Source: https://www.faculty.uci.edu/profile.cfm?faculty_id=4582
Timestamp: 2019-04-26 01:53:38+00:00

Document:
Theoretical and computational methods provide a powerful tool for the study of chemical dynamics and often help us to understand the experiments. One area of our research is the development of such methods and their application to studying the dynamics of small molecules, radicals and clusters. If the quantum effects, such as tunneling or resonance phenomena, are essential, even the simplest chemical reactions involving only three atoms, e.g. H + O2 --> OH + O, turn out to be very difficult to model numerically. This is because we cannot simply assume that the atoms move classically, i.e. according to Newton's equations of motion. In such cases we have to deal with the quantum equations for the wavefunctions (or wave packets), e.g. the time dependent SchrÃ¶dinger equation. Besides that, no matter whether they are classical or quantum the small molecules sometimes exhibit very complex behavior that we often call chaotic. Our goals are to develop numerical methods that can solve such problems most efficiently and to interpret the results of the numerical calculations. Our computational methods range from ab initio, which are designed to solve the quantum equations exactly, to those that try to employ certain approximations, such as semiclassical, simplifying the calculations while retaining the physically relevant properties of the system. There is no question about the role of computational methods in theoretical chemistry. They often allow us to look at the matter without actually conducting the experiment. However, their role in experimental chemistry is not always appreciated. A signal measured in an experiment has to be processed. Making certain assumptions about the data often helps us to reveal relevant physical information about the system in question. At this stage the efficiency of the experiment depends on how good our assumptions are and how sophisticated the computational methods we use for the signal processing are. Quite interestingly, the ideas of signal processing go back to Baron de Prony who more than 200 years ago believed that all physical processes could be described by a multi-exponential decay. This idea, somewhat modified and generalized, has recently found numerous applications in diverse areas, including chemistry. We are interested in several such applications, which range from quantum dynamics calculations to modern pulsed NMR experiments. Multidimensional NMR spectra are used for structure determination of large organic molecules. Enormous multidimensional data arrays are generated in such experiments and usually processed by conventional methods of spectral analysis based on the multidimensional Fourier transformation. In conjunction with A.J. Shaka we are applying to NMR data a new signal processing method, the filter diagonalization method (FDM) to replace the Fourier transform. This allows us to not only obtain higher resolved NMR spectra, but also to devise new experiments and produce new types of spectra that are more useful for structure determination.
(b) Structural transitions and melting in LJ74-78 Lennard-Jones clusters from adaptive exchange Monte Carlo simulations, V.A. Mandelshtam, P.A. Frantsuzov and F. Calvo, J. Phys. Chem. 2006, 110, 5326.
circumventing the broken-ergodicity problem, V.A. Sharapov, D. Meluzzi and V. A. Mandelshtam, Phys. Rev. Lett. , 2007, 98, 105701.
Superposition Approximation, V.A. Sharapov and V. A. Mandelshtam, J. Phys. Chem. , 2007, 111, 10284.
(a) Gaussian resolutions for equilibrium density matrices, P.A. Frantsuzov, A. Neumaier and V.A. Mandelshtam, Chem. Phys. Lett. 2003, 381, 117-122.
(b) Thermodynamics and equilibrium structure of Ne38 cluster: Quantum Mechanics versus Classical, C. Predescu, P.A. Frantsuzov, A. Neumaier and .A. Mandelshtam, J. Chem. Phys. 2005, 122, 154305.
(c) Structural Transformations and Melting in Neon Clusters: Quantum Mechanics versus Classical Mechanics, P.A. Frantsuzov, D. Meluzzi and V.A. Mandelshtam, Phys. Rev Lett. 2006, 96, 113401.
Variational Gaussian Wavepacket Method, P.A. Frantsuzov and V.A. Mandelshtam, J. Chem. Phys. 2008, 128, 094304.
(e) Quantum transitions in Lennard-Jones clusters, J. Deckman, P.A. Frantsuzov and V.A. Mandelshtam, Phys. Rev. E 2008, 77, 052102.
(e) Quantum Disordering versus Melting in Lennard-Jones Clusters, J. Deckman and V.A. Mandelshtam, Phys. Rev. E. 2009, 79, 022101.
(f) Effects of quantum delocalization on structural changes of Lennard-Jones clusters, J. Deckman and V.A. Mandelshtam, J. Phys. Chem. A. 2009, 113, 7394.
(a) Bound states and resonances of the hydroperoxyl radical HO2. An accurate quantum mechanical calculation using filter diagonalization, V.A. Mandelshtam, T.P. Grozdanov, and H.S. Taylor, J. Chem. Phys. 1995, 103, 10074-10084.
(b) The quantum resonance spectrum of the H3+ molecular ion for J=0. An accurate calculation using filter diagonalization, V.A. Mandelshtam and H.S. Taylor, J. Chem. Soc., Faraday Trans. 1997, 93, 847-860.
(c) The unimolecular dissociation of the OH stretching states of HOCl: Comparison with experimental data, J. Weiss, J. Hauschildt, and R. Schinke, O. Haan, S. Skokov and J. M. Bowman, V. A. Mandelshtam, K. A. Peterson, J. Chem. Phys. 2001, 115, 8880-8887.
(a) High Resolution Quantum Recurrence Spectra: Beyond the Uncertainty Principle, J. Main, V.A. Mandelshtam and H.S. Taylor, Phys. Rev. Lett. 1997, 78, 4351-4354.
(b) Periodic orbit quantization by harmonic inversion, J. Main, V.A. Mandelshtam and H.S. Taylor, Phys. Rev. Lett. 1997, 79, 825-828.
(a) Extraction of tunneling splittings from a real-time semiclassical propagation, V.A. Mandelshtam, M. Ovchinnikov, J. Chem. Phys. 1998, 108, 9206-9209.
(b) Semiclassical Spectra and Diagonal Matrix Elements by Harmonic Inversion of Cross-Correlated Periodic Orbit Sums, J.
Main, K. Weibert, V. A. Mandelshtam, and G. Wunner, Phys. Rev. E 1999, 60, 1639-1642.
(a) The multidimensional filter diagonalization method. I. Theory and numerical implementation, V.A. Mandelshtam, J. Magn. Reson. 2000, 144, 343-356.
(b) The multidimensional filter diagonalization method. II. Applications to 2D, 3D and 4D NMR experiments, A.A. De Angelis, H. Hu, V.A. Mandelshtam, and A.J. Shaka,ibid. 357-366.
(c) RRT: The Regularized Resolvent Transform for high resolution spectral estimation, J. Chen, A.J. Shaka and V. A. Mandelshtam, J. Magn. Reson. 2000, 147, 129-137.
(d) The extended Fourier transform for 2D spectral estimation, G.S. Armstrong and V.A. Mandelshtam,J. Magn. Reson. 2001, 153, 22-31.
FDM: the Filter Diagonalization Method for data processing in NMR experiments, V.A. Mandelshtam, Progress in NMR Spectroscopy 2001, 38, 159-196.
(f) Processing DOSY spectra using the regularized resolvent transform, G. S. Armstrong, N. M. Loening, J. E. Curtis, A. J. Shaka and V. A. Mandelshtam, J. Magn. Reson. 2003, 163, 139-148.
projections of 2D J spectra, G. S. Armstrong, J. H. Chen, K. E. Cano, A. J. Shaka and V. A. Mandelshtam, J. Magn. Reson. 2003, 164, 136-144.
(h) Ultra-high resolution 3D NMR spectra from limited-size data sets, J. H. Chen, D. Nietlispach, A. J. Shaka and V. A. Mandelshtam, J. Magn. Reson. 2004, 169, 215-224.
(i) Rapid high-resolution 4-dimensional NMR spectroscopy using the filter diagonalization method and its advantages for detailed structural elucidation of oligosaccharides, G.S. Armstrong, V. A. Mandelshtam, A. J. Shaka and B. Bendiak, J. Magn. Reson. 2005, 173, 160-168.
(a) Reference deconvolution, phase correction and line listing of NMR spectra by the 1D filter diagonalization method, H. Hu, Q.N. Van, V. A. Mandelshtam and A.J. Shaka, J. Magn. Reson. 2000, 134, 76-87.
(b) Multiscale filter diagonalization method for spectral analysis of noisy data with nonlocalized features, J. Chen and V.A. Mandelshtam, J. Chem. Phys. 2000, 112, 4429-4437.
(a) Pseudo-time Schrödinger equation with absorbing potential for quantum scattering calculations, A. Neumaier and V.A. Mandelshtam, Phys. Rev. Lett., 2001, 86, 5031-5034.
(c) A simple recursion polynomial expansion of the Green's function with absorbing boundary conditions. Application to the reactive scattering, V.A. Mandelshtam and H.S. Taylor, J. Chem. Phys. 1995, 103, 2903-2907.
(d) Harmonic inversion of time signals and its applications, V.A. Mandelshtam and H.S. Taylor, J. Chem. Phys. 1997, 107, 6756-6769.
(e)A low-storage filter diagonalization method for quantum eigenenergy calculation or for spectral analysis of time signals, V.A. Mandelshtam and H.S. Taylor, J. Chem. Phys. 1997, 106, 5085-5090.
(a) Harmonic inversion of time cross-correlation functions. The optimal way to perform quantum or semiclassical dynamics calculations, V.A. Mandelshtam, J. Chem. Phys. 1998, 108, 9999-10007.
(b) RRT: the Regularized Resolvent Transform for quantum dynamics calculations, V.A. Mandelshtam, J. Phys. Chem, 2001, 105, 2764-2769.
cross-correlation functions by the filter diagonalization method, V.A. Mandelshtam, J. Theor. Comp. Chem., 2003, 2, 1-9.

References: V. 
 V. 
 V. 
 V. 
 V. 
 V. 
 V. 
 V. 
 V. 
 V.