Jahn-Teller Conical Intersections Research Articles

Unraveling the Mechanisms of the Formations and Transformations of Metal-Ligand Charge Transfer States in [Ru(tpy)2]2+*: Consequences of Jahn-Teller Conical Intersections and the Pseudo-Jahn-Teller Effect.

This work investigates Jahn-Teller conical intersections (CoIns) and the pseudo-Jahn-Teller effect on the formations and transformations of the low-lying singlet metal-ligand charge transfer (1MLCT) excited states during the ultrafast evolution process of photoexcited [Ru(tpy)2]2+* (tpy = 2,2':6',2″-terpyridine). Longuet-Higgins' geometric phase analyses indicate that the potential energy surface (PES) crossing between charge transfer states 1MLCT1 and 1MLCT2 is a CoIn, originating from the change in diabatic Hamiltonian matrix elements around the CoIn. Moreover, an E⊗(b1 + b2) Jahn-Teller distortion can occur around the Franck-Condon and minimal energy CoIn (MECI) configurations, causing the molecule to distort spontaneously from the high-symmetry D2d configuration to C2v symmetry configurations that are close to it. Furthermore, the pseudo-Jahn-Teller effect can cause the molecule to distort further from C2v to C1 geometries since the former is a second-order saddle point on the whole dimensional PES but the latter is a true minimum. Eight minima in total are symmetrically distributed around the MECI. These minima are connected by the interligand electron transfer, the charge transfer, and the butterfly-like conformational inversion reactions, all of which have extremely small energy barriers.

Jahn-Teller effect among electronic resonant states of H3

SynopsisThe Jahn-Teller conical intersection among the electronic resonant states of H3 is studied. We have performed electron scattering calculations and obtained complex adiabatic potential energy surfaces that we describe using a generalized Jahn-Teller Hamiltonian. The non-adiabatic coupling and the geometric phase were also investigated.

Conical intersections and nonadiabatic coupling terms in 1,3,5-C6H3F3 +: A six state beyond Born-Oppenheimer treatment.

In order to circumvent numerical inaccuracy originating from the singularity of nonadiabatic coupling terms (NACTs), we need to perform kinetically coupled adiabatic to potentially coupled diabatic transformation of the nuclear Schrödinger Equation. Such a transformation is difficult to achieve for higher dimensional sub-Hilbert spaces due to inherent complicacy of adiabatic to diabatic transformation (ADT) equations. Nevertheless, detailed expressions of ADT equations are formulated for six coupled electronic states for the first time and their validity is extensively examined for a well-known radical cation, namely, 1,3,5-C6H3F3 + (TFBZ+). While implementing this formulation, we compute ab initio adiabatic potential energy surfaces (PESs) and NACTs within the low-lying six electronic states (X̃2E'', Ã2A2 '', B̃2E', and C̃2A2 '), where several types of nonadiabatic interactions, like Jahn-Teller conical intersections (CI), accidental CIs, accidental seams (series of degenerate points), and pseudo Jahn-Teller interactions can be observed over the Franck-Condon region of nuclear configuration space. Those interactions are depicted by exploring degenerate components of C-C asymmetric stretching, C-C symmetric stretching, and C-C-C scissoring motion (Q9x, Q9y, Q10x, Q10y, Q12x, and Q12y) to compute complete active space self-consistent field level adiabatic PESs and NACTs as implemented in the MOLPRO quantum chemistry package. Subsequently, we perform the ADT using our newly devised fifteen (15) ADT equations to locate the position of CIs, verify the quantization of NACTs, and to construct highly accurate diabatic PESs.

Nonadiabatic conical nodes are near but not at an elliptical conical intersection

Numerical nonadiabatic eigenfunctions are calculated for 2D Jahn-Teller conical intersections with the elliptical shape found in square-symmetric molecules. Hunter’s exact factorization is used to visualize the complete real-valued vibronic eigenfunctions. Point nodes are observed in the vibrational factor and the nodal structures are compared with those for circularly symmetric conical intersections. Without pseudo-rotation symmetry, essential nth order nodes at circular conical intersections split into n accidental conical nodes that are near but not at the elliptical conical intersection. For each eigenfunction, the integer electronic index that measures electronic state vector rotation around a closed vibrational path is locally stable to perturbations. Pairs of oppositely signed conical nodes can be generated or annihilated as Hamiltonian parameters are continuously varied. At annihilation, a tangential node with an electronic index of zero is created. For elliptical conical intersections, all eigenfunctions examined generate nonzero total vibrational probability density at the conical intersection.

Topological Effects in Vibronically Coupled Degenerate Electronic States: A Case Study on Nitrate and Benzene Radical Cation.

We carry out detailed investigation for topological effects of two molecular systems, NO3 radical and C6H6+ (Bz+) radical cation, where the dressed adiabatic, dressed diabatic, and adiabatic-via-dressed diabatic potential energy curves (PECs) are generated employing ab initio calculated adiabatic and diabatic potential energy surfaces (PESs). We have implemented beyond Born–Oppenheimer (BBO) theory for constructing smooth, single-valued, and continuous diabatic PESs for five coupled electronic states [J. Phys. Chem. A2017,121, 6314–6326]. In the case of NO3 radical, the nonadiabatic coupling terms (NACTs) among the low-lying five electronic states, namely, X̃2A2′ (12B2), A~2E″ (12A2 and 12B1), and B~2E′ (12A1 and 22B2), bear the signature of Jahn–Teller (JT) interactions, pseudo JT (PJT) interactions, and accidental conical intersections (CIs). Similarly, Bz+ radical cation also exhibits JT, PJT, and accidental CIs in the interested domain of nuclear configuration space. In order to generate dressed PECs, two components of degenerate in-plane asymmetric stretching modes are selectively chosen for both the molecular species (Q3x–Q3y pair for NO3 radical and Q16x–Q16y pair for Bz+ radical cation). The JT coupling between the electronic states is essentially originated through the asymmetric stretching normal mode pair, where the coupling elements exhibit symmetric and nonlinear functional behavior along Q3x and Q16x normal modes.

Vibrational and Nonadiabatic Coherence in 2D Electronic Spectroscopy, the Jahn-Teller Effect, and Energy Transfer.

Femtosecond two-dimensional (2D) Fourier transform spectroscopy generates and probes several types of coherence that characterize the couplings between vibrational and electronic motions. These couplings have been studied in molecules with Jahn-Teller conical intersections, pseudo-Jahn-Teller funnels, dimers, molecular aggregates, photosynthetic light harvesting complexes, and photosynthetic reaction centers. All have closely related Hamiltonians and at least two types of vibrations, including one that is decoupled from the electronic dynamics and one that is nonadiabatically coupled. Polarized pulse sequences can often be used to distinguish these types of vibrations. Electronic coherences are rapidly obscured by inhomogeneous dephasing. The longest-lived coherences in these systems arise from delocalized vibrations on the ground electronic state that are enhanced by a nonadiabatic Raman excitation process. These characterize the initial excited-state dynamics. 2D oscillation maps are beginning to isolate the medium lifetime vibronic coherences that report on subsequent stages of the excited-state dynamics.

Jahn–Teller and coupled Jahn–Teller/Renner–Teller effects in the calculation of adiabatic-to-diabatic transformation angle for the lowest three 2A′ states of NH2 (NHH)

We report here on the first study of topological effects for the NHH system, as carried out by treating simultaneously the two dominant effects of this system, namely, the Jahn–Teller (JT) effect and the Renner–Teller (RT) effect. Both the effects were treated rigorously as demanded by the Born–Oppenheimer approach. No approximations were made and in those cases where convergence was required, it was achieved by including the required number of states. The study concentrates on calculating the privileged adiabatic-to-diabatic transformation (ADT) angle γ12, along closed contours, which is the only needed angle to carry out the ADT in the case of relatively low energies. For this purpose, three coupled A′-states are usually considered and only in the last two extreme cases, where the area in configuration space becomes relatively large, namely 15–35 Å2, we had also to include an A″ state (the second Δ-state), a situation that enforces the more elaborate (JT/RT) effect. In this paper, we also report on potential energies as calculated along the above-mentioned contours. Among them are considered the energies associated with the two adiabatic Δ-states, 1A′ and 1A″, of different symmetry and therefore are responsible for the RT effect. These states are expected to be degenerate along the collinear axis. It was revealed that these states, in contrast to the Renner theory, are not degenerate along a finite interval of the collinear axis at the vicinity of the JT conical intersection (JT-CI). In other words, the JT-CI annihilates the RT degeneracy along this interval.

Two-dimensional Fourier transform electronic spectroscopy at a conical intersection

We report measurement and modeling of two-dimensional (2D) electronic spectra of a silicon naphthalocyanine (SiNc) in benzonitrile, a system for which the polarization anisotropy reveals passage through a square-symmetric Jahn-Teller conical intersection in ∼100 fs [D. A. Farrow, W. Qian, E. R. Smith, A. A. Ferro, and D. M. Jonas, J. Chem. Phys. 128, 144510 (2008)]. The measured 2D Fourier transform (FT) spectra indicate loss of electronic coherence on a similar timescale. The 2D spectra arising from femtosecond vibronic dynamics through the conical funnel are modeled by full non-adiabatic treatment of the coupled electronic and vibrational dynamics for a pair of un-damped Jahn-Teller active vibrations responsible for both electronic decoherence and population transfer. Additional damped Jahn-Teller active modes that can cause only decoherence or population transfer are treated with analytical response functions that can be incorporated into the numerical non-adiabatic calculation by exploiting symmetry assignment of degenerate vibronic eigenstates to one of two electronic states. Franck-Condon active totally symmetric modes are incorporated analytically. The calculations reveal that these conical intersection dynamics alone are incapable of destroying the coherence of the initially prepared wavepacket on the experimentally observed timescale and predict an unobserved recurrence in the photon echo slice at ∼200 fs. Agreement with the experimental two-dimensional electronic spectra necessitates a role for totally symmetric vibrational dynamics in causing the echo slice to decay on a ∼100 fs timescale. This extended model also reproduces the ∼100 fs ultrafast electronic anisotropy decay in SiNc when an "asymmetric solvation mode" with a small stabilization energy of ∼2 cm(-1) is included. Although calculations show that inhomogeneities in the energy gap between excited states can broaden the anti-diagonal 2D lineshape, the anti-diagonal width is dominated by totally symmetric vibrational motions in SiNc. For this shallow conical intersection, the non-adiabatic dynamics destroy electronic coherence more slowly than they destroy electronic alignment.

Dressed Adiabatic and Diabatic Potentials for the Renner–Teller/Jahn–Teller F + H2System

We follow a suggestion by Lipoff and Herschbach (Mol. Phys. 2010, 108, 1133) and compare dressed potentials to get insight regarding the low-energy dynamics (e.g., cold reaction) taking place in molecular systems. In this particular case we are interested in studying the effect of topological effects on the interacting atoms. For this purpose we consider dressed adiabatic and adiabatic-via-dressed diabatic potentials in the entrance channel of reactive systems. In a recent study of this kind for the F + H2 system (J. Chem. Phys. 2012, 136, 054104), we revealed that a single Jahn-Teller conical intersection is expected to have only a mild effect on the dynamics. This fact implies that the Born-Oppenheimer approximation is expected to be valid for this system at least for low enough energies. In the present article this study is extended to include also the Renner-Teller effect as produced by the two lower degenerate Π states. As a result we consider three electronic states which enforce the use of the adiabatic-to-diabatic transformation (ADT) matrix A. The results indicate that the topological effects as produced by the extended Renner/Teller-Jahn/Teller system are strong to the level that, most likely, abolishes the Born-Oppenheimer approximation for this system, all this in contrast to our previous findings (see above publication).

A tri-atomic Renner-Teller system entangled with Jahn-Teller conical intersections

The present study concentrates on a situation where a Renner-Teller (RT) system is entangled with Jahn-Teller (JT) conical intersections. Studies of this type were performed in the past for contours that surround the RT seam located along the collinear axis [see, for instance, G. J. Halász, Á. Vibók, R. Baer, and M. Baer, J. Chem. Phys. 125, 094102 (2006)]. The present study is characterized by planar contours that intersect the collinear axis, thus, forming a unique type of RT-non-adiabatic coupling terms (NACT) expressed in terms of Dirac-δ functions. Consequently, to calculate the required adiabatic-to-diabatic (mixing) angles, a new approach is developed. During this study we revealed the existence of a novel molecular parameter, η, which yields the coupling between the RT and the JT NACTs. This parameter was found to be a pure number η = 22/π (and therefore independent of any particular molecular system) and is designated as Renner-Jahn coupling parameter. The present study also reveals an unexpected result of the following kind: It is well known that each (complete) group of states, responsible for either the JT-effect or the RT-effect, forms a Hilbert space of its own. However, the entanglement between these two effects forms a third effect, namely, the RT/JT effect and the states that take part in it form a different Hilbert space.

Short-Time Events, Coherence, and Structural Dynamics in Photochemistry of Aqueous Halogenated Transition Metal Dianions

Ultrafast pump-probe spectroscopy, time-resolved x-ray absorption, and computational photochemistry elucidate the photochemical pathway of hexabromoplatinate dianions that propagates through distortions of nascent penta- bromoplatinate anions caused by Jahn-Teller conical intersections and terminates at aquated product complexes.

TDDFT study on quantization behaviors of nonadiabatic couplings in polyatomic systems

AbstractWe present extensive calculations on the quantization behaviors of first‐order nonadiabatic couplings (NAC) in polyatomic systems, using the method based on time‐dependent density functional theory (TDDFT). Along circular contours around Jahn–Teller conical intersections at various symmetries, such as D4h and D6h, the angular NAC are found to show apparent dependence on the contour angle, no matter how close the conical intersections are approached. This is in contrast to that the angular NAC in triatomic Jahn–Teller systems (D3h) converge to the quantized value of 1/2. The oscillatory feature of our calculated curves qualitatively resembles the analytic result of angular NAC around elliptic conical intersections in the small‐displacement limit. Furthermore, by performing the integral along the whole contour, the quantization rule on the integral of the angular NAC holds for all cases, which gives the geometric phase with a value of π. On the other hand, the angular NAC in the immediate vicinity of Renner–Teller intersections are shown to be always 1. This observation can be understood from the fact that the molecular symmetry property of the Renner–Teller intersections is always determined by the linear atomic chain. Further analysis of our results on Renner–Teller systems shows that although the quantization behavior of angular NAC can determine all NAC vectors on each atom for the triatomic systems, it cannot for the systems with more than three atoms. The NAC vectors of the latter systems are found to show both common and distinct features with respect to the atomic number and species by our TDDFT calculations. © 2012 Wiley Periodicals, Inc.

The Jahn-Teller effect in the triply degenerate electronic state of methane radical cation

A quantum dynamics study is performed to examine the complex nuclear motion underlying the first photoelectron band of methane. The broad and highly overlapping structures of the latter are found to originate from transitions to the ground electronic state, X(2)T(2), of the methane radical cation. Ab initio calculations have also been carried out to establish the potential energy surfaces for the triply degenerate electronic manifold of CH(4)(+). A suitable diabatic vibronic Hamiltonian has been devised and the nonadiabatic effects due to Jahn-Teller conical intersections on the vibronic dynamics investigated in detail. The theoretical results show fair accord with experiment.

Second-order nonadiabatic couplings from time-dependent density functional theory: Evaluation in the immediate vicinity of Jahn-Teller/Renner-Teller intersections

For a rigorous quantum simulation of nonadiabatic dynamics of electrons and nuclei, knowledge of not only the first-order but also the second-order nonadiabatic couplings (NACs) is required. Here, we propose a method to efficiently calculate the second-order NAC from time-dependent density functional theory (TDDFT), on the basis of the Casida ansatz adapted for the computation of first-order NAC, which has been justified in our previous work and can be shown to be valid for calculating second-order NAC between ground state and singly excited states within the Tamm-Dancoff approximation. Test calculations of the second-order NAC in the immediate vicinity of Jahn-Teller and Renner-Teller intersections show that calculation results from TDDFT, combined with modified linear response theory, agree well with the prediction from the Jahn-Teller/Renner-Teller models. Contrary to the diverging behavior of the first-order NAC near all types of intersection points, the Cartesian components of the second-order NAC are shown to be negligibly small near Renner-Teller glancing intersections, while they are significantly large near the Jahn-Teller conical intersections. Nevertheless, the components of the second-order NAC can cancel each other to a large extent in Jahn-Teller systems, indicating the background of neglecting the second-order NAC in practical dynamics simulations. On the other hand, it is shown that such a cancellation becomes less effective in an elliptic Jahn-Teller system and thus the role of second-order NAC needs to be evaluated in the rigorous framework. Our study shows that TDDFT is promising to provide accurate data of NAC for full quantum mechanical simulation of nonadiabatic processes.

Nonadiabatic couplings from time-dependent density functional theory. II. Successes and challenges of the pseudopotential approximation

We present extensive calculations of nonadiabatic couplings (NACs) between the electronically ground and excited states of molecules, using time-dependent density functional theory (TDDFT) within (modified) linear response [C. Hu et al. J. Chem. Phys. 127, 064103 (2007)]. Our approach is implemented in the pseudopotential framework, with the consideration of nonlinear core corrections. The features of either the ordinary Jahn-Teller conical intersections in X(3) (X=Li, Na, K, Cu, Ag, Au) trimers, or the elliptic Jahn-Teller conical intersections in NaH(2), have been well reproduced. In particular, anticipated results for the H-H(2) collision near the avoided crossing are obtained, showing appealing improvement over the first, real-time, TDDFT calculation. The other important type of intersections, Renner-Teller glancing intersection, has also been studied for several typical molecular systems (BH(2), AlH(2), CH(2)(+), SiH(2)(+)), giving results in reasonable agreement with the theoretical model. Despite these successes, it is found that for some systems, including both Jahn-Teller and Renner-Teller systems, the pseudopotential scheme might give inaccurate results for some NAC components on nonhydrogen atoms. By trying different construction schemes of pseudopotentials, e.g., using local pseudopotentials, the results of NACs are found scheme-dependent and show improvement for some cases. Since there is much freedom in constructing ab initio nonlocal pseudopotentials, our findings on TDDFT calculation of NACs in the pseudopotential scheme might be helpful to give clues for constructing more "realistic" pseudopotentials.

Jahn-Teller and related conical intersections in the benzene radical cation and the monofluoro derivate

The multi-state multi-mode vibronic interactions in the benzene radical cation and its monofluoro derivative have been investigated theoretically, based on high-level electronic structure calculations for the system parameters and a quantum treatment of the nuclear motion. The available experimental data are well reproduced. The interplay of different vibronic coupling mechanisms is pointed out leading to multiple nonadiabatic effects. The comparison between the two species treated reveals the intimate connection between Jahn-Teller conical intersections and their more general counterparts occurring between states of different spatial symmetries.

Wavepacket dynamics study of Cr(CO)5 after formation by photodissociation: relaxation through an (E ⊕ A) ⊗ e Jahn–Teller conical intersection

In the ultrafast photodissociation of Cr(CO)6, Cr(CO)5 is formed within 50 fs. Initially in an excited state, a Jahn–Teller (E ⊗ e) conical intersection is believed to then act as an efficient decay funnel to the ground state. Here, we present a Hamiltonian representing the first three electronic states of Cr(CO)5, obtained by fitting the linear vibronic coupling model to calculations using a complete active space self-consistent field (CASSCF) wavefunction. The intersection is in fact found to involve (( E ⊕ A) ⊗ e) pseudo-Jahn–Teller coupling, with the singly degenerate state playing an important role. The results of wavepacket dynamics using the multi-configuration time-dependent Hartree (MCTDH) method show that this model is consistent with the experimental data.

Renner-Teller nonadiabatic coupling terms: An ab-initio study of the HNH molecule

In this Communication we present the first theoretical/numerical treatment of nonadiabatic coupling terms (NACT) that originate from the Renner-Teller (RT) model, namely, those that follow from the splitting of an electronic level of a linear molecule when it becomes bent. These two newly formed states are characterized by different symmetries and are designated as A and B. Our main findings: (1) The RT NACTs are quantized as long as they are calculated close enough to collinear configuration of the molecule (in this case HNH). Their value is tau = 1 (the Jahn-Teller values in similar situations, are tau = (1/2)). (2) Calculation of RT NACTs at bent configurations (i.e., at a distance from the linear axis) yield decreased values, sometimes by more than 50%. This last finding implies that in strongly bent configurations the two-state Hilbert subspace (formed by the above mentioned A and B states) is affected by upper states, most likely via Jahn-Teller conical intersections. (3) This study has also important practical implications. The fact that the RT NACTs decrease in (strongly) bent situations implies that analyzing spectroscopic data employing only the two Pi-states may not be sufficient in order to achieve the required accuracy.

On the (E⊗e)-Jahn-Teller conical intersections in the 3p(E′) and 3d(E″) Rydberg electronic states of triatomic hydrogen

The static and dynamic aspects of the Jahn-Teller (JT) interactions in the 3p(E') and 3d(E") Rydberg electronic states of H3 are analyzed theoretically. The static aspects are discussed based on recent ab initio quantum chemistry results, and the dynamic aspects are examined in terms of the vibronic spectra and nonradiative decay behavior of these states. The adiabatic potential-energy surfaces of these degenerate electronic states are derived from extensive ab initio calculations. The calculated adiabatic potential-energy surfaces are diabatized following our earlier study on this system in its 2p(E') ground electronic state. The nuclear dynamics on the resulting conically intersecting manifold of electronic states is studied by a time-dependent wave-packet approach. Calculations are performed both for the uncoupled and coupled state situations in order to understand the importance of nonadiabatic interactions due to the JT conical intersections in these excited Rydberg electronic states.

Conical intersections: A perspective on the computation of spectroscopic Jahn–Teller parameters and the degenerate ‘intersection space’

We present a perspective on the computation and interpretation of force constants at points of symmetry-induced (Jahn-Teller) conical intersection. Our method is based upon the projection of the 'branching space' from the full (3N - 6)-dimensional Hessian for each component of a degenerate electronic state. For Jahn-Teller active molecules, this has the effect of removing the linear Jahn-Teller coupling from all but the interstate coupling and gradient difference vectors. The quadratic coupling constants are determined by the splitting of the harmonic vibrational frequencies within degenerate vibrational normal coordinates of the 'intersection space'. The potential energy surface topology along these normal modes is analogous to the Renner-Teller effect occurring in orbitally degenerate linear molecules. Our methodology gives a straightforward theoretical analysis of the various Jahn-Teller intersections and allows the determination of the seam curvature. Thus, we are in a position to compute the various Jahn-Teller coupling constants, in a particular coordinate system, and in addition to determine the nature of the high-symmetry Jahn-Teller geometry (i.e., minimum or saddle-point on the seam). We illustrate these concepts with various examples of different Jahn-Teller conical intersections in some small molecules.