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*.

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*.

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*.

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