25 research outputs found
Density matrix embedding: A strong-coupling quantum embedding theory
We extend our density matrix embedding theory (DMET) [Phys. Rev. Lett. 109
186404 (2012)] from lattice models to the full chemical Hamiltonian. DMET
allows the many-body embedding of arbitrary fragments of a quantum system, even
when such fragments are open systems and strongly coupled to their environment
(e.g., by covalent bonds). In DMET, empirical approaches to strong coupling,
such as link atoms or boundary regions, are replaced by a small, rigorous
quantum bath designed to reproduce the entanglement between a fragment and its
environment. We describe the theory and demonstrate its feasibility in strongly
correlated hydrogen ring and grid models; these are not only beyond the scope
of traditional embeddings, but even challenge conventional quantum chemistry
methods themselves. We find that DMET correctly describes the notoriously
difficult symmetric dissociation of a 4x3 hydrogen atom grid, even when the
treated fragments are as small as single hydrogen atoms. We expect that DMET
will open up new ways of treating of complex strongly coupled, strongly
correlated systems in terms of their individual fragments.Comment: 5 pages, 4 figure
The intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model
We obtain the phase-diagram of the half-filled honeycomb Hubbard model with
density matrix embedding theory, to address recent controversy at intermediate
couplings. We use clusters from 2-12 sites and lattices at the thermodynamic
limit. We identify a paramagnetic insulating state, with possible hexagonal
cluster order, competitive with the antiferromagnetic phase at intermediate
coupling. However, its stability is strongly cluster and lattice size
dependent, explaining controver- sies in earlier work. Our results support the
paramagnetic insulator as being a metastable, rather than a true, intermediate
phase, in the thermodynamic limit
Visualizing Complex-Valued Molecular Orbitals
We report an implementation of a program for visualizing complex-valued
molecular orbitals. The orbital phase information is encoded on each of the
vertices of triangle meshes using the standard color wheel. Using this program,
we visualized the molecular orbitals for systems with spin-orbit couplings,
external magnetic fields, and complex absorbing potentials. Our work has not
only created visually attractive pictures, but also clearly demonstrated that
the phases of the complex-valued molecular orbitals carry rich chemical and
physical information of the system, which has often been unnoticed or
overlooked
Density matrix embedding: A simple alternative to dynamical mean-field theory
We introduce DMET, a new quantum embedding theory for predicting ground-state
properties of infinite systems. Like dynamical mean-field theory (DMFT), DMET
maps the the bulk interacting system to a simpler impurity model and is exact
in the non-interacting and atomic limits. Unlike DMFT, DMET is formulated in
terms of the frequency-independent local density matrix, rather than the local
Green's function. In addition, it features a finite, algebraically
constructible bath of only one bath site per impurity site, which exactly
embeds ground-states at a mean-field level with no bath discretization error.
Frequency independence and the minimal bath make DMET a computationally simple
and very efficient method. We test the theory in the 1D and 2D Hubbard models
at and away from half-filling, and we find that compared to benchmark data,
total energies, correlation functions, and paramagnetic metal-insulator
transitions are well reproduced, at a tiny computational cost.Comment: 5 pages, 5 figure
Automated construction of molecular active spaces from atomic valence orbitals
We introduce the atomic valence active space (AVAS), a simple and well-defined automated technique for constructing active orbital spaces for use in multiconfiguration and multireference (MR) electronic structure calculations. Concretely, the technique constructs active molecular orbitals capable of describing all relevant electronic configurations emerging from a targeted set of atomic valence orbitals (e.g., the metal d orbitals in a coordination complex). This is achieved via a linear transformation of the occupied and unoccupied orbital spaces from an easily obtainable single-reference wave function (such as from a Hartree–Fock or Kohn–Sham calculations) based on projectors to targeted atomic valence orbitals. We discuss the premises, theory, and implementation of the idea, and several of its variations are tested. To investigate the performance and accuracy, we calculate the excitation energies for various transition-metal complexes in typical application scenarios. Additionally, we follow the homolytic bond breaking process of a Fenton reaction along its reaction coordinate. While the described AVAS technique is not a universal solution to the active space problem, its premises are fulfilled in many application scenarios of transition-metal chemistry and bond dissociation processes. In these cases the technique makes MR calculations easier to execute, easier to reproduce by any user, and simplifies the determination of the appropriate size of the active space required for accurate results
cPCET versus HAT:A Direct Theoretical Method for Distinguishing X-H Bond-Activation Mechanisms
Proton-coupled electron transfer (PCET) events play a key role in countless chemical transformations, but they come in many physical variants which are hard to distinguish experimentally. While present theoretical approaches to treat these events are mostly based on physical rate coefficient models of various complexity, it is now argued that it is both feasible and fruitful to directly analyze the electronic N-electron wavefunctions of these processes along their intrinsic reaction coordinate (IRC). In particular, for model systems of lipoxygenase and the high-valent oxoiron(IV) intermediate TauD-J it is shown that by invoking the intrinsic bond orbital (IBO) representation of the wavefunction, the common boundary cases of hydrogen atom transfer (HAT) and concerted PCET (cPCET) can be directly and unambiguously distinguished in a straightforward manner
Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory.
We present two efficient and intruder-free methods for treating dynamic correlation on top of general multiconfiguration reference wave functions - including such as obtained by the density matrix renormalization group (DMRG) with large active spaces. The new methods are the second order variant of the recently proposed multireference linearized coupled cluster method (MRLCC) [ Sharma, S.; Alavi, A. J. Chem. Phys. 2015 , 143 , 102815 ] and of N-electron valence perturbation theory (NEVPT2), with expected accuracies similar to MRCI+Q and (at least) CASPT2, respectively. Great efficiency gains are realized by representing the first order wave function with a combination of internal contraction (IC) and matrix product state perturbation theory (MPSPT). With this combination, only third order reduced density matrices (RDMs) are required. Thus, we obviate the need for calculating (or estimating) RDMs of fourth or higher order; these had so far posed a severe bottleneck for dynamic correlation treatments involving the large active spaces accessible to DMRG. Using several benchmark systems, including first and second row containing small molecules, Cr2, pentacene, and oxo-Mn(Salen), we show that active spaces containing at least 30 orbitals can be treated using this method. On a single node, MRLCC2 and NEVPT2 calculations can be performed with over 550 and 1100 virtual orbitals, respectively. We also critically examine the errors incurred due to the three sources of errors introduced in the present implementation - calculating second order instead of third order energy corrections, use of internal contraction, and approximations made in the reference wave function due to DMRG