Analysis of the projected Coupled Cluster Method in Electronic Structure Calculation

The electronic Schrödinger equation plays a fundamental role in molcular physics. It describes the stationary nonrelativistic behaviour of an quantum mechanical N electron system in the electric field generated by the nuclei. The (Projected) Coupled Cluster Method has been developed for the numerical computation of the ground state energy and wave function. It provides a powerful tool for high accuracy electronic structure calculations. The present paper aims to provide a rigorous analytical treatment and convergence analysis of this method. If the discrete Hartree Fock solution is sufficiently good, the quasi-optimal convergence of the projected coupled cluster solution to the full CI solution is shown. Under reasonable assumptions also the convergence to the exact wave function can be shown in the Sobolev H^1-norm. The error of the ground state energy computation is estimated by an Aubin Nitsche type approach. Although the Projected Coupled Cluster method is nonvariational it shares advantages with the Galerkin or CI method. In addition it provides size consistency, which is considered as a fundamental property in many particle quantum mechanics

Tensor Product Approximation (DMRG) and Coupled Cluster method in Quantum Chemistry

We present the Copupled Cluster (CC) method and the Density matrix Renormalization Grooup (DMRG) method in a unified way, from the perspective of recent developments in tensor product approximation. We present an introduction into recently developed hierarchical tensor representations, in particular tensor trains which are matrix product states in physics language. The discrete equations of full CI approximation applied to the electronic Schr\"odinger equation is casted into a tensorial framework in form of the second quantization. A further approximation is performed afterwards by tensor approximation within a hierarchical format or equivalently a tree tensor network. We establish the (differential) geometry of low rank hierarchical tensors and apply the Driac Frenkel principle to reduce the original high-dimensional problem to low dimensions. The DMRG algorithm is established as an optimization method in this format with alternating directional search. We briefly introduce the CC method and refer to our theoretical results. We compare this approach in the present discrete formulation with the CC method and its underlying exponential parametrization.Comment: 15 pages, 3 figure

Structure, reactivity and electronic properties of V-doped Co clusters

Structures, physical and chemical properties of V doped Co$_{13}$ clusters have been studied in detail using density functional theory based first-principles method. We have found anomalous variation in stability of the doped clusters with increasing V concentration, which has been nicely demonstrated in terms of energetics and electronic properties of the clusters. Our study explains the nonmonotonic variation in reactivity of Co$_{13-m}$V$_m$ clusters towards H$_2$ molecules as reported experimentally [J. Phys. Chem. {\bf 94}, 2744 (1990)]. Moreover, it provides useful insight into the cluster geometry and chemically active sites on the cluster surface, which can help to design better catalytic processes.Comment: 10 pages, 9 figures, 4 table

First-principles calculation on the transport properties of molecular wires between Au clusters under equilibrium

Based on the matrix Green's function method combined with hybrid tight-binding / density functional theory, we calculate the conductances of a series of gold-dithiol molecule-gold junctions including benzenedithiol (BDT), benzenedimethanethiol (BDMT), hexanedithiol (HDT), octanedithiol (ODT) and decanedithiol (DDT). An atomically-contacted extended molecule model is used in our calculation. As an important procedure, we determine the position of the Fermi level by the energy reference according to the results from ultraviolet photoelectron spectroscopy (UPS) experiments. After considering the experimental uncertainty in UPS measurement, the calculated results of molecular conductances near the Fermi level qualitatively agree with the experimental values measured by Tao et. al. [{\it Science} 301, 1221 (2003); {\it J. Am. Chem. Soc.} 125, 16164 (2003); {\it Nano. Lett.} 4, 267 (2004).]Comment: 12 pages,8 figure