Nuclear Spin-rotation Constants Research Articles

Fourier-transform microwave spectroscopy of the ClSO radical.

Pure rotational transitions of the ClSO radical have been observed by Fourier-transform microwave spectroscopy. a-type and b-type transitions, for both 35Cl and 37Cl isotopologues, were detected, and the observed very complicated fine and hyperfine components were assigned well. The intensities of the observed spectra of the two isotopologues correspond to the ratio of the isotope abundances of 35Cl and 37Cl. A total of 21 molecular constants were determined precisely for both 35ClSO and 37ClSO, including the rotational constants, centrifugal distortion constants, electronic spin-rotation constants, nuclear spin-rotation constants, magnetic hyperfine constants, and quadrupole coupling constants of chlorine. The molecular constants show ClSO to have the 2A'' electronic ground state with an out-of-plane unpaired electron. The spin density of the chlorine atom is about 10.6%, which is similar to that of the fluorine atom for FSO, about 8%. Results of the ClSO radical are compared with those of other triatomic radicals with similar structures, the XSS, XSO, and XOO radicals with X = H, F, and Cl, leading to a conclusion that the ClSO radical is more like FSO, but fairly different from the FOO and ClOO radicals.

Relativistic study of parity-violating nuclear spin-rotation tensors.

We present a four-component relativistic approach to describe the effects of the nuclear spin-dependent parity-violating (PV) weak nuclear forces on nuclear spin-rotation (NSR) tensors. The formalism is derived within the four-component polarization propagator theory based on the Dirac-Coulomb Hamiltonian. Such calculations are important for planning and interpretation of possible future experiments aimed at stringent tests of the standard model through the observation of PV effects in NSR spectroscopy. An exploratory application of this theory to the chiral molecules H2X2 (X = 17O, 33S, 77Se, 125Te, and 209Po) illustrates the dramatic effect of relativity on these contributions. In particular, spin-free and spin-orbit effects are even of opposite signs for some dihedral angles, and the latter fully dominate for the heavier nuclei. Relativistic four-component calculations of isotropic nuclear spin-rotation constants, including parity-violating electroweak interactions, give frequency differences of up to 4.2 mHz between the H2Po2 enantiomers; on the nonrelativistic level of theory, this energy difference is 0.1 mHz only.

Absolute NMR shielding scales in methyl halides obtained from experimental and calculated nuclear spin-rotation constants

The nonrelativistic ``Ramsey-Flygare relationship'' is the most used procedure to obtain semiexperimental nuclear magnetic resonance (NMR) absolute shieldings by a correspondence between NMR shieldings ($\mathbit{\ensuremath{\sigma}}$) and nuclear spin-rotation constants ($\mathbit{M}$). One of its generalizations to the relativistic framework is known as the M-V model, which was proposed few year ago by some of the authors of the present work and right now is only applied to linear molecules. This model includes terms that do not have nonrelativistic counterparts and also include the paramagnetic contribution to the NMR shielding of nuclei in free atoms. All this ensures that its results fit quite well with those of four-component (4c) calculations. The first application of the M-V model to nonlinear molecules, like methyl halides or ${\mathrm{CH}}_{3}X$ molecules ($X=\mathrm{F}$, Cl, Br, and I), is given here. The analysis of each electronic mechanism of $\mathbit{\ensuremath{\sigma}}$ shows that most of their electron correlation effects are strongly related with the same effects in $\mathbit{M}$. By including experimental data of $M$ in the M-V model most of the correlation effects are accurately taken into account for the absolute values of $\mathbit{\ensuremath{\sigma}}$. Calculations of ${\mathbit{M}}_{Y}$ and ${\mathbit{\ensuremath{\sigma}}}_{Y}$ ($Y=\mathrm{H}$, C, and $X$) were carried out within the linear response formalism at the random-phase level of approach and density functional theory in both 4c and nonrelativistic frameworks. The best fits between calculations of $\mathbit{M}$ and experimental data are obtained from calculations at 4c-PBE0 level of theory in all cases, but not for ${M}_{\ensuremath{\parallel},\mathrm{Cl}}$, which suggests that a revision of the available experimental data may be necessary. There is an additional advantage of using the M-V model: one can indirectly calculate shieldings of open-shell free atoms, which cannot be obtained at the moment by applying 4c methods.

Performance of the LRESC Model on top of DFT Functionals for Relativistic NMR Shielding Calculations.

The linear response within the elimination of the small component model (LRESC) is an insightful and computationally efficient method for including relativistic effects on molecular properties like the nuclear magnetic shielding constants, spin-rotation constant, g-tensor, and electric field gradient of heavy atom containing molecules with atoms belonging up to the sixth row of the periodic table. One of its main advantages is its capacity to analyze the electronic origin of the different relativistic correcting terms. Until now, it was always applied on top of Hartree-Fock ground-state wave functions (LRESC/HF) to calculate and analyze NMR shieldings. In this work, we show the performance of the LRESC formalism on top of some density functional theory (DFT) functionals to compute tin shielding constants in SnX4 (X = H, F, Cl, Br, I) molecular systems. We analyze the performance of each LRESC/DFT scheme on reproducing the electronic mechanisms of the shieldings, taking as a benchmark the results of relativistic calculations at the RPA level of approach (4c/RPA). As in previous works, we divide the LRESC relativistic correcting terms into two groups: core-dependent and ligand-dependent contributions. It is shown here that core-dependent corrections are well-reproduced for the selected DFT functionals, but some differences arise in the ligand-dependent ones. We focus on the performance of different functionals, including the same electron correlation part but containing different amounts of HF exchange. The best results are obtained for the BHandHLYP functional (50% of HF exchange) and the worst for BLYP (0%). When the percentage of HF exchange increases, ligand-dependent contributions are better described, and the final LRESC/DFT results are closer to those obtained with LRESC/HF and 4c/RPA methods. The spin-orbit correction to the shielding constant is one of the main ligand-dependent contributions (there are two more) with total value depending on the amount of HF exchange included in the functional. When the amount of HF exchange decreases, the spin-orbit contribution becomes larger, overestimating the shielding constant even when nonrelativisitc DFT values are much smaller than the nonrelativistic HF ones, as it happens for the heaviest molecular system studied here (SnI4).

Influence of the nuclear charge distribution and electron correlation effects on magnetic shieldings and spin-rotation tensors of linear molecules.

The nuclear charge distribution effects (NChDE) on two response properties, the NMR magnetic shielding (σ) and the nuclear spin-rotation (SR) constants (M), are analyzed. We do it employing point-like and Gaussian-like models for describing the nuclear charge density of three linear molecules: HBr, HI and HAt. According to our results, both properties are sensitive to the NChDE. We show that the NChDE are almost completely relativistic, i.e., they nearly vanish in the non-relativistic limit of both properties. We calculated the NChDE on σ and M, and analyzed the differences between them in terms of a relativistic relation between these two properties. Using that relation we found that the electronic core mechanisms are the main ones for the NChDE on the shielding of nuclei of both, molecules and free atoms. The NChDE are smaller on SR constants than on shieldings. Nevertheless, within the relativistic polarization propagator formalism at the RPA level of approach they are very important for SR constants of nuclei in heavy-atom-containing compounds. Astatine in HAt has the largest influence: MAt = −9.95 kHz for a point-like model and −50.10 kHz for a Gaussian-like model. Correlation effects must be included and we do it using different DFT schemes. The PBE0 functional gives results that are closest to experiments for Br and I, though the LDA gives the closest for hydrogen. The value of the SR constant of At is reduced among 350 kHz and 500 kHz from its RPA value, when different and usual functionals are applied. Given that the NChDE on M and σ are mostly relativistic in their origin, these effects are also dependent on electron correlation. They have also a nonvanishing dependence with the Gaunt electron–electron interactions.

Ab initio NMR parameters of BrCH3 and ICH3 with relativistic and vibrational corrections

ABSTRACTThis study is focused on two effects identified when NMR parameters are calculated based on first principles. These effects are 1. vibrational correction of properties when using ab initio optimized equilibrium geometry; 2. relativistic effects and limits of using the Flygare equation. These effects have been investigated and determined for nuclear spin-rotation constants and nuclear magnetic shieldings for the CH3Br and CH3I molecules. The most significant result is the difference between chemical shieldings determined based on the ab initio relativistic four-component Dirac-Coulomb Hamiltonian and chemical shieldings calculated using experimental values and the Flygare equation. This difference is approximately 320 ppm and 1290 ppm for 79Br and 127I in the CH3X molecule, respectively.

Nuclear quadrupole coupling in SiH2I2 due to the presence of two iodine nuclei

The rotational spectrum of diiodosilane was measured with a jet-pulsed, cavity Fourier transform microwave (FTMW) spectrometer over the frequency range 8.8–15GHz and assigned for the first time. The complete nuclear quadrupole coupling (NQC) tensors for both iodine nuclei were obtained for the 28Si, 29Si, and 30Si isotopologues of diiodosilane. In addition to the nuclear quadrupole coupling constants (NQCCs), rotational constants, centrifugal distortion constants, and nuclear spin-rotation constants were determined for each silicon isotopologue. Subtle, yet unmistakable, changes in the NQCCs of iodine upon isotopic substitution were observed and will be discussed. A r0 structure of diiodosilane was also fit via isotopic substitution, which led to the determination of bond lengths and angles: r0(SiI)=2.4236(19)Å, r0(SiH)=1.475(21)Å, ∠(ISiI)=111.27(13)°, and ∠(ISiH)=105.9(19)°. These molecular parameters will be compared to the results of a previous gas electron diffraction study.

A study of the conformational isomerism of 1-iodobutane by high resolution rotational spectroscopy

The first microwave study of 1-iodobutane, performed by Steinmetz et al. in 1977, led to the determination of the B+C parameter for the anti-anti- and gauche-anti-conformers. Nearly 40years later, this reinvestigation of 1-iodobutane, by high-resolution microwave spectroscopy, led to the determination of rotational constants, centrifugal distortion constants, nuclear quadrupole coupling constants (NQCCs), and nuclear-spin rotation constants belonging to both of the two previously mentioned conformers, in addition to the gauche-gauche-conformer, which was observed in this frequency regime for the first time. Comparisons between the three conformers of 1-iodobutane and other iodo- and bromoalkanes are made, specifically through an analysis of the nuclear quadrupole coupling constants belonging to the iodine and bromine atoms in the respective chemical environments.

Role of Spin-Dependent Terms in the Relationship among Nuclear Spin-Rotation and NMR Magnetic Shielding Tensors.

The broadly accepted procedure to obtain the experimental absolute scale of NMR magnetic shieldings, σ, is well-known for nonheavy atom-containing molecules. It was uncovered more than 40 years ago by the works of Ramsey and Flygare. They found a quite accurate relationship among σ and the nuclear spin-rotation constants. Its relativistic extension was very recently proposed, although it has an intrinsic weakness because a new SO-S two-component term needs to be considered. We show how to overcome this problem. We found that (νYS - νYatom,S) generalizes the SO-S term, where νYS = ⟨⟨[((r - rY) × α)/(|r - rY|3)]; S(4)⟩⟩, r - rY is the electron position with respect to the position of nucleus Y, and S(4) is the four-component total electron spin. When including this new term, one finds that the best of our relativistic Flygare-like models fits quite well with the results of the most accurate method available at the moment. We also show that the difference among the parallel component of σ(Xe) in XeF2 and σ(Xe) of the free atom is almost completely described by that new term.

A Study of 2-Iodobutane by Rotational Spectroscopy.

Rotational transitions belonging to 2-iodobutane (sec-butyl-iodide, CH3CHICH2CH3) were measured over the frequency range 5.5-16.5 GHz via jet-pulsed Fourier transform microwave spectroscopy. The complete nuclear quadrupole coupling tensor of iodine, χ, was obtained for the gauche (g)-, anti (a)-, and gauche' (g')-conformers as well as the four (13)C isotopologues of the gauche species. Rotational constants, centrifugal distortion constants, quadrupole coupling constants, and nuclear spin-rotation constants were determined for each species. Changes in χ of the iodine nucleus, resulting from conformational and isotopic differences, are discussed. Isotopic substitution of g-2-iodobutane allowed for an rs structure to be determined for the carbon backbone. Additionally, isotopic substitution in conjunction with an ab initio structure allowed for a fit of various r0 structural parameters belonging to g-2-iodobutane.

Absolute NMR shielding scales and nuclear spin-rotation constants in (175)LuX and (197)AuX (X = (19)F, (35)Cl, (79)Br and (127)I).

We present nuclear spin-rotation constants, absolute nuclear magnetic resonance (NMR) shielding constants, and shielding spans of all the nuclei in (175)LuX and (197)AuX (X = (19)F, (35)Cl, (79)Br, (127)I), calculated using coupled-cluster singles-and-doubles with a perturbative triples (CCSD(T)) correction theory, four-component relativistic density functional theory (relativistic DFT), and non-relativistic DFT. The total nuclear spin-rotation constants determined by adding the relativistic corrections obtained from DFT calculations to the CCSD(T) values are in general in agreement with available experimental data, indicating that the computational approach followed in this study allows us to predict reliable results for the unknown spin-rotation constants in these molecules. The total NMR absolute shielding constants are determined for all the nuclei following the same approach as that applied for the nuclear spin-rotation constants. In most of the molecules, relativistic effects significantly change the computed shielding constants, demonstrating that straightforward application of the non-relativistic formula relating the electronic contribution to the nuclear spin-rotation constants and the paramagnetic contribution to the shielding constants does not yield correct results. We also analyze the origin of the unusually large absolute shielding constant and its relativistic correction of gold in AuF compared to the other gold monohalides.

Efficient calculation of nuclear spin-rotation constants from auxiliary density functional theory.

The computation of the spin-rotation tensor within the framework of auxiliary density functional theory (ADFT) in combination with the gauge including atomic orbital (GIAO) scheme, to treat the gauge origin problem, is presented. For the spin-rotation tensor, the calculation of the magnetic shielding tensor represents the most demanding computational task. Employing the ADFT-GIAO methodology, the central processing unit time for the magnetic shielding tensor calculation can be dramatically reduced. In this work, the quality of spin-rotation constants obtained with the ADFT-GIAO methodology is compared with available experimental data as well as with other theoretical results at the Hartree-Fock and coupled-cluster level of theory. It is found that the agreement between the ADFT-GIAO results and the experiment is good and very similar to the ones obtained by the coupled-cluster single-doubles-perturbative triples-GIAO methodology. With the improved computational performance achieved, the computation of the spin-rotation tensors of large systems or along Born-Oppenheimer molecular dynamics trajectories becomes feasible in reasonable times. Three models of carbon fullerenes containing hundreds of atoms and thousands of basis functions are used for benchmarking the performance. Furthermore, a theoretical study of temperature effects on the structure and spin-rotation tensor of the H(12)C-(12)CH-DF complex is presented. Here, the temperature dependency of the spin-rotation tensor of the fluorine nucleus can be used to identify experimentally the so far unknown bent isomer of this complex. To the best of our knowledge this is the first time that temperature effects on the spin-rotation tensor are investigated.

The rotational spectrum of 17O2 up to the THz region

The investigation of the pure rotational spectrum of the 17O2 isotopic species of molecular oxygen has been extended with respect to previous investigations to the submillimeter-wave region, from 230GHz up to 1.06THz. The resulting spectroscopic parameters, which have an accuracy comparable to that of the constants obtained from an updated isotopic invariant fit involving data for three electronic states and six isotopologues [Yu et al. High resolution spectral analysis of oxygen. IV. Energy levels, partition sums, bandconstants, RKR potentials, Franck–Condon factors involving the X3Σg−, a1Δg, and b1Σg+ states. J Chem Phys 2014;141:174302/1–12], permit the prediction of the pure rotational transitions up to 2THz with an estimated uncertainty not greater than 100kHz. In the present study, high-level quantum-chemical calculations guided, supported, and complemented the determination of the hyperfine parameters of 17O, with particular effort made in determining an accurate and reliable experimental value for the nuclear spin–rotation constant. A detailed discussion about the magnitude of the nuclear spin–rotation constant in the 17O-containing O2 species for both the ground and the first excited electronic state is presented.

Four-Component Relativistic Density-Functional Theory Calculations of Nuclear Spin-Rotation Constants: Relativistic Effects in p-Block Hydrides.

We present an implementation of the nuclear spin-rotation (SR) constants based on the relativistic four-component Dirac-Coulomb Hamiltonian. This formalism has been implemented in the framework of the Hartree-Fock and Kohn-Sham theory, allowing assessment of both pure and hybrid exchange-correlation functionals. In the density-functional theory (DFT) implementation of the response equations, a noncollinear generalized gradient approximation (GGA) has been used. The present approach enforces a restricted kinetic balance condition for the small-component basis at the integral level, leading to very efficient calculations of the property. We apply the methodology to study relativistic effects on the spin-rotation constants by performing calculations on XHn (n = 1-4) for all elements X in the p-block of the periodic table and comparing the effects of relativity on the nuclear SR tensors to that observed for the nuclear magnetic shielding tensors. Correlation effects as described by the density-functional theory are shown to be significant for the spin-rotation constants, whereas the differences between the use of GGA and hybrid density functionals are much smaller. Our calculated relativistic spin-rotation constants at the DFT level of theory are only in fair agreement with available experimental data. It is shown that the scaling of the relativistic effects for the spin-rotation constants (varying between Z(3.8) and Z(4.5)) is as strong as for the chemical shieldings but with a much smaller prefactor.

H₂-AgCl: a spectroscopic study of a dihydrogen complex.

H2-AgCl has been observed on a Fourier transform microwave spectrometer equipped with laser ablation source and determined to be a dihydrogen complex. Transitions up to J = 3-2 have been measured and analyzed for four isotopologues of the complex containing ortho and para H2. The ortho and para spin states have been included in one fit, a deviation from the typical H2 complex. Rotational constants B and C, centrifugal distortion constants Δ(J) and Δ(JK), nuclear electric quadrupole coupling constants χ(aa), χ(bb), and χ(cc) for (35)Cl and (37)Cl have been fit for both spin states while nuclear spin-nuclear spin constants D(aa), D(bb), and D(cc), and nuclear spin-rotation constant C(aa) have been reported for the ortho spin state. Quantum chemical calculations predict a strong bonding interaction and the strength of the complex has been related to reported χ(aa) and Δ(J) values amongst a host of comparable species, including the AgCl monomer itself. Bond lengths have been determined for Ag-Cl, Ag-H2 center-of-mass, and H-H and are reported.

Hyperfine constants for aluminum hydride and aluminum deuteride

The nuclear quadrupole coupling and spin-rotation constants of aluminum in AlH and AlD have been determined using coupled cluster theory with single and double excitations as well as perturbative inclusion of triples [CCSD(T)] combined with large correlation-consistent basis sets, cc-pCVXZ (X=T, Q and 5) and aug-cc-pCVXZ (X=T, Q). The anharmonic vibrational frequencies have been computed using second-order vibrational perturbation theory and the effects of vibrational averaging on the hyperfine constants have been determined. The ground state dipole moment has been determined for both isotopologues (AlH and AlD) and shown to depend critically on vibrational averaging. For completeness, the isotropic and anisotropic nuclear magnetic shielding tensors are also reported. All the results agree well with the best available experimental measurements, and in some cases (spin-rotation constants and dipole moments) refine the known data. The present computational results for the vibrationally averaged electric field gradients suggest that the currently accepted nuclear quadruple moment for 27Al of 146.6±1.0mb may be slightly underestimated. Based on the experimental measurements of the nuclear quadrupole coupling for AlH (AlD) and best computational determinations of the vibrationally averaged electric field gradients, the quadruple moment of 27Al is determined to be 149±2mb(148±3mb). However, this conclusion would be further strengthened with more precise experimental measurement of the 27Al nuclear quadrupole coupling for AlH and AlD.

The Absolute Shielding Constants of Heavy Nuclei: Resolving the Enigma of the (119)Sn Absolute Shielding.

We demonstrate that the apparent disagreement between experimental determinations and four-component relativistic calculations of the absolute shielding constants of heavy nuclei is due to the breakdown of the commonly assumed relation between the electronic contribution to the nuclear spin-rotation constants and the paramagnetic contribution to the NMR shielding constants. We demonstrate that this breakdown has significant consequences for the absolute shielding constant of (119)Sn, leading to errors of about 1000 ppm. As a consequence, we expect that many absolute shielding constants of heavy nuclei will be in need of revision.

Monohydrates of cuprous chloride and argentous chloride: H2O⋅⋅⋅CuCl and H2O⋅⋅⋅AgCl characterized by rotational spectroscopy and ab initio calculations

Pure rotational spectra of the ground vibrational states of ten isotopologues of each of H(2)O⋅⋅⋅CuCl and H(2)O⋅⋅⋅AgCl have been measured and analyzed to determine rotational constants and hyperfine coupling constants for each molecule. The molecular structure and spectroscopic parameters determined from the experimental data are presented alongside the results of calculations at the CCSD(T) level. Both experiment and theory are consistent with structures that are nonplanar at equilibrium. The heavy atoms are collinear while the local C(2) axis of the water molecule intersects the axis defined by the heavy atoms at an angle, φ = 40.9(13)° for Cu and φ = 37.4(16)° for Ag. In the zero-point state, each molecule is effectively planar, undergoing rapid inversion between two equivalent structures where φ has equal magnitude but opposite sign. The equilibrium geometry has C(s) symmetry, however. The ab initio calculations confirm that the timescale of this inversion is at least an order of magnitude faster than that of rotation of the molecule in the lowest rotational energy levels. The molecular geometries are rationalized using simple rules that invoke the electrostatic interactions within the complexes. Centrifugal distortion constants, Δ(J) and Δ(JK), nuclear quadrupole coupling constants, χ(aa)(Cu), χ(aa)(Cl), (χ(bb) - χ(cc))(Cu), and (χ(bb) - χ(cc))(Cl), and the nuclear spin-rotation constant of the copper atom, C(bb)(Cu)+C(cc)(Cu), are also presented.

Concerning the electronic and geometric structure of bromodifluoroacetonitrile, CBrF 2CN

The pure rotational spectrum of bromodifluoroacetonitrile between 7.7 and 18 GHz has been measured on a chirped pulse microwave spectrometer. The spectra are dense with 889 measured transitions in the region. Rotational, centrifugal distortion, nuclear electric quadrupole coupling constants ( 79Br, 81Br, and 14N), and nuclear magnetic spin-rotation constants ( 79Br/ 81Br) were determined and are reported for the first time. Quantum chemical calculations were made of the nuclear quadrupole coupling constants to assist with assignment of the spectra. Spectra from both 13C isotopologues were measured in natural abundance. The effects of flourination on the nuclear electric quadrupole coupling tensor components for the series of monobrominated acetonitrile molecules are discussed.

The rotational spectrum of CuCCH(X̃ Σ1+): A Fourier transform microwave discharge assisted laser ablation spectroscopy and millimeter/submillimeter study

The pure rotational spectrum of CuCCH in its ground electronic state (X̃ (1)Σ(+)) has been measured in the frequency range of 7-305 GHz using Fourier transform microwave (FTMW) and direct absorption millimeter/submillimeter methods. This work is the first spectroscopic study of CuCCH, a model system for copper acetylides. The molecule was synthesized using a new technique, discharge assisted laser ablation spectroscopy (DALAS). Four to five rotational transitions were measured for this species in six isotopologues ((63)CuCCH, (65)CuCCH, (63)Cu(13)CCH, (63)CuC(13)CH, (63)Cu(13)C(13)CH, and (63)CuCCD); hyperfine interactions arising from the copper nucleus were resolved, as well as smaller splittings in CuCCD due to deuterium quadrupole coupling. Five rotational transitions were also recorded in the millimeter region for (63)CuCCH and (65)CuCCH, using a Broida oven source. The combined FTMW and millimeter spectra were analyzed with an effective Hamiltonian, and rotational, electric quadrupole (Cu and D) and copper nuclear spin-rotation constants were determined. From the rotational constants, an r(m)(2) structure for CuCCH was established, with r(Cu-C) = 1.8177(6) Å, r(C-C) = 1.2174(6) Å, and r(C-H) = 1.046(2) Å. The geometry suggests that CuCCH is primarily a covalent species with the copper atom singly bonded to the C≡C-H moiety. The copper quadrupole constant indicates that the bonding orbital of this atom may be sp hybridized. The DALAS technique promises to be fruitful in the study of other small, metal-containing molecules of chemical interest.