Spin-unrestricted Wavefunction Research Articles

Bootstrap embedding with an unrestricted mean-field bath.

A suite of quantum embedding methods have recently been developed where the Schmidt decomposition is applied to the full system wavefunction to derive basis states that preserve the entanglement between the fragment and the bath. The quality of these methods can depend heavily on the quality of the initial full system wavefunction. Most of these methods, including bootstrap embedding (BE) [M. Welborn et al; J. Chem. Phys. 145, 074102 (2016)], start from a spin-restricted mean-field wavefunction [call this restricted BE (RBE)]. Given that spin-unrestricted wavefunctions can capture a significant amount of strong correlation at the mean-field level, we suspect that starting from a spin-unrestricted mean-field wavefunction will improve these embedding methods for strongly correlated systems. In this work, BE is generalized to an unrestricted Hartree-Fock bath [call this unrestricted BE (UBE)], and UBE is applied to model hydrogen ring systems. UBE's improved versatility over RBE is utilized to calculate high spin symmetry states that were previously unattainable with RBE. Ionization potentials, electron affinities, and spin-splittings are computed using UBE with accuracy on par with spin-unrestricted coupled cluster singles and doubles. Even for cases where RBE is viable, UBE converges more reliably. We discuss the limitations or weaknesses of each calculation and how improvements to RBE and density matrix embedding theory these past few years can also improve UBE.

ChemInform Abstract: Structures and Energies of the Lowest Lying Singlet and Triplet States of C3H2 and C3F2. A Theoretical Study

The theoretically predicted geometries for the propargylene, cyclopropenylidene, vinylidenecarbene, and cyclopropyne forms of C 3 H 2 and C 3 F 2 in their singlet and triplet states are reported at the MP2/6-31G(d) level of theory, using spin-restricted wave functions for the singlets and spin-unrestricted wave functions for the triplets. The calculated vibrational spectra for the different isomers have been calculated at HF/6-31G(d) and, in some cases, at MP2/6-31G(d)

A restricted-open-shell complete-basis-set model chemistry

A restricted-open-shell model chemistry based on the complete basis set-quadratic Becke3 (CBS-QB3) model is formulated and denoted ROCBS-QB3. As the name implies, this method uses spin-restricted wave functions, both for the direct calculations of the various components of the electronic energy and for extrapolating the correlation energy to the complete-basis-set limit. These modifications eliminate the need for empirical corrections that are incorporated in standard CBS-QB3 to compensate for spin contamination when spin-unrestricted wave functions are used. We employ an initial test set of 19 severely spin-contaminated species including doublet radicals and both singlet and triplet biradicals. The mean absolute deviation (MAD) from experiment for the new ROCBS-QB3 model (3.6+/-1.5 kJ mol(-1)) is slightly smaller than that of the standard unrestricted CBS-QB3 version (4.8+/-1.5 kJ mol(-1)) and substantially smaller than the MAD for the unrestricted CBS-QB3 before inclusion of the spin correction (16.1+/-1.5 kJ mol(-1)). However, when applied to calculate the heats of formation at 298 K for the moderately spin-contaminated radicals in the G2/97 test set, ROCBS-QB3 does not perform quite as well as the standard unrestricted CBS-QB3, with a MAD from experiment of 3.8+/-1.6 kJ mol(-1) (compared with 2.9+/-1.6 kJ mol(-1) for standard CBS-QB3). ROCBS-QB3 performs marginally better than standard CBS-QB3 for the G2/97 set of ionization energies with a MAD of 4.1+/-0.1 kJ mol(-1) (compared with 4.4+/-0.1 kJ mol(-1)) and electron affinities with a MAD of 3.9+/-0.2 kJ mol(-1) (compared with 4.3+/-0.2 kJ mol(-1)), but the differences in MAD values are comparable to the experimental uncertainties. Our overall conclusion is that ROCBS-QB3 eliminates the spin correction in standard CBS-QB3 with no loss in accuracy.

Isotropic coupling constant for the nitrogen atom from correlated calculations based on spin-unrestricted wave functions

The isotropic hyperfine coupling constant for the ground electronic state of the nitrogen atom is computed from the quadratic configuration interaction correlation procedure based on a single unrestricted Hartree–Fock (UHF) determinant. The splitting is determined from the normalized spin density at the nucleus, derived by finite-field perturbation theory. Results obtained are compared with previous work based on spin-restricted reference spaces. Close accord is found between present estimates and full configuration interaction values for small basis sets. Contributions from shells of higher angular momentum functions in the basis set are similar in both approaches and for the largest unrestricted calculation the correlated results are in good accord with experiment. The UHF wave function is shown to provide a reasonable account of the K-shell contribution to the isotropic coupling and hence the UHF-based correlated calculations show much less sensitivity to the neglect of core–electron correlation than the dramatic effects observed in spin-restricted treatments.

A b i n i t i o calculation of the hyperfine coupling constants in B2

Hyperfine coupling constants for the ground electronic state of the B2 molecule, [3∑−g] , are computed using correlation procedures based on spin-unrestricted wave functions. Two distinct methods have been employed. Firstly, a variational configuration mixing approach with all configurations arising from single and double replacements in the reference wave function has been augmented by an approximate size-consistency correction. Secondly, a many-body perturbation theory procedure based on the coupled–cluster expansion with infinite-order doubles has been approximately corrected for single and triple excitations through fourth order. Both isotropic and dipolar coupling constants have been obtained as expectation values over the appropriate wave functions for the unrestricted Hartree–Fock (UHF) and the variational configuration-interaction (CI) methods. The anisotropic coupling is already satisfactorily accounted for at the UHF level, while even with the approximate correction for the effect of higher excitations, the variational CI approach still underestimates the isotropic splitting by a factor of 2. The origin of this deficiency is traced using the other correlation method in which the isotropic coupling is derived from the normalized spin density at the nucleus, obtained by finite-field perturbation theory. The effect of the inclusion of triple excitations from the UHF wave function is seen to contribute about one third of the observed value. Such excitations are not accounted for in the size-consistency corrected variational CI approach. This conclusion is confirmed by a similar finding in a full fourth-order Mo/ller–Plesset (MP) calculation.

Isotropic coupling constants for the atoms boron-fluorine from correlated calculations based on spin-unrestricted wave functions

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTIsotropic coupling constants for the atoms boron-fluorine from correlated calculations based on spin-unrestricted wave functionsIan CarmichaelCite this: J. Phys. Chem. 1989, 93, 1, 190–193Publication Date (Print):January 1, 1989Publication History Published online1 May 2002Published inissue 1 January 1989https://doi.org/10.1021/j100338a040RIGHTS & PERMISSIONSArticle Views88Altmetric-Citations18LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (586 KB) Get e-Alerts

Potential energy curves using unrestricted Mo/ller–Plesset perturbation theory with spin annihilation

Unrestricted Hartree–Fock and unrestricted Mo/ller–Plesset perturbation theory are convenient methods to compute potential energy curves for bond dissociation, since these methods approach the correct dissociation limit. Unfortunately, a spin unrestricted wave function can contain large contributions from unwanted spin states that can distort the potential energy surface significantly. The spin contamination can be removed by projection or annihilation operators. As is well known, the spin project unrestricted Hartree–Fock bond dissociation curves have a large kink at the onset of the UHF/RHF instability, and a spurious minimum just beyond. However, the spurious minimum disappears and the kink is very much less pronounced at the unrestricted Mo/ller–Plesset level with spin projection. Bond dissociation potentials for LiH and CH4 were computed at the fourth order Mo/ller–Plesset level plus spin projection,4 and good agreement was found with full CI and MR-CISD calculations.

Xα multiple scattering calculations on iron(II) porphine

Spin-restricted and spin-unrestricted Xα multiple scattering calculations are reported for iron porphine with D4h symmetry in the absence of axial ligands. A 3A2g ground state is predicted when the radius of the porphyrin ‘‘hole’’ is less than 2.0 Å, whereas a quintet ground state is expected for larger Fe–N distances. A large asymmetry is found in the occupations of the three Fe 4p orbitals. This has important implications for the interpretation of Mössbauer quadrupole coupling constants. Magnetic susceptibility and NMR results can be understood in terms of a model that involves spin-orbit mixing of an excited 3Eg state with the ground 3A2g state; an essential element in explaining the NMR data is that the proton hyperfine constants are not the same in these two states. Tentative assignments are given for observed absorptions in the optical and near-infrared regions. It is shown that spin-unrestricted wave functions are particularly suited for the qualitative interpretation of electronic structure of metallophorphyrins.