The excited states of K3 cluster: The molecular symmetry adapted non-adiabatic coupling terms and diabatic Hamiltonian matrix

Photoelectron spectra of benzene: Can path dependent diabatic surfaces provide unique observables?

While carrying out Beyond Born-Oppenheimer theory based diabatization, the solutions of adiabatic-to-diabatic transformation equations depend on the paths of integration over two-dimensional cross-sections of multi-dimensional space of nuclear degrees of freedom. It is shown that such path-dependent solutions leading to diabatic potential energy surface matrices computed along any two different paths are related through an orthogonal matrix, and thereby, those surface matrices should provide unique observables. While exploring the numerical validity of the theoretical framework, we construct diabatic Hamiltonians for the five low-lying electronic states (X̃2E1g, B̃2E2g, and C̃2A2u) of benzene radical cation (C6H6+) along three different approaches of contour integration over two dimensional nuclear planes constituted by seven non-adiabatically active normal modes. Three different diabatic surface matrices are further employed to generate the photoelectron spectra of the benzene molecule (C6H6). It is interesting to note that the spectral peak positions and intensity patterns for all three cases are almost close to each other and also exhibit very good agreement with the experimental results.

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.

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. A 2017, 121, 6314-6326]. In the case of NO₃ radical, the nonadiabatic coupling terms (NACTs) among the low-lying five electronic states, namely, X̃ ²A₂ ^' (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 (Q _3x -Q _3y pair for NO₃ radical and Q _16x -Q _16y 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 Q _3x and Q _16x normal modes.

Practical approximation of the non-adiabatic coupling terms for same-symmetry interstate crossings by using adiabatic potential energies only

A very simple equation, F_ij^App=[(∂²(V_i^a-V_j^a)/∂Q²)/(V_i^a-V_j^a)]^1/2/2, giving a reliable magnitude of non-adiabatic coupling terms (NACTs, F_ij's) based on adiabatic potential energies only (V_i^a and V_j^a) was discovered, and its reliability was tested for several prototypes of same-symmetry interstate crossings in LiF, C₂, NH₃Cl, and C₆H₅SH molecules. Our theoretical derivation starts from the analysis of the relationship between the Lorentzian dependence of NACTs along a diabatization coordinate and the well-established linear vibronic coupling scheme. This analysis results in a very simple equation, α=2κ/Δ_c, enabling the evaluation of the Lorentz function α parameter in terms of the coupling constant κ and the energy gap Δ_c (Δ_c=|V_i^a-V_j^a|_Qc ) between adiabatic states at the crossing point Q_C. Subsequently, it was shown that Q_C corresponds to the point where F_ij^App exhibit maximum values if we set the coupling parameter as κ=[(V_i^a-V_j^a)⋅(∂²(V_i^a-V_j^a)/∂Q²)]_Qc^1/2/2. Finally, we conjectured that this relation could give reasonable values of NACTs not only at the crossing point but also at other geometries near Q_C. In this final approximation, the pre-defined crossing point Q_C is not required. The results of our test demonstrate that the approximation works much better than initially expected. The present new method does not depend on the selection of an ab initio method for adiabatic electronic states but is currently limited to local non-adiabatic regions where only two electronic states are dominantly involved within a nuclear degree of freedom.

Multiple conical intersections in small linear parameter Jahn-Teller systems: the DMBE potential energy surface of ground-state C3 revisited

A new single-sheeted DMBE potential energy surface for ground-state C3 is reported. The novel analytical form accurately describes the three symmetry-equivalent C2v disjoint seams, in addition to the symmetry-required D3h one, over the entire configuration space. The present formalism warrants by built-in construction the confluence of the above crossings, and the rotation-in-plane of the C2v seams when the perimeter of the molecule fluctuates. Up to 1050 ab initio energies have been employed in the calibration procedure, of which 421 map the loci of intersection. The calculated energies have been scaled to account for the incompleteness of the basis set and truncation of the MRCI expansion, and fitted analytically with chemical accuracy. The novel form is shown to accurately mimic the region defined by the 4 conical intersections, while exhibiting similar attributes to the previously reported one [J. Chem. Phys., 2015, 143, 074302] at the regions of configuration space away from the crossing seams. Despite being mainly addressed to C3, the present approach should be applicable to adiabatic PESs of any X3 system experiencing similar topological attributes, in particular the small-linear-parameter Jahn-Teller molecules.

Five Electronic State Beyond Born-Oppenheimer Equations and Their Applications to Nitrate and Benzene Radical Cation

We present explicit form of Adiabatic to Diabatic Transformation (ADT) equations and expressions of non-adiabatic coupling terms (NACTs) for a coupled five-state electronic manifold in terms of ADT angles between electronic wave functions. ADT matrices eliminate the numerical instability arising from singularity of NACTs and transform the adiabatic Schrödinger equation to its diabatic form. Two real molecular systems NO₃ and C₆H₆⁺ (Bz⁺) are selectively chosen for the demonstration of workability of those equations. We examine the NACTs among the lowest five electronic states of the NO₃ radical [X̃²A₂^' (1²B₂), òE″ (1²A₂ and 1²B₁) and B̃²E' (1²A₁ and 2²B₂)], in which all types of non-adiabatic interactions, that is, Jahn-Teller (JT) interactions, Pseudo Jahn-Teller (PJT) interactions, and accidental conical intersections (CIs) are present. On the other hand, lowest five electronic states of Bz⁺ [X̃²E_1g (1²B_3g and 1²B_2g), B̃²E_2g (1²A_g and 1²B_1g), and C̃²A_2u (1²B_1u)] depict similar kind of complex feature of non-adiabatic effects. For NO₃ radical, the two components of degenerate in-plane asymmetric stretching mode are taken as a plane of nuclear configuration space (CS), whereas in case of Bz⁺, two pairs are chosen: One is the pair of components of degenerate in-plane asymmetric stretching mode, and the other one is constituted with one of the components each from out-of-plane degenerate bend and in-plane degenerate asymmetric stretching modes. We calculate ab initio adiabatic potential energy surfaces (PESs) and NACTs among the lowest five electronic states at the CASSCF level using MOLPRO quantum chemistry package. Subsequently, the ADT is performed using those newly developed equations to validate the positions of the CIs, evaluate the ADT angles and construct smooth, symmetric, and continuous diabatic PESs for both the molecular systems.

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.