Partitioning technique for a discrete quantum system

We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show that the effective Hamiltonian on the central graph can be constructed by adding additional potentials on the branch-root nodes, which generates the same result as does the the original Hamiltonian on the entire graph. Exactly solvable models are presented to demonstrate the main points of this paper.Comment: 7 pages, 2 figure

Application of Many-Body Rayleigh-Schrodinger Perturbation Theory to Excitations Accompanying Photoionization in Molecules

Excitations accompanying photoionizations in molecules (shake- up processes) are studied on the basis of degenerate many-body Rayleigh-Schr6dinger perturbation theory (MB - RSPT). These excitations give rise to satellite lines accompanyin ionization lines. Decomposition of correlation effects in these processes into those corresponding to single-particle excitation and single- particle ionization is discussed

Centre-of-mass separation in quantum mechanics: Implications for the many-body treatment in quantum chemistry and solid state physics

We address the question to what extent the centre-of-mass (COM) separation can change our view of the many-body problem in quantum chemistry and solid state physics. It was shown that the many-body treatment based on the electron-vibrational Hamiltonian is fundamentally inconsistent with the Born-Handy ansatz so that such a treatment can never respect the COM problem. Born-Oppenheimer (B-O) approximation reveals some secret: it is a limit case where the degrees of freedom can be treated in a classical way. Beyond the B-O approximation they are inseparable in principle. The unique covariant description of all equations with respect to individual degrees of freedom leads to new types of interaction: besides the known vibronic (electron-phonon) one the rotonic (electron-roton) and translonic (electron-translon) interactions arise. We have proved that due to the COM problem only the hypervibrations (hyperphonons, i.e. phonons + rotons + translons) have true physical meaning in molecules and crystals; nevertheless, the use of pure vibrations (phonons) is justified only in the adiabatic systems. This fact calls for the total revision of our contemporary knowledge of all non-adiabatic effects, especially the Jahn-Teller effect and superconductivity. The vibronic coupling is responsible only for removing of electron (quasi)degeneracies but for the explanation of symmetry breaking and forming of structure the rotonic and translonic coupling is necessary.Comment: 39 pages, 11 sections, 3 appendice

Ab Initio MBPT(4) Calculations of the Inversion Potential Function of NH3

The inversion potential function and the dominant (in-plane) and inversion-(in-plane) force constants are calculated by means of the fourth-order many-body perturbation theory in the extended double-zeta-plus polarization basis set. Using the ab initio potential surfaces and the non-rigid invertor Hamiltonian the inversion energy levels of 14NH3 are calculated. Despite the significant residual error in the perturbation expansion, the results indicate that the full fourth order procedure may be considered as a reliable tool for studying vibrational anharmonicity in other non-rigid molecules

Ab initio structural study of the B4H4 molecule. Asymmetric structure for a 'symmetric' system

Ab initio calculations on the B4H4 molecule using MP2, MP4, and CISD methodologies, reveal that the ground state of this system has a (planar) Cs instead of the highly symmetric Td structure, the energy difference being approximately 6 kcal/mol. An attempt is made to rationalise this finding by invoking the excited a 3Π state of the B-H unit. © 1994

On the ground states of CaC and ZnC: A multireference Brillouin-Wigner coupled cluster study

A multireference Brillouin-Wigner coupled cluster study for the ground states of CaC and ZnC was developed. Potential energy curves for both states at selected levels of theory were depicted. The large Davidson correction and the RCCSD(T) results indicated the inadequacy of the single reference treatments

Effects of electron-phonon interaction on thermal and electrical transport through molecular nano-conductors

The topic of this review is the effects of electron-phonon interaction (EPI) on the transport properties of molecular nano-conductors. A nano-conductor connects to two electron leads and two phonon leads, possibly at different temperatures or chemical potentials. The EPI appears only in the nano-conductor. We focus on its effects on charge and energy transport. We introduce three approaches. For weak EPI, we use the nonequilibrium Green’s function method to treat it perturbatively. We derive the expressions for the charge and heat currents. For weak system-lead couplings, we use the quantum master equation approach. In both cases, we use a simple single level model to study the effects of EPI on the system’s thermoelectric transport properties. It is also interesting to look at the effect of currents on the dynamics of the phonon system. For this, we derive a semi-classical generalized Langevin equation to describe the nano-conductor’s atomic dynamics, taking the nonequilibrium electron system, as well as the rest of the atomic degrees of freedom as effective baths. We show simple applications of this approach to the problem of energy transfer between electrons and phonons