Spin Annihilation Research Articles

A probabilistic spin annihilation method for quantum chemical calculations on quantum computers.

A probabilistic spin annihilation method based on the quantum phase estimation algorithm is presented for quantum chemical calculations on quantum computers. This approach can eliminate more than one spin component from the spin contaminated wave functions by single operation. Comparison with the spin annihilation operation on classical computers is given.

Isosymmetrical Phase Transition and Charge Ordering in the Mixed Valence Vanadate β-YbV4O8

The mixed valence vanadate β-YbV4O8 crystallizes in a structure related to CaFe2O4. The structure is built of a three-dimensional framework of VO6 octahedra in which the Yb ions are incorporated. At 185 K the compound undergoes an isosymmetrical phase transition which is accompanied by discontinuous changes in the lattice parameter, as well as in the interatomic distances and angles. While above the phase transition the bond valence sums indicate no clear charge separation of the tri- and tetravalent V ions over the four symmetrically independent octahedral sites, below the transition temperature a complete charge ordering is observed. The structural transition is accompanied by an anomaly in the magnetic susceptibility data, which corresponds to a paramagnetic-paramagnetic transition. This anomaly can be understood assuming that the Curie-Weiss type d electrons of the vanadium cations separate at 185 K into d electrons, which maintain their Curie-Weiss character, and others, which lose their spin moment with decreasing temperature. Thus, the unusual complete charge ordering can be attributed not only to Coulomb repulsion between the V and Yb cations but also to the spin annihilation of the vanadium cations.

Spin-projected coupled-cluster theory with single and double excitations

Coupled-cluster (CC) theory including single (S) and double (D) excitations and carried out with a spin-unrestricted Hartree–Fock (UHF) reference wave function is free from S + 1 spin contamination as can be confirmed by an analysis of the expectation value of the spin operator, Ŝ2. Contamination by the S + 2 contaminant can be projected out by an approximate procedure (APCCSD) with a projection operator, P^, represented by the product of the spin annihilation operators Âs+1 and Âs+2. The computational cost of such a projection scales with O(M6) (M is the number of basis functions). The APCCSD energy obtained after annihilation of the S + 2 contaminant can be improved by adding triple (T) excitations in a perturbative way, thus leading to APCCSD(T) energies. For the 17 examples studied, the deviation of the UHF-CCSD(T) energies from the corresponding full configuaration interaction values is reduced from 4.0 to 2.3 mhartree on the average as a result of annihilating the S + 2 contaminant in an approximate way. In the case of single-bond cleavage, APCSSD leads to a significant improvement of the energy in the region where the bonding electrons recouple from a closed shell to an open shell singlet electron pair.

Hybrid Hartee–Fock/density functional (HF/DF) calculations of adiabatic electron affinities (EA ad's) of neutral hydroquinone radicals of 1,4-benzoquinone ( 1) and 1,4-benzoquinone imine ( 2)

The adiabatic electron affinities (EA ad's) of the neutral hydroquinone radicals of 1 and 2, i.e., 1 · and 2 · , have been investigated by several quantum chemical models. The B3LYP and B3PW91 methods, used with the 6-311G( d, p) basis set, underestimated the EA ad's by about 6–8 kcal/mol, but with the 6-31+G( d) and 6-311+G( d, p) basis sets, results that are in reasonable accord with experiment were obtained, indicating the importance of diffuse functions for anions in the hybrid HF/DF calculations of EA ad's. The B3LYP-calculated results, including those for 1 and 2 (Y.H. Mariam, L. Chantranupong, J. Comput.-Aided Mol. Design 11 (1997) 345), along with literature values for the EA ad's of the phenyl and phenylnitrene radicals, give the trend in EA ad's that follows the order: phenoxyl (50.6)> 1 · (44.7)> 1 (43.7)> 2 · (38.7)>anilino (36.5)> 2 (34.7)>phenylnitrene (33.4)>phenyl (27.7). Apparently, the EA ad's of both radicals 1 · and 2 · are, respectively, greater than the EA ad's of the parent quinone and iminoquinone 1 and 2. UHF, PUHF, UMP2 and PMP2 energy calculations using B3LYP/6-311+G geometries gave wavefunctions that were found to be highly spin contaminated, and the UHF, PUHF and PMP2 models underestimated the EA ad's, while the UMP2 and the AM1 half-electron results were overestimated. Spin annihilation (in the UHF and UMP2 formalisms) of the first contaminant (quartet) does not apparently remove all the spin contamination. The results indicate, in addition to gradient corrections to the Slater exchange and the correlation functionals (Y.H. Mariam, L. Chantranupong, J. Comput.-Aided Mol. Design 11 (1997) 345), correlation, spin annihilation and inclusion of diffuse functions are important in B3LYP calculations of electron affinities for the systems studied in this work. Since the 6-31+G( d) basis set, with considerably less basis functions, is computationally less costly than the 6-311+G( d, p) basis set, it is recommended for quinone systems of interest where the computational cost is a consideration. The transferability of this computational model to larger systems is not, however, warranted and further work is needed.

Electron affinities of p-benzoquinone, p-benzoquinone imine and p-benzoquinone diimine, and spin densities of their p-benzosemiquinones computed by several quantum chemical models.

Restricted and unrestricted (U) Hartree-Fock (HF), second-order Møller-Plesset perturbation (MP2), density functional (DF), hybrid HF/DF and semiempirical (half-electron (HE) method) models have been used to calculate adiabatic electron affinities (EAad values) of p-benzoquinone (I), p-benzoquinone imine (VI) and p-benzoquinone diimine (XI), as well as expectation values (<S2>) and spin density distributions in the radical anions of I, VI and XI. The AM1/AM1-HE and ab initio calculated structures are found to be in accord with each other. The ROHF/6-31G(d) method gave the poorest EAad result. The UHF and UMP2 wave functions were found to be substantially spin contaminated (for the radicals) and the accuracies of the EAad values calculated were also poor. The use of molecular energies obtained after spin annihilation did not lead to significant improvement of the UHF and UMP2 results. In contrast to the ROHF, UHF and UMP2 results, the DF(USVWN, UBVWN, UBLYP) and hybrid HF/DF(UB3LYP) methods, as well as the AM1-HE, gave much better results. The calculated EAad values decreased, as predicted by most of the models, in the order EAad(I) > EAad(VI) > EAad(XI). The differences in the EAs, EAad(I)-EAad(VI) and EAad(I)-EAad(XI), were consistently predicted to be about 8-9 and 17-18 kcal/mol, respectively, by the DF, B3LYP and AM1-HE models. The performance of the PM3 and SAM1 models was not as good as the AM1 model. Of all the methods tested, the B3LYP/6-311G(d,p) model is concluded to give the most accurate quantitative trend (I(42.6) > VI(33.1) > XI(23.7)) in EAad. The predicted trend in EA can satisfactorily be rationalized by the calculated LUMO orbital energies, atomic charges and spin density distributions. Analysis of the spin density data predicts that phenoxyl- and anilino-type radical anions predominate in the p-benzosemiquinones of I and XI, respectively, while both phenoxyl- and anilino-type radicals contribute to the structure of the p-benzosemiquinone of VI, with the anilino-type predominating.

Density functional theory: excited states and spin annihilation

A spin-annihilation technique for a single determinant formed from Kohn-Sham orbitals is described for the calculation of excited state singlet energies. This procedure accurately calculates the 1 1 B u ← 1 1 A g vertical transition for s-trans-1,3-butadiene using the Becke-Lee-Yang Parr (BLYP) functional. For this system, extrapolating from triplet and 50:50 B u state energies gives poor results at either the UHF or BLYP levels; spin-annihilated Hartree-Fock theory is similarly unsuccessful.

UHF-MINDO/3 study of the thermally forbidden dissociation of o,o'-dibenzene in two benzene molecules : Part 1. Description of the postulated diradical intermediate

The single-determinant UHF-MINDO/3 method has been used for the description of the supposed diradical intermediate in the thermally forbidden dissociation of o,o'-dibenzene into two benzene molecules. The results of the UHF-MINDO/3 computations have been compared with those of CI-MINDO/3 calculations. The stability of the restricted Hartree-Fock (RHF) solution has been investigated and the relationship between instability and onset of diradical character discussed. The UHF-MINDO/3 method has been found to be adequate to describe well the electronic distribution in the diradical intermediate. The spin annihilation method, which has been used as a first attempt in solving the problem of spin contamination, has proven inadequate. Consequently a better spin projection technique is required.

An examination of the heats of formation for HFCO and HClCO molecules

Ab initio molecular orbital calculations with split-valence plus polarization and diffuse basis sets extended by Møller—Plesset theory up to fourth order (including single, double, triple, and quadruple excitation) and spin annihilation have been performed to examine the heats of formation for HFCO and HClCO molecules from isodesmic reaction schemes. The heat of formation of HFCO has been calculated as −93.8 ± 1.5 kcal mol −1 and that of HClCO as −45.5 ± 1.5 kcal mol −1.

Ab initio studies of the structure and thermochemistry of FO radicals

Ab initio studies have been performed with split-valence plus diffuse and polarization basis sets extended by Møller-Plesset theory up to fourth order (including single, double, triple, and quadruple excitation) and spin annihilation on the structure and thermochemistry of the FO radical. Of particular interest, the heat of formation for the FO radical has been calculated as 27.8±1 kcal mol −1 using an isodesmic reaction scheme, which is in excellent agreement with experimental values.

Unusually large effects of single excitations on the geometry of radical species and limiting spin-projection invariance of some correlated methods

For a number of radical species with heavy spin contamination, including BO, CCH, CN, CO +, NO, N 3, and BN, it is shown that single excitations have a large effect, up to several hundredths of an Å, on calculated bond distances. The effect decreases with increasing basis set size. Harmonic frequencies may be affected by as much as 200 cm −1. It is also shown that CCSD, CISD, CID, and CCD energies are effectively invariant under single spin annihilation when no major higher contaminants are present. It can be concluded that for species with heavy spin contamination, CISD is presently the method to be preferred over MP2 and even spin-projected MP2.

Ab initio and INDO SCF MO study of monosubstituted hydrazyl radicals

The unrestricted Hartree-Fock ab initio SCF MO method was applied to the monosubstituted hydrazyl radical XN-NH 2 (X = H,CH 3,HC(O),CH 3C(O) or C 6H 5) and [XNH-NH 2] .+ (X = H or CH 3). The optimized geometrical parameters for these radicals obtained via analytical gradient procedures are reported, and the isotropic hyperfine splitting constants calculated both directly from the ab initio wavefunctions and also corrected by employing a recently proposed spin annihilation method. In addition, the INDO method was used in conjunction with these same optimized geometrical parameters to calculate a further set of values for these isotropic hyperfine splitting constants. In general, satisfactory agreement was obtained between the corrected ab initio derived splittings, those from INDO, and experimentally measured values.

Ab initio study of the addition reaction of the methyl radical to ethylene and formaldehyde

A detailed study of the potential energy surfaces for methyl radical plus ethylene and methyl radical plus formaldehyde has been carried out with the 3-21G and 6-31G* basis sets at the Hartree-Fock level. Heats of reaction and barrier heights have been computed with the Moeller-Plesset perturbation theory up to the fourth order with and without annihilation of spin contamination. The results of the calculations indicate the formation of an early transition state with reactant-like structure for both reactions. In the case of methyl radical plus ethylene, spin annihilation lowers the barrier height by 7 kcal/mol, while in the reaction between methyl radical and formaldehyde the barrier is lowered by 6 kcal/mol when spin annihilation is considered. A comparison between the calculated and experimental values of the barrier height for the methyl addition to ethylene (6.8 kcal/mol vs 7.9 kcal/mol) and formaldehyde (6.3 kcal/mol vs. 6.8 kcal/mol) indicates very good agreement between theory and experiment.

Analytical gradients for unrestricted Hartree–Fock and second order Mo/ller–Plesset perturbation theory with single spin annihilation

Unrestricted Hartree–Fock (UHF) wave functions and Mo/ller–Plesset perturbation theory (UMPn) based on a single spin-unrestricted reference determinant can contain significant contamination from unwanted spin states. This contamination may lead to large distortions of the potential energy surface, particularly at the UMPn level. A simple approximation to projected UMPn theory (PMPn) improves the shape of the potential energy surface significantly. Formulas for analytical gradients of the PUHF and approximate projected UMP2 energies with single annihilation have been derived and programmed. This code has been applied to the optimization of transition states for H+C2H4, H+CH2O and H+C2H2 at the PMP2/6-31G* level.

Energetics of the reactions of FCO with O 2 using unrestricted Møller-Plesset perturbation theory with spin annihilation

The reactions of fluoroformyl radicals FCO with O 2 have been studied with ab initio molecular orbital methods. Reactants, transition structures and products were optimized at UHF/6-31G* and UMP2/6-31 G* levels of theory. The barrier heights have been computed by using unrestricted Hartree-Fock and Møller-Plesset perturbation theory up to fourth order, including single, double, and quadruple excitations. Spin contamination in the UHF wavefunction has been reduced by annihilating the largest spin contaminant. A small barrier is found for addition of O 2 to FCO to yield the FC(O)O 2 radical, and annihilation of the largest spin contaminant lowers the barrier for this reaction. The extraction of fluorine from FCO by O 2 to yield FO 2 and CO is endothermic with no additional barrier.

ChemInform Abstract: Calculated Barrier Heights for OH + C2H2 and OH + C2H4 Using Unrestricted Moller‐Plesset Perturbation Theory with Spin Annihilation.

ChemInformVolume 18, Issue 44 Preparative Organic Chemistry ChemInform Abstract: Calculated Barrier Heights for OH + C2H2 and OH + C2H4 Using Unrestricted Moller-Plesset Perturbation Theory with Spin Annihilation. C. SOSA, C. SOSA Lab. Interact. Mol., React. Chim. Photochim., CNRS, Univ. Paul Sabatier, 31062 Toulouse, FranceSearch for more papers by this authorH. B. SCHLEGEL, H. B. SCHLEGEL Lab. Interact. Mol., React. Chim. Photochim., CNRS, Univ. Paul Sabatier, 31062 Toulouse, FranceSearch for more papers by this author C. SOSA, C. SOSA Lab. Interact. Mol., React. Chim. Photochim., CNRS, Univ. Paul Sabatier, 31062 Toulouse, FranceSearch for more papers by this authorH. B. SCHLEGEL, H. B. SCHLEGEL Lab. Interact. Mol., React. Chim. Photochim., CNRS, Univ. Paul Sabatier, 31062 Toulouse, FranceSearch for more papers by this author First published: November 3, 1987 https://doi.org/10.1002/chin.198744088AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume18, Issue44November 3, 1987 RelatedInformation

Calculated barrier heights for OH + C2H2 and OH + C2H4 using unrestricted Moeller-Plesset perturbation theory with spin annihilation

The reactions of OH radical with C2H2 and CzH4 have been studied with ab initio molecular orbital techniques. Reactants, loose clusters, transition structures, and products were optimized at UHF/3-21G and UHF/6-3 1G*. The barrier heights have been computed by using unrestricted Hartree-Fock and Mdler-Plesset perturbation theory up to fourth order, including single, double, and quadruple excitations. Spin contamination in the UHF wave function has been corrected by annihilating the largest spin contaminant. The vibrational frequencies were computed by using analytical derivative methods at the UHF/3-21G level. The barrier heights for both reactions are overestimated by 7-15 kcal/mol at the UMPZ, UMP3, and UMP4 levels. Annihilation of the largest spin contaminant lowers the barrier heights by 7-15 kcal/mol. Calculations at the PMP4/6-3 lG* level are in good agreement with the estimated experiment barrier heights. The reactions of OH with acetylene and ethylene are known to be important in hydrocarbon combustion as well as atmospheric chemistry.'-5 Experimental studies on OH + C2H21-12 and OH + c2H4'-43'1-25 have shown that near room temperature the predominant mechanism involves the electrophilic addition of the OH radical to the 7r bond, forming an activated complex which can be collisionally stabilized. OH + C2H2, - C2H2,0H* (n = 1, 2) (1) (2) C2H2,0H* + M --* C2H2,OH + M In early experimental work on OH + C2H2, no pressure de- pendence of the rate constant was found at low temperature^.^^^ However, recent studies covering a wider range of temperature and pressure, and using flash photolysis/resonance fluorescence and laser pyrolysis/laser fluorescence techniques,8-10 indicate that the rate constant does depend on the pressure, consistent with eq 1 and 2. Analysis of the temperature and pressure dependence yields an activation energy of 1.3 =! 0.1 kcal/m~l,~.'~ based on an estimated heat of reaction of -36 f 6 kcal/mol for OH + C2H2 - C2H20H. At temperatures higher than 1000 K, the addition channel becomes less important because of competition from hydrogen abstraction (estimated activation energy 6-8 kcal/ The OH + C2H4 system has also received considerable atten- ti~n.-~~ In accord with eq 1 and 2, the rate for OH + C2H4 is found to be dependent on the total pressure. However, unlike addition to acetylene, a small negative activation energy has been found (-0.9 * 0.2,'3*14 -0.7 f 0.3,15 -0.6 f 0.316 kcal/mol). Several explanations have been given for this, including the for- mation of a weakly bound complex.26 Estimates of the heat of reaction for the addition process range from -29 to -32 kcal/ m0I.~3'~-'* Mass spectral methods have been used to observe directly the primary adduct, C2H40H, and to study its decom- position into CH, + CH20 and H + CH3CH0.18,'9 At higher temperatures, hydrogen abstraction becomes the dominant pathway (estimated activation energy ca. 3 kcal/m~l).',~~~~ ~ In an earlier theoretical study, Melius, Binkley, and Koszy- kowskiZ7 examined the reactions of OH with C2H2, C2H4, and HCN. Geometries were optimized at the HF/6-31G* level and energies were calculated by using fourth order unrestricted Mdler-Plesset perturbation theory (UMP4/6-3 lG**). The heats of reaction and barrier heights were estimated by applying bond additivity corrections to the UMP4 calculations (BAC-MP4). These corrections were determined by a least-squares fit to ca. 50 molecules with well-established heats of formation. For m01).~J~

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.

Ab initio calculations on the barrier height for the hydrogen addition to ethylene and formaldehyde. The importance of spin projection

AbstractHeats of reaction and barrier heights have been computed for H + CH2CH2 → C2H5, H + CH2O → CH3O, and H + CH2O → CH2OH using unrestricted Hartree‐Fock and Møller–Plesset perturbation theory up to fourth order (with and without spin annihilation), using single‐reference configuration interaction, and using multiconfiguration self‐consistent field methods with 3‐21G, 6‐31G(d), 6‐31G(d,p), and 6‐311G(d,p) basis sets. The barrier height in all three reactions appears to be relatively insensitive to the basis sets, but the heats of reaction are affected by p‐type polarization functions on hydrogen. Computation of the harmonic vibrational frequencies and infrared intensities with two sets of polarization functions on heavy atoms [6‐31G(2d)] improves the agreement with experiment. The experimental barrier height for H + C2H4 (2.04 ± 0.08 kcal/mol) is overestimated by 7‒9 kcal/mol at the MP2, MP3, and MP4 levels. MCSCF and CISD calculations lower the barrier height by approximately 4 kcal/mol relative to the MP4 calculations but are still almost 4 kcal/mol too high compared to experiment. Annihilation of the largest spin contaminant lowers the MP4SDTQ computed barrier height by 8‒9 kcal/mol. For the hydrogen addition to formaldehyde, the same trends are observed. The overestimation of the barrier height with Møller‐Plesset perdicted barrier heights for H + C2H4 → C2H5, H + CH2O → CH3O, and H + CH2O → CH2OH at the MP4SDTQ/6‐31G(d) after spin annihilation are respectively 1.8, 4.6, and 10.5 kcal/mol.

Thermal Reactions of Trans-Polyacetylene ESR Kinetics

Abstract The high-temperature spin kinetics of trans-polyacetylene in nitrogen and oxygen atmosphere is reported for 300 K T 550 K. The thermal reactions are characterized by S = 1/2 spin generation and annihilation processes. ESR intensities and linewidths are analyzed.

Optical and magneto-optical study of the transparent ionic ferromagnet Rb2CrCl4

The visible absorption spectrum of the transparent ionic ferromagnet Rb2CrCl4 has been recorded as a function of temperature from 0.85 to 50K and in magnetic fields up to 5T applied along (100), (110) and (001). Above 3K the intensities of all the bands vary approximately as T2, as predicted by Gregson et al. (1975, 1976) for a two-dimensional easy plane ferromagnet. Below 2K the 631 nm band is resolved into two components, one almost independent of temperature and the other having an intensity which increases with temperature as T2 exp(-E(0)/kT). They are assigned respectively as spin wave creation and annihilation sidebands with E(0), the zone-centre gap in the spin wave spectrum, 1.20+or-0.15K. All the bands lose intensity on applying a magnetic field, following the function T2 exp(-(E(0)+g mu BH)/kT), from which g-values are derived. The behaviour of the 631 nm band system agrees very well with the calculations of Elliott et al. (1980).