180 research outputs found
Assessing the accuracy of quantum Monte Carlo and density functional theory for energetics of small water clusters
We present a detailed study of the energetics of water clusters (HO)
with , comparing diffusion Monte Carlo (DMC) and approximate density
functional theory (DFT) with well converged coupled-cluster benchmarks. We use
the many-body decomposition of the total energy to classify the errors of DMC
and DFT into 1-body, 2-body and beyond-2-body components. Using both
equilibrium cluster configurations and thermal ensembles of configurations, we
find DMC to be uniformly much more accurate than DFT, partly because some of
the approximate functionals give poor 1-body distortion energies. Even when
these are corrected, DFT remains considerably less accurate than DMC. When both
1- and 2-body errors of DFT are corrected, some functionals compete in accuracy
with DMC; however, other functionals remain worse, showing that they suffer
from significant beyond-2-body errors. Combining the evidence presented here
with the recently demonstrated high accuracy of DMC for ice structures, we
suggest how DMC can now be used to provide benchmarks for larger clusters and
for bulk liquid water.Comment: 34 pages, 6 figure
Analytical Gradients for Projection-Based Wavefunction-in-DFT Embedding
Projection-based embedding provides a simple, robust, and accurate approach
for describing a small part of a chemical system at the level of a correlated
wavefunction method while the remainder of the system is described at the level
of density functional theory. Here, we present the derivation, implementation,
and numerical demonstration of analytical nuclear gradients for
projection-based wavefunction-in-density functional theory (WF-in-DFT)
embedding. The gradients are formulated in the Lagrangian framework to enforce
orthogonality, localization, and Brillouin constraints on the molecular
orbitals. An important aspect of the gradient theory is that WF contributions
to the total WF-in-DFT gradient can be simply evaluated using existing WF
gradient implementations without modification. Another simplifying aspect is
that Kohn-Sham (KS) DFT contributions to the projection-based embedding
gradient do not require knowledge of the WF calculation beyond the relaxed WF
density. Projection-based WF-in-DFT embedding gradients are thus easily
generalized to any combination of WF and KS-DFT methods. We provide numerical
demonstration of the method for several applications, including calculation of
a minimum energy pathway for a hydride transfer in a cobalt-based molecular
catalyst using the nudged-elastic-band method at the CCSD-in-DFT level of
theory, which reveals large differences from the transition state geometry
predicted using DFT.Comment: 15 pages, 4 figure
Exact nonadditive kinetic potentials for embedded density functional theory
We describe an embedded density functional theory (DFT) protocol in which the nonadditive kinetic energy component of the embedding potential is treated exactly. At each iteration of the Kohn–Sham equations for constrained electron density, the Zhao–Morrison–Parr constrained search method for constructing Kohn–Sham orbitals is combined with the King-Handy expression for the exact kinetic potential. We use this formally exact embedding protocol to calculate ionization energies for a series of three- and four-electron atomic systems, and the results are compared to embedded DFT calculations that utilize the Thomas–Fermi (TF) and the Thomas–Fermi–von Weisacker approximations to the kinetic energy functional. These calculations illustrate the expected breakdown due to the TF approximation for the nonadditive kinetic potential, with errors of 30%–80% in the calculated ionization energies; by contrast, the exact protocol is found to be accurate and stable. To significantly improve the convergence of the new protocol, we introduce a density-based switching function to map between the exact nonadditive kinetic potential and the TF approximation in the region of the nuclear cusp, and we demonstrate that this approximation has little effect on the accuracy of the calculated ionization energies. Finally, we describe possible extensions of the exact protocol to perform accurate embedded DFT calculations in large systems with strongly overlapping subsystem densities
Density functional theory embedding for correlated wavefunctions: Improved methods for open-shell systems and transition metal complexes
Density functional theory (DFT) embedding provides a formally exact framework
for interfacing correlated wave-function theory (WFT) methods with lower-level
descriptions of electronic structure. Here, we report techniques to improve the
accuracy and stability of WFT-in-DFT embedding calculations. In particular, we
develop spin-dependent embedding potentials in both restricted and unrestricted
orbital formulations to enable WFT-in-DFT embedding for open-shell systems, and
we develop an orbital-occupation-freezing technique to improve the convergence
of optimized effective potential (OEP) calculations that arise in the
evaluation of the embedding potential. The new techniques are demonstrated in
applications to the van-der-Waals-bound ethylene-propylene dimer and to the
hexaaquairon(II) transition-metal cation. Calculation of the dissociation curve
for the ethylene-propylene dimer reveals that WFT-in-DFT embedding reproduces
full CCSD(T) energies to within 0.1 kcal/mol at all distances, eliminating
errors in the dispersion interactions due to conventional exchange-correlation
(XC) functionals while simultaneously avoiding errors due to subsystem
partitioning across covalent bonds. Application of WFT-in-DFT embedding to the
calculation of the low-spin/high-spin splitting energy in the hexaaquairon(II)
cation reveals that the majority of the dependence on the DFT XC functional can
be eliminated by treating only the single transition-metal atom at the WFT
level; furthermore, these calculations demonstrate the substantial effects of
open-shell contributions to the embedding potential, and they suggest that
restricted open-shell WFT-in-DFT embedding provides better accuracy than
unrestricted open-shell WFT-in-DFT embedding due to the removal of spin
contamination.Comment: 11 pages, 5 figures, 2 table
Even-handed subsystem selection in projection-based embedding
Projection-based embedding offers a simple framework for embedding correlated wavefunction methods in density functional theory. Partitioning between the correlated wavefunction and density functional subsystems is performed in the space of localized molecular orbitals. However, during a large geometry change—such as a chemical reaction—the nature of these localized molecular orbitals, as well as their partitioning into the two subsystems, can change dramatically. This can lead to unphysical cusps and even discontinuities in the potential energy surface. In this work, we present an even-handed framework for localized orbital partitioning that ensures consistent subsystems across a set of molecular geometries. We illustrate this problem and the even-handed solution with a simple example of an S_N2 reaction. Applications to a nitrogen umbrella flip in a cobalt-based CO_2 reduction catalyst and to the binding of CO to Cu clusters are presented. In both cases, we find that even-handed partitioning enables chemically accurate embedding with modestly sized embedded regions for systems in which previous partitioning strategies are problematic
Energy benchmarks for water clusters and ice structures from an embedded many-body expansion
We show how an embedded many-body expansion (EMBE) can be used to calculate
accurate \emph{ab initio} energies of water clusters and ice structures using
wavefunction-based methods. We use the EMBE described recently by Bygrave
\emph{et al.} (J. Chem. Phys. \textbf{137}, 164102 (2012)), in which the terms
in the expansion are obtained from calculations on monomers, dimers, etc. acted
on by an approximate representation of the embedding field due to all other
molecules in the system, this field being a sum of Coulomb and
exchange-repulsion fields. Our strategy is to separate the total energy of the
system into Hartree-Fock and correlation parts, using the EMBE only for the
correlation energy, with the Hartree-Fock energy calculated using standard
molecular quantum chemistry for clusters and plane-wave methods for crystals.
Our tests on a range of different water clusters up to the 16-mer show that for
the second-order M\o{}ller-Plesset (MP2) method the EMBE truncated at 2-body
level reproduces to better than 0.1 m/monomer the correlation energy
from standard methods. The use of EMBE for computing coupled-cluster energies
of clusters is also discussed. For the ice structures Ih, II and VIII, we find
that MP2 energies near the complete basis-set limit reproduce very well the
experimental values of the absolute and relative binding energies, but that the
use of coupled-cluster methods for many-body correlation (non-additive
dispersion) is essential for a full description. Possible future applications
of the EMBE approach are suggested
Linear-response time-dependent embedded mean-field theory
We present a time-dependent (TD) linear-response description of excited electronic states within the framework of embedded mean-field theory (EMFT). TD-EMFT allows for subsystems to be described at different mean-field levels of theory, enabling straightforward treatment of excited states and transition properties. We provide benchmark demonstrations of TD-EMFT for both local and nonlocal excitations in organic molecules, as well as applications to chlorophyll a, solvatochromic shifts of a dye in solution, and sulfur K-edge X-ray absorption spectroscopy (XAS). It is found that mixed-basis implementations of TD-EMFT lead to substantial errors in terms of transition properties; however, as previously found for ground-state EMFT, these errors are largely eliminated with the use of Fock-matrix corrections. These results indicate that TD-EMFT is a promising method for the efficient, multilevel description of excited-state electronic structure and dynamics in complex systems
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