44,061 research outputs found
Hilbert space renormalization for the many-electron problem
Renormalization is a powerful concept in the many-body problem. Inspired by
the highly successful density matrix renormalization group (DMRG) algorithm,
and the quantum chemical graphical representation of configuration space, we
introduce a new theoretical tool: Hilbert space renormalization, to describe
many-electron correlations. While in DMRG, the many-body states in nested Fock
subspaces are successively renormalized, in Hilbert space renormalization,
many-body states in nested Hilbert subspaces undergo renormalization. This
provides a new way to classify and combine configurations. The underlying
wavefunction ansatz, namely the Hilbert space matrix product state (HS-MPS),
has a very rich and flexible mathematical structure. It provides low-rank
tensor approximations to any configuration interaction (CI) space through
restricting either the 'physical indices' or the coupling rules in the HS-MPS.
Alternatively, simply truncating the 'virtual dimension' of the HS-MPS leads to
a family of size-extensive wave function ansaetze that can be used efficiently
in variational calculations. We make formal and numerical comparisons between
the HS-MPS, the traditional Fock-space MPS used in DMRG, and traditional CI
approximations. The analysis and results shed light on fundamental aspects of
the efficient representation of many-electron wavefunctions through the
renormalization of many-body states.Comment: 23 pages, 14 figures, The following article has been submitted to The
Journal of Chemical Physic
Many-Body Expanded Full Configuration Interaction. I. Weakly Correlated Regime
Over the course of the past few decades, the field of computational chemistry
has managed to manifest itself as a key complement to more traditional
lab-oriented chemistry. This is particularly true in the wake of the recent
renaissance of full configuration interaction (FCI)-level methodologies, albeit
only if these can prove themselves sufficiently robust and versatile to be
routinely applied to a variety of chemical problems of interest. In the present
series of works, performance and feature enhancements of one such avenue
towards FCI-level results for medium to large one-electron basis sets, the
recently introduced many-body expanded full configuration interaction (MBE-FCI)
formalism [J. Phys. Chem. Lett., 8, 4633 (2017)], will be presented.
Specifically, in this opening part of the series, the capabilities of the
MBE-FCI method in producing near-exact ground state energies for weakly
correlated molecules of any spin multiplicity will be demonstrated.Comment: 38 pages, 7 tables, 3 figures, 1 SI attached as an ancillary fil
Multiconfigurational Short-Range Density-Functional Theory for Open-Shell Systems
Many chemical systems cannot be described by quantum chemistry methods based
on a singlereference wave function. Accurate predictions of energetic and
spectroscopic properties require a delicate balance between describing the most
important configurations (static correlation) and obtaining dynamical
correlation efficiently. The former is most naturally done through a
multiconfigurational (MC) wave function, whereas the latter can be done by,
e.g., perturbation theory. We have employed a different strategy, namely, a
hybrid between multiconfigurational wave functions and density-functional
theory (DFT) based on range separation. The method is denoted by MC short-range
(sr) DFT and is more efficient than perturbative approaches as it capitalizes
on the efficient treatment of the (short-range) dynamical correlation by DFT
approximations. In turn, the method also improves DFT with standard
approximations through the ability of multiconfigurational wave functions to
recover large parts of the static correlation. Until now, our implementation
was restricted to closed-shell systems, and to lift this restriction, we
present here the generalization of MC-srDFT to open-shell cases. The additional
terms required to treat open-shell systems are derived and implemented in the
DALTON program. This new method for open-shell systems is illustrated on
dioxygen and [Fe(H2O)6]3+.Comment: 37 pages, 3 figures, 4 tables, 1 appendix and 79 references Changes
in v2: 1) Appendix B and reference 81 removed 2) Removed dublicated reference
and corrected reference 31. 3) Added spin-charge cross terms to GGA (Appendix
A). Code changed accordingly and GGA results recalculated. All GGA results
are revised -only small modifications observed. Conclusions are unchange
Factorization of point configurations, cyclic covers and conformal blocks
We describe a relation between the invariants of ordered points in
and of points contained in a union of linear subspaces . This yields an attaching map for GIT quotients parameterizing
point configurations in these spaces, and we show that it respects the Segre
product of the natural GIT polarizations. Associated to a configuration
supported on a rational normal curve is a cyclic cover, and we show that if the
branch points are weighted by the GIT linearization and the rational normal
curve degenerates, then the admissible covers limit is a cyclic cover with
weights as in this attaching map. We find that both GIT polarizations and the
Hodge class for families of cyclic covers yield line bundles on
with functorial restriction to the boundary. We introduce a notion of
divisorial factorization, abstracting an axiom from rational conformal field
theory, to encode this property and show that it determines the isomorphism
class of these line bundles. As an application, we obtain a unified, geometric
proof of two recent results on conformal block bundles, one by Fedorchuk and
one by Gibney and the second author.Comment: 17 pages, 3 figure
Second-Order Self-Consistent-Field Density-Matrix Renormalization Group
We present a matrix-product state (MPS)-based quadratically convergent
density-matrix renormalization group self-consistent-field (DMRG-SCF) approach.
Following a proposal by Werner and Knowles (JCP 82, 5053, (1985)), our DMRG-SCF
algorithm is based on a direct minimization of an energy expression which is
correct to second-order with respect to changes in the molecular orbital basis.
We exploit a simultaneous optimization of the MPS wave function and molecular
orbitals in order to achieve quadratic convergence. In contrast to previously
reported (augmented Hessian) Newton-Raphson and super-configuration-interaction
algorithms for DMRG-SCF, energy convergence beyond a quadratic scaling is
possible in our ansatz. Discarding the set of redundant active-active orbital
rotations, the DMRG-SCF energy converges typically within two to four cycles of
the self-consistent procedureComment: 40 pages, 5 figures, 3 table
Can Density Matrix Embedding Theory with the Complete Activate Space Self-Consistent Field Solver Describe Single and Double Bond Breaking in Molecular Systems?
Density matrix embedding theory (DMET) [Phys. Rev. Lett.2012, 109, 186404]
has been demonstrated as an efficient wave-function-based embedding method to
treat extended systems. Despite its success in many quantum lattice models, the
extension of DMET to real chemical systems has been tested only on selected
cases. Herein, we introduce the use of the complete active space
self-consistent field (CASSCF) method as a correlated impurity solver for DMET,
leading to a method called CAS-DMET. We test its performance in describing the
dissociation of a H-H single bond in a H10 ring model system and an N=N double
bond in azomethane (CH3-N=N-CH3) and pentyldiazene (CH3(CH2)4-N=NH). We find
that the performance of CAS-DMET is comparable to CASSCF with different active
space choices when single-embedding DMET corresponding to only one embedding
problem for the system is used. When multiple embedding problems are used for
the system, the CAS-DMET is in a good agreement with CASSCF for the geometries
around the equilibrium, but not in equal agreement at bond dissociation.Comment: 28 pages, 9 figures, TOC graphi
Orbital Optimization in the Active Space Decomposition Model
We report the derivation and implementation of orbital optimization
algorithms for the active space decomposition (ASD) model, which are extensions
of complete active space self-consistent field (CASSCF) and its
occupation-restricted variants in the conventional multiconfiguration
electronic-structure theory. Orbital rotations between active subspaces are
included in the optimization, which allows us to unambiguously partition the
active space into subspaces, enabling application of ASD to electron and
exciton dynamics in covalently linked chromophores. One- and two-particle
reduced density matrices, which are required for evaluation of orbital gradient
and approximate Hessian elements, are computed from the intermediate tensors in
the ASD energy evaluation. Numerical results on
4-(2-naphthylmethyl)-benzaldehyde and [3]cyclophane and model Hamiltonian
analyses of triplet energy transfer processes in the Closs systems are
presented. Furthermore model Hamiltonians for hole and electron transfer
processes in anti-[2.2](1,4)pentacenophane are studied using an
occupation-restricted variant
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