In the recent years there has been a remarkable progress in the development of methods for the description of strong electron correlation in mols. There are now many methods that describe strong correlation in active spaces with up to 60 orbitals. However, capturing the remaining weak (dynamic) correlation outside of the active space remains a challenge. Conventional multi-ref. methods for dynamic correlation (such as internally-contracted perturbation theory, e.g. CASPT2 or NEVPT2) require computation of up to fourth-order reduced d. matrixes, which prohibits their application to systems with active spaces with more than 24 \norbitals. In this talk I will describe a new method which provides an efficient description of static and dynamic \nelectron correlation by combining the formalism of d. matrix renormalization group (DMRG) and timedependent \nmulti-ref. perturbation theory. This approach has a no. of important advantages:. 1) It is equiv. to fully uncontracted perturbation theory, but has a lower computational scaling than the contracted approaches;. 2) It avoids computation of the three- and four-particle reduced d. matrixes;. 3) It has a polynomial scaling with the no. of active orbitals and can be applied to active spaces with much more than 24 orbitals. In my talk, I will present a brief overview of multi-ref. time-dependent perturbation theory, discuss its implementation in combination with DMRG, and demonstrate its performance for strongly correlated systems with large active spaces.
In the recent years there has been a remarkable progress in the development of methods for the description of strong electron correlation in mols. There are now many methods that describe strong correlation in active spaces with up to 60 orbitals. However, capturing the remaining weak (dynamic) correlation outside of the active space remains a challenge. Conventional multi-ref. methods for dynamic correlation (such as internally-contracted perturbation theory, e.g. CASPT2 or NEVPT2) require computation of up to fourth-order reduced d. matrixes, which prohibits their application to systems with active spaces with more than 24 \norbitals. In this talk I will describe a new method which provides an efficient description of static and dynamic \nelectron correlation by combining the formalism of d. matrix renormalization group (DMRG) and timedependent \nmulti-ref. perturbation theory. This approach has a no. of important advantages:. 1) It is equiv. to fully uncontracted perturbation theory, but has a lower computational scaling than the contracted approaches;. 2) It avoids computation of the three- and four-particle reduced d. matrixes;. 3) It has a polynomial scaling with the no. of active orbitals and can be applied to active spaces with much more than 24 orbitals. In my talk, I will present a brief overview of multi-ref. time-dependent perturbation theory, discuss its implementation in combination with DMRG, and demonstrate its performance for strongly correlated systems with large active spaces.
In earlier work [J. Chem. Phys. 144, 064102 (2016)], we introduced a time-dependent formulation of the second-order N-electron valence perturbation theory (t-NEVPT2) which (i) had a lower computational scaling than the usual internally-contracted perturbation formulation, and (ii) yielded the fully uncontracted NEVPT2 energy. Here, we present a combination of t-NEVPT2 with a matrix product state (MPS) reference wavefunction (t-MPS-NEVPT2) that allows to compute uncontracted dynamic correlation energies for large active spaces and basis sets, using the time-dependent density matrix renormalization group (td-DMRG) algorithm. In addition, we report a low-scaling MPS-based implementation of strongly-contracted NEVPT2 (sc-MPS-NEVPT2) that avoids computation of the four-particle reduced density matrix. We use these new methods to compute the dissociation energy of the chromium dimer and to study the low-lying excited states in all-trans polyenes (C_4H_6 to C_(24)H_(26)), incorporating dynamic correlation for reference wavefunctions with up to 24 active electrons and orbitals.
Abstract 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).
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, Cr 2, 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.
In earlier work [A. Y. Sokolov and G. K.-L. Chan, J. Chem. Phys. 144, 064102 (2016)], we introduced a time-dependent formulation of the second-order N-electron valence perturbation theory (t-NEVPT2) which (i) had a lower computational scaling than the usual internally contracted perturbation formulation and (ii) yielded the fully uncontracted NEVPT2 energy. Here, we present a combination of t-NEVPT2 with a matrix product state (MPS) reference wavefunction (t-MPS-NEVPT2) that allows us to compute uncontracted dynamic correlation energies for large active spaces and basis sets, using the time-dependent density matrix renormalization group algorithm. In addition, we report a low-scaling MPS-based implementation of strongly contracted NEVPT2 (sc-MPS-NEVPT2) that avoids computation of the four-particle reduced density matrix. We use these new methods to compute the dissociation energy of the chromium dimer and to study the low-lying excited states in all-trans polyenes (C4H6 to C24H26), incorporating dynamic correlation for reference wavefunctions with up to 24 active electrons and orbitals.
The ab initio density matrix renormalization group (DMRG) method has been well-established and has become one of the most accurate numerical methods for the precise electronic structure solution of large active spaces. In the past few years, to capture the missing dynamic correlation, various post-DMRG approaches have been proposed through the combination of DMRG and multireference quantum chemical methods or density functional theory. With this in mind, this work provides a brief overview of ab initio DMRG principles and the new developments within post-DMRG methods. For clarity, post-DMRG methods are classified into two main categories depending on whether high-order n -electron reduced density matrices are used, and their merits and disadvantages are properly discussed. Finally, we conclude by discussing unsolved bottlenecks and giving development perspectives of post-DMRG approaches, which are expected to yield quantitative descriptions of complex electronic structures in large strongly correlated molecules and materials.
We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian.