Van Vleck Equation Research Articles

The positions of the hydrogen atoms in datolite as determined by nuclear magnetic resonance

The crystal structure of datolite, CaBSiO4(OH), was determined by Ito & Mori (1953) and Pavlov & Belov (1960), and was refined by Pant & Cruickshank (1967). Sahl (1966) suggested the probable position of the hydrogen atoms on the basis of the infrared pleochroism of the OH stretchingfrequencies in datolite. The present study has been made to determine the position of hydrogen atoms by proton magnetic resonance by referring to Pant & Cruickshank's result. The space group of datolite is P2t/c with the cell dimensions a = 4.84+0.005, b=7 .60+0.01 , c=9.62+0.01 A and B = 90 ° 9'. There are four formula units in the cell. Hydrogen atoms are bound to the hydroxyl oxygen atoms O(1), O(2), O(3), and O/,4) in Fig. 1 which shows the crystal structure projected along [100] according to Pant & Cruickshank's result. A single crystal of natural datolite having the be, ca, and ab faces was used for the measurements. The crystal was fixed to a Teflon rod of 15 cm in length which was set on a goniometer head. The crystal orientation was adjusted to the desired directions within + 1% The proton magnetic resonance spectra were recorded at room temperature at 15 ° intervals of rotation about the a*, b*, and c* axes from 0 to 180 °, using a JEOLCO JNM-W-30 spectrometer operated at 30 MHz. The absorption lines observed in a* and c* axis rotations are all single and nearly Gaussian in shape, while those in b* axis rotation split into a broad doublet. The theoretical values of the second moments were calculated on the basis of van Vleck's equation taking account of proton-proton and proton-boron interactions (Abragam, 1961). Boron has two isotopes I~B and I°B with natural abundance 80.4 and 19.6% respectively (Newton, Tyrrell & Sanders, 1959). The second moment for the proton-boron interactions was estimated by assuming a weighted average of the contributions from these isotopes. The second moments were calculated for an arrangement of hydrogen atoms located on a sphere of radius 0.97 A around the oxygen atom of the hydroxyl ion. If the space group is P21/c including the hydrogen atoms, the latter occupy the fourfold general positions. The cut-off radius in the calculations was taken to be 4.7 .&. The contributions from spins beyond this radius were found to be negligible. Thus, the position of the hydrogen atoms was first determined such that the calculated angular dependence of the second moment fitted the observed value for rotation of the crystal about the c* and a* axes. The same fitting was then repeated for rotations about the two axes, with the O H distance as the new parameter. Fig. 2 shows the comparison between the calculated and observed angular dependences, where the calculated curves are those corresponding to the best fit which was obtained from more than forty possible arrangements. The fractional coordinates of the hydrogen atom and the O H distance thus determined were given as x=0-829_+0.003, y=0 .552+0.006 , z=0.584+0-015 for H(1), and 0.970+ 0.001 A for O(1)-H(I). The starting value of O(,I)-H(I) was 0.97 /~,, which was assumed on the basis of X-ray results (Zachariasen, 1954: Zachariasen & Plettinger, 1963). However, the final value of this distance did not differ substantially from the initial one. Sahl (1966) showed from the measurement of the infrared pleochroism of the OH stretching-frequency (2=2.85,u), that the O(2)-H(2) dipole makes an angle of about 30-35 with the e axis, with the angle B(2)-O(2)-H(2), about 106t These angles agree with the corresponding values of 31.5+ 1% and 116+4 ' obtained from our n.m.r, results. The positions of hydrogen atoms shown in Fig. 1 are reasonable from an electrostatic point of view. H(1) interacts attractively with 0(5) and O(6), while it interacts repulsively with Ca(l), Ca(2), B(i) and H(2). These positions are also reasonable in view of the law of electroneutrality.

The low temperature magnetic susceptibility of (4-nitroquinoline N-oxide)copper(II) chloride

The magnetic susceptibility of Cu(4-nitroquinoline N-oxide)Cl 2 was measured in the temperature range 4.2–37.5°K in an attempt to ascertain the presence and nature of magnetic interactions, if any, in the compond. The data can be fitted to the Van Vleck equation for ecxhange coupled copper ions in a bimetallic complex with ⪡g>=2.2 and 2J=135 cm −1, but the data do not unambiguously denote the nature of the magnetism. It is suggested that appropriate structural data be collected before definite conclusions concerning the magnetic state-of-affairs be put forth.

Out-of-plane interactions in dichlorobis(2-methylpyridine)- copper(II) and dibromobis(2-methylpyridine)copper(II)

The magnetic susceptibilities of dichlorobis(2-methylpyridine)copper(II) and dibromobis(2-methylpyridine)copper(II) have been measured in the temperature range 4.2–300°K. The data for both compounds obey the Van Vleck equation for ecxhange coupled copper ions with the singlet-triplet separation being 5 cm −1 for the bromo-complex and 7.4 cm −1 for the chloro-complex. The singlet state is the ground state in both cases.

Microwave Measurements of the Dipole Moments of CFCl3 and CHCl3 and Their Pressure-Broadened Spectra

The Stark effect in the J = 2 → 3 transition was analyzed to obtain the values 1.04 ± 0.02 and 0.46 ± 0.02 D for the dipole moments of CHCl3 and CFCl3 respectively. Taking into account Stark and quadrupole interactions and using an approximation to the Van Vleck and Weisskopf pressure-broadening equation, pressure-broadened spectra for the J = 2 → 3 transition were computed for both molecules and compared with measured spectra. The results show the great effect pressure broadening can have on the general appearance of a spectrum.

Magnetic characteristics of CeAl 3, and CeAl 4

The magnetic properties of hexagonal CeAl 3 and orthorhombic CeAl 4 between 2.2 and 300°K are reported and discussed in detail. Both of these compounds exhibited deviations from Curie-Weiss behavior at low temperatures. These deviations are attributed to a combination of crystal field and exchange interactions. Detailed crystal field calculations are presented for CeAl 3 which indicate an overall splitting of 280°K. These calculations take into account the compressed nature of the hexagonal lattice in CeAl 3, a feature which introduces a second order term into the crystalline potential. Using this model and making suitable allowances for exchange interactions, it is possible to compute the susceptibility from Van Vleck's equation. The computed and experimental curves agree within 1 per cent over the entire temperature range. Detailed calculations for CeAl 4 are not possible at present because of uncertainties in the crystal symmetry; however, the saturation moment of this compound can be attributed to a large crystal field interaction which leaves only the low lying Kramer's appreciably populated below the transition temperature.

Anomalous behaviour at the 6 A 1 -2 T 2 crossover in iron (III) complexes

Transition metal complexes with configurations d 4 , d 5 , d 6 and d 7 are of two types—high-spin and low-spin— depending on the strength of the ligand field. Ligand field theory predicts that truly octahedral complexes ML 6 could exist in which both types are in thermal equilibrium at ordinary temperatures, but no completely unambiguous examples of this 6 crossover ’ situation have yet been put forward. The magnetic and spectral properties associated with nearly equi-energetic high- and lowspin states should be singularly sensitive to temperature, pressure, and minor chemical modifications of the ligating molecules. These matters are discussed in detail, for the configuration d 5 , with particular emphasis on the variation of total molecular energy with change in metal-ligand separation, and on a necessary inequality, namely ∆ (high-spin) < π < ∆ (low spin) (∆ == ligand field strength, π = mean pairing energy). Experimental data for certain FeS 6 -type com pounds, viz. iron (III) N-N -dialkylditliiocarbamates, are then reported, which reproduce qualitatively all the requirements so formulated. The reciprocal magnetic susceptibility passes through a maximum and then a minimum with increasing temperatures and also increases sharply with applied pressure; the electronic spectrum is temperature dependent; and different alkyl substituents in the ligand drastically affect the magnetism. The values of ∆ and π, as obtained from independent evidence, conform with the inequalities previously mentioned. The temperature dependence of the magnetism does not exactly conform with the predictions of the conventional van Vleck equation, but is considered to be tractable when vibrational partition functions are introduced into this equation. The pressure dependence of the magnetism leads to an estimate of the difference in molar volume of the two states, from which it is concluded that the Fe-S distances differ by about 0.07 Å, that in the low-spin state being the shorter.

NMR of a Glycine Single Crystal

The NMR absorption of a glycine single crystal was observed at 77° and 293°K for various orientations of the sample in the external magnetic field. On the basis of theoretical second moments computed from Van Vleck's equation it is concluded that the NH3+ group is a regular tetrahedron whose axis lies along the C–N bond. The N–H bond distance was determined to be 1.077±0.01 A. It is concluded from the agreement between the computed and observed angular dependence of the second moments that the proposed model is correct.

Λ-Type Doubling and Electron Configurations in Diatomic Molecules

Van Vleck's equations for $\ensuremath{\Lambda}$-type and spin doubling in $^{1}\ensuremath{\Pi}$, $^{2}\ensuremath{\Sigma}$, and $^{2}\ensuremath{\Pi}$ states are restated in convenient form for application to empirical data, explicit equations being given for each component separately in a $\ensuremath{\Lambda}$-type or spin doublet. The equations have been applied to a wide variety of data on many molecules, including data on $^{2}\ensuremath{\Pi}$ states corresponding to numerous intermediate coupling cases between $a$ and $b$, and have been found to fit excellently (cf. Figs. 1-4). Incidentally this has made possible a revision of the hitherto doubtful assignment of $J$ values for the ${Q}_{2}$ lines in the $^{2}\ensuremath{\Pi}$, $^{2}\ensuremath{\Sigma}$ bands of CaH, and has permitted identification of the $^{S}R$ branch. Empirical values of the coefficients in Van Vleck's equations have been obtained for many molecules, and are given in Tables I and II.From the observed values of these constants further confirmation of Van Vleck's theoretical results is obtained. In most of the molecules examined a $\ensuremath{\Pi}$ and a $\ensuremath{\Sigma}$ state are found which stand to each other in the relation called "pure precession" by Van Vleck, or something similar; that is, the $\ensuremath{\Pi}$ and the $\ensuremath{\Sigma}$ state act as if they had electron configurations essentially alike in all respects except that one electron has $\ensuremath{\lambda}=0$ in the $\ensuremath{\Sigma}$ state but $\ensuremath{\lambda}=1$ in the $\ensuremath{\Pi}$ state, or vice versa. The existence of such relations strongly indicates that the $n$ and $l$ values previously assigned to outer electrons in hydrides have almost the same well-defined significance as they would in an atom formed by uniting the H nucleus with the heavier nucleus. For example, in the normal ($^{2}\ensuremath{\Sigma}$) and first excited ($^{2}\ensuremath{\Pi}$) state of CdH, with configurations... $5s{\ensuremath{\sigma}}^{2}5p\ensuremath{\sigma}$ and... $5s{\ensuremath{\sigma}}^{2}5p\ensuremath{\pi}$, the present evidence shows that the last electron really behaves like a $5p$ atomic electron, even though the normal ($^{2}\ensuremath{\Sigma}$) state is formed with a small energy of formation from a normal Cd atom (... $5{s}^{2},^{1}S$) and a normal H atom ($1s,^{2}S$). Another type of case, in which a close similarity of the electron orbits to two separate atoms is evident, is one which is found in ${\mathrm{He}}_{2}$, ${\mathrm{Li}}_{2}$, and ${\mathrm{Na}}_{2}$. In ${\mathrm{He}}_{2}$ the $1s{\ensuremath{\sigma}}^{2}2p\ensuremath{\sigma}3p\ensuremath{\sigma}$, $^{3}{\ensuremath{\Sigma}}_{g}^{+}$ and the $1s{\ensuremath{\sigma}}^{2}2p\ensuremath{\sigma}2p\ensuremath{\pi}$, $^{3}\ensuremath{\Pi}_{g}$ states act as if the relation of pure precession were fulfilled. This is presumably because the $3p\ensuremath{\sigma}$ election acts essentially like $2p\ensuremath{\sigma}$, the $3p\ensuremath{\sigma}$ and $2p\ensuremath{\pi}$ both becoming $2p$ on dissociation of the molecule.---In the CaH molecule an interesting complicated case, earlier discussed by Watson, occurs in which strong $l$-uncoupling and spin uncoupling occur simultaneously in a $^{2}\ensuremath{\Pi}$ state. The theory accounts well for the observed relations in this case (Figs. 2, 3, 4).

The pendulum problem in the wave mechanics

The intermolecular contribution to the second moment of a dipolar broadened NMR absorption line of a crystalline solid is corrected for molecular vibrations by expressing it in terms of anisotropic vibration tensors of the atoms and libration tensors of the molecules involved.The expressions derived are based on an expansion of the spatial factor in Van Vleck's equation, (3 cos2θ − 1)/r3, in a power series of atomic displacements up to and including its quadratic term. These expressions are valid approximately for any molecule of which the average motion can be described in terms of the crystallographic rigid body motion formalism and are subject to the assumption of uncorrelated molecular motion. The latter assumption is examined by an application of a model of fully correlated motion.Isotropic and anisotropic vibrations in single-crystal and polycrystalline specimens are accounted for by the theoretical results derived. A comparison is presented with experimental second moments of some polycrystalline samples.This is the first treatment of the effect of anisotropic molecular vibrations on the NMR second moment.