At Play, in Density
Functional
Fields
Neepa Maitra | Hunter College of
the City University of New York
With her violin always handy, Neepa Maitra has been on a long trip into
realms of theory, ready to invoke what she calls a bit of black magic.
Her Web site guides you to her fall syllabus for “Electromagnetic Theory” at
Hunter College of the City University of New York, and to the usual topics: calculus,
fields and waves, but also some friendly advice that “collaboration with
your peers is encouraged” but “independent solutions are required.”
One link takes you off to a physicist’s comment that “the spinning
nuclei in a sample are like spies inside an unmapped and unexplored continent … all
you have to do is learn the spies' language and listen to them talk.”
Ground state density n(x) and Kohn-Sham potential vs(x) for 2 interacting electrons in a 1d-box, as its length is increased from L = 1 to L = 16. The walls of the boxes at §L=2 are not shown.
Maitra, from her office in Hunter’s North Building, has designed a new
journey into quantum mechanics and density functional theory. Her
goal is to try to improve on a leading tool in her field: time-dependent
density functional theory, or TDDFT.
TDDFT appeared in 1984 as an extension of density functional theory, an
older and more established theory that has had a huge impact on quantum chemistry
and condensed matter physics, opening up possibilities for applications
like biomolecules and drug design. The newer TDDFT has itself been taking
off in promising directions.
It can help study the behavior of electrons, say, when a molecule is placed
in a strong field to understand how to control a chemical reaction.
But Maitra, on the way to her own “independent solution,” saw
weak spots that might benefit from a new twist or two.
“It’s hard to describe many electrons interacting, like in a molecule,” she
said. “This new method will try to get better descriptions to apply
to these bigger molecules.”
Part of her work seeks ways to help keep the study of quantum mechanics “computationally
feasible.”
Storing and calculating the wave function can grow unwieldy, she said. “TDDFT
gets around the problems in a beautiful way,” she says. “In all these
systems, many electrons, interact, repel each other, and are affected by nuclei,
affected by a laser field and so on. What makes the computation difficult is
that each electron is feeling each other’s repulsion.”
TDDFT maps the system’s interactions onto a “pretend system,” one
without the interactions. From the noninteracting system, theoretically,
you can extract the properties of the true system in terms of functionals
of the electron density.
“It’s an exact mathematical construct, but it’s also a bit
of black magic,” she says. “You can derive some nice, very
physical approximations for these functionals.”
There’s another element to her innovation with TDDFT. “Sometimes
it doesn’t work,” she said. “The question is, when and where
does it not work? And how can we fix it? How can we make it more
accurate, and capture more challenging problems.”
Her path diverted briefly from physics. For one day, she was a medical
student in New Zealand, at the University of Otago. Then she got
the word from Harvard she was hoping for, packed her violin and was off.
Just as her parents had left West Bengal for New Zealand, she set out for
Cambridge, with stops to come at Berkeley and Rutgers.
Today she’s the violin teacher for her two girls, who’ll now
be the ones encouraged to come up with their own independent solutions.
Nov. 1, 2007
