Utilizing Essential Symmetry Breaking in Auxiliary-Field Quantum Monte Carlo: Application to the Spin Gaps of the C₃₆ Fullerene and an Iron Porphyrin Model Complex

Abstract

We present three distinct examples where phaseless auxiliary-field Quantum Monte Carlo (ph-AFQMC) can be reliably performed with a single-determinant trial wavefunction with essential symmetry breaking. We first utilized essential time-reversal symmetry breaking with ph-AFQMC to compute the triplet-singlet energy gap in the TS12 set. We found statistically better performance of ph-AFQMC with complexrestricted orbitals than with spin-unrestricted orbitals. We then showed the utilization of essential spin symmetry breaking when computing the single-triplet gap of a known biradicaloid, C 36 . ph-AFQMC with spin-unrestricted Hartree-Fock (ph-AFQMC+UHF) fails catastrophically even with spin-projection and predicts no biradicaloid character. With approximate Brückner orbitals obtained from regularized orbital-optimized second-order Møller-Plesset perturbation theory (κ-OOMP2), ph-1 arXiv:2001.05109v1 [physics.chem-ph] 15 Jan 2020 AFQMC quantitatively captures strong biradicaloid character of C 36 . Lastly, we applied ph-AFQMC to the computation of the quintet-triplet gap in a model iron porphyrin complex where brute-force methods with a small active space fail to capture the triplet ground state. We show unambiguously that neither triplet nor quintet is strongly correlated using UHF, κ-OOMP2, and coupled-cluster with singles and doubles (CCSD) performed on UHF and κ-OOMP2 orbitals. There is no essential symmetry breaking in this problem. By virtue of this, we were able to perform UHF+ph-AFQMC reliably with a cc-pVTZ basis set and predicted a triplet ground state for this model geometry. The largest ph-AFQMC in this work correlated 186 electrons in 956 orbitals.Our work highlights the utility, scalability, and accuracy of ph-AFQMC with a single determinant trial wavefunction with essential symmetry breaking for systems mainly dominated by dynamical correlation with little static correlation. LLNL-JRNL-801427-DRAFT

CASSCF with Extremely Large Active Spaces Using the Adaptive Sampling Configuration Interaction Method

“…The large quintet-triplet gap of ≈ 19 kcal/mol predicted by ASCI-SCF with the (44e, 44o) active space was nonetheless quite troubling as the states appeared to be fairly single-reference (based on the natural orbital occupations) and many single reference methods predict much smaller gaps (irrespective of the spin of the ground state) 81,82 . We consequently examined Indeed, ASCI-SCF pushes out relatively less correlated orbitals like the 4d x 2 −y 2 in order to incorporate more C-N σ/σ * orbitals into the active space instead.…”

“…have often found a quintet ground state 29,[77][78][79][80] , though some studies do report a triplet ground state when an extremely large active space is used40,71,81 .Ref 40 in particular presents a detailed HCISCF study of this system, making it a natural point for comparing and contrasting the ASCI-SCF method against HCISCF. Like Ref 40, we have performed our calculations on the optimized triplet geometry presented in Ref 82, employing the cc-pVDZ basis and HF orbitals of the quintet state as the initial guess.…”

Revealing the nature of electron correlation in transition metal complexes with symmetry breaking and chemical intuition

“…It is known 51 that DFT orbitals, which are optimized in the presence of mean-field electron correlations, do not break spin or spatial symmetries as easily as HF orbitals. With regard to κ-UOOMP2, the inclusion of pair-wise additive electron correlation in the orbital optimization has a similar effect, and has been used to diagnose MR character in organic molecules and fullerenes 52,53 and in one transition metal containing system (neutral iron porphyrin) 54 . Moreover, given the plethora of MR diagnostics, we take a more appealing route using singleparticle orbital theory, drawing on chemical concepts from ligand-field and molecular orbital theories.…”

Revealing the Nature of Electron Correlation in Transition Metal Complexes with Symmetry-Breaking and Chemical Intuition

“…As first encountered in Ref. 54, κ-UOOMP2 predicts unphysical GSs for the FeP species; therein, the DIIS solver was used along with an appropriate initial orbital guess to converge on the correct state. Indeed, for the twice-reduced Fe tpy and FeP species studied presently, use of the GDM solver yielded spin-pure GSs inconsistent with the AFM-coupled states deduced from experimental measurements and predicted from B3LYP, CAM-B3LYP, and B5050LYP functionals.…”