Types Of Force Fields Research Articles

Modellrechnungen von Kraftkonstanten der Tetramethyl-Verbindungen (CH3)4?nM(CD3) n ,M=Si, Ge, Sn, Pb

Fromthe experiemntal fundamental vibrational frequencies of (CH3)4 M, (CD3)4 M and (CH3)3 MCD3,M=Si, Ge, Sn, Pb, and of (CH3)2Si(CD3)2 and CH3Si(CD3)3 a transferable local symmetry type force field for (CH3)4−n M groups has been calculated. Applications involving differentM atoms and numbersn of CH3 groups are presented.

The vibrational optical spectrum of ethylenediamine crystal. Calculation of the one-phonon spectrum of the high-temperature crystal form

The infrared and Raman spectra of crystalline ethylenediamine at 200 K and 78 K have been measured from 30 cm −1 and are interpreted on the basis of the recently determined crystal structure. The complete one-phonon optical spectrum, the equilibrium structure and the lattice energy have been calculated using a refined internal force field and atom-atom type intermolecular potentials. The effect of a transition dipole-transition dipole intermolecular potential on the splitting of the internal vibrations has also been investigated. The infrared and Raman spectra of a second low-temperature phase of crystalline ethylenediamine have been measured and conclusions are obtained on the molecular conformation and on the crystal structure for this crystal phase.

The Nature of Consciousness: Some Persistent Conceptual Difficulties and a Practical Suggestion

This chapter discusses the difficulties faced in the study of brain (conscious)–mind interrelationships and makes practical suggestions that can be implemented to overcome these difficulties. The three traditional classes of answers to the mind–brain question are interactionism, parallelism, and identity. An interactionist viewpoint on the mind–brain question would seem to boil down to nothing less than the postulation of the existence of a specific type of force field in the cosmos, taking its place alongside the electromagnetic, gravitational and other known forms. The fact that this mental energy is then regarded as being fundamentally different to justify the creation of a distinct category for it does not really change the formal problem posed. As with any other discovery that is subject to scientific study, the task would appear to be (1) to develop techniques for measuring the new force reliably and (2) to examine theoretically the laws that govern it and the nature of its relationship to other known forces.

Turbulence in the randomly forced, one-dimensional Burgers flow

The randomly forced, one-dimensional Burgers flow is dealt with by the method of the characteristic functional equation. The time development of the stochastic secondary flow is studied numerically by the Monte Carlo quadrature of the integral representation of solution for two types (white and “red”) of random force fields. A turbulence-like behavior of the flow appears for a supercritical Reynolds number, and its structure is studied in detail.

Steady-State Interactions in Plasma Accelerators

Theme A N analytical study of the steady-state interactions between a gas and a force field is presented. The several different types of interactions that occur for different magnitudes of the body force and heat addition are described. The effect of maintaining an initial pressure difference across the force field is also discussed. Although the analysis is applicable for any type of body force and heat input, reference is made to plasma accelerators where the Lorentz force and Ohmic heating are the appropriate quantities. A stationary, nondiffusive, one-dimensional force field is assumed to have been created in an infinitely long channel initially containing a perfect gas at rest. A single-fluid model is used to investigate the effect of the force field on the gas. The difficulties of such an investigation are reduced considerably by only studying the steady state, which is defined as the state in which the shock and expansion waves have constant strengths and steady-state conditions exist inside the force field. With these approximations the equations that govern the flow of the gas through the force field are derived and are solved along with the equations for shock and expansion waves to determine the resulting interaction. A related problem, that of the interaction of a shock tube flow with an electromagnet ic field, has been treated analytically by Johnson, 1 who used the method of characteristics and by Rosciszewski and Gallaher,2 who used the Lax-Wendroff finite difference method. Experimental results have been reported by Zauderer and Tate.3 Two different types of force field are considered. For the first type the force field is independent of the gas velocity through it and for the other it is altered by the gas velocity. Each of these types is related to a particular class of plasma accelerators. For the case of a force field independent of the gas velocity the possibility of placing a diaphragm at the forward edge of the force field that is burst at the same instant the force field is created is also considered. The parameter formed by this initial pressure difference is represented by P and is equal to the initial pressure ahead of the diaphragm divided by the initial pressure behind it (on the force field side). The gas temperature and the type of gas are assumed to initially be the same on each side of the diaphragm. The seven possible interactions between the gas and the force field in the steady state are indicated schematically in Fig. 1. The force and initial pressure difference accelerate the gas to the right in the figure. The regions in which the flow variables have constant values for each interaction are indicated by the circled

The Vibrational Spectrum and Urey-Bradley Force Constants of the Trifluoromethyltrifluoroborate(1-) Anion

Infrared and Raman spectra for (K+) (CF3BF3−) have been obtained from 4000 to 50 cm−1. Spectral assignments were made on the basis of C3v symmetry using both 10B and 11B compounds. In addition, a normal coordinate analysis was performed to obtain the potential energy distribution of the normal modes. A Urey-Bradley type force field was used, and force constants obtained for the CF3 and BF3 groupings were compared to those in C2F6 and BF4−.

Normal coordinate analysis of CF 3H and CF 3D molecules

A rigorous normal coordinate analysis is made for the molecules CF 3H and CF 3D using all the available vibrational data: 12 frequencies, 4 Coriolis coupling constants and 3 centrifugal stretching constants. 2 types of force fields have been obtained: a General Harmonic Force Field with 12 parameters and a modified Urey-Bradley Force Field with 9 parameters. Both the force fields account for the observed data reasonably well.

Vibrational Spectra of Propionamide and Its C- and N-Deuterated Compounds

Abstract The infrared and Raman spectra of CH3CH2CONH2, CH3CD2CONH2 and their N-deuterated compounds in the solid state have been measured. The normal coordinate analysis has been made by assuming the molecular symmetry of Cs. A Urey-Bradley force field was used for the in-plane vibrations and a valence force field for the out-of-plane vibrations of the amide group. The ethyl group was treated by a Urey-Bradley type force field as well as a valence type force field. The assignments of the fundamental frequencies have been made by referring to the infrared and Raman intensities, isotopic frequency shift and the calculated frequencies by using the force constants which were taken from n-paraffins and acetamide. The agreement between the observed and the calculated frequencies in the initial calculation was good for the CH3 and the amide group vibrations but was not good enough for some vibrations involving the α-carbon atom. Only the force constants related to these vibrations were refined by the least squares method in order to obtain the best fit. The calculated frequencies in this way fit to the observed satisfactorily.

Molecular force field for sulphuryl bromide fluoride and sulphuryl chloride fluoride

A normal coordinate analysis was carried out for SO 2BrF and SO 2ClF using the Urey-Bradley type of force field. Mean vibrational amplitudes were also evaluated.

Ab initio calculation of the force field of ethylene

The force field of ethylene has been determined by the force method from SCF-MO wavefunctions. The complete quadratic force field has been calculated using a 73 3 + 1 Gaussian lobe basis set; in addition, the force constants CC stretch, CC stretch/CH stretch coupling and CC stretch/CCH angle coupling have been determined with a larger 10, 5 4 + 2 basis set. The results indicate unambiguously that Crawford's Set II type force field is the correct one, i.e., the CC stretching force constant is about 9.3 mdyn/Å and not about 11 mdyn/Å. The force constants obtained with the larger basis set differ only insignificantly from those obtained with the smaller set. The calculated values show good agreement with the most recent experimental force field. It is especially remarkable that the coupling constants agree within the experimental uncertainty. The equilibrium geometry of ethylene, which has been determined from the ab initio calculation by the force relaxation method, is in good agreement with experiment.

Infrared spectra of trans-cis diacetamide and its C- and N-deuterated compounds

The infrared spectra of trans-cis CH 3CONHCOCH 3, CD 3CONHCOCD 3 and their N-deuterated compounds in the crystalline state have been measured in the region from 4000 to 33 cm −1. The vibrational assignments have been made by referring to the infrared spectra of the related compounds and the isotopic frequency shift. The normal co-ordinate treatment has been made for the in-plane vibrations of CH 3CONHCOCH 3, CH 3CONDCOCH 3, CD 3CONHCOCD 3 and CD 3CONDCOCD 3, by using a simple Urey-Bradley type force field and the molecular model of the planar trans-cis conformation. The calculated frequencies agree well with the observed.

An empirical function for second neighbor interactions and its effect on vibrational modes and other properties of cyclo- and n-Alkanes

The set of energy functions used previously in ‘consistent force field’ calculations of various molecular properties of alkanes, is improved by using a function of three variables, f(τ) f(τ′) cosφ, where φ is the torsional angle for a CC bond and τ, τ’ are bond angles on both sides of that bond. The main effect is to remove the largest deviations of calculated frequencies as derived by the Urey-Bradley type force field.

Infrared and Raman spectra and normal vibrations of N, N-dimethylthioformamide and N, N-dimethylthioacetamide

The Raman and infrared spectra of N, N-dimethylthioformamide and N, N-dimethylthioacetamide were recorded and the vibrational frequencies are assigned. The normal co-ordinate treatment of these molecules has been carried out and the potential energy distributions calculated in order to clarify the nature of normal vibrations and investigate the magnitude of mixing up of various skeletal frequencies. The results in regard to the nature of the C-N and C=S stretching frequencies in these thioamides are compared with those of primary and secondary thioamides on the one hand and those of the corresponding ordinary tertiary amides on the other. It has been shown that the force constants of the general quadratic force field type are transferable in the series of molecules of tertiary amides and tertiary thioamides. The lowest frequency in the region of 150 cm.−1 to 160 cm.−1 has been recorded by the authors in the Raman spectra of the two tertiary thioamides under consideration. In the normal vibrational analysis of related molecules, the earlier workers only calculated this frequency, but did not record it.

Constraints and redundancies for vibrations of linear and planar molecules

For linear or planar molecules, the internal displacement coordinates associated with certain types of intramolecular force fields are vibrationally incomplete. A linear constraint inequality involving such internal coordinates is automatically satisfied if the nonlinear redundancy appropriate to an augmented complete coordinate set is taken into account. An example is discussed.

Solvent Field Corrections for Electric Dipole and Rotatory Strengths

Quantum-mechanical perturbation theory is applied to the evaluation of the electric dipole strength and the rotatory strength of a condensed system of negligibly overlapped, randomly oriented solute and solvent molecules. Besides the traditional Lorentz field corrections, a correction factor is obtained which is a function of inductive and dipolar solute—solvent interactions. An extension of the types of intermolecular force fields heretofore considered is achieved. In particular, the effect of solvent fields due to solvent molecule static dipole moment is predicted to be a decrease in solute absorption intensity and optical activity. The complexity of terms and level of approximation cannot be expected to yield more than semiquantitative relationships, but the important solvent and solute variables are identified.

Lattice modes of polyethylene

AbstractA modified Urey‐Bradley type force field was adopted to study the lattice modes of polyethylene by the GF matrices method with the intermolecular force constants which were estimated from the intermolecular potential function of methane. The frequencies of the modes were calculated at intervals of 30° for the phase differences along the a axis and the b axis. The elastic moduli of polyethylene crystal along both axes were also obtained from the intermolecular potential function.

Urey-Bradley potential constants in nitrogen dioxide, nitrite ion and dinitrogen tetroxide

The Urey-Bradley type force field has been applied to the calculation of vibrational force constants in three nitrogen oxides, NO 2, NO 2- and N 2O 4, which have in common the nitro group. For the nitrogen dioxide molecule three independent constants were adjusted to fit six observed frequencies from both 14N and 15N isotopic molecules by a least-squares method. An IBM 650 digital computer was programmed for the calculation on the tetroxide. Seven constants were used in this case, and these were fitted to nine observed in-planar mode frequencies by a least-squares method. The final set of potential constants for N 2O 4 was found to reproduce satisfactorily the frequencies of the isotopic molecule.

The Calculation of Force Constants in Some Methyl Compounds

In this paper are described force constant calculations on ethane, the methyl halides, methyl cyanide and isocyanide. The potential function used is based on a valency type force field with the introduction of one cross term rendered likely by physical considerations. The applicability of this function to the molecules under consideration is tested with the ethane molecule. The carbon-carbon bond force constant in methyl cyanide is found to be considerably greater than in ethane, indicating that the bond has some double-bond character in the cyanide, as has been suggested by Pauling, Springall and Palmer. It is found that the bending constant of the HCH angle remains very constant in the four methyl halides, there being changes, however, on passing to the other compounds. Other variations in the force constants of corresponding links, similar to these, are studied and their significance discussed.

On the assignment of the fundamental vibration frequencies in O 3 , F 2 O, Cl 2 O, NO, and N 3 -

In the preceding paper our object was to investigate critically the application of simplified types of force fields to the correlation of the vibration frequencies of triatomis molecules. Starting from the better known molecules and using them as test cases, we have been able to estimate the probable errors in the results obtained by applying the same type of field to the less well-known molecules. On the whole we have found a remarkable regularity in that isoelectronic molecules tend to have the same geometrical shape, and that the values of the force constants associated with particular deformations lie within quite strict limits. There are, however, a few cases in which this regularity is completely negatived on applying the existing assignment of the fundamental frequencies of the molecules, and for some of these we suggested re-assignments which bring them more into line with the others. The purpose of the present paper is to justify such reassignments in relation to the experimental data. We hope to show that the assignments which we have proposed in the foregoing paper provide an interpretation at least as good as, if not better than, the earlier ones. We also suggest here experiments which might be made to discriminate between the different assignments in as simple and definite a way as possible. There have been several investigations of the infra-red absorption spectrum of ozone, and one unsuccessful attempt to obtain its Raman spectrum. The most recent work is that of Hettner, Pohlman, and Schumacher, and it is of extreme importance as they show that one absorption band which all previous investigators had taken to be due to ozone (viz., at 7·6 μ) is due to nitrogen pentoxide. The results of Hettner, Pohlman, and Schumacher have been summarized in Table I, although refernce should be made to their original paper for details which would take too much space for reproduction here. The interpretation of these results which Hettner, Pohlman, and Schumacher favour is that the fundamental frequencies are the three most intense bands in the spectrum, viz., 710 cm -1 , 1037 cm -1 , and 2105 cm -1 . These they assign as v 3 , v 2 , and v 1 respectively. The notation to describe the frequencies is the conventional numerical one used and illustrated in the preceding paper. Such an assignment can only mean that the force required to alter the distance between the two basal atoms of the O 3 molecule is very much greater than that required to make a similar alteration in the distance between the apical atom and either of the basal ones. In fact, using a central force field, Hettner, pohlman, and Schumacher conclude that the ozone molecule has the form of a very sharp isosceles triangle with the apical angle close to 40°. They calculate the force constant between the basal atoms to be 20·8 x 10 5 dynes/cm and that between each of the other pairs to be 3·86 x 10 5 dynes/cm. The smallness of the latter, they say, accounts for the ease with which the ozone molecule parts with an atom of oxygen in oxidizing processes.