Conical Intersection and Potential Energy Surface Features of a Model Retinal Chromophore: Comparison of EOM-CC and Multireference Methods

This work investigates the performance of equation-of-motion coupled-cluster (EOM-CC) methods for describing the changes in the potential energy surfaces of the penta-2,4-dieniminium cation, a reduced model of the retinal chromophore of visual pigments, due to dynamical electron correlation effects. The ground-state wave function of this model includes charge-transfer and diradical configurations whose weights vary along different displacements and are rapidly changing at the conical intersection between the ground and the first excited states, making the shape of the potential energy surface sensitive to a balanced description of nondynamical and dynamical correlation. Recently, variational (MRCISD) and perturbative (MRPT2) approaches for including dynamical correlation in CASSCF-based calculations were tested along three representative ground state paths. Here, we use the same three paths to compare the performance of single-reference EOM-CC methods against MRCISD and MRCISD+Q. We find that the spin-flip variant of EOM-CCSD with perturbative inclusion of triple excitations (dT or fT) produces potential energy profiles of the two lowest electronic states in quantitative agreement with MRCISD+Q (our highest-quality reference method). The nonparallelity errors and differences in vertical energy differences of the two surfaces along these scans are less than 1.4 kcal/mol (EOM-SF-CCSD­(dT) versus MRCISD+Q). For comparison, the largest error of MRCISD versus MRCISD+Q is 1.7 kcal/mol. Our results show that the EOM-CC methods provide an alternative to multireference approaches and may be used to study photochemical systems like the one used in this work

Combined Self-Consistent-Field and Spin-Flip Tamm–Dancoff Density Functional Approach to Potential Energy Surfaces for Photochemistry

We present a new approach to calculating potential energy surfaces for photochemical reactions by combining self-consistent-field calculations for single-reference ground and excited states with symmetry-corrected spin-flip Tamm–Dancoff approximation calculations for multireference electronic states. The method is illustrated by an application with the M05-2X exchange-correlation functional to <i>cis</i>–<i>trans</i> isomerization of the penta-2,4-dieniminium cation, which is a model (with three conjugated double bonds) of the protonated Schiff base of retinal. We find good agreement with multireference configuration interaction-plus-quadruples (MRCISD+Q) wave function calculations along three key paths in the strong-interaction region of the ground and first excited singlet states

Assessment of Density Functional Theory for Describing the Correlation Effects on the Ground and Excited State Potential Energy Surfaces of a Retinal Chromophore Model

In the quest for a cost-effective level of theory able to describe a large portion of the ground and excited potential energy surfaces of large chromophores, promising approaches are rooted in various approximations to the exact density functional theory (DFT). In the present work, we investigate how generalized Kohn–Sham DFT (GKS-DFT), time-dependent DFT (TDDFT), and spin-restricted ensemble-DFT (REKS) methods perform along three important paths characterizing a model retinal chromophore (the penta-2,4-dieniminium cation) in a region of near-degeneracy (close to a conical intersection) with respect to reference high-level multiconfigurational wave function methods. If GKS-DFT correctly describes the closed-shell charge transfer state, only TDDFT and REKS approaches give access to the open-shell diradical, one which sometimes corresponds to the electronic ground state. It is demonstrated that the main drawback of the usual DFT-based methods lies in the absence of interactions between the charge transfer and the diradicaloid configurations. Hence, we test a new computational scheme based on the State-averaged REKS (SA-REKS) approach, which explicitly includes these interactions into account. The State-Interaction SA-REKS (SI-SA-REKS) method significantly improves on the REKS and the SA-REKS results for the target system. The similarities and differences between DFT and wave function-based approaches are analyzed according to (1) the active space dimensions of the wave function-based methods and (2) the relative electronegativities of the allyl and protonated Schiff base moieties

Electronic Spectra of Tris(2,2′-bipyridine)-M(II) Complex Ions in Vacuo (M = Fe and Os)

We measured the electronic spectra of mass-selected [M­(bpy)₃]²⁺ (M = Fe and Os, bpy = 2,2′-bipyridine) ions in vacuo by photodissociation spectroscopy of their N₂ adducts, [M­(bpy)₃]²⁺·N₂. Extensive band systems in the visible (predominantly charge transfer) and near-ultraviolet (ππ*) spectral regions are reported. The [M­(bpy)₃]²⁺·N₂ target ions were prepared by condensing N₂ onto electrosprayed ions in a cryogenic ion trap at ca. 25 K and then mass-selected by time-of-flight mass spectrometry. The electronic photodissociation spectra of the cold, gas-phase ions closely reflect their intrinsic properties, i.e., without perturbation by solvent effects. The spectra are interpreted using time-dependent density functional theory calculations both with and without accounting for relativistic effects

Origin of Fluorescence in 11-<i>cis</i> Locked Bovine Rhodopsin

The excited state lifetime of bovine rhodopsin (Rh) increases from ca. 100 fs to 85 ps when the C11C12 bond of its chromophore is locked by a cyclopentene moiety (Rh5). To explain such an increase, we employed <i>ab initio</i> multiconfigurational quantum chemistry to construct computer models of Rh and Rh5 and to investigate the shape of their excited state potential energy surfaces in a comparative way. Our results show that the observed Rh5 fluorescence (λ_max^f = 620 nm) is due to a previously unreported locally excited intermediate whose lifetime is controlled by a small energy barrier. The analysis of the properties and decay path of such an intermediate provides useful information for engineering rhodopsin variants with augmented fluorescence efficiencies

Probing Vibrationally Mediated Ultrafast Excited-State Reaction Dynamics with Multireference (CASPT2) Trajectories

Excited-state trajectories computed at the complete active space second-order perturbation theory (CASPT2) reveal how vibrational excitation controls the molecular approach to the intersection space that drives the photodissociation of a prototypical halogenated methyl radical, namely CF₂I. Translating the Franck–Condon structure along the ground-state CASPT2 vibrational modes in this system followed by propagating the displaced structures in the first excited doublet state simulates specific vibrational excitations and vibrationally mediated dynamics, respectively. Three distinct situations are encountered: the trajectories (i) converge to an energetically flat segment of the intersection space, (ii) locate a segment of the intersection space, and (iii) access a region where the intersection space degeneracy is lifted to form a ridge of avoided crossings. The computational protocol documented herein can be used as a tool to design control strategies based on selective excitation of vibrational modes, including adaptive feedback schemes using coherent light sources

Probing Vibrationally Mediated Ultrafast Excited-State Reaction Dynamics with Multireference (CASPT2) Trajectories

Excited-state trajectories computed at the complete active space second-order perturbation theory (CASPT2) reveal how vibrational excitation controls the molecular approach to the intersection space that drives the photodissociation of a prototypical halogenated methyl radical, namely CF₂I. Translating the Franck–Condon structure along the ground-state CASPT2 vibrational modes in this system followed by propagating the displaced structures in the first excited doublet state simulates specific vibrational excitations and vibrationally mediated dynamics, respectively. Three distinct situations are encountered: the trajectories (i) converge to an energetically flat segment of the intersection space, (ii) locate a segment of the intersection space, and (iii) access a region where the intersection space degeneracy is lifted to form a ridge of avoided crossings. The computational protocol documented herein can be used as a tool to design control strategies based on selective excitation of vibrational modes, including adaptive feedback schemes using coherent light sources

Probing Vibrationally Mediated Ultrafast Excited-State Reaction Dynamics with Multireference (CASPT2) Trajectories

Excited-state trajectories computed at the complete active space second-order perturbation theory (CASPT2) reveal how vibrational excitation controls the molecular approach to the intersection space that drives the photodissociation of a prototypical halogenated methyl radical, namely CF₂I. Translating the Franck–Condon structure along the ground-state CASPT2 vibrational modes in this system followed by propagating the displaced structures in the first excited doublet state simulates specific vibrational excitations and vibrationally mediated dynamics, respectively. Three distinct situations are encountered: the trajectories (i) converge to an energetically flat segment of the intersection space, (ii) locate a segment of the intersection space, and (iii) access a region where the intersection space degeneracy is lifted to form a ridge of avoided crossings. The computational protocol documented herein can be used as a tool to design control strategies based on selective excitation of vibrational modes, including adaptive feedback schemes using coherent light sources

Probing Vibrationally Mediated Ultrafast Excited-State Reaction Dynamics with Multireference (CASPT2) Trajectories

Excited-state trajectories computed at the complete active space second-order perturbation theory (CASPT2) reveal how vibrational excitation controls the molecular approach to the intersection space that drives the photodissociation of a prototypical halogenated methyl radical, namely CF₂I. Translating the Franck–Condon structure along the ground-state CASPT2 vibrational modes in this system followed by propagating the displaced structures in the first excited doublet state simulates specific vibrational excitations and vibrationally mediated dynamics, respectively. Three distinct situations are encountered: the trajectories (i) converge to an energetically flat segment of the intersection space, (ii) locate a segment of the intersection space, and (iii) access a region where the intersection space degeneracy is lifted to form a ridge of avoided crossings. The computational protocol documented herein can be used as a tool to design control strategies based on selective excitation of vibrational modes, including adaptive feedback schemes using coherent light sources

Probing Vibrationally Mediated Ultrafast Excited-State Reaction Dynamics with Multireference (CASPT2) Trajectories

Excited-state trajectories computed at the complete active space second-order perturbation theory (CASPT2) reveal how vibrational excitation controls the molecular approach to the intersection space that drives the photodissociation of a prototypical halogenated methyl radical, namely CF₂I. Translating the Franck–Condon structure along the ground-state CASPT2 vibrational modes in this system followed by propagating the displaced structures in the first excited doublet state simulates specific vibrational excitations and vibrationally mediated dynamics, respectively. Three distinct situations are encountered: the trajectories (i) converge to an energetically flat segment of the intersection space, (ii) locate a segment of the intersection space, and (iii) access a region where the intersection space degeneracy is lifted to form a ridge of avoided crossings. The computational protocol documented herein can be used as a tool to design control strategies based on selective excitation of vibrational modes, including adaptive feedback schemes using coherent light sources