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 is also appropriate for other aspects of chemistry including the prediction of vibrational and rotational molecular properties.
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.
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 inPhysical 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.
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 moleculewithout 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.
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 two electron problem offers a new level of accuracy and efficiency for electronic structure calculations.
Princeton University
A.B.
1995
Harvard University
Ph.D.
1999
Duke University
Postdoctoral Fellow
1999
Princeton University
NSF Postdoctoral Fellow
2001
The University of Chicago
Professor
Present
A.W. Schlimgen and D. A. Mazziotti, J. Phys. Chem. A 121, 9377-9384 (2017). "Static and dynamic electron correlation in the ligand noninnocent oxidation of nickel dithiolates"
K. Head-Marsden and D. A. Mazziotti, J. Chem. Phys. 147, 084101 (2017). "Pair 2-electron reduced density matrix theory using localized orbitals"
D. A. Mazziotti, Phys. Rev. Lett. 117, 153001 (2016). "Enhanced constraints for accurate lower bounds on many-electron quantum energies from variational two-electron reduced density matrix theory"
D. A. Mazziotti, Phys. Rev. A 94, 032516 (2016). "Pure-N-representability conditions of two-fermion reduced density matrices"
A. W. Schlimgen, C. W. Heaps, and D. A. Mazziotti, J. Phys. Chem. Lett. 7, 627-631 (2016). "Entangled electrons foil synthesis of elusive low-valent vanadium oxo complex"
A. E. Raeber and D. A. Mazziotti, Phys. Rev. A 92, 052502 (2015). "Large eigenvalue of the cumulant part of the two-electron reduced density matrix as a measure of off-diagonal long-range order"
S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A 92, 022512 (2015). "Semidefinite programming formulation of linear-scaling electronic structure theories"
K. Head-Marsden and D. A. Mazziotti, J. Chem. Phys. 142, 051102 (2015). "Communication: Satisfying fermionic statistics in the modeling of open time-dependent quantum systems with one-electron reduced density matrices"
D. A. Mazziotti, Phys. Rev. Lett. 108, 263002 (2012). "Structure of fermionic density matrices: Complete N-Representability conditions"
APS Fellow
2022
Robert S. Mulliken Lecture
University of Georgia
2018
Llewellyn John and Harriet Manchester Quantrell Award for Excellence in Undergraduate Teaching
2014
Faculty Award for Excellence in Graduate Teaching and Mentoring
2014
Microsoft Newton Award
2008
Camille Dreyfus Teacher-Scholar Award
2007
NSF CAREER Award
2007
Packard Foundation Fellowship for Science and Engineering
2005
Alfred P. Sloan Research Fellowship
2005
Dreyfus New Faculty Award
2002
National Science Foundation Mathematical Sciences Postdoctoral Fellow
2000 - 2001
David Mazziotti group draw inspiration from ancient Alexandria to optimize quantum simulations
David Mazziotti Creates New Technique To Make Modeling Molecules Easier For Quantum Simulation