Showing papers in "Molecular Physics in 1974"
TL;DR: In this paper, an ab initio gauge-invariant molecular orbital theory is developed for nuclear magnetic shielding, which is written as linear combinations of gauge invariant atomic orbitals, the wavefunctions in the presence of a uniform external magnetic field being determined by self-consistent field perturbation theory.
Abstract: An ab initio gauge-invariant molecular orbital theory is developed for nuclear magnetic shielding. The molecular orbitals are written as linear combinations of gauge-invariant atomic orbitals, the wavefunctions in the presence of a uniform external magnetic field being determined by self-consistent field perturbation theory. The final magnetic shielding result is broken up into contributions which can be related to various features of electronic structure. Calculated magnetic shielding constants are presented using three sets of atomic orbitals, all of which are taken as contracted gaussian-type functions. The first two sets are minimal and the third is slightly extended. All three levels of theory give good descriptions of shielding at first row and hydrogen atoms. Carbon and hydrogen chemical shifts calculated at the extended level are in excellent agreement with experimental values.
3,843 citations
TL;DR: In this paper, a simple level of ab initio molecular orbital theory with a split-valence shell basis with d-type polarization functions was used to predict equilibrium geometries for the ground and some low-lying excited states of AHn molecules and cations where A is carbon, nitrogen, oxygen or fluorine.
Abstract: A simple level of ab initio molecular orbital theory with a split-valence shell basis with d-type polarization functions (6–31G*) is used to predict equilibrium geometries for the ground and some low-lying excited states of AHn molecules and cations where A is carbon, nitrogen, oxygen or fluorine. The results are shown to be close to the limit for single determinant wave functions in cases where corresponding computations with more extensive bases are available. Comparison with experimental results also shows good agreement although a systematic underestimation of bond lengths up to 3 per cent is evident. For systems where no experimental data are available, the results provide predictions of equilibrium geometry.
1,964 citations
TL;DR: In this article, the chemical potential of hard-sphere fluids over the reduced density range 0·1⩽ σ 3 ρ ⩽ 0·8 was derived by means of Monte Carlo sampling.
Abstract: The ‘potential distribution’ expressions derived by Widom for the pressure and chemical potential of a fluid are developed for the special case of a hard-sphere fluid. The exact equations produced are closely related to those used in Scaled Particle Theory. They have been used to determine the chemical potential of hard-sphere fluids over the reduced density range 0·1 ⩽ σ 3 ρ ⩽ 0·8 by means of Monte Carlo sampling. The chemical potential so obtained is in excellent agreement with that found by integrating over pressure as a function of volume. It is found, however, that the chemical potential is considerably more dependent on the sample size than the pressure. The Monte Carlo results for the nearest-particle distribution around random points in the fluid are compared with the predictions of Scaled Particle Theory. The agreement is close, particularly at low densities. Two simple methods of Monte Carlo sampling of the grand canonical ensemble—an exact method and a more convenient, though inexact, modificat...
310 citations
TL;DR: In this article, the problem of defining the charge on an atom in a molecule is discussed, and a new approach is formulated in terms of electron density operators and projection operators, which are fundamental quantities in the general physical interpretation of quantum theory.
Abstract: Electron density operators and projection operators are fundamental quantities in the general physical interpretation of quantum theory In this series of papers the aim is to explore their relevance to the definition and use of chemical valence concepts Here, the problems involved in defining the charge on an atom in a molecule are discussed, and a new approach is formulated in terms of these operators The approach depends on the result that, if a projection operator P is formed representing some subspace of a molecular Hilbert space, then the probability of occupancy of that subspace is Tr DP, where D is an appropriate electron density operator In particular, the molecular one-electron Hilbert space is considered, and projection operators for atomic orbitals, atoms, pairs of atoms, atoms in threes, and so on, are found The above result allows for the definition of corresponding occupation numbers From these follow definitions of the charge on an atom in a molecule and of occupation numbers for elec
272 citations
TL;DR: A simple approximation based on asymptotic wavefunctions is used to calculate the splitting ΔV(R c) between the pair of adiabatic potential energy curves that arise from pseudo-crossing of ionic and covalent states of a diatomic molecule at a large internuclear distance R c as discussed by the authors.
Abstract: A simple approximation based on asymptotic wavefunctions is used to calculate the splitting ΔV(R c) between the pair of adiabatic potential energy curves that arise from pseudo-crossing of ionic and covalent states of a diatomic molecule at a large internuclear distance R c. In this approximation, ΔV(R c) is an exponentially decreasing function of R c and otherwise depends only on the ionization potential of the donor atom and the electron affinity and atomic radius of the acceptor atom. Results obtained for the H*(2s, 2p) + H(1s)→H+ + H- interaction are found to agree well with the ΔV(R c) derived from spectroscopic data for the B 1Σu + excited state of H2 and a variational calculation of Kolos and Wolniewicz. Results for the alkali hydride interactions, M + H→M+ + H-, agree well with estimates of ΔV(R c) derived from spectroscopic data for the A 1Σ+ excited states and a variational calculation of Brown and Shull. Results for the alkali halides agree well with photo-dissociation spectra and with collisio...
226 citations
TL;DR: In this paper, the authors computed the equation of state of a system of hard spherocylinders (cylinders with a hemisphere at each end), of length-to-breadth ratio equal to 3, in the isotropic liquid phase.
Abstract: Using the Monte Carlo method, we have computed the equation of state of a system of hard spherocylinders (cylinders with a hemisphere at each end), of length-to-breadth ratio equal to 3, in the isotropic liquid phase. We obtain a pressure slightly smaller than that predicted by the scaled-particle theory (SPT). The SPT predicts a liquid to nematic transition when the density is increased; we have observed that the isotropic liquid phase is stable up to densities significantly higher than the SPT transition density. Using the free-volume theory, we have also determined the behaviour of the pressure at very high densities, for any value of the length-to-breadth ratio γ. Moreover, we have shown that the packing fraction (number density times the volume of one spherocylinder) corresponding to the beginning of the fusion of the solid is an increasing function of γ.
226 citations
TL;DR: The X-ray photoelectron spectra of a variety of cobalt(II) and cobalt-III complexes have been investigated in this paper, showing that the 2p, 3s and 3p peaks of the high-spin cobalt (II) compounds are dominated by shake-up processes, whereas those of the 3s, 3p and 3s levels arise largely from multiplet splitting of the levels.
Abstract: The X-ray photoelectron spectra of a variety of cobalt(II) and cobalt(III) complexes have been investigated. Intense satellite lines were observed for the 2p, 3s and 3p peaks in the case of the high spin cobalt(II) compounds, but not for low spin cobalt(III) complexes. The satellites of the 2p levels are best explained as arising from shake-up processes, whereas those of the 3s and 3p levels are thought to arise largely from multiplet (exchange) splitting of the levels. Multiplet splitting of the 2p level is small and responsible for an increase in the doublet separation of the 2p1/2, 2p3/2 spin-orbit levels of the high spin cobalt(II) compounds. The chemical shifts for cobalt differ for the 2p, 3s and 3p levels of the high spin cobalt(II) compounds. Those of the 2p and 3p levels of diamagnetic cobalt(III) and low spin cobalt(II) complexes are equal. The difference in the case of the high spin cobalt(II) compounds is thought to be due to the presence of unpaired 3d electrons.
224 citations
TL;DR: In this paper, the ground-state rotational constants for all deutero isotopes of ethylene are predicted to what is considered to be better than 0·1 per cent reliability.
Abstract: The use of recently determined highly precise rotational constants for various isotopes of formaldehyde and ethylene enables the ground-state average structures to be determined to high accuracy. Harmonic corrections to the inertial constants are calculated using recently determined general harmonic force fields. In the case of formaldehyde, the data enable changes in all three structural parameters due to isotopic mass effects to be determined. For ethylene, only the change in CH bond length on deuteration is well characterized, due to the somewhat lower accuracy in the rotational constants. Using isotopic structural differences transferred from formaldehyde, and supported by calculations, ground-state rotational constants for all deutero isotopes of ethylene are predicted to what is considered to be better than 0·1 per cent reliability. The change in CH bond length on deuteration in ethylene is less than in formaldehyde. This is supported by calculations, although it appears also that the CH bond stretc...
204 citations
TL;DR: In this article, the level shifting technique of Saunders and Hillier is extended to allow guaranteed convergence of the restricted Hartree-Fock energy for many commonly found open-shell configurations.
Abstract: The ‘level-shifting’ technique of Saunders and Hillier is extended so as to allow guaranteed convergence of the restricted Hartree-Fock energy for many commonly found open-shell configurations. The proposed energy minimization scheme is compared with other procedures due to McWeeny, Roothaan and Segal. A test case calculation on the 2Σ+ ground state of boron oxide is described.
191 citations
TL;DR: In this paper, a theoretical study of the statistical mechanical description of systems composed of non-spherical convex molecules is made, where the averaged contact correlation function is introduced and approximate expressions for the averaged correlation functions are given in terms of the geometric functionals of hard convex bodies.
Abstract: A theoretical study of the statistical mechanical description of systems composed of non-spherical convex molecules is made. Thermodynamic functions of one-component and multicomponent systems of particles interacting via the pair potential of the Kihara core type are expressed by integrals over the minimum distance between two interacting convex bodies and three angles characterizing the convex body geometry. The approach is applied to the hard convex body system where the averaged contact correlation function is introduced. Exploiting ideas of the scaled particle theory the approximate expressions for the averaged correlation functions are given in terms of the geometric functionals of hard convex bodies.
159 citations
TL;DR: In this paper, computer simulation studies are reported for the Rowlinson and Ben-Naim and Stillinger models of water-water interactions, focusing on the effects of altering the size of the system and accounting for some long-range interactions by including the Onsager reaction field.
Abstract: Computer simulation studies are reported for the Rowlinson and Ben-Naim and Stillinger models of water-water interactions. Particular attention is given to the effects of altering the size of the system and to accounting for some long-range interactions by including the Onsager reaction field. It is shown that both models give a good qualitative account of the structure of liquid water but that neither is able to describe the high dielectric constant. A particularly sensitive property, the dipole-dipole correlation function, demonstrates the problems encountered in truncating the water interactions. Good agreement between the Rowlinson potential and a modified Hartree-Fock calculation suggests that the Rowlinson model is more accurate than the Ben-Naim and Stillinger form.
TL;DR: In this article, the triplet model of electron spin polarization in fluid media is evaluated, and explicit expressions are obtained in terms of the molecular parameters, the various rate constants, and the rotational correlation time.
Abstract: The triplet model of electron spin polarization in fluid media is evaluated. The model consists of an initial singlet molecule rotating in a static, externally applied magnetic field. Intersystem crossing into different zero-field states is represented by a rate matrix diagonal in the molecular frame, and this matrix is expressed as an effective spin operator. The triplet rotates, and the motion affects the polarization in the laboratory frame, and also causes spin relaxation in the triplet manifold. The triplet is chemically quenched, and the polarization appears in the doublet fragments. The model is treated in a density matrix formalism and on the basis of anisotropic rotational diffusion of the triplet molecule. Explicit expressions are obtained in terms of the molecular parameters, the various rate constants, and the rotational correlation time.
TL;DR: In this article, the free energy of dense fluids with permanent dipoles is computed through the Monte Carlo method with two types of intermolecular interaction: Stockmayer potential and hard-sphere potential with an added dipolar interaction.
Abstract: The free energy of dense fluids with permanent dipoles is computed through the Monte Carlo method with two types of intermolecular interaction: Stockmayer potential and hard-sphere potential with an added dipolar interaction. A comparison is made with the Pade representation recently proposed by Stell which is shown to be good. In the case of hard spheres with permanent dipoles we propose another equally successful perturbation theory, which is based on a partial resummation of the mixed perturbation theory first introduced by Lebowitz, Stell, and Baer. This perturbation theory is then applied to the general case of an interaction composed of a spherically symmetric two-body potential with permanent dipoles.
TL;DR: In this article, the effects of large amplitude bending for a bent triatomic molecule with those arising from the coupling of vibrational, electronic and spin angular momenta characteristic of linear molecules are given for a model hamiltonian.
Abstract: The theory is given for a model hamiltonian which combines the effects of large amplitude bending for a bent triatomic molecule with those arising from the coupling of vibrational, electronic and spin angular momenta characteristic of linear molecules. Two numerical examples are given for the application of the theory. (i) The vibronic and spin-orbit coupling between the A, 2 A 1 and [Xtilde], 2 B 1 states of PH2 is discussed in detail in terms of the 2Π u state of linear PH2 with which they correlate. The v 2 and K dependence of the doublet splitting in the A state is well represented in terms of a single spin coupling parameter for the 2Π u state. (ii) The calculations give a quantitative account of the inversion for high v 2 of the K = 0 and K = 1 levels of the bent B 2 component of the a, 3 A 2 state of CS2 arising from its correlation with a 3Δ2u state of linear CS2.
TL;DR: In this paper, a spin-restricted single-determinant molecular orbital wavefunctions for systems such as free radical ground states and lowest triplet states are described and compared with corresponding spin-unrestricted results.
Abstract: A procedure is described for the calculation of spin-restricted single-determinant molecular orbital wavefunctions for systems such as free radical ground states and lowest triplet states. It is a further development of ‘partitioning techniques’, which divide the available one-electron space (for a given basis) into three mutually orthogonal subspaces for doubly-occupied, singly-occupied and empty orbitals respectively. Necessary and sufficient conditions are derived for the calculated total energy to be stationary with respect to changes in these subspaces. These lead to an iterative procedure for the determination of self-consistent molecular orbitals. Some preliminary applications to hydrocarbon radicals are described and compared with corresponding spin-unrestricted results.
TL;DR: In this article, the Hartree-Fock-Roothaan SCF wavefunctions were used to calculate the force constants of ethane and acetylene using the following gaussian basis set: C : 7s,3p, H : 3s, CH midpoint : 1s, CC midpoint: 1s.
Abstract: The force constants of ethane and acetylene have been calculated from Hartree-Fock-Roothaan SCF wavefunctions by the force method, using the following gaussian basis set: C : 7s,3p, H : 3s, CH midpoint : 1s, CC midpoint : 1s, 1p. Agreement with experiment is good. It is important that all significant coupling constants agree in sign and magnitude with the experimental data. The assumptions of the hybrid orbital force field are shown to be in qualitative agreement with the ab initio results. The calculations confirm the experimentally observed large bend/bend interaction constants. Localized orbitals have been calculated at some distorted nuclear conformations of ethylene and a qualitative orbital following model is given which explains the signs of the significant coupling force constants. Molecular geometries have been determined by the force relaxation method. The results agree well with experiment.
TL;DR: In this article, the authors show that the major binding role in the first row of a first-row nucleus falls to the π orbitals, which have no radial node to inhibit a uniformly binding forward polarization.
Abstract: The charge migration that converts two overlapping spherical atoms into a bound molecule produces attractive Hellmann-Feynman fields at the two nuclear positions, offsetting the repulsive field that each nucleus encounters on penetrating inside the charge cloud of its neighbour. The magnitudes of these fields correlate positively with the molecular dissociation energies. The contribution of the σ valence orbitals to the field at a first-row nucleus varies regularly from binding in lithium to anti-binding in fluorine. The electrostatic effect of these orbitals is weakened by reversed polarization inside the 2s nodal sphere and is further opposed by a tiny but effective exchange polarization of the core. The major binding role in the first row thus falls to the π orbitals, which, like the σ orbital in hydrogen, have no radial node to inhibit a uniformly binding forward polarization. The net electrostatic interaction of two spherical atoms, derived with neglect of antisymmetry, is always binding. Especially ...
TL;DR: In this paper, the results of the phosphorescence microwave double resonance studies of the lowest excited triplet (T 1) states of acetophenone, benzaldehyde and their derivatives in various mixed crystals are presented and analyzed.
Abstract: The results of the phosphorescence microwave double resonance studies of the lowest excited triplet (T 1) states of acetophenone, benzaldehyde and their derivatives in various mixed crystals are presented and analysed. The zero field splittings (ZFS), the total decay rates and the relative radiative decay rates and populating rates were determined for a series of compounds in different host crystals. The correlations between ZFS, the decay rates and the energy separation between the 3nπ* and 3ππ* states were carefully examined and the results were explained in terms of the mixing of the 3nπ* and 3ππ* states. The mixing coefficients of the 3nπ* states in the T 1 states were estimated from the decay rates. Changes of the ZFS, decay rates, vibrational structures of the phosphorescence spectra of the 3ππ* aromatic carbonyl molecules were also analysed. The mechanisms responsible for the S 1 → T 1 and T 1 → S 0 processes of the 3ππ* states of these aromatic carbonyl molecules are discussed in view of the obtai...
TL;DR: In this article, the authors used microwave induced delayed phosphorescence (MIDP) experiments to study the populating and decay of the phosphorescent triplet state T 0 of seven aromatic three-ring molecules: anthracene, acridine, phenazine and phenazine.
Abstract: Microwave induced delayed phosphorescence (MIDP) experiments have been performed to study the populating and decay of the phosphorescent triplet state T 0 of seven aromatic three-ring molecules : anthracene (-h 10, -h 2d8, and -d10), acridine (-h9 and -d9) and phenazine (-h8 and -d8), all diluted in biphenyl crystals. We chose these molecules because the deactivation of T 0 goes dominantly via radiationless processes and the total decay rates of the individual spin components of T 0 determined in the experiment thus equal the radiationless decay rates. The phosphorescence emission, used as a monitor for the triplet state population, here gives an insignificant contribution to the decay. MIDP experiments only yield the true decay rates if thermal isolation between the levels is maintained throughout, and the present investigations, in which the intensity of excitation has been varied over a wide range, uncover a possible source of systematic error that has been overlooked thus far. The principal results of...
TL;DR: The photodimerization of anthracene sandwich pairs embedded in dianthracene single crystals has been studied by absorption and fluorescence spectroscopy over a wide range of temperature (6-295 K).
Abstract: The photodimerization of anthracene sandwich pairs embedded in dianthracene single crystals has been studied by absorption and fluorescence spectroscopy over a wide range of temperature (6–295 K). An excimer state has been found to be the intermediate state in the formation of the dianthracene. The fluorescence efficiency of the sandwich pair is unity at very low temperature while the quantum yield for the dimerization process is unity at high temperatures. The thermal activation energy for the photodimerization process has been determined directly as well as from temperature dependence measurements of the fluorescence intensity. The two methods yield 590 ± 25 cm-1 and 611 ± 20 cm-1 respectively for this energy. Corresponding measurements were also carried out with the perdeuterated anthracene sandwich dimer. These show a marked deuterium effect.
TL;DR: In this article, the authors applied Ewald's expansion to describe the properties of fused ions, anions and cations in terms of a velocity self-correlation function and their diffusion coefficients.
Abstract: A significant and characteristic difficulty arising in the use of statistical mechanics to describe the properties of fused salts is due to the extreme range of the electrostatic field; an accurate representation of the Coulomb energy and Coulomb forces may be obtained using Ewald's expansion. Such calculations are tested here on the model case of liquid NaCl at different temperatures. In addition, this method is applied to the description of ionic media by molecular dynamics computations. (A Born-Huggins-Mayer pair potential is used with constants derived from the solid at 298 K.) This treatment introduces cut-off distances and periodic boundary conditions. The influence of these constraints on the conservation of energy and momenta is investigated. Thermodynamic properties of molten NaCl at 1164·5, 1224·5 and 1340·5 K are calculated. The motions of individual ions, anions and cations are described in terms of a velocity self-correlation function and their diffusion coefficients are determined.
TL;DR: In this paper, the He(I) photoelectron spectra of the isoelectronic series Fe(CO)2(NO)2, Co( CO)3NO and Ni(CO4) were reported and interpreted by means of ab initio SCF-MO calculations.
Abstract: The He(I) photoelectron spectra of the isoelectronic series Fe(CO)2(NO)2, Co(CO)3NO and Ni(CO)4 are reported and interpreted by means of ab initio SCF-MO calculations. For the nitrosyl complexes it is found that ionization potentials calculated assuming Koopmans' theorem are seriously in error due to the considerably greater orbital relaxation accompanying ionization from metal than from NO valence orbitals. When such allowance is made for orbital relaxation by performing restricted Hartree-Fock (RHF) calculations on the ionic states, the experimental spectra are accurately reproduced and the observed similarity of the spectra of all three molecules is explained.
TL;DR: In this paper, the authors have shown that the large majority of guest molecules occur in two orientations and that the 65 cm-1 doublet separation is related to the occurrence of these two orientation, and the hyperfine structure is obtained for the two inplane canonical orientations of the magnetic field and also when the field bisects the angle between these two directions.
Abstract: E.S.R. experiments have been performed on the lowest triplet state of free base porphin (H2P) in a n-octane single crystal at 1·3 K. The results demonstrate that the large majority of guest molecules occur in two orientations. While the molecules in these two orientations are coplanar, they have their N-H H-N axes at right angles. The fine structure results show that the two molecular orientations have zero-field splittings that differ by a few per cent in magnitude. Further, the 65 cm-1 doublet separation which appears in the fluorescence spectrum of H2P is related to the occurrence of these two orientations. Resolved hyperfine structure is obtained for the two in-plane canonical orientations of the magnetic field and also when the field bisects the angle between these two directions. From an analysis of the fine structure and hyperfine structure results it is established that the zero-field splitting pattern is described by the parameters (average over the two orientations) the x axis is taken along the...
TL;DR: The first spectroscopic observation of bound N2-Ar van der Waals molecules has been achieved with a cryogenic long path cell maintained at 87 K as discussed by the authors, where the infra-red spectrum exhibits prominent fine structure near the N2 stretching frequency which is assigned to hindered internal rotation of N2 within the weakly bound complex.
Abstract: The first spectroscopic observation of bound N2-Ar van der Waals molecules has been achieved with a cryogenic long path cell maintained at 87 K. The infra-red spectrum exhibits prominent fine structure near the N2 stretching frequency which is assigned to hindered internal rotation of N2 within the weakly bound complex. An analysis of this fine structure yields a T-shaped equilibrium geometry in which the N2 bond axis is perpendicular to the N2-Ar van der Waals bond axis. The observed spectrum is shown to be consistent with an internal rotational barrier of 20 cm-1 (57 cal/mole). Approximately 20 per cent of the bound species are trapped by this rotational barrier and acquire a locked semi-rigid structure. The remaining 80 per cent have ill-defined geometry and undergo hindered internal rotation. The rotational envelope of an infra-red fundamental is analysed to give an estimate of the N2-Ar bond length as 3·9 A.
TL;DR: In this article, the pole strengths of the Green's functions were used to explain the relative intensities of satellite lines in the photoelectron spectra, which arise due to excitations accompanying photoionization.
Abstract: The method of Green's one-particle functions is used to explain excitations with simultaneous ionization in atoms and molecules. The relative intensities of satellite lines in the photoelectron spectra, which arise due to excitations accompanying photoionization, are found to be simply related to the pole strengths of the Green's functions. For the water molecule many such satellite lines are calculated to be in the region of 25–80 eV binding energy.
TL;DR: In this paper, a general molecular orbital method using a modified INDO scheme is given for systems involving first row elements and first row transitional elements, and the new hamiltonian matrix elements and the appropriate parameterizations are given together with results for a number of test cases.
Abstract: A general molecular orbital method using a modified INDO scheme is given for systems involving first row elements and first row transitional elements. The new hamiltonian matrix elements and the appropriate parameterizations are given together with results for a number of test cases. The splitting of the different spin terms arising from a given orbital configuration is satisfactorily accounted for and the energy differences involved agree well with spectroscopic data.
TL;DR: Perturbation theory for the angular pair correlation function g(r12 ω 1 ω 2), using a fluid with isotropic intermolecular forces as the reference system, is applied to the calculation of a variety of macroscopic properties as mentioned in this paper.
Abstract: Perturbation theory for the angular pair correlation function g(r12 ω 1 ω 2), using a fluid with isotropic intermolecular forces as the reference system, is applied to the calculation of a variety of macroscopic properties Comparisons with experiment are made for methane, oxygen and nitrogen (and carbon monoxide for infra-red and Raman band moments) in the dense fluid and liquid states Theoretical expressions are given and calculations made for thermodynamic properties (isothermal compressibility, pressure, configurational energy, entropy and specific heat) both along and away from the vapour-liquid co-existence curve, for infra-red and Raman band moments, and for neutron scattering cross sections Excellent agreement with experiment is obtained for all properties, except for the infra-red and Raman band moments; this latter comparison is inconclusive because of large experimental uncertainties The anisotropic intermolecular forces are found to have very little effect on the liquid isothermal compressi
TL;DR: In this paper, the angular dependence of the electron resonance spectrum of a spin probe dissolved in a smectic A mesophase was analyzed to obtain the angular variation of the linewidth coefficients.
Abstract: This paper reports the angular dependence of the electron resonance spectrum of a spin probe dissolved in a smectic A mesophase. The spectra were analysed to obtain the angular variation of the linewidth coefficients and hence the angular linewidth coefficients. These angular coefficients -may be interpreted by employing a theory of spin relaxation based on the strong collision model for molecular reorientation. Such an analysis yields values for the correlation times for reorientation about the long and short axes of the spin probe as well as the magnitude of the solute order parameter p4. The possibility of interpreting the angular linewidth coefficients in terms of a theory based on the diffusion model for molecular reorientation is also explored. Relatively straightforward expressions for these coefficients can only be obtained from the diffusion model when the orientational order is hrgh, as it is in a smectic phase. The analysis of the angular linewidth coefficients then provides values for the components of the diffusion tensor parallel and perpendicular to the long axis of the spin probe. The large anisotropy in the diffusion tensor may be indicative of the unhindered molecular motion about the long axis. Both models of molecular reorientation in a highly ordered system appear to provide a satisfactory account of the observed angular linewidth coefficients.
TL;DR: In this article, the problem of calculating thermodynamic functions of solvation and hydrophobic interaction of non-polar molecules in water is considered, and the functions of switched off interaction which allow one to compare calculated and experimental data are introduced and discussed.
Abstract: The problem of calculating thermodynamic functions of solvation and hydrophobic interaction of non-polar molecules in water is considered, and the functions of ‘switched off’ interaction which allow one to compare calculated and experimental data are introduced and discussed. Expressions for the free energies, entropies and internal energies of solvation and hydrophobic interaction are deduced by statistical mechanics, and the possibility of computing these quantities from information about interatomic potential functions is considered. An application of the Monte Carlo method with the Boltzmann transition probabilities between the states of a Markov chain has allowed us to evaluate configuration integrals and thermodynamic functions of solvation and hydrophobic interaction. For solvation, the calculated values are in good agreement with the experimental data if the periodic boundary conditions are observed, and in moderate agreement should these be neglected. For hydrophobic interaction, the plot of F HI...
TL;DR: In this paper, a perturbation expression for the angular pair correlation function g (2, r 12, ω1, r ω2) is derived for systems interacting via non central potentials based on the method developed by Gubbins and Gray [1].
Abstract: A perturbation expression for the angular pair correlation function g (2)(r 12, ω1, ω2) is derived for systems interacting via non central potentials based on the method developed by Gubbins and Gray [1]. The method uses the ‘correct’ (in the sense of Rushbrooke [3] and Cook and Rowlinson [4]) angle-averaged potential as the reference system about which the perturbation is made. A preliminary comparison between the original Gubbins-Gray expression for g (2)(r 12, ω1, ω2) and the present expression is made for a system of two-dimensional point dipoles.