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Internal Degrees (internal + degree)
Selected AbstractsAdiabatic decoupling of the reaction coordinateINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 10 2008J. C. Lorquet Abstract When the dynamics is constrained by adiabatic invariance, a reactive process can be described as a one-dimensional motion along the reaction coordinate in an effective potential. This simplification is often valid for central potentials and for the curved harmonic valley studied in the reaction path Hamiltonian model. For an ion,molecule reaction, the action integral ,P,, = (1/2,),P,d, is an adiabatic invariant. The Poisson bracket of ,P,,2 with Hamiltonians corresponding to a great variety of long-range electrostatic interactions is found to decrease with the separation coordinate r, faster than the corresponding potential. This indicates that the validity of the adiabatic approximation is not directly related to the shape of the potential energy surface. The leading role played by the translational momentum is accounted for by Jacobi's form of the least action principle. However, although the identification of adiabatic regions by this procedure is limited to a specific range of coordinate configurations, equivalent constraints must persist all along the reaction coordinate and must operate during the entire reaction, as a result of entropy conservation. The study of the translational kinetic energy released on the fragments is particularly appropriate to detect restrictions on energy exchange between the reaction coordinate and the bath of internal degrees of freedom. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Parametric Rietveld refinement for the evaluation of powder diffraction patterns collected as a function of pressureJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 3 2010Ivan Halasz Under the assumption that the structural parameters of a crystalline phase change `smoothly' with increasing pressure, the evolution of the parameters can be parameterized as a function of pressure using continuous monotonic functions. Four different approaches to determine the structural evolution of As2O5 with increasing pressure from a set of powder diffraction patterns collected over the pressure range from 2.5 to 19.5,GPa have been investigated. Approach (A) was the common sequential refinement of atomic coordinates with restraints on the geometry and was compared with three parameterization approaches. Approach (B) used direct parameterization by low-order polynomials of each crystallographically distinct atomic coordinate, (C) described the atoms of the asymmetric unit as a rigid body and allowed the internal degrees of freedom of the rigid body to vary with the change in pressure using rigid unit modes, and (D) described the crystal structure as a distortion of the higher-symmetry structure of As2O5 (which is here also a high-temperature phase) by using symmetry-adapted distortion modes. Approach (D) offers the possibility to directly introduce an order parameter into Rietveld refinement through an empirical power law derived from Landau theory and thus to obtain the value of the critical exponent. In contrast, the rigid-body approach did not fit the data as well. All parameterizations greatly reduce the number of required parameters. [source] A new method for the gradient-based optimization of molecular complexesJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 9 2009Jan Fuhrmann Abstract We present a novel method for the local optimization of molecular complexes. This new approach is especially suited for usage in molecular docking. In molecular modeling, molecules are often described employing a compact representation to reduce the number of degrees of freedom. This compact representation is realized by fixing bond lengths and angles while permitting changes in translation, orientation, and selected dihedral angles. Gradient-based energy minimization of molecular complexes using this representation suffers from well-known singularities arising during the optimization process. We suggest an approach new in the field of structure optimization that allows to employ gradient-based optimization algorithms for such a compact representation. We propose to use exponential mapping to define the molecular orientation which facilitates calculating the orientational gradient. To avoid singularities of this parametrization, the local minimization algorithm is modified to change efficiently the orientational parameters while preserving the molecular orientation, i.e. we perform well-defined jumps on the objective function. Our approach is applicable to continuous, but not necessarily differentiable objective functions. We evaluated our new method by optimizing several ligands with an increasing number of internal degrees of freedom in the presence of large receptors. In comparison to the method of Solis and Wets in the challenging case of a non-differentiable scoring function, our proposed method leads to substantially improved results in all test cases, i.e. we obtain better scores in fewer steps for all complexes. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009 [source] Hydrodynamic modeling of diffusion tensor properties of flexible moleculesJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 1 2009Vincenzo Barone Abstract We present a computationally efficient implementation of hydrodynamic modeling for the evaluation of diffusion tensors of molecules with internal degrees of freedom, adapted to take into account information from linear scaling computations of solvent accessible surfaces implemented in the framework of last generation continuum solvent models. Torsional angles are taken also explicitly into account, while retaining correct hydrodynamic interactions. A comparison with literature data is presented to prove the effectiveness of the approach for a wide range of molecular dimensions and solvent environments. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009 [source] Efficient calculation of configurational entropy from molecular simulations by combining the mutual-information expansion and nearest-neighbor methods,,JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 10 2008Vladimir Hnizdo Abstract Changes in the configurational entropies of molecules make important contributions to the free energies of reaction for processes such as protein-folding, noncovalent association, and conformational change. However, obtaining entropy from molecular simulations represents a long-standing computational challenge. Here, two recently introduced approaches, the nearest-neighbor (NN) method and the mutual-information expansion (MIE), are combined to furnish an efficient and accurate method of extracting the configurational entropy from a molecular simulation to a given order of correlations among the internal degrees of freedom. The resulting method takes advantage of the strengths of each approach. The NN method is entirely nonparametric (i.e., it makes no assumptions about the underlying probability distribution), its estimates are asymptotically unbiased and consistent, and it makes optimum use of a limited number of available data samples. The MIE, a systematic expansion of entropy in mutual information terms of increasing order, provides a well-characterized approximation for lowering the dimensionality of the numerical problem of calculating the entropy of a high-dimensional system. The combination of these two methods enables obtaining well-converged estimations of the configurational entropy that capture many-body correlations of higher order than is possible with the simple histogramming that was used in the MIE method originally. The combined method is tested here on two simple systems: an idealized system represented by an analytical distribution of six circular variables, where the full joint entropy and all the MIE terms are exactly known, and the R,S stereoisomer of tartaric acid, a molecule with seven internal-rotation degrees of freedom for which the full entropy of internal rotation has been already estimated by the NN method. For these two systems, all the expansion terms of the full MIE of the entropy are estimated by the NN method and, for comparison, the MIE approximations up to third order are also estimated by simple histogramming. The results indicate that the truncation of the MIE at the two-body level can be an accurate, computationally nondemanding approximation to the configurational entropy of anharmonic internal degrees of freedom. If needed, higher-order correlations can be estimated reliably by the NN method without excessive demands on the molecular-simulation sample size and computing time. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008 [source] Estimation of the absolute internal-rotation entropy of molecules with two torsional degrees of freedom from stochastic simulationsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 7 2005Eva Darian Abstract A method of statistical estimation is applied to the problem of evaluating the absolute entropy of internal rotation in a molecule with two torsional degrees of freedom. The configurational part of the entropy is obtained as that of the joint probability density of an arbitrary form represented by a two-dimensional Fourier series, the coefficients of which are statistically estimated using a sample of the torsional angles of the molecule obtained by a stochastic simulation. The internal rotors in the molecule are assumed to be attached to a common frame, and their reduced moments of inertia are initially calculated as functions of the two torsional angles, but averaged over all the remaining internal degrees of freedom using the stochastic-simulation sample of the atomic configurations of the molecule. The torsional-angle dependence of the reduced moments of inertia can be also averaged out, and the absolute internal-rotation entropy of the molecule is obtained in a good approximation as the sum of the configurational entropy and a kinetic contribution fully determined by the averaged reduced moments of inertia. The method is illustrated using Monte Carlo simulations of isomers of stilbene and halogenated derivatives of propane. The two torsional angles in cis -stilbene are found to be much more strongly correlated than those in trans -stilbene, while the degree of the angular correlation in propane increases strongly on substitution of hydrogen atoms with chlorine. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 651,660, 2005 [source] Activation of large lons in FT-ICR mass spectrometryMASS SPECTROMETRY REVIEWS, Issue 2 2005Julia Laskin Abstract The advent of soft ionization techniques, notably electrospray and laser desorption ionization methods, has enabled the extension of mass spectrometric methods to large molecules and molecular complexes. This both greatly extends the applications of mass spectrometry and makes the activation and dissociation of complex ions an integral part of these applications. This review emphasizes the most promising methods for activation and dissociation of complex ions and presents this discussion in the context of general knowledge of reaction kinetics and dynamics largely established for small ions. We then introduce the characteristic differences associated with the higher number of internal degrees of freedom and high density of states associated with molecular complexity. This is reflected primarily in the kinetics of unimolecular dissociation of complex ions, particularly their slow decay and the higher energy content required to induce decomposition,the kinetic shift (KS). The longer trapping time of Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) significantly reduces the KS, which presents several advantages over other methods for the investigation of dissociation of complex molecules. After discussing general principles of reaction dynamics related to collisional activation of ions, we describe conventional ways to achieve single- and multiple-collision activation in FT-ICR MS. Sustained off-resonance irradiation (SORI),the simplest and most robust means of introducing the multiple collision activation process,is discussed in greatest detail. Details of implementation of this technique, required control of experimental parameters, limitations, and examples of very successful application of SORI-CID are described. The advantages of high mass resolving power and the ability to carry out several stages of mass selection and activation intrinsic to FT-ICR MS are demonstrated in several examples. Photodissociation of ions from small molecules can be effected using IR or UV/vis lasers and generally requires tuning lasers to specific wavelengths and/or utilizing high flux, multiphoton excitation to match energy levels in the ion. Photodissociation of complex ions is much easier to accomplish from the basic physics perspective. The quasi-continuum of vibrational states at room temperature makes it very easy to pump relatively large amounts of energy into complex ions and infrared multiphoton dissociation (IRMPD) is a powerful technique for characterizing large ions, particularly biologically relevant molecules. Since both SORI-CID and IRMPD are slow activation methods they have many common characteristics. They are also distinctly different because SORI-CID is intrinsically selective (only ions that have a cyclotron frequency close to the frequency of the excitation field are excited), whereas IRMPD is not (all ions that reside on the optical path of the laser are excited). There are advantages and disadvantages to each technique and in many applications they complement each other. In contrast with these slow activation methods, the less widely appreciated activation method of surface induced dissociation (SID) appears to offer unique advantages because excitation in SID occurs on a sub-picosecond time scale, instantaneously relative to the observation time of any mass spectrometer. Internal energy deposition is quite efficient and readily adjusted by altering the kinetic energy of the impacting ion. The shattering transition,instantaneous decomposition of the ion on the surface,observed at high collision energies enables access to dissociation channels that are not accessible using SORI-CID or IRMPD. Finally, we discuss some approaches for tailoring the surface to achieve particular aims in SID. © 2004 Wiley Periodicals, Inc., Mass Spec Rev 24:135,167, 2005 [source] | ||||||||||