Dipole Moments and Transition Dipole Moments Calculated by Pair-Density Functional Theory with State Interaction.

We develop response-function algorithms for dipole moments and transition dipole moments for compressed multistate pair-density functional theory (CMS-PDFT). We use the method of undetermined Lagrange multipliers to derive analytical expressions and validate them using numerical differentiation. We test the accuracy of the magnitudes of predicted ground-state and excited-state dipole moments, the orientations of these dipole moments, and the orientation of transition dipole moments by comparison to experimental data. We show that CMS-PDFT has good accuracy for these quantities, and we also show that, unlike methods that neglect state interaction, CMS-PDFT yields correct behavior for the dipole moment curves in the vicinity of conical intersections. This work, therefore, opens the door to molecular dynamic simulations in strong electric fields, and we envision that CMS-PDFT can now be used to discover chemical reactions that can be controlled by an oriented external electric field upon photoexcitation of the reactants.

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory.

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.

NAST: Nonadiabatic Statistical Theory Package for Predicting Kinetics of Spin-Dependent Processes.

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.

Dipole Moment Calculations Using Multiconfiguration Pair-Density Functional Theory and Hybrid Multiconfiguration Pair-Density Functional Theory.

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 a 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-orbitals 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.

Role of Triplet States in the Photodynamics of Aniline.

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 substituted aromatic 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.

Quantum-classical hybrid algorithm for the simulation of all-electron correlation.

While chemical systems containing hundreds to thousands of electrons remain beyond the reach of quantum devices, hybrid quantum-classical algorithms present a promising pathway toward a quantum advantage. Hybrid algorithms treat the exponentially scaling part of the calculation-the static correlation-on the quantum computer and the non-exponentially scaling part-the dynamic correlation-on the classical computer. While a variety of algorithms have been proposed, the dependence of many methods on the total wave function limits the development of easy-to-use classical post-processing implementations. Here, we present a novel combination of quantum and classical algorithms, which computes the all-electron energy of a strongly correlated molecular system on the classical computer from the 2-electron reduced density matrix (2-RDM) evaluated on the quantum device. Significantly, we circumvent the wave function in the all-electron calculations by using density matrix methods that only require input of the statically correlated 2-RDM. Although the algorithm is completely general, we test it with two classical density matrix methods, the anti-Hermitian contracted Schrödinger equation (ACSE) and multiconfiguration pair-density functional theories, using the recently developed quantum ACSE method for simulating 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 developed algorithm to achieve chemically relevant and accurate results on noisy intermediate-scale quantum devices.

Full Visible Spectrum and White Light Emission with a Single, Input-Tunable Organic Fluorophore.

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, Δν̃ = 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.

Intersystem crossing in tunneling regime: T1 → S0 relaxation in thiophosgene.

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.

Electronic Transitions Responsible for C60+ Diffuse Interstellar Bands.

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 2 E1 g states or the two spin-orbit components of the lowest 2 E1 g state, as suggested before. We argue that the strong DIBs at 9632 and 9577 Å correspond to the cold excitations from the non-Franck-Condon region of the ground electronic state to the two components of the lowest 2 E1 g state split by Jahn-Teller distortion. The weak DIBs at 9428 and 9365 Å are assigned to the first vibronic transitions involving the low-energy vibrational modes and components of the lowest 2 E1 g electronic state.

Predicting Intersystem Crossing Rates with AIMS-DFT Molecular Dynamics.

Accurate prediction of the intersystem crossing rates is important for many different applications in chemistry, physics, and biology. Recently, we implemented the ab initio multiple spawning (AIMS) molecular dynamics method to describe the intersystem crossing processes, where nonradiative transitions between electronic states with different spin multiplicities are mediated by spin-orbit coupling. Our original implementation of the direct AIMS dynamics used the complete active space self-consistent field (CASSCF) method to describe multiple coupled electronic states on which multidimensional Gaussian wave packets were propagated. In this work, we improve the computational efficiency and versatility of the AIMS dynamics by interfacing it with the density functional theory (DFT). The new AIMS-DFT and the earlier AIMS-CASSCF implementations are used to investigate the effects of electronic structure methods on the predicted intersystem crossing rate constants and the lowest triplet state lifetime in the GeH2 molecule. We also compare the rates and lifetimes obtained from the AIMS simulations with those predicted by the statistical nonadiabatic transition state theory (NA-TST). In NA-TST, the probabilities of spin transitions are calculated using the Landau-Zener, weak coupling, and Zhu-Nakamura formulas. Convergence of the AIMS rate constants with respect to the simulation time and the number of initial trajectories (Gaussian wave packets) is analyzed. An excellent agreement between AIMS-DFT and AIMS-CASSCF can be explained by cancelation of two effects: higher energy barriers and a stronger spin-orbit coupling in DFT relative to CASSCF. The rate constants obtained with the AIMS-DFT dynamics are about a factor of 2 larger than those predicted by the statistical NA-TST. This is likely due to the importance of the nonlocal interstate transitions missing from the NA-TST description.

Chiral Peropyrene: Synthesis, Structure, and Properties.

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 (Δε = ±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 the peropyrene products are explained using DFT calculations. The inversion barrier for racemization was determined experimentally to be 29 kcal/mol and is supported by quantum mechanical calculations.