Self-consistent solution of Dyson’s equation up to second order for atomic systems

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.