461 research outputs found
New Benchmark Set of Transition-Metal Coordination Reactions for the Assessment of Density Functionals
We present the WCCR10 data set of ten ligand dissociation energies of large
cationic transition metal complexes for the assessment of approximate
exchange--correlation functionals. We analyze nine popular functionals, namely
BP86, BP86-D3, B3LYP, B3LYP-D3, B97-D-D2, PBE, TPSS, PBE0, and TPSSh by mutual
comparison and by comparison to experimental gas-phase data measured with
well-known precision. The comparison of all calculated data reveals a large,
system-dependent scattering of results with nonnegligible consequences for
computational chemistry studies on transition metal compounds. Considering
further the comparison with experiment, the non-empirical functionals PBE and
TPSS turn out to be among the best functionals for our reference data set. The
deviation can be lowered further by including Hartree--Fock exchange.
Accordingly, PBE0 and TPSSh are the two most accurate functionals for our test
set, but also these functionals exhibit deviations from experiment by up to 50
kJ/mol for individual reactions. As an important result we found no functional
to be reliable for all reactions. Furthermore, for some of the ligand
dissociation energies studied in this work, dispersion corrections yield
results which increase the deviation from experiment. This deviation increases
further if structure optimization including dispersion corrections is
performed. Finally, we compare our results to other benchmark studies and
highlight that the performance assessed for different density functionals
depends significantly on the reference molecule set chosen.Comment: 36 pages, 7 figures, 3 table
Interactive Chemical Reactivity Exploration
Elucidating chemical reactivity in complex molecular assemblies of a few
hundred atoms is, despite the remarkable progress in quantum chemistry, still a
major challenge. Black-box search methods to find intermediates and
transition-state structures might fail in such situations because of the
high-dimensionality of the potential energy surface. Here, we propose the
concept of interactive chemical reactivity exploration to effectively introduce
the chemist's intuition into the search process. We employ a haptic pointer
device with force-feedback to allow the operator the direct manipulation of
structures in three dimensions along with simultaneous perception of the
quantum mechanical response upon structure modification as forces. We elaborate
on the details of how such an interactive exploration should proceed and which
technical difficulties need to be overcome. All reactivity-exploration concepts
developed for this purpose have been implemented in the Samson programming
environment.Comment: 36 pages, 14 figure
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
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
Quantum information analysis of electronic states at different molecular structures
We have studied transition metal clusters from a quantum information theory
perspective using the density-matrix renormalization group (DMRG) method. We
demonstrate the competition between entanglement and interaction localization.
We also discuss the application of the configuration interaction based
dynamically extended active space procedure which significantly reduces the
effective system size and accelerates the speed of convergence for complicated
molecular electronic structures to a great extent. Our results indicate the
importance of taking entanglement among molecular orbitals into account in
order to devise an optimal orbital ordering and carry out efficient
calculations on transition metal clusters. We propose a recipe to perform DMRG
calculations in a black-box fashion and we point out the connections of our
work to other tensor network state approaches
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
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
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