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Spin-projected and extended SCF calculations.
Spin restricted, unrestricted, projected unrestricted and extended SCF wave functions energies compared, discussing calculation method for spin extended SCF functions
Second-order density matrix for a spin- projected single determinant.
Irreducible tensorial components of two-electron operator and second-order density matrix for spin- projected single-determinantal wave function
Spin projection of single-determinant wavefunctions
The components of the one- and two-particle density matrices resulting from spin projection of a single-determinant wave function are rederived by the method of expansion in terms of the natural orbitals of charge density, and the results are found to diverge from those given by Harriman and Sando for the two-particle case. The theory is generalized to include molecules with unequal numbers of electrons and basis orbitals and is applied to a number of organic molecules and ions. The correctness and internal consistency of the results argue in favor of the modification described.
Approximate spin projection of three-component UHF wavefunctions - The states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5/2-/
The approximate spin projection method of Amos et al. is extended to handle UHF wave functions having three significant components of differing multiplicity. An expression is given for the energy after single annihilation which differs from that of Amos and Hall. The new expression reproduces the results obtained from a previous exact calculation for which the weights and energies of the components are known. The extended approximate projection method is applied to the pi-electron UHF wave functions for the ground states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5(2-). The results indicate a triplet ground state for the former and a singlet ground state for the latter, in agreement with experimental ESR susceptibility measurements for these molecular ions. C5C15(-) cannont be treated by restricted Hartree-Fock theory, due to its open-shell ground state. Incorrect results are obtained for the croconate dianion, if restricted Hartree-Fock theory and singly excited configuration interactions are utilized.
MU-SPIN Project Update
The Minority University Space Interdisciplinary (MUSPIN) Network project is a comprehensive outreach and education initiative that focuses on the transfer of advanced computer networking technologies and relevant science to Historically Black Colleges and Universities (HBCU's) and Other Minority Universities (OMU's) for supporting multi-disciplinary education research.
Symmetry-projected spin-AGP methods applied to spin systems
Symmetry-projected wave function methods capture static correlation by breaking and restoring the symmetries of a system. In this article, we present the symmetry-projected spin antisymmetrized geminal power (spin-AGP) state projected onto space group symmetry as well as complex conjugation, spin-flip, and time-reversal symmetries. The method is benchmarked on the 1D XXZ model and the 2D J 1 − J 2 model with square and triangular lattices. Our results indicate that symmetry projection methods provide a powerful tool for frustrated spin systems.
The use of projection in SCF spin density calculations.
Spin-projected unrestricted self-consistent field /SCF/ methods for spin density calculations used to determine hyperfine coupling constants
Development and application of a star-mapping technique to the attitude determination of the spin-stabilized Project Scanner spacecraft
Spin stabilized Project Scanner spacecraft attitude determination by star mapping technique, describing optics, photomultiplier, reticle, electronics and sun shield
The Youngest Planet to Have a Spin-Orbit Alignment Measurement AU Mic b
We report measurements of the sky-projected spin–orbit angle for AU Mic b, a Neptune-size planet orbiting a very young (∼20 Myr) nearby pre-main-sequence M-dwarf star, which also hosts a bright, edge-on, debris disk. The planet was recently discovered from preliminary analysis of radial-velocity observations and confirmed to be transiting its host star from photometric data from the NASA’s TESS mission. We obtained radial-velocity measurements of AU Mic over the course of two partially observable transits and one full transit of planet b from high-resolution spectroscopic observations made with the Minerva-Australis telescope array. Only a marginal detection of the Rossiter–McLaughlin effect signal was obtained from the radial velocities, in part due to AU Mic being an extremely active star and the lack of full transit coverage plus sufficient out-of-transit baseline. As such, a precise determination of the obliquity for AU Mic b is not possible in this study and we find a sky-projected spin–orbit angle of λ=47{sub −54}{sup +26°}. This result is consistent with both the planet’s orbit being aligned or highly misaligned with the spin axis of its host star. Our measurement independently agrees with, but is far less precise than observations carried out on other instruments around the same time that measure a low-obliquity orbit for the planet. AU Mic is the youngest exoplanetary system for which the projected spin–orbit angle has been measured, making it a key data point in the study of the formation and migration of exoplanets—particularly given that the system is also host to a bright debris disk.
Attitude determination of the spin-stabilized Project Scanner spacecraft
Attitude determination of spin-stabilized spacecraft using star mapping technique
Symmetry-projected cluster mean-field theory applied to spin systems
We introduce S z spin-projection based on cluster mean-field theory and apply it to the ground state of strongly correlated spin systems. In cluster mean-fields, the ground state wavefunction is written as a factorized tensor product of optimized cluster states. In previous work, we have focused on unrestricted cluster mean-field, where each cluster is S z symmetry adapted. We here remove this restriction by introducing a generalized cluster mean-field (GcMF) theory, where each cluster is allowed to access all S z sectors, breaking S z symmetry. In addition, a projection scheme is used to restore global S z , which gives rise to the S z spin-projected generalized cluster mean-field (S z GcMF). Both of these extensions contribute to accounting for inter-cluster correlations. We benchmark these methods on the 1D, quasi-2D, and 2D J 1 – J 2 and XXZ Heisenberg models. Furthermore, our results indicate that the new methods (GcMF and S z GcMF) provide a qualitative and semi-quantitative description of the Heisenberg lattices in the regimes considered, suggesting them as useful references for further inter-cluster correlations, which are discussed in this work.
The cosine-sine decomposition with different-orbitals-for-different-spins determinants
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.
Nuclear spin features relevant to ab initio nucleon-nucleus elastic scattering
Effective interactions for elastic nucleon-nucleus scattering from first principles require the use of the same nucleon-nucleon interaction in the structure and reaction calculations, as well as a consistent treatment of the relevant operators at each order. Previous work using these interactions has shown good agreement with available data. Here, we study the physical relevance of one of these operators, which involves the spin of the struck nucleon, and examine the interpretation of this quantity in a nuclear structure context. Using the framework of the spectator expansion and the underlying framework of the no-core shell model, we calculate and examine spin-projected, one-body momentum distributions required for effective nucleon-nucleus interactions in $J=0$ nuclear states. The calculated spin-projected, one-body momentum distributions for $^4$He, $^6$He, and $^8$He display characteristic behavior based on the occupation of protons and neutrons in single particle levels, with more nucleons of one type yielding momentum distributions with larger values. Additionally, we find this quantity is strongly correlated to the magnetic moment of the $2^+$ excited state in the ground state rotational band for each nucleus considered. In conclusion, we find that spin-projected, one-body momentum distributions can probe the spin content of a $J=0$ wave function. This feature may allow future ab initio nucleon-nucleus scattering studies to inform spin properties of the underlying nucleon-nucleon interactions. The observed correlation to the magnetic moment of excited states illustrates a previously unknown connection between reaction observables such as the analyzing power and structure observables like the magnetic moment.
“Magic” Orientation Angles to Suppress Spin-Driven Hall Currents in Anisotropic 2D Materials with an Ideal Skyrmion Gas
The Hall effect depending on conduction electron spin projection becomes very different for anisotropic 2D crystals. In this case the spin-dependent electron current strongly determined by the orientation angle, θ, of the sample with respect to an applied electric eld. The spin-up and -down components of the direct and Hall charge currents oscillate with the angle 2θ. The direct and Hall components of the current have the structure where there are the angle-independent part, oscillation amplitude, and phase shift. All three quantitates strongly depend on the electron spin projection, electron mass ratio, and skyrmion size. We nd that there are "magic" orientation angles where the spin-up, spin-down, and total Hall currents vanish. There is a great interest in computations based on 2D materials with skyrmions. Such properties can be useful for computer logic operations based on skyrmions.
Novel Wavefunction Approaches for Studying Actinides and Other Heavy Elements (Final Report (2012-2020))
The theoretical characterization of actinide molecules is a crucial complement to their experimental study; actinides are vital to issues of national security and energy, but they are expensive and hazardous to study experimentally. However, because actinides contain a large number of electrons and are often strongly correlated, their theoretical description is difficult. We have had success studying actinide chemistry and physics using density functional theoretical approaches over the past several years, but we have found that such methods are incapable of treating strong correlations adequately. We thus shifted our research focus to the development of tractable wavefunction methods for strong correlations of actinides. Our early wavefunction-based approaches focused on extending symmetry-adapted, single-reference coupled cluster for treating strong correlations with feasible computational cost. While we have had some success along these lines, we have recently developed spin-projected unrestricted coupled cluster, which is essentially a black-box multi-reference coupled cluster theory that is superior to unrestricted coupled cluster for small- to medium-sized systems across practically all physical correlation strengths, yet preserves good quantum numbers. For actinides, however, where spin-orbit coupling is often nonnegligible, spin is no longer a fundamental symmetry. We thus propose to develop time reversal and point group projected coupled cluster, which will preserve the fundamental symmetries for actinides. Time reversal projection is achieved via the product of half-spin projection, or spin flip, and complex conjugation projection. Along with point group, these are discrete symmetries, i.e. non-continuous quantum numbers, which, in addition to being the correct symmetries for actinides, can be implemented in lower computational cost than full spin projection. We propose the development of these theories within a synergistic collaboration to use the new methods to elucidate difficult actinide chemistry.
The EBLM project – VII. Spin–orbit alignment for the circumbinary planet host EBLM J0608-59 A/TOI-1338 A
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Filtering states with total spin on a quantum computer
Starting from a general wave-function described on a set of spins or qubits, we propose several quantum algorithms to extract the components of this state on eigenstates of total spin S 2 and its z component S z . The method plays the role of total spin projection and gives access to the amplitudes of the initial state on a total spin basis. Here, the different algorithms have various degrees of sophistication depending on the requested tasks. They can either solely project onto the subspace with good total spin or completely uplift the degeneracy in this subspace. In the former case, when the projection on the total spin j is made, we show that the number of operations for the projection can be reduced from a quadratic to a linear dependence in j. After each measurement, the state collapses to one of the spin eigenstates that could be used for postprocessing. For this reason, we call the method total quantum spin filtering.