Improving MP2 bandgaps with low-scaling approximations to EOM-CCSD.

Despite its reasonable accuracy for ground-state properties of semiconductors and insulators, second-order Møller-Plesset perturbation theory (MP2) significantly underestimates bandgaps. In this work, we evaluate the bandgap predictions of partitioned equation-of-motion MP2 (P-EOM-MP2), which is a second-order approximation to EOM coupled-cluster theory with single and double excitations. On a test set of elemental and binary semiconductors and insulators, we find that P-EOM-MP2 overestimates bandgaps by 0.3 eV on average, which can be compared to the underestimation by 0.6 eV on average exhibited by the G0W0 approximation with a Perdew-Burke-Ernzerhof reference. We show that P-EOM-MP2, when interpreted as a Green's function-based theory, has a self-energy that includes all first- and second-order diagrams and a few third-order diagrams. We find that the GW approximation performs better for materials with small gaps and P-EOM-MP2 performs better for materials with large gaps, which we attribute to their superior treatment of screening and exchange, respectively.

Dynamical correlation energy of metals in large basis sets from downfolding and composite approaches.

Coupled-cluster theory with single and double excitations (CCSD) is a promising ab initio method for the electronic structure of three-dimensional metals, for which second-order perturbation theory (MP2) diverges in the thermodynamic limit. However, due to the high cost and poor convergence of CCSD with respect to basis size, applying CCSD to periodic systems often leads to large basis set errors. In a common "composite" method, MP2 is used to recover the missing dynamical correlation energy through a focal-point correction, but the inadequacy of finite-order perturbation theory for metals raises questions about this approach. Here, we describe how high-energy excitations treated by MP2 can be "downfolded" into a low-energy active space to be treated by CCSD. Comparing how the composite and downfolding approaches perform for the uniform electron gas, we find that the latter converges more quickly with respect to the basis set size. Nonetheless, the composite approach is surprisingly accurate because it removes the problematic MP2 treatment of double excitations near the Fermi surface. Using this method to estimate the CCSD correlation energy in the combined complete basis set and thermodynamic limits, we find that CCSD recovers 85%-90% of the exact correlation energy at rs = 4. We also test the composite approach with the direct random-phase approximation used in place of MP2, yielding a method that is typically (but not always) more cost effective due to the smaller number of orbitals that need to be included in the more expensive CCSD calculation.

Integrative Approaches for the Identification and Localization of Specialized Metabolites in Tripterygium Roots.

Members of the genus Tripterygium are known to contain an astonishing diversity of specialized metabolites. The lack of authentic standards has been an impediment to the rapid identification of such metabolites in extracts. We employed an approach that involves the searching of multiple, complementary chromatographic and spectroscopic data sets against the Spektraris database to speed up the metabolite identification process. Mass spectrometry-based imaging indicated a differential localization of triterpenoids to the periderm and sesquiterpene alkaloids to the cortex layer of Tripterygium roots. We further provide evidence that triterpenoids are accumulated to high levels in cells that contain suberized cell walls, which might indicate a mechanism for storage. To our knowledge, our data provide first insights into the cell type specificity of metabolite accumulation in Tripterygium and set the stage for furthering our understanding of the biological implications of specialized metabolites in this genus.

Active space approaches combining coupled-cluster and perturbation theory for ground states and excited states.

We evaluate the performance of approaches that combine coupled-cluster and perturbation theory based on a predefined active space of orbitals. Coupled-cluster theory is used to treat excitations that are internal to the active space and perturbation theory is used for all other excitations, which are at least partially external to the active space. We consider a variety of schemes that differ in how the internal and external excitations are coupled. Such approaches are presented for ground states and excited states within the equation-of-motion formalism. Results are given for the ionization potentials and electron affinities of a test set of small molecules and for the correlation energy and band gap of a few periodic solids.

On the Relation between Equation-of-Motion Coupled-Cluster Theory and the GW Approximation.

We discuss the analytic and diagrammatic structure of ionization potential (IP) and electron affinity (EA) equation-of-motion coupled-cluster (EOM-CC) theory, in order to put it on equal footing with the prevalent GW approximation. The comparison is most straightforward for the time-ordered one-particle Green's function, and we show that the Green's function calculated by EOM-CC with single and double excitations (EOM-CCSD) includes fewer ring diagrams at higher order than does the GW approximation, due to the former's unbalanced treatment of time-ordering. However, the EOM-CCSD Green's function contains a large number of vertex corrections, including ladder diagrams, mixed ring-ladder diagrams, and exchange diagrams. By including triple excitations, the EOM-CCSDT Green's function includes all diagrams contained in the GW approximation, along with many high-order vertex corrections. In the same language, we discuss a number of common approximations to the EOM-CCSD equations, many of which can be classified as elimination of diagrams. Finally, we present numerical results by calculating the principal charged excitations energies of the molecules contained in the so-called GW100 test set [ J. Chem. Theory Comput. 2015 , 11 , 5665 - 5687 ]. We argue that (in molecules) exchange is as important as screening, advocating for a Hartree-Fock reference and second-order exchange in the self-energy.

Detection and correction of endotracheal-tube position in premature neonates.

Due to the short airways in premature children, an accurate position of the endotracheal tube (ETT) is crucial for adequate mechanical ventilation. Verification of ETT-position is done in chest radiographs. However, ETT-position varies substantially with head movement. When the head is flexed, the tube might appear too deeply inserted, and inadvertent extubation may occur in cases of retraction of ETT after radiography. Extension of the cervical spine will suggest an inappropriately high ETT-position, so that intended corrections can lead to main-stem intubation. Radiographic visible skeletal structures could serve as reference points to allow the detection of head declination and imperfect positioning of ETT. Ratios of anatomical landmarks were used to estimate head position. In this study, 111 radiographs of 24 preterm neonates with a gestational age of 24-29 weeks and weights of 500-1,000 g were analyzed. A mathematical algorithm for the detection and correction of ETT-positions, based on common chest radiographs, was developed. In 108 cases (97.3%), ETT-distance from the midtracheal level was less than 2 mm after use of the proposed correction.Thus, the suggested correction equation for head position enables verification of the actual ETT-position without requiring a defined placement of the head during radiography. Moreover, it can be helpful for estimating the depth of ETT-insertion in conditions when radiography is not available.

Correction of compliance and resistance altered by endotracheal tube leaks.

OBJECTIVE: Measurements of lung compliance and resistance are influenced by endotracheal tube leaks. To keep compliance and resistance reliable, we developed an algorithm to correct inspiratory and expiratory volume and flow mathematically. DESIGN: Prospective, clinical study. SETTING: University research laboratory and neonatal intensive care unit. MODEL: A ventilated lung model with a linear pressure-volume relationship and with adjustment of an increasing endotracheal tube leak was investigated. PATIENTS: A total of 21 ventilated premature neonates (median weight, 1220 g; range, 640-2160 g; median leak, 32%; range, 24-56%) were studied. MEASUREMENTS AND MAIN RESULTS: Compliance and resistance were calculated from the recordings of flow, volume, and airway pressure over time employing linear regression of the equation of motion to obtain compliance and resistance. Compliance and resistance altered by leaks were corrected and compared with measurements without leak. Compliance and resistance of the lung model could be corrected up to an endotracheal tube leak size of 86%. Compliance and resistance without leak and after leak correction did not differ significantly for all infants using the linear regression method (p >.05). For the correction of compliance in 15 and for the correction of resistance in 12 of the 21 infants, the coefficients of variation of ten measured breaths without leak were greater or equal to the differences of the values of compliance and resistance between conditions of no leak and corrected leak, respectively. CONCLUSION: Pulmonary compliance and resistance can be reliably corrected even in the presence of a substantial endotracheal tube leak, which makes pulmonary function tests more reliable.

Correction of compliance and resistance altered by endotracheal tube leaks and non-linear pressure/volume-relationships.

Measurements of lung compliance (C) and resistance (R) are influenced by endotracheal tube leaks (ETTL) as well as non-linear pressure/volume relationships (P/V relationship). To keep C and R reliable, we developed an algorithm to mathematically correct inspiratory and expiratory volume (V) and flow. In this study, a ventilated lung model for non-linear P/V relationship with adjustment of an increasing ETTL was studied. In addition, the recordings (airway pressure, flow, and volume) of 21 infants (median weight: 1,220 g, range: 640-2,160 g, with a median leak size of 32%, range: 24-56%) were investigated. C and R were calculated continuously from the recordings of flow, volume, and airway pressure over time according to the changing volume. A method especially developed for the analysis of non-linear pressure-volume-relationship (APVNL) was employed. C and R affected by leaks were corrected applying the newly developed mathematical algorithm and compared with measurements without leakage. C could be corrected up to a leak of 80% and R up to 55% leak at half tidal V for the model with non-linear P/V-R. C and R without leak and after leak correction did not differ significantly in all infants where the APVNL method was applied (P > 0.05).

Calculation of intratracheal airway pressure in ventilated neonatal piglets with endotracheal tube leaks.

OBJECTIVE: In ventilated neonates, only the applied pressure of the ventilator is adjusted and monitored. When an endotracheal tube leaks, intratracheal pressure decreases depending on the size of the endotracheal tube and of the leak. Furthermore, an increase in resistance and/or compliance might delay the increase of intratracheal pressure during inspiration and its decline during expiration. Short inspiratory time can cause insufficient ventilation, because intratracheal pressure peak might not be reached. Short expiratory time may lead to air trapping, because intratracheal pressure could not return to baseline. The aim of this study was to develop a mathematical algorithm to calculate intratracheal pressure continuously during ventilation and to evaluate the accuracy of this method. DESIGN: Prospective, animal study. SETTING: University research laboratory. SUBJECTS: To verify the mathematical algorithm, eight neonatal piglets (1600-2600 g) were studied under different endotracheal tube leak conditions (45% to 98%). The median compliance and resistance were 1.06 mL/cm H2O/kg and 123 cm H2O/L/sec, respectively. INTERVENTIONS: Pressure decreases caused by the different endotracheal tubes were measured in a model while air flow was increased stepwise. Based on these results, a mathematical method was developed to calculate intratracheal pressure under leak conditions continuously in relation to the flow through the endotracheal tube as well as to calculate the values of resistance, compliance, and applied pressure of the ventilator. MEASUREMENTS AND MAIN RESULTS: The intratracheal pressure calculated was compared with the measured intratracheal pressure over time. The differences between measured and calculated intratracheal pressure related to peak applied pressure of the ventilator did not exceed 10%. The medians of absolute amounts of differences between measured and calculated intratracheal pressure were <1 cm H2O. CONCLUSIONS: The accuracy of the calculation of intratracheal pressure ensures adequate monitoring of artificial ventilation, even in the presence of endotracheal tube leaks. This might decrease the risk of barotrauma and improve the effectiveness of ventilation.