Density Matrix Renormalization Group for Transcorrelated Hamiltonians: Ground and Excited States in Molecules

Abstract

We present the theory of a density matrix renormalization group (DMRG) algorithm which can solve for both the ground and excited states of non-Hermitian transcorrelated Hamiltonians and show applications in molecular systems. Transcorrelation (TC) accelerates the basis set convergence rate by including known physics (such as, but not limited to, the electron–electron cusp) in the Jastrow factor used for the similarity transformation. It also improves the accuracy of approximate methods such as coupled cluster singles and doubles (CCSD) as shown by recent studies. However, the non-Hermiticity of the TC Hamiltonians poses challenges for variational methods like DMRG. Imaginary-time evolution on the matrix product state (MPS) in the DMRG framework has been proposed to circumvent this problem, but this is currently limited to treating the ground state and has lower efficiency than the time-independent DMRG (TI-DMRG) due to the need to eliminate Trotter errors. In this work, we show that with minimal changes to the existing TI-DMRG algorithm, namely, replacing the original Davidson solver with the general Davidson solver to solve the non-Hermitian effective Hamiltonians at each site for a few low-lying right eigenstates, and following the rest of the original DMRG recipe, one can find the ground and excited states with improved efficiency compared to the original DMRG when extrapolating to the infinite bond dimension limit in the same basis set. An accelerated basis set convergence rate is also observed, as expected, within the TC framework.

Transcorrelated coupled-cluster methods. II. Molecular systems

“…A key recent finding has been that the non-Hermitian property of the TC method, long considered to be a nuisance, can actually be helpful in inducing compactness (and therefore ease of approximation) in the desired (right-eigenvector) solution, through the use of appropriate realistic Jastrow factors, substantially reducing the multi-configurational character of even strongly-correlated systems. This has been found for a variety of systems, including the 2D Hubbard model 76 , 3D uniform electron gas 79 , and molecular systems 80,90,94 . This means that the TC method can improve the convergence of the method, and further evidence of this will be provided in this paper for a yet larger range of molecular systems.…”

“…Furthermore, it can also be used to calculate excited states. 90 We are currently investigating methods to improve the Jastrow factors, such as incorporation of spin-dependency, as well as their optimization using multi-determinantal reference functions.…”

The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

“…More recently, Liao et al have also demonstrated a time-independent TC-DMRG algorithm capable of handling the non-Hermitian TC Hamiltonian. 152 However, in this work, all TC-DMRG results have been obtained with the TD-DMRG method.…”

Efficient Exploitation of Numerical Quadrature with Distance-Dependent Integral Screening in Explicitly Correlated F12 Theory: Linear Scaling Evaluation of the Most Expensive RI-MP2-F12 Term

“…Motivated by the inherent advantages of such an approach, including the precise description of dynamic correlation and the consequential ability to employ a significantly reduced one-electron basis set size for accurate calculations, various strategies have been proposed to mitigate the complexity of the ansatz while retaining its benefits: examples are variational Hylleraas-configuration interaction (Hylleraas-CI), − usage of explicitly correlated Gaussian (ECG) wave functions, − or transcorrelated (TC) approaches. − These methods are generally linked with significant computational costs, limiting their applicability to small system sizes. Nevertheless, the growing interest in the advancement of TC methods has recently resulted in several promising approaches that enable highly accurate calculations. − …”