Three-state Conical Intersections Research Articles

Different flavors of exact-factorization-based mixed quantum-classical methods for multistate dynamics.

The exact factorization approach has led to the development of new mixed quantum-classical methods for simulating coupled electron-ion dynamics. We compare their performance for dynamics when more than two electronic states are occupied at a given time, and analyze: (1) the use of coupled versus auxiliary trajectories in evaluating the electron-nuclear correlation terms, (2) the approximation of using these terms within surface-hopping and Ehrenfest frameworks, and (3) the relevance of the exact conditions of zero population transfer away from nonadiabatic coupling regions and total energy conservation. Dynamics through the three-state conical intersection in the uracil radical cation as well as polaritonic models in one dimension are studied.

Cavity-induced non-adiabatic dynamics and spectroscopy of molecular rovibrational polaritons studied by multi-mode quantum models

We study theoretically the quantum dynamics and spectroscopy of rovibrational polaritons formed in a model system composed of a single rovibrating diatomic molecule, which interacts with two degenerate, orthogonally polarized modes of an optical Fabry-Pérot cavity. We employ an effective rovibrational Pauli-Fierz Hamiltonian in length gauge representation and identify three-state vibro-polaritonic conical intersections (VPCIs) between singly excited vibro-polaritonic states in a two-dimensional angular coordinate branching space. The lower and upper vibrational polaritons are of mixed light-matter hybrid character, whereas the intermediate state is purely photonic in nature. The VPCIs provide effective population transfer channels between singly excited vibrational polaritons, which manifest in rich interference patterns in rotational densities. Spectroscopically, three bright singly excited states are identified when an external infrared laser field couples to both a molecular and a cavity mode. The non-trivial VPCI topology manifests as pronounced multi-peak progression in the spectral region of the upper vibrational polariton, which is traced back to the emergence of rovibro-polaritonic light-matter hybrid states. Experimentally, ubiquitous spontaneous emission from cavity modes induces a dissipative reduction of intensity and peak broadening, which mainly influences the purely photonic intermediate state peak as well as the rovibro-polaritonic progression.

Theoretical approach to modeling the early nonadiabatic events of ESIPT originating from three-state conical intersection in quinophthalone.

We explore the excited-state intramolecular proton transfer process of quinophthalone theoretically. This molecule possesses three low-lying singlet excited states ([Formula: see text] and [Formula: see text]) in a narrow energy gap of less than the N-H stretching frequency. Dynamics simulations show nonadiabatic wavepacket transfer to [Formula: see text] and [Formula: see text] upon initiating the wavepacket on [Formula: see text]. Multiple accessible conical intersections that lie in the Franck-Condon region facilitate the nonadiabatic wavepacket transfer. Nuclear densities associated with the proton transfer promoting vibrations would start accumulating on [Formula: see text] and [Formula: see text] within a few tens of femtoseconds, validating the involvement of these vibrations in the nonadiabatic events that occur before the proton transfer process. Our findings emphasize the necessity of refined kinetic models for assigning the time constants of ultrafast transient spectroscopy measurements due to the simultaneous evolution of nonadiabatic events and proton transfer kinetics in quinophthalone.

Optimization of Three State Conical Intersections by Adaptive Penalty Function Algorithm in Connection with the Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory Method (MRSF-TDDFT).

A new adaptive algorithm for penalty function optimization for minimum-energy three-states conical intersections (ME3CI) is suggested. The new algorithm differs from the original penalty function algorithm by (a) removing the redundancy in the target function, (b) using an adaptive increment for the penalty function weighting factor, and (c) using tighter convergence criteria for the energy gap. The latter was introduced to guarantee convergence to a true conical intersection rather than to a narrowly avoided crossing geometry. The new algorithm was tested in the optimization of the ME3CI geometries in butadiene and malonaldehyde, where all of the previously found true ME3CI geometries were recovered. The previously found butadiene's CI3/2/1 turned out to be a narrowly avoided crossing. For butadiene, seven new ME3CI geometries have been located. Because of the removal of the redundancy and the use of the adaptive weighting factor, the convergence rate of the new algorithm is noticeably improved as compared to that of the previously proposed penalty function algorithm. The application to malonaldehyde and butadiene demonstrates that the three-state conical intersections may be more abundant and hence more involved in the photochemistry than previously thought. The recently developed mixed-reference spin flip (MRSF)-TDDFT method yields ME3CI geometries and relative energies quantitatively consistent with the previously reported calculations at a much reduced computational cost.

Multiple ESIPT pathways originating from three-state conical intersections in tropolone.

Internal conversion decay dynamics associated with the potential energy surfaces of three low-lying singlet excited electronic states, S1 (ππ*, A'), S2 (ππ*, A'), and S3 (nπ*, A″), of tropolone are investigated theoretically. Energetic and spatial aspects of conical intersections of these electronic states are explored with the aid of the linear vibronic coupling approach. Symmetry selection rules suggest that non-totally symmetric modes would act as coupling modes between S1 and S3 as well as between S2 and S3. We found that the S1-S2 interstate coupling via totally symmetric modes is very weak. A diabatic vibronic Hamiltonian consisting of 32 vibrational degrees of freedom is constructed to simulate the photoinduced dynamics of S0 → S1 and S0 → S2 transitions. We observe a direct nonadiabatic population transfer from S1 to S3, bypassing S2, during the initial wavepacket propagation on S1. On the other hand, the initial wavepacket evolving on S2 would pass through the S2-S3 and S1-S3 conical intersections before reaching S1. The presence of multiple proton transfer channels on the S1-S2-S3 coupled potential energy surfaces of tropolone is analyzed. Our findings necessitate the treatment of proton tunneling dynamics of tropolone beyond the adiabatic symmetric double well potentials.

Three-state conical intersection optimization methods: development and implementation at QM/MM level

Two-state conical intersection optimization methods at both QM and QM/MM levels have been extensively implemented in many commercial and noncommercial packages in the past decade. In contrast, three-state conical intersection optimization methods are less concerned, in particular the QM/MM-based ones. In this work, we have developed a penalty function-based three-state conical intersection optimization approach in the framework of the QM/MM method. We first present the fundamental formulation of this approach, and its algorithm and implementation in our package; then, we have carried out several pilot applications on molecular systems in vacuo and aqueous solution to demonstrate the efficiency of our implemented method. Our current developments enable efficient determination of three-state conical intersection structures of molecules in solution and biological systems, which is at the heart of understanding the photophysical and photochemical mechanisms of large systems at the atomistic level.

Molecular features in complex environment: Cooperative team players during excited state bond cleavage.

Photoinduced bond cleavage is often employed for the generation of highly reactive carbocations in solution and to study their reactivity. Diphenylmethyl derivatives are prominent precursors in polar and moderately polar solvents like acetonitrile or dichloromethane. Depending on the leaving group, the photoinduced bond cleavage occurs on a femtosecond to picosecond time scale and typically leads to two distinguishable products, the desired diphenylmethyl cations (Ph2CH+) and as competing by-product the diphenylmethyl radicals (). Conical intersections are the chief suspects for such ultrafast branching processes. We show for two typical examples, the neutral diphenylmethylchloride (Ph2CH–Cl) and the charged diphenylmethyltriphenylphosphonium ions () that the role of the conical intersections depends not only on the molecular features but also on the interplay with the environment. It turns out to differ significantly for both precursors. Our analysis is based on quantum chemical and quantum dynamical calculations. For comparison, we use ultrafast transient absorption measurements. In case of Ph2CH–Cl, we can directly connect the observed signals to two early three-state and two-state conical intersections, both close to the Franck-Condon region. In case of the , dynamic solvent effects are needed to activate a two-state conical intersection at larger distances along the reaction coordinate.

Surface hopping investigation of the relaxation dynamics in radical cations.

Ionization processes can lead to the formation of radical cations with population in several ionic states. In this study, we examine the dynamics of three radical cations starting from an excited ionic state using trajectory surface hopping dynamics in combination with multiconfigurational electronic structure methods. The efficiency of relaxation to the ground state is examined in an effort to understand better whether fragmentation of cations is likely to occur directly on excited states or after relaxation to the ground state. The results on cyclohexadiene, hexatriene, and uracil indicate that relaxation to the ground ionic state is very fast in these systems, while fragmentation before relaxation is rare. Ultrafast relaxation is facilitated by the close proximity of electronic states and the presence of two- and three-state conical intersections. Examining the properties of the systems in the Franck-Condon region can give some insight into the subsequent dynamics.

Measurement of Ionic Resonances in Alkyl Phenyl Ketone Cations via Infrared Strong Field Mass Spectrometry

Strong-field excitation of alkyl phenyl ketone molecules reveals an electronic resonance at 1370 nm in the radical cations upon measuring mass spectra as a function of excitation wavelength from 1240 to 1550 nm. The ratio of the benzoyl fragment ion to parent ion signal in acetophenone increases from 1:1.5 at 1240 nm excitation to 5:1 at 1370 nm (0.9 eV), and back to 1:1 at 1450 nm. Unlike acetophenone and propiophenone, the homologous molecules acetone and ethylbenzene exhibit no wavelength-dependent fragmentation patterns over the range from 1240 to 1550 nm, supporting the hypothesis that the electronic structure of the alkyl phenyl ketone cation enables the one-photon transition. Calculations on the acetophenone and propiophenone radical cations show the existence of a bright state, D2, 0.87 and 0.88 eV, respectively, above the ground-state D0 minimum. Calculations of the potential energy surfaces of the acetophenone radical cation suggest that a D2 → D0 radiationless transition precedes dissociation on D0. Upon population transfer to the D2 surface, the wavepacket motion is directed toward a three-state conical intersection (D0/D1/D2) that facilitates the photodissociation by converting electronic to vibrational energy on the D0 surface.

Nuclear dynamics for a three-state Jahn–Teller model system

We report wavepacket dynamics on a model system with a three-state conical intersection. Quantum wavepacket dynamics using the multiconfigurational time-dependent Hartree method have been carried out for the T ⊗ (e + t(2)) Jahn-Teller problem, using a Jahn-Teller vibronic model Hamiltonian. The effects of the magnitude of the coupling parameters and of the initial position of the wavepacket on the dynamics around the three-state conical intersection have been considered. It was found that the effect of the coupling strength is not dramatic for the population transfer in most cases, but the details of the dynamics and the involvement of the different modes are affected by it.

Inside Cover: A Time‐Dependent Picture of the Ultrafast Deactivation of keto‐Cytosine Including Three‐State Conical Intersections (ChemPhysChem 17/2010)

The relaxation mechanism of cytosine is investigated by L. González and J. González-Vázquez on p. 3617 using ab initio molecular dynamics. Possible deactivation pathways include three-state conical intersections.

A Time‐Dependent Picture of the Ultrafast Deactivation of keto‐Cytosine Including Three‐State Conical Intersections

Using mixed quantum-classical dynamics, the lowest part of the UV absorption spectrum and the first deactivation steps of keto-cytosine have been investigated. The spectrum shows several strong peaks, which mainly come from the S(1) and S(2) states, with minor contributions from the S(3). The semiclassical trajectories, launched from these three states, clearly indicate that at least four states are involved in the relaxation of keto-cytosine to the ground state. Non-adiabatic transfer between the ππ* and nπ* excited states and deactivation via three-state conical intersections is observed in the very early stage of the dynamics. In less than 100 fs, a large amount of population is deactivated to the ground state via several mechanisms; some population remains trapped in the S(2) state. The latter two events can be connected to the fs and ps transients observed experimentally.

On the Extent and Connectivity of Conical Intersection Seams and the Effects of Three-State Intersections

We discuss the connectivity of intersection spaces and the role of minimal energy points within these intersection spaces (minimal energy conical intersections or MECIs) in promoting nonadiabatic transitions. We focus on malonaldeyde as a specific example, where there is a low-lying three-state conical intersection. This three-state intersection is the global minimum on the bright excited electronic state, but it plays a limited role in population transfer in our ab initio multiple spawning (AIMS) simulations because the molecule must traverse a series of two-state conical intersections to reach the three-state intersection. Due to the differences in seam space dimensionality separating conventional (two-state) and three-state intersections, we suggest that dynamical effects arising directly from a three-state intersection may prove difficult to observe in general. We also use a newly developed method for intersection optimization with geometric constraints to demonstrate the connectivity of all the stationary points in the intersection spaces for malonaldehyde. This supports the conjecture that all intersection spaces are connected, and that three-state intersections play a key role in extending this connectivity to all pairs of states, e.g. the S1/S0 and S2/S1 intersection spaces.

Conical intersections and ultrafast intramolecular excited-state dynamics in nucleic acid bases and electron donor–acceptor molecules

Conical intersections play important roles in photochemistry and photobiology through their preeminent control over the course of electronic relaxation processes. In this Letter, we present results from a combined experimental and computational study of ultrafast internal conversion in nucleic acid bases and intramolecular charge transfer in N, N-dialkylaminobenzonitriles, which indicate that these photoprocesses occur through three-state conical intersections involving an intermediate electronic state.

Three-state conical intersections in cytosine and pyrimidinone bases

Three-state conical intersections have been located and characterized for cytosine and its analog 5-methyl-2-pyrimidinone using multireference configuration-interaction ab initio methods. The potential energy surfaces for each base contain three different three-state intersections: two different S(0)-S(1)-S(2) intersections (gs/pi pi(*)/n(N)pi(*) and gs/pi pi(*)/n(O)pi(*)) and an S(1)-S(2)-S(3) intersection (pi pi(*)/n(N)pi(*)/n(O)pi(*)). Two-state seam paths from these intersections are shown to be connected to previously reported two-state conical intersections. Nonadiabatic coupling terms have been calculated, and the effects of the proximal third state on these quantities are detailed. In particular, it is shown that when one of these loops incorporates more than one seam point, there is a profound and predictable effect on the phase of the nonadiabatic coupling terms, and as such provides a diagnostic for the presence and location of additional seams. In addition, it is shown that each of the three three-state conical intersections located on cytosine and 5-methyl-2-pyrimidinone is qualitatively similar between the two bases in terms of energies and character, implying that, like with the stationary points and two-state conical intersections previously reported for these two bases, there is an underlying pattern of energy surfaces for 2-pyrimidinone bases, in general, and this pattern also includes three-state conical intersections.

Two- and three-state conical intersections in the uracil cation

The excited states of the uracil radical cation have been studied theoretically using multireference configuration interaction and quasidegenerate perturbation theory methods. The ground state is an 2A″ state and three electronically excited states have been calculated with adiabatic energies 1.00 eV (D 1( 2A′)), 1.79 eV (D 2( 2A″)), and 2.31 eV (D 3( 2A′)). Two-state conical intersections between the ground state D 0 and the first excited state D 1 have been located 0.45 eV above the ground state minimum. Furthermore, three-state conical intersections between the states D 0, D 1 and D 2 have been located 0.95 eV above the D 0 minimum. These conical intersections may play an important role in photoionization processes in uracil.

On the Characterization of Three-State Conical Intersections Using a Group Homomorphism Approach: The Two-State Degeneracy Spaces

Second-order degenerate perturbation theory, in conjunction with the group homomorphism method for describing a similarity transformation, are used to characterize the subspace of two-state conical intersections contained in the branching space of a three-state conical intersection. It is shown by explicit calculation, using the lowest three-state conical intersection of (CH)3N2, that a second-order treatment yields highly accurate absolute energies, even at significant distances from the reference point of three-state intersection. The excellent agreement between the second order and ab initio results depends on the average energy component, which is computed using 5 first-order terms and 15 second-order terms. The second-order absolute energy change over the range rho = 0.0-0.3 au, where rho is the distance from the three-state conical intersection in the branching space coordinates, is approximately 6500 and 9500 cm(-1) for the E(1=2) and E(2=3) seams, respectively, with the maximum ab initio energy deviation from degeneracy of 200 cm(-1) occurring at rho = 0.3 au. The characteristic parameters gIJ and hIJ are also predicted to great accuracy, even at large rho, with the error growing to only 10-15% at rho = 0.3 au.

Ab Initio Molecular Dynamics of Excited-State Intramolecular Proton Transfer around a Three-State Conical Intersection in Malonaldehyde

Excited-state potential energy surface (PES) characterization is carried out at the CASSCF and MRSDCI levels, followed by ab initio dynamics simulation of excited-state intramolecular proton transfer (ESIPT) on the S2(pipi*) state in malonaldehyde. The proton-transfer transition state lies close to an S2/S1 conical intersection, leading to substantial coupling of proton transfer with electronic relaxation. Proton exchange proceeds freely on S2, but its duration is limited by competition with twisting out of the molecular plane. This rotamerization pathway leads to an intersection of the three lowest singlet states, providing the first detailed report of ab initio dynamics around a three-state intersection (3SI). There is a significant energy barrier to ESIPT on S1, and further pyramidalization of the twisted structure leads to the minimal energy S1/S0 intersection and energetic terminal point of excited-state dynamics. Kinetics and additional mechanistic details of these pathways are discussed. Significant depletion of the spectroscopic state and recovery of the ground state is seen within the first 250 fs after photoexcitation.

Three-State Conical Intersections in Nucleic Acid Bases

The involvement of three-state conical intersections in the photophysics and radiationless decay processes of the nucleobases has been investigated using multireference configuration interaction methods. Three-state conical intersections have been located for the pyrimidine base, uracil, and the purine base, adenine. In uracil, a three-state degeneracy between the S(0), S(1), and S(2) states has been located at 6.2 eV above the ground-state minimum energy. This energy is 0.4 eV higher than vertical excitation to S(2) and at least 1.3 eV higher than the two-state conical intersections found previously. In adenine, two different three-state degeneracies between the S(1), S(2), and S(3) states have been located at energies close to the vertical excitation energies. The energetics of these three-state conical intersections suggest they can play a role in a radiationless decay pathway present in adenine. The existence of two different seams of three-state conical intersections indicates that these features are common and complicate the potential energy surfaces of adenine and possibly many other aromatic molecules.

Competitive Decay at Two- and Three-State Conical Intersections in Excited-State Intramolecular Proton Transfer

We demonstrate the existence of a simultaneous degeneracy (not required by symmetry) of three electronic states in malonaldehyde. This is one of the first reports of such a triple degeneracy involving S0, S1, and S2 in a molecule with a closed-shell ground state. We further report on a two-state S2/S1 conical intersection which is higher in energy than the three-state intersection, but closer to the Franck-Condon point. First-principles quantum dynamics calculations of the photochemistry after excitation to S2 show that there is a competition between these intersections, with more than half of the population decaying to S1 through the higher energy S2/S1 intersection. Surprisingly, much of the population which makes it to the triple degeneracy point is not funneled directly to S0, but rather remains trapped on S1. We attribute this to the large dimensionality of the branching plane at a three-state intersection (the degeneracy is lifted along at least five distinct molecular displacements).