Biomedical subjects

Vladimir A Mandelshtam

Publications and source records attributed to Vladimir A Mandelshtam.

14 recordsLinked to original sources

PubMed2006

Multiple structural transformations in Lennard-Jones clusters: generic versus size-specific behavior.

The size-temperature "phase diagram" for Lennard-Jones clusters LJn with sizes up to n=147 is constructed based on the analysis of the heat capacities and orientational bond order parameter distributions computed by the exchange Monte Carlo method. Two distinct types of "phase transitions" accompanied by peaks in the heat capacities are proven to be generic. Clusters with Mackay atom packing in the overlayer undergo a lower-temperature melting (or Mackay-anti-Mackay) transition that occurs within the overlayer. All clusters undergo a higher-temperature transition, which for the three-layer clusters is proven to be the 55-atom-core-melting transition. For the two-layer clusters, the core/overlayer subdivision is ambiguous, so the higher-temperature transition is better characterized as the breaking of the local icosahedral coordination symmetry. A pronounced size-specific behavior can typically be observed at low temperatures and often occurs in clusters with highly symmetric global minima. An example of such behavior is LJ135, which undergoes a low-temperature solid-solid transition, besides the two generic transitions, i.e., the overlayer reconstruction and the core melting.

Journal Article↗

PubMed2006

Structural transitions and melting in LJ(74-78) Lennard-Jones clusters from adaptive exchange Monte Carlo simulations.

Phase changes in Lennard-Jones (LJ) clusters containing between 74 and 78 atoms are investigated by means of exchange Monte Carlo simulations in the canonical ensemble. The replica temperatures are self-adapted to facilitate the convergence. Although the 74- and 78-atom clusters have icosahedral global minima, the clusters with 75-77 atoms have decahedral ground-state structures and they undergo a structural transition to icosahedral minima before melting. The structural transitions are characterized by quenching and by looking at the Q4 and Q6 orientational bond order parameters. The transition temperatures are estimated to be 0.114, 0.065, and 0.074 reduced units for LJ75, LJ76, and LJ77, respectively. These values, their ordering and the associated latent heats are compared with other estimates based on the harmonic superposition approach.

Journal Article↗

PubMed2006

Structural transformations and melting in neon clusters: quantum versus classical mechanics.

The extraordinary complexity of Lennard-Jones (LJ) clusters, which exhibit numerous structures and "phases" when their size or temperature is varied, presents a great challenge for accurate numerical simulations, even without accounting for quantum effects. To study the latter, we utilize the variational Gaussian wave packet method in conjunction with the exchange Monte Carlo sampling technique. We show that the quantum nature of neon clusters has a substantial effect on their size-temperature "phase diagrams," particularly the critical parameters of certain structural transformations. We also give a numerical confirmation that none of the nonicosahedral structures observed for some classical LJ clusters are favorable in the quantum case.

Journal Article↗

PubMed2005

Size-temperature phase diagram for small Lennard-Jones clusters.

The size-temperature "phase diagram" for small Lennard-Jones clusters LJn (n< or =147) is constructed based on the analysis of the heat capacities Cv(T) , computed by the parallel tempering Monte Carlo method. Two types of "phase transitions" are often observed: the higher-temperature solid-liquid transition, due to melting of the cluster core, and the lower-temperature melting that occurs within the surface layer. The latter transition can only be observed for clusters with Mackay packing of the overlayer.

Journal Article↗

PubMed2005

Identification of two isomers from an organic mixture by double-stimulated-echo NMR and construction of the DOSY spectra by the regularized resolvent transform method.

DOSY-NMR experiments were used to characterize two structural isomers that have different shapes, but identical mass fragmentation patterns, from an organic mixture. It is shown that the spherical molecule diffuses faster than the ellipsoidal one. This distinct behaviour is tentatively explained in terms of microfriction effects from the solvent. Finally, to increase the resolution and efficiency of the 2D DOSY map construction, the data were treated with the regularized resolvent transform method. This method provides good separation for mildly overlapped peaks and requires fewer points than other classical DOSY processing methods.

Journal Article↗

PubMed2005

Thermodynamics and equilibrium structure of Ne38 cluster: quantum mechanics versus classical.

The equilibrium properties of classical Lennard-Jones (LJ38) versus quantum Ne38 Lennard-Jones clusters are investigated. The quantum simulations use both the path-integral Monte Carlo (PIMC) and the recently developed variational-Gaussian wave packet Monte Carlo (VGW-MC) methods. The PIMC and the classical MC simulations are implemented in the parallel tempering framework. The classical heat capacity Cv(T) curve agrees well with that of Neirotti et al. [J. Chem. Phys. 112, 10340 (2000)], although a much larger confining sphere is used in the present work. The classical Cv(T) shows a peak at about 6 K, interpreted as a solid-liquid transition, and a shoulder at approximately 4 K, attributed to a solid-solid transition involving structures from the global octahedral (Oh) minimum and the main icosahedral (C5v) minimum. The VGW method is used to locate and characterize the low energy states of Ne38, which are then further refined by PIMC calculations. Unlike the classical case, the ground state of Ne38 is a liquidlike structure. Among the several liquidlike states with energies below the two symmetric states (Oh and C5v), the lowest two exhibit strong delocalization over basins associated with at least two classical local minima. Because the symmetric structures do not play an essential role in the thermodynamics of Ne38, the quantum heat capacity is a featureless curve indicative of the absence of any structural transformations. Good agreement between the two methods, VGW and PIMC, is obtained. The present results are also consistent with the predictions by Calvo et al. [J. Chem. Phys. 114, 7312 (2001)] based on the quantum superposition method within the harmonic approximation. However, because of its approximate nature, the latter method leads to an incorrect assignment of the Ne38 ground state as well as to a significant underestimation of the heat capacity.

Journal Article↗

PubMed2005

Rapid high-resolution four-dimensional NMR spectroscopy using the filter diagonalization method and its advantages for detailed structural elucidation of oligosaccharides.

Four-dimensional nuclear magnetic resonance spectroscopy with high resolution of signals in the indirect dimensions is reported as an implementation of the filter diagonalization method (FDM). Using an oligosaccharide derivatized with 13C-labeled acetyl isotags, a four-dimensional constant-time pulse sequence was tailored for conjoint use with the FDM. Results demonstrate that high resolution in all dimensions can be achieved using a relatively short experimental time period (19 h), even though the spectrum is highly congested in the direct and all three indirect dimensions. The combined use of isotags, constant-time pulse sequences, and FDM permits rapid isolation of sugar ring proton spin systems in multiple dimensions and enables all endocyclic J-couplings to be simply measured, the key goal to assigning sugar stereochemistry and anomeric configuration. A general method for rapid, unambiguous elucidation of spin systems in oligosaccharides has been a long-sought goal of carbohydrate NMR, and isotags combined with the FDM now enable this to be easily performed. Additional general advantages of the FDM program for generating high-resolution 2D slices in any dimension from a 4D spectrum are emphasized.

Carbon Isotopes↗

PubMed2004

Quantum statistical mechanics with Gaussians: equilibrium properties of van der Waals clusters.

The variational Gaussian wave-packet method for computation of equilibrium density matrices of quantum many-body systems is further developed. The density matrix is expressed in terms of Gaussian resolution, in which each Gaussian is propagated independently in imaginary time beta=(k(B)T)(-1) starting at the classical limit beta=0. For an N-particle system a Gaussian exp[(r-q)(T)G(r-q)+gamma] is represented by its center qinR(3N), the width matrix GinR(3Nx3N), and the scale gammainR, all treated as dynamical variables. Evaluation of observables is done by Monte Carlo sampling of the initial Gaussian positions. As demonstrated previously at not-very-low temperatures the method is surprisingly accurate for a range of model systems including the case of double-well potential. Ideally, a single Gaussian propagation requires numerical effort comparable to the propagation of a single classical trajectory for a system with 9(N(2)+N)/2 degrees of freedom. Furthermore, an approximation based on a direct product of single-particle Gaussians, rather than a fully coupled Gaussian, reduces the number of dynamical variables to 9N. The success of the methodology depends on whether various Gaussian integrals needed for calculation of, e.g., the potential matrix elements or pair correlation functions could be evaluated efficiently. We present techniques to accomplish these goals and apply the method to compute the heat capacity and radial pair correlation function of Ne(13) Lennard-Jones cluster. Our results agree very well with the available path-integral Monte Carlo calculations.

Journal Article↗

PubMed2004

Ultra-high resolution 3D NMR spectra from limited-size data sets.

The advantage of the filter diagonalization method (FDM) for analysis of triple-resonance NMR experiments is demonstrated by application to a 3D constant time (CT) HNCO experiment. With a 15N-,13C-labeled human ubiquitin sample (1.0 mM), high spectral resolution was obtained at 500 MHz in 25 min with only 6-8 increments in each of the CT dimensions. This data set size is about a factor of 50-100 smaller than typically required, yet FDM analysis results in a fully resolved spectrum with a sharp peak for each HNCO resonance. Unlike Fourier transform (FT) processing, in which spectral resolution in each dimension is inversely proportional to the acquisition time in this dimension, FDM is a true multi-dimensional method; the resolution in all dimensions is determined by the total information content of the entire signal. As the CT dimensions of the 3D HNCO signal have approximate time-reversal symmetry, they can each be doubled by combining the usual four hyper-complex data sets. This apparent quadrupling of the data is important to the success of the method. Thus, whenever raw sensitivity is not limiting, well-resolved n-dimensional spectra can now be obtained in a small fraction of the usual time. Alternatively, to maximize sensitivity, evolution periods of faster relaxing nuclei may be radically shortened, the total required resolution being obtained through chemical shift encoding of other, more slowly relaxing, spins. Improvements similar to those illustrated with a 3D HNCO spectrum are expected for other triple-resonance spectra, where CT evolution in the indirect dimensions is implemented.

Algorithms↗

PubMed2004

Rapid 3D NMR using the filter diagonalization method: application to oligosaccharides derivatized with 13C-labeled acetyl groups.

Rapid 3D NMR spectroscopy of oligosaccharides having isotopically labeled acetyl "isotags" was made possible with high resolution in the indirect dimensions using the filter diagonalization method (FDM). A pulse sequence was designed for the optimal correlation of acetyl methyl protons, methyl carbons, and carbonyl carbons. The multi-dimensional nature of the FDM, coupled with the advantages of constant-time evolution periods, resulted in marked improvements over Fourier transform (FT) and mirror-image linear prediction (MI-LP) processing methods. The three methods were directly compared using identical data sets. A highly resolved 3D spectrum was achieved with the FDM using a very short experimental time (28 min).

Models, Theoretical↗

PubMed2003

Progress on the two-dimensional filter diagonalization method. An efficient doubling scheme for two-dimensional constant-time NMR.

An efficient way to treat two-dimensional (2D) constant-time (CT) NMR data using the filter diagonalization method (FDM) is presented. In this scheme a pair of N- and P-type data sets from a 2D CT NMR experiment are processed jointly by FDM as a single data set, twice as large, in which the signal effectively evolves in time for twice as long. This scheme is related to "mirror-image" linear prediction, but with the distinction that the data are directly used, without any preprocessing such as Fourier transformation along one dimension, or point-by-point reflection. As the signal has nearly perfect Lorentzian line shape in the CT dimension, it can be efficiently handled by the FDM approach. Applied to model and experimental signals, the scheme shows significant resolution improvement, and appears to tolerate noise reasonably well. Other complex aspects of multidimensional FDM are discussed and illustrated.

Computer Simulation↗

PubMed2003

Processing DOSY spectra using the regularized resolvent transform.

A new method for processing diffusion ordered spectroscopy (DOSY) data is presented. This method, the regularized resolvent transform (iRRT-the i denoting the adaptation of the method to evaluate the inverse Laplace transform), is better than conventional processing techniques for generating 2D DOSY spectra using data that has poor chemical shift resolution. From the same data, it is possible to use the iRRT to generate 1D subspectra corresponding to different components of the sample mixture; these subspectra compare favorably to 1D spectra of the pure substances. Both the 2D spectra and the 1D subspectra offer a vast improvement over results generated using a conventional processing technique (non-linear least-squares fitting). Consequently, we present the iRRT as a stable and reliable tool for solving the inverse Laplace transform problem present in experiments such as DOSY.

Acyclic Monoterpenes↗

PubMed2003

Regularized resolvent transform for direct calculation of 45 degrees projections of 2D J spectra.

The regularized resolvent transform (RRT) has been applied in a novel way to J-resolved spectra. This involves the direct calculation of the 45 degrees projection without constructing the 2D spectrum. The results show a significant resolution enhancement over that obtained by the 45 degrees projection of a 2D Fourier spectrum, even for much larger signals. In particular, RRT is able to resolve peaks that belong to different overlapping multiplets in a very crowded spectral region, where the conventional technique fails for any signal size. The resolving power of this method along with the significantly shorter signals required, make this method a powerful tool in spectral assignment.

Algorithms↗

PubMed2002

Comment on "Spectral filters in quantum mechanics: a measurement theory perspective".

We criticize a paper by Vijay and Wyatt [Phys. Rev. E 63, 4351 (2000)], in which the authors suggest that energy levels computed, from the same set of matrix-vector products, with the filter diagonalization method (FDM) and the Fourier spectral analysis using the same Chebyshev correlation function are of comparable accuracy. We explain why the FDM is superior and demonstrate it numerically, using the same test matrix as that employed in the above paper. We also compare the FDM with the Lanczos method, another commonly used iterative technique for computing eigenvalues. We find that eigenvalues in a low-density region near the middle of the spectrum converge more quickly with the FDM, but that the Lanczos method requires fewer matrix-vector products to converge all the eigenvalues.

Letter↗