The photoisomerization of 11-cis-retinal protonated schiff base in gas phase: Insight from spin-flip density functional theory

Revisiting the Half-and-Half Functional

Hybrid density functionals typically provide significantly better accuracy than semilocal functionals. Conventional wisdom holds that incorporating more than 20-25% exact exchange is deleterious to thermochemical properties and should only be used as a last resort, for problems that are dominated by self-interaction error. In such cases, the Becke-Lee-Yang-Parr "half-and-half" functional (BH&H-LYP) has emerged as a go-to choice, especially in time-dependent density functional theory calculations for excitation energies. Here, we examine the assumption that 50% Hartree-Fock exchange sacrifices thermochemical accuracy. Using a sequence of functionals B(α)LYP, with different percentages of exact exchange (0 ≤ α ≤ 100), we find that BH&H-LYP (with α = 50) is nearly optimal and affords accuracy similar to B3LYP for thermochemistry, barrier heights, and excitation energies. Although BH&H-LYP is significantly less accurate than B3LYP for atomization energies, this emerges as the sole rationale for the taboo against values α > 25. Overall, BH&H-LYP is a reasonable choice for problems that are dominated by self-interaction error, including charge-transfer complexes and core-level excitation energies. While B3LYP remains more accurate for valence excitation energies, the use of 50% exact exchange appears to be an acceptable compromise, and BH&H-LYP can be used without undue concern over its diminished accuracy for ground-state properties.

The development of the QM/MM interface and its application for the on-the-fly QM/MM nonadiabatic dynamics in JADE package: Theory, implementation, and applications

Understanding the nonadiabatic dynamics of complex systems is a challenging task in computational photochemistry. Herein, we present an efficient and user-friendly quantum mechanics/molecular mechanics (QM/MM) interface to run on-the-fly nonadiabatic dynamics. Currently, this interface consists of an independent set of codes designed for general-purpose use. Herein, we demonstrate the ability and feasibility of the QM/MM interface by integrating it with our long-term developed JADE package. Tailored to handle nonadiabatic processes in various complex systems, especially condensed phases and protein environments, we delve into the theories, implementations, and applications of on-the-fly QM/MM nonadiabatic dynamics. The QM/MM approach is established within the framework of the additive QM/MM scheme, employing electrostatic embedding, link-atom inclusion, and charge-redistribution schemes to treat the QM/MM boundary. Trajectory surface-hopping dynamics are facilitated using the fewest switches algorithm, encompassing classical and quantum treatments for nuclear and electronic motions, respectively. Finally, we report simulations of nonadiabatic dynamics for two typical systems: azomethane in water and the retinal chromophore PSB3 in a protein environment. Our results not only illustrate the power of the QM/MM program but also reveal the important roles of environmental factors in nonadiabatic processes.

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.

Benchmarking two-photon absorption strengths of rhodopsin chromophore models with CC3 and CCSD methodologies: An assessment of popular density functional approximations

This work presents the investigations of the impact of an increasing electron correlation in the hierarchy of coupled-cluster methods, i.e., CC2, CCSD, and CC3, on two-photon absorption (2PA) strengths for the lowest excited state of the minimal rhodopsin's chromophore model-cis-penta-2,4-dieniminium cation (PSB3). For a larger chromophore's model [4-cis-hepta-2,4,6-trieniminium cation (PSB4)], CC2 and CCSD calculations of 2PA strengths were performed. Additionally, 2PA strengths predicted by some popular density functional theory (DFT) functionals differing in HF exchange contribution were assessed against the reference CC3/CCSD data. For PSB3, the accuracy of 2PA strengths increases in the following order: CC2 < CCSD < CC3, with the CC2 deviation from both higher-level methods exceeding 10% at 6-31+G* basis sets and 2% at aug-cc-pVDZ basis set. However, for PSB4, this trend is reversed and CC2-based 2PA strength is larger than the corresponding CCSD value. Among the DFT functionals investigated, CAM-B3LYP and BHandHLYP provide 2PA strengths in best compliance with reference data, however, with the error approaching an order of magnitude.

Trajectory surface hopping molecular dynamics simulations for retinal protonated Schiff-base photoisomerization

Global switching trajectory surface hopping molecular dynamics simulations are performed using accurate on-the-fly (TD)CAM-B3LYP/6-31G potential energy surfaces to study retinal protonated Schiff-base photoisomerization up to S₁ excitation. The simulations detected two-layer conical intersection networks: one is at an energy as high as 8 eV and the other is in the energy range around 3-4 eV. Six conical intersections within the low-layer energy region that correspond to active conical intersections under experimental conditions are found via the use of pairwise isomers, within which nonadiabatic molecular dynamics simulations are performed. Eight isomer products are populated with simulated sampling trajectories from which the simulated quantum yield in the gas phase is estimated to be 0.11 (0.08) moving from the all-trans isomer to the 11-cis (11-cis to all-trans) isomer in comparison with an experimental value of 0.09 (0.2) in the solution phase. Each conical intersection is related to one specific twist angle accompanying a related CC double bond motion during photoisomerization. Nonplanar distortion of the entire dynamic process has a significant role in the formation of the relevant photoisomerization products. The present simulation indicates that all hopping points show well-behaved potential energy surface topology, as calculated via the conventional TDDFT method, at conical intersections between S₁ and S₀ states. Therefore, the present nonadiabatic dynamics simulations with the TDDFT method are very encouraging for simulating various large systems related to retinal Schiff-base photoisomerization in the real world.

Ultrafast Photoisomerization of N-(2-Methoxybenzylidene)aniline: Nonadiabatic Surface-Hopping Study

We investigated the ultrafast photoisomerization of N-(2-methoxybenzylidene)aniline in the gas phase excited into the second singlet (S₂) state by nonadiabatic surface-hopping dynamics calculations. Two trans isomers (1E and 1E') were taken into consideration in our dynamics simulation. Three conical intersections (CIs) were characterized in the optimization. The CI between S₂ and the first singlet (S₁) states presents a nearly planar structure, while the other two CIs (CI_twist-I and CI_twist-II) between S₁ and the ground (S₀) states show nearly perpendicular geometries. After two trans isomers excited to the S₂ state, the torsion of the C-N bond connected the phenyl group and the stretch of the central bridging bond make the molecule reach CI_planar, and the S₂/S₁ hopping occurs. During the S₁-state dynamics, the molecule moves to a S₁/S₀ CI (CI_twist-I or CI_twist-II) by the rotation of the central bridging bond. The cis isomer is obtained through a barrierless pathway in the S₀ state with the torsion of the three bridging bonds. There is a main channel and an alternative one for the photoisomerization process of both trans isomers. CI_twist-I and CI_twist-II act as S₁/S₀ decay funnels in the main isomerization channels of 1E and 1E' isomers, respectively, and the photochemical processes of 1E and 1E' lead to different cis isomers.

Carbonyl Stretch as a Franck-Condon Active Mode and Driving Force for Excited-State Decay of 8-Methoxy-4-methyl-2H-benzo[g]chromen-2-one from nπ* State

The fluorescence of most organic chromophore is emitted from the ππ* state, whereas the nπ* state, as a dark state, plays an important role in quenching the fluorescence when its energy is close to the ππ* state. Herein, we report a theoretical study on the fluorescence quenching of 8-methoxy-4-methyl-2H-benzo[g]chromen-2-one by the nπ* state and propose a new mechanism for describing the vibronic coupling between the ππ* and nπ* states. By applying extended multistate complete-active-space second-order perturbation theory (XMS-CASPT2) to optimize the geometries, the geometry distortion of the ππ* state along the out-of-plane mode is observed. This geometry distortion causes the stretching vibration of the carbonyl group to be coupled with the C-C bonds of the pyran ring, which become a Franck-Condon active mode upon photoexcitation and provides a driving force for nonradiative decay from the nπ* state, even if it is energetically unfavorable. This mechanism is significantly different from the previously proposed "proximity effect" and cannot be captured by the popularly used time-dependent density functional theory (TDDFT) and complete-active-space self-consistent field (CASSCF) methods.

The solvent effect on the excited-state intramolecular proton transfer of cyanine derivative molecules

Essential comprehension of the ESIPT mechanism in different solvents is helpful to design excellent fluorescent probes for lysosome organelles.

How Methylation Modifies the Photophysics of the Native All- trans-Retinal Protonated Schiff Base: A CASPT2/MD Study in Gas Phase and in Methanol

A comparison between the free-energy surfaces of the all- trans-retinal protonated Schiff base (RPSB) and its 10-methylated derivative in gas phase and methanol solution is performed at CASSCF//CASSCF and CASPT2//CASSCF levels. Solvent effects were included using the average solvent electrostatic potential from molecular dynamics method. This is a QM/MM (quantum mechanics/molecular mechanics) method that makes use of the mean field approximation. It is found that the methyl group bonded to C10 produces noticeable changes in the solution free-energy profile of the S₁ excited state, mainly in the relative stability of the minimum energy conical intersections (MECIs) with respect to the Franck-Condon (FC) point. The conical intersections yielding the 9- cis and 11- cis isomers are stabilized while that yielding the 13- cis isomer is destabilized; in fact, it becomes inaccessible by excitation to S₁. Furthermore, the planar S₁ minimum is not present in the methylated compound. The solvent notably stabilizes the S₂ excited state at the FC geometry. Therefore, if the S₂ state has an effect on the photoisomerization dynamics, it must be because it permits the RPSB population to branch around the FC point. All these changes combine to speed up the photoisomerization in the 10-methylated compound with respect to the native compound.

Nonadiabatic dynamics simulation of photoisomerization mechanism of the second stablest isomer of N-salicilydenemethylfurylamine

The photoisomerization processes of the second stablest isomer in the aromatic Schiff base, N-salicilydenemethylfurylamine, in the gas phase have been studied by static electronic structure calculations and surface-hopping dynamics simulations based on the Zhu-Nakamura theory. Various stable structures are obtained in the optimization because of different orientations of methyl-furyl part with respect to the salicylaldimine part and different orientations of hydroxy group with respect to the benzene ring. Upon photoexcitation into the first excited state, bond isomerization in the salicylaldimine part is completely suppressed until the strong excited-state hydrogen bond is broken. The decay pathway involves two excited-state minima, one in cis-enol form and the other in cis-keto form. After the excited-state proton transfer, twists of bonds lead to a conical intersection between the ground and excited states. After internal conversion around a conical intersection, the molecule is stabilized in cis- or trans-keto form. If the reverse hydrogen transfer process occurs in the ground state, the molecule will finally end up in the cis-enol region. The cis-keto and trans-keto isomers are observed as photoproducts. According to our full-dimensional nonadiabatic dynamics simulations, we find the excited-state intramolecular proton transfer and torsions of three single bonds in the chain to be responsible for photoisomerization of the second stablest isomer of N-salicilydenemethylfurylamine.

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.

The new competitive mechanism of hydrogen bonding interactions and transition process for the hydroxyphenyl imidazo [1, 2-a] pyridine in mixed liquid solution

The new competitive mechanism of intermolecular and intramolecular hydrogen bond can be proposed with an improved mixed model. Upon the photoinduced process, the twisting intramolecular charge transfer (TICT) structure of the hydroxyphenyl imidazo [1, 2-a] pyridine (HPIP) can be obtained. TICT character prompts the fluorescent inactivation via non-radiative decay process. For exploring the photochemical and photophysical properties, the electronic spectra and the infrared (IR) vibrational spectra of titled compounds have been detailedly investigated. In addition, the frontier molecular orbitals (MOs) analysis visually reveals that the unbalanced electron population can give rise to the torsion of molecular structure. To further give an attractive insight into the non-radiative decay process, the potential energy curves have been depicted on the ground state (S₀), the first excited state (S₁) and the triple excited state (T₁). Minimum energy crossing point (MECP) has been found in the S₁ and T₁ state. On the MECP, the intersystem crossing (ISC) might be dominant channel. The density functional theory (DFT) and the time-dependent density functional theory (TDDFT) methods have been throughout employed in the S₀ state, T₁ state and S₁ state, respectively. The theoretical results are consistent with experiment in mixed and PCM model.

Assessment of Approximate Coupled-Cluster and Algebraic-Diagrammatic-Construction Methods for Ground- and Excited-State Reaction Paths and the Conical-Intersection Seam of a Retinal-Chromophore Model

As a minimal model of the chromophore of rhodopsin proteins, the penta-2,4-dieniminium cation (PSB3) poses a challenging test system for the assessment of electronic-structure methods for the exploration of ground- and excited-state potential-energy surfaces, the topography of conical intersections, and the dimensionality (topology) of the branching space. Herein, we report on the performance of the approximate linear-response coupled-cluster method of second order (CC2) and the algebraic-diagrammatic-construction scheme of the polarization propagator of second and third orders (ADC(2) and ADC(3)). For the ADC(2) method, we considered both the strict and extended variants (ADC(2)-s and ADC(2)-x). For both CC2 and ADC methods, we also tested the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) variants. We have explored several ground- and excited-state reaction paths, a circular path centered around the S1/S0 surface crossing, and a 2D scan of the potential-energy surfaces along the branching space. We find that the CC2 and ADC methods yield a different dimensionality of the intersection space. While the ADC methods yield a linear intersection topology, we find a conical intersection topology for the CC2 method. We present computational evidence showing that the linear-response CC2 method yields a surface crossing between the reference state and the first response state featuring characteristics that are expected for a true conical intersection. Finally, we test the performance of these methods for the approximate geometry optimization of the S1/S0 minimum-energy conical intersection and compare the geometries with available data from multireference methods. The present study provides new insight into the performance of linear-response CC2 and polarization-propagator ADC methods for molecular electronic spectroscopy and applications in computational photochemistry.

Excited States and Photochemistry of Chromophores in the Photoactive Proteins Explored by the Combined Quantum Mechanical and Molecular Mechanical Calculations

A photoactive protein usually contains a unique chromophore that is responsible for the initial photoresponse and functions of the photoactive protein are determined by the interaction between the chromophore and its protein surroundings. The combined quantum mechanical and molecular mechanical (QM/MM) approach is demonstrated to be a very useful tool for exploring structures and functions of a photoactive protein with the chromophore and its protein surroundings treated by the QM and MM methods, respectively. In this review, we summarize the basic formulas of the QM/MM approach and emphasize its applications to excited states and photoreactions of chromophores in rhodopsin protein, photoactive yellow protein, and green fluorescent protein.

A DFT/TDDFT investigation of the excited state proton transfer reaction of fisetin chromophore

In the present work, 3, 3', 4', 7-tetrahydroxyflavone (fisetin), as one of the most extensive distributed flavonoids, has been investigated on the excited state proton transfer (ESPT) based on the time-dependent density functional theory (TDDFT) method. The calculated absorption and fluorescence spectra based on the TDDFT method are in agreement with the experimental results. Two kinds of structures of fisetin chromophore are found in the first excited (S1) state, which may be due to the proton transfer reactive. Hydrogen bond strengthening has been testified in the S1 state based on comparing staple bond lengths and bond angles involved in hydrogen bonding between the S0 state and the S1 state. In addition, the calculated infrared spectra at the O-H stretching vibrational region and calculated hydrogen bond energy also declare the phenomenon of hydrogen bond strengthening. The frontier molecular orbitals (MOs) analysis and Natural bond orbital (NBO) manifest the intramolecular charge transfer of fisetin chromophore, which reveals the tendency of proton transfer. The potential energy surfaces of the S0 and S1 states are constructed to explain the mechanism of the proton transfer in excited state in detail.

Photoisomerization action spectrum of retinal protonated Schiff base in the gas phase

The photophysical behaviour of the isolated retinal protonated n-butylamine Schiff base (RPSB) is investigated in the gas phase using a combination of ion mobility spectrometry and laser spectroscopy. The RPSB cations are introduced by electrospray ionisation into an ion mobility mass spectrometer where they are exposed to tunable laser radiation in the region of the S1 ← S0 transition (420-680 nm range). Four peaks are observed in the arrival time distribution of the RPSB ions. On the basis of predicted collision cross sections with nitrogen gas, the dominant peak is assigned to the all-trans isomer, whereas the subsidiary peaks are assigned to various single, double and triple cis geometric isomers. RPSB ions that absorb laser radiation undergo photoisomerization, leading to a detectable change in their drift speed. By monitoring the photoisomer signal as a function of laser wavelength an action spectrum, extending from 480 to 660 nm with a clear peak at 615 ± 5 nm, is obtained. The photoisomerization action spectrum is related to the absorption spectrum of isolated retinal RPSB molecules and should help benchmark future electronic structure calculations.

Photoisomerization mechanism of 1,1'-dimethyl-2,2'-pyridocyanine in the gas phase and in solution

The trans→cis and cis→trans photoisomerization mechanisms of 1,1'-dimethyl-2,2'-pyridocyanine have been investigated theoretically in the gas phase and in methanol. Two-dimensional potential energy surfaces were computed for the ground and first excited singlet states of the isolated molecule using complete active space self-consistent field method. Our computations suggest that the torsion around the central C-C bonds with carbon-out-of-plane motion is the preferred photoisomerization mechanism. In the gas phase, conical intersections were found near the minima of excited state. The excited-state decay follows a barrierless minimum-energy pathway before the molecule moves to the excited-state global minimum (minS1) and the system relaxes to the ground state through a conical intersection. In methanol, the system would first reach a stationary structure of C2 symmetry after the trans form is electronically excited. Solvent polarity effects were investigated in chloroform, dichloromethane, 1-propanol, ethanol, methanol, and water. There is a significant barrier between the stationary structure of C2 symmetry and minS1 in the excited state in high polarity solvents. Thus, Me-1122P has a much longer lifetime of the excited state in solvents of high polarity.

Retinal shows its true colours: photoisomerization action spectra of mobility-selected isomers of the retinal protonated Schiff base

Isomers of the retinal protonated Schiff base are separated and probed using laser radiation in a tandem ion mobility spectrometer yielding isomer-specific electronic spectra.