29 research outputs found
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
Accurate spline solutions of the Dirac equation with parity-nonconserving potential
The complete system of the B-spline solutions for the Dirac equation with the
parity-nonconserving (PNC) weak interaction effective potential is obtained.
This system can be used for the accurate evaluation of the radiative
corrections to the PNC amplitudes in the multicharged ions and neutral atoms.
The use of the scaling procedure allows for the evaluation of the PNC matrix
elements with relative accuracy .Comment: 7 page
Loop-after-loop contribution to the second-order Lamb shift in hydrogenlike low-Z atoms
We present a numerical evaluation of the loop-after-loop contribution to the
second-order self-energy for the ground state of hydrogenlike atoms with low
nuclear charge numbers Z. The calculation is carried out in the Fried-Yennie
gauge and without an expansion in Z \alpha. Our calculation confirms the
results of Mallampalli and Sapirstein and disagrees with the calculation by
Goidenko and coworkers. A discrepancy between different calculations is
investigated. An accurate fitting of the numerical results provides a detailed
comparison with analytic calculations based on an expansion in the parameter Z
\alpha. We confirm the analytic results of order \alpha^2 (Z\alpha)^5 but
disagree with Karshenboim's calculation of the \alpha^2 (Z \alpha)^6 \ln^3(Z
\alpha)^{-2} contribution.Comment: RevTex, 19 pages, 4 figure
The Standard Model in Strong Fields: Electroweak Radiative Corrections for Highly Charged Ions
Electroweak radiative corrections to the matrix elements are calculated for highly charged hydrogenlike ions. These
matrix elements constitute the basis for the description of the most parity
nonconserving (PNC) processes in atomic physics. The operator
represents the parity nonconserving relativistic effective atomic Hamiltonian
at the tree level. The deviation of these calculations from the calculations
valid for the momentum transfer demonstrates the effect of the strong
field, characterized by the momentum transfer ( is the
electron mass). This allows for a test of the Standard Model in the presence of
strong fields in experiments with highly charged ions.Comment: 27 LaTex page
The second-order electron self-energy in hydrogen-like ions
A calculation of the simplest part of the second-order electron self-energy
(loop after loop irreducible contribution) for hydrogen-like ions with nuclear
charge numbers is presented. This serves as a test for the
more complicated second-order self-energy parts (loop inside loop and crossed
loop contributions) for heavy one-electron ions. Our results are in strong
disagreement with recent calculations of Mallampalli and Sapirstein for low
values but are compatible with the two known terms of the analytical
-expansion.Comment: 13 LaTex pages, 2 figure
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 (-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, HO, and F as well as the first excited state of CH. 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 - and -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