4,118 research outputs found
CheMPS2: a free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry
The density matrix renormalization group (DMRG) has become an indispensable
numerical tool to find exact eigenstates of finite-size quantum systems with
strong correlation. In the fields of condensed matter, nuclear structure and
molecular electronic structure, it has significantly extended the system sizes
that can be handled compared to full configuration interaction, without losing
numerical accuracy. For quantum chemistry (QC), the most efficient
implementations of DMRG require the incorporation of particle number, spin and
point group symmetries in the underlying matrix product state (MPS) ansatz, as
well as the use of so-called complementary operators. The symmetries introduce
a sparse block structure in the MPS ansatz and in the intermediary contracted
tensors. If a symmetry is non-abelian, the Wigner-Eckart theorem allows to
factorize a tensor into a Clebsch-Gordan coefficient and a reduced tensor. In
addition, the fermion signs have to be carefully tracked. Because of these
challenges, implementing DMRG efficiently for QC is not straightforward.
Efficient and freely available implementations are therefore highly desired. In
this work we present CheMPS2, our free open-source spin-adapted implementation
of DMRG for ab initio QC. Around CheMPS2, we have implemented the augmented
Hessian Newton-Raphson complete active space self-consistent field method, with
exact Hessian. The bond dissociation curves of the 12 lowest states of the
carbon dimer were obtained at the DMRG(28 orbitals, 12 electrons,
D=2500)/cc-pVDZ level of theory. The contribution of
core correlation to the bond dissociation curve of the carbon
dimer was estimated by comparing energies at the DMRG(36o, 12e,
D=2500)/cc-pCVDZ and DMRG-SCF(34o, 8e,
D=2500)/cc-pCVDZ levels of theory.Comment: 16 pages, 13 figure
The density matrix renormalization group for ab initio quantum chemistry
During the past 15 years, the density matrix renormalization group (DMRG) has
become increasingly important for ab initio quantum chemistry. Its underlying
wavefunction ansatz, the matrix product state (MPS), is a low-rank
decomposition of the full configuration interaction tensor. The virtual
dimension of the MPS, the rank of the decomposition, controls the size of the
corner of the many-body Hilbert space that can be reached with the ansatz. This
parameter can be systematically increased until numerical convergence is
reached. The MPS ansatz naturally captures exponentially decaying correlation
functions. Therefore DMRG works extremely well for noncritical one-dimensional
systems. The active orbital spaces in quantum chemistry are however often far
from one-dimensional, and relatively large virtual dimensions are required to
use DMRG for ab initio quantum chemistry (QC-DMRG). The QC-DMRG algorithm, its
computational cost, and its properties are discussed. Two important aspects to
reduce the computational cost are given special attention: the orbital choice
and ordering, and the exploitation of the symmetry group of the Hamiltonian.
With these considerations, the QC-DMRG algorithm allows to find numerically
exact solutions in active spaces of up to 40 electrons in 40 orbitals.Comment: 24 pages; 10 figures; based on arXiv:1405.1225; invited review for
European Physical Journal
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
Hybridization and spin-orbit coupling effects in quasi-one-dimensional spin-1/2 magnet Ba3Cu3Sc4O12
We study electronic and magnetic properties of the quasi-one-dimensional
spin-1/2 magnet Ba3Cu3Sc4O12 with a distinct orthogonal connectivity of CuO4
plaquettes. An effective low-energy model taking into account spin-orbit
coupling was constructed by means of first-principles calculations. On this
basis a complete microscopic magnetic model of Ba3Cu3Sc4O12, including
symmetric and antisymmetric anisotropic exchange interactions, is derived. The
anisotropic exchanges are obtained from a distinct first-principles numerical
scheme combining, on one hand, the local density approximation taking into
account spin-orbit coupling, and, on the other hand, projection procedure along
with the microscopic theory by Toru Moriya. The resulting tensors of the
symmetric anisotropy favor collinear magnetic order along the structural chains
with the leading ferromagnetic coupling J1 = -9.88 meV. The interchain
interactions J8 = 0.21 meV and J5 = 0.093 meV are antiferromagnetic. Quantum
Monte Carlo simulations demonstrated that the proposed model reproduces the
experimental Neel temperature, magnetization and magnetic susceptibility data.
The modeling of neutron diffraction data reveals an important role of the
covalent Cu-O bonding in Ba3Cu3Sc4O12.Comment: 11 pages, 12 figure
Tree tensor network state with variable tensor order: an efficient multireference method for strongly correlated systems
We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement
Structural, electronic, vibrational and dielectric properties of LaBGeO from first principles
Structural, electronic, vibrational and dielectric properties of LaBGeO
with the stillwellite structure are determined based on \textit{ab initio}
density functional theory. The theoretically relaxed structure is found to
agree well with the existing experimental data with a deviation of less than
. Both the density of states and the electronic band structure are
calculated, showing five distinct groups of valence bands. Furthermore, the
Born effective charge, the dielectric permittivity tensors, and the vibrational
frequencies at the center of the Brillouin zone are all obtained. Compared to
existing model calculations, the vibrational frequencies are found in much
better agreement with the published experimental infrared and Raman data, with
absolute and relative rms values of 6.04 cm, and , respectively.
Consequently, numerical values for both the parallel and perpendicular
components of the permittivity tensor are established as 3.55 and 3.71 (10.34
and 12.28), respectively, for the high-(low-)frequency limit
New Approaches for ab initio Calculations of Molecules with Strong Electron Correlation
Reliable quantum chemical methods for the description of molecules with
dense-lying frontier orbitals are needed in the context of many chemical
compounds and reactions. Here, we review developments that led to our
newcomputational toolbo x which implements the quantum chemical density matrix
renormalization group in a second-generation algorithm. We present an overview
of the different components of this toolbox.Comment: 19 pages, 1 tabl
- …