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.

What Controls the Quality of Photodynamical Simulations? Electronic Structure Versus Nonadiabatic Algorithm

The field of nonadiabatic dynamics has matured over the last decade with a range of algorithms and electronic structure methods available at the moment. While the community currently focuses more on developing and benchmarking new nonadiabatic dynamics algorithms, the underlying electronic structure controls the outcome of nonadiabatic simulations. Yet, the electronic-structure sensitivity analysis is typically neglected. In this work, we present a sensitivity analysis of the nonadiabatic dynamics of cyclopropanone to electronic structure methods and nonadiabatic dynamics algorithms. In particular, we compare wave function-based CASSCF, FOMO-CASCI, MS- and XMS-CASPT2, density-functional REKS, and semiempirical MRCI-OM3 electronic structure methods with the Landau-Zener surface hopping, fewest switches surface hopping, and ab initio multiple spawning with informed stochastic selection algorithms. The results clearly demonstrate that the electronic structure choice significantly influences the accuracy of nonadiabatic dynamics for cyclopropanone even when the potential energy surfaces exhibit qualitative and quantitative similarities. Thus, selecting the electronic structure solely on the basis of the mapping of potential energy surfaces can be misleading. Conversely, we observe no discernible differences in the performance of the nonadiabatic dynamics algorithms across the various methods. Based on the above results, we discuss the present-day practice in computational photodynamics.

Modelling Photoionisation in Isocytosine: Potential Formation of Longer-Lived Excited State Cations in its Keto Form

Studying the effects of UV and VUV radiation on non-canonical DNA/RNA nucleobases allows us to compare how they release excess energy following absorption with respect to their canonical counterparts. This has attracted much research attention in recent years because of its likely influence on the origin of our genetic lexicon in prebiotic times. Here we present a CASSCF and XMS-CASPT2 theoretical study of the photoionisation of non-canonical pyrimidine nucleobase isocytosine in both its keto and enol tautomeric forms. We analyse their lowest energy cationic excited states including 2 π + , 2 n O + and 2 n N + and compare these to the corresponding electronic states in cytosine. Investigating lower-energy decay pathways we find - unexpectedly - that keto-isocytosine+ presents a sizeable energy barrier potentially inhibiting decay to its cationic ground state, whereas enol-isocytosine+ features a barrierless and consequently ultrafast pathway analogous to the one previously found for the canonical (keto) form of cytosine+ . Dynamic electron correlation reduces the energy barrier in the keto form substantially (by ∼1 eV) but it is nevertheless still present. We additionally compute the UV/Vis absorption signals of the structures encountered along these decay channels to provide spectroscopic fingerprints to assist future experiments in monitoring these intricate photo-processes.

Theoretical Study of the Photoisomerization Mechanism of All-Trans-Retinyl Acetate

The compound 9-cis-retinyl acetate (9-cis-RAc) is a precursor to 9-cis-retinal, which has potential application in the treatment of some hereditary diseases of the retina. An attractive synthetic route to 9-cis-RAc is based on the photoisomerization reaction of the readily available all-trans-RAc. In the present study, we examine the mechanism of the photoisomerization reaction with the use of state-of-the-art electronic structure calculations for two polyenic model compounds: tEtEt-octatetraene and tEtEtEc-2,6-dimethyl-1,3,5,7,9-decapentaene. The occurrence of photoisomerization is attributed to a chain-kinking mechanism, whereby a series of S₁/S₀ conical intersections associated with kinking deformations at different positions along the polyenic chain mediate internal conversion to the S₀ state, and subsequent isomerization around one of the double bonds. Two other possible photoisomerization mechanisms are taken into account, but they are rejected as incompatible with simulation results and/or the available spectroscopic data.

The Molpro quantum chemistry package

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces

Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way and, therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces. This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections and on-the-fly photodynamics simulations, both of which depend heavily on the ability of the method to properly explore the potential energy surface. Because such applications require nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly enhances the scope of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. A detailed account of the analytical nuclear gradient and derivative coupling theories is presented. Emphasis is given to the software infrastructure that allows one to make use of these methods. Notable applications of multireference electron correlation methods to chemistry, including geometry optimizations and on-the-fly dynamics, are summarized at the end followed by a discussion of future prospects.

A QM/MM study of the initial excited state dynamics of green-absorbing proteorhodopsin

The primary photochemical reaction of the green-absorbing proteorhodopsin is studied by means of a hybrid quantum mechanics/molecular mechanics (QM/MM) approach. The simulations are based on a homology model derived from the blue-absorbing proteorhodopsin crystal structure. The geometry of retinal and the surrounding sidechains in the protein binding pocket were optimized using the QM/MM method. Starting from this geometry the isomerization was studied with a relaxed scan along the C13[double bond, length as m-dash]C14 dihedral. It revealed an "aborted bicycle pedal" mechanism of isomerization that was originally proposed by Warshel for bovine rhodopsin and bacteriorhodopsin. However, the isomerization involved the concerted rotation about C13[double bond, length as m-dash]C14 and C15[double bond, length as m-dash]N, with the latter being highly twisted but not isomerized. Further, the simulation showed an increased steric interaction between the hydrogen at the C14 of the isomerizing bond and the hydroxyl group at the neighbouring tyrosine 200. In addition, we have simulated a nonadiabatic trajectory which showed the timing of the isomerization. In the first 20 fs upon excitation the order of the conjugated double and single bonds is inverted, consecutively the C13[double bond, length as m-dash]C14 rotation is activated for 200 fs until the S1-S0 transition is detected. However, the isomerization is reverted due to the specific interaction with the tyrosine as observed along the relaxed scan calculation. Our simulations indicate that the retinal - tyrosine 200 interaction plays an important role in the outcome of the photoisomerization.

Ultrafast and radiationless electronic excited state decay of uracil and thymine cations: computing the effects of dynamic electron correlation

In this article we characterise the radiationless decay of the first few electronic excited states of the cations of DNA/RNA nucleobases uracil and thymine, including the effects of dynamic electron correlation on energies and geometries (optimised with XMS-CASPT2). In both systems, we find that one state of ²n and another two of ²π⁺ character can be populated following photoionisation, and their different minima and interstate crossings are located. We find strong similarities between uracil and thymine cations: with accessible conical intersections suggesting that depopulation of their electronic excited states takes place on ultrafast timescales in both systems, suggesting that they are photostable in agreement with previous theoretical (uracil⁺) evidence. We find that dynamic electron correlation separates the energy levels of the "3-state" conical intersection (D₂/D₁/D₀)_CI previously located with CASSCF for uracil⁺, which will therefore have a different geometry and higher energy. Simulating the electronic and vibrational absorptions allows us to characterise spectral fingerprints that could be used to monitor these cation photo-processes experimentally.

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.

Assessment of the Potential Energy Hypersurfaces in Thymine within Multiconfigurational Theory: CASSCF vs. CASPT2

The present study provides new insights into the topography of the potential energy hypersurfaces (PEHs) of the thymine nucleobase in order to rationalize its main ultrafast photochemical decay paths by employing two methodologies based on the complete active space self-consistent field (CASSCF) and the complete active space second-order perturbation theory (CASPT2) methods: (i) CASSCF optimized structures and energies corrected with the CASPT2 method at the CASSCF geometries and (ii) CASPT2 optimized geometries and energies. A direct comparison between these strategies is drawn, yielding qualitatively similar results within a static framework. A number of analyses are performed to assess the accuracy of these different computational strategies under study based on a variety of numerical thresholds and optimization methods. Several basis sets and active spaces have also been calibrated to understand to what extent they can influence the resulting geometries and subsequent interpretation of the photochemical decay channels. The study shows small discrepancies between CASSCF and CASPT2 PEHs, displaying a shallow planar or twisted ¹(ππ*) minimum, respectively, and thus featuring a qualitatively similar scenario for supporting the ultrafast bi-exponential deactivation registered in thymine upon UV-light exposure. A deeper knowledge of the PEHs at different levels of theory provides useful insight into its correct characterization and subsequent interpretation of the experimental observations. The discrepancies displayed by the different methods studied here are then discussed and framed within their potential consequences in on-the-fly non-adiabatic molecular dynamics simulations, where qualitatively diverse outcomes are expected.

Exploring the isomerization paths of push–pull hexatrienes

The first photo-excited singlet state of all-trans donor (amine), acceptor (cyano)-substituted hexatriene forms donor side-twisted minima and its passage towards the cis–trans–trans isomer is characterized by an S₀/S₁ conical intersection.

Efficient on-the-fly ab initio semiclassical method for computing time-resolved nonadiabatic electronic spectra with surface hopping or Ehrenfest dynamics

We derive a somewhat crude, yet very efficient semiclassical approximation for computing nonadiabatic spectra. The resulting method, which is a generalization of the multiple-surface dephasing representation, includes quantum effects through interference of mixed quantum-classical trajectories and through quantum treatment of the collective electronic degree of freedom. The method requires very little computational effort beyond the fewest-switches surface hopping or Ehrenfest locally mean-field dynamics and is very easy to implement. The proposed approximation is tested by computing the absorption and time-resolved stimulated emission spectra of pyrazine using the four-dimensional three-surface model which allows for comparison with the numerically exact quantum spectra. As expected, the multiple-surface dephasing representation is not suitable for high-resolution linear spectra, yet it seems to capture all the important features of pump-probe spectra. Finally, the method is combined with on-the-fly ab initio evaluation of the electronic structure (i.e., energies, forces, electric-dipole, and nonadiabatic couplings) in order to compute fully dimensional nonadiabatic spectra of pyrazine without approximations inherent to analytical, including vibronic-coupling models. The Appendix provides derivations of perturbative expressions for linear and pump-probe spectra of arbitrary mixed states and for arbitrary laser pulse shapes.

The role of the low-lying dark nπ* states in the photophysics of pyrazine: a quantum dynamics study

The excited state dynamics of pyrazine has attracted considerable attention in the last three decades. It has long been recognized that after UV excitation, the dynamics of the molecule is impacted by strong non-adiabatic effects due to the existence of a conical intersection between the B2u(ππ*) and B3u(nπ*) electronic states. However, a recent study based on trajectory surface hopping dynamics simulations suggested the participation of the Au(nπ*) and B2g(nπ*) low-lying dark electronic states in the ultrafast radiationless decay of the molecule after excitation to the B2u(ππ*) state. The purpose of this work was to pursue the investigation of the role of the Au(nπ*) and B2g(nπ*) states in the photophysics of pyrazine. A linear vibronic coupling model hamiltonian including the four lowest excited electronic states and the sixteen most relevant vibrational degrees of freedom was constructed using high level XMCQDPT2 electronic structure calculations. Wavepacket propagations using the MCTDH method were then performed and used to simulate the absorption spectrum and the electronic state population dynamics of the system. Our results show that the Au(nπ*) state plays an important role in the photophysics of pyrazine.

Quantum dynamics of the photostability of pyrazine

We propose a new mechanism for the radiationless decay of photoexcited pyrazine to its ground electronic state involving a conical intersection between the dark A_u(nπ) state and the ground state.