Assessment of DFT functionals with fluorine–fluorine coupling constants†

Density functional theory (DFT) calculations of nuclear magnetic resonance (NMR) spin–spin coupling constants (SSCCs) provide an important contribution for understanding experimentally observed values. It is known that calculated SSCCs using DFT methods correlate well with those experimentally measured. Unlike most of SSCCs, in fluorine compounds, fluorine–fluorine SSCC J_FF shows that the Fermi contact (FC) term is not dominant, particularly for J_FF in polyfluorinated organic molecules. In order to devise a DFT approach that would correctly reproduce the variation of SSCCs within a series of fluorine compounds, we test several DFT-based approaches, using different exchange and correlation functionals. Isotropic contributions to NMR fluorine–fluorine coupling constants (FC, spin-dipolar, SD, paramagnetic spin-orbit, PSO, and diamagnetic spin-orbit, DSO) have been calculated. Results show that DFT methods give appropriate values for ⁿJ_FF (n = 4 to 7), while for geminal and vicinal J_FF present large deviations from experimental values. For the latter SSCCs (²J_FF and ³J_FF), the four contributions (FC, SD, PSO and DSO) are analysed as a function of the local and nonlocal exchange in 1,1- and 1,2-difluoroethylene. Although FC term is not dominant for these SSCCs, the variation of this contribution with exchange is remarkable. On the other hand, SD and PSO contributions can be suitably computed without and with exact exchange, respectively.     

Measurement of Δ1J(199Hg, 31P) in [HgPCy3(OAc)2]2 and relativistic ZORA DFT investigations of mercury–phosphorus coupling tensors

Using ³¹P solid-state NMR spectroscopy, anisotropy in the indirect ¹⁹⁹Hg-³¹P spin–spin coupling tensor (ΔJ) for powdered [HgPCy₃(OAc)₂]₂ (1) has been measured as 4700±300 Hz. Zeroth-order regular approximation (ZORA) density functional theory (DFT) calculations, including scalar and spin-orbit relativistic effects, performed on 1 and a series of other related compounds show that ΔJ(¹⁹⁹Hg, ³¹P) arises entirely from the ZORA Fermi-contact–spin-dipolar cross term. The calculations validate assumptions made in the spectral analysis of 1 and in previous determinations of ΔJ in powder samples, namely that J is axially symmetric and shares its principal axis system with the direct dipolar coupling tensor (D). Agreement between experiment and theory for various ¹⁹⁹Hg, ³¹P spin–spin coupling anisotropies is reasonable; however, experimental values of ¹J(¹⁹⁹Hg, ³¹P)_iso are significantly underestimated by the calculations. The most important improvements in the agreement were obtained as a result of including more of the crystal lattice in the model used for the calculations, e.g., a change of 43% was noted for ¹J(¹⁹⁹Hg, ³¹P)_iso in [HgPPh₃(NO₃)₂]₂ depending on whether the two or three nearest nitrate ions are included in the model. Finally, we have written a computer program to simulate the effects of non-axial symmetry in J and of non-coincidence of the J and D on powder NMR spectra. Simulations clearly show that both of these effects have a pronounced impact on the ³¹P NMR spectrum of ¹⁹⁹Hg–³¹P spin pairs, suggesting that the effects should be observable experimentally if a suitable compound can be identified.     

Ramsey terms for two-, three-, and four-bond coupling involving 15N and 17O in hydrogen-bonded and nonhydrogen-bonded systems: are coupling constants sensitive to RAHBs?

Ab initio EOM-CCSD/(qzp,qz2p) calculations have been performed on complexes with intermolecular hydrogen bonds involving ¹⁵N and ¹⁷O, and molecules with and without intramolecular hydrogen bonds involving these nuclei. Coupling constants across intermolecular hydrogen bonds are well approximated by the Fermi-contact (FC) term. In general, ^2hJ(X–Y) for intramolecular coupling across X–H^…Y hydrogen bonds are not sensitive to the presence of resonance-assisted hydrogen bonds (RAHBs). However, ^2hJ(O–O) for coupling across the intramolecular hydrogen bond in malonaldehyde is greater than ^2hJ(O–O) for its saturated counterpart, so that ^2hJ(O–O) is sensitive to the presence of the RAHB. This is also the case for the sulphur analogues of malonaldehyde. For these unsaturated hydrogen-bonded molecules, molecules with carboxyl groups, and trans-glyoxal, J is dominated by the paramagnetic spin orbit (PSO) term. For these systems, the primary mode of coupling transmission is through the conjugated chain. For complexes with intermolecular hydrogen bonds, saturated molecules with intramolecular hydrogen bonds, unsaturated and saturated molecules in which the hydrogen bond has been broken, and unsaturated molecules with intramolecular N–H^…N or O–H^…N hydrogen bonds, J is dominated by the FC term. FC domination in hydrogen-bonded systems indicates that the primary transmission mode is across the hydrogen bond.     

NMR 1 J(HD) coupling in HD as a function of interatomic distance in the presence of an external magnetic field

A theoretical study has been made of the dependence of the ¹ J(HD) coupling in HD on the interatomic distance R in the presence of a static uniform magnetic field B ₀. The behaviour of all coupling terms arising from Ramsey's magnetic electron-nucleus interactions, Fermicontact (FC), spin-dipolar (SD) and paramagnetic (PSO) and diamagnetic (DSO) spin-orbital interactions is analysed qualitatively for large R. It is concluded that the PSO, DSO and SD terms become negligibly small as R increases. Detailed calculations were carried out for the FC term following two different approaches: detailed full CI calculations within a non-perturbative approach; and explicit diagonalization of the Hamiltonian operator restricted to the subspace spanned by the ¹Σ⁺;_g and the ³Σ⁺;_u states. Within the approximations considered, the FC term of ¹ J(HD) is found to be independent of B ₀ and to increase by several orders of magnitude, in agreement with previous results by Bacskay, G. B., 1995, Chem. Phys. Lett., 242, 507, until a critical distance R(B ₀) is reached, beyond which it almost vanishes. The quenching of the coupling at R(B ₀) is due to the splitting of the ³Σ⁺;_u state in the presence of the field B ₀. The stronger the field the shorter is R(B ₀).     

Calculated spin-spin coupling surfaces in the water molecule; prediction and analysis of J (O,H), J (O,D) and J (H,D) in water isotopomers

Ab initio symmetry and internal valence coordinate oxygen–proton and proton–proton spin–spin coupling surfaces for the water molecule have been computed for the first time. Calculations have been performed at the SOPPA (CCSD) level using a large basis set and a grid of forty-nine geometries on the two surfaces. Equilibrium values differ significantly from some other calculated values especially for the Fermi contact terms. The bond length dependence of J(O, H) is ‘normal’ i.e. J(O, H₁) is much more sensitive to stretching the O–H₁ bond than the O–H₂ bond. This contrasts greatly with the corresponding situation in methane.

The surfaces have been averaged over the nuclear motion using a recent highly accurate force field to give values of J (O, H) and J (O, D) for H₂ ¹⁷O, HD¹⁷O and D₂ ¹⁷O and J(H, D) for HD¹⁶O, HD¹⁷O and HD¹⁸O over a range of temperatures. For J (O, H) and J (O, D) bond stretching at first order is the dominant part of the nuclear motion correction with second order bending making an important contribution. For J (H, D) the second order bending is by far the largest contribution to the nuclear motion corrections although the other terms partially cancel this contribution. Non-additivity can be largely attributed to the bending term for J (O, H). As expected, the bending terms also contribute relatively more to the temperature dependence of the couplings for J (O, H), J (O, D) and J (H, D). Our calculated J (O, H) in H₂ ¹⁷O of -77.22Hz at 293K is in very good agreement with Wasylishen and Friedrich's observed value of -78.70 (±0.02) Hz in cyclohexane at this temperature. Our calculated J(H, D) in HD ¹⁶O at 323K of -1.233Hz is close to a recent experimental value of -1.114 (±0.003) Hz in nitromethane-d ₃ observed by Sergeyev et al. at that temperature.     

Microscopic study of low-lying yrast spectra and deformation systematics in neutron-rich <Superscript>98–106</Superscript>Sr isotopes

Variation-after-projection (VAP) calculations in conjunction with Hartree-Bogoliubov (HB) ansatz have been carried out for A = 98–106 strontium isotopes. In this framework, the yrast spectra with J ^Π ≥ 10⁺, B(E2) transition probabilities, quadrupole deformation parameter and occupation numbers for various shell model orbits have been obtained. The results of the calculation for yrast spectra give an indication that it is important to include the hexadecapole-hexadecapole component of the two-body interaction for obtaining various nuclear structure quantities in Sr isotopes. Besides this, it is also found that the simultaneous polarization of p _3/2 and f _5/2 proton subshells is a significant factor in making a sizeable contribution to the deformation in neutron-rich Sr isotopes.     

Effective dynamic moment of inertia of 118Xe and 130Ba

The effective moment of inertia J_eff⁽²⁾ of ¹¹⁸Xe and ¹³⁰Ba has been measured using sum-spectrometer techniques. The data are discussed using arguments based on particle alignments and results of cranking calculations. J_band⁽²⁾ and J_eff⁽²⁾ are compared in order to estimate the contribution of particle alignments to the total increase in angular momentum.     

Exploring the reaction of iodine with α‐diazo esters

In this paper we describe the unprecedented reaction between α‐diazo esters 1 and iodine. The reaction, carried out in the presence of aqueous NaHCO₃, afforded the Z‐isomer of the corresponding unsaturated‐2‐iodo ester 8 . The configuration of compounds 8 was determined using the ³J_{C? H} coupling between carbonyl carbon atom and alkene proton. Mechanistic considerations accounting for the observed phenomena and including quantum chemical calculations are proposed. Copyright © 2008 John Wiley & Sons, Ltd.     

Indirect carbon–carbon spin–spin couplings across one,two and three bonds in pyridine and diazine systems: experiment and theory

An excellent linear correlation is found between a large body of experimental spin–spin carbon–carbon couplings, J(CC), across one, two and three bonds in pyridine and diazine ring systems and the corresponding B3PW91/6‐311++G(d,p)//B3PW91/6‐311++G(d,p) computations. The correlation does not differ significantly from the simplest relationship possible, J(CC)_exp. = J(CC)_calcd., within a small and random spread of about 1 Hz. There are 276 experimental values considered, and 124 out of these are new and come from the present work. The aromatic carbon–carbon couplings vary from ?7.6 through +78.5 Hz. It is shown that the correlation provides a reliable tool for predictions of the signs of aromatic J(CC)'s even if the magnitudes of the latter are of the order of 1 Hz. It is demonstrated, for the first time, that the relatively weak ² J(CC) couplings, in the heteroaromatic systems studied, can bear either sign and span a considerable range of about 11 Hz. The character of the correlation indicates that rovibronic effects on aromatic J(CC)'s and those of nuclear motions on aromatic J(CC)'s are practically negligible. All of this is in a perfect agreement with our recent extensive studies on aromatic J(CC)'s in analogous benzene ring system. Substituent effects on the aromatic J(CC)'s turn out to be significant not only for ¹J(CC)'s but also for most of ³J(CC)'s and ² J(CC)'s, and the computation neatly reciprocates these trends. Copyright © 2008 John Wiley & Sons, Ltd.     

Theoretical ab initio calculation of the indirect nuclear spin-spin coupling constants of monohetero cyclopropanes and cyclopropenes via the equations-of-motion method

Nonempirical calculations using the equations-of-motion approach, which includes the main portion of electron correlation effects, are reported for the one-bond coupling constants in the three-membered rings borirane, cyclopropane, azirane, oxirane, silirane, phosphirane, and thiirane and related double-bond analogs. The important overall result is that the ¹J(CC) and ¹J(CC) constants are spread over broad ranges, much wider in the case of the double-bond species, with a nearly regular increase with the electronegativity of the central heteroatom. For the boron cycles the smallest ¹J(CC)'s are predicted, with ¹J(CC) surprisingly lower than ¹J(CC). This exceptional pattern is accounted for in terms of the peculiar electronic structure of these rings formed by the electron-deficient B atom. The ¹J(Heteroatom-C), ¹J(Heteroatom-H) and ¹J(CH) couplings correlate correctly with the available experimental data.     

Analysis of the 2ν3 band of CD3F at 5.06 μm recorded under high resolution

The 2ν₃(A₁) band of ¹²CD₃F near 5.06 μm has been recorded with a resolution of 20–24 × 10⁻³ cm⁻¹. The value of the parameter (α^B − α^A) for this band was found to be very small and, therefore, the K structure of the R(J) and P(J) manifolds was unresolved for J < 15 and only partially resolved for larger J values. The band was analyzed using standard techniques and values for the following constants determined: ν₀ = 1977.178(3) cm⁻¹, B″ = 0.68216(9) cm⁻¹, D″_J = 1.10(30) × 10⁻⁶ cm⁻¹, α^B = (B″ − B′) = 3.086(7) × 10⁻³ cm⁻¹, and β^J = (D″_J − D′_J) = −3.24(11) × 10⁻⁷ cm⁻¹. A value of α^A = (A″ − A′) = 2.90(5) × 10⁻³ cm⁻¹ has been obtained through band contour simulations of the R(J) and P(J) multiplets.     

Pionic degrees of freedom in atomic nuclei and quasielastic knockout of pions by high-energy electrons

The microscopic mechanism of the identical bands in odd-odd nucleus ¹⁹⁴Tl and its neighbor odd-A nuclei ^193,195Tl is investigated using the particle-number-conserving (PNC) method for treating the cranked shell model with monopole and quadrupole pairing interactions. It is found that the blocking effect of the high-j intruder orbital plays an important role in the variation of moments of inertia (J⁽¹⁾ and J⁽²⁾) with rotational frequency for the superdeformed bands and identical bands. The variation of the occupation probability of each cranked orbital and the contributions to moment of inertia from each cranked orbital are presented.     

Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector terms

We extend a recent calculation of the nuclear energy density functional in the framework of chiral perturbation theory by computing the isovector surface and spin-orbit terms: ([(?)\vec] r_p - [(?)\vec] r_n\vec \nabla \rho _p - \vec \nabla \rho _n )² G _d(r \rho) + ([(?)\vec] r_p - [(?)\vec] r_n\vec \nabla \rho _p - \vec \nabla \rho _n ·([(J)\vec]_p - [(J)\vec]_n\vec J_p - \vec J_n )G _so(r \rho) + ([(J)\vec]_p - [(J)\vec]_n\vec J_p - \vec J_n )² G _J(r \rho) pertaining to different proton and neutron densities. Our calculation treats systematically the effects from 1p \pi -exchange, iterated 1p \pi -exchange, and irreducible 2p \pi -exchange with intermediate D \Delta -isobar excitations, including Pauli-blocking corrections up to three-loop order. Using an improved density-matrix expansion, we obtain results for the strength functions G _d(r \rho) , G _so(r \rho) and G _J(r \rho) which are considerably larger than those of phenomenological Skyrme forces. These (parameter-free) predictions for the strength of the isovector surface and spin-orbit terms as provided by the long-range pion-exchange dynamics in the nuclear medium should be examined in nuclear structure calculations at large neutron excess.     

Decoupling of holes in thetJ model atJ=2t fromspl(2, 1) symmetry

The binding energy of twop=0 holes in thetJ model on a square lattice is shown to vanish atJ=2t due to thespl(2, 1) symmetry at this point. In any back-ground of antiferromagnetic type, with finite total spin in an infinite volume, the binding energy atx=0 hole doping vanishes at least as (J–2t)² asJ2t. These exact results may serve as tests of more comprehensive calculations of interactions of holes in thetJ model.     

Nuclear fusion rates from resonant states of 3Hedμ molecular ion

We present new theoretical calculations of nuclear fusion rates λ _f ^J from the resonant states of the muonic molecular ion ³Hedμ ⁺⁺ with total angular momenta J=0,1. As a byproduct, new very accurate variational wave functions for these states have been obtained. Using these wave functions, the probability density |Ψ(R=0)|² in a fusion region has been calculated by extrapolating the variational solution to small internuclear distances by means of the multi-channel adiabatic solution. Calculated fusion rates for the states J=0 and J=1 are: λ _f ⁰ =1.9·10⁵s^-1 and λ _f ¹ =0.65·10³s^-1, respectively. This revised version was published online in August 2006 with corrections to the Cover Date.     

Productions of X(1835) as baryonium with sizable gluon content

X(1835) has been treated as a baryonium with sizable gluon content, and to be almost flavor singlet. This picture allows us to rationally understand X(1835) production in J/ψ radiative decays, and its large couplings with pˉ, η^′ππ. The processes ϒ(1S) → γX(1835) and J/ψ → ωX(1835) have been examined. It has been found that Br(ϒ(1S) → γX(1835))Br(X(1835) → pˉ) < 6.45×10^-7, which is compatible with CLEO's recent experimental result (Phys. Rev. D 73, 032001 (2006) hep-ex/0510015). The branching fractions Br(J/ψ → ωX(1835)), Br(J/ψ → ρX(1835)) with X(1835) → pˉ and X(1835) → η^′π⁺π^- have been estimated by the quark-pair creation model. We show that they are heavily suppressed, so the signal of X(1835) is very difficult, if not impossible, to be observed in these processes. The experimental checks for these estimations are expected. The existence of the baryonium nonet is conjectured, and a model-independent derivation of their production branching fractions is presented.     

Abelian dyons in the maximal Abelian projection of SU(2) gluodynamics

Correlations of the topological charge Q, the electric current J ^e, and the magnetic current J ^m in SU(2) lattice gauge theory in the maximal Abelian projection are investigated. It is found that the correlator 〈〈QJ ^eJ^m〉〉 is nonzero for a wide range of values of the bare charge. It is shown that: (i) the Abelian monopoles in the maximal Abelian projection are dyons which carry fluctuating electric charge; (ii) the sign of the electric charge e(x) coincides with that of the product of the monopole charge m(x) and the topological charge density Q(x). Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 161–165 (10 February 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Breaking of the SU(4) limit for the Gamow-Teller strength in N ∼ Z nuclei

We have performed large-scale shell model calculations of the Gamow-Teller strength distributions in N ∼ Z pf -shell nuclei. These calculations were motivated by the experimental attempts to measure the low-lying GT strength for the even-even N = Z + 2 or N = Z - 2 nuclei ⁴⁶Ti , ⁵⁰Cr , ⁵⁴Fe and ⁶²Ge , where a sizable low-energy GT strength could be interpreted as reminiscence of SU(4) symmetry; in the limit of exact SU(4) symmetry the GT_- strength would be concentrated in a single transition to the lowest T = 0, J = 1⁺ state in the daughter. We confirm that the SU(4) symmetry is strongly broken by the spin-orbit interaction and by increasing neutron excess.     

Microscopic study of low-lying yrast spectra in <Superscript>100–108</Superscript>Mo isotopes

Variation-after-projection (VAP) calculations in conjunction with Hartree-Bogoliubov (HB) ansatz have been carried out for A=100−108 molybdenum (Mo) isotopes. In this framework, the yrast spectra with J _max ^π ≥10⁺, B(E2) transition probabilities, quadrupole (β₂) and hexadecapole (β₄) deformation parameters, moment of inertia (I) and square of cranking frequency (ω²) for even-even Mo isotopes have been obtained. The results of the calculation give an indication that it is important to include the hexadecapole-hexadecapole component of the two-body interaction for obtaining various nuclear structure quantities in these Mo isotopes.     

The 27-plet baryons with spin 3/2 under SU(3) symmetry

We investigate the spin-3/2 baryons in the 27-plet based on flavor SU(3) symmetry. For J ^p = 3/2⁺, we find all the candidates for non-exotic members. For J ^p = 3/2^-, we predict a new non-exotic member Λ(1780). Fitting the mass spectrum and calculating the widths of the members show an approximate symmetry of the 27-plet of SU(3). We find that the exotic members have relatively large widths and the Ξ(1950) has spin and parity J ^p = 3/2^-. The possibility of assigning the non-exotic candidates to an octet is also analyzed.