Spin-rotation Interaction Constants Research Articles

High-resolution laser excitation spectroscopy: Analysis of the B2Σ +- X2Σ + system of CaCl

Single-mode cw dye laser excitation spectra of the (0, 0), (1, 1), and (2, 2) bands of the B 2Σ +- X 2Σ + system of CaCl have been observed and assigned. Some 300 independent photo-luminescence spectra have been used in making the rotational assignment and demonstrate the power of the technique of line-by-line analysis in unraveling complex spectra. Spectroscopic constants (cm −1) obtained from a weighted least squares fit of the data are given below. Numbers in parentheses refer to 95% confidence limits in the last digit. X 2 Σ + B 2 Σ + T e 0 16856.69(2) ω e 369.8(10) 366.8(10) ω ex e 1.13(20) 1.28(20) B e 0.15200(54) 0.15448(54) α e 0.00063(34) 0.00073(35) D e 1.027(16) × 10 −7 1.097(17) × 10 −7 γ e (spin-rotation) +0.003 −0.0630(16) The ground-state rotational constant is in excellent agreement with the previous value obtained from the analysis of the C 2Π r- X 2Σ +. The B-state spin-rotation interaction constant is consistent with the pure precession estimate of the interaction between the A 2Π r and B 2Σ + states, which, in the one electron approximation, both have the unpaired electron in a calcium 4 p orbital.

Magnetic shielding studies on the alkali molecules Na2 and Cs2 by NMR

NMR in the alkali molecules Na2 and Cs2 is performed by the atom-molecule exchange optical pumping method. The shielding differences σ(Na)−σ(Na2)=(29±16)·10−6 and σ(Cs)−σ(Cs2)=(221±12)·10−6 are obtained. The investigation of the contribution of the valence electron to the magnetic shielding is supported by a NMR experiment in free Cs+ ions, which yields the shielding difference σ(Cs)−σ(Cs+)=(14±12)·10−6. These measurements allow an estimation of the spin rotation interaction constant in these molecules.

High-resolution infrared spectrum of the ν3 and ν2 + ν3 − ν2 bands of 14N 16O 2

The infrared absorption spectrum of the ν 3 band of 14NO 2 has been recorded with a resolution and a frequency accuracy much improved over the previous investigations. The K- and N-line assignments have been greatly extended and a more accurate set of spectroscopic constants derived. Several lines in the subbands with K a ≥ 3 have been observed to be doubled by spin-rotation interaction and spin-rotation interaction constants have been obtained. Several weak series of lines in the spectrum ( K a = 0, 1, 2, and 3) have been unambiguously assigned to the “hot band” ν 2 + ν 3 − ν 2. Lines of the K a = 3, 4, 5, and 6 sub-bands of ν 3 have been found to be perturbed by a Coriolis interaction with the K a = 4, 5, 6, and 7 levels of 2 ν 2.

Nuclear magnetic relaxation of 31P in phosphorous halides

31P NMR spin–lattice relaxation time measurements in the laboratory frame, T1, and in the rotating coordinate frame, T1ρ, are reported for an equimolar mixture of PBr3 and PCl3. Relaxation times were measured as a function of temperature. T1ρ was measured also as a function of offset and lock-field strength. The lock-field dependent T1ρ technique is shown to be inadequate for exact determinations of scalar spin–spin coupling constants. We report for all four molecular species PBr3, PBr2Cl, PBrCl2, and PCl3 the following quantities: activation energies and frequency factors for chemical exchange and molecular reorientation and spin–lattice relaxation times for the bromines and chlorines. These quantities are obtained from the temperature dependent T1ρ measurements, which are shown to be suited for the study of chemical exchange processes when the exchange rates are in the order of 103–105 s−1. Using known values for quadrupolar coupling constants, we derive the temperature dependence of the reorientation correlation time. The known temperature dependence of the correlation time is in turn used for a complete analysis of the temperature dependent T1 measurements. All possible relaxation mechanisms contributing to T1 are identified and experimental values for the spin–rotation interaction constant and the chemical shift anisotropy are determined. The accuracy of the various parameters varies from a few percent to mere estimates.

ChemInform Abstract: NUCLEAR MAGNETIC SHIELDING OF HYDROGEN IN THE HYDRIDES OF THE ELEMENTS

AbstractWerte für die molekularen diamagnetischen und paramagnetischen Komponenten der Wasserstoffabschirmung in einfachen binären Elementhydriden werden zusammengestellt.

ChemInform Abstract: NUCLEAR MAGNETIC SHIELDING OF FLUORINE IN THE FLUORIDES OF THE ELEMENTS

AbstractDie kernmagnetischen Abschirmungsparameter binärer Fluoridmoleküle und ‐ionen ändern sich periodisch mit der Atomzahl des Zentralatoms.

Nuclear magnetic shielding of hydrogen in the hydrides of the elements

Values have been assembled for the molecular diamagnetic and paramagnetic components of the proton shielding in the simple binary hydrides of the elements, and are shown to increase in periodic fashion with the atomic number of the heavy atom. For molecules for which the diamagnetic term σd is unknown, this has been calculated by Flygare's method. An absolute value of the paramagnetic term is afforded by the spin-rotation interaction constants which are now known with reasonable accuracy for 13 of the hydrides (σp has been calculated where necessary from Ramsey and Flygare's equations). For the remaining hydrides, σp has been obtained by subtracting σd from the observed shielding referred to an absolute scale. The dependence of the terms on the size and shape of the molecule and the position of the hydrogen is illustrated by the values for diborane and tetra-hydroborate ion. Factors determining the periodicity are discussed; this is remarkably symmetrical for the diamagnetic and paramagnetic terms. Although proton shielding is often described as dominated by the diamagnetic term, the periodic correlation shows that variations in the resultant shielding may be determined by changes in the paramagnetic term, e.g. down the Group of the heavy atom and across the second Row (the lithium Row).

Nuclear magnetic shielding of fluorine in the fluorides of the elements

Nuclear magnetic shielding parameters for the (spin-paired) binary fluoride molecules and ions vary periodically with the atomic number of the central atom. The diamagnetic term σd has been calculated by Flygare's method, and experimental values of σp for 17 binary fluorides have been obtained from spin-rotation interaction constants (with Ramsey's and Flygare's equations) and from the shielding anisotropy for some linear molecules. These values of σp agree with those obtained by substracting σd(calc.) from the resultant shielding referred to an absolute scale, and σp has been obtained in this way for the remaining molecular fluorides and complex ions. The term σd increases periodically with the number of electrons in the molecule, but the resultant shielding follows the larger and more irregular variations in σp; |σpF| increases sharply across the Row of the central atom for the typical elements and also for the transition metals with empty d(t2g) orbitals. Fluorine is highly shielded, however, in the d6 hexafluoride molecules and ions, possibly because of circulations of the π*→σ* type which contribute positive terms to σp in CIF. The increase in |σpF| across the Row of the central atom is ascribed to increasing imbalance of the fluorine 2p electrons with increasing covalency, to the increase in <r–3>2p, and to the tendency of (ΔE)–1 to increase. Down the Group of the central atom |σpF| tends to increase with (ΔE)–1, against the tendency of <r–3>2p to decrease (for the typical elements), although there are important anomalies which may show the influence of the radius term. Near the bottom of the later Groups the increase in |σpF| is slowed or reversed. Periodic correlations for other nuclei such as 13C show corresponding patterns of variation in σp and these are evident also in 1H shielding. The periodic correlation shows the basis of the familiar relation between fluorine shielding and electronegativity of the central atom and of the important exceptions to this relation.

Some molecular properties of LiH and LiD

The results of both experiment and theory have been combined to produce some new and accurate properties of LiH and LiD. The measurement of some specific ground state hyperfine and Zeeman energies by molecular beam electric resonance (MBER) is discussed. The importance of vibrationally averaging expressions for molecular constants obtained from accurate experimental measurements as well as molecular properties obtained in theoretical ab initio calculations using well-correlated wavefunctions is emphasized. New values for the electric quadrupole moment of 7Li and D are presented: QLi = −4.26×10−26 cm2 and QD = 2.9×10−27 cm2. In addition, as a check on both experiment and theory, the molecular rotational gJ factor and spin-rotation interaction constants are calculated and compared.

ChemInform Abstract: NUCLEAR SHIELDING AND MAGNETIC HYPERFINE STRUCTURE OF HYDROGEN CYANIDE

Abstract A millimeter-wave molecular beam maser has been used to resolve the magnetic hyperfine structure of hydrogen cyanide. The spin-rotation interaction constants have been measured for the three nuclei 14 N, 13 C, and H. The paramagnetic nuclear shielding factors have been calculated for the three nuclear sites. The spin-rotation constants for 14 N in H 12 C 14 N, for H in H 12 C 14 N and for 13 C in D 13 C 14 N are + 10.4 kHz, −3.7 kHz, and +15.0 kHz, respectively. The respective paramagnetic shielding factors are −408.98 × 10 −6 , −73.40 × 10 −6 , and −249.52 × 10 −6 .

Nuclear shielding and magnetic hyperfine structure of hydrogen cyanide

A millimeter-wave molecular beam maser has been used to resolve the magnetic hyperfine structure of hydrogen cyanide. The spin-rotation interaction constants have been measured for the three nuclei 14N, 13C, and H. The paramagnetic nuclear shielding factors have been calculated for the three nuclear sites. The spin-rotation constants for 14N in H 12C 14N, for H in H 12C 14N and for 13C in D 13C 14N are + 10.4 kHz, −3.7 kHz, and +15.0 kHz, respectively. The respective paramagnetic shielding factors are −408.98 × 10 −6, −73.40 × 10 −6, and −249.52 × 10 −6.

Comparison of 31P Spin—Rotation Interaction Constants Derived from Chemical Shift Data and from NMR Relaxation and Viscosity Data

The complete rotational diffusion tensors of the three symmetric top molecules PCl3, PBr3, and POCl3 are obtained from viscosity and halogen NMR relaxation time data. These tensors allow us to obtain estimates of the average correlation times for each molecule, which in turn are used in Hubbard's isotropic spin—rotation equation to derive NMR values of their spin—rotation interaction constants Ceff. These and similarly derived values of Ceff for a number of other 31P compounds are compared to values of the spin—rotation interaction constant Cσ deduced from an absolute shielding scale based on a recent molecular beam determination of the 31P spin—rotation interaction tensor in PH3. In contrast to previous work the values of Cσ are in reasonable agreement with the values of Ceff, therefore offering evidence for the validity of Hubbard's relationship. Earlier discrepancies between Cσ and Ceff appear to be mainly due to poor estimates of the average correlation times, although effects of anisotropy appear to contribute slightly. The results of this paper offer evidence that the so-called microviscosity approach should be the favored method for estimating average reorientational correlation times in complex rigid molecules and correlation times for reorientation perpendicular to the symmetry axis in symmetric top molecules whenever direct quadrupolar or dielectric relaxation times are not available. The derived rotational diffusion tensors for PCl3, PBr3, and POCl3 are used to discuss a recent extension to Hubbard's isotropic spin—rotation equation which takes account of the anisotropic rotational motions in symmetric top molecules. In favorable circumstances this approach can be used to calculate the entire spin—rotation interaction tensor for a nucleus in a symmetric top molecule.

Proton Spin Relaxation and Molecular Motion in Liquid Thiophene

Proton spin relaxation and molecular motion in liquid thiophene are studied in the temperature range 300–550°K by measuring spin—lattice relaxation time, T1, and the coefficient of self-diffusion, D, using spin—echo technique. The value of T1 varies from 24.0 sec at 300°K to 72.0 sec at 550°K with a maximum of 94.0 sec at 490°K. The value of D varies from 2.4× 10−5cm2/sec at 300°K to 38.0× 10−5cm2/sec at 550°K. These results have been analyzed in terms of three relaxation mechanisms: inter and intramolecular dipolar interactions and spin—rotation interactions. The analysis shows that (i) the rotational diffusion constant perpendicular to the plane of the molecule varies from 0.21× 1011sec−1 at 300°K to 3.5× 1011sec−1 at 550°K and obeys an Arrhenius equation up to 500°K with an activation energy 3.2 kcal/mole, (ii) the value of the angular velocity correlation time varies from 1.4× 10−14sec at 300°K to 10.8× 10−14sec at 550°K. An estimate of the spin—rotation interaction constant gives 13TrC≲ 1.0 kHz. The reorientational motion is found to be diffusional up to about 480°K.

Molecular-Beam Magnetic Resonance Studies of HD andD2

The results of some recent molecular-beam magnetic resonance experiments on HD and ${\mathrm{D}}_{2}$ are reported. A discussion is given of the shifts and distortions of the separated oscillatory field resonance pattern produced by inhomogeneities in the external magnetic field and by the Bloch-Siegert effect. The sign of the electron-coupled spin-spin interaction constant in HD was remeasured to be positive. Its magnitude was determined to be 47(7) Hz. The spectrum of the $J=1$ state of ${\mathrm{D}}_{2}$ was observed for external fields less than 160 G, and the spin-rotation and second-rank tensor interaction constants were determined to be ${c}_{d}=+8.768(3)$ and $d=+25.2414(14)$ kHz. Using the calculated value ${d}_{M}^{\ensuremath{'}}=+2.737(1)$ kHz for the magnetic spin-spin interaction constant, the value of the electric quadrupole interaction constant was determined from the observed value $d$ to be $\frac{\mathrm{eqQ}}{h}=+225.044(24)$ kHz in the first rotational state of ${\mathrm{D}}_{2}$. Hyperfine transitions were observed for the first time in the second rotational state of ${\mathrm{D}}_{2}$. The hyperfine constants were determined from the transitions in the limit of zero external magnetic field to be ${c}_{d}=+8.723(20)$, ${d}_{M}^{\ensuremath{'}}=2.725(14)$, and $\frac{\mathrm{eqQ}}{h}=+223.38(18)$ kHz in the second rotational state. The effects of isotopic substitution and nuclear motion on the hyperfine constants in molecular hydrogen are discussed.

Second-order spin-orbit splitting in 2Δ states of diatomic molecules

The anomalous doublet splitting encountered in some nearly case (b) 2Δ states derived from the configuration σπ 2 has been investigated. Especially for the 2Δ states of GeH, GeD, SnH and SnD this anomaly manifests itself through a large and irregular isotopic shift in the spin-orbit coupling constant, a positive value of this constant and an unreasonably large value of the first-order spin-rotation interaction constant. Taking into account the interaction (second-order) with 2II states, it has been shown that the isotopic-shift anomaly can be removed, but not the anomaly with respect to the sign of the spin-orbit coupling constant. The interaction with 2II states also leads to some new terms which, especially for GeH and GeD, very likely outweigh the first- order spin-rotation interaction, rather like the situation for the spin splitting of the 2∑ states. For all the examples studied (SiH, SiD, GeH, GeD, SnH, SnD) the results show that the interaction must be due to an unobserved 2II state lying above the 2Δ state.

Determination of spin–rotation interaction constants in fluorinated methane molecules by means of nuclear spin relaxation measurements

The proton and fluorine spin relaxation time T1 has been measured in CH4, CF4, CHF3, and CH3F gases at low densities. By measuring the dependence of T1 on density near the characteristic T1 minimum, new information has been obtained on the spin–rotation interaction coupling constants in CF4, CHF3, and CH3F. The CH4 system was used to test the validity of this method since the spin–rotation coupling constants are accurately known for CH4. The correlation function for the spin–rotation interaction was found to be exponential within experimental error for all of the molecules studied. In the analysis of the experimental data, the effects of the dipolar interactions and of nuclear spin symmetry considerations were completely neglected. The validity of these approximations is discussed in the Appendix.

Nuclear magnetic relaxation by spin-rotation interaction.

Spin-rotation interaction constants, c, are calculated from the paramagnetic term of the nuclear magnetic shielding constant, σ p, using a relationship originally due to Ramsey. Calculated values show excellent agreement with experimental determinations from molecular beam measurements. Since σ p can be easily estimated from the chemical shift of the nuclear resonance this provides a general method for estimating spin-rotation interaction constants. Chemical shift anisotropies allow the components c ⊥ and c ‖ of the spin-rotation interaction tensor to be determined. Generally both components have the same sign and are of similar magnitude. The r.m.s. value of the spin-rotation interaction constant, required to calculate nuclear spin-lattice relaxation times, is not expected to differ appreciably from average values obtained from molecular beam measurements or magnetic shielding. Values for the molecular angular velocity correlation time, τ sr, calculated directly from nuclear spin-lattice relaxation times...

Electron resonance spectrum of gaseous SeO in its3Σ and1Δ states

The gas phase electron resonance spectrum of SeO in its 3Σ and 1Δ states has been studied. Values of the rotational constant B 0 and ‘spin-spin’ splitting parameter λ in the 3Σ state, previously determined from the ultraviolet spectrum, are shown to be consistent with the electron resonance results, and we are also able to estimate the spin-rotation interaction constant. In addition, the 3Σ spectrum shows 77Se hyperfine structure. The 1Δ spectrum yields values for the rotational constant (and hence bond length) and rotational g factor.

Anisotropic Molecular Reorientation in Methyl-d3-acetylene in the Liquid State

The temperature dependence of deuteron and proton spin–lattice relaxation times, T1, has been measured in methyl-d3-acetylene and methylacetylene-d1 using the adiabatic fast passage method. The difference in activation energies obtained from deuteron T1 data for acetylenic deuteron (Ea = 1.7 kcal/mole) and methyl-d3 deuterons (Ea = 1.1 kcal/mole) demonstrates that the reorientation is anisotropic without assumption of any model for reorientation. Assuming the validity of the rotational diffusion equation the deuteron T1's due to quadrupolar interactions were analyzed in terms of rotational diffusion constants D⊥ and D|. At −30°C D⊥ = 1.3 ± 0.15 × 1011sec−1 and D| = 18.3 ± 1.2 × 1011sec−1 in methyl-d3-acetylene. The applicability of the rotational diffusion mechanism for the description of the reorientation about the main symmetry axis is questionable as is shown by a comparison of τ| with the time for the mean period of rotation of a free rotor. At temperatures above the bp the spin–rotation interactions contribute to the relaxation rates of protons, in addition to dipolar interactions which are predominant at lower temperatures. The spin–rotation interaction constants were approximately estimated to be 0.6–4.0 kHz for the acetylenic proton in methyl-d3-acetylene and 6–25 kHz for the methyl group in methylacetylene-d1. The results indicate the importance of inertial effects.

The asymmetric rotor in electronic spectroscopy: Centrifugal distortion and electron spin coupling effects in the spectra of NH 2 and CH 2

Centrifugal distortion constants and three spin-rotation interaction constants of NH 2 , X¯ , 2 B 1 are derived from the data of Dressler and Ramsay. The values of the spin-rotation constants are e aa = − 0.292 ± 0.007 cm −1 , e bb = −0.054 ± 0.007 cm −1 , and e cc = −0.001 ± 0.007 cm −1 , showing an asymmetry effect in the spin splitting, and are in good agreement with those predicted by Dixon on the basis of a single electron configuration wave function. The energy levels of the a, 1 A 1 state of CH 2 calculated with revised parameters are used as evidence that the a, 1 A 1 state is perturbed by the X¯ , 3 g − state and an estimate of the separation is given.