We present numerical results for the equation of state of an infinite chain of hydrogen atoms. A variety of modern many-body methods are employed, with exhaustive cross-checks and validation. Approaches for reaching the continuous space limit and the thermodynamic limit are investigated, proposed, and tested. The detailed comparisons provide a benchmark for assessing the current state of the art in many-body computation, and for the development of new methods. The ground-state energy per atom in the linear chain is accurately determined versus bondlength, with a confidence bound given on all uncertainties.

The recent advent of the density matrix renormalization group (DMRG) theory has delivered a new capability to compute multireference (MR) wave function with large configuration space, which far exceeds the limitation of conventional approaches. Here, we provide an overview of our recent work on the developments of ab initio DMRG methods in the context of the active space approaches and their applications to MR chemical systems.

We report an extension of our previous development that incorporated quantum-chemical density matrix renormalization group (DMRG) into the complete active space second-order perturbation theory (CASPT2) [Y. Kurashige and T. Yanai, J. Chem. Phys. 135, 094104 (2011)]. In the previous study, the combined theory, referred to as DMRG-CASPT2, was built upon the use of pseudo-canonical molecular orbitals (PCMOs) for one-electron basis. Within the PCMO basis, the construction of the four-particle reduced density matrix (4-RDM) using DMRG can be greatly facilitated because of simplicity in the multiplication of 4-RDM and diagonal Fock matrix in the CASPT2 equation. In this work, we develop an approach to use more suited orbital basis in DMRG-CASPT2 calculations, e.g., localized molecular orbitals, in order to extend the domain of applicability. Because the multiplication of 4-RDM and generalized Fock matrix is no longer simple in general orbitals, an approximation is made to it using the cumulant reconstruction neglecting higher-particle cumulants. Also, we present the details of the algorithm to compute 3-RDM of the DMRG wavefunction as an extension of the 2-RDM algorithm of Zgid et al. [J. Chem. Phys. 128, 144115 (2008)] and Chan et al. [J. Chem. Phys. 128, 144117 (2008)]. The performance of the extended DMRG-CASPT2 approach was examined for large-scale multireference systems, such as low-lying excited states of long-chain polyenes and isomerization potential of {[Cu(NH3)3]2O2}(2+).

The self-energy embedding theory (SEET), in which the active space self-energy is embedded in the self-energy obtained from a perturbative method treating the non-local correlation effects, was recently developed in our group. In SEET, the double counting problem does not appear and the accuracy can be improved either by increasing the perturbation order or by enlarging the active space. This method was first calibrated for the 2D Hubbard lattice showing promising results. In this paper, we report an extension of SEET to quantum chemical ab initio Hamiltonians for applications to molecular systems. The self-consistent second-order Green's function method is used to describe the non-local correlations, while the full configuration interaction method is carried out to capture strong correlation within the active space. Using few proof-of-concept examples, we show that SEET yields results of comparable quality to n-electron valence state second-order perturbation theory with the same active space, and furthermore, the full active space can be split into smaller active spaces without further implementation. Moreover, SEET avoids intruder states and does not require any high-order reduced density matrices. These advantages show that SEET is a promising method to describe physical and chemical properties of challenging molecules requiring large active spaces.