To make practical the molecular dynamics simulation of large scale reactive chemical systems (1000s of atoms), we developed ReaxFF, a force field for reactive systems. ReaxFF uses a general relationship between bond distance and bond order on one hand and between bond order and bond energy on the other hand that leads to proper dissociation of bonds to separated atoms. Other valence terms present in the force field (angle and torsion) are defined in terms of the same bond orders so that all these terms go to zero smoothly as bonds break. In addition, ReaxFF has Coulomb and Morse (van der Waals) potentials to describe nonbond interactions between all atoms (no exclusions). These nonbond interactions are shielded at short range so that the Coulomb and van der Waals interactions become constant as Rij → 0. We report here the ReaxFF for hydrocarbons. The parameters were derived from quantum chemical calculations on bond dissociation and reactions of small molecules plus heat of formation and geometry data for...

http://www.wag.caltech.edu/publications/sup/pdf/471.pdf

ReaxFF: A Reactive Force Field for Hydrocarbons

The rigorous expression for the transmission of a thin absorbing film on a transparent substrate is manipulated to yield formulae in closed form for the refractive index and absorption coefficient. A procedure is presented to calculate the thickness to an accuracy of better than 1% with similar accuracies in the values of n. A method to correct for errors due to slit width is also given. Various formulae to calculate the absorption coefficient accurately over almost three orders of magnitude are discussed. Only data from the transmission spectrum are used and the procedure is simple, fast and very accurate. All formulae are in closed form and can be used on a programmable pocket calculator.

https://iopscience.iop.org/article/10.1088/0022-3735/16/12/023/pdf

Determination of the thickness and optical constants of amorphous silicon

Electronic Spectra of Polyatomic Molecules

We review various methods of deriving expressions for quantum-mechanical quantities in the limit when hslash is small (in comparison with the relevant classical action functions). To start with we treat one-dimensional problems and discuss the derivation of WKB connection formulae (and their reversibility), reflection coefficients, phase shifts, bound state criteria and resonance formulae, employing first the complex method in which the classical turning points are avoided, and secondly the method of comparison equations with the aid of which uniform approximations are derived, which are valid right through the turningpoint regions. The special problems associated with radial equations are also considered. Next we examine semiclassical potential scattering, both for its own sake and also as an example of the three-stage approximation method which must generally be employed when dealing with eigenfunction expansions under semiclassical conditions, when they converge very slowly. Finally, we discuss the derivation of semiclassical expressions for Green functions and energy level densities in very general cases, employing Feynman's path-integral technique and emphasizing the limitations of the results obtained. Throughout the article we stress the fact that all the expressions obtained involve quantities characterizing the families of orbits in the corresponding purely classical problems, while the analytic forms of the quantal expressions depend on the topological properties of these families. This review was completed in February 1972.

https://iopscience.iop.org/article/10.1088/0034-4885/35/1/306/pdf

Semiclassical approximations in wave mechanics

Fine structure has been observed in the nuclear paramagnetic resonance absorption line for protons in crystalline hydrates. The magnetic field of 6820 gauss was provided by a permanent magnet, the inherent stability of which facilitated detailed study of line shape. Measurements on a single crystal of CaSO4·2H2O show a splitting into four component lines with maximum separation varying from zero to 22 gauss, depending upon the direction of the externally applied magnetic field in the crystal. Both the number of component lines and the dependence of their spacing on field direction are calculated by treating the magnetic dipole‐dipole interaction as a perturbation of the proton two‐spin system within the water molecule; the effect of the more distant protons, neglected in this calculation, gives a finite width to the component lines. Variation of the splitting with field direction determines the orientation of the line joining protons in the water molecule, which is found to be consistent with positions ascribed to hydrogen nuclei in the lattice through simple considerations of chemical bonding. The distance between protons in the water molecule is measured by the splitting to be 1.58A for CaSO4·2H2O; if one assumes an H–O–H bond angle of 108°, the O–H distance is 0.98A. Powdered hydrates show a characteristic fine structure arising from isotropic distribution in solid angle of single crystal granules. This type of fine structure determines the proton‐proton distance somewhat less accurately than does the single crystal experiment.

Nuclear Resonance Absorption in Hydrated Crystals: Fine Structure of the Proton Line

The Water Vapor Molecule

The Infra-Red Spectra of Polyatomic Molecules. Part II

The theory of hindered rotation in methyl alcohol developed by Burkhard and Dennison has been extended to include the second‐order Stark effect as well as a detailed discussion of K‐type doubling. It has been applied to an interpretation of the microwave spectrum of normal methanol and of two isotopic molecules, C13H3O16H and C12H3O18H3 recently measured by Hughes, Good, and Coles. A very convincing fit between the predicted and observed lines is obtained which serves to determine many of the molecular constants, as well as providing a substantial number of self‐consistency checks.The height of the potential barrier (on the assumption of a sinusoidal potential) is found to be 374.8 cm−1. The CH distance in the methyl group cannot be obtained with any accuracy from the present data but is consistent with the CH distance in methane, namely, 1.093A, and has been taken to have this value. The remaining dimensions are, however, well determined and are: OH distance=0.937A, CO distance=1.434A, COH angle=105°56′,...

The Methyl Alcohol Molecule and Its Microwave Spectrum

An interference filter of the reflection type consists in its simplest form of a perfectly reflecting mirror on which is placed a thin layer of a dielectric material. The outer surface of the dielectric is coated with a very thin metallic film. When properly constructed such a filter reflects 100 percent of radiation at the frequencies 2nν0, and 0 percent of radiation at the frequencies (2n + 1)ν0.A transmission filter consists of a thin dielectric layer, both sides of which are coated with very thin metallic films. A well made filter will transmit up to approximately 40 percent of the incident radiation at the frequencies nν0. The transmission bands can be made quite narrow, and the transmission between the maxima may be less than 1 percent although it does not fall to zero.The theory, which consists of a straightforward application of the Maxwell equations, is initially applied to a single metallic film backed by dielectric media. The reflection and transmission coefficients, as well as the phase shifts, are obtained and are given in terms of the thickness and the optical constants of the film.The reflection coefficient for the reflection filter is developed next and is expressed as a function of the properties of a single metallic film. The general formula is quite complicated but degenerates to a simple form when the wave-length becomes long (i.e. for the infra-red region). By using the filter at oblique incidence it is shown that polarized radiation may be produced.The transmission filter is studied and its properties may again be formulated in terms of the properties of a single metallic film. The values of the optical constants are deduced, which lead to the construction of an efficient transmission filter. Silver films have approximately these values in the visible region of the spectrum, but fail to possess them either in the ultraviolet or in the infra-red region. The theory shows that when the filter is tilted so that the angle of incidence is no longer normal, the transmission band shifts towards shorter wave-lengths, and splits into two bands, one of which is polarized parallel and the other perpendicular to the plane of incidence. This phenomenon is observed with experimental filters.

David M. Dennison

Papers

The Water Vapor Molecule

The Infra-Red Spectra of Polyatomic Molecules. Part II

The Methyl Alcohol Molecule and Its Microwave Spectrum

Reflection and Transmission Interference Filters

The Infrared Spectra of Polyatomic Molecules Part I