Quantum Monte Carlo Treatment of the Charge Transfer and Diradical Electronic Character in a Retinal Chromophore Minimal Model

Abstract

The penta-2,4-dieniminium cation (PSB3) displays similar ground state and first excited state potential energy features as those of the retinal protonated Schiff base (RPSB) chromophore in rhodopsin. Recently, PSB3 has been used to benchmark several electronic structure methods, including highly correlated multireference wave function approaches, highlighting the necessity to accurately describe the electronic correlation in order to obtain reliable properties even along the ground state (thermal) isomerization paths. In this work, we apply two quantum Monte Carlo approaches, the variational Monte Carlo and the lattice regularized diffusion Monte Carlo, to study the energetics and electronic properties of PSB3 along representative minimum energy paths and scans related to its thermal cis–trans isomerization. Quantum Monte Carlo is used in combination with the Jastrow antisymmetrized geminal power ansatz, which guarantees an accurate and balanced description of the static electronic correlation thanks to the multiconfigurational nature of the antisymmetrized geminal power term, and of the dynamical correlation, due to the presence of the Jastrow factor explicitly depending on electron–electron distances. Along the two ground state isomerization minimum energy paths of PSB3, CASSCF calculations yield wave functions having either charge transfer or diradical character in proximity of the two transition state configurations. Here, we observe that at the quantum Monte Carlo level of theory, only the transition state with charge transfer character can be located. The conical intersection, which becomes highly sloped, is observed only if the path connecting the two original CASSCF transition states is extended beyond the diradical one, namely by increasing the bond-length-alternation (BLA). These findings are in good agreement with the results obtained by MRCISD+Q calculations, and they demonstrate the importance of having an accurate description of the static and dynamical correlation when studying isomerization and transition states of conjugated systems.

A 3‐D bonding perspective of the factors influencing the relative stability of the S1/S0 conical intersections of the penta‐2,4‐dieniminium cation (PSB3)

“…Now we will undertake a comparison of the results of the SSR‐ ω PBEh/cc‐pVDZ calculations with the results of other calculations available in the literature . The SA‐CASSCF calculations from the literature yield the occurrence of the S 1 minimum for torsion θ around the C6C7 bond at the BLA value of −0.012 Ǻ.…”

“…This picture of the S 1 /S 0 crossing in PSB3, however, has since been challenged by more advanced theoretical computations which found a considerable influence of the dynamic electron correlation on the geometry at which the S 1 /S 0 crossing occurs . In particular, according to the quantum Monte Carlo calculations, the S 1 /S 0 crossing was discovered to occur at a significantly positive BLA value of 0.061 Å, in strong disagreement with the CASSCF picture.…”

“…The interplay between the diradicaloid and (zwitter‐)ionic states that occurs along the path to S 1 /S 0 conical intersections (CIs) has been an object of thorough theoretical investigation . The analysis of the electronic structure of the S 1 and S 0 states of RPSB and the simplified model PSB3 however, has long being dominated by the results of the complete active space self‐consistent field (CASSCF) calculations, which predicted that a transfer of an electron from the carbon chain to the cationic nitrogen occurs in the S 1 state of the molecule; this results in the inversion of the bond lengths of the formally double and formally single bonds, that is, the bond length alternation (BLA) .…”

“…In particular, according to the quantum Monte Carlo calculations, the S 1 /S 0 crossing was discovered to occur at a significantly positive BLA value of 0.061 Å, in strong disagreement with the CASSCF picture. The morphology of the S 1 and S 0 potential energy surfaces (PESs) in the vicinity of the S 1 /S 0 CI of PSB3 was studied with a variety of the high level wave‐function and density functional methods that clarified unambiguously which computational methods were suitable for the task . The total electronic charge density distribution in the S 0 and S 1 states of PSB3 however, has not been the subject of such a thorough investigation.…”

Bias cancellation in one-determinant fixed-node diffusion Monte Carlo: Insights from fermionic occupation numbers

“…Bias cancellation limits of such an approach are however unknown, that somewhat hampers widespread usage of FN-DMC as a benchmark method. Deviations of the order of 0.3 kcal/mol (relative errors exceeding 7%), unacceptable at the benchmark level (relative errors should not exceed say 2-3%), of unknown nature found in complexes with multiply bound hydrogen bond acceptors like HCN dimer or formaldehyde (FD) dimer 41 start to delineate its limits and motivate our further elaborations in this field.In multireference systems, it is known that SDs do not suffice for 46 , and, SJ Ψ T s should contain additional dominant configurations so that the FN bias well cancels out [49][50][51][52][53] . On the other hand, in closedshell systems, the effect of additional determinants is expected to be negligible.…”