Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory

Abstract

We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, ͑i͒ total correlation energies in long polyenes and ͑ii͒ the isomerization curve of the ͓Cu 2 O 2 ͔ 2+ core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a ͑24e ,24o͒ active space and 268 atomic orbitals in the polyenes and a ͑28e ,32o͒ active space and 278 atomic orbitals in ͓Cu 2 O 2 ͔ 2+ .

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

“…Calculation and storage of such high order RDMs is limited to an active space of around 25 orbitals beyond which it become prohibitively expensive [54][55][56][57] . To circumvent this difficulty, some researches have resorted to approximating the higher body RDM by reconstructing its disconnected part by antisymmetric multiplication of lower body RDM and ignoring the density cumulant which is the connected part 53,[58][59][60][61][62] . The RDM reconstruction can be performed by setting the three body and four body cumulants to zero as was done for n-electron valence perturbation theory (NEVPT2) 60 ; which resulted in severe numerical problems rendering the theory virtually unusable.…”

“…The RDM reconstruction can be performed by setting the three body and four body cumulants to zero as was done for n-electron valence perturbation theory (NEVPT2) 60 ; which resulted in severe numerical problems rendering the theory virtually unusable. Canonical Transformation (CT) theory 53,58,59 also sets three and higher body cumulants to zero and is known to suffer from intruder state problems (the CT intruder states are different than the ones in perturbation theory). A much milder approximation is to use the exact three body cumulants but setting the four body cumulants to zero 61,62 .…”

“…8 IC, now widely used in MR theories 7,9,41,[51][52][53] aggressively truncates the many body basis and reduces the cost of the calculation from exponential to merely polynomial in the number of active space orbitals. The difficulty with IC is that the working equations become extremely cumbersome and can often only be derived using domain specific computer algebra systems.…”

Multi-component symmetry-projected approach for molecular ground state correlations

“…(restricted active-space second order perturbation theory) [41], CR-CC (completely renormalized coupled-cluster) [40], and DMRG-SC-CTSD (density-matrix renormalization group with strongly contracted canonical transformation including only single and double excitations) [42] methods provide the likely correct profile for this system, we ranked the S-UHF, S-GHF, KS-UHF, and KS-GHF methods according to how close they came to the former methods. We observed that the more symmetries restored the closer the profile got to the reference methods.…”

A state interaction spin-orbit coupling density matrix renormalization group method

“…In transition metal systems, active spaces with up to 50 orbitals can be routinely converged to chemical accuracy. 26,28,29,31,34,35,[38][39][40][41]43,44,48 In this work, we describe a method to combine a treatment of spin-orbit coupling with a density matrix renormalization group description of the electronically near-degenerate individual states. We use a state interaction approach, [53][54][55][56][57][58] whereby DMRG wavefunctions are determined for spinpure electronic states, and the Hamiltonian with spin-orbit coupling is recomputed within this basis and diagonalized.…”