Coupled 3D (J ≥ 0) Time-Dependent Wave Packet Calculation for the F + H2 Reaction on Accurate Ab Initio Multi-State Diabatic Potential Energy Surfaces.

We had calculated adiabatic potential energy surfaces (PESs), nonadiabatic, and spin-orbit (SO) coupling terms among the lowest three electronic states (12A', 22A', and 12A″) of the F + H2 system using the multireference configuration interaction (MRCI) level of theory, and the adiabatic-to-diabatic transformation equations were solved to formulate the diabatic Hamiltonian matrix [J. Chem. Phys. 2020, 153, 174301] for the entire region of the nuclear configuration space. The accuracy of such diabatic PESs is explored by performing scattering calculations to evaluate integral cross sections (ICSs) and rate constants. The nonadiabatic and SO effects are studied by utilizing coupled 3D time-dependent wave packet formalism with zero and nonzero total angular momentum on multiple adiabatic/diabatic surfaces calculation. We depict the convergence profiles of reaction probabilities for the reactive as well as nonreactive processes on various electronic states at different collision energies with respect to total angular momentum including all helicity quantum numbers. Finally, total ICSs are calculated as functions of collision energies for the initial rovibrational state (v = 0, j = 0) of the H2 molecule along with the temperature-dependent rate coefficient, where those quantities are compared with previous theoretical and experimental results.

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.

Coupled three-dimensional quantum mechanical wave packet study of proton transfer in H2+ + He collisions on accurate ab initio two-state diabatic potential energy surfaces.

We have carried out fully close-coupled three dimensional quantum mechanical wave packet dynamical calculations for the reaction He+H2+→HeH++H on the ground electronic adiabatic potential energy surface and on the lowest two electronic states of newly constructed ab initio calculated diabatic potential energy surfaces for the system [Naskar et al., J. Phys. Chem. A 127, 3832 (2023)]. With the reactant diatom (H2+) in its roto-vibrational ground state (v = 0, j = 0), the calculations have been carried out in hyperspherical coordinates to obtain the reaction attributes. Convergence profiles of the reaction probability with respect to the total angular momentum quantum number at different collision energies are presented for the title reaction. State-to-state as well as initial state selected integral reaction cross sections are calculated from the fully converged reaction probabilities over a range of collision energies. The integral cross section values computed using the two-state diabatic potential energy surfaces are significantly lower than those obtained using the ground electronic state adiabatic potential energy surface and are in much better agreement with the available experimental results than the latter for total energy greater than 1.1 eV. Therefore, it becomes clear that it is important to include the nonadiabatic coupling terms for a quantitative prediction of the dynamical observables.

Beyond Born-Oppenheimer Constructed Diabatic Potential Energy Surfaces for HeH2.

First-principles based beyond Born-Oppenheimer theory has been employed to construct multistate global Potential-Energy Surfaces (PESs) for the HeH2+ system by explicitly incorporating the Nonadiabatic Coupling Terms (NACTs). Adiabatic PESs and NACTs for the lowest four electronic states (12A', 22A', 32A' and 42A') are evaluated as functions of hyperangles for a grid of fixed values of the hyperradius in hyperspherical coordinates. Conical intersection between different states are validated by integrating the NACTs along appropriately chosen contours. Subsequently, adiabatic-to-diabatic (ADT) transformation angles are determined by solving the ADT equations to construct the diabatic potential matrix for the HeH2+ system which are smooth, single-valued, continuous, and symmetric and are suitable for performing accurate scattering calculations for the titled system.

Effect of surface temperature on quantum dynamics of D2 on Cu(111) using a chemically accurate potential energy surface.

The effect of surface mode vibrations on the reactive scattering of D2, initialized in the ground rovibrational state (v = 0, j = 0), from a Cu(111) surface is investigated for different surface temperature situations. We adopt a time and temperature dependent effective Hamiltonian [Dutta et al., J. Chem. Phys. 154, 104103 (2021)] constructed by combining the linearly coupled many oscillator model [Sahoo et al., J. Chem. Phys. 136, 084306 (2012)] and the static corrugation model [M. Wijzenbroek and M. F. Somers, J. Chem. Phys. 137, 054703 (2012)] potential within the mean-field approach. Such an effective Hamiltonian is employed for six-dimensional quantum dynamical calculations to obtain temperature dependent reaction and state-to-state scattering probability profiles as a function of incidence energy of colliding D2 molecules. As reported in the experimental studies, the movements of surface atoms modify the dissociative scattering dynamics at higher surface temperature by exhibiting vibrational quantum and surface atoms' recoil effects in the low and high collision energy domains, respectively. Finally, we compare our present theoretical results with the experimental and other theoretical outcomes, as well as discuss the novelty of our findings.

Construction of Beyond Born-Oppenheimer Based Diabatic Surfaces and Generation of Photoabsorption Spectra: The Touchstone Pyrazine (C4 N2 H4 ).

We construct theoretically "exact" and numerically "accurate" Beyond Born-Oppenheimer (BBO) based diabatic potential energy surfaces (PESs) of pyrazine (C4 N2 H4 ) molecule involving lowest four excited adiabatic PESs (S1 to S4 ) and nonadiabatic coupling terms (NACTs) among those surfaces as functions of nonadiabatically active normal modes (Q1 , Q6a , Q9a and Q10a ) to compute its photoabsorption (PA) spectra. Those adiabatic PESs are calculated using CASSCF as well as MRCI based methodologies, where NACTs are obtained from CP-MCSCF approach. Employing ab initio quantities (adiabatic PESs and NACTs), it is possible to depict the conical intersections (CIs) and develop matrices of diabatic PESs over six normal mode planes. Once single-valued, smooth, symmetric and continuous 2×2 and 4×4 diabatic surface matrices are in hand for the first time, such matrices are used to perform multi-state multi-mode nuclear dynamics with the aid of Time-Dependent Discrete Variable Representation (TDDVR) methodology initializing the product type wavefunction on 1 1 B 1 u ${{1}^{1}{B}_{1u}}$ (S1 ) and 1 1 B 2 u ${{1}^{1}{B}_{2u}}$ (S2 ) states to obtain the corresponding PA spectra. TDDVR calculated spectra for those states (S1 and S2 ) obtained from BBO based 2×2 and 4×4 diabatic surface matrices show good and better agreement with the experimental results, respectively. Both of these calculated results depict better peak progression over the existing profiles of Multi-Configuration Time-Dependent Hartree (MCTDH) dynamics over 2×2 Vibronic Coupling Model (VCM) Hamiltonian.

Accurate Calculation of Rate Constant and Isotope Effect for the F + H2 Reaction by the Coupled 3D Time-Dependent Wave Packet Method on the Newly Constructed Ab Initio Ground Potential Energy Surface.

We employ coupled three-dimensional (3D) time dependent wave packet formalism in hyperspherical coordinates for reactive scattering problem on the newly constructed ab initio calculated ground adiabatic potential energy surface for the F + H2/D2 reaction. The convergence profiles for various reactive channels are depicted at low collision energy regimes with respect to the total angular momentum (J) quantum numbers. For two different reactant diatomic molecules (H2 and D2) initially at their respective ground roto-vibrational state (v = 0, j = 0), calculated state-to-state as well as total integral cross sections as a function of collision energy, temperature dependent rate constants, and the kinetic isotope effect for various reactivity profiles of F + H2 and F + D2 reactions are presented along with previous theoretical and experimental results.

Jahn-Teller Effect in Orthorhombic Manganites: Ab Initio Hamiltonian and Roto-vibrational Spectrum.

For the first time, using three different electronic structure methodologies, namely, CASSCF, RS2c, and MRCI(SD), we construct ab initio adiabatic potential energy surfaces (APESs) and nonadiabatic coupling term (NACT) of two electronic states (5Eg) of MnO69- unit, where eight such units share one La atom in LaMnO3 crystal. While fitting those APESs with analytic functions of normal modes (Qx, Qy), an empirical scaling factor is introduced considering the mass ratio of eight MnO69- units with and without one La atom to explore the environmental (mass) effect on MnO69- unit. When the roto-vibrational levels of MnO69- Hamiltonian are calculated, peak positions computed from ab initio constructed excited APESs are found to be enough close with the experimental satellite transitions [ J. Exp. Theor. Phys. 2016, 122, 890-901] endorsing our earlier model results [ J. Chem. Phys. 2019, 150, 064703]. In order to explore the electron-nuclear coupling in an alternate way, theoretically "exact" and numerically "accurate" beyond Born-Oppenheimer (BBO) theory based diabatic potential energy surfaces (PESs) of MnO69- are constructed to generate the photoelectron (PE) spectra. The PE spectral band also exhibits good peak by peak correspondence with the higher satellite transitions in the dielectric function spectra of the LaMnO3 complex.

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, Q9x, Q9y, Q13x, Q13y, Q18x, Q18y, Q10x, Q10y, Q12x and Q12y) 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.

Dynamical calculations of O(3P) + OH(2Π) reaction on the CHIPR potential energy surface using the fully coupled time-dependent wave-packet approach in hyperspherical coordinates.

We have carried out quantum dynamics calculations for the O + OH → H + O2 reaction on the CHIPR [A. J. C. Varandas, J. Chem. Phys., 2013, 138, 134117] potential energy surface (PES) for ground state HO2 using the fully coupled 3D time-dependent wavepacket formalism [S. Adhikari and A. J. C. Varandas, Comput. Phys. Commun., 2013, 184, 270] in hyperspherical coordinates. Reaction probabilities for J > 0 are calculated for different initial rotational states of the OH radical (v = 0; j = 0, 1). State-to-state as well as total integral cross sections and rate-coefficients are evaluated and compared with previous theoretical calculations and available experimental studies. Using the rate constant for the forward (hereinafter considered to be H + O2 → O + OH) and backward (O + OH → H + O2) reactions of this reactive system, the equilibrium constant of the reversible process [H + O2 ⇌ O + OH] is calculated as a function of temperature and compared with previous experimental measurements.

A beyond Born-Oppenheimer treatment of C6H6 + radical cation for diabatic surfaces: Photoelectron spectra of its neutral analog using time-dependent discrete variable representation.

We employ theoretically "exact" and numerically "accurate" Beyond Born-Oppenheimer (BBO) treatment to construct diabatic potential energy surfaces (PESs) of the benzene radical cation (C6H6 +) for the first time and explore the workability of the time-dependent discrete variable representation (TDDVR) method for carrying out dynamical calculations to evaluate the photoelectron (PE) spectra of its neutral analog. Ab initio adiabatic PESs and nonadiabatic coupling terms are computed over a series of pairwise normal modes, which exhibit rich nonadiabatic interactions starting from Jahn-Teller interactions and accidental conical intersections/seams to pseudo Jahn-Teller couplings. Once the electronic structure calculation is completed on the low-lying five doublet electronic states (X̃2E1g, B̃2E2g, and C̃2A2u) of the cationic species, diabatization is carried out employing the adiabatic-to-diabatic transformation (ADT) equations for the five-state sub-Hilbert space to compute highly accurate ADT angles, and thereby, single-valued, smooth, symmetric, and continuous diabatic PESs and couplings are constructed. Subsequently, such surface matrices are used to perform multi-state multi-mode nuclear dynamics for simulating PE spectra of benzene. Our theoretical findings clearly depict that the spectra for X̃2E1g and B̃2E2g-C̃2A2u states obtained from BBO treatment and TDDVR dynamics exhibit reasonably good agreement with the experimental results as well as with the findings of other theoretical approaches.

Effect of surface temperature on quantum dynamics of H2 on Cu(111) using a chemically accurate potential energy surface.

The effect of surface atom vibrations on H2 scattering from a Cu(111) surface at different temperatures is being investigated for hydrogen molecules in their rovibrational ground state (v = 0, j = 0). We assume weakly correlated interactions between molecular degrees of freedom and surface modes through a Hartree product type wavefunction. While constructing the six-dimensional effective Hamiltonian, we employ (a) a chemically accurate potential energy surface according to the static corrugation model [M. Wijzenbroek and M. F. Somers, J. Chem. Phys. 137, 054703 (2012)]; (b) normal mode frequencies and displacement vectors calculated with different surface atom interaction potentials within a cluster approximation; and (c) initial state distributions for the vibrational modes according to Bose-Einstein probability factors. We carry out 6D quantum dynamics with the so-constructed effective Hamiltonian and analyze sticking and state-to-state scattering probabilities. The surface atom vibrations affect the chemisorption dynamics. The results show physically meaningful trends for both reaction and scattering probabilities compared to experimental and other theoretical results.

Charge Transfer Processes for H + H2+ Reaction Employing Coupled 3D Wavepacket Approach on Beyond Born-Oppenheimer Based Ab Initio Constructed Diabatic Potential Energy Surfaces.

The dynamics of the H + H2+ reaction has been analyzed from the electronically first excited state of diabatic potential energy surfaces constructed by employing the Beyond Born-Oppenheimer theory [J. Chem. Phys. 2014, 141, 204306]. We have employed the coupled 3D time-dependent wavepacket formalism in hyperspherical coordinates for multisurface reactive scattering problems. To be specific, the charge transfer processes have been investigated extensively by calculating state-to-state as well as total reaction probabilities and integral cross sections, when the reaction process is initiated from the first excited electronic state (21A'). We have depicted the convergence profiles of reaction probabilities for the competing charge transfer processes, namely, reactive charge transfer (RCT) and nonreactive charge transfer (NRCT) processes for different total energies with respect to total angular momentum, J. Total and state-to-state integral cross sections are calculated as a function of total energy for the initial rovibrational state, namely, v = 0, j = 0 level of H2+ (2Σg+) molecule and are compared with previous theoretical calculations. Finally, we have calculated temperature-dependent rate constants using our presently evaluated cross sections and compared their average with the experimentally measured one.

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.

Beyond Born-Oppenheimer constructed diabatic potential energy surfaces for F + H2 reaction.

First principles based beyond Born-Oppenheimer theory has been implemented on the F + H2 system for constructing multistate global diabatic Potential Energy Surfaces (PESs) through the incorporation of Nonadiabatic Coupling Terms (NACTs) explicitly. The spin-orbit (SO) coupling effect on the collision process of the F + H2 reaction has been included as a perturbation to the non-relativistic electronic Hamiltonian. Adiabatic PESs and NACTs for the lowest three electronic states (12A', 22A', and 12A″) are determined in hyperspherical coordinates as functions of hyperangles for a grid of fixed values of the hyperradius. Jahn-Teller (JT) type conical intersections between the two A' states translate along C2v and linear geometries in F + H2. In addition, A' and A″ states undergo Renner-Teller (RT) interaction at collinear configurations of this system. Both JT and RT couplings are validated by integrating NACTs along properly chosen contours. Subsequently, we have solved adiabatic-to-diabatic transformation (ADT) equations to evaluate the ADT angles for constructing the diabatic potential matrix of F + H2, including the SO coupling terms. The newly calculated diabatic PESs are found to be smooth, single-valued, continuous, and symmetric and can be invoked for performing accurate scattering calculations on the F + H2 system.

ADT: A Generalized Algorithm and Program for Beyond Born-Oppenheimer Equations of "N" Dimensional Sub-Hilbert Space.

The major bottleneck of first principle based beyond Born-Oppenheimer (BBO) treatment originates from large number and complicated expressions of adiabatic to diabatic transformation (ADT) equations for higher dimensional sub-Hilbert spaces. In order to overcome such shortcoming, we develop a generalized algorithm, "ADT" to generate the nonadiabatic equations through symbolic manipulation and to construct highly accurate diabatic surfaces for molecular processes involving excited electronic states. It is noteworthy to mention that the nonadiabatic coupling terms (NACTs) often become singular (removable) at degenerate point(s) or along a seam in the nuclear configuration space (CS) and thereby, a unitary transformation is required to convert the kinetically coupled (adiabatic) Hamiltonian to a potentially (diabatic) one to avoid such singularity(ies). The "ADT" program can be efficiently used to (a) formulate analytic functional forms of differential equations for ADT angles and diabatic potential energy matrix and (b) solve the set of coupled differential equations numerically to evaluate ADT angles, residue due to singularity(ies), ADT matrices, and finally, diabatic potential energy surfaces (PESs). For the numerical case, user can directly provide ab initio data (adiabatic PESs and NACTs) as input files to this software or can generate those input files through in-built python codes interfacing MOLPRO followed by ADT calculation. In order to establish the workability of our program package, we selectively choose six realistic molecular species, namely, NO2 radical, H3+, F + H2, NO3 radical, C6H6+ radical cation, and 1,3,5-C6H3F3+ radical cation, where two, three, five and six electronic states exhibit profound nonadiabatic interactions and are employed to compute diabatic PESs by using ab initio calculated adiabatic PESs and NACTs. The "ADT" package released under the GNU General Public License v3.0 (GPLv3) is available at https://github.com/AdhikariLAB/ADT-Program and also as the Supporting Information of this article.

Fully coupled (J > 0) time-dependent wave-packet calculations using hyperspherical coordinates for the H + O2 reaction on the CHIPR potential energy surface.

Quantum dynamics of the H + O2→ O + OH reaction has been extensively studied on the adiabatic ground state of CHIPR [A. J. C. Varandas, J. Chem. Phys., 2013, 138, 134117] potential energy surfaces by employing a coupled 3D time-dependent wavepacket approach in hyperspherical coordinates. Calculations have been performed for all non-zero J values for various initial rotational states of the diatom [O2(v = 0, j = 1-5)]. State-to-state and total integral cross sections are calculated using fully converged reaction probabilities, where initial state selected and Boltzmann averaged thermal rate constants are also subsequently calculated. Moreover, a comparison of various reaction attributes obtained by using the fully close coupled approach with the ones obtained from the J-shifting approximation and extrapolation scheme is presented along with other theoretical results and experimental observations.

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.

Cubic perturbed centrifugally stabilized excited state in orthorhombic manganites.

A model Hamiltonian for centrifugally stabilized electronic-vibrational motion of a cubic perturbed upper "Mexican hat" potential surface for a Mn3+ ion in an octahedral symmetry is formulated, and its eigenspectrum is explored. Theoretically calculated eigenvalues for cubic perturbed ground and excited electronic states are employed to interpret the origin of higher energy narrow side bands (satellite transitions) appearing in the dielectric function spectra of the LaMnO3 complex, which exhibit anomalous temperature dependence in the vicinity of the Néel temperature, TN ≃ 140 K [N. N. Kovaleva et al., J. Exp. Theor. Phys. 122, 890 (2016)].

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.