Solvation dynamics in a Brownian dipolar lattice. Comparison between computer simulation and various molecular theories of solvation dynamics

Several recent theoretical and computer simulation studies have considered solvation dynamics in a Brownian dipolar lattice which provides a simple model solvent for which detailed calculations can be carried out. In this article a fully microscopic calculation of the solvation dynamics of an ion in a Brownian dipolar lattice is presented. The calculation is based on the non‐Markovian molecular hydrodynamic theory developed recently. The main assumption of the present calculation is that the two‐particle orientational correlation functions of the solid can be replaced by those of the liquid state. It is shown that such a calculation provides an excellent agreement with the computer simulation results. More importantly, the present calculations clearly demonstrate that the frequency‐dependent dielectric friction plays an important role in the long time decay of the solvation time correlation function. We also find that the present calculation provides somewhat better agreement than either the dynamic mean spherical approximation (DMSA) or the Fried–Mukamel theory which use the simulated frequency‐dependent dielectric function. It is found that the dissipative kernels used in the molecular hydrodynamic approach and in the Fried–Mukamel theory are vastly different, especially at short times. However, in spite of this disagreement, the two theories still lead to comparable results in good agreement with computer simulation, which suggests that even a semiquantitatively accurate dissipative kernel may be sufficient to obtain a reliable solvation time correlation function. A new wave vector and frequency‐dependent dissipative kernel (or memory function) is proposed which correctly goes over to the appropriate expressions in both the single particle and the collective limits. This form is expected to lead to better results than all the existing descriptions.

Solvation dynamics in liquid water. A novel interplay between librational and diffusive modes

A microscopic calculation of the solvation dynamics of an ion in liquid water is presented. The calculated solvation time correlation function shows an ultrafast Gaussian decay which carries about 70%–90% of the strength followed by a biexponential decay with time constants equal to 250 fs and 1 ps. These results are in excellent agreement with the computer simulations of Maroncelli and Fleming and also with the experimental findings of Barbara and Jarzeba. In addition, we find that both the rotational librations and the intermolecular translational vibrational modes of water contribute significantly to the initial Gaussian decay.

Sorbate properties and cage-to-cage diffusion of argon in NaCaA: a molecular dynamics study

Detailed molecular dynamics simulations of argon in zeolite NaCaA are reported. Thermodynamic, structural, and dynamical properties of the sorbate as a function of temperature have been obtained. The properties calculated include various site-site radial distribution functions, different energy distribution functions, selfdiffusion coefficients, the power spectra, and properties relating to cage-to-cage diffusion. The results suggest that sorbate is delocalized above 300 K. Both modes of cage-to-cage diffusion-the surface-mediated and centralized diffusion-are associated with negative barrier heights. Surprisingly, rate of cage-to-cage diffusion is associated with negative and positive activation energies below and above 500 K. The observed differences in the behavior of the rate of cage-to-cage diffusion between Xe-NaY and Ar-NaCaA systems and the nature of the potential energy surface are discussed. Presence of sorbatezeolite interactions results in significant enhancement in the rate of cage-to-cage diffusion and rate of cage visits. It is shown that properties dependent on the long-time behavior such as the diffusion coefficient and the rate of cages visited exhibit the expected Arrhenius dependence on temperature.

Synthesis, Reactivity, Structural Aspects, and Solution Dynamics of Cyclopalladated Compounds of N,N `,N `'-Tris(2-anisyl)guanidine

N,N',N `'-Tris(2-anisyl)guanidine, (ArNH)(2)C=NAr (Ar = 2-(MeO)C6H4), was cyclopallaclated with Pd(OC(O)R)(2) (R = Me, CF3) in toluene at 70 degrees C to afford palladacycles Pd{kappa(2)(C,N)-C6H3-(OMe)-3(NHC(NHAr)(=NAr))-2}(mu-OC(O)R)](2)(R = Me (1a) and CF3 (1b)) in 87% and 95% yield, respectively. Palladacycle 1a was subjected to a metathetical reaction with LiBr in aqueous ethanol at 78 degrees C to afford palladacycle Pd{kappa(2)(C,N)-C6H3(OMe)-3(NHC(NHAr)(=NAr))-2}(mu-Br)](2) (2) in 90% yield. Palladacycle 2 was subjected to a bridge-splitting reaction with Lewis bases in CH2Cl2 to afford the monomeric palladacycles Pd{kappa(2)(C,N)-C6H3(OMe)-3(NHC(NHAr)(=NAr))-2}Br(L)] (L = 2,6-Me2C5H3N (3a), 2,4-Me2C5H3N (3b), 3,5-Me2C5H3N (3c), XyNC (Xy = 2,6-Me2C6H3; 4a), (BuNC)-Bu-t (4b), and PPh3 (5)) in 87-95% yield. Palladacycle 2 upon reaction with 2 equiv of XyNC in CH2Cl2 afforded an unanticipated palladacycle, Pd{kappa(2)(C,N)-C(=NXy)(C6H3(OMe)-4)-2(N=C-(NH Ar)(2))-3} Br(CNXy)] (6) in 93% yield, and the driving force for the formation of 6 was ascribed to a ring contraction followed by amine-imine tautomerization. Palladacycles 1 a,b revealed a dimeric transoid in-in conformation with ``open book'' framework in the solid state. In solution, 1 a exhibited a fluxional behavior ascribed to the six-membered ``(C,N)Pd'' ring inversion and partly dissociates to the pincer type and kappa(2)-O,O'-OAc monomeric palladacycles by an anchimerically assisted acetate cleavage process as studied by variable-temperature H-1 NMR data. Palladacycles 3a,b revealed a unique trans configuration around the palladium with lutidine being placed trans to the Pd-C bond, whereas cis stereochemistry was observed between the Pd-C bond and the Lewis base in 4a (as determined by X-ray diffraction data) and 5 (as determined by P-31 and C-13 NMR data). The aforementioned stereochemical difference was explained by invoking relative hardness/softness of the donor atoms around the palladium center. In solution, palladacycles 3a-c exist as a mixture of two interconverting boat conformers via a planar intermediate without any bond breaking due to the six-membered ``(C,N)Pd'' ring inversion, whereas palladacycles 4a,b and 5 exist as a single isomer, as deduced from detailed H-1 NMR studies.

A Molecular Dynamics Study of Atomic Correlations in Glassy BzS3t

Glassy B&, the parent compound of the superionic conductor LiI-Li&B& has been studied by the molecular dynamics technique using a new potential model. The results suggest that the glass is made up of local units of four-membered B2S2 rings bridged by sulfur atoms, leading to a chainlike structure. Various pair correlation functions have been analyzed, and the B2Sz rings have been found to be planar. The calculated neutron structure factor shows a peak at 1.4 A-' which has been attributed to B-B correlations at 5.6 A. The glass transition temperature of the simulated system has been calculated to be around 800 K.

Analysis of Hydrogen Bonding and Stability of Protein Secondary Structures in Molecular Dynamics Simulation

Molecular Dynamics (MD) simulations provide an atomic level account of the molecular motions and have proven to be immensely useful in the investigation of the dynamical structure of proteins. Once an MD trajectory is obtained, specific interactions at the molecular level can be directly studied by setting up appropriate combinations of distance and angle monitors. However, if a study of the dynamical behavior of secondary structures in proteins becomes important, this approach can become unwieldy. We present herein a method to study the dynamical stability of secondary structures in proteins, based on a relatively simple analysis of backbone hydrogen bonds. The method was developed for studying the thermal unfolding of beta-lactamases, but can be extended to other systems and adapted to study relevant properties.

1H NMR study of molecular dynamics and phase transition in (NH4)2ZnBr4

The proton second moment (M2) and spin-lattice relaxation time (T1) have been measured in (NH4)2ZnBr4 in the range 77-300 K. The room-temperature spectrum shows a structure which disappears around 243 K. The signal is strong and narrow even at 77 K. Proton T1 shows a maximum at 263 K, caused by spin rotation interaction and decreases with decreasing temperature till 235 K, where it shows a sudden increase. Below 235 K, again it decreases and shows a slope change around 216.5 K (reported Tc). From 216.5 K, T1 decreases continuously without exhibiting any minimum down to 77 K. The narrow line at 77 K, and absence of a T1 minimum down to 77 K indicate the possibility of quantum mechanical tunnelling in this system. Motional parameters such as activation energy and pre-exponential factor have been evaluated for the reorientational motion of the NH+4 ion.

E. C. G. Sudarshan and Symmetry in Classical Dynamics, Optics and Quantum Mechanics

We review work initiated and inspired by Sudarshan in relativistic dynamics, beam optics, partial coherence theory, Wigner distribution methods, multimode quantum optical squeezing, and geometric phases. The 1963 No Interaction Theorem using Dirac's instant form and particle World Line Conditions is recalled. Later attempts to overcome this result exploiting constrained Hamiltonian theory, reformulation of the World Line Conditions and extending Dirac's formalism, are reviewed. Dirac's front form leads to a formulation of Fourier Optics for the Maxwell field, determining the actions of First Order Systems (corresponding to matrices of Sp(2,R) and Sp(4,R)) on polarization in a consistent manner. These groups also help characterize properties and propagation of partially coherent Gaussian Schell Model beams, leading to invariant quality parameters and the new Twist phase. The higher dimensional groups Sp(2n,R) appear in the theory of Wigner distributions and in quantum optics. Elegant criteria for a Gaussian phase space function to be a Wigner distribution, expressions for multimode uncertainty principles and squeezing are described. In geometric phase theory we highlight the use of invariance properties that lead to a kinematical formulation and the important role of Bargmann invariants. Special features of these phases arising from unitary Lie group representations, and a new formulation based on the idea of Null Phase Curves, are presented.

Dielectric Relaxation Spectroscopy for Evaluation of the Influence of Solvent Dynamics on Ion Transport in Succinonitrile-Salt Plastic Crystalline Electrolytes

Influence of succinonitrile (SN) dynamics on ion transport in SN-lithium perchlorate (LiClO4) electrolytes is discussed here via dielectric relaxation spectroscopy. Dielectric relaxation spectroscopy (similar to 2 x 10(-3) Hz to 3 MHz) of SN and SN-LiClO4 was studied as a function of salt content (up to 7 mol % or 1 M) and temperature (-20 to +60 degrees C). Analyses of real and imaginary parts of permittivity convincingly reveal the influence Of trans gauche isomerism and solvent-salt association (solvation) effects on ion transport. The relaxation processes are highly dependent on the salt concentration and temperature. While pristine SN display only intrinsic dynamics (i.e., trans-gauche isomerism) which enhances with an increase in temperature, SN-LiClO4 electrolytes especially at high salt concentrations (similar to 0.04-1 M) show salt-induced relaxation processes. In the concentrated electrolytes, the intrinsic dynamics was observed to be a function of salt content, becoming faster with an increase in salt concentration. Deconvolution of the imaginary part of the permittivity spectra using Havriliak-Negami (HN) function show a relaxation process corresponding to the above phenomena. The permittivity data analyzed using HN and Kohlrausch-Williams-Watta (KWW) functions show non-Debye relaxation processes and enhancement in the trans phase (enhanced solvent dynamics) as a function of salt concentration and temperature.

Patent Price Dynamics in the Context of Patent Age and Patent Latent Variables

The decision to patent a technology is a difficult one to make for the top management of any organization. The expected value that the patent might deliver in the market is an important factor that impacts this judgement. Earlier researchers have suggested that patent prices are better indicators of value of a patent and that auction prices are the best way of determining value. However, the lack of public data on pricing has prevented research on understanding the dynamics of patent pricing. Our paper uses singleton patent auction price data of Ocean Tomo LLC to study the prices of patents. We describe price characteristics of these patents. The price of these patents was correlated with their age, and a significant correlation was found. A price - age matrix was developed and we describe the price characteristics of patents using four quadrants of the matrix, namely young and old patents with low and high prices. We also found that patents owned by small firms get transacted more often and inventor owned patents attracted a better price than assignee owned patents.

Dynamics of I-asterisk(P-2(1/2)) production inthe ultraviolet photodissociation of alkyn iodides

The relative quantum yields, phi*, for the production of I*(P-2(1/2)) at 266, 280, and similar to 305 nm are reported for a series of primary alkyl iodides using the technique of two-photon laser-induced fluorescence for the detection of I(P-2(3/2)) and I*(P-2(1/2)) atoms. Results are analyzed by invoking the impulsive energy disposal model, which summarizes the dynamics of dissociation as a single parameter. Comparison of our data with those calculated by a more sophisticated time-dependent quantum mechanical model is also made. Near the red edge of the alkyl iodide A band, absorption contribution from the (3)Q(1) state is important and the dynamics near the (3)Q(0)-(1)Q(1) curve-crossing region seem to be influenced by the kinematics of the dissociation process

Dynamics of zeolite cage and its effect on the diffusion properties of sorbate: persistence of diffusion anomaly in NaA zeolite

Recent computer simulations on zeolites Y and A have found that the diffusion coefficient and the rate of intercage diffusion exhibit, apart from a linear dependence on the reciprocal of the square of the sorbate diameter, an anomalous peak as sorbate diameter approaches the window diameter. Here we report molecular dynamics simulations of zeolite NaA incorporating framework flexibility as a function of sorbate diameter in order to verify the existence of anomalous diffusion. Results suggest persistence of anomalous diffusion or ring effect. This suggests that the anomalous behavior is a general effect characteristic of zeolites Y and A. The barrier for diffusion across the eight-ring window is seen to be negative and is found to decrease with sorbate size. The effect of sorbate on the cage motion has also been investigated. Results suggest that the window expands during intercage migration only if the sorbate size is comparable to the window diameter. Flexible cage simulations yield a higher value for the diffusion coefficient and also the rate of intercage diffusion. This increase has been shown to be due to an increase in the intercage diffusions via the centralized diffusion mode rather than the surface-mediated mode. It is shown that this increase arises from an increase in the single particle density distribution in the region near the cage center.

Effect of the valine-threonine constraint on the dynamics of the proline helix — A molecular dynamics study

Proline residues in helices play an important role in the structure of proteins. The proline residue introduces a kink in the helix which varies from about 5-degrees to 50-degrees. The presence of other residues such as threonine or valine near the proline region can influence the flexibility exhibited by the kinked helix, which can have an important biological role. In the present paper, the constraint introduced by threonine and valine on a proline helix is investigated by molecular dynamics studies. The systems considered am (1) a poly-alanine helix with threonine-proline residues (TP) and (2) a poly-alanine helix with valine-threonine-proline residues (VTP), in the middle. Molecular dynamics simulations are carried out on these two systems for 500 ps. The results are analyzed in terms of structural transitions, bend-related parameters and sidechain orientations.

Ultrafast underdamped solvation: Agreement between computer simulation and various theories of solvation dynamics

A theoretical analysis of the three currently popular microscopic theories of solvation dynamics, namely, the dynamic mean spherical approximation (DMSA), the molecular hydrodynamic theory (MHT), and the memory function theory (MFT) is carried out. It is shown that in the underdamped limit of momentum relaxation, all three theories lead to nearly identical results when the translational motions of both the solute ion and the solvent molecules are neglected. In this limit, the theoretical prediction is in almost perfect agreement with the computer simulation results of solvation dynamics in the model Stockmayer liquid. However, the situation changes significantly in the presence of the translational motion of the solvent molecules. In this case, DMSA breaks down but the other two theories correctly predict the acceleration of solvation in agreement with the simulation results. We find that the translational motion of a light solute ion can play an important role in its own solvation. None of the existing theories describe this aspect. A generalization of the extended hydrodynamic theory is presented which, for the first time, includes the contribution of solute motion towards its own solvation dynamics. The extended theory gives excellent agreement with the simulations where solute motion is allowed. It is further shown that in the absence of translation, the memory function theory of Fried and Mukamel can be recovered from the hydrodynamic equations if the wave vector dependent dissipative kernel in the hydrodynamic description is replaced by its long wavelength value. We suggest a convenient memory kernel which is superior to the limiting forms used in earlier descriptions. We also present an alternate, quite general, statistical mechanical expression for the time dependent solvation energy of an ion. This expression has remarkable similarity with that for the translational dielectric friction on a moving ion.