Chemistry Department

Building 555

Brookhaven National Laboratory

P.O. Box 5000

Upton, NY 11973-5000

Phone: (631) 344-4367

FAX: (631) 344-5815

e-mail

B.Sc. Chemistry, Chengdu University of Sciences and Technology (presently,
Sichuan University), China 1985

M.Sc. Atomic & Molecular Physics, Chengdu University of Sciences and
Technology, China 1988

Ph.D. Physical Chemistry, Göteborg University, Sweden 2000

G. Nyman (Göteborg, Sweden); J. T. Muckerman, Brookhaven National Laboratory

**Brookhaven National Laboratory, Chemistry Department, Upton, NY**

Chemist, 10/2007 - present

Associate Chemist, 10/2005 - 9/2007

Assistant Chemist, 8/2004 - 9/2005

Goldhaber Fellow (Research Associate), 8/2001 - 7/2004

Research Associate, 10/2000 - 7/2001

**The University of Queensland, Chemistry Department, Brisbane, Australia**

Visiting Scholar, 4/1996 - 08/1997

**Universidade de Coimbra, Departamento de Quimica, Coimbra, Portugal**

Visiting Scientist, 4/2000 - 5/2000

Visiting Auxiliary Professor, 3/1995 - 3/1996

**The Chinese Academy of Sciences, Chengdu Institute of Organic Chemistry,
China**

Associate Professor in Research, 1/1994 - 3/1995

Assistant Professor in Research, 7/1991 - 12/1993

Department Seminar Committee Member, 2006 - present

Session Chair: The 62nd OSU International Symposium on Molecular
Spectroscopy, Columbus, Ohio, June, 2007

Panelist: DOE Workshop on Basic Research Needs for Clean and Efficient
Combustion of 21st Century Transportation Fuels, Arlington, VA, October 30 -
November 1, 2006

Panelist: DOE Theory and Modeling in Nanoscience Workshop, San Francisco,
CA,May 9 - 12, 2002

- The National Science and Technology Progress Prize (The Third Prize), issued by The Ministry of National Education of China, 1999
- The Gertrude and Maurice Goldhaber Distinguished Postdoctoral Fellowship Award, Brookhaven National Laboratory, 2001

Theory and computation of the dynamics of chemical reactions, and the bound and quasi-bound (or resonance) rovibrational states of molecules; simulation of photodissociation processes; ab initio calculations and potential energy surfaces; direct dynamics of catalytic reactions; theoretical studies of nanostructures.

We are constantly developing methods and algorithms for computing new properties, and for making spectroscopy and dynamics calculations more accurate and more efficient.

Two-layer Lanczos diagonalization algorithm: In variational studies of
molecular spectroscopy, one challenging task is to diagonalize a huge matrix
resulting from the representation of the Hamiltonian in a large basis set.
Therefore, rigorous quantum dynamics (QD) calculations were limited to
tetra-atomic molecules before 2002. In order to overcome this difficulty, we
developed a two-layer Lanczos iterative approach using a
"divide-and-conquer" strategy based on the properties of the representation
of the Hamiltonian in orthogonal polyspherical coordinates. Using the
two-layer Lanczos method, we are now able to carry out rigorous QD
calculations of the vibrational spectra of polyatomic molecules containing
up to six atoms. The algorithm has been applied to the CH_{4}, CH_{3}D, H_{3}O_{2}^{-} and
(H_{2})_{3} systems. To the best of our knowledge, these are of the first
calculated five-/six-atom molecules (or ions) using a rigorous QD method
without any dynamical approximations. This work was presented in an invited
talk at the 225th ASC meeting (New Orleans, 2003), at a chemistry seminar at
Stony Brook University (2003) and New York University (2004), and at the AMO
seminar at Stony Brook University (2007) in addition to talks at the
Goldhaber Symposium (BNL, 2002) and the 59th OSU International Symposium of
Molecular Spectroscopy (Ohio, 2004). By implementing with the two-layer
Lanczos algorithm, a universal program TetraVib has been developed for
studying the rovibrational spectra of general four-atomic molecules.
Currently, we are developing a general program for five-atom systems.

A coherent discrete-variable representation method: It is still impossible to perform a rigorous quantum dynamics study of systems larger than six atoms even using the advanced diagonalization algorithms such as the basis-contracted Lanczos method of Wang and Carrington or our two-layer Lanczos method owing to the huge size of the Hamiltonian matrix. One has to exploit several techniques at the same time to attack the problem. In this research, we attempted to reduce the basis size by constructing simple and compact basis functions. Toward this end, we have developed a coherent discrete-variable representation (ZDVR) method. In this approach, inspired by a coherent-state formalism in momentum and conjugate coordinates, the multidimensional quadrature pivots are obtained by diagonalizing a complex coordinate operator matrix in a finite basis set, which is spanned by the lowest eigenstates of a two-dimensional reference Hamiltonian. The orthonormal eigenvectors define a collocation matrix connecting the localized ZDVR basis functions and the finite basis set. Since the diagonalization of the new coordinate operator is exact within the selected basis set, the ZDVR method has the same convergence speed as the one-dimensional (1D) potential-optimized discrete variable representation (PO-DVR) approach. The ZDVR method provides exponential convergence and accurate energies. It is the only multidimensional PODVR method with Gaussian quadrature accuracy so far. We are currently pursuing this direction of research for constrained 2D cases such as DVRs on a sphere.

A K-dependent adiabatic approach to the Renner-Teller (RT) effect for triatomic molecules: We have developed a new adiabatic approach for studying the rovibronic spectra of triatomic molecules with the consideration of the RT effect. This method is an extended version of the BDD (Barrow, Dixon and Duxbury) adiabatic approximation that removes the assumption that K is a good quantum number, and uses hyperspherical coordinates and the coupled-channel method. The algorithm makes it possible to accurately compute the rovibronic energy levels of the third kind of RT molecules for which the barrier to linearity is very large for the lower electronic state of the RT pair. In collaboration with Trevor Sears and Gregory Hall (BNL), the algorithm has been successfully applied to the HCCl and HCBr molecules. Six articles have been published.

Direct ab initio molecular dynamics: In this project, we have developed an
accurate and efficient direct ab initio molecular dynamics program,
DualOrthGT. The program is applicable to the study of radical-radical
bimolecular reactions, which are important reactions in combustion
environments. It is very challenging to study the dynamics of
radical-radical reactions because of the strong correlation energy, spin
contamination, and the size-consistent problem in such systems. In
particular, the size-consistent problem essentially excludes the possibility
of using density functional theory (DFT) or other single-determinant methods
in most cases. In order to deal with those issues, the DualOrthGT program is
implemented with four advanced techniques: the predictor-corrector
symplectic reversible integrator of Martyna and Tuckerman for solving
Hamilton's equations of nuclear motion, CASSCF-guided (when necessary)
electronic wave functions, an accurate dual-level ab initio method (either
ab initio methods or basis sets) for electronic structure calculations, and
a graph theory procedure for identifying instantaneous molecular fragment
identities throughout the trajectory. The program has been successfully
applied to the study of several atmospheric and/or combustion-related
reactions such as O(^{1}D) + CH_{4}, ^{1}CH_{2} +
C_{2}H_{2}, and HOCO + X (X = H, CH_{3}, O, O_{2},
OH, HO_{2}, Cl and ClO, etc.), and the photo-initiated reactions of molecules
or ions. Recently, we also used the Car-Parrinello molecular dynamics (CPMD)
method to study the behavior of complex systems such as boron nitride
nanotubes.

Dissociative recombination: We have developed a spherical electron cloud
hopping (SECH) molecular dynamics method for studying the product branching
ratios in the dissociative recombination (DR) of polyatomic ions with
electrons. The method consists of a direct ab initio technique, the surface
hopping method, and the SECH model. The SECH model is designed to mimic the
quantum delocalization of the scattered electron in a classical mechanic
manner. Since the SECH MD method is a classical mechanics-based algorithm,
it is capable of studying large polyatomic ions. The preliminary application
of this method to CH^{+}, H_{3}O^{+} and H^{+}(H_{2}O)_{3}
is very promising. Computed
branching fractions of products are in excellent agreement with experiments.
We expect that we can now realistically simulate the product branching
ratios of DR of polyatomic ions beyond H_{3}^{+} and its isotopic ions. Although
quantum dynamics approaches have been widely used for calculating the rate
coefficients of DR, they are infeasible for the study of product branching
ratios of general polyatomic molecular ions. This work has been presented at
a BNL Chemistry Colloquium (2008), the Telluride Workshop on Spectroscopy
and Dynamics (2008), and the BNL Goldhaber Symposium (2008).

114. A spherical electron cloud hopping model for studying product
branching ratios of dissociative recombination; Yu, H.-G.; *J. Chem. Phys*.
**128**, 194106 (2008).

100. *Ab initio* and direct
dynamics studies of the reaction of singlet methylene with acetylene and the
lifetime of the cyclopropene complex; Yu, H.-G. and Muckerman, J.T.; *J.
Phys. Chem. A* **109**,** **1890 (2005).

99. Full-dimension quantum
calculations of vibrational spectra of six-atom molecules I. Theory and
numerical results; Yu, H.-G.; *J. Chem. Phys*. **120**, 2270 (2004).

88. Two-layer Lanczos iteration
approach to molecular spectroscopic calculation; Yu, H.-G.; *J. Chem. Phys*.
**117**, 8190 (2002).

67. A 4D quantum scattering study of the
Cl + CH_{4} «
HCl + CH_{3} reaction *via* spectral transform iteration; Yu, H.-G.
and Nyman, G.; *J.Chem. Phys*. **110**, 7233 (1999).

60.
The calculation of vibrational eigenstates by MINRES filter diagonalization;
Yu, H.-G. and Smith, S.C.; *Ber. Buns. Phys. Chem.* **101**, 400
(1997) (invited).

- G. Nyman and H.-G. Yu, "Quantum theory of bimolecular chemical reactions,"
*Rep. Prog. Phys*.**63**, 1001-1059 (2000). - G. Nyman and H.-G. Yu,
"Iterative digonalization of large sparse matrix by using spectral
transformation and filter diagonalization,"
*J. Comp. Meth. Sci.*29 (2001).

1. Z. H. Zhu and H.-G. Yu, *Molecular Structure and Potential Energy
Functions *(in Chinese), (Science Press of China, Beijing, 1997)