Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions

We present an investigation into the use of an explicitly correlated plane wave basis for periodic wavefunction expansions at the level of second-order M{\o}ller-Plesset perturbation theory (MP2). The convergence of the electronic correlation energy with respect to the one-electron basis set is investigated and compared to conventional MP2 theory in a finite homogeneous electron gas model. In addition to the widely used Slater-type geminal correlation factor, we also derive and investigate a novel correlation factor that we term Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic results for two electrons in a box and allows for a further improved convergence of the correlation energies with respect to the employed basis set. We find the combination of the infinitely delocalized plane waves and local short-ranged geminals provides a complementary, and rapidly convergent basis for the description of periodic wavefunctions. We hope that this approach will expand the scope of discrete wavefunction expansions in periodic systems.Comment: 15 pages, 13 figure

Comparison of laser speckle contrast imaging with laser Doppler for assessing microvascular function

Objective: To compare the inter-day reproducibility of post-occlusive reactive hyperaemia (PORH) and sympathetic vasomotor reflexes assessed by single-point laser Doppler flowmetry (SP-LDF), integrating-probe LDF (IP-LDF) and laser speckle contrast imaging (LSCI), and the spatial variability of PORH assessed by IP-LDF and LSCI. We also evaluated the relationship between IP-LDF and LSCI perfusion values across a broad range of skin blood flows. Methods: Eighteen healthy adults (50% male, age 27 ± 4 years) participated in this study. Using SP-LDF, IP-LDF and LSCI, an index of skin blood flow was measured on the forearm during PORH (1-, 5- and 10-min occlusions) and on the finger pad during inspiratory gasp and cold pressor tests. These tests were repeated 3-7 days later. Data were converted to cutaneous vascular conductance (CVC; laser Doppler flow/mean arterial pressure) and expressed as absolute and relative changes from pre-stimulus CVC (ΔCVCABS and ΔCVCREL, respectively), as well as normalised to peak CVC for the PORH tests. Reproducibility was expressed as within-subjects coefficients of variation (CV, in %) and intraclass correlation coefficients. Results: The reproducibility of PORH on the forearm was poorer when assessed with SP-LDF and IP-LDF compared to LSCI (e.g., CV for 5-min PORH ΔCVCABS = 35, 27 and 19%, respectively), with no superior method of data expression. In contrast, the reproducibility of the inspiratory gasp and cold pressor test responses on the finger pad were better with SP-LDF and IP-LDF compared to LSCI (e.g., CV for inspiratory gasp ΔCVCREL = 13, 7 and 19%, respectively). The spatial variability of PORH responses was poorer with IP-LDF compared to LSCI (e.g., CV ranging 11-35% versus 3-16%, respectively). The association between simultaneous LSCI and IP-LDF perfusion values was non-linear. Conclusion: The reproducibility of cutaneous PORH was better when assessed with LSCI compared to SP-LDF and IP-LDF; probably due to measuring larger skin areas (lower inter-site variability). However, when measuring sympathetic vasomotor reflexes on the finger pad, reproducibility was better with SP-LDF and IP-LDF, perhaps due to the high sensitivity of LSCI to changes in skin blood flow at low levels

A regularized second-order correlation method from Green's function theory

We present a scalable single-particle framework to treat electronic correlation in molecules and materials motivated by Green's function theory. We derive a size-extensive Brillouin-Wigner perturbation theory from the single-particle Green's function by introducing the Goldstone self-energy. This new ground state correlation energy, referred to as Quasi-Particle MP2 theory (QPMP2), avoids the characteristic divergences present in both second-order M{\o}ller-Plesset perturbation theory (MP2) and Coupled Cluster Singles and Doubles (CCSD) within the strongly correlated regime. We show that the exact ground state energy and properties of the Hubbard dimer are reproduced by QPMP2 and demonstrate the advantages of the approach for the six-, eight- and ten-site Hubbard models where the metal-to-insulator transition is qualitatively reproduced, contrasting with the complete failure of traditional methods. We apply this formalism to characteristic strongly correlated molecular systems and show that QPMP2 provides an efficient, size-consistent regularization of MP2

The coupled-cluster self-energy

An improved description of electronic correlation in molecules and materials can only be achieved by uncovering connections between different areas of electronic structure theory. A general unifying relationship between the many-body self-energy and coupled-cluster theory has remained hitherto unknown. Here, we present a formalism for constructing the coupled-cluster self-energy from the coupled-cluster ground state energy. Our approach illuminates the fundamental connections between the many-body self-energy and the coupled-cluster equations. As a consequence, we naturally arrive at the coupled-cluster quasiparticle and Bethe-Salpeter equations describing correlated electrons and excitons. This deep underlying structure explains the origin of the connections between RPA, $GW$-BSE and coupled-cluster theory, whilst also elucidating the relationship between vertex corrections and the amplitude equations