Molecular Symmetry Properties of Conical Intersections and Nonadiabatic Coupling Terms: Theory and Quantum Chemical Demonstration for Cyclopenta-2,4-dienimine (C5H4NH)

Beyond Born-Oppenheimer based diabatic surfaces of 1,3,5-C6H3F3+ to generate the photoelectron spectra using time-dependent discrete variable representation approach

In this article, Beyond Born-Oppenheimer (BBO) treatment is implemented to construct diabatic potential energy surfaces (PESs) of 1,3,5-C₆H₃F₃⁺ over a series [eighteen (18)] of two-dimensional (2D) nuclear planes constituted with eleven normal modes (Q₂, Q_9x, Q_9y, Q_13x, Q_13y, Q_18x, Q_18y, Q_10x, Q_10y, Q_12x and Q_12y) to include all possible nonadiabatic interactions among six coupled electronic states (X̃²E'', , B̃²E' and ). We had formulated explicit expressions of adiabatic to diabatic transformation (ADT) equations [S. Mukherjee, J. Dutta, B. Mukherjee, S. Sardar and S. Adhikari, J. Chem. Phys., 2019, 150, 064308] for the same system forming six state sub-Hilbert space and at present, these ADT equations are solved by incorporating MRCI level ab initio adiabatic PESs and CP-MCSCF calculated nonadiabatic coupling terms (NACTs) to derive diabatic PESs and couplings. Such single-valued, smooth, symmetric and continuous diabatic surface matrices are utilized to carry out multi-state multi-mode nuclear dynamics with the help of time-dependent discrete variable representation (TDDVR) methodology to compute the photoelectron (PE) spectra of 1,3,5-C₆H₃F₃. Our theoretically calculated spectra for X̃²E'', and states using BBO treatment and TDDVR dynamics show peak by peak correspondence with the experimental results as well as better than the findings of the multi-configuration time-dependent Hartree (MCTDH) method.

The role of electron-nuclear coupling on multi-state photoelectron spectra, scattering processes and phase transitions

We present first principle based beyond Born-Oppenheimer (BBO) theory and its applications on various models as well as realistic spectroscopic and scattering processes, where the Jahn-Teller (JT) theory is brought in conjunction with the BBO approach on the phase transition of lanthanide complexes. Over one and half decades, our development of BBO theory is demonstrated with ab initio calculations on representative molecules of spectroscopic interest (NO2 radical, Na3 and K3 clusters, NO3 radical, C6H6+ and 1,3,5-C6H3F3+ radical cations) as well as triatomic reactive scattering processes (H+ + H2 and F + H2). Such an approach exhibits the effect of JT, Renner-Teller (RT) and pseudo Jahn-Teller (PJT) type of interactions. While implementing the BBO theory, we generate highly accurate diabatic potential energy surfaces (PESs) to carry out quantum dynamics calculation and find excellent agreement with experimental photoelectron spectra of spectroscopic systems and cross-sections/rate constants of scattering processes. On the other hand, such electron-nuclear couplings incorporated through JT theory play a crucial role in dictating higher energy satellite transitions in the dielectric function spectra of the LaMnO3 complex. Overall, this article thoroughly sketches the current perspective of the BBO approach and its connection with JT theory with various applications on physical and chemical processes.

Ab initio constructed diabatic surfaces of NO2 and the photodetachment spectra of its anion

A thorough investigation has been performed for electronic structure, topological effect, and nuclear dynamics of NO2 molecule, where the adiabatic potential energy surfaces (PESs), conical intersections between the ground (X(2)A1) and the first excited state (A(2)B2), and the corresponding non-adiabatic coupling terms between those states are recalculated [Chem. Phys. 416, 11 (2013)] to achieve enough accuracy in dynamics. We employ beyond Born-Oppenheimer theory for these two state sub-Hilbert space to carry out adiabatic to diabatic transformation (ADT) to obtain the ADT angles and thereby, to construct single-valued, smooth, and continuous diabatic PESs. The analytic expressions for the adiabatic PESs and ADT angles are provided to represent a two-state three-mode diabatic Hamiltonian of NO2 for performing nuclear dynamics to calculate the photo-electron spectra of its anion. It appears that not only Jahn-Teller type coupling but also Renner-Teller interaction contributes significantly on the overall spectrum. The coupling between the electronic states (X(2)A1 and A(2)B2) of NO2 is essentially through the asymmetric stretching mode, where the functional form of such interaction is distinctly symmetric and non-linear.

Effects of molecular symmetry on quantum reaction dynamics: novel aspects of photoinduced nonadiabatic dynamics

Nonadiabatic coupling terms (NACTs) between different electronic states lead to fast radiationless decay in photoexcited molecules. Using molecular symmetry, i.e., symmetry with respect to permutation of identical nuclei and inversion of the molecule in space, the irreducible representations of the NACTs can be determined with a combination of molecular symmetry arguments and quantization rules. Here, we extend these symmetry rules for electronic states and coupling elements and demonstrate the importance of molecular symmetry for nonadiabatic nuclear dynamics. As an example, we consider the NACTs related to the torsion around the CN bond in C5H4NH. We present the results of quantum dynamical simulations of the photoinduced large amplitude torsion on three coupled electronic states and show how the interference between wavepackets leads to radiationless decay, which depends on the symmetry of the NACTs. Moreover, we show that the nuclear spin of the system determines the symmetry of the initial nuclear wave function and thus influences the torsional dynamics. This may open new possibilities for nuclear spin selective laser control of nuclear dynamics.

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.

Renner-Teller intersections along the collinear axes of polyatomic molecules: H2CN as a case study

The tetra-atomic C(2)H(2)(+) cation is known to form Renner-Teller-type intersections along its collinear axis. Not too long ago, we studied the nonadiabatic coupling terms (NACTs) of this molecule [G. J. Halász et al., J. Chem. Phys. 126, 154309 (2007)] and revealed two kinds of intersections. (i) By employing one of the hydrogens as a test particle, we revealed the fact that indeed the corresponding (angular) NACTs produce topological (Berry) phases that are equal to 2pi, which is a result anticipated in the case of Renner-Teller intersections. (ii) However, to our big surprise, repeating this study when one of the atoms (in this case a hydrogen) is shifted from the collinear arrangement yields for the corresponding topological phase a value that equals pi (and not 2pi). In other words, shifting (even slightly) one of the atoms from the collinear arrangement causes the intersection to change its character and become a Jahn-Teller intersection. This somewhat unexpected novel result was later further analyzed and confirmed by other groups [e.g., T. Vertesi and R. Englman, J. Phys. B 41, 025102 (2008)]. The present article is devoted to another tetra-atomic molecule, namely, the H(2)CN molecule, which just like the C(2)H(2)(+) ion, is characterized by Renner-Teller intersections along its collinear axis. Indeed, we revealed the existence of Renner-Teller intersections along the collinear axis, but in contrast to the C(2)H(2)(+) case a shift of one atom from the collinear arrangement did not form Jahn-Teller intersections. What we found instead is that the noncollinear molecule was not affected by the shift and kept its Renner-Teller character. Another issue treated in this article is the extension of (the two-state) Berry (topological) phase to situations with numerous strongly interacting states. So far the relevance of the Berry phase was tested for systems characterized by two isolated interacting states, although it is defined for any number of interacting states [M. V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984)]. We intend to show how to overcome this limitation and get a valid, fully justified definition of a Berry phase for an isolated system of any number of interacting states (as is expected).