On the Vertical and Adiabatic Excitation Energies of the 2Ag State of trans-1,3-Butadiene

Extended N-centered ensemble density functional theory of double electronic excitations

A recent work (arXiv:2401.04685) has merged N-centered ensembles of neutral and charged electronic ground states with ensembles of neutral ground and excited states, thus providing a general and in-principle exact (so-called extended N-centered) ensemble density functional theory of neutral and charged electronic excitations. This formalism made it possible to revisit the concept of density-functional derivative discontinuity, in the particular case of single excitations from the highest occupied Kohn-Sham (KS) molecular orbital, without invoking the usual "asymptotic behavior of the density" argument. In this work, we address a broader class of excitations, with a particular focus on double excitations. An exact implementation of the theory is presented for the two-electron Hubbard dimer model. A thorough comparison of the true physical ground- and excited-state electronic structures with that of the fictitious ensemble density-functional KS system is also presented. Depending on the choice of the density-functional ensemble as well as the asymmetry of the dimer and the correlation strength, an inversion of states can be observed. In some other cases, the strong mixture of KS states within the true physical system makes the assignment "single excitation" or "double excitation" irrelevant.

Reference Energies for Double Excitations: Improvement and Extension

In the realm of photochemistry, the significance of double excitations (also known as doubly excited states), where two electrons are concurrently elevated to higher energy levels, lies in their involvement in key electronic transitions essential in light-induced chemical reactions as well as their challenging nature from the computational theoretical chemistry point of view. Based on state-of-the-art electronic structure methods (such as high-order coupled-cluster, selected configuration interaction, and multiconfigurational methods), we improve and expand our prior set of accurate reference excitation energies for electronic states exhibiting a substantial amount of double excitations [Loos et al. J. Chem. Theory Comput. 2019, 15, 1939]. This extended collection encompasses 47 electronic transitions across 26 molecular systems that we separate into two distinct subsets: (i) 28 "genuine" doubly excited states where the transitions almost exclusively involve doubly excited configurations and (ii) 19 "partial" doubly excited states which exhibit a more balanced character between singly and doubly excited configurations. For each subset, we assess the performance of high-order coupled-cluster (CC3, CCSDT, CC4, and CCSDTQ) and multiconfigurational methods (CASPT2, CASPT3, PC-NEVPT2, and SC-NEVPT2). Using as a probe the percentage of single excitations involved in a given transition (%T1) computed at the CC3 level, we also propose a simple correction that reduces the errors of CC3 by a factor of 3, for both sets of excitations. We hope that this more complete and diverse compilation of double excitations will help future developments of electronic excited-state methodologies.

Modeling voltammetry curves for proton coupled electron transfer: The importance of nuclear quantum effects

We investigate rates of proton-coupled electron transfer (PCET) in potential sweep experiments for a generalized Anderson-Holstein model with the inclusion of a quantized proton coordinate. To model this system, we utilize a quantum classical Liouville equation embedded inside of a classical master equation, which can be solved approximately with a recently developed algorithm combining diffusional effects and surface hopping between electronic states. We find that the addition of nuclear quantum effects through the proton coordinate can yield quantitatively (but not qualitatively) different IV curves under a potential sweep compared to electron transfer (ET). Additionally, we find that kinetic isotope effects give rise to a shift in the peak potential, but not the peak current, which would allow for quantification of whether an electrochemical ET event is proton-coupled or not. These findings suggest that it will be very difficult to completely understand coupled nuclear-electronic effects in electrochemical voltammetry experiments using only IV curves, and new experimental techniques will be needed to draw inferences about the nature of electrochemical PCET.

Evaluation of full valence correlation energies and gradients

Complete-active-space self-consistent field (CASSCF) wave functions are central to understanding strongly correlated molecules as they capture the entirety of electronic interactions within a subset of the orbital space. The most interesting case for CASSCF is the full valence limit, where all bonding and an equal number of virtual orbitals are included in the active space, and no approximation is made in selecting the important valence orbitals or electrons. While conventional algorithms require exponential computational time to evaluate full valence CASSCF, this article shows that the method of increments can do the same with polynomial effort, in a new method denoted iCASSCF. The method of increments can also provide density matrices and other necessary ingredients for the construction of the nuclear gradient. These goals are met through a many-body expansion that breaks the problem into smaller pieces that are subsequently reassembled to form close approximations of conventional CAS results. Practical demonstrations on a number of medium-sized molecules, with up to 116 valence electrons correlated in 116 orbitals, show the power of this methodology.

Single, Double Electronic Excitations and Exciton Effective Conjugation Lengths in π-Conjugated Systems

The 21Ag and 11Bu excited states of two prototypical π-conjugated compounds, polyacetylene and polydiacetylene, are investigated with the recently developed particle-particle random phase approximation (pp-RPA) method combined with the B3LYP functional. The polymer-limit transition energies are estimated as 1.38 and 1.72 eV for the 21Ag and 11Bu states, respectively, from an extrapolation of the computed excitation energies of model oligomers. These values increase to 1.95 and 2.24 eV for the same transitions when ground-state structures with ∼33% larger bond length alternation are adopted. Applying the pp-RPA to the vertical excitation energies in oligodiacetylene, the polymer-limit transition energies of the 21Ag and 11Bu states are computed to be 2.06 and 2.28 eV, respectively. These results are in good agreement with experimental values or theoretical best estimates, indicating that the pp-RPA method shows great promise for understanding many photophysical phenomena involving both single and double excitations.

Two-Photon Excited State Dynamics of Dark Valence, Rydberg, and Superexcited States in 1,3-Butadiene

Two-photon absorption in systems with parity permits access to states that cannot be prepared by one-photon absorption. Here we present the first time-resolved photoelectron spectroscopy study using this technique, applied to 1,3-butadiene, in which we investigated the dynamics of its dark valence, Rydberg, and superexcited states. The dark valence state dynamics are accessed via the Rydberg manifold, excited by two photons of 400 nm. We find that the 'dark' 2(1)Ag state populated in this manner has a much longer lifetime than when accesses via the 1(1)Bu 'bright' valence state when populated by one photon of 200 nm. In addition, we compared the dynamics of the 3sπ- and 3dπ-Rydberg states. These Rydberg states relax to the valence manifold on a subpicosecond time scale, with the 3sπ-Rydberg state decay rate being larger due to a stronger valence-Rydberg mixing. Finally, we investigated superexcited valence states that fragment or autoionize within 200 fs, likely without involving Rydberg states.

25th anniversary article: Design of polymethine dyes for all-optical switching applications: guidance from theoretical and computational studies

All-optical switching--controlling light with light--has the potential to meet the ever-increasing demand for data transmission bandwidth. The development of organic π-conjugated molecular materials with the requisite properties for all-optical switching applications has long proven to be a significant challenge. However, recent advances demonstrate that polymethine dyes have the potential to meet the necessary requirements. In this review, we explore the theoretical underpinnings that guide the design of π-conjugated materials for all-optical switching applications. We underline, from a computational chemistry standpoint, the relationships among chemical structure, electronic structure, and optical properties that make polymethines such promising materials.

Double excitations from modified Hartree Fock subsequent minimization scheme

Doubly excited states have nowadays become important in technological applications, e.g., in increasing the efficiency of solar cells and therefore, their description using ab initio methods is a great theoretical challenge as double excitations cannot be described by linear response theories based on a single Slater determinant. In the present work we extend our recently developed Hartree-Fock (HF) approximation for calculating singly excited states [M. Tassi, I. Theophilou, and S. Thanos, Int. J. Quantum Chem. 113, 690 (2013)] in order to allow for the calculation of doubly excited states. We describe the double excitation as two holes in the subspace spanned from the occupied HF orbitals and two particles in the subspace of virtual HF orbitals. A subsequent minimization of the energy results to the determination of the spin orbitals of both the holes and the particles in the occupied and virtual subspaces, respectively. We test our method, for various atoms, H2 and polyene molecules which are known to have excitations presenting a significant double excitation character. Importantly, our approach is computationally inexpensive.

Application of the dressed time-dependent density functional theory for the excited states of linear polyenes

Dressed Time-Dependent Density Functional Theory (Maitra et al., J Chem Phys 2004, 120, 5932) is applied to selected linear polyenes. Limits of validity of the approximation are briefly discussed. The implementation strategy is described. Results for the 2(1)B(u) and 2(1)A(g) states of selected linear polyenes are presented and compared with accessible experimental and theoretical results.

Computational prediction of absorbance maxima for a structurally diverse series of engineered green fluorescent protein chromophores

By virtue of its self-sufficiency to form a visible wavelength chromophore within the confines of its tertiary structure, the Aequorea victoria green fluorescent protein (GFP) is single-handedly responsible for the ever-growing popularity of fluorescence imaging of recombinant fusion proteins in biological research. Engineered variants of GFP with altered excitation or emission wavelength maxima have helped to expand the range of applications of GFP. The engineering of the GFP variants is usually done empirically by genetic modifications of the chromophore structure and/or its environment in order to find variants with new photophysical properties. The process of identifying improved variants could be greatly facilitated if augmented or guided by computational studies of the chromophore ground and excited-state properties and dynamics. In pursuit of this goal, we now report a thorough investigation of computational methods for prediction of the absorbance maxima for an experimentally validated series of engineered GFP chromophore analogues. The experimental dataset is composed of absorption maxima for 10 chemically distinct GFP chromophore analogues, including a previously unreported Y66D variant, measured under identical denaturing conditions. For each chromophore analogue, excitation energies and oscillator strengths were calculated using configuration interaction with single excitations (CIS), CIS with perturbative correction for double substitutions [CIS(D)], and time-dependent density functional theory (TD DFT) using several density functionals with solvent effects included using a polarizable continuum model. Comparison of the experimental and computational results show generally poor quantitative agreement with all methods attempted. However, good linear correlations between the calculated and experimental excitation energies (R2>0.9) could be obtained. Oscillator strengths obtained with TD DFT using pure density functionals also correlate well with the experimental values. Interestingly, most of the computational methods used in this work fail in the case of nonaromatic Y66S and Y66L protein chromophores, which may be related to a significant contribution of double excitations to their excited-state wavefunctions. These results provide an important benchmark of the reliability of the computational methods as applied to GFP chromophore analogues and lays a foundation for the computational design of GFP variants with improved properties for use in biological imaging.

Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group

We have devised a local ab initio density matrix renormalization group algorithm to describe multireference correlations in large systems. For long molecules that are extended in one of their spatial dimensions, we can obtain an exact characterization of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (in the sense of full configuration interaction, with 1-10 microE(h) precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.

Singly and doubly excited states of butadiene, acrolein, and glyoxal: Geometries and electronic spectra

Excited-state geometries and electronic spectra of butadiene, acrolein, and glyoxal have been investigated by the symmetry adapted cluster configuration interaction (SAC-CI) method in their s-trans conformation. Valence and Rydberg states below the ionization threshold have been precisely calculated with sufficiently flexible basis sets. Vertical and adiabatic excitation energies were well reproduced and the detailed assignments were given taking account of the second moments. The deviations of the vertical excitation energies from the experiment were less than 0.3 eV for all cases. The SAC-CI geometry optimization has been applied to some valence and Rydberg excited states of these molecules in the planar structure. The optimized ground- and excited-state geometries agree well with the available experimental values; deviations lie within 0.03 A and 0.7 degrees for the bond lengths and angles, respectively. The force acting on the nuclei caused by the excitations has been discussed in detail by calculating the SAC-CI electron density difference between the ground and excited states; the geometry relaxation was well interpreted with the electrostatic force theory. In Rydberg excitations, geometry changes were also noticed. Doubly excited states (so-called 2 (1)A(g) states) were investigated by the SAC-CI general-R method considering up to quadruple excitations. The characteristic geometrical changes and large energetic relaxations were predicted for these states.

A computational strategy for geometry optimization of ionic and covalent excited states, applied to butadiene and hexatriene

We propose a computational strategy that enables ionic and covalent pipi* excited states to be described in a balanced way. This strategy depends upon (1) the restricted active space self-consistent field method, in which the dynamic correlation between core sigma and valence pi electrons can be described by adding single sigma excitations to all pi configurations and (2) the use of a new conventional one-electron basis set specifically designed for the description of valence ionic states. Together, these provide excitation energies comparable with more accurate and expensive ab initio methods--e.g., multiconfigurational second-order perturbation theory and multireference configuration interaction. Moreover, our strategy also allows full optimization of excited-state geometries--including conical intersections between ionic and covalent excited states--to be routinely carried out, thanks to the availability of analytical energy gradients. The prototype systems studied are the cis and trans isomers of butadiene and hexatriene, for which the ground 1A(1/g), lower-lying dark (i.e., symmetry forbidden covalent) 2A(1/g) and spectroscopic 1B(2/u) (valence ionic) states were investigated.

Double excitations within time-dependent density functional theory linear response

Within the adiabatic approximation, time-dependent density functional theory yields only single excitations. Near states of double excitation character, the exact exchange-correlation kernel has a strong dependence on frequency. We derive the exact frequency-dependent kernel when a double excitation mixes with a single excitation, well separated from the other excitations, in the limit that the electron--electron interaction is weak. Building on this, we construct a nonempirical approximation for the general case, and illustrate our results on a simple model.

A global investigation of excited state surfaces within time-dependent density-functional response theory

This work investigates the capability of time-dependent density functional response theory to describe excited state potential energy surfaces of conjugated organic molecules. Applications to linear polyenes, aromatic systems, and the protonated Schiff base of retinal demonstrate the scope of currently used exchange-correlation functionals as local, adiabatic approximations to time-dependent Kohn-Sham theory. The results are compared to experimental and ab initio data of various kinds to attain a critical analysis of common problems concerning charge transfer and long range (nondynamic) correlation effects. This analysis goes beyond a local investigation of electronic properties and incorporates a global view of the excited state potential energy surfaces.