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Register a new userMulti-Reference Epstein-Nesbet Perturbation Theory with Density Matrix Renormalization Group Reference Wavefunction
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The accurate electronic structure calculation for strongly correlated chemical systems requires an adequate description for both static and dynamic electron correlation, and is a persistent challenge for quantum chemistry. In order to account for static and dynamic electron correlations accurately and efficiently, in this work we propose a new method by integrating the density matrix renormalization group (DMRG) method and multi-reference second-order Epstein-Nesbet perturbation theory (ENPT2) with a selected configuration interaction (SCI) approximation. Compared with previous DMRG-based dynamic correlation methods, the DMRG-ENPT2 method extends the range of applicability, allowing us to efficiently calculate systems with very large active space beyond 30 orbitals. We demonstrate this by performing calculations on H$_2$S with an active space of (16e, 15o), hexacene with an active space of (26e, 26o) and 2D H$_{64}$ square lattice with an active space of (42e, 42o).
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The density-matrix renormalization group (DMRG) method, which can deal with a large active space composed of tens of orbitals, is nowadays widely used as an efficient addition to traditional complete active space (CAS)-based approaches. In this paper, we present the DMRG algorithm with a multi-level (ML) control of the active space based on chemical intuition-based hierarchical orbital ordering, which is called as ML-DMRG with its self-consistent field variant ML-DMRG-SCF. Ground and excited state calculations of H2O, N2, indole, and Cr2 with comparisons to DMRG references using fixed number of kept states (M) illustrate that MLtype DMRG calculations can obtain noticeable efficiency gains. It is also shown that the orbital re-ordering based on hierarchical multiple active subspaces may be beneficial for reducing computational time for not only ML-DMRG calculations but also DMRG ones with fixed M values.
We introduce the transcorrelated Density Matrix Renormalization Group (tcDMRG) theory for the efficient approximation of the energy for strongly correlated systems. tcDMRG encodes the wave function as a product of a fixed Jastrow or Gutzwiller correlator and a matrix product state. The latter is optimized by applying the imaginary-time variant of time-dependent (TD) DMRG to the non-Hermitian transcorrelated Hamiltonian. We demonstrate the efficiency of tcDMRG at the example of the two-dimensional Fermi-Hubbard Hamiltonian, a notoriously difficult target for the DMRG algorithm, for different sizes, occupation numbers, and interaction strengths. We demonstrate fast energy convergence of tcDMRG, which indicates that tcDMRG could increase the efficiency of standard DMRG beyond quasi-monodimensional systems and provides a generally powerful approach toward the dynamic correlation problem of DMRG.
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 multi-reference perturbation (MRPT) or configuration interaction (MRCI) methods with internal contraction (ic) approximation. These methods can use active space scalable to relatively larger size references than has previously been possible. However, they are still hardly applicable to systems with active space larger than 30 orbitals because of high computation and storage costs of high-order reduced density matrices (RDMs) and the number of virtual orbitals are normally limited to few hundreds. In this work, we propose a new effective implementation of DMRG-MRCI, in which we use re-constructed CASCI-type configurations from DMRG wave function via the entropy-driving genetic algorithm (EDGA), and integrate 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, DMRG-ec-MRCI method is promising for dealing with 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 potential energy curve of Cr$_{2}$, single-triplet gaps of higher n-acene molecules and the energy of Eu-BTBP(NO$_3$)$_3$ complex.
The similarities between Hartree-Fock (HF) theory and the density-matrix renormalization group (DMRG) are explored. Both methods can be formulated as the variational optimization of a wave-function ansatz. Linearization of the time-dependent variational principle near a variational minimum allows to derive the random phase approximation (RPA). We show that the non-redundant parametrization of the matrix product state (MPS) tangent space [J. Haegeman et al., Phys. Rev. Lett. 107, 070601 (2011)] leads to the Thouless theorem for MPS, i.e. an explicit non-redundant parametrization of the entire MPS manifold, starting from a specific MPS reference. Excitation operators are identified, which extends the analogy between HF and DMRG to the Tamm-Dancoff approximation (TDA), the configuration interaction (CI) expansion, and coupled cluster theory. For a small one-dimensional Hubbard chain, we use a CI-MPS ansatz with single and double excitations to improve on the ground state and to calculate low-lying excitation energies. For a symmetry-broken ground state of this model, we show that RPA-MPS allows to retrieve the Goldstone mode. We also discuss calculations of the RPA-MPS correlation energy. With the long-range quantum chemical Pariser-Parr-Pople Hamiltonian, low-lying TDA-MPS and RPA-MPS excitation energies for polyenes are obtained.
We have studied the Metal-Insulator like Transition (MIT) in lithium and beryllium ring-shaped clusters through ab initio Density Matrix Renormalization Group (DMRG) method. Performing accurate calculations for different interatomic distances and using Quantum Information Theory (QIT) we investigated the changes occurring in the wavefunction between a metallic-like state and an insulating state built from free atoms. We also discuss entanglement and relevant excitations among the molecular orbitals in the Li and Be rings and show that the transition bond length can be detected using orbital entropy functions. Also, the effect of different orbital basis on the effectiveness of the DMRG procedure is analyzed comparing the convergence behavior.
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