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We construct the effective Hartree potential for H2 on Cu(111) as introduced in our earlier work [Dutta et al., J. Chem. Phys. 154, 104103 (2021), and Dutta et al., J. Chem. Phys. 157, 194112 (2022)] starting from the same gas–metal interaction potential obtained for 0 K. Unlike in that work, we now explicitly account for surface expansion at 925 K and investigate different models to describe the surface vibrational modes: (i) a cluster model yielding harmonic normal modes at 0 K and (ii) slab models resulting in phonons at 0 and 925 K according to the quasi-harmonic approximation—all consistently calculated at the density functional theory level with the same exchange–correlation potential. While performing dynamical calculations for the H2(v = 0, j = 0)–Cu(111) system employing Hartree potential constructed with 925 K phonons and surface temperature, (i) the calculated chemisorption probabilities are the highest compared to the other approaches over the energy domain and (ii) the threshold for the reaction probability is the lowest, in close agreement with the experiment. Although the survival probabilities (v′ = 0) depict the expected trend (lower in magnitude), the excitation probabilities (v′ = 1) display a higher magnitude since the 925 K phonons and surface temperature are more effective for the excitation process compared to the phonons/normal modes obtained from the other approaches investigated to describe the surface. [ABSTRACT FROM AUTHOR]

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 ( X ̃ 2 E 1 g , B ̃ 2 E 2 g , and C ̃ 2 A 2 u ) of benzene radical cation ( C 6 H 6 + ) 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. [ABSTRACT FROM AUTHOR]

We have carried out fully close-coupled three dimensional quantum mechanical wave packet dynamical calculations for the reaction He + H 2 + → 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 ( H 2 + ) 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The "accuracy" of diabatic Hamiltonian matrix elements solely depends on the level of ab initio calculation and on the included set of coupled electronic manifold forming a "true" sub‐Hilbert space (SHS). If ab initio calculations are performed with enough accuracy, existence of SHS can be validated only when the Curl Condition attains zero within numerical precision. For the first time, we depict a theoretical and algorithmic formulation on the calculation of Curl Condition to demonstrate the existence of SHS on molecular processes or chemical reactions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We employ theoretically "exact" and numerically "accurate" Beyond Born–Oppenheimer (BBO) treatment to construct diabatic potential energy surfaces (PESs) of the benzene radical cation ( C 6 H 6 + ) 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 ( X ̃ 2 E 1 g , B ̃ 2 E 2 g , and C ̃ 2 A 2 u ) 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 X ̃ 2 E 1 g and B ̃ 2 E 2 g − C ̃ 2 A 2 u 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. [ABSTRACT FROM AUTHOR]

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 C2 v 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. [ABSTRACT FROM AUTHOR]

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)]. [ABSTRACT FROM AUTHOR]

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- C 6 H 3 F 3 + (TFBZ+). While implementing this formulation, we compute ab initio adiabatic potential energy surfaces (PESs) and NACTs within the low-lying six electronic states ( X ̃ 2 E ′ ′ , Ã 2 A 2 ′ ′ , B ̃ 2 E ′ , and C ̃ 2 A 2 ′ ), 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. [ABSTRACT FROM AUTHOR]

The workability of beyond Born-Oppenheimer theory to construct diabatic potential energy surfaces (PESs) of a charge transfer atom-diatom collision process has been explored by performing scattering calculations to extract accurate integral cross sections (ICSs) and rate constants for comparison with most recent experimental quantities. We calculate non-adiabatic coupling terms among the lowest three singlet states of H3+ system (1¹A', 2¹A', and 3¹A') using MRCI level of calculation and solve the adiabatic-diabatic transformation equation to formulate the diabatic Hamiltonian matrix of the same process [S. Mukherjee et al., J. Chem. Phys. 141, 204306 (2014)] for the entire region of nuclear configuration space. The nonadiabatic effects in the D+ +H2 reaction has been studied by implementing the coupled 3D time-dependent wave packet formalism in hyperspherical coordinates [S. Adhikari and A. J. C. Varandas, Comput. Phys. Commun. 184, 270 (2013)] with zero and non-zero total angular momentum (J) on such newly constructed accurate (ab initio) diabatic PESs of H3+. We have depicted the convergence profiles of reaction probabilities for the reactive non-charge transfer, non-reactive charge transfer, and reactive charge transfer processes for different collisional energies with respect to the helicity (K) and total angular momentum (J) quantum numbers. Finally, total and state-to-state ICSs are calculated as a function of collision energy for the initial rovibrational state (v = 0, j = 0) of the H2 molecule, and consequently, those quantities are compared with previous theoretical and experimental results. [ABSTRACT FROM AUTHOR]

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 (X~;2E′′, , B~;2E′ 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 X~;2E′′, 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. [ABSTRACT FROM AUTHOR]

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 (X²A1) and the first excited state (A²B2), 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 photoelectron 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 (X²A1 and A²B2) of NO2 is essentially through the asymmetric stretching mode, where the functional form of such interaction is distinctly symmetric and non-linear. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We propose a strategy of using a stochastic optimization technique, namely, simulated annealing to design optimum laser pulses (both IR and UV) to achieve greater fluxes along the two dissociating channels (O18 + O16O16 and O16 + O16O18) in O16O16O18 molecule. We show that the integrated fluxes obtained along the targeted dissociating channel is larger with the optimized pulse than with the unoptimized one. The flux ratios are also more impressive with the optimized pulse than with the unoptimized one. We also look at the evolution contours of the wavefunctions along the two channels with time after the actions of both the IR and UV pulses and compare the profiles for unoptimized (initial) and optimized fields for better understanding the results that we achieve. We also report the pulse parameters obtained as well as the final shapes they take. [ABSTRACT FROM AUTHOR]

A recently proposed coupled three-dimensional time-dependent wave-packet formalism in hyperspherical coordinates is shown to yield accurate results for the reactive non-charge transfer process in the title system at collision energies as low as 100 K, where the lowest sheet of the accurate double many body expansion form for the singlet H+3 is used. The results are compared with available experimental data as well as time-independent calculations, and the agreement shown to be generally good. [ABSTRACT FROM AUTHOR]

We calculate the adiabatic Potential Energy Surfaces (PESs) and the Non-Adiabatic Coupling Terms (NACTs) for the three lowest singlet states of H+3 in hyperspherical coordinates as functions of hyperangles (θ and ɸ) for a grid of fixed values of hyperradius (1.5 ≤ ρ ≤ 20 bohrs) using the MRCI level of methodology employing ab initio quantum chemistry package (MOLPRO). The NACT between the ground and the first excited state translates along the seams on the θ - ɸ space, i.e., there are six Conical Intersections (CIs) at each θ (60° ≤ θ ≤ 90°) within the domain, 0 ≤ ɸ ≤ 2p. While transforming the adiabatic PESs to the diabatic ones, such surfaces show up six crossings along those seams. Our beyond Born-Oppenheimer approach could incorporate the effect of NACTs accurately and construct single-valued, continuous, smooth, and symmetric diabatic PESs. Since the location of CIs and the spatial amplitudes of NACTs are most prominent around ρ = 10 bohrs, generally only those results are depicted. [ABSTRACT FROM AUTHOR]

It is shown that the Born–Oppenheimer–Huang non-adiabatic coupling terms (NACTs) in a molecular Hamiltonian can be considered as equivalent to a friction force in classical mechanics and consequently responsible for the formation of triatomic species like HeH 2 + . The classical equation of motion is solved accordingly for a test case of a helium atom approaching an H 2 + molecule at its potential minimum along the collinear axis and lines parallel to it and also for the C 2 v geometry. It is shown that the singular NACTs between the first two excited states slow down the motion of the three quasi-ions (He, H, H) + while approaching each other and result in substantial loss of kinetic energy in the collision process. These results have profound implications for the formation of di- and triatomic species in the early universe, during the chemical synthesis epoch following the nucleosynthesis that followed the Big Bang. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

By computing the non-adiabatic coupling terms and the adiabatic-to-diabatic transformation angle along closed contours in nuclear configuration space using the CASSCF method and the aug-cc-pVTZ basis set for the lowest three electronic states of HeH2+, we explore the conical intersection between states in near collinear and noncollinear geometries, particularly in the C2v geometry. [ABSTRACT FROM AUTHOR]

We perform four-dimensional (4Dx2D) as well as six-dimensional (6D) quantum dynamics on a parametrically time- and temperature-dependent effective Hamiltonian for D2(v, j)-Cu(111) system, where such effective potential has been derived through a mean-field approach between molecular degrees of freedom and surface modes with Bose-Einstein probability factor for their initial state distribution. We present the convergence of the theoretically calculated sticking probabilities employing 4Dx2D quantum dynamics with increasing number of surface atoms as well as layers for rigid surface and the surface at a particular temperature, where the temperature-dependent sticking probabilities appear exclusively dictated by those surface modes directed along the Z-axis. The sticking and state-to-state transition probabilities obtained from 6D quantum dynamics are shown as a function of initial kinetic energy of the diatom at different surface temperature. Theoretically calculated sticking probabilities display the similar trend with the experimentally measured one. [ABSTRACT FROM AUTHOR]

We follow a suggestion by Lipoff and Herschbach [Mol. Phys. 108, 1133 (2010)] and compare dressed and bare adiabatic 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 to study the effect of conical intersections (ci) on the interacting atoms. For this purpose, we consider vibrational dressed adiabatic and vibrational dressed diabatic potentials in the entrance channel of reactive systems. According to our study, the most one should expect, in case of F + H2, is a mild effect of the (1, 2) ci on its reactive/exchange process-an outcome also supported by experiment. This happens although the corresponding dressed and bare potential barriers (and the corresponding van der Waals potential wells) differ significantly from each other. [ABSTRACT FROM AUTHOR]

We perform ab initio calculation using quantum chemistry package (MOLPRO) on the excited states of Na3 cluster and present the adiabatic PESs for the electronic states 22E′ and 12A1′, and the non-adiabatic coupling (NAC) terms among those states. Since the ab initio calculated NAC elements for the states 22E′ and 12A1′ demonstrate the numerical validity of so called 'Curl Condition,' such states closely form a sub-Hilbert space. For this subspace, we employ the NAC terms to solve the 'adiabatic-diabatic transformation (ADT)' equations to obtain the functional form of the transformation angles and pave the way to construct the continuous and single valued diabatic potential energy surface matrix by exploiting the existing first principle based theoretical means on beyond Born-Oppenheimer treatment. Nuclear dynamics has been carried out on those diabatic surfaces to reproduce the experimental spectrum for system B of Na3 cluster and thereby, to explore the numerical validity of the theoretical development on beyond Born-Oppenheimer approach for adiabatic to diabatic transformation. [ABSTRACT FROM AUTHOR]