Stochastic Resolution of Identity for Real-Time Second-Order Green's Function: Ionization Potential and Quasi-Particle Spectrum.

We develop a stochastic resolution of identity approach to the real-time second-order Green's function (real-time sRI-GF2) theory, extending our recent work for imaginary-time Matsubara Green's function [ Takeshita et al. J. Chem. Phys. 2019 , 151 , 044114 ]. The approach provides a framework to obtain the quasi-particle spectra across a wide range of frequencies and predicts ionization potentials and electron affinities. To assess the accuracy of the real-time sRI-GF2, we study a series of molecules and compare our results to experiments as well as to a many-body perturbation approach based on the GW approximation, where we find that the real-time sRI-GF2 is as accurate as self-consistent GW. The stochastic formulation reduces the formal computatinal scaling from O(Ne5) down to O(Ne3) where Ne is the number of electrons. This is illustrated for a chain of hydrogen dimers, where we observe a slightly lower than cubic scaling for systems containing up to Ne ≈ 1000 electrons

Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources

Proposals for near-term experiments in quantum chemistry on quantum computers leverage the ability to target a subset of degrees of freedom containing the essential quantum behavior, sometimes called the active space. This approximation allows one to treat more difficult problems using fewer qubits and lower gate depths than would otherwise be possible. However, while this approximation captures many important qualitative features, it may leave the results wanting in terms of absolute accuracy (basis error) of the representation. In traditional approaches, increasing this accuracy requires increasing the number of qubits and an appropriate increase in circuit depth as well. Here we introduce a technique requiring no additional qubits or circuit depth that is able to remove much of this approximation in favor of additional measurements. The technique is constructed and analyzed theoretically, and some numerical proof of concept calculations are shown. As an example, we show how to achieve the accuracy of a 20 qubit representation using only 4 qubits and a modest number of additional measurements for a simple hydrogen molecule. We close with an outlook on the impact this technique may have on both near-term and fault-tolerant quantum simulations

A deterministic alternative to the full configuration interaction quantum Monte Carlo method

Development of exponentially scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, is a useful algorithm that allows exact diagonalization through stochastically sampling determinants. The method derives its utility from the information in the matrix elements of the Hamiltonian, along with a stochastic projected wave function, to find the important parts of Hilbert space. However, the stochastic representation of the wave function is not required to search Hilbert space efficiently, and here we describe a highly efficient deterministic method to achieve chemical accuracy for a wide range of systems, including the difficult Cr$_{2}$ dimer. In addition our method also allows efficient calculation of excited state energies, for which we illustrate with benchmark results for the excited states of C$_{2}$.Comment: 4 pages, 2 figure

General method for the development of models of electronic structure and bonding: covalent bonds, recoupled pair bonds and through-pair interactions

The concept of the chemical bond is essential to our understanding of molecular phenomena. G. N. Lewis laid the groundwork for our understanding of chemical bonds nearly a century ago in his classic 1916 paper in the Journal of the American Chemical Society, “The Atom and the Molecule.” This model was given a firm theoretical foundation by W. Heitler and F. London shortly after the discovery of quantum mechanics. The 1930s were most fruitful with the formulation of valence bond theory by L. Pauling, G. W. Wheland and J. C. Slater and molecular orbital theory by F. Hund and R. S. Mulliken. However, in spite of significant advances in both computational and experimental methods, little progress has been made in the development of rigorous conceptual models of electronic structure based on high-level solutions of the molecular Schrödinger equation. In this dissertation a novel method for the general and systematic development of comprehensive electronic structure models is introduced. This computationally driven design approach is applied to refine our understanding of generalized valence bond (GVB) theory and to the development of the recoupled pair bonding model. The recoupled pair bond model consists of two conceptual components, the recoupled pair bond and the recoupled pair bond dyad. The fundamental aspects of the recoupled pair bond, where the electrons that compose an atomic or molecular lone pair is recoupled, are introduced through the analysis of the ground, 2Π, and low-lying excited, 4Σ–, states of CF, OF and SF. It is shown that the conditional nature of recoupled pair bonds formed with 2p and 3p lone pairs, but not 2s lone pairs, is straightforward in the framework of GVB theory and is largely governed by the Pauli exclusion principle and can be correlated with the correlation of the lone pair and electronegativity of the ligand. Knowledge of the presence or absence of recoupled pair bonds offer valuable insights into the available ligand addition pathways a molecular species may participate in. In the presence of a recoupled pair bond one such addition pathway is the formation of a recoupled pair bond dyad. The ground and excited states of CF2 and SF2 are used to show that the formation of a recoupled pair bond dyad is also well predicted by the spatial correlation of the orbitals involved and the electronegativity of the ligand. Application of the model in conjunction with an atom-by-atom approach, that constructs molecules of increasing complexity through the systematic addition of atoms, shows that the recoupled pair bonding model is extremely general and accounts for many aspects of the anomalous behavior of the late p-block elements beyond the first row. In this dissertation this model is also used to rationalize the electronic structure of two pairs of molecules, NXOH and XO2, X = O or S, where the molecules in each pair differ by one valence isoelectronic atom yet display vastly different properties. It is found that the perplexing behavior of these valence isoelectronic species is accounted for by the presence or absence of recoupled pair bonds, recoupled pair bond dyads and through-pair interactions

Range-Separated Stochastic Resolution of Identity: Formulation and Application to Second Order Green's Function Theory

We develop a range-separated stochastic resolution of identity approach for the $4$-index electron repulsion integrals, where the larger terms (above a predefined threshold) are treated using a deterministic resolution of identity and the remaining terms are treated using a stochastic resolution of identity. The approach is implemented within a second-order Greens function formalism with an improved $O(N^3)$ scaling with the size of the basis set, $N$. Moreover, the range-separated approach greatly reduces the statistical error compared to the full stochastic version ({\it J. Chem. Phys.} {\bf 151}, 044144 (2019)), resulting in computational speedups of ground and excited state energies of nearly two orders of magnitude, as demonstrated for hydrogen dimer chains

Autonomous in situ calibration of ion‐sensitive field effect transistor pH sensors

Ion‐sensitive field effect transistor‐based pH sensors have been shown to perform well in high frequency and long‐term ocean sampling regimes. The Honeywell Durafet is widely used due to its stability, fast response, and characterization over a large range of oceanic conditions. However, potentiometric pH monitoring is inherently complicated by the fact that the sensors require careful calibration. Offsets in calibration coefficients have been observed when comparing laboratory to field‐based calibrations and prior work has led to the recommendation that an in situ calibration be performed based on comparison to discrete samples. Here, we describe our work toward a self‐calibration apparatus integrated into a SeapHOx pH, dissolved oxygen, and CTD sensor package. This Self‐Calibrating SeapHOx is capable of autonomously recording calibration values from a high quality, traceable, primary reference standard: equimolar tris buffer. The Self‐Calibrating SeapHOx\u27s functionality was demonstrated in a 6‐d test in a seawater tank at Scripps Institution of Oceanography (La Jolla, California, U.S.A.) and was successfully deployed for 2 weeks on a shallow, coral reef flat (Lizard Island, Australia). During the latter deployment, the tris‐based self‐calibration using 15 on‐board samples exhibited superior reproducibility to the standard spectrophotometric pH‐based calibration using \u3e 100 discrete samples. Standard deviations of calibration pH using tris ranged from 0.002 to 0.005 whereas they ranged from 0.006 to 0.009 for the standard spectrophotometric pH‐based method; the two independent calibration methods resulted in a mean pH difference of 0.008. We anticipate that the Self‐Calibrating SeapHOx will be capable of autonomously providing climate quality pH data, directly linked to a primary seawater pH standard, and with improvements over standard calibration techniques

Unexpected role of communities colonizing dead coral substrate in the calcification of coral reefs

Global and local anthropogenic stressors such as climate change, acidification, overfishing, and pollution are expected to shift the benthic community composition of coral reefs from dominance by calcifying organisms to dominance by non-calcifying algae. These changes could reduce the ability of coral reef ecosystems to maintain positive net calcium carbonate accretion. However, relationships between community composition and calcification rates remain unclear. We performed field experiments to quantify the metabolic rates of the two most dominant coral reef substrate types, live coral and dead coral substrate colonized by a mixed algal assemblage, using a novel underwater respirometer. Our results revealed that calcification rates in the daytime were similar for the live coral and dead coral substrate communities. However, in the dark, while live corals continued to calcify at slower rates, the dead coral substrate communities exhibited carbonate dissolution. Daytime net photosynthesis of the dead coral substrate communities was up to five times as much as for live corals, which we hypothesize may have created favorable conditions for the precipitation of carbonate minerals. We conclude that: (1) calcification from dead coral substrate communities can contribute to coral reef community calcification during the day, and (2) dead coral substrate communities can also contribute to carbonate mineral dissolution at night, decreasing ecosystem calcification over a diel cycle. This provides evidence that reefs could shift from slow, long-term accretion of calcium carbonate to a state where large daily cycling of calcium carbonate occurs, but with little or no long-term accumulation of the carbonate minerals needed to sustain the reef against erosional forces