962 resultados para Schwinger Variational Principle
Resumo:
Has international law ever, and, if it has not, can it ever, truly freed itself from the strictures of neocolonialism and the drive by a privileged elite to dominate the world scene? This article begins by inquiring into the nature of neocolonialism and, in so doing, pays particular attention to the writings of former Ghanaian President Kwame Nkrumah. It then proceeds to determine how neocolonialist designs surface in international law today by briefly looking at two aspects of international law in particular, namely customary international law, with specific reference to the counterterrorism context, and the principle of self-defence. In the final analysis, this article argues for a necessary and eternal scepticism of international law and the agendas of its privileged gatekeepers. Like classic State power, it opens itself to, and often operates as, neocolonial overreach, and to quote Nkrumah, “[t]he cajolement, the wheedlings, the seductions and the Trojan horses of neo-colonialism must be stoutly resisted, for neo-colonialism is a latter-day harpy, a monster which entices its victims with sweet music.”
Resumo:
Variation calculations of the vibration–rotation energy levels of many isotopomers of HCN are reported, for J=0, 1, and 2, extending up to approximately 8 quanta of each of the stretching vibrations and 14 quanta of the bending mode. The force field, which is represented as a polynomial expansion in Morse coordinates for the bond stretches and even powers of the angle bend, has been refined by least squares to fit simultaneously all observed data on the Σ and Π state vibrational energies, and the Σ state rotational constants, for both HCN and DCN. The observed vibrational energies are fitted to roughly ±0.5 cm−1, and the rotational constants to roughly ±0.0001 cm−1. The force field has been used to predict the vibration rotation spectra of many isotopomers of HCN up to 25 000 cm−1. The results are consistent with the axis‐switching assignments of some weak overtone bands reported recently by Jonas, Yang, and Wodtke, and they also fit and provide the assignment for recent observations by Romanini and Lehmann of very weak absorption bands above 20 000 cm−1.
Resumo:
We report the results of variational calculations of the rovibrational energy levels of HCN for J = 0, 1 and 2, where we reproduce all the ca. 100 observed vibrational states for all observed isotopic species, with energies up to 18000 cm$^{-1}$, to about $\pm $1 cm$^{-1}$, and the corresponding rotational constants to about $\pm $0.001 cm$^{-1}$. We use a hamiltonian expressed in internal coordinates r$_{1}$, r$_{2}$ and $\theta $, using the exact expression for the kinetic energy operator T obtained by direct transformation from the cartesian representation. The potential energy V is expressed as a polynomial expansion in the Morse coordinates y$_{i}$ for the bond stretches and the interbond angle $\theta $. The basis functions are built as products of appropriately scaled Morse functions in the bond-stretches and Legendre or associated Legendre polynomials of cos $\theta $ in the angle bend, and we evaluate matrix elements by Gauss quadrature. The hamiltonian matripx is factorized using the full rovibrational symmetry, and the basis is contracted to an optimized form; the dimensions of the final hamiltonian matrix vary from 240 $\times $ 240 to 1000 $\times $ 1000.We believe that our calculation is converged to better than 1 cm$^{-1}$ at 18 000 cm$^{-1}$. Our potential surface is expressed in terms of 31 parameters, about half of which have been refined by least squares to optimize the fit to the experimental data. The advantages and disadvantages and the future potential of calculations of this type are discussed.
Resumo:
The triatomic spin-rovibronic variational code RVIB3 has been extended to include the effect of two uncoupled electrons, for both (3)Sigma(-) and (3)Pi (Renner-Teller) electronic states. The spin-orbital-rotational kinetic energy is included in the usual way, via terms (J+L+S). The phenomenological terms AL.S and lambda 2/3(3S(z)(2)) are introduced to reproduce the 3 spin-orbit and spin-spin splittings, respectively. Calculations are performed to evaluate the spin-rovibronic energy levels of CCO (X) over tilde (3) Sigma(-) and CCO (A) over tilde (3) Pi for which the Born-Oppenheimer potentials are derived from high-accuracy ab initio calculations.
Resumo:
We have favoured the variational (secular equation) method for the determination of the (ro-) vibrational energy levels of polyatomic molecules. We use predominantly the Watson Hamiltonian in normal coordinates and an associated given potential in the variational code 'Multimode'. The dominant cost is the construction and diagonalization of matrices of ever-increasing size. Here we address this problem, using pertubation theory to select dominant expansion terms within the Davidson-Liu iterative diagonalization method. Our chosen example is the twelve-mode molecule methanol, for which we have an ab initio representation of the potential which includes the internal rotational motion of the OH group relative to CH3. Our new algorithm allows us to obtain converged energy levels for matrices of dimensions in excess of 100 000.