A Self Consistent Field Formulation of Excited State Mean Field Theory

We show that, as in Hartree Fock theory, the orbitals for excited state mean field theory can be optimized via a self-consistent one-electron equation in which electron-electron repulsion is accounted for through mean field operators. In addition to showing that this excited state ansatz is sufficiently close to a mean field product state to admit a one-electron formulation, this approach brings the orbital optimization speed to within roughly a factor of two of ground state mean field theory. The approach parallels Hartree Fock theory in multiple ways, including the presence of a commutator condition, a one-electron mean-field working equation, and acceleration via direct inversion in the iterative subspace. When combined with a configuration interaction singles Davidson solver for the excitation coefficients, the self consistent field formulation dramatically reduces the cost of the theory compared to previous approaches based on quasi-Newton descent.Comment: 6 pages, 3 tables, 1 figure, plus supplementary materia

Studying excited-state-specific perturbation theory on the Thiel set

We explore the performance of a recently-introduced $N^5$-scaling excited-state-specific second order perturbation theory (ESMP2) on the singlet excitations of the Thiel benchmarking set. We find that, without regularization, ESMP2 is quite sensitive to $\pi$ system size, performing well in molecules with small $\pi$ systems but poorly in those with larger $\pi$ systems. With regularization, ESMP2 is far less sensitive to $\pi$ system size and shows a higher overall accuracy on the Thiel set than CC2, EOM-CCSD, CC3, and a wide variety of time-dependent density functional approaches. Unsurprisingly, even regularized ESMP2 is less accurate than multi-reference perturbation theory on this test set, which can in part be explained by the set's inclusion of some doubly excited states but none of the strong charge transfer states that often pose challenges for state-averaging. Beyond energetics, we find that the ESMP2 doubles norm offers a relatively low-cost way to test for doubly excited character without the need to define an active space

OpenFermion: The Electronic Structure Package for Quantum Computers

Quantum simulation of chemistry and materials is predicted to be an important application for both near-term and fault-tolerant quantum devices. However, at present, developing and studying algorithms for these problems can be difficult due to the prohibitive amount of domain knowledge required in both the area of chemistry and quantum algorithms. To help bridge this gap and open the field to more researchers, we have developed the OpenFermion software package (www.openfermion.org). OpenFermion is an open-source software library written largely in Python under an Apache 2.0 license, aimed at enabling the simulation of fermionic models and quantum chemistry problems on quantum hardware. Beginning with an interface to common electronic structure packages, it simplifies the translation between a molecular specification and a quantum circuit for solving or studying the electronic structure problem on a quantum computer, minimizing the amount of domain expertise required to enter the field. The package is designed to be extensible and robust, maintaining high software standards in documentation and testing. This release paper outlines the key motivations behind design choices in OpenFermion and discusses some basic OpenFermion functionality which we believe will aid the community in the development of better quantum algorithms and tools for this exciting area of research.Comment: 22 page

Self Consistent Excited State Mean Field Theory: Development and Applications

In the wide spectrum of excited state quantum chemistry methods, there is no direct analogue to Hartree-Fock theory. This dissertation presents the theory and initial applications for a self consistent framework for Excited State Mean Field (ESMF) theory. This method presents a self consistent equation analogous to the Roothaan-Hall equation, that is constructed with mean-field one-electron operators. The convergence criteria is described by a commutator condition between Fock-type operators and density operators, just like in Hartree-Fock theory. Finally, this method is accelerated via direct inversion of the iterative subspace (DIIS), akin to acceleration in the ground state theory. Futhermore, this work discusses applications of ESMF to larger solvated systems, afforded by ESMF's scaling -- the method costs roughly twice the cost of a Hartree-Fock calculation. Getting an accurate physical picture of excited states in solvated systems is challenging, and the second half of this dissertation focuses on a comparative analysis of various methods, their degree of correlation, and their ability to qualitatively describe donor and acceptor regions for a charge transfer excitation. This comparison shows that ESMF can accurately describe the degree of participation of solvent water molecules in the excitation, unlike Density Functional Theory (DFT) based methods. However, when there is minimal participation from the solvent, Restricted Open-shell Kohn Sham methods fare better, indicating that the lack of correlation in ESMF prevents the method from providing a more quantitatively accurate picture. Using ESMF as a stepping rung for developing a hierarchy of excited state specific methods is a promising platform to achieve affordable excited state specific calculations