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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Materials Data on Rb(PRu)2 by Materials Project

Rb(RuP)2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Rb1+ is bonded in a body-centered cubic geometry to eight equivalent P3- atoms. All Rb–P bond lengths are 3.62 Å. Ru+2.50+ is bonded to four equivalent P3- atoms to form a mixture of edge and corner-sharing RuP4 tetrahedra. All Ru–P bond lengths are 2.32 Å. P3- is bonded in a 8-coordinate geometry to four equivalent Rb1+ and four equivalent Ru+2.50+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K(PRu)2 by Materials Project

K(RuP)2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. K1+ is bonded in a body-centered cubic geometry to eight equivalent P3- atoms. All K–P bond lengths are 3.53 Å. Ru+2.50+ is bonded to four equivalent P3- atoms to form a mixture of corner and edge-sharing RuP4 tetrahedra. All Ru–P bond lengths are 2.31 Å. P3- is bonded in a 8-coordinate geometry to four equivalent K1+ and four equivalent Ru+2.50+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Intramolecular 1,2 C-H Addition of o -Methyl Groups to Form Unique Ruthenium Pincer Tuck-in Complexes

New RPN H P ligands containing 2,4-xylyl (4mXPN H P) and mesityl (MesPN H P) groups on the phosphorus atoms were synthesized. 4mXPN H P reacts with [(cymene)RuCl 2 ] 2 followed by PMe 3 to produce κ 3 -4mXPN H PRu(PMe 3 )Cl 2 . MesPN H P reacts with [(cymene)RuCl 2 ] 2 to produce monomeric κ 3 -MesPN H PRuCl 2 that reacts with CO forming κ 3 -MesPN H PRu(CO)Cl 2 . Surprisingly, dehydrohalogenation of these complexes results in the activation of ortho methyl groups of the pincer ligands, rather than formation of κ 3 -RPNPRuLCl complexes. This results from transient κ 3 -RPNPRuLCl formation followed by 1,2-addition of an ortho C-H bond across the Ru-amide bond. The transient amide complex of κ 4 -4mXPN H PRu(PMe 3 )Cl was trapped with CO forming κ 3 -4mXPNPRu(PMe 3 )(CO)Cl. In contrast, κ 4 -MesPNHPRu(CO)Cl does not react with ligands to trap the expected amide complex of reverse C-H addition. Instead, CO and PMe 3 displace the chloride ligand forming cationic complexes. In both cases, hemi-lability of the pincer ligand was observed spectroscopically. In conclusion, the new complexes serve as precursors to moderately active catalysts for the acceptorless dehydrogenative coupling of n-butanol.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Double Intramolecular 1,2 C–H Addition of o -Methyl Groups To Form Ruthenium Pincer Double Tuck-In Complexes

Ruthenium pincer complexes have a rich history of coordination and reaction chemistries. In this work, we report our discoveries of previously unreported Ru pincer coordination geometries. We found that mono tuck-in κ 4 -ArPN H PRuLCl complexes react with NaN(SiMe 3 ) 2 producing double tuck-in mer-κ 5 -ArPN H PRuL complexes. Interestingly, when κ 4 -MesPN H PRuCl is dehydrohalogenated, the resulting double tuck-in complex binds N 2 , forming the nitrogen complex κ 5 -MesPN H PRuN 2 . Further, the mer-κ 5 -ArPN H PRuL complexes thermally isomerize to the fac-κ 5 -ArPN H PRuL isomers, which is an uncommon reaction for pincer complexes. The mer-κ 5 -ArPN H PRuL complexes react with CO and CO 2 to form amide κ 4 -ArPN H PRu(CO)L or carbamate κ 5 -ArPN(CO 2 )PRuL complexes, respectively, supporting the hypothesis that the κ 4 -ArPNPRuL amide intermediates are accessible and reactive.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗