## Vladimir A. Mandelshtam

Professor, Chemistry

School of Physical Sciences

School of Physical Sciences

PH.D., Inst. of Spectroscopy, Acad. of Sciences of USSR, 1991

B.S., M.S., 1987, Moscow Institute of Steel and Alloys

Phone: (949) 824-5509

Fax: (949) 824-8571

Email: mandelsh@uci.edu

University of California, Irvine

2103 Natural Sciences II

Mail Code: 2025

Irvine, CA 92697

**Research Interests**

Theoretical and Computational Chemistry: Numerical Methods; Quantum Dynamics; Statistical Mechanics

**URL**

**Academic Distinctions**

Emerson Fellow, 1998

UCI Faculty Career Development Awards, 1999, 2001

Alfred P. Sloan Research Fellow, 2002-2004

UCI Faculty Career Development Awards, 1999, 2001

Alfred P. Sloan Research Fellow, 2002-2004

**Appointments**

1991-1997, University of Southern California

1997-1998, University of California, San Diego

1997-1998, University of California, San Diego

**Research Abstract**

Our research explores theoretical and computational problems in diverse areas of Physical Chemistry: from quantum dynamics of small molecules to processing experimental data. While the key aspect in most of our projects

is the use of state-of-the-art numerical methods, their development is always driven by the challenges we face when dealing with real problems in Chemistry and Physics.

Our probably most significant accomplishment was the development of the Filter Diagonalization Method with its numerous applications to quantum dynamics calculations as well as to data processing in Fourier Transform (FT) experiments, such as Nuclear Magnetic Resonance (NMR) experiments and FT mass spectrometry. The method was originally formulated by Danny Neuhauser (UCLA, 1995) and designed for efficient calculations of the bound and resonance states in a quantum scattering problem, but was then reformulated as a method of solving one of the central problems in signal processing, the Harmonic Inversion Problem (HIP), i.e., fitting a time signal by a sum of complex exponentials (or complex sinusoids). Later FDM was generalized to the solution of the multidimensional HIP, as well as for the related problem, i.e., the multidimensional spectral reconstruction. The latter allowed us to not only obtain highly resolved NMR spectra using relatively small data arrays, but also devise new NMR experiments and produce new types of spectra that are more useful for structure determination. FDM is now well established method of spectral analysis used by a number of physicists, chemists, and engineers.

Our earlier work involved the theoretical and computational topics associated with the quantum scattering problem corresponding to a few-atom chemical reaction, albeit with complex dynamics (the complexity in such systems is typically manifested by the existence of a large number of bound and narrow resonance states). The goals were to develop numerical methods that could solve such problems most efficiently and apply these methods to previously unexplored complex systems. Our computational methods ranged from the first principles, i.e., the methods designed to solve the quantum dynamics equations exactly, to those employing various approximations, such as semiclassical, thus simplifying the calculations while retaining the physically relevant properties of the systems in question.

Our more recent interests involve the development of theoretical and computational tools to study complex many-body systems, such as molecular and atomic clusters and quantum liquids. Some examples are rare gas atomic liquids and clusters, neutral and ionic molecular clusters [(H

Yet, in our studies exploration of NQEs represent one of the central goals, both methodologically and conceptually. Namely, we are interested in using and developing exact and approximate methods for treating quantum many body systems, and we apply these methods to find new and interesting effects. Some highlights of our most recent activities and findings are

(1) Developing approximate methods for treating many-body quantum systems using variational approaches.

(2) Developing novel sampling approaches (within the Monte Carlo framework) for simulations of solid-solid phase transitions in clusters.

(3) Producing an accurate equation of state for a quantum neon liquid.

(4) Constructing the phase diagrams of classical and quantum Lennard-Jones clusters as a function of size, temperature, and quantum parameter. (The use of the quantum parameter allowed us to summarize the properties of clusters of all rare gas atoms and some molecular clusters simultaneously in one phase diagram.)

(5) Demonstrating that the quantum isotope effect is significant in water clusters, ion-water clusters X

is the use of state-of-the-art numerical methods, their development is always driven by the challenges we face when dealing with real problems in Chemistry and Physics.

Our probably most significant accomplishment was the development of the Filter Diagonalization Method with its numerous applications to quantum dynamics calculations as well as to data processing in Fourier Transform (FT) experiments, such as Nuclear Magnetic Resonance (NMR) experiments and FT mass spectrometry. The method was originally formulated by Danny Neuhauser (UCLA, 1995) and designed for efficient calculations of the bound and resonance states in a quantum scattering problem, but was then reformulated as a method of solving one of the central problems in signal processing, the Harmonic Inversion Problem (HIP), i.e., fitting a time signal by a sum of complex exponentials (or complex sinusoids). Later FDM was generalized to the solution of the multidimensional HIP, as well as for the related problem, i.e., the multidimensional spectral reconstruction. The latter allowed us to not only obtain highly resolved NMR spectra using relatively small data arrays, but also devise new NMR experiments and produce new types of spectra that are more useful for structure determination. FDM is now well established method of spectral analysis used by a number of physicists, chemists, and engineers.

Our earlier work involved the theoretical and computational topics associated with the quantum scattering problem corresponding to a few-atom chemical reaction, albeit with complex dynamics (the complexity in such systems is typically manifested by the existence of a large number of bound and narrow resonance states). The goals were to develop numerical methods that could solve such problems most efficiently and apply these methods to previously unexplored complex systems. Our computational methods ranged from the first principles, i.e., the methods designed to solve the quantum dynamics equations exactly, to those employing various approximations, such as semiclassical, thus simplifying the calculations while retaining the physically relevant properties of the systems in question.

Our more recent interests involve the development of theoretical and computational tools to study complex many-body systems, such as molecular and atomic clusters and quantum liquids. Some examples are rare gas atomic liquids and clusters, neutral and ionic molecular clusters [(H

_{2}O)_{n}, (H_{2})_{n}, H^{-}(H2)_{n}, X^{-}(H_{2}O)_{n}, etc.] and their various isotopologues. In these studies we are typically interested in the behavior associated with the structural and phase transitions that take place when, e.g., the temperature of the system T and/or its size n is changed. Accurate numerical simulations of phase transition is notoriously very difficult due to the need to correctly sample at least two structural motifs (or two distinct funnels of the energy landscape) separated by generally large energy barriers. Furthermore, all molecular/atomic systems display (to various degree) nuclear quantum effects (NQEs). The latter are generally not included into numerical simulations, not because they are negligibly small, but because taking them into account is both complicated and extremely expensive, thus making the simulations of clusters even more challenging.Yet, in our studies exploration of NQEs represent one of the central goals, both methodologically and conceptually. Namely, we are interested in using and developing exact and approximate methods for treating quantum many body systems, and we apply these methods to find new and interesting effects. Some highlights of our most recent activities and findings are

(1) Developing approximate methods for treating many-body quantum systems using variational approaches.

(2) Developing novel sampling approaches (within the Monte Carlo framework) for simulations of solid-solid phase transitions in clusters.

(3) Producing an accurate equation of state for a quantum neon liquid.

(4) Constructing the phase diagrams of classical and quantum Lennard-Jones clusters as a function of size, temperature, and quantum parameter. (The use of the quantum parameter allowed us to summarize the properties of clusters of all rare gas atoms and some molecular clusters simultaneously in one phase diagram.)

(5) Demonstrating that the quantum isotope effect is significant in water clusters, ion-water clusters X

^{-}(H_{2}O)_{n}(X = F, Cl, Br, I), etc. For example, structurally the (H_{2}O)_{n}clusters are different from their (D_{2}O)_{n}isotopologues.

Publications

**Link to this profile**

**Last updated**

03/18/2020