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 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 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*.

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 N_{2} 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.

Selected References

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"