Showing papers in "Journal of Chemical Physics in 1979"

Investigation of exchange processes by two‐dimensional NMR spectroscopy

Abstract: A new general technique for the investigation of exchange processes in molecular systems is proposed and demonstrated. Applications comprise the study of chemical exchange, of magnetization transfer by inter‐ and intramolecular relaxation in liquids, and of spin diffusion and cross‐relaxation processes in solids.

Kinetics of swelling of gels

Abstract: We present a theory of the kinetics of the swelling of a gel. The characteristic time of swelling is proportional to the square of a linear dimension of the gel and is also proportional to the diffusion coefficient of the gel network, which is defined as D=E/f where E is the longitudinal bulk modulus of the network, and f is the coefficient of friction between the network and the gel fluid. This constitutes an essential difference between the present theory and the previous theory which is based on the assumption that the swelling time is determined by the diffusion coefficient of the fluid molecules. Experimental data are shown for spheres of 5% polyacrylamide gels and are analyzed using the present theory. The value of the diffusion coefficient obtained from the macroscopic swelling experiments shows excellent agreement with that obtained microscopically using laser light scattering spectroscopy.

On some approximations in applications of Xα theory

Abstract: An approximate Xα functional is proposed from which the charge density fitting equations follow variationally. LCAO Xα calculations on atomic nickel and diatomic hydrogen show the method independent of the fitting (auxiliary) bases to within 0.02 eV. Variational properties associated with both orbital and auxiliary basis set incompleteness are used to approach within 0.2 eV the Xα total energy limit for the nitrogen molecule.

NMR in rotating solids

Abstract: The NMR free induction decay from a spinning sample having inhomogeneous anisotropic interactions (chemical shifts, first order quadrupole couplings) takes the form of a train of rotational spin echoes. The Fourier transform of the echo envelope is a sharp spectrum from which the effects of anisotropy have been removed. The Fourier transform of the echo shape contains information concerning the anisotropies: This information can be extracted by a moment analysis. The effects of localized homonuclear spin–spin interactions are to convert the ’’isotropic’’ spectrum into a characteristic powder pattern. Second order quadrupole coupling produces a similar effect. It is shown in this case that the usual second‐order level shifts cannot be used to calculated this pattern, which must be described by a proper average Hamiltonian theory. Finally it is shown that rotational spin echoes provide a convenient means of studying very slow random molecular rotations (τc≲1 sec).

On the determination of Born–Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei

Abstract: We show how the presence of a conical intersection in the adiabatic potential energy hypersurface can be handled by including a new vector potential in the nuclear‐motion Schrodinger equation. We show how permutational symmetry of the total wave function with respect to interchange of nuclei can be enforced in the Born–Oppenheimer approximation both in the absence and the presence of conical intersections. The treatment of nuclear‐motion wave functions in the presence of conical intersections and the treatment of nuclear‐interchange symmetry in general both require careful consideration of the phases of the electronic and nuclear‐motion wave functions, and this is discussed in detail.

A classical analog for electronic degrees of freedom in nonadiabatic collision processes

Abstract: It is shown how a formally exact classical analog can be defined for a finite dimensional (in Hilbert space) quantum mechanical system. This approach is then used to obtain a classical model for the electronic degrees of freedom in a molecular collision system, and the combination of this with the usual classical description of the heavy particle (i.e., nuclear) motion provides a completely classical model for the electronic and heavy particle degrees of freedom. The resulting equations of motion are shown to be equivalent to describing the electronic degrees of freedom by the time‐dependent Schrodinger equation, the time dependence arising from the classical motion of the nuclei, the trajectory of which is determined by the quantum mechanical average (i.e., Ehrenfest) force on the nuclei. Quantizing the system via classical S‐matrix theory is shown to provide a dynamically consistent description of nonadiabatic collision processes; i.e., different electronic transitions have different heavy particle trajectories and, for example, the total energy of the electronic and heavy particle degrees of freedom is conserved. Application of this classical model for the electronic degrees of freedom (plus classical S‐matrix theory) to the two‐state model problem shows that the approach provides a good description of the electronic dynamics.

Time‐dependent theory of Raman scattering

Abstract: A time‐dependent picture of vibrational Raman scattering in the weak field limit is presented. From this viewpoint we can separate the static effects, due to the coordinate dependence of the electronic transition dipole, from the dynamic effects that arise from wave packet propagation on the Born–Oppenheimer surfaces. Away from resonance, the energy uncertainty relation gives the propagation time necessary to obtain the cross section as being inversely proportional to the mismatch of the excitation frequency with the excited surface. The wave packet, given by the initial vibrational wave function times the transition dipole, hardly moves on the excited surface when the excitation frequency is far from resonance. As the excitation frequency is tuned closer to resonance, the propagated wave packet samples a larger portion of the surface. Using the short time approximation to the propagator, we obtain formulas for the cross section that are applicable for Raman scattering by polyatomics. The short time approximation is expected to be good away from resonance independent of the nature of the surface, and also on resonance with a repulsive surface. For an attractive surface, the approximation gives the average resonant cross section useful in the case when the vibrational structures cannot be observed.

Studies of molecular association in H2O and D2O vapors by measurement of thermal conductivity

Abstract: The thermal conductivities of H2O and D2O vapors were measured in a modified thick hot wire cell between 358 and 386 K at pressures ranging from 100 to 1000 Torr. Analysis of the data indicates that molecular association to form a dimeric species is the main source of enhancement of the thermal conductivity of both vapors. The enthalpy and entropy of association of the H2O dimer are −3.59 kcal mol−1 and −18.59 cal deg−1 mol−1, respectively. The enthalpy and entropy of association of the D2O dimer are −3.66 kcal mol−1 and −18.67 cal deg−1 mol−1, respectively. The measured enthalpy of association of the H2O dimer is in agreement with recently reported ab initio molecular orbital calculations on the H2O dimer. The entropies of association of the H2O and D2O dimers are calculated theoretically and are found to be in agreement with the measured values.

IMPROVED Ab Initio EFFECTIVE CORE POTENTIALS FOR MOLECULAR CALCULATIONS

Abstract: We have investigated the sources of error in bond lengths and dissociation energies computed from ab initio effective potentials derived from Phillips–Kleinman type pseudo‐orbitals. We propose an alternate pseudo‐orbital, effective potential treatment with the primary objective of agreement with all‐electron molecular calculations. This new treatment forces the pseudo‐orbitals to match precisely the Hartree–Fock orbitals in the valence region and thereby eliminates the major cause of error in the earlier calculations. Effective core potentials derived from these revised pseudo‐orbitals were used to compute potential energy curves for the ground states of F2, Cl2, and LiCl and the results are compared with previous all‐electron and effective potential calculations. Our effective potentials yield dissociation energies and bond lengths which are in excellent agreement with the all‐electron values. Furthermore, in contrast to other procedures, our revised effective potentials result in an excellent descriptio...

Field induced ion evaporation from liquid surfaces at atmospheric pressure

Abstract: A mass spectrometer system which is capable of sampling ions directly from an atmospheric pressure source has been constructed and used to investigate ions which are evaporated from the surface of highly charged water droplets. Solutions of electrolytes are sprayed into the air, and a large charge imparted to the droplets by induction; an electric field applied across the plume of evaporating spray extracts small ions, probably already clustered with solvent molecules, which are drawn through a 25 μm orifice into the vacuum chamber. Differential pumping is applied and the ions are focused into a quadrupole mass filter. Approximately 30 univalent anions and cations of various sizes and structures have been tested, and almost all have been observed to evaporate; significant exceptions are Ag+, Tl+, and Cu+. Furthermore, certain molecules such as urea and acetanilide, when present as neutrals in the sprayed water, are observed to remain attached to the ions when these evaporate. The experimental results are ...

An accurate intermolecular potential for helium

Abstract: A simple realistic and precise empirical intermolecular potential is proposed for helium. It possesses nearly the correct Hartree–Fock repulsion as well as the correct long range behavior. It was fitted to recent accurate intermediate temperature second virial coefficients and thermal conductivity data as well as high temperature viscosity values. It is able to predict second virial coefficients over an extended temperature range from 1.5 to 1475 K. Above 100 K it reproduces substantially all of the transport properties to within experimental error in a manner superior to all other potentials in existence. Below 100 K where the transport data are less reliable, it produces a good representation of the isotopic differences in the viscosity. It also predicts differential cross sections reasonably well. In spite of a few remaining discrepancies, when all the different macroscopic properties are considered, the potential produces the best representation of the helium interaction available at this time.

The virial theorem and stress calculation in molecular dynamics

Abstract: In molecular dynamics, the pressure in a homogeneous system in equilibrium may be calculated by two different methods. The first is based on the virial theorem of Clausius and gives the pressure at the boundary of the system. The second is based on the notion of stress, which is the sum of the appropriate components of the interatomic forces intercepted by an area, and of the components of momentum flux across the area, averaged over the area and over time. We show by means of a detailed comparison of the forces involved that the two methods are equivalent in the thermodynamic limit. In a small system with arbitrary boundary conditions, the neglect of a part of the interactions between the system and the wall results in some error in the pressure calculated by the virial method. In the special case of a system with periodic boundaries, there is no external ’’wall,’’ and the internal pressures calculated by the two methods are the same. However, with comparable effort in computation, the stress method makes more efficient use of the data and yields a result of greater precision than does the virial method. In a system not in equilibrium or not homogeneous, the stress method remains valid but the virial method leads to ambiguous results. These considerations indicate that the method of stress calculation is more general than the virial method.

On first‐row diatomic molecules and local density models

Abstract: The total Xα energy accurate to 0.3 eV is computed for H2, B2, C2, N2, O2, CO, and F2. Relative to experiment, the Xα model (α=0.7) is accurate to within ΔRe=0.1 bohr, ΔDe=2 eV, and Δωe=300 cm−1 for these molecules. Except for the lightest first‐row diatomic molecules, the Xα and experimental dissociation energies are bracketed by those of the Hartree–Fock model (from below) and the Local Spin Density model (from above).

Criterion of minimum state density in the transition state theory of bimolecular reactions

Abstract: We discuss two minimum‐density‐of‐states criteria for the location of generalized transition states for chemical reactions. One is due to Bunker and Pattengill; the other is due to Wong and Marcus. We prove that both provide upper bounds on the exact classical equilibrium rate constant. In addition, we show that for several‐dimensional systems both methods are exact at threshold, and in the limit of an infinite number of dimensions they agree with the variational theory of reactions of Wigner, Horiuti, and Keck. However, it is also shown that for a finite number of degrees of freedom both methods yield rate constants which are only as accurate as or less accurate than rate constants given by the variational theory of reactions. We note that, where tested by others for actual systems, the differences of the results obtained with the variational and Bunker–Pattengill criteria have been minor.

Effective convergence to complete orbital bases and to the atomic Hartree–Fock limit through systematic sequences of Gaussian primitives

Abstract: Optimal starting points for expanding molecular orbitals in terms of atomic orbitals are the self‐consistent‐field orbitals of the free atoms and accurate information about the latter is essential for the construction of effective AO bases for molecular calculations. For expansions of atomic SCF orbitals in terms of Gaussian primitives, which are of particular interest for applications in polyatomic quantum chemistry, previous information has been limited in accuracy. In the present investigation a simple procedure is given for finding expansions of atomic self‐consistent‐field orbitals in terms of Gaussian primitives to arbitrarily high accuracy. The method furthermore opens the first avenue so far for approaching complete basis sets through systematic sequences of atomic orbitals. It is shown that, for expansions of atomic SCF orbitals in terms of even‐tempered Gaussian primitives, the energy‐ optimized exponents are simple analytic functions of the number of primitives used in the expansions.With the h...

Chemisorption geometry of hydrogen on Ni(111): Order and disorder

Abstract: The location of a half monolayer of ordered hydrogen adatoms on Ni(111) has been analyzed by Low‐Energy Electron Diffraction (LEED), Thermal Desorption Spectroscopy (TDS), and Work Function (Δφ) measurements. It is found that the hydrogen atoms are arranged in an overlayer of graphitic structure with a (2×2) unit cell with respect to the substrate unit cell. In the ordered regions, the hydrogen adatoms occupy both types of three fold hollow sites without a detectable difference in the Ni–H bond lengths between the two sites. The Ni–H bond length is found to be 1.84±0.06 A, corresponding to an overlayer‐substrate spacing of 1.15±0.1 A. The relation between this structure and its observed order–disorder phase diagram as a function of temperature and hydrogen coverage is discussed. The disorder is discussed in detail, and a novel ’’atomic band structure’’ interpretation is given.

Translational friction coefficients of rigid, symmetric top macromolecules. Application to circular cylinders

Abstract: The hydrodynamic interaction equations and the interaction tensor that appear in the theoretical formalism for calculating translational friction coefficients of rigid particles modeled as assemblies of beads, are formulated in cylindrical coordinates For symmetric top particles, the cylindrical shielding tensors of symmetry‐equivalent beads are the same, and have only five nonzero components This effects a great simplification with respect to the Cartesian formalism Application is made to the end‐effect correction, for translational motion of right circular cylinders modeled as stacks of rings, extrapolated to zero bead size No appreciable changes in the translational friction coefficients are found when the hollow cylindrical models are capped at the ends with disc‐shaped plates For finite cylinders with axial ratio p≳2, our results, as well as those from other theoretical and experimental studies, are in remarkable disagreement with the previous calculations by Broersma

The Xα valence bond theory of weak electronic coupling. Application to the low‐lying states of Mo2Cl84−

Abstract: We show that valence bond (VB) concepts can be introduced into Xα theory. The resulting Xα–VB model yields energy states which either are pure multiplets or can be combined by straightforward projection to give pure multiplets. The new theory should be more computationally efficient than Hartree–Fock‐based CI models. A preliminary study of the δ→δ* transition in Mo2Cl84− yields an excitation energy closer to experiment than previous theoretical values, including those obtained to date from GVB–CI calculations.

Theory of twisting and bending of chain macromolecules; analysis of the fluorescence depolarization of DNA

Abstract: An elastic model of semiflexible chain macromolecules is developed in order to treat internal rotatory Brownian motion in the DNA helix. Dynamical equations for torsion and bending of the chain are generated, using results from classical elasticity and hydrodynamic theories. The rotational diffusion equation in normal coordinates is derived, and the initial‐boundary value problem solved for the conditions of a nanosecond fluorescence depolarization experiment. The resulting time distribution function of the angular orientation of a fluorescent probe, embedded in a chain at thermal equilibrium, is used to compute the emission anisotropy. The predicted decay law is unusual, with exponentials in ∼t due to twisting and in ∼t1/4 due to bending. Comparison with published data for ethidium–DNA complex reveals that the decay of the anisotropy arises primarily from twisting of the DNA helix, with a small contribution from bending. By fitting theory and experiment, the torsional rigidity C of DNA may be obtained.

The graphical unitary group approach to the electron correlation problem. Methods and preliminary applications

Abstract: Recent theoretical research by Paldus and by Shavitt has strongly suggested that the unitary group approach to the many body problem may be useful in molecular electronic problems. The graphical unitary group approach (GUGA) has now been developed into an extraordinarily powerful theoretical method. The theoretical/methodological contributions made here include a solution of the upper walk problem, the restriction of configuration space employed to the multireference interacting space, and the restructuring of the Hamiltonian in terms of loop types. Several test calculations are examined in detail to illustrate the unique features of the method. For large general multireference configuration interaction (CI) problems, computation times are typically only 15% of those reported using state‐of‐the‐art conventional techniques. Finally, these methods are applied to the vertical electronic spectrum of ketene, and excellent agreement with experiment is found.

Quantum number and energy scaling for nonreactive collisions

Abstract: Two new theoretical developments are presented in this article. First an energy corrected sudden (ECS) approximation is derived by explicitly incorporating both the internal energy level spacing and the finite collision duration into the sudden S‐matrix. An application of this ECS approximation to the calculation of rotationally inelastic cross sections is shown to yield accurate results for the H+–CN system. Second, a quantum number and energy scaling relationship for nonreactive S‐matrix elements is derived based on the ECS method. A few detailed illustrations are presented and scaling predictions are compared to exact results for R–T, V–T, and V–R, T processes in various atom–molecule systems. The agreement is uniformly very good — even when the sudden approximation is inaccurate. An important result occurs in the analysis of V–T processes: the effects of anharmonic wave functions (coupling) and decreasing vibrational energy gaps (energetics) are separated. Each factor makes significant contributions to the deviation of the anharmonic from the harmonic scaling relationship.

A quantum-statistical Monte Carlo method; path integrals with boundary conditions

Abstract: A new Monte Carlo method for problems in quantum‐statistical mechanics is described. The method is based on the use of iterated short‐time Green’s functions, for which ’’image’’ approximations are used. It is similar to the use of Feynman or Wiener path integrals but with a modification to take account of hard‐core boundary conditions. It is applied to two one‐dimensional test problems: that of a single particle in a hard‐walled box and that of two hard particles in a hard‐walled box. For these test problems, the results are in excellent agreement with exact quantum‐mechanical results both at high temperatures (near the classical limit) and at very low temperatures such that essentially only the ground state is occupied. Generalizations to three‐dimensional systems, to many‐body systems, and to more realistic potentials are discussed briefly.

Infrared spectra of chemisorbed CO on Rh

Abstract: The infrared spectrum of CO chemisorbed on alumina‐supported Rh atoms has been investigated. In agreement with previous work, three types of adsorbed species have been clearly distinguished on the basis of their C–O stretching frequencies. Species I, assigned as Rh(CO)2, is formed only with Rh atoms which are isolated from each other. Species II, assigned as Rh–CO, and III, assigned as Rh2CO, are formed on Rh clusters having two or more Rh atoms. CO‐species II and III undergo interactions with neighbor CO species causing an increase in wave number as coverage increases. Based on infrared intensity measurements for species I, the OC–Rh–CO angle is ∼90°. Chemisorbed 13CO yields the expected infrared spectrum on Rh, and rapid isotopic exchange between 13CO(ads) and 12CO(g) is observed which cannot be explained by the observed rate of desorption of CO from the supported Rh surface.

Electronic excited state transport in solution

Abstract: The transport of electronic excitations between randomly distributed sites is examined. The Green function solution to the master equation is expanded as a diagrammatic series. Topological reduction of the series results in an expression for the Green function which is equivalent in form to the Green function solution of a generalized diffusion equation. The diagrammatic technique used suggests an interesting class of self‐consistent approximations. This self‐consistent method of approximation is applied to the specific case of the Forster transfer rate. The solutions obtained are well‐behaved for all times and all site densities and indicate that transport is nondiffusive at short times and diffusive at long times. The mean squared displacement of the excitation and the time derivative of the mean squared displacement are calculated. These calculations illustrate that the time regime in which diffusive transport occurs is dependent on density. For low density systems transport becomes diffusive only at v...

Electronic structure of homoleptic transition metal hydrides: TiH4, VH4, CrH4, MnH4, FeH4, CoH4, and NiH4

Abstract: Ab initio molecular electronic structure theory has been applied to the family of transition metal tetrahydrides TiH4 through NiH4. For the TiH4 molecule a wide range of contracted Gaussian basis sets has been tested at the self‐consistent‐field (SCF) level of theory. The largest basis, labeled M(14s 11p 6d/10s 8p 3d), H(5s 1p/3s 1p), was used for all members of the series and should yield wave functions approaching true Hartree‐Fock quality. Predicted SCF dissociation energies (relative to M+4H) and M–H bond distances are TiH4 132 kcal, 1.70 A; VH4 86 kcal, 1.64 A; CrH4 65 kcal, 1.59 A; MnH4 – 36 kcal, 1.58 A; FeH4 0 kcal, 1.58 A; CoH4 27 kcal, 1.61 A; and NiH4 18 kcal, 1.75 A. It should be noted immediately that each of these SCF dissociation energies will be increased by electron correlation effects by perhaps as much as 90 kcal. For all of these molecules except TiH4 excited states have also been studied. One of the most interesting trends seen for these excited states is the shortening of the M–H bon...

A Monte Carlo simulation of the hydrophobic interaction

Abstract: The hydrophobic interaction between two apolar (Lennard–Jones) spheres dissolved in a model of liquid water (ST 2 water) is simulated using the force‐bias Monte Carlo technique recently devised by the authors. Importance sampling techniques are devised and used to give a relatively accurate determination of the potential of mean force of the two apolar spheres as a function of their separation. This determination shows that there are two relatively stable configurations for the spheres. In one configuration each member of the pair sits in its own water cage with one water molecule fitting between them. There is a free energy barrier separating this from the other stable configuration which is such that no water molecule sits between the spheres. This conclusion is shown to be quantitatively consistent with the recent semiempirical theory of Pratt and Chandler and is in disagreement with some previous Monte Carlo studies.

LEED analysis of acetylene and ethylene chemisorption on the Pt(111) surface: Evidence for ethylidyne formation

Abstract: The stable surface species formed from the chemisorption of acetylene (C2H2) or ethylene (C2H4) on the Pt(111) surface (T∼300–350 K) has been studied by a low‐energy electron diffraction intensity analysis. High resolution electron energy loss spectra reported by Ibach et al. have been interpreted by comparison to infrared data on relevant model compounds. The surface species most consistent with these studies is ethylidyne ( C–CH3). The species is coordinated to a threefold surface site with the C–C axis normal to the surface within an uncertainty of ∼15°. A saturated C–C bond length of 1.50±0.05 A and three equivalent Pt–C bond lengths of 2.00±0.05 A are determined by the LEED analysis and are consistent with the reported structures of ethylidyne in organometallic clusters. The ethylidyne group forms readily upon exposure of C2H4 to the Pt(111) surface at T∼300 K with the loss of one hydrogen atom per ethylene. The complete conversion of C2H2 to ethylidyne requires the presence of hydrogen atoms and pro...

Molecular dynamics study of the hydration of Lennard‐Jones solutes

Abstract: In order to clarify the nature of hydrophobic interactions in water, we have used the molecular dynamics simulation method to study a system comprising two Lennard‐Jones solute particles and 214 water molecules. Although the solutes were placed initially in contact, forces in the system drive them slightly apart to permit formation of vertex‐sharing solvent ’’cages.’’ Definite orientational preferences have been observed for water molecules in the first solvation layer around the Lennard‐Jones solutes; these preferences are loosely reminiscent of structure in clathrates. Nevertheless, substantial local disorder is obviously present. The dynamical data show that translational and rotational motions of solvation–sheath water molecules are perceptibly slower (by at least 20%) than those in pure bulk water.

Vibrational spectroscopy of cation‐site interactions in phosphate glasses

Abstract: Thirty different binary metal oxide glasses having the metaphosphate composition have been prepared containing cations from the following groups: alkali metals, alkaline earths, transition metals, and lanthanide and actinide metals. Far infrared absorption assigned to the cation vibration in its oxygen cage has been measured for these glasses. Empirical ionic models are proposed correlating the absorption maximum with the cation mass, charge, and ionic radius. Discrepancies between the observed and predicted vibrational frequency indicate a more covalent interaction between the metal cation and the glass network. Raman intensities and vibrational frequencies of the network metaphosphate vibrations have been obtained and provide additional evidence about the cation–site interaction.