All-sapphire fiber-optic sensor for the simultaneous measurement of ultra-high temperature and high pressure.

An all-sapphire fiber-optic extrinsic Fabry-Perot interferometric (EFPI) sensor for the simultaneous measurement of ultra-high temperature and high pressure is proposed and experimentally demonstrated. The sensor is fabricated based on all-sapphire, including a sapphire fiber, a sapphire capillary and a sapphire wafer. A femtosecond (fs) laser is employed to drill a through hole at the side wall of the sapphire capillary to allow gas flow. The sapphire fiber is inserted from one side of the sapphire capillary. The sapphire wafer is fixed at the other side of the sapphire capillary. The first Fabry-Perot (FP) cavity, composed of the end face of the sapphire fiber and the front surface of the sapphire wafer, is used for measuring pressure, while the second FP cavity, composed of the two surfaces of the sapphire wafer, is used for measuring temperature. Experimental results show that the sensor can simultaneously measure ultra-high temperature and gas pressure within the temperature range of 20 - 1400 °C and the pressure range of 0 - 5 MPa. The temperature sensitivity is 0.0033 µm/°C, and the pressure sensitivity decreases as the temperature increases, reaching 1.8016 µm/MPa and 0.3253 µm/MPa at temperatures of 20 °C and 1400 °C, respectively.

ChemPotPy: A Python Library for Analytic Representations of Potential Energy Surfaces and Diabatic Potential Energy Matrices.

Constructing analytic representations of global and semiglobal potential energy surfaces is difficult and can be laborious, and it is even harder when one needs coupled potential energy surfaces and their electronically nonadiabatic couplings. When accomplished, however, the resulting potential functions are a valuable resource. To facilitate the convenient use of potentials that have been developed, we provide a collection of existing surfaces in a library with consistent units and formats. A potential energy surface library of this type, namely PotLib, was built more than 20 years ago. However, that library only provided pristine Fortran subroutines for each potential energy surface, and therefore, it is not as user-friendly as would be desirable. Here, we report the creation of ChemPotPy, a CHEMical library of POTential energy surfaces in PYthon. ChemPotPy is a user-friendly library for analytic representation of single-state and multistate potential energy surfaces and couplings. A given entry in the library contains an analytic potential energy function or analytic functions for a set of coupled potential energy surfaces, and depending on the case, it may also include analytic or numerical gradients, nonadiabatic coupling vectors, and/or diabatic potential energy matrices and their gradients. Only three inputs, namely, the chemical formula of the system, the name of the potential energy surface or surface set, and the Cartesian geometry, are required. ChemPotPy uses the same units for input and output quantities of all surfaces and surface sets to facilitate general interfaces with the dynamics programs. The initial version of the library contains 338 entries, and we anticipate that more will be added in the future.

An Accurate Density Coherence Functional for Hybrid Multiconfiguration Density Coherence Functional Theory.

We present hybrid multiconfiguration density coherence functional theory (HMC-DCFT), and we optimize a density coherence functional by parametrization against a diverse data set of 59 bond energies and 60 barrier heights. We compare the results to calculations on the same data set by CASSCF, CASPT2, six Kohn-Sham and hybrid Kohn-Sham exchange-correlation functionals, and three on-top functionals for pair-density functional theory (PDFT) and hybrid PDFT. The new functional has better accuracy than all compared methods.

Global Potential Energy Surfaces by Compressed-State Multistate Pair-Density Functional Theory: The Lowest Doublet States Responsible for the N(4Su) + C2(a 3Πu) → CN(X 2Σ+) + C(3Pg) Reaction.

Global potential energy surfaces (PESs) for the 1 2A' and 1 2A″ states of the C2N system responsible for the N(4Su) + C2(a 3Πu) → CN(X 2Σ+) + C(3Pg) reaction are mapped using compressed-state multistate pair-density functional theory (CMS-PDFT), which is a multi-state version of multiconfiguration pair-density functional theory (MC-PDFT). Calculations are also performed at selected geometries by explicitly correlated multireference configuration interaction with quadruple corrections, MRCI-F12+Q, and the comparison of the two sets of calculations shows that CMS-PDFT describes the globally reactive PESs well, including the bond-breaking asymptotes. We conclude that CMS-PDFT is an efficient method for constructing PESs for strongly correlated reactive systems. The PESs for producing CN + C are found to be barrierless and proceed through intermediate complexes. The CMS-PDFT PESs were fitted with a neural network method, and quasiclassical trajectories were computed on the resulting analytic PESs. These trajectories predict that the reaction produces vibrationally excited CN.

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory.

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn-Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin-orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

Threshold switching memristor-based stochastic neurons for probabilistic computing.

Biological neurons exhibit dynamic excitation behavior in the form of stochastic firing, rather than stiffly giving out spikes upon reaching a fixed threshold voltage, which empowers the brain to perform probabilistic inference in the face of uncertainty. However, owing to the complexity of the stochastic firing process in biological neurons, the challenge of fabricating and applying stochastic neurons with bio-realistic dynamics to probabilistic scenarios remains to be fully addressed. In this work, a novel CuS/GeSe conductive-bridge threshold switching memristor is fabricated and singled out to realize electronic stochastic neurons, which is ascribed to the similarity between the stochastic switching behavior observed in the device and that of biological ion channels. The corresponding electric circuit of a stochastic neuron is then constructed and the probabilistic firing capacity of the neuron is utilized to implement Bayesian inference in a spiking neural network (SNN). The application prospects are demonstrated on the example of a tumor diagnosis task, where common fatal diagnostic errors of a conventional artificial neural network are successfully circumvented. Moreover, in comparison to deterministic neuron-based SNNs, the stochastic neurons enable SNNs to deliver an estimate of the uncertainty in their predictions, and the fidelity of the judgement is drastically improved by 81.2%.

Decomposition of the Electronic Energy in Terms of Density, Density Coherence, and the Connected Part of the Two-Body Reduced Density Matrix.

We analyzed static and dynamic electron correlation by decomposing the total electronic energy of calculations by restricted Hartree-Fock theory, complete active-space self-consistent field (CASSCF) theory, and multireference configuration interaction (MRCI). We used three different schemes to break down the relative energy contributions to the potential energy curves for the dissociation of H2, F2, and N2. The first decomposition scheme involves the classical and nonclassical components of the energy. The second and third recognize the part of the energy that is not expressible in terms of the one-body reduced density matrix; this is called the connected energy. The unconnected component is further decomposed into a part calculable from the density and the part calculable from the density coherence. The first decomposition scheme shows that the sum of the one-electron energy and the classical two-electron energy contains a negligible portion of the static correlation. This quantity has a relatively small variance between the three levels, especially for CASSCF and MRCI. This provides an explanation of why multiconfiguration pair-density functional theory and multiconfiguration density-coherence functional theory are able to improve the CASSCF energy. The latter two decompositions show that the connected energy contains a significant portion of static correlation. The energy representable by either the density or the density coherence is significantly different at the three levels. Mixing the density and density coherence between different methods may lead to a systematic error in the bond dissociation energy and the equilibrium bond distance, indicating that the density energy component and the density coherence energy component both include a significant amount of both static and dynamic correlation. These wave function decompositions can be useful for developing new functionals for density functional theory, density-coherence functional theory, density matrix functional theory, and pair-density functional theory and for guiding expectations for these theories.

Multiconfiguration Density-Coherence Functional Theory.

This paper presents a new theory called multiconfiguration density coherence functional theory (MC-DCFT). This theory provides a new route to define density functionals for multiconfiguration wave functions, in particular by using the one-particle density matrix in the coordinate representation. The theory is illustrated by calculating the dissociation curve of four heteronuclear and homonuclear diatomic molecules, namely, H2, F2, N2, and HF, using density coherence functionals converted from PBE, BLYP, and PW91. By introducing two parameters in the converted density functionals, we are able to calculate bond dissociation energies of comparable accuracy as those calculated by multiconfiguration pair-density functional theory (MC-PDFT) and complete active space second-order perturbation theory (CASPT2). This demonstrates that it would be possible to build a successful multiconfiguration density functional theory based on density coherence.

Multiconfigurational Effects on the Density Coherence.

This paper is a study of density coherences in multiconfiguration self-consistent field theory and Kohn-Sham (KS) density functional theory. We visualize and compare the nondiagonal elements of the first-order reduced density matrix in the electronic coordinate representation. This is the electronic density coherence, and it also appears in Hartree-Fock (HF) theory in the integrand of the exchange integral. The density coherence is calculated as a function of the internuclear distance for three diatomic molecules (H2, F2, and HF) using both restricted and unrestricted KS and HF theory, as well as the complete active space self-consistent field method. We identify a group of closely associated peaks corresponding to the coherence of electrons on opposite sides of the center of the molecule, and we call this the exchange massif. We find that Slater-determinant methods with a higher percentage of HF exchange tend to underestimate the density coherence at the exchange massif. We explain the trends in terms of a multireference diagnostic and the number of unpaired electrons.

Unmasking Static Correlation Error in Hybrid Kohn-Sham Density Functional Theory.

To uncover the way Hartree-Fock exchange brings static correlation error into hybrid Kohn-Sham density functional theory, we compare the potential energy curves of four diatomic molecules, namely, H2, F2, HF, and NaF, using both restricted and unrestricted Kohn-Sham theory. We find that increasing the percentage of Hartree-Fock exchange significantly increases the static correlation error because Hartree-Fock exchange replaces the ability of local exchange in density functionals to account for the localization effects associated with static correlation.

Spin Splitting Energy of Transition Metals: A New, More Affordable Wave Function Benchmark Method and Its Use to Test Density Functional Theory.

Accurately predicting the spin splitting energy of chemical species is important for understanding their reactivity and magnetic properties, but it is very challenging, especially for molecules containing transition metals. One impediment to progress is the scarcity of accurate benchmark data. Here we report a set of calculations designed to yield reliable benchmarks for simple transition-metal complexes that can be used to test density functional methods that are affordable for large systems of more practical interest. Various wave function methods are tested against experiment for Fe2+, Fe3+, and Co3+, including CASSCF, CASPT2, CASPT3, MRCISD, MRCISD+Q, ACPF, AQCC, CCSD(T), and CASPT2/CCSD(T) and also a new method called CASPT2.5, which is performed by taking the average of the CASPT2 and CASPT3 energies. We find that MRCISD+Q, ACPF, and AQCC require smaller active spaces for good accuracy than are required by CASPT2 and CASPT3, and this aspect may be important for calculations on larger molecules; here we find that CASPT2.5 extrapolated to a complete basis set is the most suitable method-in terms of computational cost and in terms of accuracy on monatomic systems-and therefore we chose this method for molecular benchmarks. Then Kohn-Sham density functional calculations with 60 exchange-correlation functionals are tested for FeF2, FeCl2, and CoF2. We find that MN15-L, M06-SX, and revM06 have very good agreement with CASPT2.5 benchmarks in terms of both the spin splitting energy and the optimized geometry for each spin state. In addition, we recommend def2-TZVP as the most suitable basis set to perform density functional calculations for molecular spin splitting energies; extra polarization functions in the basis set do not help to increase the accuracy of the spin splitting energy in KS calculations.

Shaping metal-organic framework materials with a honeycomb internal structure.

A self-assembly technology allows metal-organic framework materials to constitute a honeycomb internal structure while being shaped into millimeter-scale spheres. The ZIF-8 load is up to 83 wt% through solidification of chitosan (CS). This approach can be expanded to other morphologies (fibers) or crystals and is transformative for industrial manufacturing of nanomaterials.