Refinement of the experimental energy levels of higher 2D Rydberg states of the lithium atom with very accurate quantum mechanical calculations

Very accurate variational non-relativistic calculations are performed for four higher Rydberg (2)D states (1s(2)nd(1), n = 8,..., 11) of the lithium atom ((7)Li). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions and finite nuclear mass is used. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The results of the calculations allow for refining the experimental energy levels determined with respect to the (2)S 1s(2)2s(1) ground state.     

Simplex-inspired algorithms for solving a class of convex programming problems

We consider a class of convex programming problems whose objective function is given as a linear function plus a convex function whose arguments are linear functions of the decision variables and whose feasible region is a polytope. We show that there exists an optimal solution to this class of problems on a face of the constraint polytope of dimension not more than the number of arguments of the convex function. Based on this result, we develop a method to solve this problem that is inspired by the simplex method for linear programming. It is shown that this method terminates in a finite number of iterations in the special case that the convex function has only a single argument. We then use this insight to develop a second algorithm that solves the problem in a finite number of iterations for an arbitrary number of arguments in the convex function. A computational study illustrates the efficiency of the algorithm and suggests that the average-case performance of these algorithms is a polynomial of low order in the number of decision variables. The work of T. C. Sharkey was supported by a National Science Foundation Graduate Research Fellowship. The work of H. E. Romeijn was supported by the National Science Foundation under Grant No. DMI-0355533.     

Polymers from intermediates obtained from hydrogen cyanide

The recent demonstration of an easy synthesis of diiminosuccinonitrile (DISN) from hydrogen cyanide and cyanogen, the reduction of DISN to diaminomaleonitrile (DAMN), and the use of these compounds to form difunctional heterocycles has made several new polyamide intermediates accessible. The 1- and 2-methyl-1,2,3-triazole-4,5-dicarbonyl chlorides have been polymerized interfacially to form high-melting polyamides of good heat stability. Interfacial polymerization of 1-methylimidazole-4,5-dicarbonyl chloride and trans-2,5-dimethylpiperazine has given a polyamide that is water-soluble. The 2,6- and 2,3-pyrazinedicarbonyl chlorides have been similarly converted to high-melting polyamides. 2,6-Dicyano-3,5-dipiperazinylpyrazine has been prepared from tetracyanopyrazine and piperazine and reacted with toluene diisocyanate to form a strong, stiff polyurea. Polyamides were also made from 2,3-diaminoquinoxaline, 1,4,5,6-tetrahydro-5,6-dioxo-2,3-pyrazinedicarbonitrile, and DAMN.     

Charge asymmetry and rovibrational excitations of HD+

Average values of the interparticle distances for rovibrationally excited HD⁺ are calculated using a method where the Born–Oppenheimer (BO) approximation is not assumed. The difference between the proton–electron and deuteron–electron distances is used to describe the charge asymmetry in the system. All-particle one-centre explicitly correlated Gaussian functions are used in the calculations of the HD⁺ rovibrational states. In this work, the non-BO method is extended to calculate the rovibrational states corresponding to the total rotational quantum number of two (N = 2). The algorithms for calculating the Hamiltonian and overlap matrix elements, and the matrix elements of the analytical energy gradient determined with respect to the exponential parameters of the Gaussians, are presented. The gradient is employed in the variational optimisation of the parameters, which is key in obtaining very accurate rovibrational energies in the calculations. The algorithm for calculating the average interparticle distances is also shown. The charge asymmetry of HD⁺ near the dissociation limit occurs, as expected, with the electron preferentially being near to the deuteron. The asymmetry for a particular vibrational level increases with rotational excitations. The rovibrational transition energies are also calculated and compared with available experimental data.     

The free energy of a reaction coordinate at multiple constraints: a concise formulation

The free energy as a function of the reaction coordinate (rc) is the key quantity for the computation of equilibrium and kinetic quantities. When it is considered as the potential of mean force, the problem is the calculation of the mean force for given values of the rc. We reinvestigate the PMCF (potential of mean constraint force) method which applies a constraint to the rc to compute the mean force as the mean negative constraint force and a metric tensor correction. The latter allows for the constraint imposed to the rc and possible artefacts due to multiple constraints of other variables which for practical reasons are often used in numerical simulations. Two main results are obtained that are of theoretical and practical interest. First, the correction term is given a very concise and simple shape which facilitates its interpretation and evaluation. Secondly, a theorem describes various rcs and possible combinations with constraints that can be used without introducing any correction to the constraint force. The results facilitate the computation of free energy by molecular dynamics simulations.     

Cooperative games with large cores

A payoff vector in ann-person cooperative game is said to be acceptable if no coalition can improve upon it. The core of a game consists of all acceptable vectors which are feasible for the grand coalition. The core is said to be large if for every acceptable vectory there is a vectorx in the core withx?y. This paper examines the class of games with large cores.     

Explicitly correlated Gaussian calculations of the (2)D Rydberg states of the boron atom

Accurate non-relativistic variational calculations are performed for the seven lowest members of the (2)D Rydberg series (1s(2)2s2p(2), and 1s(2)2s(2)nd, n = 3, [ellipsis (horizontal)], 8) of the boron atom. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian basis functions and the effect of the finite nuclear mass is directly included in the calculations allowing for determining the isotopic shifts of the energy levels. The Gaussian basis is optimized independently for each state with the aid of the analytic energy gradient with respect to the Gaussian parameters. The calculations represent the highest accuracy level currently achievable for the considered states. The computed energies are compared with the available experimental data.     

Investigation of porphyrins and metalloporphyrins by liquid matrix-assisted laser desorption mass spectrometry

Laser desorption mass spectrometry with liquid matrix-assistance has been used to study a series of selected porphyrins and metalloporphyrins. This work presents the results of using a liquid matrix with fibrous material as the substrate for liquid matrix assisted laser desorption of porphyrins and metalloporphyrins. The liquid matrices used for porphyrin studies were o-nitrophenyl octyl ether (NPOE) and 15-crown-5. The use of a liquid matrix with soft laser ionization enhances molecular ion formation. We also have investigated the use of NPOE as a liquid matrix for identifying mixtures of up to six porphyrins in a single shot spectrum without prior separation. The (M + H)⁺ peak of each metalloporphyrin component in the mixture is clearly indicated in the spectra and no obvious interference effects were observed.     

Use of High-Resolution Mass Spectrometry to Identify Products from Microwave Discharges in COAL-D2O Mixtures

Reactions of carbonaceous materials and H O in microwave discharges are known to produce H₂, HCN, CO, CO₂, and light hydrocarbon gases (primarily C₁ and C₂) in varying amounts. To determine if the solid or the H₂O is the source of hydrogen in formation of the above products, Fu and Blaustein reacted coal and graphite with D₂O.¹ Low-resolution mass spectra of the gaseous products from the D₂O experiments indicated the possibility of non-deuterated and corresponding deuterated compounds in the reaction mixture. Conventional separation and analytical techniques are not applicable to mixtures of this type. This communication describes the use of a high-resolution mass spectrometer, operated at a resolution 35 percent less than theoretically required for separation of the H₂-D doublet, to electrically measure precise masses for mixtures containing micromole amounts of deuterated and non-deuterated light gases.