# Showing papers in "Journal of Chemical Physics in 1976"

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TL;DR: In this article, the possibilities for the extension of spectroscopy to two dimensions are discussed, including the elucidation of energy level diagrams, the observation of multiple quantum transitions, and the recording of high-resolution spectra in inhomogenous magnetic fields.

Abstract: The possibilities for the extension of spectroscopy to two dimensions are discussed. Applications to nuclear magnetic resonance are described. The basic theory of two‐dimensional spectroscopy is developed. Numerous possible applications are mentioned and some of them treated in detail, including the elucidation of energy level diagrams, the observation of multiple quantum transitions, and the recording of high‐resolution spectra in inhomogenous magnetic fields. Experimental results are presented for some simple spin systems.

2,916 citations

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TL;DR: In this paper, the authors considered electron transfer between biological molecules in terms of a nonadiabatic multiphonon nonradiative decay process in a dense medium and derived an explicit, compact and useful expression for the electron transfer probability.

Abstract: This paper considers electron transfer between biological molecules in terms of a nonadiabatic multiphonon nonradiative decay process in a dense medium. This theoretical approach is analogous to an extended quantum mechanical theory of outer sphere electron transfer processes, incorporating the effects of both low‐frequency medium phonon modes and the high‐frequency molecular modes. An explicit, compact and useful expression for the electron transfer probability is derived, which is valid throughout the entire temperature range, exhibiting a continuous transition from temperature independent tunneling between nuclear potential surfaces at low temperatures to an activated rate expression at high temperatures. This result drastically differs at low temperatures from the common, semiclassical, Gaussian approximation for the transition probability. The experimental data of De Vault and Chance [Biophys. J. 6, 825 (1966)] on the temperature dependence of the rate of electron transfer from cytochrome to the chlorophyll reaction center in the photosynthetic bacterium Chromatium are properly accounted for in terms of the present theory.

1,228 citations

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TL;DR: In this paper, a theoretical argument is developed to find in which conditions this ion evaporation can occur; to that end solvation free enthalpies of cluster ions are derived from existing experimental data and the absolute reaction rate theory is applied.

Abstract: Experiments are briefly reported which show that small ions separate or ’’evaporate’’ from evaporating droplets carrying electrical charges. A theoretical argument is developed to find in which conditions this ion evaporation can occur; to that end solvation free enthalpies of cluster ions are derived from existing experimental data and the absolute reaction rate theory is applied. The conditions for ion evaporation are compared with those for Rayleigh instability and it is shown that the first process should occur only when the drop reaches sizes of the order of 10−6 cm. The ion evaporation process must be operative in the evaporation of highly electrified cloud droplets when their solute concentration is low.

1,212 citations

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TL;DR: In this article, the potential energies for the water dimer in various geometrical configurations have been calculated with a configuration-interaction method and the correlation effects for the entire potential surface have been analyzed in terms of inter− and intramolecular effects; the substantial coupling found between these effects, particularly in the vicinity of equilibrium position, is discussed.

Abstract: The potential energies for the water dimer in various geometrical configurations have been calculated with a configuration–interaction method. The computed dimerization binding energies corresponding to the potential minima for the linear, cyclic, and bifurcated configurations are −5.6, −4.9, and −4.2 kcal/mol, respectively; the correlation effects account for −1.1, −1.2, and −0.9 kcal/mol, respectively, of the total binding energy for these three dimeric forms. The correlation effects for the entire potential surface have been analyzed in terms of inter‐ and intramolecular effects; the substantial coupling found between these effects, particularly in the vicinity of equilibrium position, is discussed. The computational technique employed, in particular an analysis on the selection criteria for the configuration state functions, is discussed, and its reliability is assessed. Two analytical expressions for the water dimer potential surface obtained by fitting the calculated energies are presented. The potential surface given here is being used to determine the structure of liquid water (in the pairwise approximation and with Monte Carlo techniques); this latter work will be reported elsewhere.

1,085 citations

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TL;DR: In this article, the authors used a capillary technique for small samples to measure the isothermal compressibility κ T of water to −26°C and showed that the anomalous characteristics are due to the sensitivity of the volume to temperature changes, suggesting a geometrical basis for the cooperative behavior.

Abstract: Using a capillary technique for small samples, the isothermal compressibility κ T of water has been measured to −26°C. Accelerating increases of κ T at the lower temperatures can be described by an expression of the form κ T =Aeγ [where e= (T−T s )/T s ], which is known to describe anomalies encountered in the vicinity of a thermodynamic singularity located at T s . The implication that the thermodynamic and certain other properties of water at lower temperatures may be decomposed into a normal component and an anomalous component which diverges at T s =−45°C is supported by analysis of numerous other thermodynamic and relaxation data which extend into the supercooled regime. The anomalous characteristics are shown to originate primarily in the sensitivity of the volume to temperature changes, suggesting a geometrical basis for the cooperative behavior. The singularity at T s =−45°C may be a lambda transition associated with the cooperative formation of an open hydrogen‐bonded network, but the near coincidence of T s with the experimental homogeneous nucleation temperature suggests, as an alternative, that T s may correspond to the limit of mechanical stability for the supercooled liquid phase.

771 citations

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TL;DR: This method is computationally simple and numerically well behaved, and has been incorporated into a new molecular SCF program HONDO, and preliminary tests indicate that it is competitive with existing methods especially for highly angularly dependent functions.

Abstract: This paper is concerned with the efficient computation of the ubiquitous electron repulsion integral in molecular quantum mechanics. Differences and similarities in organization of existing Gaussian integral programs are discussed, and a new strategy is developed. An analysis based on the theory of orthogonal polynomials yields a general formula for basis functions of arbitrarily high angular momentum. (ηiηj∥ηkηl) = Σα=1,nIx(uα) Iy(uα) I*z(uα) By computing a large block of integrals concurrently, the same I factors may be used for many different integrals. This method is computationally simple and numerically well behaved. It has been incorporated into a new molecular SCF program HONDO. Preliminary tests indicate that it is competitive with existing methods especially for highly angularly dependent functions.

670 citations

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TL;DR: In this paper, a general theoretical framework for introducing manybody or lattice effects into gas/solid scattering is presented, which is restricted to classical scattering off harmonic lattices but is otherwise completely general.

Abstract: A general theoretical framework for introducing many‐body or lattice effects into gas/solid scattering is presented. The theory is presently restricted to classical scattering off harmonic lattices but is otherwise completely general. It is nonperturbative and valid for arbitrary lattice temperature. The theory is based on a formulation of lattice dynamics suggested by and related to the Kubo–Mori theory of generalized Brownian motion. This formulation leads to a generalized Langevin equation (GLE) in which only the coordinates of the gas atom and the n∼1–6 surface atoms directly struck by the gas atom appear explicitly. The remainder of the lattice, which functions as a harmonic heat bath, affects the collision through a friction kernel and a Gaussian random force appearing in the GLE. The GLE can be solved in terms of a tractable number of (n+1) ‐particle gas–surface trajectories using approximate stochastic techniques. Stochastic solution yields thermally averaged temporal gas particle probability distribution functions (pdf). From the long time limit of these pdf’s all temperature dependent gas–surface cross sections can be found. In the limit of zero friction, the theory gives a convenient method for calculating atom–oscillator thermally averaged cross sections which circumvents laborious Monte Carlo classical trajectory sampling and which can be generalized to treat other gas phase collision problems.

661 citations

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TL;DR: In this article, three basis sets (minimal s −p, extended s−p, and minimal s -p with d functions on second row atoms) are used to calculate geometries and binding energies of 24 molecules containing second-row atoms, and d functions are found to be essential in the description of both properties for hypervalent molecules and to be important in the calculations of two-heavy-atom bond lengths even for molecules of normal valence.

Abstract: Three basis sets (minimal s–p, extended s–p, and minimal s–p with d functions on second row atoms) are used to calculate geometries and binding energies of 24 molecules containing second row atoms. d functions are found to be essential in the description of both properties for hypervalent molecules and to be important in the calculations of two‐heavy‐atom bond lengths even for molecules of normal valence.

565 citations

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TL;DR: In this article, a method is developed for the analysis of data composed of random noise, plus an unknown constant "baseline", plus a sum (or an integral over a continuous distribution) of exponential decay functions.

Abstract: A method is developed for the analysis of data composed of random noise, plus an unknown constant ’’baseline,’’ plus a sum (or an integral over a continuous distribution) of exponential decay functions. It is based on the expansion of the solution of a Fredholm integral equation of the first kind in the eigenfunctions of the kernel. In contrast to the Fourier transform solution [Gardner et al., J. Chem. Phys. 31, 978 (1959)], the finite time range of the data is exactly accounted for, and no extrapolation or iteration is necessary. A computer program is available for the analysis of sums of exponentials. It is completely automatic in that the only input are the data (not necessarily in equal intervals of time); no potentially biased initial estimates of either the number or values of the amplitudes and decay constants are needed. These parameters and their standard deviations are decided with a linear hypothesis test corrected approximately for nonlinearity. Tests with simulated two‐, three‐, and four‐com...

545 citations

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TL;DR: In this paper, the authors examined the second order thermodynamic properties of a simple ionic MX and MX2 type glasses and showed that the vitreous state in this case is insensitive to the thermodynamic stress history up to a maximum computationally permissible relaxation time of around 10−10 sec.

Abstract: Some applications of molecular dynamics calculations to the vitreous state have been examined for simple ionic MX and MX2 type glasses. The MX system which corresponds to a hypothetical vitreous and supercooled amorphous KCl is found to undergo an isobaric transition in the region of 0.3 Tf and an isothermal transition at around 35 kbar (T=Tf). The transition is evidenced by a discontinuity in second order thermodynamic properties and may be associated with a virtual disappearance of translational diffusion. By employing a variety of irreversible stress histories, the vitreous state in this case is shown to be insensitive to the thermodynamic stress history up to a maximum computationally permissible relaxation time of around 10−10 sec. Simulations are also reported for some ionic liquids of MX2 stoichiometry which, in contrast with KCl, have glass‐forming ability (BeF2, ZnCl2, and SiO2). Although the relaxation times involved in laboratory glass formation far exceed the long‐time limit of computer ’’expe...

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TL;DR: In this paper, a new method for solving the coupled linear differential equations which appear in the theoretical statement of many types of scattering phenomena is described, combining the speed advantage of propagation methods with the inherent stability of R • matrix methods.

Abstract: We describe in detail a new method for solving the coupled linear differential equations which appear in the theoretical statement of many types of scattering phenomena. Combining the speed advantage of propagation methods with the inherent stability of R‐matrix methods, this method is fast and is unaffected by exponential growth of closed channels. We describe the propagation of the R‐matrix in terms of a collinear reactive scattering problem, and provide numerical results for several systems, clearly demonstrating the speed, stability, and accuracy of this method.

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TL;DR: In this paper, the random-walk method of solving the Schrodinger equation for molecular wavefunctions is extended to incorporate the effects of electron spin in several one-to-four-electron systems.

Abstract: The random‐walk method of solving the Schrodinger equation for molecular wavefunctions is extended to incorporate the effects of electron spin in several one‐ to four‐electron systems. Improved calculation procedures reduce computation requirements for high accuracy by a factor of about 10. Results are given for the systems H 2P, H+3 D3h 1A′1, H2 3Σ+u, linear equidistant H4 1Σ+g, and Be 1S.

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TL;DR: In this article, a molecular theory of surface tension is developed for a liquid-gas interface of a one component system and the Helmholtz free energy is obtained from a rigorous expansion in powers of derivatives of density ρ and is minimized by the calculus of variations.

Abstract: A molecular theory of surface tension is developed for a liquid–gas interface of a one component system. The Helmholtz free energy, the quantity minimized in the van der Waals approach, is obtained here from a rigorous expansion in powers of derivatives of density ρ and is minimized by the calculus of variations. The coefficient A (ρ) of the term in the square of the density gradient is (kT/6) Fdr r2C (r,ρ), C being the direct correlation function. In the case in which ρ varies in one direction x only, the solution of the Euler–Lagrange differential equation is analyzed in detail. This describes the cases of a single phase and of two coexisting phases and leads to the equal area Maxwell construction. The effect of an external field on the solution is discussed. The Euler–Lagrange differential equation provides a differential statement of Bernoulli’s theorem. In a three dimensional treatment the stress tensor formula is obtained from the corresponding Euler–Lagrange partial differential equation. A (differ...

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Chalmers University of Technology

^{1}, Northwestern University^{2}, Osaka University^{3}, Judson College^{4}TL;DR: In this paper, a numerical-variational method for performing self-consistent molecular calculations in the Hartree-Fock-Slater (HFS) model is presented, where wavefunctions are expanded in terms of basis sets constructed from numerical HFS solutions of selected one-center atom-like problems.

Abstract: A numerical-variational method for performing self-consistent molecular calculations in the Hartree-Fock-Slater (HFS) model is presented Molecular wavefunctions are expanded in terms of basis sets constructed from numerical HFS solutions of selected one-center atomlike problems Binding energies and wavefunctions for the molecules are generated using a discrete variational method for a given molecular potential In the self-consistent-charge (SCC) approximation to the complete self-consistent-field (SCF) method, results of a Mulliken population analysis of the molecular eigenfunctions are used in each iteration to produce 'atomic' occupation numbers The simplest SCC potential is then obtained from overlapping spherical atomlike charge distributions Molecular ionization energies are calculated using the transition-state procedure; results are given for CO, H2O, H2S, AlCl, InCl, and the Ni5O surface complex Agreement between experimental and theoretical ionization energies for the free-molecule valence levels is generally within 1 eV The simple SCC procedure gives a reasonably good approximation to the molecular potential, as shown by comparison with experiment, and with complete SCF calculations for CO, H2O, and H2S

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TL;DR: In this article, a formalism is developed for obtaining ab initio effective core potentials from numerical Hartree-Fock wavefunctions and such potentials are presented for C, N, O, F, Cl, Fe, Br, and I.

Abstract: A formalism is developed for obtaining ab initio effective core potentials from numerical Hartree–Fock wavefunctions and such potentials are presented for C, N, O, F, Cl, Fe, Br, and I. The effective core potentials enable one to eliminate the core electrons and the associated orthogonality constraints from electronic structure calculations on atoms and molecules. The effective core potentials are angular momentum dependent, basis set independent, and stable against variational collapse of their eigenfunctions to core functions. They are derived from neutral atom wavefunctions using a pseudo‐orbital transformation which is motivated by considerations of the expected accuracy of their use and of basis set economy in molecular calculations. Then the accuracy is demonstrated by multiconfiguration Hartree–Fock calculations of potential energy curves for HF, HCl, HBr, HI, F2, Cl2, Br2, and I2 and one‐electron properties for HF and HBr. The differences between valence‐electron calculations employing the present...

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TL;DR: In this article, the suitability of the Wigner method as a tool for semiclassical dynamics is investigated, and qualitatively introduced the difficulties encountered in some applications, and derive quantitative means of surmounting these difficulties.

Abstract: We investigate the suitability of the Wigner method as a tool for semiclassical dynamics. In spite of appearances, the dynamical time evolution of Wigner phase space densities is found not to reduce to classical dynamics in most circumstances, even as h→0. In certain applications involving highly ’coherent’ density matrices, this precludes direct h‐expansion treatment of quantum corrections. However, by selective resummation of terms in the Wigner–Moyal series for the quantum phase space propagation it is possible to arrive at a revised or renormalized classicallike dynamics which solves the difficulties of the direct approach. In this paper, we review the Wigner method, qualitatively introduce the difficulties encountered in certain semiclassical applications, and derive quantitative means of surmounting these difficulties. Possible practical applications are discussed.

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TL;DR: A comprehensive description of instrumental and theoretical methods employed to make accurate measurements of rotational correlation times using passage saturation transfer electron paramagnetic resonance (ST-EPR) is given in this paper.

Abstract: A comprehensive description is given of instrumental and theoretical methods employed to make accurate measurements of rotational correlation times using passage saturation transfer electron paramagnetic resonance (ST–EPR). Saturation transfer methods extend by several orders of magnitude the sensitivity of EPR to very slow motion; for example, for nitroxide spin labels, correlation times as long as 10−3 sec become accessible to measurement. Two ST–EPR detection schemes are discussed in detail: dispersion, detected 90° out of phase with respect to the 100 kHz field modulation, and absorption, detected 90° out of phase with respect to the second harmonic of the 50 kHz field modulation. The sensitivities of these configurations are illustrated with experimental spectra obtained from a system obeying isotropic Brownian rotational diffusion; namely, maleimide spin labeled human oxyhemoglobin in aqueous glycerol solutions. Two theoretical approaches, one employing coupled Bloch equations and the other utilizing the stochastic Liouville equation for the density matrix with the orientation variables treated by transition rate matrix or orthogonal eigenfunction expansion methods, are in excellent agreement with each other and with model system spectra. Both experimental and theoretical spectra depend on a number of relaxation processes other than rotational diffusion; consequently, considerable care must be taken to ensure the accuracy of measured rotational correlation times. Although the absorption method is currently the more sensitive and convenient one to apply with most conventional (commercial) spectrometers, the dispersion ST–EPR method is potentially more powerful, providing strong motivation for future technological efforts to decrease noise levels in dispersion experiments.

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TL;DR: In this paper, the upper and lower bounds of the multipole van der Waals coefficients C6, C8, and C10 for hydrogen, noble gas, and alkali atoms are established.

Abstract: Upper and lower bounds of the multipole van der Waals coefficients C6, C8, and C10 for hydrogen, noble gas, and alkali atoms are established. Nonadditive three‐body coefficients involving dipole, quadrupole, and octupole interactions are also determined. For the dipole polarizabilities a three‐term, two‐point Pade approximant is used to obtain the upper bound and a two‐term Pade approximant is used to obtain the lower bound. For the quadrupole and octupole polarizabilities a one‐term approximation of the dynamic polarizability is used, except for the helium quadrupole polarizability, where extended approximations are possible.

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TL;DR: In this paper, PPPP-SCF-CI calculations were carried out to describe the electron correlation in the excited singlet π,π* states of the polyacenes [C4n+2H2n+4], and the results led to the following: (1) new excited states entailing the promotion of two electrons from the ground state (some of them predicted previously by other authors), and (2) a partial reordering of those (well-known) excited states already accounted for by a S•CI representation.

Abstract: In order to describe the electron correlation in the excited singlet π,π* states of the polyacenes [C4n+2H2n+4], we have carried out PPP–SCF–CI calculations including all single and double excitations in the CI expansion up to n=5, including all triple excitations up to n=3, and all quadruple excitations up to n=2. Compared to previous CI descriptions which included single excitations only, e.g., the classic work of Pariser [J. Chem. Phys. 24, 250 (1956)], our calculations lead us to predict the following: (1) ’’new’’ excited states entailing the promotion of two electrons from the ground state (some of them predicted previously by other authors), and (2) a partial reordering of those (well‐known) excited states already accounted for by a S‐CI representation. Single and double excitations in a CI expansion (D‐CI) satisfactorily describe the ordering of all excited states up to 7 eV; the effect of higher excitations is to correct the excitation energies overestimated by the D‐CI description. Our predicted spectra provide a consistent assignment of all one‐ and two‐photon spectral data but do not yield a quantitative agreement.

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TL;DR: A general theory of fluorescence correlation spectroscopy (FCS) including the effects of translational and rotational motions and chemical reactions, in ideal solutions, is given in this article.

Abstract: A general theory of fluorescence correlation spectroscopy (FCS), including the effects of translational and rotational motions and chemical reactions, in ideal solutions, is given. The development is carried out explicitly for symmetric rotors of parallel transition moments and generalized to arbitrary configurations of the moments and to asymmetric rotors in the appendices. In addition, the effects of experimental geometry on the measured FCS correlation function are discussed in detail and the optimum geometries, for experiments seeking to measure different quantities, are given. We conclude with a brief discussion of signal‐to‐noise ratios and prospects for applications.

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TL;DR: In this article, a rapidly converging iterative method is presented to solve the manyelectron Schrodinger equation within a Hilbert space confined to functions with at most two electrons outside an internal space defined by the orbitals of a reference function.

Abstract: A rapidly converging iterative method is presented to solve the many‐electron Schrodinger equation within a Hilbert space confined to functions with at most two electrons outside an internal space defined by the orbitals of a reference function. The wavefunction is given in terms of external two‐electron clusters represented by coefficients and density matrices referring directly to the basis functions. All matrix elements are obtained from generalized Coulomb and exchange operators. Only one operator per correlated electron pair is required for each iteration cycle.

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TL;DR: In this paper, a diagrammatic many-body perturbation theory is formulated through third order and applied to LiH, BH, and HF with various sizes of two-center Slater orbital basis sets.

Abstract: Diagrammatic many‐body perturbation theory is formulated through third order and applied to LiH, BH, and HF with various sizes of two‐center Slater orbital basis sets. The most extensive calculations use 46 orbitals to recover 94, 95, and 97% of the experimental correlation energy for the three molecules, respectively, when the perturbation expansion is carried through third order with pair restrictions and including selections of higher‐order diagrams via denominator shifts. A detailed analysis of the ’’pair’’ correlation energies relative to SCF occupied orbitals is given, including both inter‐ and intrapair contributions for the different spin cases.

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TL;DR: In this paper, a 3D reactive and non-reactive integral and differential cross sections for the H+H_2 exchange reaction on the Porter-Karplus potential energy surface are presented.

Abstract: Accurate three‐dimensional reactive and nonreactive quantum mechanical cross sections for the H+H_2 exchange reaction on the Porter–Karplus potential energy surface are presented. Tests of convergence in the calculations indicate an accuracy of better than 5% for most of the results in the energy range considered (0.3 to 0.7 eV total energy). The reactive differential cross sections are exclusively backward peaked, with peak widths increasing monotonically from about 32° at 0.4 eV to 51° at 0.7 eV. Nonreactive inelastic differential cross sections show backwards to sidewards peaking, while elastic ones are strongly forward peaked with a nearly monotonic decrease with increasing scattering angle. Some oscillations due to interferences between the direct and exchange amplitudes are obtained in the para‐to‐para and ortho‐to‐ortho antisymmetrized cross sections above the effective threshold for reaction. Nonreactive collisions do not show a tendency to satisfy a "j_z‐conserving" selection rule. The reactive cross sections show significant rotational angular momentum polarization with the m_j=m′_j=0 transition dominating for low reagent rotational quantum number j. In constrast, the degeneracy averaged rotational distributions can be fitted to statistical temperaturelike expressions to a high degree of accuracy. The integral cross sections have an effective threshold total energy of about 0.55 eV, and differences between this quantity and the corresponding 1D and 2D results can largely be interpreted as resulting from bending motions in the transition state. In comparing these results with those of previous approximate dynamical calculations, we find best overall agreement between our reactive integral and differential cross sections and the quasiclassical ones of Karplus, Porter, and Sharma [J. Chem. Phys. 43, 3259 (1965)], at energies above the quasiclassical effective thresholds. This results in the near equality of the quantum and quasiclassical thermal rate constants at 600 K. At lower temperatures, however, the effects of tunneling become very important with the quantum rate constant achieving a value larger than the quasiclassical one by a factor of 3.2 at 300 K and 18 at 200 K.

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TL;DR: In this article, a unified statistical theory for bimolecular chemical reactions is developed, which is correct for this situation, and if the reaction proceeds via a long-lived collision complex, it reduces to the statistical model of Light and Nikitin.

Abstract: A unified statistical theory for bimolecular chemical reactions is developed. In the limit of a ’’direct’’ mechanism it becomes the usual transition state theory, which is correct for this situation, and if the reaction proceeds via a long‐lived collision complex it reduces to the statistical model of Light and Nikitin. A general criterion for locating the ’’dividing surfaces’’ that are central to statistical theory is also discussed. This prescription (Keck’s variational principle) is shown not only to locate the usual dividing surfaces that pass through saddle points and minima of the potential energy surface, but it also selects the critical surfaces relevant to the ’’orbiting’’ and ’’nonadiabatic trapping’’ models of complex formation.

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TL;DR: The Dirac-Frenkel-McLachlan variational principle for the time dependent Schrodinger equation and a variational correction procedure for wavefunctions and transition amplitudes are reviewed in this paper.

Abstract: Explicitly time dependent methods for semiclassical dynamics are explored using variational principles. The Dirac–Frenkel–McLachlan variational principle for the time dependent Schrodinger equation and a variational correction procedure for wavefunctions and transition amplitudes are reviewed. These variational methods are shown to be promising tools for the solution of semiclassical problems where the correspondence principle, classical intuition, or experience suggest reasonable trial forms for the time dependent wavefunction. Specific trial functions are discussed for several applications, including the curve crossing problem. The useful semiclassical content of the time dependent Hartree approximation is discussed. Procedures for the variational propagation of density matrices are also derived.

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TL;DR: The HeI2 van der Waals complex was prepared from a dilute mixture of iodine in helium at a pressure of 100 atm by supersonic expansion through a nozzle into a vacuum as mentioned in this paper.

Abstract: The HeI2 van der Waals complex was prepared from a dilute mixture of iodine in helium at a pressure of 100 atm by supersonic expansion through a nozzle into a vacuum. Laser‐induced fluorescence excitation spectra were recorded for the B←X transition of HeI2 as well as corresponding spectra for the He2I2 and I2 molecules in the expanding gas. I2 was found to be cooled by the expansion to a rotational temperature of 0.4 K, and a vibrational temperature of 50 K. Similarly, cold internal temperatures were attained by the van der Waals complexes. Evidence was found for vibrational predissociation of the HeI2 complex in both the X and B electronic states. The vibrational predissociation rate was found to depend weakly upon the degree of excitation of the I–I stretching mode, ν1. For ν1=1 in the X state the predissociation rate was found to be greater than 5×106 s−1. In the B state the vibrational predissociation rate is ∼5×1010 s−1 for ν1=27, decreasing to <5×109 s−1 for ν1⩽7. The small (3.4–4.0 cm−1) blue shifts of the vibronic bands of the HeI2spectrum relative to corresponding bands of I2 indicate (1) the van der Waals complex is slightly more strongly bound in the X state than it is in the B state, and (2) the I–I bonding in both the X and B states of iodine is largely unaffected by the formation of the van der Waals bond with helium.

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TL;DR: In this paper, the Massey-Mohr generalized oscillator strength surface is parametrized by simultaneous fitting to (1) empirical data, (2) the Bethe sum rule, and (3) doubly differential cross sections for ionization.

Abstract: Relativistic electron and proton impact cross sections are obtained and represented by analytic forms which span the energy range from threshold to 109 eV. For ionization processes, the Massey–Mohr continuum generalized oscillator strength surface is parametrized. Parameters are determined by simultaneous fitting to (1) empirical data, (2) the Bethe sum rule, and (3) doubly differential cross sections for ionization. Branching ratios for dissociation and predissociation from important states of N2 and O2 are determined. The efficiency for the production of atomic nitrogen and oxygen by protons with kinetic energy less than 1 GeV is determined using these branching ratio and cross section assignments.

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TL;DR: In this article, a liquid-vapor system in a gravitational field is examined using the grand canonical distribution functions ρs(r1,r2) and direct correlation functions cs(r 1, r2) for a nonuniform system.

Abstract: A liquid–vapor system in a gravitational field is examined using the grand canonical distribution functions ρs(r1...rs) and direct correlation functions cs(r1...rs) for a nonuniform system. The limit of zero field is taken under the assumption that ρ1(z) approaches a limit representing a two‐phase system. The limiting behavior is discussed in terms of an infinite continuous matrix calculated from c2(r1,r2) and ρ1(z). The vanishing of eigenvalues in zero field implies the appearance of long‐ranged correlations. The correlations are shown to be in the horizontal directions, confined to the interface, and macroscopic in range. The situation in an interface is briefly contrasted with the effect of a rigid wall in order to illustrate the fact that spontaneous symmetry breaking rather than the inhomogeneity of ρ1(z) is responsbile for the long‐ranged correlations. The invariance properties of a system in a gravitational field are used to give a new derivation of the conventional choice of the dividing surface. A microscopic expression for the surface tension is used to calculate the range of the interfacial correlations.

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TL;DR: In this paper, a simple application of Kubo's line shape theory to the domain of vibrational frequencies is presented, compared with the experiment, and used for predictions in vibrational modes where vibrational dephasing processes are predominant in determining the shape of condensed phase band contour.

Abstract: A simple application of Kubo’s line shape theory to the domain of vibrational frequencies is presented, compared with the experiment, and used for predictions. In vibrational modes where vibrational dephasing processes are predominant in determining the shape of the condensed phase band contour, the formalism shows that the vibrational correlation obeys a fast modulation mechanism (’’motional narrowing’’), e.g., in quinoline, tetravinyl tin, and isopropyl alcohol. However, even smaller molecules such as chloroform and methyl iodide show similar characteristics and only in exceptional cases (the uncoupled O–D stretch of D2O in H2O) is the modulation slow. This behavior is a consequence of the short modulation times (order of fractions of a picosecond) in the liquid which determine the phase loss of the vibrational amplitude after a brief period of a quasistatic distribution of molecular environments (’’rigid lattice’’) —times which can be approximately identified with the inverse average collision frequency. In order to compare theory and experiment quantitatively, the model requires that the vibrational second spectral moment must be measured in addition to the vibrational correlation function. Comparisons with vibrational memory functions, obtained from the correlation functions via the modified Langevin equation, corroborate the usefulness of the model.