Dynamic and Nondynamic Electron Correlation Energy Decomposition Based on the Node of the Hartree-Fock Slater Determinant

Distinguishing between dynamic and nondynamic electron correlation energy is a fundamental concept in quantum chemistry. It can be challenging to make a clear distinction between the two types of correlation energy or to determine their actual contributions in specific cases using wave function theory. This is because both single-reference and multireference methods cover both types of correlation energy to some extent. Fixed-node diffusion quantum Monte Carlo (FNDMC) accurately covers dynamic correlations, but it is limited in overall accuracy by the node of the trial wave function. We introduce a methodology for partitioning an exact electron correlation energy into its dynamic and nondynamic components. This is accomplished by restricting a ground-state solution from sharing its node with a spin-restricted Hartree-Fock Slater determinant. The FNDMC method is used as a tool to conveniently project out a lowest-energy state obeying such a boundary condition. The proposed approach provides an unambiguous and useful procedure for separating electron correlation energy, as demonstrated on multiple systems, including the He atom, bond breaking of H2, the parametric H2-H2 system, the Be-Ne atomic series with low- and high-spin states for C, N, and O atoms, and small molecules such as BH, HF, and CO at both equilibrium and elongated configurations, respectively.

Triplet sensitization enables bidirectional isomerization of diazocine with 130 nm redshift in excitation wavelengths

Diazocines are bridged azobenzenes with phenyl rings connected by a CH2-CH2 group. Despite this rather small structural difference, diazocine exhibits improved properties over azobenzene as a photoswitch and most importantly, its Z configuration is more stable than the E isomer. Herein, we reveal yet another unique feature of this emerging class of photoswitches. In striking contrast to azobenzenes and other photochromes, diazocine can be selectively switched in E → Z direction and most intriguingly from its thermodynamically stable Z to metastable E isomer upon successive excitation of two different triplet sensitizers present in solution at the same time. This approach leads to extraordinary large redshift of excitation wavelengths to perform isomerization i.e. from 400 nm blue to 530 nm green light (Z → E) and from 530 nm green to 740 nm far-red one (E → Z), which falls in the near-infrared window in biological tissue. Therefore, this work opens up of potential avenues for utilizing diazocines for example in photopharmacology, smart materials, light energy harvesting/storage devices, and out-of-equilibrium systems.

Benchmarking fundamental gap of Sc2C(OH)2 MXene by many-body methods

Sc₂C(OH)₂ is a prototypical non-magnetic member of MXenes, a promising transition-metal-based 2D material family, with a direct bandgap. We provide here a benchmark of its fundamental gap Δ obtained from many-body GW and fixed-node diffusion Monte Carlo methods. Both approaches independently arrive at a similar value of Δ ∼ 1.3 eV, suggesting the validity of both methods. Such a bandgap makes Sc₂C(OH)₂ a 2D semiconductor suitable for optoelectronic applications. The absorbance spectra and the first exciton binding energy (0.63 eV), based on the Bethe-Salpeter equation, are presented as well. The reported results may serve to delineate experimental uncertainties and enable selection of reasonable approximations such as density functional theory functionals, for use in modeling of related MXenes.

Noncovalent Interactions by the Quantum Monte Carlo Method: Strong Influence of Isotropic Jastrow Cutoff Radii

We present a paradigmatic example of a strong effect of Jastrow cutoff radii setup on the accuracy of noncovalent interaction energy differences within one-determinant Slater-Jastrow fixed-node diffusion Monte Carlo (1FNDMC) simulations using isotropic Jastrow terms and effective-core potentials. Analysis of total energies, absolute and relative errors, and local energy variance of energy differences vs the reference results suggests a simple procedure to marginalize the related biases. The presented data showcase improvements in dispersion-bounded systems within such a 1FNDMC method.

Fractional Charge by Fixed-Node Diffusion Monte Carlo Method

Fixed-node diffusion Monte Carlo (FNDMC) method is a stochastic quantum many-body approach that has a great potential in electronic structure theory. We examine how FNDMC total energy E(N) satisfies exact constraints, linearity and derivative discontinuity, versus fractional electron number N, if combined with mean-field trial wave functions that miss such features. H and Cl atoms with fractional charge reveal that FNDMC method is well able to restore the piecewise linearity of E(N). The method uses ensemble and projector ingredients to achieve the correct charge localization. A water-solvated Cl^{-} complex illustrates superior performance of FNDMC method for charged noncovalent systems.

Photoionization and trans-to-cis isomerization of β-cyclodextrin-encapsulated azobenzene induced by two-color two-laser-pulse excitation

Azobenzene (1) and the complex resulting from the incorporation of 1 with cyclodextrin (1/CD) are attractive for light-driven applications such as micromachining and chemical biology tools. The highly sensitive photoresponse of 1 is crucial for light-driven applications containing both 1 and 1/CD to reach their full potential. In this study, we investigated the photoionization and trans-to-cis isomerization of 1/CD induced by one- and two-color two-laser pulse excitation. Photoionization of 1/CD, which was induced by stepwise two-photon absorption, was observed using laser pulse excitation at 266nm. Additionally, simultaneous irradiation with 266 and 532nm laser pulses increased the trans-to-cis isomerization yield (Υ_t→c) by 27%. It was concluded that the increase in Υ_t→c was caused by the occurrence of trans-to-cis isomerization in the higher-energy singlet state (S_n), which was reached by S₁→S_n transition induced by laser pulse excitation at 532nm. The results of this study are potentially applicable in light-driven applications such as micromachining and chemical biology tools.

Optical Gaps in Pristine and Heavily Doped Silicon Nanocrystals: DFT versus Quantum Monte Carlo Benchmarks

We present a time-dependent density functional theory (TDDFT) study of the optical gaps of light-emitting nanomaterials, namely, pristine and heavily B- and P-codoped silicon crystalline nanoparticles. Twenty DFT exchange-correlation functionals sampled from the best currently available inventory such as hybrids and range-separated hybrids are benchmarked against ultra-accurate quantum Monte Carlo results on small model Si nanocrystals. Overall, the range-separated hybrids are found to perform best. The quality of the DFT gaps is correlated with the deviation from Koopmans' theorem as a possible quality guide. In addition to providing a generic test of the ability of TDDFT to describe optical properties of silicon crystalline nanoparticles, the results also open up a route to benchmark-quality DFT studies of nanoparticle sizes approaching those studied experimentally.

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

The accuracy of the fixed-node diffusion Monte Carlo (FNDMC) depends on the node location of the supplied trial state Ψ_{T}. The practical FNDMC approaches available for large systems rely on compact yet effective Ψ_{T}, most often containing an explicitly correlated single Slater determinant (SD). However, SD nodes may be better suited to one system than to another, which may possibly lead to inaccurate FNDMC energy differences. It remains a challenge how to estimate nonequivalence or appropriateness of SDs. Here we use the differences of a measure based on the Euclidean distance between the natural orbital occupation number (NOON) vector of the SD and the exact solution in the NOON vector space, which can be viewed as a measure of SD nonequivalence and as a qualitative measure of the expected degree of nondynamic-correlation-related bias in FNDMC energy differences. This is explored on a set of small noncovalent complexes and covalent bond breaking of Si_{2} vs N_{2}. It turns out that NOON-based measures well reflect the magnitude and sign of the bias present in the data available, thus providing insights into the nature of bias cancellation in SD FNDMC energy differences.

Rhodopsin Absorption from First Principles: Bypassing Common Pitfalls

Bovine rhodopsin is the most extensively studied retinal protein and is considered the prototype of this important class of photosensitive biosystems involved in the process of vision. Many theoretical investigations have attempted to elucidate the role of the protein matrix in modulating the absorption of retinal chromophore in rhodopsin, but, while generally agreeing in predicting the correct location of the absorption maximum, they often reached contradicting conclusions on how the environment tunes the spectrum. To address this controversial issue, we combine here a thorough structural and dynamical characterization of rhodopsin with a careful validation of its excited-state properties via the use of a wide range of state-of-the-art quantum chemical approaches including various flavors of time-dependent density functional theory (TDDFT), different multireference perturbative schemes (CASPT2 and NEVPT2), and quantum Monte Carlo (QMC) methods. Through extensive quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations, we obtain a comprehensive structural description of the chromophore-protein system and sample a wide range of thermally accessible configurations. We show that, in order to obtain reliable excitation properties, it is crucial to employ a sufficient number of representative configurations of the system. In fact, the common use of a single, ad hoc structure can easily lead to an incorrect model and an agreement with experimental absorption spectra due to cancelation of errors. Finally, we show that, to properly account for polarization effects on the chromophore and to quench the large blue-shift induced by the counterion on the excitation energies, it is necessary to adopt an enhanced description of the protein environment as given by a large quantum region including as many as 250 atoms.