We improve the methodology to construct a complete active space-configuration interaction (CAS-CI) expansion for density-matrix renormalization group (DMRG) wave functions using a matrix-product state representation, inspired by the sampling-reconstructed CAS [SR-CAS; Boguslawski , K. ; J. Chem. Phys. 2011 , 134 , 224101 ] algorithm. In our scheme, the genetic algorithm, in which the "crossover" and "mutation" processes can be optimized based on quantum information theory, is employed when reconstructing a CAS-CI-type wave function in the Hilbert space. Analysis of results for ground and excited state wave functions of conjugated molecules, transition metal compounds, and a lanthanide complex illustrate that our scheme is very efficient for searching the most important CI expansions in large active spaces.
We improve the methodology to construct a complete active space-configuration interaction (CAS-CI) expansion for density-matrix renormalization group (DMRG) wave functions using a matrix-product state representation, inspired by the sampling-reconstructed CAS [SR-CAS; Boguslawski , K. ; J. Chem. Phys. 2011 , 134 , 224101 ] algorithm. In our scheme, the genetic algorithm, in which the "crossover" and "mutation" processes can be optimized based on quantum information theory, is employed when reconstructing a CAS-CI-type wave function in the Hilbert space. Analysis of results for ground and excited state wave functions of conjugated molecules, transition metal compounds, and a lanthanide complex illustrate that our scheme is very efficient for searching the most important CI expansions in large active spaces.
The constructions of configuration interaction (CI) expansions from a matrix-product state (MPS) involves numerous matrix operations and the skillful sampling of important configurations when in a huge Hilbert space. In this work, we present an efficient procedure for constructing CI expansions from MPS using the Charm++ parallel programming framework, upon which automatic load balancing and object migration facilities can be employed. This procedure was employed in the MPS-to-CI utility (Moritz et al., J. Chem. Phys. 2007, 126, 224109), sampling-reconstructed complete active space algorithm (SR-CAS, Boguslawski et al., J. Chem. Phys. 2011, 134, 224101) and entanglement-driven genetic algorithm (EDGA, Luo et al., J. Chem. Theory Comput. 2017, 13, 4699-4710). It enhances productivity and allows the sampling programs evolve to their population-expansion versions (e.g., EDGA with population expansion [PE-EDGA]). Examples of 1,2-dioxetanone and firefly dioxetanone anion (FDO-) molecules demonstrated that 1) the procedure could be flexibly employed among various multi-core architectures; 2) the parallel efficiencies could be persistently improved simply by increasing the proportion of asynchronous executions; 3) PE-EDGA could construct a CAS-type CI wave function from a huge Hilbert space, with 0.9952 CI completeness and 96.7% correlation energy via ~1.66x10^6 configurations (only 0.0000028% of the total configurations) of a bi-radical state of FDO- molecule using the full valence active space within a few hours.
We present a procedure to construct a configuration-interaction expansion containing arbitrary excitations from an underlying full-configuration-interaction-type wave function defined for a very large active space. Our procedure is based on the density-matrix renormalization group (DMRG) algorithm that provides the necessary information in terms of the eigenstates of the reduced density matrices to calculate the coefficient of any basis state in the many-particle Hilbert space. Since the dimension of the Hilbert space scales binomially with the size of the active space, a sophisticated Monte Carlo sampling routine is employed. This sampling algorithm can also construct such configuration-interaction-type wave functions from any other type of tensor network states. The configuration-interaction information obtained serves several purposes. It yields a qualitatively correct description of the molecule's electronic structure, it allows us to analyze DMRG wave functions converged for the same molecular system but with different parameter sets (e.g., different numbers of active-system (block) states), and it can be considered a balanced reference for the application of a subsequent standard multi-reference configuration-interaction method.
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 a 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 insight into chemically interesting features of the molecule under study such as the distribution of α and β 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].
The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry makes it practical to evaluate static correlation in a large active space, while dynamic correlation provides a critical correction to the DMRG reference for strong-correlated systems and is usually obtained using multireference perturbation (MRPT) or configuration interaction (MRCI) methods with internal contraction (ic) approximation. These methods can use an active space scalable to relatively larger size references than has previously been possible. However, they are still hardly applicable to systems with an active space larger than 30 orbitals and/or a large basis set because of high computation and storage costs of high-order reduced density matrices (RDMs) and the crucial dependence of the MRCI Hamiltonian dimension on the number of virtual orbitals. In this work, we propose a new effective implementation of DMRG-MRCI, in which we use reconstructed CASCI-type configurations from DMRG wave function via the entropy-driving genetic algorithm (EDGA) [Luo et al. J. Chem. Theory Comput. 2017, 13, 4699−4710.] and integrate it with MRCI by an external contraction (ec) scheme. This bypasses the bottleneck of computing high-order RDMs in traditional DMRG dynamic correlation methods with ic approximation, and the number of MRCI configurations is not dependent on the number of virtual orbitals. Therefore, the DMRG-ec-MRCI method is promising for dealing with a larger active space than 30 orbitals and large basis sets. We demonstrate the capability of our DMRG-ec-MRCI method in several benchmark applications, including the evaluation of the potential energy curve of Cr 2, single-triplet gaps of higher n-acene molecules, and the energy of the Eu-BTBP(NO 3 ) 3 complex.
Abstract The construction of configuration‐interaction (CI) expansions from a matrix product state (MPS) involves numerous matrix operations and the skillful sampling of important configurations in a large Hilbert space. In this work, we present an efficient procedure for constructing CI expansions from MPS employing the parallel object‐oriented Charm++ programming framework, upon which automatic load‐balancing and object migrating facilities can be employed. This procedure was employed in the MPS‐to‐CI utility (Moritz et al., J. Chem. Phys. 2007, 126, 224109), the sampling‐reconstructed complete active‐space algorithm (SR‐CAS, Boguslawski et al., J. Chem. Phys. 2011, 134, 224101), and the entanglement‐driven genetic algorithm (EDGA, Luo et al., J. Chem. Theory Comput. 2017, 13, 4699). It enhances productivity and allows the sampling programs to evolve to their population‐expansion versions, for example, EDGA with population expansion (PE‐EDGA). Further, examples of 1,2‐dioxetanone and firefly dioxetanone anion (FDO−) molecules demonstrated the following: (a) parallel efficiencies can be persistently improved by simply by increasing the proportions of the asynchronous executions and (b) a sampled CAS‐type CI wave function of a bi‐radical‐state FDO− molecule utilizing the full valence (30e,26o) active space can be constructed within a few hours with using thousands of cores.
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 Ansätze 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.