Intersection Seam Research Articles

Floquet-Engineered Photodissociation Simulated Using Coupled Potential Energy and Dipole Matrices.

We simulate the nonadiabatic molecular dynamics of ammonia photodissociation in the presence of an external laser field by using an approximate Floquet Hamiltonian. The dipole-field interaction gives rise to seams of light-induced conical intersection (LICI), which can significantly change the topography of the coupled potential energy surfaces. We perform quasiclassical trajectories based on recently reported diabatic potential energy matrices (DPEM) and dipole matrices. It is shown that the branching ratio of ground and excited state NH2 is drastically altered by laser-dipole interaction, which is a signature of nonadiabatic effects induced by light.

UV wavelength-dependent photoionization quantum yields for the dark 1nπ* state of aqueous thymidine.

Despite the important role of the dark 1nπ* state in the photostability of thymidine in aqueous solution, no detailed ultraviolet (UV) wavelength-dependent investigation of the 1nπ* quantum yield (QY) in aqueous thymidine has been experimentally performed. Here, we investigate the wavelength-dependent photoemission spectra of aqueous thymidine from 266.7 to 240 nm using liquid-microjet photoelectron spectroscopy. Two observed ionization channels are assigned to resonant ionizations from 1ππ* to the cationic ground state D0 (π-1) and 1nπ* to the cationic excited state D1 (n-1). The weak 1nπ* → D1 ionization channel appears due to ultrafast 1ππ* → 1nπ* internal conversion within the pulse duration of ∼180 fs. The obtained 1nπ* quantum yields exhibit a strong wavelength dependence, ranging from 0 to 0.27 ± 0.01, suggesting a hitherto uncharacterized 1nπ* feature. The corresponding vertical ionization energies (VIEs) of D0 and D1 of aqueous thymidine are experimentally determined to be 8.47 ± 0.12 eV and 9.22 ± 0.29 eV, respectively. Our UV wavelength-dependent QYs might indicate that different structural critical points to connect the multidimensional 1ππ*/1nπ* conical intersection seam onto the multidimensional potential energy surface of the 1ππ* state might exist and determine the relaxation processes of aqueous thymidine upon UV excitation.

Accurate and Efficient Schemes for Mapping Out Two Isolated Seams of Conical Intersections with Neural Networks Solely Based on Adiabatic Energies: A Case Study of H+ + NO(X2Π) → H + NO+(X1Σ+).

A new scheme in the neural network (NN) diabatization approach that solely utilizes the adiabatic energies for constructing the global diabatic potential energy matrices (PEMs) of the molecular systems with two isolated seams of conical intersections (CIs) is proposed. Taking a prototype charge transfer reaction H+ + NO(X2Π) → H + NO+(X1Σ+), where two seams of CIs are located at the different linear geometries N-O-H and O-N-H, for example, the diabatization with the new scheme including a diabatic state constraint is shown to map out the topographies of both two linear CIs with 100% of the success rate in 10 different trainings, while the diabatization without such constraint hardly represents CIs, in which the avoided crossings appear instead. Simultaneously, we propose a scheme to separate the whole reactive space into three different regions and define the minimal Euclidean distances for each region to efficiently sample the energy points for the NN trainings. Through adjusting the minimal Euclidean distances, the number of the adiabatic energy data needed in the construction of diabatic PEM can be heavily decreased, lowered from ∼2000 to ∼280 energy points, which is much less than the number (>22 000) of ab initio energy points used in earlier spline diabatic PEM. Further quantum dynamic calculations show that the reaction probabilities, vibrational state distributions, and vibrational state resolved differential cross sections are well reproduced on the new NN diabatic PEM, validating these schemes for constructing the diabatic PEM.

Fitting of Coupled Potential Energy Surfaces via Discovery of Companion Matrices by Machine Intelligence.

Fitting coupled potential energy surfaces is a critical step in simulating electronically nonadiabatic chemical reactions and energy transfer processes. Analytic representation of coupled potential energy surfaces enables one to perform detailed dynamics calculations. Traditionally, fitting is performed in a diabatic representation to avoid fitting the cuspidal ridges of coupled adiabatic potential energy surfaces at conical intersection seams. In this work, we provide an alternative approach by carrying out fitting in the adiabatic representation using a modified version of the Frobenius companion matrices, whose usage was first proposed by Opalka and Domcke. Their work involved minimizing the errors in fits of the characteristic polynomial coefficients (CPCs) and diagonalizing the resulting companion matrix, whose eigenvalues are adiabatic potential energies. We show, however, that this may lead to complex eigenvalues and spurious discontinuities. To alleviate this problem, we provide a new procedure for the automatic discovery of CPCs and the diagonalization of a companion matrix by using a special neural network architecture. The method effectively allows analytic representation of global coupled adiabatic potential energy surfaces and their gradients with only adiabatic energy input and without experience-based selection of a diabatization scheme. We demonstrate that the new procedure, called the companion matrix neural network (CMNN), is successful by showing applications to LiH, H3, phenol, and thiophenol.

The anion photoelectron spectrum and diabatization of tetrazolyl.

The potential energy surface of tetrazolyl [cyclic (N4CH)] has a conical intersection seam between the two lowest-energy electronic states near the ground state minimum geometry. This work treats that molecule. The potential energy surfaces used in this study are based on a least-squares fitting procedure that includes abinitio energies, energy gradients, and derivative couplings described using polynomials up to fourth-order and abinitio data obtained from multireference configuration interaction wave functions. A five-electronic-state description was generated with a root mean square absolute energy error of 9.6cm-1, compared to 326.8cm-1 when only second-order terms were used. The time-independent multimode vibronic coupling in the KDC approximation was used to simulate and analyze the anion ultraviolet photoelectron spectrum of tetrazolide.

Development of Parallel On-the-Fly Crystal Algorithm for Global Exploration of Conical Intersection Seam Space.

Conical intersection (CI) seams are configuration spaces of a molecular system where two or more (spin) adiabatic electronic states are degenerate in energy. They play essential roles in photochemistry because nonradiative decays often occur near the minima of the seam, i.e., the minimum energy CIs (MECIs). Thus, it is important to explore the CI seams and discover the MECIs. Although various approaches exist for CI seam exploration, most of them are local in nature, requiring reasonable initial guesses of geometries and nuclear gradients during the search. Global search algorithms, on the other hand, are powerful because they can fully sample the configurational space and locate important MECIs missed by local algorithms. However, global algorithms are often computationally expensive for large systems due to their poor scalability with respect to the number of degrees of freedom. To overcome this challenge, we develop the parallel on-the-fly Crystal algorithm to globally explore the CI seam space, taking advantage of its superior scaling behavior. Specifically, Crystal is coupled with on-the-fly evaluations of the excited and ground state energies using multireference electronic structure methods. Meanwhile, the algorithm is parallelized to further boost its computational efficiency. The effectiveness of this new algorithm is tested for three types of molecular photoswitches of significant importance in material and biomedical sciences: photostatin (PST), stilbene, and butadiene. A rudimentary implementation of the algorithm is applied to PST and stilbene, resulting in the discovery of all previously identified MECIs and several new ones. A refined version of the algorithm, combined with a systematic clustering technique, is applied to butadiene, resulting in the identification of an unprecedented number of energetically accessible MECIs. The results demonstrate that the parallel on-the-fly Crystal algorithm is a powerful tool for automated global CI seam exploration.

Topology of Conical Intersection Seams and the Geometric Phase.

In this paper, we demonstrate two topological properties of crossing seams, that is, the sets of points in the N-dimensional space of nuclear coordinates where two electronic eigenstates are degenerate. We shall examine the typical case of states of the same spin with accidental degeneracies, whereby the crossing seam is of dimension N - 2. The first property we demonstrate is that a crossing seam has no boundary, therefore, it must either extend asymptotically to infinite values of one or more coordinates or wrap on itself. The second property is that two (or more) crossing seams can intersect each other but in such a way that neither of them ends at the intersection. When N = 3, the crossing seam is a line in a 3D space; this is so in triatomic molecules but also in reduced dimensionality treatments of larger polyatomics. The above-mentioned rules then mean that the crossing seam is a line of infinite length or a closed loop and can split into three branches but not in two. The example of the first two excited 1A' states of H2Cl+ illustrates these rules and shows their usefulness for computational search and characterization of crossing seams.

Minimum-Energy Conical Intersections by Compressed Multistate Pair-Density Functional Theory.

Compressed multistate pair-density functional theory (CMS-PDFT) is a multistate version of multiconfiguration pair-density functional theory that can capture the correct topology of coupled potential energy surfaces (PESs) around conical intersections. In this work, we develop interstate coupling vectors (ISCs) for CMS-PDFT in the OpenMolcas and PySCF/mrh electronic structure packages. Yet, the main focus of this work is using ISCs to calculate minimum-energy conical intersections (MECIs) by CMS-PDFT. This is performed using the projected constrained optimization method in OpenMolcas, which uses ISCs to restrain the iterations to the conical intersection seam. We optimize the S1/S0 MECIs for ethylene, butadiene, and benzene and show that CMS-PDFT gives smooth PESs in the vicinities of the MECIs. Furthermore, the CMS-PDFT MECIs are in good agreement with the MECI calculated by the more expensive XMS-CASPT2 method.

A diabatization method based upon integrating the diabatic potential gradient difference.

In this work we develop a new scheme to construct a diabatic potential energy matrix (DPEM). We propose a diabatization method which is based on integrating the diabatic potential gradient difference to diabatize adiabatic ab initio energies. This method is capable of performing high-precision adiabatic-to-diabatic transformations, with a unique advantage in effectively handling the significant fluctuations in derivative-couplings caused by conical intersection (CI) seams. The above scheme is applied to the DPEM construction of the Na(3p) + H2 → NaH + H reaction. The fitting data including adiabatic energies, energy gradients and derivative-couplings obtained from a previous benchmark DPEM are diabatized and fitted using a general neural network fitting procedure to generate the DPEM. The produced DPEM can effectively describe nonadiabatic processes involving different electronic states. We further perform quantum dynamical calculations on the new DPEM and the previous benchmark DPEM, and the obtained results demonstrate the effectiveness of our scheme.

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.

Machine Learning Seams of Conical Intersection: A Characteristic Polynomial Approach.

The machine learning of potential energy surfaces (PESs) has undergone rapid progress in recent years. The vast majority of this work, however, has been focused on the learning of ground state PESs. To reliably extend machine learning protocols to excited state PESs, the occurrence of seams of conical intersections between adiabatic electronic states must be correctly accounted for. This introduces a serious problem, for at such points, the adiabatic potentials are not differentiable to any order, complicating the application of standard machine learning methods. We show that this issue may be overcome by instead learning the coordinate-dependent coefficients of the characteristic polynomial of a simple decomposition of the potential matrix. We demonstrate that, through this approach, quantitatively accurate machine learning models of seams of conical intersection may be constructed.

The 2-pyridone/2-hydroxypyridine tautomerism in gas phase: An excited state roaming reaction.

Multiconfigurational methods (CASSCF and CASPT2) were employed to gain a new understanding of the mechanism of the gas-phase phototautomerization of 2-pyridone/2-hydroxypyridine. Potential energy curves and crossing points of the low-lying excited states were analyzed. The results show that the tautomerization only occurs from 2-pyridone to 2-hydroxypyridine after electronic excitation to the S1 (ππ*) state. From this state, the system would be able to reach a conical intersection between S1 and the dissociative S2 (πσ*) due to vibrational effects. Then, it can evolve to the hydroxy form in its ground state by reaching an intersection seam between the S0 and the πσ* states. For this to happen, a roaming process responsible for the hydrogen atom migration would be required; otherwise, the system would revert to the 2-pyridone tautomer. The unfeasibility of the reverse process after optical excitation from the lactim to the lactam form is explained by the great amount of energy needed to reach the conical intersection between the ππ* and πσ* states. These findings would provide new insights into the understanding of the photophysics and photochemistry of a primordial heterocycle, considered a prebiotic model known to be found in interstellar clouds.

Photodissociation dynamics of methylamine in the blue edge of the A-band. I. The H-atom elimination channel.

The photodissociation dynamics of methylamine (CH3NH2) upon excitation in the blue edge of the first absorption A-band, in the 198-203nm range, are investigated by means of nanosecond pump-probe laser pulses and velocity map imaging combined with H(2S)-atom detection through resonance enhanced multiphoton ionization. The images and corresponding translational energy distributions for the H-atoms produced show three different contributions associated with three reaction pathways. The experimental results are complemented by high-level abinitio calculations. The potential energy curves computed as a function of the N-H and C-H bond distances allow us to draw a picture of the different mechanisms. Major dissociation occurs through N-H bond cleavage and it is triggered by an initial geometrical change, i.e., from a pyramidal configuration of the C-NH2 with respect to the N atom to a planar geometry. The molecule is then driven into a conical intersection (CI) seam where three outcomes can take place: first, threshold dissociation into the second dissociation limit, associated with the formation of CH3NH(Ã), is observed; second, direct dissociation after passage through the CI leading to the formation of ground state products; and third, internal conversion into the ground state well in advance to dissociation. While the two last pathways were previously reported at a variety of wavelengths in the 203-240nm range, the former had not been observed before to the best of our knowledge. The role of the CI and the presence of an exit barrier in the excited state, which modify the dynamics leading the two last mechanisms, are discussed considering the different excitation energies used.

Mode-dependent H atom tunneling dynamics of the S1 phenol is resolved by the simple topographic view of the potential energy surfaces along the conical intersection seam.

Mode-dependent H atom tunneling dynamics of the O-H bond predissociation of the S1 phenol has been theoretically analyzed. As the tunneling is governed by the complicated multi-dimensional potential energy surfaces that are dynamically shaped by the upper-lying S1(ππ*)/S2(πσ*) conical intersection, the mode-specific tunneling dynamics of phenol (S1) has been quite formidable to be understood. Herein, we have examined the topography of the potential energy surface along the particular S1 vibrational mode of interest at the nuclear configurations of the S1 minimum and S1/S2 conical intersection. The effective adiabatic tunneling barrier experienced by the reactive flux at the particular S1 vibrational mode excitation is then uniquely determined by the topographic shape of the potential energy surface extended along the conical intersection seam coordinate associated with the particular vibrational mode. The resultant multi-dimensional coupling of the specific vibrational mode to the tunneling coordinate is then reflected in the mode-dependent tunneling rate as well as nonadiabatic transition probability. Remarkably, the mode-specific experimental result of the S1 phenol tunneling reaction [K. C. Woo and S. K. Kim, J. Phys. Chem. A 123, 1529-1537 (2019)] (in terms of the qualitative and relative mode-dependent dynamic behavior) could be well rationalized by semi-classical calculations based on the mode-specific topography of the effective tunneling barrier, providing the clear conceptual insight that the skewed potential energy surfaces along the conical intersection seam (strongly or weakly coupled to the tunneling reaction coordinate) may dictate the tunneling dynamics in the proximity of the conical intersection.

Prototropically Controlled Dynamics of Cytosine Photodecay

The effect of the existence of several prototropic tautomers of cytosine on its UV/vis spectra and the excited state decay dynamics is studied by spectral and nonadiabatic molecular dynamics (NAMD) simulations in connection with the mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) method. Simulated UV/vis spectra provide a strong indication that the H3N keto-amino cytosine tautomer (the least anticipated species) may be present under experimental conditions. The NAMD simulations yield a wide range of excited state decay constants for various tautomers of cytosine, ranging from ∼1.3 ps for the biologically relevant H1N keto-amino tautomer to ∼0.1 ps for the keto-imino tautomer. The slowness of the H1N decay dynamics follows from the presence of a barrier on the excited state energy surface separating the Franck-Condon structure from the major decay funnel, the conical intersection seam. It is suggested that the experimentally observed photodecay dynamics may result from a combination of the decay processes of various tautomers (H3N in particular) present simultaneously under the experimental conditions.

Alkylated green fluorescent protein chromophores: dynamics in the gas phase and in aqueous solution.

Fluorescent labelling of macromolecular samples, including using the green fluorescent protein (GFP), has revolutionised the field of bioimaging. The ongoing development of fluorescent proteins require a detailed understanding of the photophysics of the biochromophore, and how chemical derivatisation influences the excited state dynamics. Here, we investigate the photophysical properties associated with the S1 state of three alkylated derivatives of the chromophore in GFP, in the gas phase using time-resolved photoelectron imaging, and in water using femtosecond fluorescence upconversion. The gas-phase lifetimes (1.6-10 ps), which are associated with the intrinsic (environment independent) dynamics, are substantially longer than the lifetimes in water (0.06-3 ps), attributed to stabilisation of both twisted intermediate structures and conical intersection seams in the condensed phase. In the gas phase, alkylation on the 3 and 5 positions of the phenyl ring slows the dynamics due to inertial effects, while a 'pre-twist' of the methine bridge through alkylation on the 2 and 6 positions significantly shortens the excited state lifetimes. Formation of a minor, long-lived (≫ 40 ps) excited state population in the gas phase is attributed to intersystem crossing to a triplet state, accessed because of a T1/S1 degeneracy in the so-called P-trap potential energy minimum associated with torsion of the single-bond in the bridging unit connecting to the phenoxide ring. A small amount of intersystem crossing is supported through TD-DFT molecular dynamics trajectories and MS-CASPT2 calculations. No such intersystem crossing occurs in water at T = 300 K or in ethanol at T ≈ 77 K, due to a significantly altered potential energy surface and P-trap geometry.

Mapping the photochemistry of cyclopentadiene: from theory to ultrafast X-ray scattering.

The photoinduced ring-conversion reaction when cyclopentadiene (CP) is excited at 5.10 eV is simulated using surface-hopping semiclassical trajectories with XMS(3)-CASPT2(4,4)/cc-pVDZ electronic structure theory. In addition, PBE0/def2-SV(P) is employed for ground state propagation of the trajectories. The dynamics is propagated for 10 ps, mapping both the nonadiabatic short-time dynamics (<300 fs) and the increasingly statistical dynamics on the electronic ground state. The short-time dynamics yields a mixture of hot CP and bicyclo[2.1.0]pentene (BP), with the two products reached via different regions of the same conical intersection seam. On the ground state, we observe slow conversion from BP to CP which is modelled by RRKM theory with a transition state determined using PBE0/def2-TZVP. The CP products are furthermore associated with ground state hydrogen shifts and some H-atom dissociation. Finally, the prospects for detailed experimental mapping using novel ultrafast X-ray scattering experiments are discussed and observables for such experiments are predicted. In particular, we assess the possibility of retrieving electronic states and their populations alongside the structural dynamics.

Direct structural observation of ultrafast photoisomerization dynamics in sinapate esters

Sinapate esters have been extensively studied for their potential application in ‘nature-inspired’ photoprotection. There is general consensus that the relaxation mechanism of sinapate esters following photoexcitation with ultraviolet radiation is mediated by geometric isomerization. This has been largely inferred through indirect studies involving transient electronic absorption spectroscopy in conjunction with steady-state spectroscopies. However, to-date, there is no direct experimental evidence tracking the formation of the photoisomer in real-time. Using transient vibrational absorption spectroscopy, we report on the direct structural changes that occur upon photoexcitation, resulting in the photoisomer formation. Our mechanistic analysis predicts that, from the photoprepared ππ* state, internal conversion takes place through a conical intersection (CI) near the geometry of the initial isomer. Our calculations suggest that different CI topographies at relevant points on the seam of intersection may influence the isomerization yield. Altogether, we provide compelling evidence suggesting that a sinapate ester’s geometric isomerization can be a more complex dynamical process than originally thought.

Excited-State Barrier Controls E → Z Photoisomerization in p-Hydroxycinnamate Biochromophores.

Molecules based on the deprotonated p-hydroxycinnamate moiety are widespread in nature, including serving as UV filters in the leaves of plants and as the biochromophore in photoactive yellow protein. The photophysical behavior of these chromophores is centered around a rapid E → Z photoisomerization by passage through a conical intersection seam. Here, we use photoisomerization and photodissociation action spectroscopies with deprotonated 4-hydroxybenzal acetone (pCK–) to characterize a wavelength-dependent bifurcation between electron autodetachment (spontaneous ejection of an electron from the S1 state because it is situated in the detachment continuum) and E → Z photoisomerization. While autodetachment occurs across the entire S1(ππ*) band (370–480 nm), E → Z photoisomerization occurs only over a blue portion of the band (370–430 nm). No E → Z photoisomerization is observed when the ketone functional group in pCK– is replaced with an ester or carboxylic acid. The wavelength-dependent bifurcation is consistent with potential energy surface calculations showing that a barrier separates the Franck–Condon region from the E → Z isomerizing conical intersection. The barrier height, which is substantially higher in the gas phase than in solution, depends on the functional group and governs whether E → Z photoisomerization occurs more rapidly than autodetachment.

The competitive mechanism between photoisomerization and excited state intramolecular proton transfer process of 2′-Hydroxychalcone system

The photoisomerization and excited state intramolecular proton transfer (ESIPT) are the most common processes in molecular photoswitches. Their coexistence and competing relationship in molecules usually make the deactivation process of the molecules become complex. In the current work, we study the underlying deactivation mechanism of trans-form 2′-hydroxychalcone (2′HC), which possesses both photoisomerization and ESIPT in the excited state, by combining high-level electronic structure calculations and on-the-fly surface hopping dynamics simulations. Four minimum energy conical intersections (MECIs) are found to be involved in the whole deactivation process. Following excitation to the S3 state of the most stable trans-enol tautomer, a strong coupling from the ππ* onto the nπ* state facilitates the ultrafast S3/S1 internal conversion process through an intricate conical intersection seam among S1, S2 and S3 state. The subsequent S1 to S0 state relaxation pathway is divided into two branches. The first process is initiated by twisting motion of C8─C9 bridging bond, which decays directly to the ground state via enol MECI. The other one is triggered by an ultrafast ESIPT process firstly and followed by twisting motion of the C1─C7 bond, leading the system funnel to the ground state by a keto type MECI, and finally generates the precursor of coloured flavanone. The proposed S3→(S2) S1 → S0 two step decay pattern is consistent with previous experimental observations. At the molecular microscopic level, the CO bond alternation motion plays a vital role in the whole relaxation process. Our results indicate that further practical application of 2′HC as molecular photoswitches can be achieved by modifying the molecular structure to enhance the ESIPT process.