574 research outputs found
Sequential decoupling of negative-energy states in Douglas-Kroll-Hess theory
Here, we review the historical development, current status, and prospects of
Douglas--Kroll--Hess theory as a quantum chemical relativistic electrons-only
theory.Comment: 15 page
Vibrational Density Matrix Renormalization Group
Variational approaches for the calculation of vibrational wave functions and
energies are a natural route to obtain highly accurate results with
controllable errors. However, the unfavorable scaling and the resulting high
computational cost of standard variational approaches limit their application
to small molecules with only few vibrational modes. Here, we demonstrate how
the density matrix renormalization group (DMRG) can be exploited to optimize
vibrational wave functions (vDMRG) expressed as matrix product states. We study
the convergence of these calculations with respect to the size of the local
basis of each mode, the number of renormalized block states, and the number of
DMRG sweeps required. We demonstrate the high accuracy achieved by vDMRG for
small molecules that were intensively studied in the literature. We then
proceed to show that the complete fingerprint region of the sarcosyn-glycin
dipeptide can be calculated with vDMRG.Comment: 21 pages, 5 figures, 4 table
Finite-size version of the excitonic instability in graphene quantum dots
By a combination of Hartree-Fock simulations, exact diagonalization, and
perturbative calculations, we investigate the ground-state properties of
disorder-free circular quantum dots formed in a graphene monolayer. Taking the
reference chemical potential at the Dirac point, we study N \leq 15 interacting
particles, where the fine structure constant {\alpha} parametrizes the Coulomb
interaction. We explore three different theoretical concepts: (i) Sucher's
positive projection ("no-pair") approach, (ii) a more general Hamiltonian
conserving both N and the number of additional electron-hole pairs, and (iii)
the full quantum electrodynamics (QED) problem, where only N is conserved. We
find that electron-hole pair production is important for {\alpha} 1. This
corresponds to a reconstruction of the filled Dirac sea and is a finite-size
version of the bulk excitonic instability. We also address the effects of an
orbital magnetic field.Comment: 9 pages, 10 figures, to appear in PR
Explicitly correlated Gaussian functions with shifted-center and projection techniques in pre-Born-Oppenheimer calculations
Numerical projection methods are elaborated for the calculation of
eigenstates of the non-relativistic many-particle Coulomb Hamiltonian with
selected rotational and parity quantum numbers employing shifted explicitly
correlated Gaussian functions, which are, in general, not eigenfunctions of the
total angular momentum and parity operators. The increased computational cost
of numerically projecting the basis functions onto the irreducible
representations of the three dimensional rotation-inversion group is the price
to pay for the increased flexibility of the basis functions. This increased
flexibility allowed us to achieve a substantial improvement for the variational
upper bound to the Pauli-allowed ground-state energy of the
Hpppee molecular ion treated as an explicit
five-particle system. We compare our pre-Born-Oppenheimer result for this
molecular ion with rovibrational results including non-adiabatic corrections.Comment: 29 pages, 3 figures, 4 table
Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules
We present a new class of tensor network states that are specifically
designed to capture the electron correlation of a molecule of arbitrary
structure. In this ansatz, the electronic wave function is represented by a
Complete-Graph Tensor Network (CGTN) ansatz which implements an efficient
reduction of the number of variational parameters by breaking down the
complexity of the high-dimensional coefficient tensor of a
full-configuration-interaction (FCI) wave function. We demonstrate that CGTN
states approximate ground states of molecules accurately by comparison of the
CGTN and FCI expansion coefficients. The CGTN parametrization is not biased
towards any reference configuration in contrast to many standard quantum
chemical methods. This feature allows one to obtain accurate relative energies
between CGTN states which is central to molecular physics and chemistry. We
discuss the implications for quantum chemistry and focus on the spin-state
problem. Our CGTN approach is applied to the energy splitting of states of
different spin for methylene and the strongly correlated ozone molecule at a
transition state structure. The parameters of the tensor network ansatz are
variationally optimized by means of a parallel-tempering Monte Carlo algorithm
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
Block-Diagonalization of Operators with Gaps, with Applications to Dirac Operators
We present new results on the block-diagonalization of Dirac operators on
three-dimensional Euclidean space with unbounded potentials. Classes of
admissible potentials include electromagnetic potentials with strong Coulomb
singularities and more general matrix-valued potentials, even non-self-adjoint
ones. For the Coulomb potential, we achieve an exact diagonalization up to
nuclear charge Z=124 and prove the convergence of the Douglas-Kroll-He\ss\
approximation up to Z=62, thus improving the upper bounds Z=93 and Z=51,
respectively, by H.\ Siedentop and E.\ Stockmeyer considerably. These results
follow from abstract theorems on perturbations of spectral subspaces of
operators with gaps, which are based on a method of H.\ Langer and C.\ Tretter
and are also of independent interest
Semi- and Non-relativistic Limit of the Dirac Dynamics with External Fields
We show how to approximate Dirac dynamics for electronic initial states by
semi- and non-relativistic dynamics. To leading order, these are generated by
the semi- and non-relativistic Pauli hamiltonian where the kinetic energy is
related to and , respectively. Higher-order
corrections can in principle be computed to any order in the small parameter
v/c which is the ratio of typical speeds to the speed of light. Our results
imply the dynamics for electronic and positronic states decouple to any order
in v/c << 1.
To decide whether to get semi- or non-relativistic effective dynamics, one
needs to choose a scaling for the kinetic momentum operator. Then the effective
dynamics are derived using space-adiabatic perturbation theory by Panati et. al
with the novel input of a magnetic pseudodifferential calculus adapted to
either the semi- or non-relativistic scaling.Comment: 42 page
Reliable estimation of prediction uncertainty for physico-chemical property models
The predictions of parameteric property models and their uncertainties are
sensitive to systematic errors such as inconsistent reference data, parametric
model assumptions, or inadequate computational methods. Here, we discuss the
calibration of property models in the light of bootstrapping, a sampling method
akin to Bayesian inference that can be employed for identifying systematic
errors and for reliable estimation of the prediction uncertainty. We apply
bootstrapping to assess a linear property model linking the 57Fe Moessbauer
isomer shift to the contact electron density at the iron nucleus for a diverse
set of 44 molecular iron compounds. The contact electron density is calculated
with twelve density functionals across Jacob's ladder (PWLDA, BP86, BLYP, PW91,
PBE, M06-L, TPSS, B3LYP, B3PW91, PBE0, M06, TPSSh). We provide systematic-error
diagnostics and reliable, locally resolved uncertainties for isomer-shift
predictions. Pure and hybrid density functionals yield average prediction
uncertainties of 0.06-0.08 mm/s and 0.04-0.05 mm/s, respectively, the latter
being close to the average experimental uncertainty of 0.02 mm/s. Furthermore,
we show that both model parameters and prediction uncertainty depend
significantly on the composition and number of reference data points.
Accordingly, we suggest that rankings of density functionals based on
performance measures (e.g., the coefficient of correlation, r2, or the
root-mean-square error, RMSE) should not be inferred from a single data set.
This study presents the first statistically rigorous calibration analysis for
theoretical Moessbauer spectroscopy, which is of general applicability for
physico-chemical property models and not restricted to isomer-shift
predictions. We provide the statistically meaningful reference data set MIS39
and a new calibration of the isomer shift based on the PBE0 functional.Comment: 49 pages, 9 figures, 7 table
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