Photoionization-induced dynamics of ammonia: ab initio potential energy surfaces and time-dependent wave packet calculations for the ammonia cation

Compensation States Approach in the Hybrid Diabatization Scheme: Extension to Multidimensional Data and Properties

The diabatization of reactive systems for more than just a couple of states is a very demanding problem and generally requires advanced diabatization techniques. Especially for dissociative processes, the drastic changes in the adiabatic wave functions often would require large diabatic state bases, which quickly become impractical. Recently, we addressed this problem by the compensation states approach developed in the context of our hybrid diabatization scheme. This scheme utilizes wave function as well as energy data in combination with a diabatic potential model. In regions where the initial diabatic state basis becomes insufficient for an appropriate representation of the adiabatic states, new model states are generated. The new model states compensate for the state space not spanned by the initial diabatic basis. Such a compensation state is obtained by projecting the initial diabatic state space out of the adiabatic wave function. This yields a very efficient basis representation of the electronic Hamiltonian. The present work presents two new aspects. First, it is shown how other operators like the spin-orbit operator in the framework of the Effective Relativistic Coupling by Asymptotic Representation (ERCAR) can be evaluated in this compact model state space without losing the correct wave function information and accuracy. Second, the extension of the approach to multidimensional potential energy surface models is presented for methyl iodide including the C-I dissociation coordinate and the angular H3C-I bending coordinates.

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 Unified Hamiltonian Formalism of Spin-Orbit Jahn-Teller and Pseudo-Jahn-Teller Problems in All Axial Symmetries

Spatial degeneracy of electronic states closely connects spin-orbit coupling and vibronic coupling, which together determine properties of materials, especially heavy element compounds. Accurate description of those materials entails accurate mathematical formulas for spin-orbit vibronic Hamiltonians. For the first time ever, we in this work derive the Hamiltonian formalism to describe all spin-orbit Jahn-Teller and pseudo-Jahn-Teller vibronic problems in all axial symmetries. The conventional one-electron approximation of spin-orbit coupling, which was the foundation of all previous studies in this field, is not involved in the present work. Actually, the present formalism is applicable to all time-reversal symmetric hermitian Hamiltonian that has a Rank-1 dependence on the spin operator, without any restriction on the type and the number of term symbols and vibrational modes.

Triplet Separation after the Fastest Intramolecular Singlet Fission in the Smallest Chromophore

Singlet fission is of key importance in harvesting solar energy in solar cells, as it generates a pair of triplet excitons on the incidence of a photon. This phenomenon is not yet widely employed in the organic photovoltaics industry mostly because of the rarity of singlet fission chromophores. Pyrazino[2,3-g]quinoxaline-1,4,6,9-tetraoxide was recently designed as the smallest intramolecular singlet fission chromophore, and it undergoes the fastest singlet fission with a 16 fs time scale. The subsequent separation of the generated triplet-pair is of likewise importance as their efficient generation. Through quantum chemistry calculations and quantum dynamics simulations, we show that the triplet-pair separates to residing on two chromophores with an ∼80% probability on each collision between a chromophore with the triplet-pair and a ground state chromophore. Avoided crossing, instead of conical intersection, is involved in the efficient exciton separation.

The ultrafast vibronic dynamics of ammonia's D̃ state

Using vacuum-ultraviolet time-resolved velocity map imaging of photoelectrons, we study ultrafast coupled electronic and nuclear dynamics in low-lying Rydberg states of ammonia. Vibrationally-resolved internal vibrational relaxation (IVR) is observed in a progression of the e' bending modes. This vibrational progression is only observed in the D̃ state, and is lost upon ultrafast internal conversion to the C̃ and B̃ electronic states. Due to the ultrashort time scale of the internal conversion (ca. 64 fs), and the vibronic resolution, the non-adiabatic coupling vectors are identified and verified with ab initio calculations. The time-scale of this IVR process is highly surprising and significant because IVR is usually treated as an incoherent process that proceeds statistically, according to a "Fermi's Golden Rule"-like model, where the process scales with the available degrees of freedom. Here, we show that it can be highly non-statistical, restricted to only a very small subset of vibrational motions.

Permutation invariant polynomial neural network based diabatic ansatz for the (E + A) × (e + a) Jahn-Teller and Pseudo-Jahn-Teller systems

In this work, the permutation invariant polynomial neural network (PIP-NN) approach is employed to construct a quasi-diabatic Hamiltonian for system with non-Abelian symmetries. It provides a flexible and compact NN-based diabatic ansatz from the related approach of Williams, Eisfeld, and co-workers. The example of H₃ ⁺ is studied, which is an (E + A) × (e + a) Jahn-Teller and Pseudo-Jahn-Teller system. The PIP-NN diabatic ansatz is based on the symmetric polynomial expansion of Viel and Eisfeld, the coefficients of which are expressed with neural network functions that take permutation-invariant polynomials as input. This PIP-NN-based diabatic ansatz not only preserves the correct symmetry but also provides functional flexibility to accurately reproduce ab initio electronic structure data, thus resulting in excellent fits. The adiabatic energies, energy gradients, and derivative couplings are well reproduced. A good description of the local topology of the conical intersection seam is also achieved. Therefore, this diabatic ansatz completes the PIP-NN based representation of DPEM with correct symmetries and will enable us to diabatize even more complicated systems with complex symmetries.

Vibrationally resolved photoelectron angular distributions of ammonia

We present a theoretical study of vibrationally resolved photoelectron angular distributions for ammonia in both laboratory and molecular frames, in the photon energy range up to 70 eV, where only valence and inner-valence ionization is possible. We focus on the band resulting from ionization of the 3a₁ HOMO orbital leading to NH₃⁺ in the electronic ground state, , for which the dominant vibrational progression corresponds to the activation of the umbrella inversion mode. We show that, at room temperature, the photoelectron angular distributions for randomly oriented molecules or molecules whose principal C₃ symmetry axis is aligned along the light polarization direction are perfectly symmetric with respect to the plane that contains the intermediate D_3h conformation connecting the pyramidal structures associated with the double-well potential of the umbrella inversion mode. These distributions exhibit symmetric, nearly perfect two-lobe shapes in the whole range of investigated photon energies. In contrast, for molecules where the initial vibrational state is localized in one of the two wells, a situation that can experimentally be achieved by introducing an external electric field, the molecular-frame photoelectron angular distributions (MFPADs) are in general asymmetric, but the degree of asymmetry of the two lobes dramatically changes and oscillates with photoelectron energy. We also show that, at ultracold temperatures, where all aligned molecules initially lie in the delocalized ground vibrational state, the photoelectron angular distributions are perfectly symmetric, but the two-lobe shape is only observed when the final vibrational state of the resulting NH₃⁺ cation has even parity. When the latter vibrational state has odd parity, the angular distributions are much more involved and, at photoelectron energies of ∼10 eV, they directly reflect the bi-pyramidal geometry of the molecule in its ground vibrational state. These results suggest that, in order to obtain structural information from MFPADs in ammonia and likely in other molecules containing a similar double-well potential, one could preferably work at ultracold temperatures, which is not the case for most molecules.

Diabatic States of Molecules

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

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.

Simulation of the photodetachment spectra of the nitrate anion (NO3-) in the B 2E' energy range and non-adiabatic electronic population dynamics of NO3

The photodetachment spectrum of the nitrate anion (NO3-) in the energy range of the NO3 second excited state is simulated from first principles using quantum wave packet dynamics. The prediction...

Accurate quantum dynamics simulation of the photodetachment spectrum of the nitrate anion (NO3 -) based on an artificial neural network diabatic potential model

The photodetachment spectrum of the nitrate anion (NO₃ ^-) is simulated from first principles using wavepacket quantum dynamics propagation and a newly developed accurate full-dimensional fully coupled five state diabatic potential model. This model utilizes the recently proposed complete nuclear permutation inversion invariant artificial neural network diabatization technique [D. M. G. Williams and W. Eisfeld, J. Phys. Chem. A 124, 7608 (2020)]. The quantum dynamics simulations are designed such that temperature effects and the impact of near threshold detachment are taken into account. Thus, the two available experiments at high temperature and at cryogenic temperature using the slow electron velocity-map imaging technique can be reproduced in very good agreement. These results clearly show the relevance of hot bands and vibronic coupling between the X̃ ²A₂ ^' ground state and the B̃ ²E' excited state of the neutral radical. This together with the recent experiment at low temperature gives further support for the proper assignment of the ν₃ fundamental, which has been debated for many years. An assignment of a not yet discussed hot band line is also proposed.

Laser-induced electron diffraction of the ultrafast umbrella motion in ammonia

Visualizing molecular transformations in real-time requires a structural retrieval method with Ångström spatial and femtosecond temporal atomic resolution. Imaging of hydrogen-containing molecules additionally requires an imaging method sensitive to the atomic positions of hydrogen nuclei, with most methods possessing relatively low sensitivity to hydrogen scattering. Laser-induced electron diffraction (LIED) is a table-top technique that can image ultrafast structural changes of gas-phase polyatomic molecules with sub-Ångström and femtosecond spatiotemporal resolution together with relatively high sensitivity to hydrogen scattering. Here, we image the umbrella motion of an isolated ammonia molecule (NH₃) following its strong-field ionization. Upon ionization of a neutral ammonia molecule, the ammonia cation (NH₃ ⁺) undergoes an ultrafast geometrical transformation from a pyramidal ( Φ HNH = 107 ° ) to planar ( Φ HNH = 120 ° ) structure in approximately 8 femtoseconds. Using LIED, we retrieve a near-planar ( Φ HNH = 117   ±   5 ° ) field-dressed NH₃ ⁺ molecular structure 7.8 - 9.8 femtoseconds after ionization. Our measured field-dressed NH₃ ⁺ structure is in excellent agreement with our calculated equilibrium field-dressed structure using quantum chemical ab initio calculations.

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.

Time-resolved formation of excited atomic and molecular states in XUV-induced nanoplasmas in ammonia clusters

High intensity XUV radiation from a free-electron laser (FEL) was used to create a nanoplasma inside ammonia clusters with the intent of studying the resulting electron-ion interactions and their interplay with plasma evolution. In a plasma-like state, electrons with kinetic energy lower than the local collective Coulomb potential of the positive ionic core are trapped in the cluster and take part in secondary processes (e.g. electron-impact excitation/ionization and electron-ion recombination) which lead to subsequent excited and neutral molecular fragmentation. Using a time-delayed UV laser, the dynamics of the excited atomic and molecular states are probed from -0.1 ps to 18 ps. We identify three different phases of molecular fragmentation that are clearly distinguished by the effect of the probe laser on the ionic and electronic yield. We propose a simple model to rationalize our data and further identify two separate channels leading to the formation of excited hydrogen.

Vibronic interaction in CO3− photo-detachment: Jahn–Teller effects beyond structural distortion and general formalisms for vibronic Hamiltonians in trigonal symmetries

Expansion formalisms for trigonal Jahn–Teller and pseudo-Jahn–Teller vibronic Hamiltonians are developed and used to study and correctly interpret the photoelectron spectrum of CO₃⁻.

Wavepacket dynamics and the multi-configurational time-dependent Hartree approach

Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.

Simulation of Vibronic Spectra of Flexible Systems: Hybrid DVR-Harmonic Approaches

Our general framework for the simulation of vibrational signatures in electronic spectra has been extended to treat one large-amplitude motion (LAM) at the anharmonic level, coupled to the other small-amplitude motions (SAM) treated as harmonic. The coupling between LAM and SAM is minimized thanks to the use of delocalized internal coordinates, which are built automatically from the molecular topology. General LAMs can be employed, ranging from intrinsic reaction coordinates to rigid or flexible paths based on the distinguished coordinate approach. The anharmonic model is based on a fully numerical method based on the discrete variable representation (DVR) theory, supporting different types of boundary conditions. The inclusion of this model in a general-purpose electronic structure code makes available to the user a large panel of quantum chemistry models, for both isolated and condensed phases. The flexibility and reliability of the new framework are illustrated by some case studies, covering various types of LAMs, ranging from a small test case, the photoelectron spectrum of ammonia, to larger systems, such as phenylanthracene and cyclobutanone.

Revisiting the (E + A) ⊗ (e + a) problems of polyatomic systems with trigonal symmetry: general expansions of their vibronic Hamiltonians

In this work, we derive general expansions in vibrational coordinates for the (E + A) ⊗ (e + a) vibronic Hamiltonians of molecules with one and only one C₃ axis.

Nonadiabatic dynamics of floppy hydrogen bonded complexes: the case of the ionized ammonia dimer

Non-adiabatic dynamics of a floppy hydrogen bonded ammonia dimer was studied by ab initio molecular dynamics simulations.

Quantum dynamics on a three-sheeted six-dimensional ab initio potential-energy surface of the phosphine cation: Simulation of the photoelectron spectrum and the ultrafast radiationless decay dynamics

A diabatic three-sheeted six-dimensional potential-energy surface has been constructed for the ground state and the lowest excited state of the PH3 (+) cation. Coupling terms of Jahn-Teller and pseudo-Jahn-Teller origin up to eighth order had to be included to describe the pronounced anharmonicity of the surface due to multiple conical intersections. The parameters of the diabatic Hamiltonian have been optimized by fitting the eigenvalues of the potential-energy matrix to ab initio data calculated at the CASSCF/MRCI level employing the correlation-consistent triple-ζ basis. The theoretical photoelectron spectrum of phosphine and the non-adiabatic nuclear dynamics of the phosphine cation have been computed by propagating nuclear wave packets with the multiconfiguration time-dependent Hartree method. The theoretical photoelectron bands obtained by Fourier transformation of the autocorrelation function agree well with the experimental results. It is shown that the ultrafast non-radiative decay dynamics of the first excited state of PH3 (+) is dominated by the exceptionally strong Jahn-Teller coupling of the asymmetric bending vibrational mode together with a hyperline of conical intersections with the electronic ground state induced by the umbrella mode. Time-dependent population probabilities have been computed for the three adiabatic electronic states. The non-adiabatic Jahn-Teller dynamics within the excited state takes place within ≈5 fs. Almost 80% of the excited-state population decay to the ground state within about 10 fs. The wave packets become highly complex and delocalized after 20 fs and no further significant transfer of electronic population seems to occur up to 100 fs propagation time.

Nonadiabatic nuclear dynamics of the ammonia cation studied by surface hopping classical trajectory calculations

The Landau-Zener (LZ) type classical-trajectory surface-hopping algorithm is applied to the nonadiabatic nuclear dynamics of the ammonia cation after photoionization of the ground-state neutral molecule to the excited states of the cation. The algorithm employs a recently proposed formula for nonadiabatic LZ transition probabilities derived from the adiabatic potential energy surfaces. The evolution of the populations of the ground state and the two lowest excited adiabatic states is calculated up to 200 fs. The results agree well with quantum simulations available for the first 100 fs based on the same potential energy surfaces. Three different time scales are detected for the nuclear dynamics: Ultrafast Jahn-Teller dynamics between the excited states on a 5 fs time scale; fast transitions between the excited state and the ground state within a time scale of 20 fs; and relatively slow partial conversion of a first-excited-state population to the ground state within a time scale of 100 fs. Beyond 100 fs, the adiabatic electronic populations are nearly constant due to a dynamic equilibrium between the three states. The ultrafast nonradiative decay of the excited-state populations provides a qualitative explanation of the experimental evidence that the ammonia cation is nonfluorescent.

Toward spin-orbit coupled diabatic potential energy surfaces for methyl iodide using effective relativistic coupling by asymptotic representation

The theoretical treatment of state-state interactions and the development of coupled multidimensional potential energy surfaces (PESs) is of fundamental importance for the theoretical investigation of nonadiabatic processes. Usually, only derivative or vibronic coupling is considered, but the presence of heavy atoms in a system can render spin-orbit (SO) coupling important as well. In the present study, we apply a new method recently developed by us (J. Chem. Phys. 2012, 136, 034103, and J. Chem. Phys. 2012, 137, 064101) to generate SO coupled diabatic PESs along the C-I dissociation coordinate for methyl iodide (CH3I). This is the first and mandatory step toward the development of fully coupled full-dimensional PESs to describe the multistate photodynamics of this benchmark system. The method we use here is based on the diabatic asymptotic representation of the molecular fine structure states and an effective relativistic coupling operator. It therefore is called effective relativistic coupling by asymptotic representation (ERCAR). This approach allows the efficient and accurate generation of fully coupled PESs including derivative and SO coupling based on high-level ab initio calculations. In this study we develop a specific ERCAR model for CH3I that so far accounts only for the C-I bond cleavage. Details of the diabatization and the accuracy of the results are investigated in comparison to reference ab initio calculations and experiments. The energies of the adiabatic fine structure states are reproduced in excellent agreement with ab initio SO-CI data. The model is also compared to available literature data, and its performance is evaluated critically. This shows that the new method is very promising for the construction of fully coupled full-dimensional PESs for CH3I to be used in future quantum dynamics studies.

The Jahn-Teller effect in the electron momentum spectroscopy of ammonia

The 1e and 3a(1) bands of the ammonia molecule have been studied using the high-resolution electron momentum spectroscopy at impact energies of 1200 and 600 eV. Several slices of 1e and 3a(1) bands in the different binding energy ranges were selected, and their electron-momentum distributions were carefully compared. The discernable difference among the distributions of the selected slices of the 1e band shows that the Jahn-Teller effect indeed influences the electron momentum distribution of the 1e orbital of ammonia.