Vladimir A. MandelshtamProfessor, Chemistry 

Research Interests 
Theoretical and Computational Chemistry  
URL  www.chem.uci.edu/people/faculty/mandelsh/  
Academic Distinctions 
Emerson Fellow, 1998 UCI Faculty Career Development Awards, 1999, 2001 Alfred P. Sloan Research Fellow, 20022004 

Appointments 
19911997, University of Southern California 19971998, University of California, San Diego 

Research Abstract 
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 + O_{2} > 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 multiexponential 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.  
Publications 
Thermodynamic Properties of Classical LennardJones Clusters: (a) The sizetemperature phase diagram for small LennardJones clusters, P.A. Frantsuzov and V.A. Mandelshtam, Phys. Rev. E 2005, 72, 037102 (Link to article text) (b) Structural transitions and melting in LJ_{7478} LennardJones clusters from adaptive exchange Monte Carlo simulations, V.A. Mandelshtam, P.A. Frantsuzov and F. Calvo, J. Phys. Chem. 2006, 110, 5326. (Link to article text) (c) Multiple structural transformations in LennardJones clusters: Generic versus sizespecific behavior, V.A. Mandelshtam and P.A. Frantsuzov, J. Chem. Phys. 2006, 124, 20451 (Link to article text) (d) Lowtemperature structural transitions: circumventing the brokenergodicity problem, V.A. Sharapov, D. Meluzzi and V. A. Mandelshtam, Phys. Rev. Lett. , 2007, 98, 105701. (Link to article text) (d) SolidSolid structural transformations in LennardJones clusters: Accurate simulations versus the Harmonic Superposition Approximation, V.A. Sharapov and V. A. Mandelshtam, J. Phys. Chem. , 2007, 111, 10284. (Link to article text) 

Quantum Statistical Mechanics (a) Gaussian resolutions for equilibrium density matrices, P.A. Frantsuzov, A. Neumaier and V.A. Mandelshtam, Chem. Phys. Lett. 2003, 381, 117122. (Link to article text (b) Thermodynamics and equilibrium structure of Ne_{38} cluster: Quantum Mechanics versus Classical, C. Predescu, P.A. Frantsuzov, A. Neumaier and .A. Mandelshtam, J. Chem. Phys. 2005, 122, 154305. (Link to article text) (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. (Link to article text) (d) Equilibrium properties of quantum water clusters by the Variational Gaussian Wavepacket Method, P.A. Frantsuzov and V.A. Mandelshtam, J. Chem. Phys. 2008, 128, 094304. (Link to article text) (e) Quantum transitions in LennardJones clusters, J. Deckman, P.A. Frantsuzov and V.A. Mandelshtam, Phys. Rev. E 2008, 77, 052102. (Link to article text) (e) Quantum Disordering versus Melting in LennardJones Clusters, J. Deckman and V.A. Mandelshtam, Phys. Rev. E. 2009, 79, 022101. (Link to article text) (f) Effects of quantum delocalization on structural changes of LennardJones clusters, J. Deckman and V.A. Mandelshtam, J. Phys. Chem. A. 2009, 113, 7394. (Link to article text) 

Resonance calculations using FDM: (a) Bound states and resonances of the hydroperoxyl radical HO_{2}. An accurate quantum mechanical calculation using filter diagonalization, V.A. Mandelshtam, T.P. Grozdanov, and H.S. Taylor, J. Chem. Phys. 1995, 103, 1007410084. (Link to article text) (b) The quantum resonance spectrum of the H_{3}^{+} 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, 847860. (Link to article text) (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, 88808887. (Link to article text) 

Periodic orbit quantization: (a) High Resolution Quantum Recurrence Spectra: Beyond the Uncertainty Principle, J. Main, V.A. Mandelshtam and H.S. Taylor, Phys. Rev. Lett. 1997, 78, 43514354. (Link to article text) (b) Periodic orbit quantization by harmonic inversion, J. Main, V.A. Mandelshtam and H.S. Taylor, Phys. Rev. Lett. 1997, 79, 825828. (Link to article text) 

Using crosscorrelation functions for semiclassical quantization: (a) Extraction of tunneling splittings from a realtime semiclassical propagation, V.A. Mandelshtam, M. Ovchinnikov, J. Chem. Phys. 1998, 108, 92069209. (Link to article text) (b) Semiclassical Spectra and Diagonal Matrix Elements by Harmonic Inversion of CrossCorrelated Periodic Orbit Sums, J. Main, K. Weibert, V. A. Mandelshtam, and G. Wunner, Phys. Rev. E 1999, 60, 16391642. (Link to article text) 

Superresolution methods for multidimensional spectral analysis: (a) The multidimensional filter diagonalization method. I. Theory and numerical implementation, V.A. Mandelshtam, J. Magn. Reson. 2000, 144, 343356. ( Link to article text) (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. 357366. (Link to article text) (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, 129137. (Link to article text) (d) The extended Fourier transform for 2D spectral estimation, G.S. Armstrong and V.A. Mandelshtam,J. Magn. Reson. 2001, 153, 2231. (Link to article text) (e) A detailed review article: FDM: the Filter Diagonalization Method for data processing in NMR experiments, V.A. Mandelshtam, Progress in NMR Spectroscopy 2001, 38, 159196. (Link to article text) (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, 139148. ( Link to article text) (g) Regularized resolvent transform for direct calculation of 45 degrees 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, 136144. ( Link to article text) (h) Ultrahigh resolution 3D NMR spectra from limitedsize data sets, J. H. Chen, D. Nietlispach, A. J. Shaka and V. A. Mandelshtam, J. Magn. Reson. 2004, 169, 215224. ( Link to article text) (i) Rapid highresolution 4dimensional 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, 160168. ( Link to article text) 

1D FDM for NMR: (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, 7687. (Link to article text) (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, 44294437. (Link to article text) 

Efficient numerical methods for quantum scattering: (a) Pseudotime Schrödinger equation with absorbing potential for quantum scattering calculations, A. Neumaier and V.A. Mandelshtam, Phys. Rev. Lett., 2001, 86, 50315034. (Link to article text) (b) Further generalization and numerical implementation of pseudotime Schrödinger equations for quantum scattering calculations, A. Neumaier and V.A. Mandelshtam, J. Theor. Comp. Chem. , 2002, 1, 0000 (Link to article text) (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, 29032907. (Link to article text) (d) Harmonic inversion of time signals and its applications, V.A. Mandelshtam and H.S. Taylor, J. Chem. Phys. 1997, 107, 67566769. (Link to article text) (e)A lowstorage 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, 50855090. (Link to article text) 

Inversion of time crosscorrelation functions: (a) Harmonic inversion of time crosscorrelation functions. The optimal way to perform quantum or semiclassical dynamics calculations, V.A. Mandelshtam, J. Chem. Phys. 1998, 108, 999910007. (Link to article text) (b) RRT: the Regularized Resolvent Transform for quantum dynamics calculations, V.A. Mandelshtam, J. Phys. Chem, 2001, 105, 27642769. (Link to article text) (c) On harmonic inversion of crosscorrelation functions by the filter diagonalization method, V.A. Mandelshtam, J. Theor. Comp. Chem., 2003, 2, 19. (Link to article text) 

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Last updated  03/15/2010  