Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network

Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional base model parameterization of complex binary geological media. For inversion purposes, it has the attractive feature that random draws from an uncorrelated standard normal distribution yield model realizations with spatial characteristics that are in agreement with the training set. In comparison with the most commonly used parametric representations in probabilistic inversion, we find that our dimensionality reduction (DR) approach outperforms principle component analysis (PCA), optimization-PCA (OPCA) and discrete cosine transform (DCT) DR techniques for unconditional geostatistical simulation of a channelized prior model. For the considered examples, important compression ratios (200 - 500) are achieved. Given that the construction of our parameterization requires a training set of several tens of thousands of prior model realizations, our DR approach is more suited for probabilistic (or deterministic) inversion than for unconditional (or point-conditioned) geostatistical simulation. Probabilistic inversions of 2D steady-state and 3D transient hydraulic tomography data are used to demonstrate the DR-based inversion. For the 2D case study, the performance is superior compared to current state-of-the-art multiple-point statistics inversion by sequential geostatistical resampling (SGR). Inversion results for the 3D application are also encouraging

Highly <i>cis</i>-1,4 Selective Polymerization of Dienes with Homogeneous Ziegler−Natta Catalysts Based on NCN-Pincer Rare Earth Metal Dichloride Precursors

The first aryldiimine NCN-pincer ligated rare earth metal dichlorides (2,6-(2,6-C6H3R2NCH)2-C6H3)LnCl2(THF)2 (Ln = Y, R = Me (1), Et (2), iPr (3); R = Et, Ln = La (4), Nd (5), Gd (6), Sm (7), Eu (8), Tb (9), Dy (10), Ho (11), Yb (12), Lu (13)) were successfully synthesized via transmetalation between 2,6-(2,6-C6H3-R2NCH)2-C6H3Li and LnCl3(THF)1∼3.5. These complexes are isostructural monomers with two coordinating THF molecules, where the pincer ligand coordinates to the central metal ion in a κC:κN:κN‘ tridentate mode, adopting a meridional geometry. Complexes 1−6, 9−11, and 13 combined with aluminum tris(alkyl)s and [Ph3C][B(C6F5)4] established a homogeneous Ziegler−Natta catalyst system, which exhibited high activities and excellent cis-1,4 selectivities for the polymerizations of butadiene (Tp = 25 °C, 99.9%; 0 °C, 100%) and isoprene (Tp = 25 °C, 98.8%). Remarkably, such high cis-1,4 selectivity almost remained at elevated polymerization temperatures up to 80 °C and did not vary with the type of the central lanthanide element, however, which was influenced obviously by the ortho substituent of the N-aryl ring of the ligands and the bulkiness of the aluminum alkyls. The Ln-Al bimetallic cations were considered as the active species. These results shed new light on improving the catalytic performance of the conventional Ziegler−Natta catalysts for the specific selective polymerization of dienes

Highly <i>cis</i>-1,4 Selective Polymerization of Dienes with Homogeneous Ziegler−Natta Catalysts Based on NCN-Pincer Rare Earth Metal Dichloride Precursors

The first aryldiimine NCN-pincer ligated rare earth metal dichlorides (2,6-(2,6-C6H3R2NCH)2-C6H3)LnCl2(THF)2 (Ln = Y, R = Me (1), Et (2), iPr (3); R = Et, Ln = La (4), Nd (5), Gd (6), Sm (7), Eu (8), Tb (9), Dy (10), Ho (11), Yb (12), Lu (13)) were successfully synthesized via transmetalation between 2,6-(2,6-C6H3-R2NCH)2-C6H3Li and LnCl3(THF)1∼3.5. These complexes are isostructural monomers with two coordinating THF molecules, where the pincer ligand coordinates to the central metal ion in a κC:κN:κN‘ tridentate mode, adopting a meridional geometry. Complexes 1−6, 9−11, and 13 combined with aluminum tris(alkyl)s and [Ph3C][B(C6F5)4] established a homogeneous Ziegler−Natta catalyst system, which exhibited high activities and excellent cis-1,4 selectivities for the polymerizations of butadiene (Tp = 25 °C, 99.9%; 0 °C, 100%) and isoprene (Tp = 25 °C, 98.8%). Remarkably, such high cis-1,4 selectivity almost remained at elevated polymerization temperatures up to 80 °C and did not vary with the type of the central lanthanide element, however, which was influenced obviously by the ortho substituent of the N-aryl ring of the ligands and the bulkiness of the aluminum alkyls. The Ln-Al bimetallic cations were considered as the active species. These results shed new light on improving the catalytic performance of the conventional Ziegler−Natta catalysts for the specific selective polymerization of dienes

Tridentate CCC-Pincer Bis(carbene)-Ligated Rare-Earth Metal Dibromides. Synthesis and Characterization

The first xylene-bridged bis(N-heterocyclic carbene) (bis(NHC))-ligated CCC-pincer rare-earth metal dibromides (PBNHC)LnBr2(THF) (PBNHC = 2,6-(2,4,6-Me3C6H2NCHCHNCCH2)2C6H3; 1: Ln = Sc; 2: Ln = Lu; 3: Ln = Sm) were prepared by in situ treatment of a THF suspension of 2,6-bis(1-mesitylimidazolium methyl)-1-bromobenzene dibromides ((PBNHC-Br)·2HBr) and lanthanide trichlorides (LnCl3) with dropwise addition of nBuLi at room temperature. The overall molecular structure of these complexes is an isostructrual monomer of a THF solvate. The monoanionic xylene-bridged bis(NHC)s bond to the central metal as a tridentate CCC-pincer moiety in a κC:κC:κC′ mode, which, in combination with the two trans-located bromo units, generates a twisted tetragonal-bipyramidal geometry

CCC-Pincer Bis(carbene) Lanthanide Dibromides. Catalysis on Highly <i>cis</i>-1,4-Selective Polymerization of Isoprene and Active Species

A series of CCC-pincer 2,6-xylenyl bis(carbene)-ligated rare-earth metal dibromides (PBNHC)LnBr2(THF) ((PBNHC) = 2,6-(2,4,6-Me3C6H2NCHCHNCCH2)2C6H3; Ln = Sc (1), Y (2), La (3), Nd (4), Sm (5), Gd (6), Dy (7), Ho (8), Tm (9), Lu (10)) have been synthesized. Upon activation with AlR3 (R = Me, Et, iBu) and [Ph3C]+[B(C6F5)4]−, complexes 2, 4, 6, 7, and 8 exhibited high activity and cis-1,4 selectivity (99.6%, 25 °C) toward the polymerization of isoprene, although complexes 1, 3, 5, 9, and 10 were inert. The selectivity was not affected by the nature of the central metal and AlR3 and was maintained at elevated temperatures up to 80 °C (97.4%). The yttrium hydrido aluminate cation [(PBNHC)Y(μ-H)2AliBu2]+ was identified as the active species according to NMR spectroscopic analysis

Tridentate CCC-Pincer Bis(carbene)-Ligated Rare-Earth Metal Dibromides. Synthesis and Characterization

The first xylene-bridged bis(N-heterocyclic carbene) (bis(NHC))-ligated CCC-pincer rare-earth metal dibromides (PBNHC)LnBr2(THF) (PBNHC = 2,6-(2,4,6-Me3C6H2NCHCHNCCH2)2C6H3; 1: Ln = Sc; 2: Ln = Lu; 3: Ln = Sm) were prepared by in situ treatment of a THF suspension of 2,6-bis(1-mesitylimidazolium methyl)-1-bromobenzene dibromides ((PBNHC-Br)·2HBr) and lanthanide trichlorides (LnCl3) with dropwise addition of nBuLi at room temperature. The overall molecular structure of these complexes is an isostructrual monomer of a THF solvate. The monoanionic xylene-bridged bis(NHC)s bond to the central metal as a tridentate CCC-pincer moiety in a κC:κC:κC′ mode, which, in combination with the two trans-located bromo units, generates a twisted tetragonal-bipyramidal geometry

CCC-Pincer Bis(carbene) Lanthanide Dibromides. Catalysis on Highly <i>cis</i>-1,4-Selective Polymerization of Isoprene and Active Species

A series of CCC-pincer 2,6-xylenyl bis(carbene)-ligated rare-earth metal dibromides (PBNHC)LnBr2(THF) ((PBNHC) = 2,6-(2,4,6-Me3C6H2NCHCHNCCH2)2C6H3; Ln = Sc (1), Y (2), La (3), Nd (4), Sm (5), Gd (6), Dy (7), Ho (8), Tm (9), Lu (10)) have been synthesized. Upon activation with AlR3 (R = Me, Et, iBu) and [Ph3C]+[B(C6F5)4]−, complexes 2, 4, 6, 7, and 8 exhibited high activity and cis-1,4 selectivity (99.6%, 25 °C) toward the polymerization of isoprene, although complexes 1, 3, 5, 9, and 10 were inert. The selectivity was not affected by the nature of the central metal and AlR3 and was maintained at elevated temperatures up to 80 °C (97.4%). The yttrium hydrido aluminate cation [(PBNHC)Y(μ-H)2AliBu2]+ was identified as the active species according to NMR spectroscopic analysis

Regioselective Chain Shuttling Polymerization of Isoprene: An Approach To Access New Materials from Single Monomer

Chain shuttling polymerization (CSP) has exhibited unique privilege to combine monomer sequences of different properties into one macromolecular chain, which, however, is difficult to achieve because of low chain transfer efficiency and thus lead to poor architecture control over the resulting polymers. Herein, we reported that the pyridyl–methylene fluorenyl scandium complex <b>1</b> in combination with [Ph₃C]­[B­(C₆F₅)₄] and Al^<i>i</i>Bu₃ showed a high transfer efficiency (93.8%) in the presence of 10 equiv of Al^<i>i</i>Bu₃ toward the chain-transfer polymerization (CTP) of isoprene (IP) in high 1,4-selectivity (83%). Meanwhile, under the same conditions, the analogous lutetium precursor <b>3</b> based system was 3,4-regioselective and exhibited almost perfect chain transfer efficiency (96.5–100%) in a wide range of Al^<i>i</i>Bu₃-to-Lu ratios from 10:1 to 100:1, indicating that each Lu generated apparently 100 polyisoprene (PIP) macromolecules. Both CTPs performed fluently without compromising the selectivity and the activity and had comparable chain transfer rate constants. Based on this, 1,4- and 3,4-regioselective CSPs were realized by mixing <b>1</b> and <b>3</b> in various ratios to give a series of PIPs bearing different distribution of 1,4- and 3,4-PIP sequences and <i>T</i>_g values. This work provides a new strategy to access stereoregular and architecture controlled polymers from a single monomer

Alternating Copolymerization of Cyclohexene Oxide and Carbon Dioxide Catalyzed by Organo Rare Earth Metal Complexes

The mono(cyclopentadienyl)-ligated rare earth metal bis(alkyl) complexes (C5Me4SiMe3)Ln(CH2SiMe3)2(THF) (Ln = Y (1a), Dy (1b), Lu (1c), Sc (1d)) and polyhydride complexes [(C5Me4SiMe3)Ln(μ-H)2]4(THF)x (2a:  Ln = Y, x = 1; 2b:  Ln = Dy, x = 2; 2c:  Ln = Lu, x = 1) are active as single-component catalysts, not only for the ring-opening homopolymerization of cyclohexene oxide (CHO), but also for the alternating copolymerization of CHO and CO2. The homopolymerization of CHO in bulk took place much more rapidly than that in solution and afforded in high yields the corresponding polyether with Mn = (50−80) × 103 and Mw/Mn ≅ 2 in most cases. The copolymerization of CHO and CO2 by 1a−c and 2a−c at 70−110 °C under 12 atm of CO2 yielded the corresponding polycarbonate with Mn = (14−40) × 103, Mw/Mn = 4−6, and carbonate linkages = 90−99% with TOF ranging from 1000 to 2000 g polymer/(mol-Ln h). In contrast, the Sc alkyl complex 1d gave a polymer containing high ether linkages (carbonate linkages = 23%) under the similar conditions because of its higher activity for CHO homopolymerization. The stoichiometric reaction of the bis(alkyl) complexes 1a, c, and d with CO2 afforded quantitatively the corresponding bis(carboxylate) complexes [(C5Me4SiMe3)Ln(μ-η:η1-O2CCH2SiMe3)2]2 (Ln = Y (3a), Lu (3b), Sc (3c)), which adopt a dimeric structure through the carboxylate bridges. The isolated carboxylate complexes 3a, b also showed moderate activity for the alternating copolymerization of CHO and CO2, which thus constituted a rare example of a well-defined, catalytically active carboxylate intermediate that was isolated directly from the reaction of a true catalyst system

Tetranuclear Rare Earth Metal Polyhydrido Complexes Composed of “(C₅Me₄SiMe₃)LnH₂” Units. Unique Reactivities toward Unsaturated C−C, C−N, and C−O Bonds

The tetranuclear Lu and Y polyhydrido complexes [(C5Me4SiMe3)Ln(μ-H)2]4(THF) (Ln = Lu, Y) undergo novel multiple hydrogenation reactions with unsaturated organic compounds such as benzonitrile, γ-butyrolactone, styrene, and 1,4-bis(trimethylsilyl)-1,3-butadiyne to afford a series of structurally characterizable polynuclear complexes that possess novel structures and are otherwise difficult to access. Most of these reactions are unprecedented and can be attributed to the unique cooperative effects of multiple active sites in the polyhydrido rare earth metal complexes