 |
| Born Ridgewood, New Jersey, 1973. |
| Princeton University, A.B., 1995. |
| Harvard University, Ph.D., 1999. |
| Duke University, Postdoctoral Fellow, 1999. |
| Princeton University, NSF Postdoctoral Fellow, 2000-2001. |
| The University of Chicago, Assistant Professor, 2001-. |
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| Accolades |
| 2007 Camille Dreyfus Teacher-Scholar Award. |
| 2007 NSF CAREER Award. |
| 2005 Packard Foundation Fellowship for Science and Engineering. |
| 2005 Alfred P. Sloan Research Fellowship. |
| 2000-2001 National Science Foundation Mathematical Sciences Postdoctoral Fellow. |
| 1995-1998 National Science Foundation Graduate Fellow. |
| 1995 Newport Chemistry Award. |
| 1995 Princeton Chapter of Sigma Xi. |
| 1995 Summa Cum Laude at Princeton University. |
| 1990 Westinghouse Science Talent Search, semifinalist. |
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| David A. Mazziotti |
| Associate Professor (effective July 1, 2008) |
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| Research Interests: |
| Advancement in reduced-density-matrix theory is
fostering the development of a new paradigm in
theoretical chemistry that promises to promote
unprecedented growth in our ability to explore
computationally a myriad of chemical questions from
structure to reactivity. The immediate impact of my
research has been the development of new electronic
structure methods with improved accuracy and
efficiency for small-to-medium-sized atoms and
molecules - both ground and excited-state properties.
These methods will assist chemists in investigating
experimental properties such as molecular geometries,
bond stretching, bond polarity, electron density,
dissociation, and excitation energies with reliable,
consistent accuracy. The new methodology is not limited
to electronic structure but rather is also appropriate for
other aspects of chemistry including the prediction of
vibrational and rotational molecular properties. |
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| While both Hartree-Fock and density functional theory
work within the framework of a single electron, the
importance of the electron pairing in the chemical bond is
well-known to every chemist. In my research the electron
pair is elevated to a more prominent role in electronic
structure. The dream of rigorously describing all chemical
properties through only two electrons has existed for many
years. It was initially inspired by the observation that
because electrons interact only two-at-a-time, the
electronic energy may be expressed exactly as a simple,
known functional of the coordinates of two electrons. The
distribution of the two electrons, however, may not
properly represent a realistic, many-electron system. The
development of systematic rules for constraining two
electrons to represent a collection of more-than-two
electrons is called the N-representability problem (this
name was first proposed by Professor John Coleman). The
N signifies the number of electrons in the collection. |
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| In 1994 Professor Carmela Valdemoro achieved an
approximate solution to the problem through a mapping
of the Schrödinger equation for an N-electron atom onto
a contracted Schrödinger equation (CSE) for an effective
two-electron atom. Through independent efforts in the
late-90s, Professor Nakatsuji at Kyoto University and I at
Harvard University verified and extended Valdemoro's
initial success. My 1998 paper in Physical Review A
introduces the term reconstruction to describe the
approximation of the four-electron distribution in terms
of the two-electron distribution. The paper explores the
delicate relationship between the N-representability
problem and reconstruction; effectively, reconstruction
provides an approximate solution to the important
problem of representing many-electrons by only two
electrons. My research computes the reconstruction
within a framework known as cumulant theory. |
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| Motivated by the contracted Schrödinger equation, we
have also recently developed variational two-electron
methods with systematic, nontrivial N-representability
conditions. This second class of two-electron methods
directly computes the effective two-electron probability
distribution of a many-electron atom or molecule
without any higher-electron probability distributions.
Variational optimization of the ground-energy energy in
terms of only two effective electrons is treatable by a
class of optimization techniques known as semidefinite
programming. The variational two-electron method has
been accurately applied to generating potential energy
surfaces of molecules including the difficult-to-predict
dissociation curve for N2 where wavefunction methods
fail to give physically meaningful results. |
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| While two-electron approaches are still in their early
stages, the direct determination of chemical properties
by mapping any atom or molecule onto an effective twoelectron
problem offers a new level of accuracy and
efficiency for electronic structure calculations. |
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| Selected References |
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Perturbation Theory Corrections to
the Two-particle Reduced Density
Matrix Variational Method. Journal of Chemical Physics, 121, 1201 (2004).
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Exactness of Wave Functions from
Two-body Exponential
Transformations in Many-body
Quantum Theory. Physical Review
A, 69, 012507 (2004).
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Boson Correlation Energies via
Variational Minimization with the
Two-particle Reduced Density
Matrix: Exact N-representability
Conditions for Harmonic Interactions. Physical
Review A, 69, 042511 (2004). |
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Invariance of the Cumulant
Expansion under 1-particle Unitary
Transformations in Reduced
Density Matrix Theory. Chemical
Physics Letters, 387, 485 (2004). |
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Spectral Difference Lanczos
Method for Efficient Time
Propagation in Quantum Control
Theory. Journal of Chemical
Physics, 120, 5962 (2004). |
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Spectral Differences in Real-space
Electronic Structure. Journal of
Chemical Physics, 120, 574 (2004). |
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Towards Idempotent Reduced
Density Matrices via Particle-Hole
Duality: McWeeny's Purification
and Beyond. Physical Review E, 68,
066701 (2003). |
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Extraction of Electronic Excited
States from the Ground-state Two-particle
Reduced Density Matrix.
Physical Review A, 68, 052501
(2003). |
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Variational Minimization of Atomic
and Molecular Ground-state
Energies via the Two-particle
Reduced Density Matrix. Physical
Review A, 65, 062511 (2002). |
| Cumulants and the Contracted Schrödinger Equation. in Many-electron Densities and Density Matrices, edited by J. Cioslowski (Boston, Kluwer, 2000) |
| Boson Correlation Energy from Reduced Hamiltonian Interpolation. Physical Review Letters, 83, 5185 (1999). |
| Contracted Schrödinger Equation: Determining Quantum Energies and Two-particle Density Matrices without Wave Functions. Physical Review A, 57, 4219 (1998). |
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Physical Chemistry 