Research Interests:
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.
Research Accomplishments:
·
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 CH4, CH3D, H3O2-
and (H2)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(1D) + CH4,
1CH2 + C2H2,
and HOCO + X (X = H, CH3, O, O2, OH, HO2,
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+, H3O+
and H+(H2O)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 H3+ 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). |
