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The Lagrange-based Grassmann interpolation (G-Int) method has been extended for open-shell systems using restricted open-shell methods in building spin contamination-free potential energy surfaces.
We present a variant of the approximate second order coupled-cluster method (CC2) with a two-parameter size-consistent Brillouin–Wigner (BW-s) partitioning instead of a Møller–Plesset (MP) partitioning for the unperturbed Hamiltonian, which we refer to as BWs-CC2. The computational complexity of this model scales identically to CC2 with molecular size. Conventional CC2 and its regularized BWs-CC2 variants, as well as conventional MP2 and two of its regularized BW-s2 variants, were assessed on a 535 element database spanning thermochemistry, non-covalent interactions, barrier heights, and isomerization energies. To ensure a well-defined model chemistry, the assessment was performed using internally stable spin-polarized Hartree–Fock (HF) orbitals in the finite aug-cc-pVQZ basis without counterpoise corrections. As a result of using stable orbitals, contrary to conventional wisdom, we find that CC2 substantially outperforms MP2 on molecules with significantly spin contaminated reference orbitals without a significant increase in error on systems with a spin-pure reference, showing the value of its single substitutions. While no single choice of regularization parameters can be optimal for all datasets, we find that BWs-CC2 generally outperforms both CC2 and BW-s2 with a single judicious parameter choice. Additional tests on dipole moments and bond lengths of diatomics provide further support for the utility of this choice. Furthermore, the main outliers and poorest performing cases are associated with large amounts of spin-contamination in the HF reference, which is indicative of systems with either strong correlation or extensive artificial symmetry breaking. Overall, these findings argue that the perception of the quality of the CC2 ground state should be reevaluated and that it can be further improved upon by the soundly based BWs-CC2 variant with the recommended parameter choice.
Spin-flip (SF) methods applied to excited-state approaches like the Bethe–Salpeter equation allow access to the excitation energies of open-shell systems, such as molecules and defects in solids. The eigenstates of these solutions, however, are generally not eigenstates of the spin operator S^ 2 . Even for simple cases where the excitation vector is expected to be, for example, a triplet state, the value of S^ 2 may be found to differ from 2.00; this difference is called 'spin contamination'. The expectation values S^ 2 must be computed for each excitation vector, to assist with the characterization of the particular excitation and to determine the amount of spin contamination of the state. Here, our aim is to provide for the first time in the SF methods literature a comprehensive resource on the derivation of the formulas for S^ 2 as well as its computational implementation. After a brief discussion of the theory of the SF Bethe–Salpeter equation (BSE) and some examples further illustrating the need for calculating S^ 2 , we present the derivation for the general equation for computing S^ 2 with the eigenvectors from an SF-BSE calculation, how it is implemented in a Python script, and timing information on how this calculation scales with the size of the SF-BSE Hamiltonian.
We report the spin decomposition of a spin-contaminated different-orbitals-for-different-spins (DODS) wave function is formulated in terms of the Krylov space of the $\hat{S}^2$ ||operator. The number of determinants that contribute to the various projected spin eigenfunctions vertical | $\psi ; S, M \rangle$ depends on the sparsity of the orbital overlap matrix X between the α and β spatial orbitals. The cosine-sine decomposition (CSD) procedure may be applied to this overlap matrix, and the resulting redundant orbital transformations may be applied to the α and β spatial orbitals. This produces a sparse X' matrix in the transformed basis in which each row or column has either one or two nonzero elements. This sparse X' matrix simplifies the spin-decomposition procedure in three ways:1) it reduces the number of contributing determinants within the Krylov basis functions and within the projected spin functions, 2) it reduces the effective orbital dimension through elimination of the frozen core and frozen virtual orbitals, and 3) it simplifies the spin-decomposition procedure in both the original and transformed bases by limiting the Krylov space dimension. These simplifications all reduce the computational effort for the spin-decomposition process. This procedure is implemented within a string-based DODS determinant formulation and applied to spin projection of unrestricted Hartree-Fock determinants.
Here, we investigate the use of orbital-optimized references in conjunction with single-reference coupled-cluster theory with single and double substitutions (CCSD) for the study of core excitations and ionizations of 18 small organic molecules, without the use of response theory or equation-of-motion (EOM) formalisms. Three schemes are employed to successfully address the convergence difficulties associated with the coupled-cluster equations, and the spin contamination resulting from the use of a spin symmetry-broken reference, in the case of excitations. In order to gauge the inherent potential of the methods studied, an effort is made to provide reasonable basis set limit estimates for the transition energies. Overall, we find that the two best-performing schemes studied here for ΔCCSD are capable of predicting excitation and ionization energies with errors comparable to experimental accuracies. The proposed ΔCCSD schemes reduces statistical errors against experimental excitation energies by more than a factor of two when compared to the frozen-core core–valence separated (FC-CVS) EOM-CCSD approach – a successful variant of EOM-CCSD tailored towards core excitations.
The extension of least-squares tensor hypercontracted second- and third-order Møller–Plesset perturbation theory (LS-THC-MP2 and LS-THC-MP3) to open-shell systems is an important development due to the scaling reduction afforded by THC and the ubiquity of molecular ions, radicals, and other open-shell reactive species. The complexity of wavefunction-based quantum-chemical methods such as Møller–Plesset and coupled cluster theory is reflected in the steep scaling of the computational costs with the molecular size. The least-squares tensor hypercontraction (LS-THC) method is an efficient, single-step factorization for the two-electron integral tensor but can also be used to factorize the double excitation amplitudes, leading to significant scaling reduction. Herein we extend this promising method to open-shell variants of LS-THC-MP2 and -MP3 by using diagrammatic techniques and explicit spin summation. The accuracy of the resulting methods for open-shell species is benchmarked on standard test systems such as regular alkanes as well as realistic systems involving bond breaking, radical stabilization, and other effects. We find that open-shell LS-THC-MPn methods exhibit errors highly comparable to those produced by closed-shell LS-THC-MPn and are highly insensitive to particular chemical interactions, geometries, or even moderate spin contamination.
We present GSCDB137, a rigorously curated benchmark library of 137 data sets (8377 entries) covering main-group and transition-metal reaction energies and barrier heights, (intra- and intermolecular) noncovalent interactions, dipole moments, polarizabilities, electric-field response energies, and vibrational frequencies. Legacy data from GMTKN55 and MGCDB84 have been updated to today's best reference values; redundant or low-quality points were removed, and many new, property-focused sets were added. Testing 29 popular density functional approximations (DFAs) confirms the expected Jacob's-ladder hierarchy overall but also reveals notable exceptions: functional performance for frequencies and electric-field properties correlates poorly with that for other ground-state energetics. ωB97M-V and ωB97X-V are the most balanced hybrid meta-GGA and hybrid GGA, respectively; B97M-V and revPBE-D4 lead the meta-GGA and GGA classes. Double hybrids lower mean errors by about 30% versus their hybrid analogues but demand careful frozen-core, basis set, and spin contamination treatment. GSCDB137 offers a comprehensive, openly documented platform for rigorous validation of DFA and universal machine learning potentials, and training of the next generation of exchange-correlation functionals.
Multiple ERI (Electron Repulsion Integral) tensor contractions (METC) with several matrices are ubiquitous in quantum chemistry. In response theories, the contraction operation, rather than ERI computations, can be the major bottleneck, as its computational demands are proportional to the multiplicatively combined contributions of the number of excited states and the kernel pre-factors. Here, this paper presents several high-performance strategies for METC. Optimal approaches involve either the data layout reformations of interim density and Fock matrices, the introduction of intermediate ERI quartet buffer, and loop-reordering optimization for a higher cache hit rate. The combined strategies remarkably improve the performance of the MRSF (mixed reference spin flip)-TDDFT (time-dependent density functional theory) by nearly 300%. The results of this study are not limited to the MRSF-TDDFT method and can be applied to other METC scenarios.
The study of a layered crystalline Sn(IV) phosphate by solid-state NMR has demonstrated that the 31 P T 1 relaxation of phosphate groups, dependent on spinning rate is completely controlled by the limited spin diffusion to paramagnetic ions found by EPR. The spin-diffusion constant, D(SD), was estimated as 2.04 10 –14 cm 2 s –1 . Finally, the conclusion was supported by the 31 P T 1 time measurements in zirconium phosphate 1–1, also showing paramagnetic ions and in diamagnetic compound (NH 4 ) 2 HPO 4 .
Multiple previous studies using several different probes have shown considerable evidence for the existence of cosmological–scale anisotropy and a Hubble–scale axis. One of the probes that show such evidence is the distribution of the directions toward which galaxies spin. The advantage of the analysis of the distribution of galaxy spin directions compared to the cosmic microwave background anisotropy is that the ratio of galaxy spin directions is a relative measurement, and therefore less sensitive to background contamination such as Milky Way obstruction. Another advantage is that many spiral galaxies have spectra, and therefore allow to analyze the location of such axis relative to Earth. This paper shows an analysis of the distribution of the spin directions of over 90K galaxies with spectra. That analysis is also compared to previous analyses using the Earth–based Sloan Digital Sky Survey, Panoramic Survey Telescope and Rapid Response System, and Dark Energy Spectroscopic Instrument Legacy Survey, as well as space–based data collected by Hubble Space Telescope. Finally, the results show very good agreement between the distribution patterns observed with the different telescopes. The dipole or quadrupole axes formed by the spin directions of the galaxies with spectra do not necessarily go directly through Earth.
Topological insulator–magnetic insulator (TI–MI) heterostructures hold significant promise in the field of spintronics, offering the potential for manipulating magnetization through topological surface state–enabled spin-orbit torque. However, many TI–MI interfaces are plagued by issues such as contamination within the magnetic insulator layer and the presence of a low-density transitional region of the topological insulator. These interfacial challenges often obscure the intrinsic behavior of the TI–MI system. In this study, we addressed these challenges by depositing sputtered Bi 2 Te 3 on liquid phase epitaxy grown Y 3 Fe 5 O 12 /Gd 3 Ga 5 O 12 . The liquid phase epitaxy grown Y 3 Fe 5 O 12 has been previously shown to have exceptional interface quality, without an extended transient layer derived from interdiffusion processes of the substrate or impurity ions, thereby eliminating rare-earth impurity-related losses in the MI at low temperatures. At the TI–MI interface, high-resolution depth-sensitive polarized neutron reflectometry confirmed the absence of a low-density transitional growth region of the TI. By overcoming these undesirable interfacial effects, we isolate and probe the intrinsic low-temperature magnetization dynamics and transport properties of the TI–MI interface. In conclusion, our findings revealed strong spin pumping at low temperatures, accompanied by an additional in-plane anisotropy. The enhanced spin pumping at low temperatures is correlated with the observed suppression of bulk conduction and the weak antilocalization in the TI film, highlighting the interplay between the transport and spin pumping behavior in the TI–MI system.
The second Mellin moments ⟨ x ⟩ of the nucleon’s unpolarized, polarized, and transversity parton distribution functions are computed. Two lattice QCD ensembles at the physical pion mass are used: these were generated using a tree-level Symanzik-improved gauge action and 2 + 1 flavor tree-level improved Wilson Clover fermions coupling via 2-level HEX-smearing. The moments are extracted from forward matrix elements of local leading twist operators. We determine renomalization factors in RI-(S)MOM and match to MS ¯ at scale 2 GeV. Our findings show that operators that exhibit vanishing kinematics at zero momentum can have significantly reduced excited-state contamination. The resulting polarized moment is used to quantify the longitudinal contribution to the quark spin-orbit correlation. All our results agree within two sigma with previous lattice results. Published by the American Physical Society 2024
ABSTRACT Cosmological weak lensing measurements rely on a precise measurement of the shear two-point correlation function (2PCF) along with a deep understanding of systematics that affect it. In this work, we demonstrate a general framework for detecting and modelling the impact of PSF systematics on the cosmic shear 2PCF and mitigating its impact on cosmological analysis. Our framework can detect PSF leakage and modelling error from all spin-2 quantities contributed by the PSF second and higher moments, rather than just the second moments, using the cross-correlations between galaxy shapes and PSF moments. We interpret null tests using the HSC Year 3 (Y3) catalogs with this formalism and find that leakage from the spin-2 combination of PSF fourth moments is the leading contributor to additive shear systematics, with total contamination that is an order-of-magnitude higher than that contributed by PSF second moments alone. We conducted a mock cosmic shear analysis for HSC Y3 and find that, if uncorrected, PSF systematics can bias the cosmological parameters Ωm and S8 by ∼0.3σ. The traditional second moment-based model can only correct for a 0.1σ bias, leaving the contamination largely uncorrected. We conclude it is necessary to model both PSF second and fourth moment contaminations for HSC Y3 cosmic shear analysis. We also reanalyse the HSC Y1 cosmic shear analysis with our updated systematics model and identify a 0.07σ bias on Ωm when using the more restricted second moment model from the original analysis. We demonstrate how to self-consistently use the method in both real space and Fourier space, assess shear systematics in tomographic bins, and test for PSF model overfitting.
Excited states in 53 Cr were studied via the 52 Cr (𝑑, 𝑝𝛾) reaction up to the neutron-separation threshold. Proton-𝛾 angular correlations and 𝛾 decay branching ratios were measured in particle-𝛾 coincidences between the Super-Enge Split-Pole Spectrograph (SE-SPS) and CeBr 3 Array (CeBrA) demonstrator of the John D. Fox Accelerator Laboratory at Florida State University. Previous spin-parity assignments from a (𝑑,𝑝) singles experiment at the SE-SPS are supported and 𝛾-ray transitions in 53 Cr are reported. We firmly assign higher-lying excited states to 53 Cr because overlapping excited states and contaminants could be identified better due to the complementary 𝛾-decay information. We also correct some of the previously reported excitation energies and present a reanalysis of previously measured 52 Cr (𝑑, 𝑝) 53 Cr angular distributions guided by the complementary 𝛾-ray information. Based on this reanalysis, the fragmentation of the neutron 2𝑝 3/2 , 2𝑝 1/2 , 1𝑓 5/2 , 1𝑔 9/2 , and 2𝑑 5/2 single-particle strengths is reassessed for 53 Cr. Here, a comparison to the corresponding strengths in 55 Fe is presented.
Diamond has superlative material properties for a broad range of quantum and electronic technologies. However, heteroepitaxial growth of single crystal diamond remains limited, impeding integration and evolution of diamond-based technologies. Here, we directly bond single-crystal diamond membranes to a wide variety of materials including silicon, fused silica, sapphire, thermal oxide, and lithium niobate. Our bonding process combines customized membrane synthesis, transfer, and dry surface functionalization, allowing for minimal contamination while providing pathways for near unity yield and scalability. We generate bonded crystalline membranes with thickness as low as 10 nm, sub-nm interfacial regions, and nanometer-scale thickness variability over 200 by 200 μm 2 areas. We measure spin coherence times T 2 for nitrogen vacancy centers in 150 nm-thick bonded membranes of up to 623 ± 21 μs, suitable for advanced quantum applications. We demonstrate multiple methods for integrating high quality factor nanophotonic cavities with the diamond heterostructures, highlighting the platform versatility in quantum photonic applications. Furthermore, we show that our ultra-thin diamond membranes are compatible with total internal reflection fluorescence (TIRF) microscopy, which enables interfacing coherent diamond quantum sensors with living cells while rejecting unwanted background luminescence. The processes demonstrated herein provide a full toolkit to synthesize heterogeneous diamond-based hybrid systems for quantum and electronic technologies.
Magnetic force microscopy (MFM) enables mapping local magnetic fields across a sample surface with nanoscale resolution. To perform MFM, an atomic force microscopy (AFM) probe whose tip has been magnetized vertically (i.e., perpendicular to the probe cantilever) is oscillated at a fixed height above the sample surface. The resultant shifts in the oscillation phase or frequency, which are proportional to the magnitude and sign of the vertical magnetic force gradient at each pixel location, are then tracked and mapped. Although the spatial resolution and sensitivity of the technique increases with decreasing lift height above the surface, this seemingly straightforward path to improved MFM images is complicated by considerations such as minimizing topographical artifacts due to shorter range van der Waals forces, increasing the oscillation amplitude to further improve sensitivity, and the presence of surface contaminants (in particular water due to humidity under ambient conditions). In addition, due to the orientation of the probe's magnetic dipole moment, MFM is intrinsically more sensitive to samples with an out-of-plane magnetization vector. Here, high-resolution topographical and magnetic phase images of single and bicomponent nanomagnet artificial spin-ice (ASI) arrays obtained in an inert (argon) atmosphere glovebox with <0.1 ppm O 2 and H 2 O are reported. Further, optimization of lift height and drive amplitude for high resolution and sensitivity while simultaneously avoiding the introduction of topographical artifacts is discussed, and detection of the stray magnetic fields emanating from either end of the nanoscale bar magnets (~250 nm long and <100 nm wide) aligned in the plane of the ASI sample surface is shown. Likewise, using the example of a Ni-Mn-Ga magnetic shape memory alloy (MSMA), MFM is demonstrated in an inert atmosphere with magnetic phase sensitivity capable of resolving a series of adjacent magnetic domains each ~200 nm wide.
Experiments searching for weakly interacting massive particle dark matter are now detecting background events from solar neutrino-electron scattering. However, the dominant radioactive background in state-of-the-art experiments such as LZ and XENONnT is beta decays from radon contamination. In spite of careful detector material screening, radon progenitor atoms are ubiquitous and long-lived, and radon is extremely soluble in liquid xenon. We propose a change of phase and demonstrate that crystalline xenon offers more than a factor × 500 exclusion against radon ingress, compared with the liquid state. This level of radon exclusion would allow crystallized versions of existing experiments to probe spin-independent cross sections near 10 − 47 cm 2 in roughly 11 years, as opposed to the 35 years required otherwise. Published by the American Physical Society 2024
Applications of near-surface nitrogen-vacancy (NV) centers in diamond are often limited by surface defects created during processing. Understanding and controlling plasma-induced surface damage is important for preserving the optical and spin properties of diamond NV centers. We report molecular dynamics simulations of a novel form of plasma-aided atomic layer etching of diamond. In this proposed scheme, the initial surface modification step consists of Ar + ion bombardment. This creates an amorphous layer at the surface, the thickness of which is controlled by the ion energy. Amorphization is known to help smooth the surface, at least locally, and would also serve to sputter clean an initially contaminated surface. A second step impacts the amorphous carbon layer with O + between about 1 and 5 eV. Simulations show that this energy range will remove the amorphous carbon but will not etch the underlying diamond. Though this energy range is not trivial to achieve in a conventional low-temperature plasma, potential methods for creating these low-energy O + ions are discussed. In addition to a-C etching, the O + impacts are predicted to remove any isolated (100) diamond terraces by selectively attacking the edges of the terraces. The proposed atomic layer etching (ALE) approach reverses the conventional ALE sequence in which the surface modification step is usually chemical modification (oxidation in this case), followed by a removal step using Ar + impacts. This plasma ALE procedure is predicted to create a diamond surface that is atomically flat and defect free.