Multiple solutions of unrestricted Hartree‐Fock equations: The SNH<sup>+</sup> radical as an example

Flores, Jesús R.; Largo‐Cabrerizo, J.

doi:10.1002/jcc.540100303

Cited by 12 publications

(6 citation statements)

References 27 publications

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“…This is especially true when the underlying equations that govern such quantities yield multiple solutions with differing degrees of physical relevance, thus making the task of understanding them much more challenging. The simplest and most familiar examples of such equations are the nonlinear self-consistent-field (SCF) Hartree–Fock (HF) and Kohn–Sham (KS) density-functional theory (DFT) equations. − …”

Section: Introductionmentioning

confidence: 99%

QSym²: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure

Huynh,

Wibowo-Teale,

Wibowo-Teale

2023

J. Chem. Theory Comput.

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Symmetry provides a powerful machinery to classify, interpret, and understand quantum-mechanical theories and results. However, most contemporary quantum chemistry packages lack the ability to handle degeneracy and symmetry breaking effects, especially in non-Abelian groups, and they are not able to characterize symmetry in the presence of external magnetic or electric fields. In this article, a program written in Rust entitled QSym 2 that makes use of group and representation theories to provide symmetry analysis for a wide range of quantum-chemical calculations is introduced. With its ability to generate character tables symbolically on-the-fly and by making use of a generic symmetry-orbit-based representation analysis method formulated in this work, QSym 2 is able to address all of these shortcomings. To illustrate these capabilities of QSym 2 , four sets of case studies are examined in detail in this article: (i) high-symmetry C84H64, C60, and B9 – to demonstrate the analysis of degenerate molecular orbitals (MOs); (ii) octahedral Fe(CN)6 3– to demonstrate the analysis of symmetry-broken determinants and MOs; (iii) linear hydrogen fluoride in a magnetic field to demonstrate the analysis of magnetic symmetry; and (iv) equilateral H3 + to demonstrate the analysis of density symmetries.

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Section: Introductionmentioning

confidence: 99%

QSym²: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure

Huynh,

Wibowo-Teale,

Wibowo-Teale

2023

J. Chem. Theory Comput.

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“…In such self-consistent-field ͑SCF͒ based approaches a solution is iteratively sought such that the energy functional is stationary with respect to variation of the spin-orbitals. [59][60][61][62] Ensuring convergence to a global minimum is extremely challenging even for the smallest of systems. 56 A necessary criterion for ensuring convergence to a local minimum is the positive definiteness of the orbital Hessian, the second-order changes of the energy functional with respect to infinitesimal variations of the orbitals.…”

Section: Introductionmentioning

confidence: 99%

The electronic structure of oxo-Mn(salen): Single-reference and multireference approaches

Sears

Sherrill

2006

The Journal of Chemical Physics

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Using single- and multireference approaches we have examined many of the low-lying electronic states of oxo-Mn(salen), several of which have not been explored previously. Large complete-active-space self-consistent-field (CASSCF) computations have been performed in pursuit of an accurate ordering for the lowest several electronic states. Basis set and relativistic effects have also been considered. For the geometry considered, our best results indicate the ground spin state to be a closed-shell singlet, followed by a pair of low-lying triplet states, with additional singlet states and the lowest quintet state lying significantly higher in energy. Hartree-Fock and density functional theory (DFT) results are obtained and are compared to the more robust CASSCF results. The Hartree-Fock results are qualitatively incorrect for the relative energies of the states considered. Popular density functionals such as BP86 and B3LYP are superior to Hartree-Fock for this problem, but they give inconsistent answers regarding the ordering of the lowest singlet and triplet states and they greatly underestimate the singlet-quintet gap. We obtained multiple Hartree-Fock and DFT solutions within a given spin multiplicity, and these solutions have been subjected to wave function stability analysis.

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“…We should stress that the [HNS] +" radical ions present a case of instability of UHF-wavefunctions. Redondo and coworkers [4] recently analysed this problem in some detail. Each of the ionized structures 1C, 2C and TSC has at least three different UHF-solutions depending on the initial spin density distribution and SCF convergence procedure.…”

Section: Stability Of the Hns Systemmentioning

confidence: 99%

“…In general, 1 refers to the HNS form, 2 to the HSN form and TS to the transition structure for a 1,2-hydrogen shift connecting both equilibrium structures. Geometries of both isomeric forms have been analysed in detail in previous papers [3,4]; we note only that, while in the form 1, the N=S distance is compressed and the bond angle opened following excitation or ionization; the corresponding variations in form 2 occur in opposite directions. This is also in contrast to the variations observed in the isovalent HP=S system [10].…”

Section: Stability Of the Hns Systemmentioning

confidence: 99%

“…While the phosphorus analogues (XPS; X=F, C1, Br) have been generated in the gas phase [1], the sulfur-halogen-nitrogen species are in fact known to exhibit sulfurhalogen (XS~N) rather than nitrogen-halogen bonds [2]. Earlier theoretical calculations predicted, however, that the simplest thionitroso form H-N=S is more stable than its H-S-N isomer either in the neutral [3] or ionized [4] state. In addition, HNS is calculated to be reasonably stable relative to fragmentation processes [3].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A mass spectrometric andab initiomolecular orbital characterization of thionitrosyl hydride (H-N=S)

et al. 1993

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We report for the first time an experimental realization of a 'quantum timetranslation machine' via superpositions of time evolutions as suggested by Aharonov, Anandan, Popescu and Vaidman (1990, phy.7. Rev. Lett., 64, 2965). The physical system consists of two coupled spins 1/2 and the amplification scheme is applied to the heteronuclear coupling between the two spins. We give a simple explanation of the phenomenon and suggest possible classical analogues.In a recent communication [l], Aharonov and coworkers introduced a new notion: 'a superposition of time evolutions (rather than of states) of a quantum system'. These superpositions are created by coupling a quantum mechanical system S to an external quantum mechanical system I in such a way that the time evolution of system S depends on the state of system I. During a short time, the two coupled systems are allowed to evolve freely. After this evolution period, the state of the system S depends on a quantum variable of system I represented by the eigenvalues of an operator IL1 acting only on system I. The superposition of time evolutions of system S is then obtained by forcing system I into a state that is a superposition of the eigenstates of Ifi. This projection of the state of system 1 affects the subsystem S via the entanglement that was established during the free evolution of the coupled systems. The resulting state of the system S can then differ considerably from any state that it could have reached by free evolution during the same time, but may be similar to a state that would have resulted from a prolonged evolution under the same Hamiltonian. Aharonov and coworkers therefore compared the effect to that of a time-translation machine.In this paper we give a demonstration that such a time translation can actually be realized in the laboratory. Qur experimental system resembles closely one of the examples suggested by Aharonov el al., consisting of an ensemble of spins S = 1/2 in a magnetic field whose strength depends on a quantum mechanical space coordinate. In our experiment, the strength of the magnetic field acting on the system S is not correlated to a spatial coordinate, but to the state of a second spin I. More specifically, our system consists of two spins S = 1/2 and I = 1/2 that are coupled to each other via an Ising-type interaction:X.sl = hJ& I:.(1) where S_ and Z: are the 3 components of the spin angular momentum operators acting on the two spins. The observed spin S evolves under the influence of the heteronuclear coupling to the spin I which can be in the eigenstate i(k) or 1~') of

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Multiple solutions of unrestricted Hartree‐Fock equations: The SNH⁺ radical as an example

Cited by 12 publications

References 27 publications

QSym²: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure

QSym²: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure

The electronic structure of oxo-Mn(salen): Single-reference and multireference approaches

A mass spectrometric andab initiomolecular orbital characterization of thionitrosyl hydride (H-N=S)

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Multiple solutions of unrestricted Hartree‐Fock equations: The SNH+ radical as an example

Cited by 12 publications

References 27 publications

QSym2: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure

QSym2: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure

The electronic structure of oxo-Mn(salen): Single-reference and multireference approaches

A mass spectrometric andab initiomolecular orbital characterization of thionitrosyl hydride (H-N=S)

Contact Info

Product

Resources

About

Multiple solutions of unrestricted Hartree‐Fock equations: The SNH⁺ radical as an example

QSym²: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure

QSym²: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure