Faddeev-Jackiw canonical path integral quantization for a general scenario, its proper vertices and generating functionals

We generalize the Faddeev-Jackiw canonical path integral quantization for the scenario of a Jacobian with J=1 to that for the general scenario of non-unit Jacobian, give the representation of the quantum transition amplitude with symplectic variables and obtain the generating functionals of the Green function and connected Green function. We deduce the unified expression of the symplectic field variable functions in terms of the Green function or the connected Green function with external sources. Furthermore, we generally get generating functionals of the general proper vertices of any n-points cases under the conditions of considering and not considering Grassmann variables, respectively; they are regular and are the simplest forms relative to the usual field theory.

Dynamics of quantum dissipation systems interacting with fermion and boson grand canonical bath ensembles: Hierarchical equations of motion approach

A hierarchical equations of motion formalism for a quantum dissipation system in a grand canonical bath ensemble surrounding is constructed on the basis of the calculus-on-path-integral algorithm, together with the parametrization of arbitrary non-Markovian bath that satisfies fluctuation-dissipation theorem. The influence functionals for both the fermion or boson bath interaction are found to be of the same path integral expression as the canonical bath, assuming they all satisfy the Gaussian statistics. However, the equation of motion formalism is different due to the fluctuation-dissipation theories that are distinct and used explicitly. The implications of the present work to quantum transport through molecular wires and electron transfer in complex molecular systems are discussed. (c) 2007 American Institute of Physics.

Electronic structures of 4d transition metal monoxides by density functional theory

Bond distances, dissociation energies, ionization potentials and electron affinities of 4d transition metal monoxides from YO to CdO and their positive and negative ions were studied by use of density functional methods B3LYP, BLYP, B3PW91, BPW91, B3P86, BP86, SVWN, MPW1PW91 and PBE1PBE. It was found that calculated properties are highly dependent on the functionals employed, especially for dissociation energy. For most neutral species, pure density functionals BLYP, BPW91 and BP86 have good performance in predicting dissociation energy than hybrid density functionals B3LYP, B3PW91 and B3P86. In addition, BLYP gives the largest bond distance compared with other density functional methods, while SVWN gives shortest bond distance, largest dissociation energy and electron affinity. For the ground state, the spin multiplicity of the charged species can be obtained by +/- 1 of their corresponding neutral species.

Electronic structures of MCO (M = Nb, Ta, Rh, Ir, Pd, Pt) molecules by density functional theory

Equilibrium geometries, vibrational frequencies, and dissociation energies of the transition metal carbonyls MCO (M = Nb, Ta, Rh, Ir, Pd, Pt) were studied by use of diverse density functional methods B3LYP, BLYP, B3P86, B3PW91, BHLYP, BP86, and PBE1PBE. It was found that the ground electronic state is (6)Sigma(+) for NbCO and TaCO, (2)Sigma(+) for RhCO,(2)Delta for IrCO, and (1)Sigma(+) for PdCO and PtCO, in agreement with previous theoretical studies. The calculated properties are highly dependent on the functionals employed, in particular for the dissociation energy. For most of the molecules, the predicted bond distance is in agreement with experiments and previous theoretical results. BHLYP is the worst method in reproducing the experimental results compared with the other density functional methods for the title molecules.

Density-functional study of lanthanum, ytterbium, and lutetium dimers

La-2, Yb-2, and Lu-2 have been studied by use of the density-functional methods B3LYP, BLYP, B3PW91, BHLYP, BP86, B3P86, MPW1PW91, and PBE1PBE. In these density-functional methods, the exchange functional is from either Becke's three-parameter HF-DFT hybrid exchange functional (B3), pure DFT exchange functional of 1988 (B), a modification of the half-and-half HF/DFT hybrid method (BH), Perdew-Wang 1991 (PW91), or Barone's modified PW91 (MPW1), while the correlation functional is from either Lee, Yang, and Parr (LYP), Perdew-Wang 1991 (PW91), or Perdew 86 (P86). PBE1PBE is the generalized-gradient-approximation exchange-correlation functional of Perdew, Burke, and Ernzerhof. For La-2, the calculated bond distance is in reasonable agreement with the experiment, but the calculated vibrational frequency is underestimated significantly compared with the experiment. Only BP86 and B3P86 have the best performance in reproducing the experimental dissociation energy for La-2. For the van der Waals dimer Yb-2, three functionals, B3LYP, BLYP, and BHLYP have excellent performance in reproducing the spectroscopic constants compared with both the experiment and previous theoretical studies.

Electronic structures of 3d-metal mononitrides

Bond distances, vibrational frequencies, electron affinities, ionization potentials, and dissociation energies of the title molecules in neutral, positively, and negatively charged ions were studied by use of density functional methods B3LYP, BLYP, BHLYP, BPW91, and B3PW91. The calculated results are compared with experiments and previous theoretical studies. It was found that the calculated properties are highly dependent on the functionals employed, in particular for the dissociation energy and vibrational frequency. For neutral species, pure density functional methods BLYP and BPW91 have relatively good performance in reproducing the experimental bond distance and vibrational frequency. For cations, hybrid exchange functional methods B3LYP and B3PW91 are good in predicting the dissociation energy. For both neutral and charged species, BHLYP tends to give smaller dissociation energy.