Measurement of longitudinal relaxation times in crowded 1H NMR spectra using one- and two-dimensional maximum quantum (MAXY) NMR spectroscopy

Methods for measuring longitudinal relaxation times of protons in heavily overlapped ¹H NMR spectra are introduced and exemplified using a solution of cholesteryl acetate. The methods are based on 1-dimensional and 2-dimensional maximum quantum NMR spectroscopy (MAXY), which makes possible the selective detection of CH, CH₂ and CH₃ ¹H NMR resonances. A modification of the BIRD pulse sequence to achieve selective inversion of protons bonded to either ¹²C or ¹³C is given. The approach should find application in studies of molecular dynamics where isotopic enrichment is not possible and the level of available sample dictates the use of ¹H NMR spectroscopy.     

A Sequential Method for Discrete Optimization Problems and its Application to the Assignment, Travelling Salesman, and Three Machine Scheduling Problems

A discrete optimization problem is defined in which a numberof items are to be arranged in a sequence of positions in orderto obtain a minimum cost configuration. A simple sequentialmethod is proposed for the solution of this problem. The methodis composed of two stages. The first stage builds up an initialarrangement by introducing the items into the positions individually.The second stage adjusts these positions until no further improvementcan be made by a simple alteration of the arrangement. The aimof the method is to provide near optimum results with relativelylittle calculation. The scheme is shown to be successful ona number of well known problems in operations research.     

A simulation study of the effects of adsorbent energy on the diffusion of molecules in slit pores: 1 commensurate slit widths

Equilibrium molecular dynamics simulation has been used to study the self-diffusion coefficients (from correlation of the molecular velocity) and the collective, or centre of mass diffusion coefficients (from correlation of the streaming velocity) of a Lennard-Jones fluid in model slit pores. The slit widths were chosen to be integer multiples of the Lennard-Jones adsorbate diameter, and therefore are close to being commensurate with layered adsorbate structures. Slits of reduced width H* = 3 and 5 were examined at a reduced temperature of T* = 1.0. The adsorbate densities ranged from 0.3 to 0.9 in reduced units. The adsorbent adsorbate interaction was modelled as a simple potential with inverse 4th power attraction plus hard wall repulsion, and systems with reduced parameter u₀* ranging from ?5 to +5 were studied. Molecule-wall scattering was represented by a diffuse reflection algorithm. The density distributions show strong layering in the attractive system, but this is absent in the most repulsive slits, except at very high densities. Self-diffusion is only weakly dependent on u₀* and slit width at high densities, but a strong dependence on u₀* appears at low densities. The collective diffusion coefficient is less easy to calculate with high accuracy; nevertheless, it is clear that there is a strong dependence of this property on u₀* Trajectory plots show zones in which the particles are more or less strongly localized, but undergo irregular oscillatory motion corresponding to regions of high density in the single-particle distributions.     

Parameterization of a potential function for the Ca2+ −Ne and Ca2+ −N2 interactions using high-level ab initio data

Ab initio calculations have been carried out at the CCSD(T)/aug-cc-pVTZ level on di-nitrogen and neon interacting with a calcium (II) cation. The interaction of nitrogen with the Ca²⁺ cation is examined for end-on and side-on approaches. The two adjustable parameters in the TrAZ potential (A ^Ca2+-Ne , b ^Ca2+-Ne ) are fitted to the Ca²⁺-Ne potential energy curve and combination rules are then applied in reverse to get A ^Ca2+-Ca2+ , b ^Ca2+-Ca2+ . Combining these with values of A^NN, 6^NN enables the Ca²⁺-N₂ potential energy curves to be predicted a priori. Agreement with the ab initio data is found to improve dramatically when the anisotropy of the nitrogen polarizability is included in the induced interaction energy. Other combination rules are tried but are not found to have an impact on the agreement between the a priori potential and the ab initio data     

A simple method to calculate dispersion coefficients for isolated and condensed-phase species

(Molecular Physics, 1998, 95, 549–570)     

Enhanced effect of magnetic field gradients using multiple quantum NMR spectroscopy applied to self-diffusion coefficient measurement

NMR spectroscopy can be used to measure molecular self-diffusion coefficients using a modified spin-echo pulse sequence known as the longitudinal eddy current delay (LED) method which incorporates pulsed magnetic field gradients. The effect of such gradients on multiple quantum coherences is investigated and shown to be of benefit for the measurement of diffusion coefficients using modest gradient strengths. The multiple quantum coherences involved in the spin operator 8I _x I _y I _y S _y of a weakly coupled SI₃ spin system (¹³CH₃ at natural abundance, in alanine in this case) were studied. The multiple quantum coherences included the quadruple-quantum (QQ) order of (3I + S), double-quantum (DQ) order of (3I - S) and (3I + S), and zero-quantum (ZQ) order of (I - S) with effective magnetogyric ratios of (3γ_H + γ_C), (3γ_H - γ_C), (γ_H + γ_C) and (γ_H - γ_C) respectively. The results show that the use of higher level quantum coherences for diffusion coefficient measurement can have the practical effect of significantly enhancing the gradient strength and this is important for slowly diffusing species.     

Extension of Dynamic Programming to Multi-plant Renewal

Discounting formulae and dynamic programming methods have beenproposed for single machine replacement problems with and withouttechnological change. But it is often essential to considercapacity replacement collectively in terms of all the plantsowned by a company as the replacement decisions are not independent.This paper proposes a model for capacity renewal and describeshow the problem can be tackled by dynamic programming combinedwith a priority ordering system.     

A simulation study of the pore size dependence of transport selectivity in cylindrical pores

The equilibrium adsorption and transport properties of mixtures of methane and carbon dioxide, modelled as spherical molecules, have been studied in cylindrical model pores with graphitic properties over a range of cylinder radii. The equilibrium isotherms exhibit packing transitions similar to those observed for single adsorbates; as a consequence, optimum separation factors are found at particular radii, depending on the fugacity (or pressure) in the system. The equations of non-equilibrium thermodynamics have been developed so as to represent the flux of each component in a Fickian form, as a coefficient multiplying the gradient of the total density. Diffusion coefficients were calculated from streaming velocity correlations and NEMD was used to obtain the ‘apparent’ viscous component. The results show that diffusion coefficients from equilibrium molecular dynamics and viscous diffusion coefficients from non-equilibrium calculations are identical within the errors of the calculation. It follows that equilibrium and dynamic separation factors have the same values over a range of pore sizes.