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MgPr2 crystallizes in the orthorhombic Cmcm space group. The structure is two-dimensional and consists of two MgPr2 sheets oriented in the (0, 1, 0) direction. Mg is bonded in a body-centered cubic geometry to eight equivalent Pr atoms. There are four shorter (3.37 Å) and four longer (3.38 Å) Mg–Pr bond lengths. Pr is bonded in a 8-coordinate geometry to four equivalent Mg atoms.
Sc13Os3Br16 crystallizes in the orthorhombic Pnnm space group. The structure is two-dimensional and consists of two Sc13Os3Br16 sheets oriented in the (0, 0, 1) direction. there are five inequivalent Sc sites. In the first Sc site, Sc is bonded in a 6-coordinate geometry to two Os and four Br atoms. There are one shorter (2.69 Å) and one longer (2.80 Å) Sc–Os bond lengths. There are a spread of Sc–Br bond distances ranging from 2.70–3.31 Å. In the second Sc site, Sc is bonded in a 6-coordinate geometry to two Os and four Br atoms. There are one shorter (2.64 Å) and one longer (2.77 Å) Sc–Os bond lengths. There are a spread of Sc–Br bond distances ranging from 2.80–3.31 Å. In the third Sc site, Sc is bonded to two equivalent Os and four Br atoms to form distorted ScOs2Br4 octahedra that share corners with two equivalent ScBr6 octahedra, an edgeedge with one ScOs2Br4 octahedra, and faces with two equivalent ScOs2Br4 pentagonal pyramids. The corner-sharing octahedral tilt angles are 29°. Both Sc–Os bond lengths are 2.68 Å. There are a spread of Sc–Br bond distances ranging from 2.75–3.02 Å. In the fourth Sc site, Sc is bonded to two equivalent Os and four Br atoms to form a mixture of distorted edge and face-sharing ScOs2Br4 pentagonal pyramids. Both Sc–Os bond lengths are 2.76 Å. There are a spread of Sc–Br bond distances ranging from 2.80–2.84 Å. In the fifth Sc site, Sc is bonded to six Br atoms to form corner-sharing ScBr6 octahedra. The corner-sharing octahedral tilt angles are 29°. There are two shorter (2.69 Å) and four longer (2.73 Å) Sc–Br bond lengths. There are two inequivalent Os sites. In the first Os site, Os is bonded in a 8-coordinate geometry to eight Sc atoms. In the second Os site, Os is bonded in a body-centered cubic geometry to eight Sc atoms. There are six inequivalent Br sites. In the first Br site, Br is bonded in a distorted T-shaped geometry to three Sc atoms. In the second Br site, Br is bonded in a 4-coordinate geometry to four Sc atoms. In the third Br site, Br is bonded in a 3-coordinate geometry to three Sc atoms. In the fourth Br site, Br is bonded in a 4-coordinate geometry to four Sc atoms. In the fifth Br site, Br is bonded in a 2-coordinate geometry to two equivalent Sc atoms. In the sixth Br site, Br is bonded in a 2-coordinate geometry to four Sc atoms.
Sr2YbCu2(BiO4)2 crystallizes in the tetragonal I4/mmm space group. The structure is two-dimensional and consists of two Sr2YbCu2(BiO4)2 sheets oriented in the (0, 0, 1) direction. Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sr–O bond distances ranging from 2.62–2.85 Å. Yb3+ is bonded in a body-centered cubic geometry to eight equivalent O2- atoms. All Yb–O bond lengths are 2.43 Å. Cu+1.50+ is bonded in a square co-planar geometry to five O2- atoms. There are four shorter (1.87 Å) and one longer (2.79 Å) Cu–O bond lengths. Bi3+ is bonded to five O2- atoms to form a mixture of distorted corner and edge-sharing BiO5 square pyramids. There are one shorter (2.06 Å) and four longer (2.64 Å) Bi–O bond lengths. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded to two equivalent Sr2+, two equivalent Yb3+, and two equivalent Cu+1.50+ atoms to form distorted OSr2Yb2Cu2 octahedra that share corners with eight equivalent OSr2Yb2Cu2 octahedra, corners with two equivalent OSrBi4 square pyramids, edges with three equivalent OSr2Yb2Cu2 octahedra, and faces with four equivalent OSr2Yb2Cu2 octahedra. The corner-sharing octahedra tilt angles range from 0–66°. In the second O2- site, O2- is bonded to one Sr2+ and four equivalent Bi3+ atoms to form distorted OSrBi4 square pyramids that share corners with four equivalent OSr2Yb2Cu2 octahedra, corners with four equivalent OSrBi4 square pyramids, and edges with four equivalent OSrBi4 square pyramids. The corner-sharing octahedral tilt angles are 45°. In the third O2- site, O2- is bonded in a 1-coordinate geometry to four equivalent Sr2+, one Cu+1.50+, and one Bi3+ atom.
Sr2Mg1 crystallizes in the monoclinic C2/m space group. The structure is two-dimensional and consists of two Sr2Mg1 sheets oriented in the (1, 0, 0) direction. there are two inequivalent Sr sites. In the first Sr site, Sr is bonded in a 4-coordinate geometry to four equivalent Mg atoms. All Sr–Mg bond lengths are 3.63 Å. In the second Sr site, Sr is bonded in a 4-coordinate geometry to four equivalent Mg atoms. All Sr–Mg bond lengths are 3.62 Å. Mg is bonded in a body-centered cubic geometry to eight Sr atoms.
BaO10 crystallizes in the tetragonal P4/mcc space group. The structure is two-dimensional and consists of two oxygen molecules and two BaO8 sheets oriented in the (0, 0, 1) direction. In each BaO8 sheet, Ba is bonded in a body-centered cubic geometry to eight equivalent O atoms. All Ba–O bond lengths are 2.82 Å. O is bonded in a bent 120 degrees geometry to one Ba and one O atom. The O–O bond length is 1.29 Å.
MgPr2 crystallizes in the monoclinic C2/m space group. The structure is two-dimensional and consists of two MgPr2 sheets oriented in the (1, 0, 0) direction. Mg is bonded in a body-centered cubic geometry to eight Pr atoms. There are a spread of Mg–Pr bond distances ranging from 3.40–3.43 Å. There are two inequivalent Pr sites. In the first Pr site, Pr is bonded in a 4-coordinate geometry to four equivalent Mg atoms. In the second Pr site, Pr is bonded in a 12-coordinate geometry to four equivalent Mg atoms.
Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm for which we adopt an adaptive variational approach to perform the required quantum imaginary time evolution. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits, which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We benchmark AVQMETTS on statevector simulators and perform thermal energy calculations of integrable and nonintegrable quantum spin models in one and two dimensions and demonstrate an approximately linear system-size scaling of the circuit complexity. We further map out the finite-temperature phase transition line of the two-dimensional transverse field Ising model. Finally, we study the impact of noise on AVQMETTS calculations using a phenomenological noise model.
An adaptive learning algorithm coupled with 3D momentum-based feedback is used to identify intense laser pulse shapes that control $H_{3}^{+}$ formation from ethane. Specifically, we controlled the ratio of D 2 H + to $D_{3}^{+}$ produced from the D 3 C-CH 3 isotopologue of ethane, which selects between trihydrogen cations formed from atoms on one or both sides of ethane. We are able to modify the D 2 H + :$D_{3}^{+}$ ratio by a factor of up to three. In addition, two-dimensional scans of linear chirp and third-order dispersion are conducted for a few fourth-order dispersion values while the D 2 H + and $D_{3}^{+}$ production rates are monitored. The optimized pulse is observed to influence the yield, kinetic energy release, and angular distribution of the D 2 H + ions while the $D_{3}^{+}$ ion dynamics remain relatively stable. We subsequently conducted COLTRIMS experiments on C 2 D 6 to complement the velocity map imaging data obtained during the control experiments and measured the branching ratio of two-body double ionization. Two-body $D_{3}^{+}$ + $C_{2}D_{3}^{+}$ is the dominant final channel containing $D_{3}^{+}$ ions, although the three-body D + $D_{3}^{+}$ + $C_{2}D_{2}^{+}$ final state is also observed.