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Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn-Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin-orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

The dynamics of excited heteroaromatic molecules is a key to understanding the photoprotective properties of many biologically relevant chromophores that dissipate their excitation energy nonreactively and thereby prevent the detrimental effects of ultraviolet radiation. Despite their structural variability, most heteroaromatic compounds share a common feature of a repulsive 1πσ* potential energy surface. This surface can lead to photoproducts, and it can also facilitate the population transfer back to the ground electronic state by means of a 1πσ*/S0 conical intersection. Here, we explore a hidden relaxation route involving the triplet electronic state of aniline, which has recently been discovered by means of time-selected photofragment translational spectroscopy [J. Chem. Phys. 2019, 151, 141101]. By using the recently available analytical gradients for multiconfiguration pair-density functional theory, it is now possible to locate the minimum energy crossing points between states of different spin and therefore compute the intersystem crossing rates with a multireference method, rather than with the less reliable single-reference methods. Using such calculations, we demonstrate that the population loss of aniline in the T1(3ππ*) state is dominated by C6H5NH2→C6H5NH⸱ + H⸱ dissociation, and we explain the long nonradiative lifetimes of the T1(3ππ*) state at the excitation wavelengths of 294‑264 nm.

The T1 excited state relaxation in thiophosgene has attracted much attention as a relatively simple model for the intersystem crossing (ISC) transitions in polyatomic molecules. The very short (20–40 ps) T1 lifetime predicted in several theoretical studies strongly disagrees with the experimental values (∼20 ns) indicating that the kinetics of T1 → S0 ISC is not well understood. We use the nonadiabatic transition state theory (NA-TST) with the Zhu–Nakamura transition probability and the multireference perturbation theory (CASPT2) to show that the T1 → S0 ISC occurs in the quantum tunneling regime. We also introduce a new zero-point vibrational energy correction scheme that improves the accuracy of the predicted ISC rate constants at low internal energies. The predicted lifetimes of the T1 vibrational states are between one and two orders of magnitude larger than the experimental values. This overestimation is attributed to the multidimensional nature of quantum tunneling that facilitates ISC transitions along the non-minimum energy path and is not accounted for in the one-dimensional NA-TST.

The dipole moment is the molecular property that most directly indicates molecular polarity. The accuracy of computed dipole moments depends strongly on the quality of the calculated electron density, and the breakdown of single-reference methods for strongly correlated systems can lead to poor predictions of the dipole moments in those cases. Here, we derive the analytical expression for obtaining the electric dipole moment by multiconfiguration pair density functional theory (MC-PDFT), and we assess the accuracy of MC-PDFT for predicting dipole moments at equilibrium and nonequilibrium geometries. We show that MC-PDFT dipole moment curves have reasonable behavior even for stretched geometries, and they significantly improve upon the CASSCF results by capturing more electron correlation. The analysis of a dataset consisting of 18 first-row transition metal diatomics and 6 main-group polyatomic molecules with multireference character suggests that MC-PDFT and its hybrid extension (HMC-PDFT) perform comparably to CASPT2 and MRCISD+Q methods and have a mean unsigned deviation of 0.2–0.3 D with respect to the best available dipole moment reference values. We explored the dependence of the predicted dipole moments upon the choice of the on-top density functional and active space, and we recommend the tPBE and hybrid tPBE0 on-top choices for the functionals combined with the moderate correlated participating orbital scheme for selecting the active space. With these choices, the mean unsigned deviations (in debyes) of the calculated equilibrium dipole moments from the best estimates are 0.77 for CASSCF, 0.29 for MC-PDFT, 0.24 for HMC-PDFT, 0.28 for CASPT2, and 0.25 for MRCISD+Q. These results are encouraging because the computational cost of MC-PDFT or HMC-PDFT is largely reduced compared to the CASPT2 and MRCISD+Q methods.

We present a nonadiabatic statistical theory (NAST) package for predicting kinetics of spin-dependent processes, such as intersystem crossings, spin-forbidden unimolecular reactions, and spin crossovers. The NAST package can calculate the probabilities and rates of transitions between the electronic states of different spin multiplicities. Both the microcanonical (energy-dependent) and canonical (temperature-dependent) rate constants can be obtained. Quantum effects, including tunneling, zero-point vibrational energy, and reaction path interference, can be accounted for. In the limit of an adiabatic unimolecular reaction proceeding on a single electronic state, NAST reduces to the traditional transition state theory. Because NAST requires molecular properties at only a few points on potential energy surfaces, it can be applied to large molecular systems, used with accurate high-level electronic structure methods, and employed to study slow nonadiabatic processes. The essential NAST input data include the nuclear Hessian at the reactant minimum, as well as the nuclear Hessians, energy gradients, and spin-orbit coupling at the minimum energy crossing point (MECP) between two states. The additional computational tools included in the NAST package can be used to extract the required input data from the output files of electronic structure packages, calculate the effective Hessian at the MECP, and fit the reaction coordinate for more advanced NAST calculations. We describe the theory, its implementation, and three examples of application to different molecular systems.

While the treatment of chemically relevant systems containing hundreds or even thousands of electrons remains beyond the reach of quantum devices, the development of quantum-classical hybrid algorithms to resolve electronic correlation presents a promising pathway toward a quantum advantage in the computation of molecular electronic structure. Such hybrid algorithms treat the exponentially scaling part of the calculation -- the static (multireference) correlation -- on the quantum computer and the non-exponentially scaling part -- the dynamic correlation -- on the classical computer. While a variety of such algorithms have been proposed, due to the dependence on the wave function of most classical methods for dynamic correlation, the development of easy-to-use classical post-processing implementations has been limited. Here we present a novel hybrid-classical algorithm that computes a molecule's all-electron energy and properties on the classical computer from a critically important simulation of the static correlation on the quantum computer. Significantly, for the all-electron calculations we circumvent the wave function by using density-matrix methods that only require input of the statically correlated two-electron reduced density matrix (2-RDM), which can be efficiently measured in the quantum simulation. Although the algorithm is completely general, we test it with two classical 2-RDM methods, the anti-Hermitian contracted Schr\"odinger equation (ACSE) theory and multiconfiguration pair-density functional theory (MC-PDFT), using the recently developed quantum ACSE method for the simulation of the statically correlated 2-RDM. We obtain experimental accuracy for the relative energies of all three benzyne isomers and thereby, demonstrate the ability of the quantum-classical hybrid algorithms to achieve chemically relevant results and accuracy on currently available quantum computers.

The blue emission of M2biQ can be tuned to specific wavelengths throughout the visible region by changing the identity of the cation it interacts with. These optical properties are observed in MeCN solution and the solid state. White light is obtained in MeCN by using either the proper ratio of zinc ions or acid. Thus, M2biQ acts as a nearly universal emitter (λem = 468-690 nm) with large Stokes shifts (116-306 nm, Δν = 7,042-11,823 cm-1). Full spectral profiles as well as quantum yields, lifetimes, and the crystal structures of key RGB and yellow emitters are reported. Emission wavelengths correlate with cationic radius, and TD-DFT calculations show that, for 1:1 complexes, the smaller the ion, the shorter the N-cation bond, and the greater the bathochromic emission shift.

The T1 excited state relaxation in thiophosgene has attracted much attention as a relatively simple model for the intersystem crossing (ISC) transitions in polyatomic molecules. The very short (20-40 ps) T1 lifetime predicted in several theoretical studies strongly disagrees with the experimental values (∼20 ns) indicating that the kinetics of T1 → S0 ISC is not well understood. We use the nonadiabatic transition state theory (NA-TST) with the Zhu-Nakamura transition probability and the multireference perturbation theory (CASPT2) to show that the T1 → S0 ISC occurs in the quantum tunneling regime. We also introduce a new zero-point vibrational energy correction scheme that improves the accuracy of the predicted ISC rate constants at low internal energies. The predicted lifetimes of the T1 vibrational states are between one and two orders of magnitude larger than the experimental values. This overestimation is attributed to the multidimensional nature of quantum tunneling that facilitates ISC transitions along the non-minimum energy path and is not accounted for in the one-dimensional NA-TST.

Diffuse interstellar bands (DIBs) are puzzling absorption features believed to contain critical information about molecular evolution in space. Despite the fact that C60+ recently became the first confirmed carrier of several DIBs, the nature of the corresponding transitions is not understood. Using electronic structure methods, we show that the two strong C60+ DIBs cannot be explained by electronic transitions to the two different excited 2E1g states or the two spin–orbit components of the lowest 2E1g state, as suggested before. We argue that the strong DIBs at 9632 and 9577 A correspond to the cold excitations from the non-Franck–Condon region of the ground electronic state to the two components of the lowest 2E1g state split by Jahn–Teller distortion. The weak DIBs at 9428 and 9365 A are assigned to the first vibronic transitions involving the low-energy vibrational modes and components of the lowest 2E1g electronic state.

Nonadiabatic transition state theory (NA-TST) is a powerful tool to investigate the nonradiative transitions between electronic states with different spin multiplicities. The statistical nature of NA-TST provides an elegant and computationally inexpensive way to calculate the rate constants for intersystem crossings, spin-forbidden reactions, and spin-crossovers in large complex systems. The relations between the microcanonical and canonical versions of NA-TST and the traditional transition state theory are shown, followed by a review of the basic steps in a typical NA-TST rate constant calculation. These steps include evaluations of the transition probability and coupling between electronic states with different spin multiplicities, a search for the minimum energy crossing point (MECP), and computing the densities of states and partition functions for the reactant and MECP structures. The shortcomings of the spin-diabatic version of NA-TST related to ill-defined state coupling and state counting are highlighted. In three examples, we demonstrate the application of NA-TST to intersystem crossings in the active sites of metal-sulfur proteins focusing on [NiFe]-hydrogenase, rubredoxin, and Fe2S2-ferredoxin. © 2016 Wiley Periodicals, Inc.

Diffuse interstellar bands (DIBs) are puzzling absorption features believed to contain critical information about molecular evolution in space. Despite the fact that C

Herein we describe the synthesis, structure, and properties of chiral peropyrenes. Using p-terphenyl-2,2″,6,6″-tetrayne derivatives as precursors, chiral peropyrenes were formed after a 4-fold alkyne cyclization reaction promoted by triflic acid. Due to the repulsion of the two aryl substituents within the same bay region, the chiral peropyrene adopts a twisted backbone with an end-to-end twist angle of 28° that was unambiguously confirmed by X-ray crystallographic analysis. The chiral peropyrene products absorb and emit in the green region of the UV–visible spectrum. Circular dichroism spectroscopy shows strong Cotton effects (Δe = ±100 M–1 cm–1 at 300 nm). The Raman data shows the expected D-band along with a split G-band that is due to longitudinal and transversal G modes. This data corresponds well with the simulated Raman spectra of chiral peropyrenes. The chiral peropyrene products also display circularly polarized luminescence. The cyclization reaction mechanism and the enantiomeric composition of ...

A detailed study of Ni-doped Mg(0 0 0 1) surface performed by PAW method and the gradient corrected density functional GGA-PBE within the framework of generalized Kohn–Sham density functional theory (DFT) is presented in this work. Structural and electronic properties of magnesium surface interaction with nickel for the purpose of such compounds use for creation of hydrogen storage matrixes were investigated here. Choice of the PBE functional was caused by the good accordance of its prediction of the cell parameters with experimental results. It was shown that Ni atoms prefer to substitute for Mg atoms. Using NEB method, the diffusion barrier was calculated, and the most probable reaction path was established. In particular, when the Ni atom dopes the magnesium surface, it can migrate to the bulk and substitute for Mg in subsurface layers. Also a possibility of nickel cluster formation on clean surface of magnesium was examined. The kinetic factors hinder the movement of the nickel atoms to each other and make problematic the formation of clusters. The studies presented here showed that the diffusion barriers of the nickel atom migration from the cluster on the surface to the bulk of magnesium are 1.179 eV and 1.211 eV for the forward and reverse reactions, respectively. Therefore an improvement of the hydrogenation properties of Ni-doped magnesium surface depends on deposition not of the individual atoms, but their clusters. Hydrogenation of Ni cluster doping the magnesium surface was investigated. Initially Kubas complexes arise on the Ni cluster with hydrogen–hydrogen bond lengths equal to 0.80–0.87 A. Next the cluster needs to be saturated by hydrogen atoms to allow them later to migrate from cluster to magnesium.

LixBC3 intercalated compounds with various configurations are studied for their possible application as electrode materials for lithium current sources. For this purpose, the band structure and the density of states were calculated for each structure, and energy stability and possible deformations due to a change in the unit cell volume during intercalation are investigated.

The formation constants of bismuth(III) methylthiourea complexes in aqueous solution were determined at 298 K and an acidity of 2 M HClO4 using the “ligand-oxidized ligand species” potentiometric method and the methylthiourea (mtu)-symmetric dimethylformamidine disulfide (mFDS) redox pair. The formation function was obtained, and the conditional (βn*) and true (βn) formation constants of Bi(mtu)n3+ (1 ≤ n ≤ 8) were calculated. The value of β1 and the formation of complexes with coordination numbers higher than six was confirmed by spectrophotometry.

A Pb(II) complex with ceftriaxone (H2Ceftria) antibiotic was synthesized by reaction of ceftriaxone disodium salt (hemi)heptahydrate with lead nitrate in water–ethanol medium. The complex was characterized on the basis of complexometric titration, spectrophotometric and thermogravimetric analyses, capillary electrophoresis, IR, Raman and UV–vis spectroscopies, and density functional theory calculations. Pb(II) is five-coordinate with distorted square pyramidal geometry. The coordination of Ceftria2− to Pb(II) occurs through N and O of the triazine, lactam carbonyl, carboxylate, and amine groups. The antibacterial activity study showed that Klebsiella pneumoniae is resistant to [Pb(Ceftria)]·3H2O. The antibacterial activity of [Pb(Ceftria)]·3H2O against Staphylococcus aureus is reduced compared with ceftriaxone. In contrast, the antibacterial activity of [Pb(Ceftria)]·3H2O against Escherichia coli is 28% higher than that of ceftriaxone antibiotic.