A "moment-conserving" reformulation of GW theory.

We show how to construct an effective Hamiltonian whose dimension scales linearly with system size, and whose eigenvalues systematically approximate the excitation energies of GW theory. This is achieved by rigorously expanding the self-energy in order to exactly conserve a desired number of frequency-independent moments of the self-energy dynamics. Recasting GW in this way admits a low-scaling O[N4] approach to build and solve this Hamiltonian, with a proposal to reduce this further to O[N3]. This relies on exposing a novel recursive framework for the density response moments of the random phase approximation, where the efficient calculation of its starting point mirrors the low-scaling approaches to compute RPA correlation energies. The frequency integration of GW, which distinguishes so many different GW variants, can be performed without approximation directly in this moment representation. Furthermore, the solution to the Dyson equation can be performed exactly, avoiding analytic continuation, diagonal approximations, or iterative solutions to the quasiparticle equation, with the full-frequency spectrum obtained from the complete solution of this effective static Hamiltonian. We show how this approach converges rapidly with respect to the order of the conserved self-energy moments and is applied across the GW100 benchmark dataset to obtain accurate GW spectra in comparison to traditional implementations. We also show the ability to systematically converge all-electron full-frequency spectra and high-energy features beyond frontier excitations, as well as avoiding discontinuities in the spectrum, which afflict many other GW approaches.

Constructing "Full-Frequency" Spectra via Moment Constraints for Coupled Cluster Green's Functions.

We propose an approach to build "full-frequency" quasiparticle spectra from conservation of a set of static expectation values. These expectation values define the moments of the spectral distribution, resulting in an efficient and systematically improvable expansion. By computing these initial moment constraints at the coupled-cluster level, we demonstrate convergence in both correlated state-specific and full spectral quantities, while requiring a fraction of the effort of traditional Green's function approaches. Tested across the GW100 benchmark set for charged excitation spectra, we can converge frontier excitations to within the inherent accuracy of the CCSD approximation, while obtaining a simultaneous representation of the entire excitation spectrum at all energy scales.

Scalable and Predictive Spectra of Correlated Molecules with Moment Truncated Iterated Perturbation Theory.

A reliable and efficient computation of the entire single-particle spectrum of correlated molecules is an outstanding challenge in the field of quantum chemistry, with standard density functional theory approaches often giving an inadequate description of excitation energies and gaps. In this work, we expand upon a recently introduced approach that relies on a fully self-consistent many-body perturbation theory coupled to a nonperturbative truncation of the effective dynamics at each step. We show that this yields a low-scaling and accurate method across a diverse benchmark test set that is capable of treating moderate levels of strong correlation effects, and we detail an efficient implementation for applications involving up to ∼1000 orbitals on parallel resources. We then use this method to characterize the spectral properties of the antimalarial drug molecule artemisinin, resolving discrepancies in previous works concerning the active sites of the lowest-energy fundamental excitations of the system.

Efficient Excitations and Spectra within a Perturbative Renormalization Approach.

We present a self-consistent approach for computing the correlated quasiparticle spectrum of charged excitations in iterative O[N5] computational time. This is based on the auxiliary second-order Green's function approach [Backhouse, O. J. Chem. Theory Comput., 2000], in which a self-consistent effective Hamiltonian is constructed by systematically renormalizing the dynamical effects of the self-energy at second-order perturbation theory. From extensive benchmarking across the W4-11 molecular test set, we show that the iterative renormalization and truncation of the effective dynamical resolution arising from the 2h1p and 1h2p spaces can substantially improve the quality of the resulting ionization potential and electron affinity predictions compared to benchmark values. The resulting method is shown to be superior in accuracy to similarly scaling quantum chemical methods for charged excitations in EOM-CC2 and ADC(2), across this test set, while the self-consistency also removes the dependence on the underlying mean-field reference. The approach also allows for single-shot computation of the entire quasiparticle spectrum, which is applied to the benzoquinone molecule and demonstrates the reduction in the single-particle gap due to the correlated physics, and gives direct access to the localization of the Dyson orbitals.

Wave Function Perspective and Efficient Truncation of Renormalized Second-Order Perturbation Theory.

We present an approach to a renormalized second-order Green's function perturbation theory (GF2), which avoids all dependency on continuous variables, grids, or explicit Green's functions and is instead formulated entirely in terms of static quantities and wave functions. Correlation effects from MP2 diagrams are iteratively incorporated to modify the underlying spectrum of excitations by coupling the physical system to fictitious auxiliary degrees of freedom, allowing for single-particle orbitals to delocalize into this additional space. The overall approach is shown to be rigorously O[N5], after an appropriate compression of this auxiliary space. This is achieved via a novel scheme, which ensures that a desired number of moments of the underlying occupied and virtual spectra are conserved in the compression, allowing a rapid and systematically improvable convergence to the limit of the effective dynamical resolution. The approach is found to then allow for the qualitative description of stronger correlation effects, avoiding the divergences of MP2, as well as its orbital-optimized version. On application to the G1 test set, we find that modification up to only the third spectral moment of the underlying spectrum from which the double excitations are built are required for accurate energetics, even in strongly correlated regimes. This is beyond simple self-consistent changes to the density matrix of the system but far from requiring a description of the full dynamics of the frequency-dependent self-energy.

A Re-evaluation of Factors Controlling the Nature of Complementary Hydrogen-Bonded Networks.

The energy profiles of hydrogen-bonded heterocyclic aromatics have been decomposed into atomistic energy contributions using the Interacting Quantum Atoms (IQA) method. The resulting energy contributions have been sequenced by the Relative Energy Gradient (REG) approach to determine their influence upon the shape of these energy profiles. The results show inadequacies in Jorgensen's secondary interaction hypothesis (SIH). A novel method of finding a condensed analogy for the interaction between the molecules is presented. The findings of this work further doubt the validity of the SIH, and reinforce previous warnings against its misguided use.