Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

Abstract

We present two efficient and intruder-free methods for treating dynamic correlation on top of general multi-configuration 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 multi-reference linearized coupled cluster method (MRLCC) [S. Sharma, A. Alavi, J. Chem. Phys. 143, 102815 (2015)], 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, Cr2, pentacene and oxo-Mn(Salen), we shown 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 wavefunction due to DMRG.

Second-Order Multireference Algebraic Diagrammatic Construction Theory for Photoelectron Spectra of Strongly Correlated Systems

“…Such algebraic complexity is a common feature of many internally-contracted multi-reference theories. 31,41,54,59,113 To speed up tedious derivation and implementation of MR-ADC(2), we have developed a Python program that automatically generates equations and code for arbitrary-order MR-ADC(n) approximation. Our code generator is a modified version of the SecondQuantizationAlgebra (SQA) program developed by Neuscamman and co-workers.…”

Multi-reference algebraic diagrammatic construction theory for excited states: General formulation and first-order implementation

“…To remove linear dependencies, we first diagonalize the overlap matrices S [0 ′ ] , S [+1 ′ ] , and S [−1 ′ ] defined in Eqs. (75), (81) and (86), respectively. We then arrange the resulting eigenvalues s p that satisfy the following condition:…”

Toward the efficient local tailored coupled cluster approximation and the peculiar case of oxo-Mn(Salen)

“…Moreover, its closely lying singlet and triplet states pose a considerable challenge for multireference methods. Over the years, several multireference studies has been published 76,98,99 , some of which employed the DMRG method [100][101][102] and recently the first DMRG results with dynamic correlation treatment were presented 30,103 . Our aim was to contribute to these efforts by exploring the effect of the active space and basis set dependence.…”