Reference Excitation Energies of Increasingly Large Molecules: A QMC Study of Cyanine Dyes

Abstract

We revisit here the lowest vertical excitations of cyanine dyes using quantum Monte Carlo and leverage recent developments to systematically improve on previous results. In particular, we employ a protocol for the construction of compact and accurate multideterminant Jastrow-Slater wave functions for multiple states, which we have recently validated on the excited-state properties of several small prototypical molecules. Here, we obtain quantum Monte Carlo excitation energies in excellent agreement with high-level coupled cluster for all the cyanines where the coupled cluster method is applicable. Furthermore, we push our protocol to longer chains, demonstrating that quantum Monte Carlo is a viable methodology to establish reference data at system sizes which are hard to reach with other high-end approaches of similar accuracy. Finally, we determine which ingredients are key to an accurate treatment of these challenging systems and rationalize why a description of the excitation based on only active π orbitals lacks the desired accuracy for the shorter chains.

Hierarchy Configuration Interaction: Combining Seniority Number and Excitation Degree

“…The hCI pathway presented here offers several interesting possibilities to pursue. One could generalize and adapt hCI for excited states and open-shell systems, develop coupled-cluster methods based on an analogous excitation–seniority truncation of the excitation operator, − and explore the accuracy of hCI trial wave functions for quantum Monte Carlo simulations. − …”

Double Hybrid Density Functionals for the Electronic Excitation Energies of Linear Cyanines

“…A direct comparison of Monte Carlo and CC3 methods against exFCI values reveals an obvious agreement of the CC3 values with that of exFCI, with differences of around 0.04 eV (The values of the vertical excitation energies of all previous benchmark values and other tested methods are summarized in Table .). Moreover, CC3 values obtained in the later study were 0.04 eV or less close to extrapolated CC3 values (exCC3) obtained by Send et al; see Table . Extrapolated FCI (exFCI) values were obtained based on the configuration interaction using a perturbative selection made iteratively (CIPSI) wave function, and the extrapolation of the basis set was calculated as FCI/aug-cc-pVTZ = [FCI/aug-cc-pVDZ + (CCSDT/aug-cc-pVTZ – CCSDT/aug-cc-pVDZ)]; for more details, see the corresponding articles. , We have therefore adopted CC3 values for linear cyanine dyes CN3–CN15 as the reference values (TBE); see Table .…”

“…This transition is dependent on the length of the carbon chain resulting in the so-called “vinyl shift”, where a systematic increase of approximately 80 nm in the electronic excitation λ max is observed for each additional carbon atom in the chain. , The electronic transition shift present in cyanines can be simply modeled as a pedagogic particle in a box system . Although the electronic excitations of cyanines are apparently simple, the accurate theoretical prediction of the photophysical properties of this important class of dyes is far from simple and is, in fact, challenging. ,− Actually, cyanine molecular systems are frequently used as models to benchmark theoretical methods for excited electronic state calculations. ,− , …”

“…The inaccuracies of the different density functionals associated with the electronic excitation energies of cyanines were attributed to the difficulty of capturing the differential electron-correlation effects between the ground and excited electronic states within the adiabatic approximation to the TD-DFT regime. ,,− A notable exception to the previous generalization is the Minnesota family of density functionals, in particular M05-2X, M06-HF, M06-2X, M08-HX, and M08-SO, where the mean absolute error (MAE) with respect to the benchmark diffusion Monte Carlo (DMC) results falls in the range 0.10 to 0.35 eV . However, if the Minnesota functionals are benchmarked against the more accurate and recent CC3 results, an almost systematic decrease in their accuracy of around 0.15 eV will be obtained for the series CN5 – CN11 (see Figure ), resulting in an overall MAE range between 0.25 and 0.40 eV. On the other hand, the performance of double hybrid (DH) functionals was not systematically investigated for the electronic excitation of cyanines, though some promising results were previously obtained.…”

Hierarchy Configuration Interaction: Combining Seniority Number and Excitation Degree

“…One could generalize and adapt hCI for excited states 44 and open-shell systems, 45 develop coupledcluster methods based on an analogous excitation-seniority truncation of the excitation operator, [46][47][48] and explore the accuracy of hCI trial wave functions for quantum Monte Carlo simulations. [49][50][51]…”