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

On the description of conical intersections between excited electronic states with LR-TDDFT and ADC(2)

Conical intersections constitute the conceptual bedrock of our working understanding of ultrafast, nonadiabatic processes within photochemistry (and photophysics). Accurate calculation of potential energy surfaces within the vicinity of conical intersections, however, still poses a serious challenge to many popular electronic structure methods. Multiple works have reported on the deficiency of methods like linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) or algebraic diagrammatic construction to second-order [ADC(2)]-approaches often used in excited-state molecular dynamics simulations-to describe conical intersections between the ground and excited electronic states. In the present study, we focus our attention on conical intersections between excited electronic states and probe the ability of AA LR-TDDFT and ADC(2) to describe their topology and topography, using protonated formaldimine and pyrazine as two exemplar molecules. We also take the opportunity to revisit the performance of these methods in describing conical intersections involving the ground electronic state in protonated formaldimine-highlighting in particular how the intersection ring exhibited by AA LR-TDDFT can be perceived either as a (near-to-linear) seam of intersection or two interpenetrating cones, depending on the magnitude of molecular distortions within the branching space.

Assessment of the Electron Correlation Treatment on the Quantum-Classical Dynamics of Retinal Protonated Schiff Base Models: XMS-CASPT2, RMS-CASPT2, and REKS Methods

We compare the performance of three different multiconfigurational wave function-based electronic structure methods and two implementations of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method. The study is characterized by three features: (i) it uses a small set of quantum-classical trajectories rather than potential energy surface mapping, (ii) it focuses, exclusively, on the photoisomerization of retinal protonated Schiff base models, and (iii) it probes the effect of both methyl substitution and the increase in length of the conjugate π-system. For each tested method, the corresponding analytical gradients are used to drive the quantum-classical (Tully's FSSH method) trajectory propagation, including the recent multistate XMS-CASPT2 and RMS-CASPT2 gradients. It is shown that while CASSCF, XMS-CASPT2, and RMS-CASPT2 yield consistent photoisomerization dynamics descriptions, REKS produces, in some of these systems, qualitatively different behavior that is attributed to a flatter and topographically different excited state potential energy surface. The origin of this behavior can be traced back to the effect of the employed density functional approximation. The above studies are further expanded by benchmarking, at the CASSCF and REKS levels, the electronic structure methods using a QM/MM model of the visual pigment rhodopsin.

Doubly Tuned Exchange-Correlation Functionals for Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory

It is demonstrated that significant accuracy improvements in MRSF-TDDFT can be achieved by introducing two different exchange-correlation (XC) functionals for the reference Kohn-Sham DFT and the response part of the calculations, respectively. Accordingly, two new XC functionals of doubly tuned Coulomb attenuated method-vertical excitation energy (DTCAM-VEE) and DTCAM-AEE were developed on the basis of the "adaptive exact exchange (AEE)" concept in the framework of the Coulomb-attenuating XC functionals. The values by DTCAM-VEE are in excellent agreement with those of Thiel's set [mean absolute errors (MAEs) and the interquartile range (IQR) values of 0.218 and 0.327 eV, respectively]. On the other hand, DTCAM-AEE faithfully reproduced the qualitative aspects of conical intersections (CIs) of trans-butadiene and thymine and the nonadiabatic molecular dynamics (NAMD) simulations on thymine. The latter functional also remarkably exhibited the exact 1/R asymptotic behavior of the charge-transfer state of an ethylene-tetrafluoroethylene dimer and the accurate potential energy surfaces (PESs) along the two torsional angles of retinal protonated Schiff base model with six double bonds (rPSB6). Overall, DTCAM-AEE generally performs well, as its MAE (0.237) and IQR (0.41 eV) are much improved as compared to BH&HLYP. The current idea can also be applied to other XC functionals as well as other variants of linear response theories, opening a new way of developing XC functionals.

Galván I, Alavi A, Aleotti F, Aquilante F, Autschbach J, Avagliano D, Baiardi A, Bao JJ, Battaglia S, Birnoschi L, Blanco-González A, Bokarev SI, Broer R, Cacciari R, Calio PB, Carlson RK, Carvalho Couto R, Cerdán L, Chibotaru LF, Chilton NF, Church JR, Conti I, Coriani S, Cuéllar-Zuquin J, Daoud RE, Dattani N, Decleva P, de Graaf C, Delcey M, De Vico L, Dobrautz W, Dong SS, Feng R, Ferré N, Filatov(Gulak) M, Gagliardi L, Garavelli M, González L, Guan Y, Guo M, Hennefarth MR, Hermes MR, Hoyer CE, Huix-Rotllant M, Jaiswal VK, Kaiser A, Kaliakin DS, Khamesian M, King DS, Kochetov V, Krośnicki M, Kumaar AA, Larsson ED, Lehtola S, Lepetit MB, Lischka H, López Ríos P, Lundberg M, Ma D, Mai S, Marquetand P, Merritt ICD, Montorsi F, Mörchen M, Nenov A, Nguyen VHA, Nishimoto Y, Oakley MS, Olivucci M, Oppel M, Padula D, Pandharkar R, Phung QM, Plasser F, Raggi G, Rebolini E, Reiher M, Rivalta I, Roca-Sanjuán D, Romig T, Safari AA, Sánchez-Mansilla A, Sand AM, Schapiro I, Scott TR, Segarra-Martí J, Segatta F, Sergentu DC, Sharma P, Shepard R, Shu Y, Staab JK, Straatsma TP, Sørensen LK, Tenorio BNC, Truhlar DG, Ungur L, Vacher M, Veryazov V, Voß TA, Weser O, Wu D, Yang X, Yarkony D, Zhou C, Zobel JP, Lindh R. The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory: Multireference Advantages with the Practicality of Linear Response Theory

The density functional theory (DFT) and linear response (LR) time-dependent (TD)-DFT are of the utmost importance for routine computations. However, the single reference formulation of DFT suffers in the description of open-shell singlet systems such as diradicals and bond-breaking. LR-TDDFT, on the other hand, finds difficulties in the modeling of conical intersections, doubly excited states, and core-level excitations. In this Perspective, we demonstrate that many of these limitations can be overcome by recently developed mixed-reference (MR) spin-flip (SF)-TDDFT, providing an alternative yet accurate route for such challenging situations. Empowered by the practicality of the LR formalism, it is anticipated that MRSF-TDDFT can become one of the major workhorses for general routine tasks.

High-performance strategies for the recent MRSF-TDDFT in GAMESS

Multiple ERI (Electron Repulsion Integral) tensor contractions (METC) with several matrices are ubiquitous in quantum chemistry. In response theories, the contraction operation, rather than ERI computations, can be the major bottleneck, as its computational demands are proportional to the multiplicatively combined contributions of the number of excited states and the kernel pre-factors. This paper presents several high-performance strategies for METC. Optimal approaches involve either the data layout reformations of interim density and Fock matrices, the introduction of intermediate ERI quartet buffer, and loop-reordering optimization for a higher cache hit rate. The combined strategies remarkably improve the performance of the MRSF (mixed reference spin flip)-TDDFT (time-dependent density functional theory) by nearly 300%. The results of this study are not limited to the MRSF-TDDFT method and can be applied to other METC scenarios.

Photoisomerization of phytochrome chromophore models: an XMS-CASPT2 study

Phytochromes are a superfamily of photoreceptors that harbor linear tetrapyrroles as chromophores. Upon light illumination, the linear tetrapyrrole chromophore undergoes a double bond isomerization which starts a photocycle. In this work, we studied the photoisomerization of chromophore models designed based on the C- and D-rings of the phycocyanobilin (PCB) chromophore. In total, five different models with varying substitutions were investigated. Firstly, the vertical excitation energies were benchmarked using different computational methods to establish the relative order of the excited states. Based on these calculations, we computed the photoisomerization profiles using the extended multi-state (XMS) version of the CASPT2 method. The profiles were obtained for both the clockwise and counterclockwise rotations of the C₁₅C₁₆ bond in the Z and E isomers using a linear interpolation of internal coordinates between the Franck-Condon and MECI geometries. In the minimal chromophore model that lacks the substitutions at the pyrrole rings, the isomerization involves both C₁₄-C₁₅ and C₁₅C₁₆ bonds of the methine bridge between the C- and D-rings, resembling the hula-twist motion. The MECIs are characterized by a partial charge transfer between the two pyrrole rings pointing towards a twisted intramolecular charge transfer. Systematic introduction of substituents leads to an increase in the steric repulsion between the two pyrrole rings causing a pretwist of the dihedral around the C₁₅C₁₆ bond, which creates a preference for the counterclockwise isomerization. An introduction of the carbonyl group at the D-ring increases the extent of charge transfer which changes the isomerization mechanism from hula-twist to one-bond flip.

Difficulty of the evaluation of the barrier height of an open-shell transition state between closed shell minima: The case of small C4n rings

C_4n cyclacenes exhibit strong bond-alternation in their equilibrium geometry. In the two equivalent geometries, the system keeps an essentially closed-shell character. The two energy minima are separated by a transition state suppressing the bond-alternation, where the wave function is strongly diradical. This paper discusses the physical factors involved in this energy difference and possible evaluations of the barrier height. The barrier given as the energy difference between the restricted density functional theory (DFT)/B3LYP for the equilibrium and the broken symmetry DFT/B3LYP of the transition state is either negative or small, in contradiction with the most reliable Wave Function Theory calculations. The minimal (two electrons in two molecular orbitals) Complete Active Space self-consistent field (CASSCF) overestimates the barrier, and the subsequent second-order perturbation cancels it. Due to the collective character of the spin-polarization effect, it is necessary to perform a full π CASSCF + second-order perturbation to reach a reasonable value of the barrier, but this type of treatment cannot be applied to large molecules. DFT procedures treating on an equal foot the closed-shell and open-shell geometries have been explored, such as Mixed-Reference Spin-Flip Time-dependent-DFT and a new spin-decontamination proposal, namely, DFT-dressed configuration interaction, but the results still depend on the density functional. M06-2X without or with spin-decontamination gives the best agreement with the accurate wave function results.

InteraChem: Exploring Excited States in Virtual Reality with Ab Initio Interactive Molecular Dynamics

InteraChem is an ab initio interactive molecular dynamics (AI-IMD) visualizer that leverages recent advances in virtual reality hardware and software, as well as the graphical processing unit (GPU)-accelerated TeraChem electronic structure package, in order to render quantum chemistry in real time. We introduce the exploration of electronically excited states via AI-IMD using the floating occupation molecular orbital-complete active space configuration interaction method. The optimization tools in InteraChem enable identification of excited state minima as well as minimum energy conical intersections for further characterization of excited state chemistry in small- to medium-sized systems. We demonstrate that finite-temperature Hartree-Fock theory is an efficient method to perform ground state AI-IMD. InteraChem allows users to track electronic properties such as molecular orbitals and bond order in real time, resulting in an interactive visualization tool that aids in the interpretation of excited state chemistry data and makes quantum chemistry more accessible for both research and educational purposes.

Assessing the Performances of CASPT2 and NEVPT2 for Vertical Excitation Energies

Methods able to simultaneously account for both static and dynamic electron correlations have often been employed, not only to model photochemical events but also to provide reference values for vertical transition energies, hence allowing benchmarking of lower-order models. In this category, both the complete-active-space second-order perturbation theory (CASPT2) and the N-electron valence state second-order perturbation theory (NEVPT2) are certainly popular, the latter presenting the advantage of not requiring the application of the empirical ionization-potential-electron-affinity (IPEA) and level shifts. However, the actual accuracy of these multiconfigurational approaches is not settled yet. In this context, to assess the performances of these approaches, the present work relies on highly accurate (±0.03 eV) aug-cc-pVTZ vertical transition energies for 284 excited states of diverse character (174 singlet, 110 triplet, 206 valence, 78 Rydberg, 78 n → π*, 119 π → π*, and 9 double excitations) determined in 35 small- to medium-sized organic molecules containing from three to six non-hydrogen atoms. The CASPT2 calculations are performed with and without IPEA shift and compared to the partially contracted (PC) and strongly contracted (SC) variants of NEVPT2. We find that both CASPT2 with IPEA shift and PC-NEVPT2 provide fairly reliable vertical transition energy estimates, with slight overestimations and mean absolute errors of 0.11 and 0.13 eV, respectively. These values are found to be rather uniform for the various subgroups of transitions. The present work completes our previous benchmarks focused on single-reference wave function methods ( J. Chem. Theory Comput. 2018, 14, 4360; J. Chem. Theory Comput. 2020, 16, 1711), hence allowing for a fair comparison between various families of electronic structure methods. In particular, we show that ADC(2), CCSD, and CASPT2 deliver similar accuracies for excited states with a dominant single-excitation character.

Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections

Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.

Describing ground and excited state potential energy surfaces for molecular photoswitches using coupled cluster models

In this article, we use two extensively studied systems, a retinal model system and azobenzene, to explore the use of coupled cluster models for describing ground and singlet excited state potential energy surfaces of photoswitchable systems. While not being suitable for describing nuclear dynamics of photoisomerization, coupled cluster models have useful attributes, such as the inclusion of dynamical correlation, their black box nature, and the systematic improvement offered by truncation level. Results for the studied systems show that when triple excitations (here through the CC3 model) are included, ground and excited state potential energy surfaces for isomerization paths may reliably be generated, also for states of doubly excited character. For ground state equilibrium cis- and trans-azobenzene, the molecular geometry and basis set is seen to significantly impact the vertical excitation energies for the two lowest excited states. Efficient implementations of coupled cluster models can therefore constitute valuable tools for investigating photoswitchable systems and can be used for preliminary black box studies to gather information before more complicated excited state dynamics approaches are pursued.

Signatures of Conical Intersection Dynamics in the Time-Resolved Photoelectron Spectrum of Furan: Theoretical Modeling with an Ensemble Density Functional Theory Method

The non-adiabatic dynamics of furan excited in the ππ* state (S2 in the Franck-Condon geometry) was studied using non-adiabatic molecular dynamics simulations in connection with an ensemble density functional method. The time-resolved photoelectron spectra were theoretically simulated in a wide range of electron binding energies that covered the valence as well as the core electrons. The dynamics of the decay (rise) of the photoelectron signal were compared with the excited-state population dynamics. It was observed that the photoelectron signal decay parameters at certain electron binding energies displayed a good correlation with the events occurring during the excited-state dynamics. Thus, the time profile of the photoelectron intensity of the K-shell electrons of oxygen (decay constant of 34 ± 3 fs) showed a reasonable correlation with the time of passage through conical intersections with the ground state (47 ± 2 fs). The ground-state recovery constant of the photoelectron signal (121 ± 30 fs) was in good agreement with the theoretically obtained excited-state lifetime (93 ± 9 fs), as well as with the experimentally estimated recovery time constant (ca. 110 fs). Hence, it is proposed to complement the traditional TRPES observations with the trXPS (or trNEXAFS) measurements to obtain more reliable estimates of the most mechanistically important events during the excited-state dynamics.

Donor acceptor fluorophores: synthesis, optical properties, TD-DFT and cytotoxicity studies

Donor-π-acceptor (D-π-A) fluorophores consisting of a donor unit, a π linker, and an acceptor moiety have attracted attention in the last decade. In this study, we report the synthesis, characterization, optical properties, TD-DFT, and cytotoxicity studies of 17 near infrared (NIR) D-π-A analogs which have not been reported so far to the best of our knowledge. These fluorophores have chloroacrylic acid as the acceptor unit and various donor units such as indole, benzothiazole, benzo[e]indole, and quinoline. The fluorophores showed strong absorption in the NIR (700-970 nm) region due to their enhanced intramolecular charge transfer (ICT) between chloroacrylic acid and the donor moieties connected with the Vilsmeier-Haack linker. The emission wavelength maxima of the fluorophores were in between 798 and 870 nm. Compound 20 with a 4-quinoline donor moiety showed an emission wavelength above 1000 nm in the NIR II window. The synthesized fluorophores were characterized by 1H NMR and 13C NMR, and their optical properties were studied. Time dependent density functional theory (TD-DFT) calculations showed that the charge transfer occurs from the donor groups (indole, benzothiazole, benzo[e]indole, and quinoline) to the acceptor chloroacrylic acid moiety. Fluorophores with [HOMO] to [LUMO+1] transitions were shown to possess a charge separation character. The cytotoxicity of selected fluorophores, 4, 7, 10 and 12 was investigated against breast cancer cell lines and they showed better activity than the anti-cancer agent docetaxel.

Machine Learning-Assisted Excited State Molecular Dynamics with the State-Interaction State-Averaged Spin-Restricted Ensemble-Referenced Kohn-Sham Approach

We present a machine learning-assisted excited state molecular dynamics (ML-ESMD) based on the ensemble density functional theory framework. Since we represent a diabatic Hamiltonian in terms of generalized valence bond ansatz within the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS) method, we can avoid singularities near conical intersections, which are crucial in excited state molecular dynamics simulations. We train the diabatic Hamiltonian elements and their analytical gradients with the SchNet architecture to construct machine learning models, while the phase freedom of off-diagonal elements of the Hamiltonian is cured by introducing the phase-less loss function. Our machine learning models show reasonable accuracy with mean absolute errors of ∼0.1 kcal/mol and ∼0.5 kcal/mol/Å for the diabatic Hamiltonian elements and their gradients, respectively, for penta-2,4-dieniminium cation. Moreover, by exploiting the diabatic representation, our models can predict correct conical intersection structures and their topologies. In addition, our ML-ESMD simulations give almost identical result with a direct dynamics at the same level of theory.

Accurate Molecular Geometries in Complex Excited-State Potential Energy Surfaces from Time-Dependent Density Functional Theory

The interplay of electronic excitations and structural changes in molecules impacts nonradiative decay and charge transfer in the excited state, thus influencing excited-state lifetimes and photocatalytic reaction rates in optoelectronic and energy devices. To capture such effects requires computational methods providing an accurate description of excited-state potential energy surfaces and geometries. We suggest time-dependent density functional theory using optimally tuned range-separated hybrid (OT-RSH) functionals as an accurate approach to obtain excited-state molecular geometries. We show that OT-RSH provides accurate molecular geometries in excited-state potential energy surfaces that are complex and involve an interplay of local and charge-transfer excitations, for which conventional semilocal and hybrid functionals fail. At the same time, the nonempirical OT-RSH approach maintains the high accuracy of parametrized functionals (e.g., B3LYP) for predicting excited-state geometries of small organic molecules showing valence excited states.

Photoinduced Changes in Aromaticity Facilitate Electrocyclization of Dithienylbenzene Switches

The concepts of excited-state aromaticity and antiaromaticity have in recent years with increasing frequency been invoked to rationalize the photochemistry of cyclic conjugated organic compounds, with the long-term goal of using these concepts to improve the reactivities of such compounds toward different photochemical transformations. In this regard, it is of particular interest to assess how the presence of a benzene motif affects photochemical reactivity, as benzene is well-known to completely change its aromatic character in its lowest excited states. Here, we investigate how a benzene motif influences the photoinduced electrocyclization of dithienylethenes, a major class of molecular switches. Specifically, we report on the synthesis of a dithienylbenzene switch where the typical nonaromatic, ethene-like motif bridging the two thienyl units is replaced by a benzene motif, and show that this compound undergoes electrocyclization upon irradiation with UV-light. Furthermore, through a detailed quantum chemical analysis, we demonstrate that the electrocyclization is driven jointly and synergistically by the loss of aromaticity in this motif from the formation of a reactive, antiaromatic excited state during the initial photoexcitation, and by the subsequent relief of this antiaromaticity as the reaction progresses from the Franck–Condon region. Overall, we conclude that photoinduced changes in aromaticity facilitate the electrocyclization of dithienylbenzene switches.

Variational Principles in Quantum Monte Carlo: The Troubled Story of Variance Minimization

We investigate the use of different variational principles in quantum Monte Carlo, namely, energy and variance minimization, prompted by the interest in the robust and accurate estimation of electronic excited states. For two prototypical, challenging molecules, we readily reach the accuracy of the best available reference excitation energies using energy minimization in a state-specific or state-average fashion for states of different or equal symmetry, respectively. On the other hand, in variance minimization, where the use of suitable functionals is expected to target specific states regardless of the symmetry, we encounter severe problems for a variety of wave functions: as the variance converges, the energy drifts away from that of the selected state. This unexpected behavior is sometimes observed even when the target is the ground state and generally prevents the robust estimation of total and excitation energies. We analyze this problem using a very simple wave function and infer that the optimization finds little or no barrier to escape from a local minimum or local plateau, eventually converging to a lower-variance state instead of the target state. For the increasingly complex systems becoming in reach of quantum Monte Carlo simulations, variance minimization with current functionals appears to be an impractical route.

Combining Graphics Processing Units, Simplified Time-Dependent Density Functional Theory, and Finite-Difference Couplings to Accelerate Nonadiabatic Molecular Dynamics

Starting from our recently published implementation of nonadiabatic molecular dynamics (NAMD) on graphics processing units (GPUs), we explore further approaches to accelerate ab initio NAMD calculations at the time-dependent density functional theory (TDDFT) level of theory. We employ (1) the simplified TDDFT schemes of Grimme et al. and (2) the Hammes-Schiffer-Tully approach to obtain nonadiabatic couplings from finite-difference calculations. The resulting scheme delivers an accurate physical picture while virtually eliminating the two computationally most demanding steps of the algorithm. Combined with our GPU-based integral routines for SCF, TDDFT, and TDDFT derivative calculations, NAMD simulations of systems of a few hundreds of atoms at a reasonable time scale become accessible on a single compute node. To demonstrate this and to present a first, illustrative example, we perform TDDFT/MM-NAMD simulations of the rhodopsin protein.

Nonadiabatic Photodynamics of Retinal Protonated Schiff Base in Channelrhodopsin 2

Channelrhodopsin 2 (ChR2) is a light-gated ion channel and an important tool in optogenetics. Photoisomerization of retinal protonated Schiff base (RPSB) in ChR2 triggers channel activation. Despite the importance of ChR2 in optogenetics, the detailed mechanism for photoisomerization and channel activation is still not fully understood. Here, we report on computer simulations to investigate the photoisomerization mechanism and its effect on the activation of ChR2. Nonadiabatic dynamics simulation of ChR2 was carried out using the ab initio multiple spawning (AIMS) method and quantum mechanics/molecular mechanics (QM/MM) with a restricted ensemble Kohn-Sham (REKS) treatment of the QM region. Our results agree well with spectroscopic measurements and reveal that the RPSB isomerization is highly specific around the C₁₃=C₁₄ bond and follows the "aborted bicycle-pedal" mechanism. In addition, RPSB photoisomerization facilitates its deprotonation and partially increases the hydration level in the channel, which could trigger subsequent channel opening and ion conduction.

Assessment of MC-PDFT Excitation Energies for a Set of QM/MM Models of Rhodopsins

A methodology for the automatic production of quantum mechanical/molecular mechanical (QM/MM) models of retinal-binding rhodopsin proteins and subsequent prediction of their spectroscopic properties has been proposed recently by some of the authors. The technology employed for the evaluation of the excitation energies is called Automatic Rhodopsin Modeling (ARM), and it involves the use of the complete active space self-consistent field (CASSCF) method followed by a multiconfiguration second-order perturbation theory (in particular, CASPT2) calculation of external correlation energies. Although it was shown that ARM is capable of successfully reproducing and predicting spectroscopic property trends in chromophore-embedding protein sets, practical applications of such technology are limited by the high computational costs of the multiconfiguration perturbation theory calculations. In the present work we benchmark the more affordable multiconfiguration pair-density functional theory (MC-PDFT) method whose accuracy has been recently validated for retinal chromophores in the gas phase, indicating that MC-PDFT could potentially be used to analyze large (e.g., few hundreds) sets of rhodopsin proteins. Here, we test this theory for a set of rhodopsin QM/MM models whose experimental absorption maxima (λ a max) have been measured. The results indicate that MC-PDFT may be employed to calculate λ a max values for this important class of photoresponsive proteins.

Two-State, Three-Mode Parametrization of the Force Field of a Retinal Chromophore Model

In recent years, the potential energy surfaces of the penta-2,4-dieniminium cation have been investigated using several electronic structure methods. The resulting pool of geometrical, electronic, and energy data provides a suitable basis for the construction of a topographically correct analytical model of the molecule force field and, therefore, for a better understanding of this class of molecules, which includes the chromophore of visual pigments. In the present contribution, we report the construction of such a model for regions of the force field that drive the photochemical and thermal isomerization of the central double bound of the cation. While previous models included only two modes, it is here shown that the proposed three-mode model and corresponding set of parameters are able to reproduce the complex topographical and electronic structure features seen in electronically correlated data obtained at the XMCQDPT2//CASSCF/6-31G* level of theory.

Theoretical modelling of the dynamics of primary photoprocess of cyclopropanone

Photodecomposition of cyclopropanone is investigated by static quantum chemical calculations and non-adiabatic molecular dynamics (NAMD) simulations.

Is the choice of a standard zeroth-order hamiltonian in CASPT2 ansatz optimal in calculations of excitation energies in protonated and unprotonated schiff bases of retinal?

To account for systematic error of CASPT2 method empirical modification of the zeroth-order Hamiltonian with Ionization Potential-Electron Affinity (IPEA) shift was introduced. The optimized IPEA value (0.25 a.u.), called standard IPEA (S-IPEA), was recommended but due to its unsatisfactory performance in multiple metallic and organic compounds it has been questioned lately as a general parameter working properly for all molecules under CASPT2 study. As we are interested in Schiff bases of retinal, an important question emerging from this conflict of choice, to use or not to use S-IPEA, is whether the introduction of the modified zeroth-order Hamiltonian into CASPT2 ansatz does really improve their energetics. To achieve this goal, we assessed an impact of the IPEA shift value, in a range of 0-0.35 a.u., on vertical excitation energies to low-lying singlet states of two protonated (RPSBs) and two unprotonated (RSBs) Schiff bases of retinal for which experimental data in gas phase are available. In addition, an effect of geometry, basis set, and active space on computed VEEs is also reported. We find, that for these systems, the choice of S-IPEA significantly overestimates both S₀ →S₁ and S₀ →S₂ energies and the best theoretical estimate, in reference to the experimental data, is provided with either unmodified zeroth-order Hamiltonian or small value of the IPEA shift in a range of 0.05-0.15 a.u., depending on active space and basis set size, equilibrium geometry, and character of the excited state. © 2018 Wiley Periodicals, Inc.

Analytical derivatives of the individual state energies in ensemble density functional theory method. I. General formalism

The state-averaged (SA) spin restricted ensemble referenced Kohn-Sham (REKS) method and its state interaction (SI) extension, SI-SA-REKS, enable one to describe correctly the shape of the ground and excited potential energy surfaces of molecules undergoing bond breaking/bond formation reactions including features such as conical intersections crucial for theoretical modeling of non-adiabatic reactions. Until recently, application of the SA-REKS and SI-SA-REKS methods to modeling the dynamics of such reactions was obstructed due to the lack of the analytical energy derivatives. In this work, the analytical derivatives of the individual SA-REKS and SI-SA-REKS energies are derived. The final analytic gradient expressions are formulated entirely in terms of traces of matrix products and are presented in the form convenient for implementation in the traditional quantum chemical codes employing basis set expansions of the molecular orbitals. The implementation and benchmarking of the derived formalism will be described in a subsequent article of this series.

Description of ground and excited electronic states by ensemble density functional method with extended active space

An extended variant of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method, the REKS(4,4) method, designed to describe the ground electronic states of strongly multireference systems is modified to enable calculation of excited states within the time-independent variational formalism. The new method, the state-interaction state-averaged REKS(4,4), i.e., SI-SA-REKS(4,4), is capable of describing several excited states of a molecule involving double bond cleavage, polyradical character, or multiple chromophoric units. We demonstrate that the new method correctly describes the ground and the lowest singlet excited states of a molecule (ethylene) undergoing double bond cleavage. The applicability of the new method for excitonic states is illustrated with π stacked ethylene and tetracene dimers. We conclude that the new method can describe a wide range of multireference phenomena.

Accurate Excited-State Geometries: A CASPT2 and Coupled-Cluster Reference Database for Small Molecules

We present an investigation of the excited-state structural parameters determined for a large set of small compounds with the dual goals of defining reference values for further works and assessing the quality of the geometries obtained with relatively cheap computational approaches. In the first stage, we compare the excited-state geometries obtained with ADC(2), CC2, CCSD, CCSDR(3), CC3, and CASPT2 and large atomic basis sets. It is found that CASPT2 and CC3 results are generally in very good agreement with one another (typical differences of ca. 3 × 10^–3 Å) when all electrons are correlated and when the aug-cc-pVTZ atomic basis set is employed with both methods. In a second stage, a statistical analysis reveals that, on the one hand, the excited-state (ES) bond lengths are much more sensitive to the selected level of theory than their ground-state (GS) counterparts and, on the other hand, that CCSDR(3) is probably the most cost-effective method delivering accurate structures. Indeed, CCSD tends to provide too compact multiple bond lengths on an almost systematic basis, whereas both CC2 and ADC(2) tend to exaggerate these bond distances, with more erratic error patterns, especially for the latter method. The deviations are particularly marked for the polarized CO and CN bonds, as well as for the puckering angle in formaldehyde homologues. In the last part of this contribution, we provide a series of CCSDR(3) GS and ES geometries of medium-sized molecules to be used as references in further investigations.

Excited-state minima and emission energies of retinal chromophore analogues: Performance of CASSCF and CC2 methods as compared with CASPT2

This study provides gas-phase S₁ excited-state geometries along with emission and adiabatic energies for methylated/demethylated and ring-locked analogues of protonated Schiff base retinal models comprising system of five conjugated double bonds (PSB5), using second order multiconfiguration perturbation theory (CASPT2). CASPT2 results serve as reference data to assess the performance of CC2 (second-order approximate coupled cluster singles and doubles) and a commonly used CASSCF/CASPT2 protocol, that is, complete active space self-consistent field (CASSCF) geometry optimization followed by CASPT2 energy calculation. We find that the CASSCF methodology fails to locate planar S₁ minimum energy structures for four out of five investigated planar models in contrast to CC2 and CASPT2 methods. However, for those which were found: one planar and two twisted minima, there is an excellent agreement between CASSCF and CASPT2 results in terms of geometrical parameters, one-electron properties, as well as emission and adiabatic energies. CC2 performs well for in-plane S₁ minima and their spectroscopic and electronic properties. However, this picture deteriorates for twisted minima. As expected, the CC2 description of the S₂ electronic state, with strong multireference and significant double excitation character, is very poor, exhibiting errors in transition energies exceeding 1 eV. They may be substantially diminished by recalculating transition energies with CASPT2 method. Our work shows that CASSCF/CASPT2 and CC2 shortcomings may influence gas-phase retinal analogues' excited state description in a dramatic way. © 2017 Wiley Periodicals, Inc.

Dual-Functional Tamm-Dancoff Approximation: A Convenient Density Functional Method that Correctly Describes S1/S0 Conical Intersections

Time-dependent Kohn-Sham density functional theory has been used successfully to compute vertical excitation energies, especially for large molecular systems. However, the lack of double excitation character in the excited amplitudes produced by linear response in the adiabatic approximation holds it back from broader applications in photochemistry; for example, it shows (3N - 7)-dimensional conical intersection seams (where N is the number of atoms) between ground and excited states, although the correct dimensionality is 3N - 8. In this letter, we present a new, conceptually simple, easy-to-implement, and easy-to-use way to employ time-dependent Kohn-Sham density functional theory that has global accuracy comparable with the conventional single-functional version and that recovers the double cone topology of the potential energy surfaces at S₁/S₀ conical intersection seams. The new method is called the dual-functional Tamm-Dancoff approximation (DF-TDA).

Theoretical description of protein field effects on electronic excitations of biological chromophores

Photoinitiated phenomena play a crucial role in many living organisms. Plants, algae, and bacteria absorb sunlight to perform photosynthesis, and convert water and carbon dioxide into molecular oxygen and carbohydrates, thus forming the basis for life on Earth. The vision of vertebrates is accomplished in the eye by a protein called rhodopsin, which upon photon absorption performs an ultrafast isomerisation of the retinal chromophore, triggering the signal cascade. Many other biological functions start with the photoexcitation of a protein-embedded pigment, followed by complex processes comprising, for example, electron or excitation energy transfer in photosynthetic complexes. The optical properties of chromophores in living systems are strongly dependent on the interaction with the surrounding environment (nearby protein residues, membrane, water), and the complexity of such interplay is, in most cases, at the origin of the functional diversity of the photoactive proteins. The specific interactions with the environment often lead to a significant shift of the chromophore excitation energies, compared with their absorption in solution or gas phase. The investigation of the optical response of chromophores is generally not straightforward, from both experimental and theoretical standpoints; this is due to the difficulty in understanding diverse behaviours and effects, occurring at different scales, with a single technique. In particular, the role played by ab initio calculations in assisting and guiding experiments, as well as in understanding the physics of photoactive proteins, is fundamental. At the same time, owing to the large size of the systems, more approximate strategies which take into account the environmental effects on the absorption spectra are also of paramount importance. Here we review the recent advances in the first-principle description of electronic and optical properties of biological chromophores embedded in a protein environment. We show their applications on paradigmatic systems, such as the light-harvesting complexes, rhodopsin and green fluorescent protein, emphasising the theoretical frameworks which are of common use in solid state physics, and emerging as promising tools for biomolecular systems.

Mechanism of ultrafast non-reactive deactivation of the retinal chromophore in non-polar solvents

Counterion sensitive photodynamics of the retinal chromophore in solution.