissociative ethane adsorption on Pt{110}-(1 x 2)

The dissociation of ethane on Pt{110}-(1 x 2) has been studied using supersonic molecular beam and temperature-programmed reaction techniques. The study unequivocally shows that the stable dissociation product of ethane on Pt{110}-(1 x 2) at all coverages is CCH2 at 350-400 K and CCH at 440 K. Temperature-programmed-reaction (TPR) experiments indicate that the CCH2 species decomposes to CCH with a reaction-limited peak temperature of 430 K. Above 450 K, the CCH species becomes unstable and decomposes with a peak temperature of 540 K. By 600 K, ethane dehydrogenates completely to form a surface carbon layer. The sticking probability is initially 0.02 at 370 K and 0.03 at 600 K and follows a linear (1-2theta) dependence for coverages of up to theta = 0.4 ML, where theta is defined as the number of C2Hx units per (1 x 2) unit cell. However, a much weaker coverage dependence at 800 K suggests that the carbon agglomerates into high-density islands.     

Conformational behavior of cis-2-methoxy, cis-2-methylthio, and cis-2-methylselenocyclohexanol: a theoretical and experimental investigation

Studies on the conformational equilibria of 2-methoxy, 2-methylthio, and 2-methylselenocyclohexanol are reported. Dynamic NMR spectroscopy experiments at 203-210 K were performed, which provided the percentages of each conformer in equilibrium. Theoretical calculations using the B3LYP method and aug-cc-pvdz basis set were applied to determine the differences in energy between the conformers. The analysis of the potential energy surface of each conformer showed the presence of two rotamers. Natural bond orbital analysis provided an explanation of which factors are driving the rotamer and conformer preferences.     

Microcalorimetry of O2 and NO on flat and stepped platinum surfaces

Using the single-crystal adsorption calorimeter (SCAC), coverage-dependent heats of adsorption and sticking probabilities are reported for O₂ and NO on Pt{1 1 1}, Pt{2 1 1} and Pt{4 1 1} at 300 K. At low coverage, oxygen adsorption is dissociative for all Pt surfaces. The highest initial heat of adsorption is found on Pt{2 1 1}, with a value of 370 kJ/mol, followed by those on Pt{4 1 1} (310 kJ/mol) and Pt{1 1 1} (300 kJ/mol). We attribute this relatively large difference in the dissociative heat of adsorption at low coverage to the step character of the {2 1 1} surface. Initial sticking probabilities, s_o, are similar for the three surfaces, 0.22 on Pt{1 1 1}, 0.17 on Pt{2 1 1} and 0.18 on Pt{4 1 1}, rapidly decreasing as the oxygen coverage increases. For nitric oxide, the initial heats of adsorption are very similar and consistent with either dissociative or molecular adsorption, with values of 182 kJ/mol on Pt{1 1 1}, 192 kJ/mol on Pt{2 1 1} and 217 kJ/mol on Pt{4 1 1}. The s_o value is virtually identical for all three systems, with values ranging from 0.82 to 0.85, suggesting that the initial sticking probability is insensitive to the surface structure and adsorption is intrinsically precursor mediated. SCAC data are also used to evaluate pre-exponential factors, ν, for first-order desorption at high coverage where adsorption is non-dissociative. Values of 3 × 10¹⁸, 6 × 10¹⁸ and 2 × 10¹⁸ s^?1 for O₂, and 4 × 10¹⁹, 6 × 10¹⁷ and 2 × 10²⁰ s^?1 for NO on Pt{1 1 1}, Pt{2 1 1} and Pt{4 1 1}, respectively, are found. These unexpectedly high values are rationalised in terms of conventional transition state theory entropy changes.     

Sol gel synthesis of 3-n-propyl(4-aminomethyl)pyridinium silsesquioxane chloride and the enhanced electrocatalytic activity of LbL films

Journal of Sol-Gel Science and Technology - A silsesquioxane based on a silica matrix and 4-(aminomethyl)pyridine group was successfully synthesized using the sol–gel process with the...     

Comparison of modern Langevin integrators for simulations of coarse-grained polymer melts

For a wide range of phenomena, current computational ability does not always allow for atomistic simulations of high-dimensional molecular systems to reach time scales of interest. Coarse-graining (CG) is an established approach to alleviate the impact of computational limits while retaining the same algorithms used in atomistic simulations. It is important to understand how algorithms such as Langevin integrators perform on non-trivial CG molecular systems, and in particular how large of an integration time step can be used without introducing unacceptable amounts of error into averaged quantities of interest. To investigate this, we examined three different Langevin integrators on a CG polymer melt: the recently developed BAOAB method by Leimkuhler and Matthews [J. Chem. Phys. 138 (17), 05B601_1 (2013)], the Grønbech-Jensen and Farago method [Mol. Phys. 111 (8), 983-991 (2013)], or G-JF, and the frequently used Brünger–Brooks–Karplus integrator [Chem. Phys. Lett. 105 (5), 495-500 (1984)], known as BBK. We compute and analyse key statistical properties for each. Our results indicate that the integrators perform similarly for a small friction parameter; however outside this regime, the use of large integration steps produces significant deviations from the predicted diffusivity and steady-state distributions for all methods examined with the exception of G-JF.     

Direct sticking and differential adsorption heats as probes of structural transitions: O2 on the stepped Ni[211] surface

Coverage-dependent heats of adsorption and sticking probabilities for oxygen on Ni[211] have been measured at 300 K using single-crystal adsorption calorimetry. The data are consistent with a switch from dissociative chemisorption at low coverage to oxide formation above 2 ML adatom coverage. The initial heat of adsorption is 620 kJ mol(-)(1), considerably higher than for any low Miller index nickel surface; this is attributed to the presence of low coordination step atoms that are preferably occupied up to 1 ML. As the coverage increases, the heat is found to drop very rapidly, indicating the presence of strong lateral adatom repulsions, which ultimately drive a transition from the chemisorption regime to oxide film formation at higher coverage. The shape of the coverage-dependent sticking probability is consistent with a direct adsorption mechanism at low coverage. At higher coverage, the transition between the chemisorption and oxidation regimes is relatively complex compared with low Miller index nickel surfaces. This is discussed in terms of the influence of the step sites on the [211] surface.     

Adsorption dynamics of water on Pt{110}-(1 x 2)

The dynamics of H(2)O adsorption on Pt{110}-(1 x 2) is studied using supersonic molecular beam and temperature programed desorption techniques. The sticking probabilities are measured using the King and Wells method at a surface temperature of 165 K. The absolute initial sticking probability s(0) of H(2)O is 0.54+/-0.03 for an incident kinetic energy of 27 kJmol. However, an unusual molecular beam flux dependence on s(0) is also found. At low water coverage (theta<1), the sticking probability is independent of coverage due either to diffusion in an extrinsic precursor state formed above bilayer islands or to incorporation into the islands. We define theta=1 as the water coverage when the dissociative sticking probability of D(2) on a surface predosed with water has dropped to zero. The slow falling H(2)O sticking probability at theta>1 results from compression of the bilayer and the formation of multilayers. Temperature programed desorption of water shows fractional order kinetics consistent with hydrogen-bonded islands on the surface. A remarkable dependence of the initial sticking probability on the translational (1-27 kJ/mol) and internal energies of water is observed: s(0) is found to be essentially a step function of translational energy, increasing fivefold at a threshold energy of 5 kJ/mol. The threshold migrates to higher energies with increasing nozzle temperature (300-700 K). We conclude that both rotational state and rotational alignment of the water molecules in the seeded supersonic expansion are implicated in dictating the adsorption process.     

How Sensitive is the Amide I Vibration of the Polypeptide Backbone to Electric Fields?

Site‐selective isotopic labeling of amide carbonyls offers a nonperturbative means to introduce a localized infrared probe into proteins. Although this strategy has been widely used to investigate various biological questions, the dependence of the underlying amide I vibrational frequency on electric fields (or Stark tuning rate) has not been fully determined, which prevents it from being used in a quantitative manner in certain applications. Herein, through the use of experiments and molecular dynamics simulations, the Stark tuning rate of the amide I vibration of an isotopically labeled backbone carbonyl in a transmembrane α‐helix is determined to be approximately 1.4 cm^?1/(MV/cm). This result provides a quantitative basis for using this vibrational model to assess local electric fields in proteins, among other applications. For instance, by using this value, we are able to show that the backbone region of a dipeptide has a surprisingly low dielectric constant.