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Notes: Ferro- and antiferromagnetic molecular crystals are in several ways quite distinct from the conventional metallic alloys or oxidic crystals studied in solid state physics. The exchange coupling constants are usually very small for crystals of free radical molecules. Some molecular crystals show a typical magnetic behavior at a very low temperature range and another kind of behavior at a higher temperature. This feature cannot be quantitatively explained by using the conventional Ising model of ferromagnetic (FM) and antiferromagnetic (AFM) materials. In this work we show that a magnon-based approach is capable of explaining the observed AFM→FM and FM→AFM transitions in crystals of free radical molecules in a natural manner. A three-dimensional lattice is, in general, anisotropic in magnetic properties. For instance, in a molecular crystal, FM interactions may be observed along a particular direction while AFM interactions dominate along the others. Also, the coupling constants can vary widely along the three crystal axes. We have classified ferro- and antiferromagnetic molecular crystals into four distinct types, viz., FFF, AFF, AAF, and AAA, for orthorhombic or higher crystal symmetries. The anisotropic Heisenberg spin Hamiltonian operators for these four systems have been expressed in terms of magnon variables. The magnon dispersion relations have been determined, and by using these relationships the magnon population has been calculated for the low temperature range as well as for the medium and high temperature ranges. These calculations rely on the choice of the population distribution function. The low temperature calculation involves the Planck distribution. Since the magnon–magnon interaction increases very rapidly above the Neél temperature, we have made use of the classical limit, that is, a Boltzmann distribution for each spin site, and the zeroth-order one-magnon energy to calculate the magnon population at higher temperature ranges. All these calculations are based on the consideration of a macroscopically large crystal of a specific shape, and the validity of the results rests on the assumption that the bulk magnetic properties remain unchanged for a macroscopically large crystal of any other shape. Then we have derived expressions for the overall magnetization in macroscopically large crystals of the four types in the two temperature ranges, and the corresponding magnetic susceptibilities (χ). In doing so, we have made use of a typical Weiss molecular field in each case. The resulting expressions are general enough, that is, they are for an anisotropic crystal and remain valid in wide ranges of temperature. They also agree with available experimental data. The FFF and the AAA systems do not exhibit any unusual trend. As T→0, the FFF system attains saturation whereas the AFF, AAF, and AAA systems all show an approximate T2 dependence of χ(parallel). At a sufficiently high temperature, all four types exhibit bulk paramagnetism that follow the Curie–Weiss-type law. The FFF susceptibility develops a characteristic (T−TC)−1 dependence on temperature whereas the antiferromagnetic systems have susceptibilities proportional to (T+TN)−1 where TC and TN are the Curie–Weiss point and the Neél temperatures, respectively. Expressions derived in this work can easily explain an AFM→FM transition occurring in the AFF and AAF molecular crystals at a very low temperature. The low temperature antiferromagnetic susceptibility is singular at a temperature T0 that is sufficiently small and usually varies within 0–5 K. The low temperature expression holds up to a fraction of a degree below T0. The singularity indicates that the high temperature expression becomes valid at a temperature slightly above T0. The high temperature susceptibility is basically ferromagnetic in nature, thereby explaining the AFM→FM transition that should occur at a temperature around the singular point. At least one AAF substance, phenyl-substituted triphenyl verdazyl, shows a FM→AFM transition at about 100 K. This phenomenon, which has not been explained heretofore, can be accounted for if we include the possibility of a temperature-dependent ferromagnetic Weiss constant of the form γ(T)=γ0 exp[−T/T*]. The critical temperature T* is usually very large so that γ normally appears to be independent of temperature, but it can be of the order of one hundred degrees Kelvin when stereo–electronic effects cause a lateral displacement in the stacking of the free radical monomers along the FM direction. A concise account of the limitation of the theory has been given in the form of concluding remarks. © 1999 American Institute of Physics.

Notes: A detailed theoretical treatment of the effect of a homogeneous external magnetic field on a general molecule is carried out in this work at the nonrelativistic level. The Hamiltonian considered here is, although nonrelativistic, explicitly spin-adapted through order v2/c2. The effects of the anomalous magnetic moment of each particle, hyperfine interactions and spin–orbit interactions have been systematically included in it. This Hamiltonian is reexpressed in a preferred set of coordinates so as to facilitate the removal of the center of mass motion by exploiting the properties of the total pseudomomentum. The reduced Hamiltonian operator at zero total pseudomomentum represents the dynamics of the electrons and the nuclei belonging to a neutral molecule in relative coordinates. The same operator can be separated as a sum of the electronic Hamiltonian, the nuclear Hamiltonian, and the electronic–nuclear coupling. The effect of a strong magnetic field on molecular vibration and rotation is then described for a general diatomic molecule. The interelectronic and the electron–nuclear kinetic coupling terms are obviously responsible for the known phenomenal increase in the bond dissociation energy at a strong magnetic field under the Born–Oppenheimer approximation. The case of nuclear spin isomerism has been discussed in the specific context of ortho and para hydrogen. This leads to a prediction of the critical field strength beyond which ortho hydrogen may be formed as the major product even at an extremely low temperature. The basic tenets of the adiabatic approximation are examined, and the influence of the electronic–nuclear kinetic coupling on the evaluation of the vibronic interaction parameters is discussed in an Appendix. © 2001 American Institute of Physics.

Notes: Relativistic dynamics of two spin-1/2 particles in an external, homogeneous magnetic field is investigated here. The problem is important for a preliminary understanding of the effect of magnetic field on atoms and molecules at the relativistic level. The relativistic Hamiltonian is formulated in three distinct forms which involve the Bethe–Salpeter interaction, generalized Breit interaction and projected Breit interaction. The total pseudomomentum of the two-particle system is conserved in each case, and its components are distinct in the zero-charge sector. This permits the separation of the center of mass motion from the Hamiltonian of the neutral two-particle system. The resulting Hamiltonian operator describes the movement of the two particles in relative coordinates. It is further simplified by using suitable unitary transformations so as to reduce the one-particle operator for the first particle into a diagonal form. The effective equation of motion for the movement of the second particle in relative coordinates is then identified. A second set of transformations convert the two-particle relative Hamiltonian into a form where the one-particle operator for each spin-1/2 particle is completely diagonalized and separable into positive and negative energy states. The correspondingly transformed interaction operators can be written in an order by order expansion from which the odd terms are removable by using suitable Foldy–Wouthuysen type transformations in a systematic way. The resulting Hamiltonian operator reduces to previously known expressions when the magnetic field is switched off. Thus the two sets of transformations which convert the one particle parts completely into separable as well as diagonal forms also transform the interaction operator to generate terms consistently through order v2/c2. The field dependence lies entirely in the diagonalized one-particle parts, which is a consequence of the initial choice of interaction operators. Our results also include expressions corresponding to the interaction operator being projected. The Bethe–Salpeter and projected Breit cases lead to the same interaction operators for a hydrogen atom in the nonrelativistic limit. In the same limit the methodology directly yields the anomalous Zeeman interaction term, some correction to it, and terms which can account for nuclear magnetic resonance. All these terms are embedded in the final two-particle Hamiltonian operator. These, along with the previously known, field-independent, terms which describe the hyperfine interactions, can account for electronic and magnetic resonance spectroscopies on the basis of the same Hamiltonian. © 2001 American Institute of Physics.

Notes: The stepwise acid dissociation constants for p-benzohydroquinone (QH2) in aqueous media have been explicitly calculated for the first time, with the INDO parametrized SCF-MO method. We have optimized the geometries of QH2, QH-, and Q2- and of the QH2 · 6H2O, QH- · (H3O+) · 5H2O, and Q2- · (H3O+)2 · 4H2O systems that model the solvated species. The presence of the associated water molecules (and hydronium ions) account for the stabilization due to hydrogen bonding as well as for a part of the effect of interaction of these molecules with the respective reaction fields in an aqueous medium. To simulate the first solvation shell in a more complete manner, four more water molecules have been considered to be placed above and below the quinonoid ring and the optimized geometries of the resulting hydrated species, QH2 · 10H2O, QH- · (H3O+) · 9H2O, and QH- · (H3O+) · 8H2O, have been determined. The standard free-energy changes calculated for the dissociation of QH2 into QH- and H+ is 0.0251 Hartree (65.9 kJ mol-1) and that of QH- into Q2- and H+ is 0.0285 Hartree (74.8 kJ mol-1). Experimentally observed dissociation constants for these two steps correspond to free-energy changes of 0.0214 Hartree (56.2 kJ mol-1) and 0.0248 Hartree (65.1 kJ mol-1), respectively. © 1995 John Wiley & Sons, Inc.

Notes: Relativistic basis sets for first-row atoms have been constructed by using the near-Hartree-Fock (nonrelativistic) eigenvectors calculated by Partridge. These bases generate results of near-Dirac-Hartree-Fock quality. Relativistic total and orbital energies, relativistic corrections to the total energy, and magnetic interaction energies for the first-row atoms have been presented. The smallest Gaussian expansions (13s8 p expansions) yield Dirac-Hartree-Fock total energies accurate through six significant digits, while the largest expansions (18s13p expansions) give these energies accurate through seven significant digits. These results are more accurate than some of the results reported earlier, particularly for the open-shell atoms, indicating that the basis employed is reasonably economical for relativistic calculations. © 1995 John Wiley & Sons, Inc.