Yinghua Wu                           CV, Research Statement 

6400 Freret St. Rm 2015

New Orleans, LA 70118

Email: ywu2@tulane.edu

Tel: 1-205-238-0113  

Education:

University of Science and Technology of China, B.S.

Yale University, Ph.D. in Physical Chemistry with Prof. Victor S. Batsita

Tulane University, Postdoc in Physical Chemistry with Prof. Michael F. Herman

Research Interest

1. Quantum dynamics for large systems, system-bath interactions, coherent control.

2. Semiclassical description of quantum dynamics, surface hopping methods, forward-backward semiclassical methods, higher order corrections to semiclassical methods.

3. Magnetically induced singlet-triplet transitions.

Previous Work

1. Matching pursuit split operator Fourier transform method. [2,3,7]

A wave function grows exponentially with increasing dimensionality in grid representation or coherent state representation with the identity operator. This is a major obstacle to describe quantum dynamics for multi-dimensional systems. The idea to overcome this restriction is to use the minimum number of basis functions to represent a wave function. For instance, a multi-dimensional Gaussian basis function would require a lot of points to represent it on a grid, but it is just one single point in Gaussian basis function. For a random wave function, we use the Matching Pursuit algorithm (Mallat and Zhang 1993) to find the minimum number of Gaussian basis functions to represent it. Then, for each Gaussian basis function, the kinetic operator becomes analytical. This method has been used to study Excited-State Intramolecular Proton-Transfer in 2-(2’-hydroxyphenyl)-oxazole, a real molecular system involving 35 degrees of freedom. We further extended this method to nonadiabatic systems. Chen and Batista recently studied the photoabsorption spectrum of Pyrazine, a two state 24D system.

 2. Nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method. [6,8]

Surface hopping methods have been used to describe nonadiabatic quantum dynamics for a few decades. Some of them, such as the Tully’s fewest hop method, are very efficient and accurate. But, most involve assumptions at some level. The nonadiabatic HK method, however, is rigorously derived from the time-dependent Schrödinger equation. No assumption is made. This method was first attempted by Yang and Herman heuristically, as an approximation to Herman’s nonadiabatic surface hopping theory based on the primitive Van Vleck propagator. Our theoretical study and numerical simulations justified the method and corrected a small error in the hopping amplitude. To my knowledge, this is the first and the only semiclassical surface hopping method based on the first principle. We have shown that it satisfies the TDSE through order hbar^1. Implementation is easy, and very similar to the Tully’s fewest switch surface hopping method and the single surface HK SC-IVR method.

3. Proof of the stationary phase approximation. [8]

The stationary phase approximation is frequently used in chemistry and physics. For example, the Van Vleck propagator can be obtained by integrating the Herman-Kluk propagator by means of the stationary phase approximation. The Herman-Kluk propagator can be obtained by inserting the coherent state identity operator twice, and then applying the stationary phase approximation to integrate out one set of the phase space variables. The forward-backward SC-IVR method also involves the stationary phase approximation. Miller even went as far as to say semiclassical approximation was stationary phase approximation. In the derivation of the nonadiabatic HK method, we have shown that the error of the stationary phase approximation is h-bar order higher than the leading term. In this part of derivation, the exponent is complex. Our derivation is a simple extension of Wong’s derivation, where the exponent is real (actually a much harder problem than complex exponent, I guess mathematicians are too proud to even bother with a weaker corollary after a major lemma). Please note that the stationary phase approximation is not convergent. It is an asymptotic approximation.

4. On the hbar^2 terms in the primitive nonadiabatic semiclassical surface hopping propagator proposed by Herman.[in preparation]

It is commonly accepted that a semiclassical method is valid if it is accurate to hbar^1. In real simulations however, hbar is finite and in atomic unit is 1. So, actually, the hbar^2 terms may be quite large. We found by numerical tests that, in the primitive nonadiabatic semiclassical hopping propagator, not all the hbar^2 terms can be ignored. We thus further studied its analytical properties regarding the hbar^2 terms and proved that not only is it accurate to the first order of hbar, all the hbar^2 terms involving nonadiabatic coupling vector are also canceled, and the remaining error terms are due to the intrinsic hbar^2 error of the Van Vleck propagator. The primitive nonadiabatic semiclassical propagator has the following properties,

(a). classical dynamics is needed to cancel the hbar^0 terms and some of hbar^1 terms,

(b). energy is conserved at a hopping point so that the classical action S is well defined, in order for (a) to be true for hopping trajectories,

(c). during a sudden hop, the change in momentum only occurs in the direction parallel to the nonadiabatic coupling vector so that the classical actions S still has the usual properties, in order for (a) to be true for hopping trajectories,

(d). both transmission and reflection types of hops are possible, and they are responsible for the cancellation of  the other hbar^1 terms and hbar^2 terms involving interstate coupling,

(e). the remaining error is O(hbar^2), caused by the intrinsic semiclassical error of the Van Vleck propagator.

5. A quantum propagator in the adiabatic representation.[in preparation]

Nonadiabatic quantum dynamical processes can be studied rigorously by employing the split operator Fourier transform method, but it has to be generalized to nonadiabatic problems with matrix diagonalization in diabatic representation. After all the hard work is done by whatever means, transformations are needed to convert the wave functions to the adiabatic representation if transition amplitudes are of interest. This transformation process involves point-wise matrix diagonalization and multiplication, which are unmanageable for multidimensional problems. To avoid point-wise diagonalization problem, we have developed a quantum propagation scheme in the adiabatic representation based on the perturbation expansion. This propagation scheme can be easily implemented with the MPSOFT method and other methods.

Awards

2006 Best presentation by a postdoc at 2006 Southwest Theoretical Chemists Conference 
2003-2004 Research Fellowship, Yale University
2001-2003 Teaching Assistantship, Yale University

List of Publications:

[1].  Semiclassical molecular dynamics simulations of the excited state photodissociation dynamics of H2O in the A 1B1 band, by Yinghua Wu and Victor S. Batista  J. Phys. Chem. B 106, 8271, 2002

[2]. Matching Pursuit for Simulations of Quantum Processes, by Yinghua Wu and Victor S. Batista   J. Chem. Phys. 118, 6720, 2003   J. Chem. Phys. 119, 7606, 2003.

[3]. Quantum Tunneling in Multidimensional Systems: A Matching-Pursuit Description, by Yinghua Wu and Victor S. Batista.   J. Chem. Phys., 121,1676, 2004

[4]. Matching-Pursuit Split Operator Fourier Transform Computations of Thermal Correlation Functions, by Xin Chen, Yinghua Wu and Victor S. Batista  J. Chem. Phys. 122, 64102, 2005

[5]. Matching-pursuit/split-operator Fourier-transform simulations of nonadiabatic quantum dynamics, by Yinghua Wu, Michael F. Herman, and Victor S. Batista  J. Chem. Phys. 122, 114114, 2005

[6]. Nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method revisited: Applications to Tully’s three model systems, by Yinghua Wu and Michael F. Herman  J. Chem. Phys. 123, 144106, 2005

[7]. Matching-Pursuit Split-Operator Fourier-Transform Simulations of Excited-State Intramolecular Proton-Transfer in 2-(2’-hydroxyphenyl)-oxazole, by Yinghua Wu and Victor S. Batista  J. Chem. Phys. 124, 224305, 2006

[8]. A justification for the nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method. Yinghua Wu and Michael F. Herman  J. Chem. Phys. 125, 154116, 2006 

Contributions at Conferences

Aug, 2002     Implementation of the Matching Pursuit algorithm for quantum dynamics based on coherent state representation. (poster)
              Yinghua Wu and Victor S. Batista
              ACS Meeting, Boston, MA
April, 2003   Matching Pursuit for semiclassical initial value representation method. (poster)
              Yinghua Wu and Victor S. Batista
              ACS Meeting, New York, NY
May, 2006     Nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method. (talk)
              Yinghua Wu and Michael F. Herman
              Southeast Theoretical Chemists Conference, Atlanta, GA
Sep, 2006     A justification for the nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method. (talk)
              Yinghua Wu and Michael F. Herman
              ACS Meeting, San Francisco, CA
Oct, 2006     Nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method. (talk, awarded best presentation by a postdoc)
              Yinghua Wu and Michael F. Herman
              Southwest Theoretical Chemists Conference, Austin, TX