Showing papers in "Journal of Chemical Physics in 1977"

Hyperpolarizabilities of the nitroanilines and their relations to the excited state dipole moment

Abstract: We have measured the second and third order hyperpolarizabilities of the three nitroaniline isomers and of two related molecules. For some isomers the intramolecular charge transfer is found to cause a very large enhancement of the second order polarizabilities. We present a theory relating this contribution to the first excited state of energy, oscillator strength, and dipole moment of the molecules. Experimental results are accounted for with an excellent accuracy.

Gaussian basis sets for molecular calculations. The representation of 3d orbitals in transition‐metal atoms

Abstract: Augmented (4d) and (5d) Gaussian basis sets are presented which provide a balanced description of the 4s23dn−2, 4s3dn−1, and 3dn configurations of transition−metal atoms. When compared to accurate Hartree–Fock calculations, the (4d) and (5d) expansions in the literature, which have been optimized for the 4s23dn−2 configuration, can lead to errors of several eV for states of the latter configurations where the 3d orbitals become more diffuse. The augmented sets reported here consist of a single diffuse basis function added to the original sets, where the orbital exponent of the added function was optimized for the 3dn configuration. Basis sets and contraction schemes are presented for the atoms Sc through Cu.

Critical point wetting

Abstract: It is shown that in any two‐phase mixture of fluids near their critical point, contact angles against any third phase become zero in that one of the critical phases completely wets the third phase and excludes contact with the other critical phase. A surface layer of the wetting phase continues to exist under a range of conditions when this phase is no longer stable as a bulk. At some temperature below the critical, this perfect wetting terminates in what is described as a first‐order transition of the surface. This surface first‐order transition may exhibit its own critical point. The theory is qualitatively in agreement with observations.

Optical nonlinearities of conjugated molecules. Stilbene derivatives and highly polar aromatic compounds

Abstract: We have investigated the influence of donor and acceptor substituents on the second and third order hyperpolarizabilities β and γ of large conjugated molecules such as stilbene and styrene derivatives. This was performed by two independent measurements of β and γ using the techniques of dc electric‐field induced second‐harmonic generation and tunable four‐wave mixing in liquids and solutions. For trans−stilbene derivatives, β and γ are typically 10 times larger than for the corresponding benzene compounds, and are strongly correlated with the mesomeric effect of the substituents. A series of disubstituted molecules with strong donor–acceptor intramolecular charge transfer exhibit very large β, and it is shown that this enhancement can be predicted from the basic properties of the first electronic excited state.

Theory of the hydrophobic effect

Abstract: A microscopic theory is developed which can describe many of the structural and thermodynamic properties of infinitely dilute solutions of apolar solutes in liquid water. The theory is based on an integral equation for the pair correlation functions associated with spherical apolar species dissolved in water. It requires as input the experimentally determined oxygen–oxygen correlation function for pure liquid water. The theory is tested by computing thermodynamic properties for aqueous solutions of apolar solute species. The predictions of both the Henry’s Law constant and the entropy of solution are in good agreement with experiment. The calculation of the latter quantity is essentially independent of any adjustable parameters. It is shown how the correlation functions we have calculated can be used to predict the solubility of more complicated, aspherical, and nonrigid solutes in liquid water. For the more complex molecules it is convenient to study the difference between the excess chemical potential o...

The intrinsic reaction coordinate. An ab initio calculation for HNC→HCN and H−+CH4→CH4+H−

Abstract: A practical method of calculating the intrinsic reaction coordinate starting at a saddle point is proposed. The method has been used in combination with the analytical evaluation of the energy gradient for the calculation of the reaction coordinate on an ab initio potential energy surface. The reaction coordinates are obtained for the HNC to HCN isomerization and the SN2 exchange reaction involving H−+CH4→CH4+H−.

Initial and final state effects in the ESCA spectra of cadmium and silver oxides

Abstract: The factors which influence chemical shifts are examined in order to elucidate the cause of the anomalous chemical shifts for Cd and Ag oxides. The effects of extra‐atomic relaxation are accounted for using a procedure employing experimental Auger and binding energies. Atomic partial ionic charges for some simple Cd, Ag, and Zn compounds are calculated from experimental binding energies using a model which includes the effects of lattice potentials and extra‐atomic relaxation. Inclusion of extra‐atomic relaxation effects did not have a drastic effect on the relative ionicities computed for these selected compounds. However, for CdO, a large extra‐atomic relaxation energy contribution reduces the binding energy by 0.5 eV more than is predicted from nearest neighbor electronegativity arguments.

Theory of thermal unimolecular reactions at low pressures. I. Solutions of the master equation

Abstract: The master equation for a thermal unimolecular reaction in gases at low pressures is formulated. Steady‐state solutions are derived in analytical form with an exponential model of collisional transition probabilities, (i) for vibrational energy transfer in molecules with variable densities of states, and (ii) for combined rotational and vibrational energy transfer in molecules with variable heights of the centrifugal barriers. Other models of transition probabilities are treated numerically. The diffusion limit of energy transfer is discussed. In all cases, the nonequilibrium populations of excited states and the weak collision efficiency factors βc are calculated.

The Structure of Water Dimer from Molecular Beam Electric Resonance Spectroscopy.

Abstract: Molecular beams of hydrogen bonded water dimer, generated in a supersonic nozzle, have been studied using electric resonance spectroscopy. Radiofrequency and microwave transitions have been observed in (H2 16O)2, (D2 16O)2, and (H2 18O)2. Transitions arising from both pure rotation and rotation–tunneling occur. The pure rotational transitions have been fit to a rigid rotor model to obtain structural information. Information on the relative orientation of the two monomer units is also contained in the electric dipole moment component along the A inertial axis μa, which is obtained from Stark effect measurements. The resultant structure is that of a ’’trans‐linear’’ complex with an oxygen–oxygen distance ROO of 2.98(1) A, the proton accepting water axis is 58(6) ° with respect to ROO, and the proton donating water axis at −51(6) ° with respect to ROO. This structure is consistent with a linear hydrogen bond and the proton acceptor tetrahedrally oriented to the hydrogen bond. The limits of uncertainty are wh...

Self‐consistent molecular orbital methods. XVIII. Constraints and stability in Hartree–Fock theory

Abstract: Constraints that may be applied to the spin orbitals used in Hartree–Fock theory are classified and discussed. Once a constrained stationary wavefunction has been obtained by a self‐consistent procedure, it may be tested for stability both internally (with constraints remaining) and externally (with some constraints removed). Methods for carrying out these tests are presented. In addition, a general technique is described for further energy minimization following detection of an instability.

Theory of thermal unimolecular reactions at low pressures. II. Strong collision rate constants. Applications

Abstract: Theoretical expressions for the strong collision rate constants of thermal unimolecular reactions at low pressures k0sc are discussed. The rate constant is split up into various factors: a basic expression for a simplified harmonic oscillator model, a factor accounting for anharmonicity effects, a factor accounting for the energy dependence of the density of states, an overall rotation factor accounting for the effects of centrifugal barriers, and an internal rotation factor accounting for the barriers of hindered rotors. Simplified and easily applicable expressions for these factors are derived. The theory is applied in detail to many practical examples. The comparison with experimental results demonstrates the large importance of the weak collision effects which have been treated in part I of this article. Empirical values for the weak collision efficiencies βc are derived and compared with predicted values.

New numerical methods applied to solving the one‐dimensional eigenvalue problem

Abstract: Two new numerical methods, the log derivative and the renormalized Numerov, are developed and applied to the calculation of bound‐state solutions of the one‐dimensional Schroedinger equation. They are efficient and stable; no convergence difficulties are encountered with double minimum potentials. A useful interpolation formula for calculating eigenfunctions at nongrid points is also derived. Results of example calculations are presented and discussed.

Information theory, distance matrix, and molecular branching

Abstract: Information theory was used in defining several measures of the topological properties of molecules, namely, information for adjacency, incidence, polynomial coefficients of the adjacency matrix, and for distances of molecular graphs. The latter was found to have a greater ability for discrimination between structural isomers than all known topological indices and to be a very appropriate measure of branching. All the quantities related to the distance matrix (two information measures, the Weiner number and the largest eigenvalue of the characteristic polynomial) were found to reflect in the same way the main features of molecular branching. On this basis, as well as on the basis of general expressions for information content and Wiener number derived for tree graphs, the essence of molecular branching was expressed in a number of rules. It was shown that these theoretical rules on branching are in agreement with the intuitive understanding of branching and are reflected in a large number of molecular properties.

Dielectric dispersion and dielectric friction in electrolyte solutions. II

Abstract: Presented herein is a thorough investigation of the consequences of coupling ion migration to dielectric relaxation in the solvent. A self‐consistent continuum model is developed from both local (stress tensor) and global (dissipation function) considerations. The friction coefficient of a moving ion is computed in terms of the dimensionless coupling parameter where e is the ion charge, η is the solvent viscosity, e0 and e∞ are the low and high frequency dielectric constants of the solvent, respectively, τD is the Debye dielectric relaxation time of the pure solvent, and R is the ionic radius. For small ions the computed frictional drag is practically independent of ion radius, provided some degree of hydrodynamic slip is allowed at the ion surface. The effect of ion migration on the dielectric relaxation time of the solution is analyzed in detail. It is shown that the Debye–Falkenhagen effect should lead to an increase in the observed relaxation time, while the kinetic ion–solvent coupling introduces one...

Generalization of the classical theory of capillarity

Abstract: Gibbs’ concept of dividing surfaces is supplemented explicitly by the concepts of dividing lines and dividing points. The general forms of the fundamental equations for dividing surfaces and lines are established by considering the proper extensive geometric properties, in addition to area and length. The detailed description of the fluid part of a capillary system by these fundamental equations is used to obtain the general conditions of equilibrium. Proper generalizations of the Laplace equation, the Neumann relation, and the Young equation are derived.

The Rayleigh depolarization ratio and rotational Raman spectrum of water vapor and the polarizability components for the water molecule

Abstract: This paper describes the observation and computer simulation of the rotational Raman spectrum of water vapor and the measurement of the depolarization ratio for Rayleigh scattering from water vapor, which was found to be (3.0±1.4) ×10−4. These results were combined with the value of the mean polarizability to calculate the principal polarizability components of the water molecule. At 514.5 nm, they are (in units of 10−24 cm3): αxx=1.468±0.003, αyy =1.415±0.013, and αzz=1.528±0.013, where the x axis is the dipole axis and the y axis is perpendicular to the molecular plane.

Theory of elasticity of polymer networks. The effect of local constraints on junctions

Abstract: The effects of restrictions on the fluctuations of network junctions imposed by neighboring chains are treated by resort to a model in which these restrictions are represented by domains of constraint. Whereas in a phantom network devoid of such constraints the displacements of junctions from their mean positions are invariant with strain, involvements with neighbors in a real network render them dependent on the strain. The observed stress consequently is increased above predictions for the equivalent phantom network. On the plausible assumption that the dimensions of the domains are transformed linearly (affinely) by the macroscopic strain, the constraints become less restrictive in the direction of a principal extension λt with increase in λt. Hence, the relative enhancement of the stress diminishes with the strain. The characteristic departures of the observed tension (f) –extension (α) curve for elongation from the expression f∝kT (α−α−2) of previous molecular theories are qualitatively reproduced by...

An accurate intermolecular potential for argon

Abstract: A potential function for ArKr is derived which is able to reproduce the best data available for the differential and the integral cross section, the second virial coefficient and the diffusion and viscosity within the quoted experimental errors.

Structure and thermodynamics of the liquid–vapor interface

Abstract: This paper is concerned with the effects that density fluctuations in different regions of a liquid–vapor interface have on the interfacial thermodynamic and structural properties. The total volume V is divided into a square array of columns whose width is the order of the bulk correlation length. The canonical partition function is written as a sum of constrained partition functions, each describing a system with a given number of particles in each column. Changes in the occupation number of each column (i.e., density fluctuations) are related to changes in position of the local Gibbs dividing surface, and the free energy of such distortions of the Gibbs surface is estimated using macroscopic ideas similar to those used in the capillary wave theory by Buff, Lovett, and Stillinger. Corrections to the interface tension as calculated for a single column with periodic boundary conditions are given. We make a self‐consistent choice of the column width which yields a scaling law originally porposed by Widom. F...

Selective excitation and detection in multilevel spin systems: Application of single transition operators

Abstract: An alternative definition of single transition operators is given for the description of selective excitation and detection experiments in multilevel spin systems. This definition has the virtues of a simple physical interpretation and easy application to arbitrarily complicated systems. Some applications to the excitation and detection of multiple quantum transitions in spin 1 and spin 3/2 systems as well as in coupled spin systems are described.

Operator formalism for double quantum NMR

Abstract: An operator formalism is presented which conveniently treats the interaction of a spin‐1 nucleus with a weak radio frequency field. The Hamiltonian in the rotating frame is H=−Δω Iz−ω1Ix+(1/3) ωQ[3 I2z−I (I+1)], where Δω is the resonance offset (Δω=ω0−ω), ω1 is the intensity of the rf field, and ωQ is the quadrupolar splitting. Nine fictitious spin−1/2 operators, Ip,i where p=x,y,z and i=1,2,3, are defined where p refers to the transition between two of the levels and i the Cartesian component. The operators, which are the generators of the group SU (3), satisfy spin‐1/2 commutation relations [Ip,j, Ip,k]=i Ip,l, where j,k,l=1,2,3 or cyclic permutation. Thus each p defines a three‐dimensional space termed p space. For irradiation near one of the quadrupolar satellites, for example, Δω=ωQ+δω with δω, ω1≪ωQ, it is shown that the effective Hamiltonian can be written H?−δωIx,3−√2 ω1Ix,1, i.e., a fictitious spin‐1/2 Hamiltonian in x space with effective magnetogyric ratio γ along the 3 (resonance offset) axis and √2 γ along the 1 (rf field) axis. For irradiation near the center we can effect double quantum transitions between m=±1. The formalism allows us to write the effective operators for these transitions. For example, if we take Δω=δω again with δω, ω1≪ωQ we find the effective double quantum (DQ) Hamiltonian H?−2 δω Iz,1−(ω21/ωQ) Iz,3. Thus the z space is referred to as the double quantum frame with effective magnetogyric ratio 2γ along the 1 (resonance offset) axis and (ω1/ωQ) γ along the 3 (rf field) axis. The limiting expressions are compared with exact calculations for arbitrary ω1 done by high speed computer. The theory is applied to various cases of irradiation including our previously reported technique of Fourier transform double quantum NMR. Various pulse sequences for preparing, storing, and maintaining the evolution of double quantum coherence are analyzed for single crystal and polycrystalline samples. Finally, the effects of rf phase on the double quantum phase are presented briefly, and the possibility of double quantum spin locking is analyzed.

Inversion of the Kirkwood–Buff theory of solutions: Application to the water–ethanol system

Abstract: A general procedure is outlined whereby experimental data such as partial molar volumes, isothermal compressibilities, and partial vapor pressures may be processed to obtain information on the extent of the affinity between two species in a mixture of two (or more) components. A particular example of the water–ethanol system is processed in this manner to obtain the quantities Gαβ which are integrals over the pair correlation functions between two species α and β. This information is relevant to several topics of interest in the field of aqueous solutions, such as the solvation of solutes, hydrophobic interactions, and structural changes in the solvent brought by the addition of solutes to water. More generally it may be used to characterize the properties of various mixtures on a molecular level.

Stochastic‐molecular theory of spin–relaxation for liquid crystals

Abstract: The theory of spin relaxation for liquid crystals is examined with the objective of properly analyzing the statistical interdependence of the faster rotational reorientation of the individual spin‐bearing molecules and the (slower) director or order‐parameter fluctuations. The analysis is presented in terms of a composite Markov process including both types of motions. It is shown that one recovers a sum of spectral‐density terms which, in lowest order in fluctuations, correspond to (1) reorientation of the molecule relative to the equilibrium potential of mean torque, (2) effects of director fluctuations, and (3) a negative cross‐term between these two processes which bears a simple relation to (2). Detailed results are given for the particular models of director fluctuations in the nematic phase, quasicritical order fluctuations on either side of the isotropic–nematic phase transition, and slow fluctuations in the local structure. Effects of localized cooperative modes of molecular reorientation are als...

On three‐dimensional rotational averages

Abstract: In theories which describe the response of freely rotating molecules to externally imposed stimuli it is frequently necessary to average rotationally a product of direction cosines relating space‐fixed and molecular coordinate frames. In this paper a systematic method for deriving the required tensor averages is presented, and results up to the seventh rank are explicitly shown. Where appropriate both reducible and irreducible expressions are given and their equivalence is demonstrated. Finally, some useful identities relating rotational averages of different ranks are noted.

A new tunneling path for reactions such as H+H2→H2+H

Abstract: The standard tunneling path in transition state theory for reactions such as H+H2→H2+H has been the so‐called reaction path, namely the path of steepest ascent to the saddle point. This path is now known to give numerical results for the reaction probability which are in disagreement with the exact quantum mechanical ones by an order of magnitude at low tunneling energies. A new tunneling path corresponding to a line of vibrational endpoints is proposed. It is much shorter and is shown to give results in agreement with the quantum ones to within about a factor of two. A semiclassical basis for choosing this new path is given.

An experimental determination of absolute half‐cell emf’s and single ion free energies of solvation

Abstract: The concept of absolute half‐cell emf is discussed and defined as VMS‐φM for the reaction M→M+(solution)+e−(M), where VMS is the electrostatic potential difference between metal electrode and solution and φM the work function of metal in contact with solution. It is shown that this quantity is equal to VRS‐φR, where VRS is the electrostatic potential difference between a reference electrode in air above the solution and the solution, and φR the work function in air of this reference. The quantity VRS′, the potential difference between reference electrode and the solution surface, was found experimentally by the vibrating condenser method for a number of half‐cells, and φR was determined photoelectrically. It is shown from the variation of VRS′ with electrolyte concentration that the potential difference betwen the bulk of pure H2O and its air interface is ∼0.05 V, the surface being negative relative to bulk, and that this potential is increasingly screened out as electrolyte concentration increases. From ...

Polarized Raman Scattering Studies of Orientational Order in Uniaxial Liquid Crystalline Phases

Abstract: The measurement of vibrational Raman depolarization ratios has been used to study molecular orientational order in uniaxial single domain nematic and smectic liquid crystal samples. This technique is demonstrated to obtain the same microscopic order parameter 〈P2〉=1/2 〈3 cos2ϑ−1〉, where ϑ is the angle between a molecular long axis and the uniaxial direction, as other existing methods. In addition, the next higher moment of the orientational distribution function 〈P4〉=1/8 〈35 cos4 ϑ−30 cos2ϑ+3〉 has been measured for the first time. The physical basis, theoretical apparatus, and experimental methods necessary for the application of this technique are thoroughly detailed in this paper. Measurements are presented of the temperature dependence of 〈P2〉 and 〈P4〉 of N‐ (p′‐butoxybenzylidene) ‐p‐cyanoaniline (BBCA) dissolved in N‐ (p′‐methoxybenzylidene) ‐p‐cyanoaniline (MBBA) and of pure MBBA in the isotropic and nematic phases, and in the isotropic, nematic, smectic A, and smectic B phases of N‐ (p′‐butoxybenzyl...

Theoretical studies of highly expanded free jets: Influence of quantum effects and a realistic intermolecular potential

Abstract: An earlier approximate theory proposed by Knuth and Fisher and Miller and Andres for solving the Boltzmann equation to calculate speed ratios and temperatures in free jet expansions has been extended to take account of quantum effects and realistic potentials in the collision integrals. The calculations show that quantum effects lead to a substantial increase in terminal speed ratios in helium but not in heavier gases. For He the speed ratios depend sensitively on the shape of the potential. Despite the approximate nature of the theory the predictions are in reasonable agreement with recent experiments. The theory predicts that the presently highest achieved speed ratio in He of 225 can be increased to 700 if condensation does not occur. At this speed ratio the quasiequilibrium gas phase temperature is roughly 10−3 K.

Dynamics of confined polymer chains

Abstract: We study the motions of a single polymer chain trapped inside a very thin capillary (or slit). We incorporate all excluded volume effects and hydrodynamic interactions through a scaling analysis. We find that the Debye–Bueche approximation, which was qualitatively correct for three‐dimensional dilute solutions, becomes completely incorrect for confined chains: the local fluctuations of the monomer concentration which are ignored in the Debye–Bueche picture allow for channels of easy flow of the solvent inside the chain. We obtain scaling formulas (with unknown numerical coefficients) for the diffusion constant and we also analyze the internal mode structure: inside a tube, for wavelengths larger than the diameter, we recover an unexpectedly simple structure of Rouse modes. Finally, we analyze the possibility of ’’sucking in’’ one chain inside a slightly tapered pore, by imposing a certain flow of the solvent. We find that the threshold pressure difference Δpc for aspiration of the chain depends only on th...

Abinitio configuration interaction study of the valence states of O2

Abstract: Configuration interaction calculations have been performed for the 62 electronic states of O2 arising from O atoms in the lowest 3P, 1D, and 1S states. The calculations used an extended one‐particle basis set, and included internal and semi‐internal electron correlation effects. Numerical values for potential curves are reported for all states. Detailed comparison with experiment and other calculations is made for the seven lowest bound states: X 3Σg−, a 1Δg, b 2Σg+, c 1Σu−, C 3Δu, A 3Σu+, and B 3Σu−. For these seven states the maximum error in the calculated spectroscopic constants Re, De, Te, and ωe are 0.04 A, 0.4 eV, 0.2 eV, and 120 cm−1, respectively.