A numerical canonical transformation approach to quantum many body problems

We present a new approach for numerical solutions of ab initio quantum chemistry systems. The main idea of the approach, which we call canonical diagonalization, is to diagonalize directly the second quantized Hamiltonian by a sequence of numerical canonical transformations.Comment: 10 pages, 3 encapsulated figures. Parts of the paper are substantially revised to refer to previous similar method

Controlling the accuracy of the density matrix renormalization group method: The Dynamical Block State Selection approach

We have applied the momentum space version of the Density Matrix Renormalization Group method ($k$-DMRG) in quantum chemistry in order to study the accuracy of the algorithm in the new context. We have shown numerically that it is possible to determine the desired accuracy of the method in advance of the calculations by dynamically controlling the truncation error and the number of block states using a novel protocol which we dubbed Dynamical Block State Selection (DBSS). The relationship between the real error and truncation error has been studied as a function of the number of orbitals and the fraction of filled orbitals. We have calculated the ground state of the molecules CH$_2$, H$_2$O, and F$_2$ as well as the first excited state of CH$_2$. Our largest calculations were carried out with 57 orbitals, the largest number of block states was 1500--2000, and the largest dimensions of the Hilbert space of the superblock configuration was 800.000--1.200.000.Comment: 12 page

Accurate ab initio spin densities

We present an approach for the calculation of spin density distributions for molecules that require very large active spaces for a qualitatively correct description of their electronic structure. Our approach is based on the density-matrix renormalization group (DMRG) algorithm to calculate the spin density matrix elements as basic quantity for the spatially resolved spin density distribution. The spin density matrix elements are directly determined from the second-quantized elementary operators optimized by the DMRG algorithm. As an analytic convergence criterion for the spin density distribution, we employ our recently developed sampling-reconstruction scheme [J. Chem. Phys. 2011, 134, 224101] to build an accurate complete-active-space configuration-interaction (CASCI) wave function from the optimized matrix product states. The spin density matrix elements can then also be determined as an expectation value employing the reconstructed wave function expansion. Furthermore, the explicit reconstruction of a CASCI-type wave function provides insights into chemically interesting features of the molecule under study such as the distribution of $\alpha$- and $\beta$-electrons in terms of Slater determinants, CI coefficients, and natural orbitals. The methodology is applied to an iron nitrosyl complex which we have identified as a challenging system for standard approaches [J. Chem. Theory Comput. 2011, 7, 2740].Comment: 37 pages, 13 figure

Ab initio Calculation of Molecular Hydrogen Electronic States' Properties: Fine Structure Spin-Spin Constants.

International audienceThe aim of this work is the ab initio study of the properties of the electronically excited states of the H2 molecule for progressively higher states. Computations are performed using the recent DYCI code developed by Mitrushenkov. The DYCI code allows the very accurate calculation of the energies of molecular electronic excited states and of their properties such as transition moments, fine structure constants (spin-orbit and spin-spin), non-adiabatic coupling matrix elements. Fine structure spin-spin constants for Rydberg series np3Pi u (n = 2,3,4), nd3Pi g (n = 3,4,5), nd3Delta g (n = 3,4) and for the first three TMPH2191math001 states have been calculated for a range of internuclear distances spanning 0.6 to 12 bohr. Comparison with available experimental results is provided

Ab initio calculation of molecular hydrogen electronic states' properties: transition matrix elements among triplet electronic states

International audienceThe aim of this work is the ab initio study of the properties of the electronically excited states of the H2 molecule for progressively higher states. Computations are performed using the optimized full CI code which allowed us to make very accurate calculations of the energies of the molecular electronic excited states and of their properties, such as transition moments, fine structure constants (spin-orbit and spin-spin), non-adiabatic coupling matrix elements. Seventeen new transition matrix elements among the triplet electronic states dissociating to the second (H(1s)+H(2l)) and third (H(1s)+H(3l)) asymptotes have been calculated for internuclear distances ranging from 0.6 to 12 bohr. They involve the following upper electronic states: 4,5,6 Delta g and 13Delta u. The potential energies of the 13Delta u and 43Pi u electronic states have also been obtained for similar internuclear distances

Ab initio calculation of molecular hydrogen electronic states' properties: fine structure spin-spin constants

International audienceThe aim of this work is the ab initio study of the properties of the electronically excited states of the H2 molecule for progressively higher states. Computations are performed using the recent DYCI code developed by Mitrushenkov. The DYCI code allows the very accurate calculation of the energies of molecular electronic excited states and of their properties such as transition moments, fine structure constants (spin-orbit and spin-spin), non-adiabatic coupling matrix elements. Fine structure spin-spin constants for Rydberg series np3Pi u (n = 2,3,4), nd3Pi g (n = 3,4,5), nd3Delta g (n = 3,4) and for the first three TMPH2191math001 states have been calculated for a range of internuclear distances spanning 0.6 to 12 bohr. Comparison with available experimental results is provided

Quantum chemistry using the density matrix renormalization group II

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