Computation of vibrational energy levels and eigenstates of fluoroform using the multiconfiguration time-dependent Hartree method

Vibronic coupling in the energetically six lowest electronic states of oxirane radical cation

Multi-dimensional quantum mechanical simulations are carried out to understand the multi-state and multi-mode vibronic interactions in the first six low-lying viz., X̃2B1, Ã2A1, B̃2B2, C̃2A2, D̃2A1, and Ẽ2B1 electronic states of c-C2H4O·+. Vibronic coupling theory is applied to study interactions among electronic states using symmetry selection rules. A model 6 × 6 diabatic electronic Hamiltonian is constructed. The parameters of the diabatic Hamiltonian are estimated by performing extensive ab initio electronic structure calculations, using the EOM-IP-CCSD method. The nuclear dynamics calculations are performed with both time-independent and time-dependent quantum mechanical methods. The calculated vibronic structures of six electronic states are found to be in excellent agreement with the available experimental findings. Progressions found in the theoretical spectrum are assigned in terms of vibrational modes. It is found that extremely strong vibronic interactions among the X̃2B1-Ã2A1, B̃2B2-C̃2A2, and D̃2A1-Ẽ2B1 electronic states results into highly overlapping vibronic bands due to multiple multi-state conical intersections. The impact of associated nonadiabatic effects on the vibronic structure and dynamics of the mentioned electronic states is examined at length. Interesting comparison is made with the results obtained for the isomeric acetaldehyde radical cation.

Jahn-Teller and pseudo-Jahn-Teller effects on the vibronic structure of the photoionized spectrum of cyanopropyne

Nonadiabatic quantum dynamics are carried out to illustrate the photoionized spectrum of the cyanopropyne (CH3-C≡C-C≡N) as reported in recent experimental measurements [Lamarre et al., J. Mol. Spectrosc. 315, 206 (2015)]. A detailed electronic structure calculation is performed to analyze the topographical details of the first five ionized states, of which three are degenerate states (X̃2E, B̃2E, and C̃2E) and two are non-degenerate states (Ã2A1 and D̃2A1). The degenerate E states of the C3V symmetry molecule are prone to Jahn-Teller (JT) instability, and in addition, symmetry allowed A1 - E vibronic coupling, i.e., pseudo-Jahn-Teller (PJT), effects are expected to have a significant impact in the detailed vibronic structure of these electronic states. The JT splittings of X̃2E and B̃2E degenerate states are small, whereas it is quite large at three high frequencies in the C̃2E electronic states. The large energy separation of X̃2E from the other states and the non-zero PJT coupling of the B̃2E state with the close-lying Ã2A1 state indicate the uncoupled nature of the X̃, Ã, and B̃ vibronic bands of C4H3N. The intersection minima of B̃ and C̃ states with the D̃ state nearly coincide with the energetic minimum of D̃ state. Therefore, the PJT couplings among these states will lead to a strong vibronic interaction to shape the respective band structure. To completely understand the JT and PJT interactions in the photoionized spectrum of C4H3N, the vibronic coupling model Hamiltonian was constructed to perform nuclear dynamics studies for these electronic states. The vibrational progressions in each vibronic band are identified and compared with the available experimental data in the literature. The impacts of JT and PJT effects in the first five ionized states of cyanopropyne are investigated and discussed in detail.

Photoionization of aziridine: Nonadiabatic dynamics of the first six low-lying electronic states of the aziridine radical cation

In this article, the theoretical photoionization spectroscopy of the aziridine (C2H5N) molecule is investigated. To start with, we have optimized the geometry of this molecule at the neutral electronic ground state at the density functional theory/augmented correlation-consistent polarized valence triple zeta level of theory using the G09 program. The electronic structure calculations were restricted to the first six low-lying electronic states in order to account for the experimental photoelectron spectrum of the C2H5N molecule. The first six low-lying electronic states (X̃2A', Ã2A', B̃2A″, C̃2A″, D̃2A', and Ẽ2A') of the potential energy surfaces (PESs) are calculated by both equation of motion-ionization potential-coupled cluster singles and doubles and multi-configuration quasi-degenerate perturbation theory ab initio quantum chemistry methods along the dimensionless normal displacement coordinates in which multiple conical intersections were established among the considered electronic states. A (6 × 6) model vibronic Hamiltonian is constructed on a diabatic electronic basis, using the symmetry selection rules and Taylor series expansion. The Cs symmetry point group of the aziridine molecule leads to electronic states symmetry of either A' or A″, and these states are close in energy, due to which the same symmetry electronic states avoid each other. To get a smooth diabatic PES, a fourfold diabatization scheme is used, which is implemented in the General Atomic and Molecular Electronic Structure Systems suite of programs. All the parameters used in the diabatic vibronic coupling model Hamiltonian are calculated in terms of the normal modes of vibrational coordinates. Finally, the vibronic model Hamiltonian constructed for the coupled six electronic states is used to solve both time-independent and time-dependent Schrödinger equations using the multi-configuration time-dependent Hartree program module to obtain the dynamical observables. The theoretical vibronic band structure is found to be in good accord with the available experimental results.

Vibronic coupling and ultrafast relaxation dynamics in the first five excited singlet electronic states of bithiophene

The vibronic structure and nuclear dynamics in the first five excited singlet electronic states of bithiophene (2T) are investigated here. Specifically, considerations are given to comprehend the first two structureless and broad electronic absorption bands and the role of nonadiabatic coupling in the excited state relaxation mechanism of 2T in the gas phase. Associated potential energy surfaces (PESs) are established by constructing a model vibronic coupling Hamiltonian using 18 vibrational degrees of freedom and extensive ab initio electronic structure calculations. The topographies of these PESs are critically examined, and multiple conical intersections are established. The nuclear dynamics calculations are performed by propagating wave packets on the coupled electronic manifold. The present theoretical results are in good agreement with the experimental observations. It is found that strong nonadiabatic coupling between the S1-S4 and S1-S5 states along totally symmetric modes is predominantly responsible for the structureless and broad first absorption band, and overlapping S2, S3, S4, and S5 states form the second absorption band. Photorelaxation from the highly excited S5 to the lowest S1 state takes place through a cascade of diabatic population transfers among the S1-S4-S5 electronic manifold within the first ∼100 fs. Totally symmetric C=C stretching, C-S stretching, C-H wagging, ring puckering, and inter-ring bending modes collectively drive such relaxation dynamics.

Construction of a Mode-Combination Hamiltonian under the Grid-Based Representation for the Quantum Dynamics of OH + HO2 → O2 + H2O

In this work, a systematic construction framework on a mode-combination Hamiltonian operator of a typical polyatomic reaction, OH + HO2 → O2 + H2O, is developed. First, a set of Jacobi coordinates are employed to construct the kinetic energy operator (KEO) through the polyspherical approach ( Phys. Rep. 2009, 484, 169). Second, due to the multiconfigurational electronic structure of this system, a non-adiabatic potential energy surface (PES) is constructed where the first singlet and triplet states are involved with spin-orbital coupling. To improve the training database, the training set of random energy data was optimized through a popular iterative optimization approach with extensive trajectories. Here, we propose an automatic trajectory method, instead of the classical trajectory on a crude PES, where the gradients are directly computed by the present ab initio calculations. Third, on the basis of the training set, the potential function is directly constructed in the canonical polyadic decomposition (CPD) form ( J. Chem. Theory Comput. 2021, 17, 2702-2713) which is helpful in propagating the nuclear wave function under the grid-based representation. To do this, the Gaussian process regression (GPR) approach for building the CPD form, called the CPD-GPR method ( J. Phys. Chem. Lett. 2022, 13, 11128-11135) is adopted where we further revise CPD-GPR by introducing the mode-combination (mc) scheme leading to the present CPD-mc-GPR approach. Constructing the full-dimension non-adiabatic Hamiltonian operator with mode combination, as test calculations, the nuclear wave function is propagated to preliminarily compute the reactive probability of OH + HO2 → O2 + H2O where the reactants are prepared in vibrational ground states and in the first triplet electronic state.

Eigenstate calculation in the state-averaged (multi-layer) multi-configurational time-dependent Hartree approach

A new approach for the calculation of eigenstates with the state-averaged (multi-layer) multi-configurational time-dependent Hartree (MCTDH) approach is presented. The approach is inspired by the recent work of Larsson [J. Chem. Phys. 151, 204102 (2019)]. It employs local optimization of the basis sets at each node of the multi-layer MCTDH tree and successive downward and upward sweeps to obtain a globally converged result. At the top node, the Hamiltonian represented in the basis of the single-particle functions (SPFs) of the first layer is diagonalized. Here p wavefunctions corresponding to the p lowest eigenvalues are computed by a block Lanczos approach. At all other nodes, a non-linear operator consisting of the respective mean-field Hamiltonian matrix and a projector onto the space spanned by the respective SPFs is considered. Here, the eigenstate corresponding to the lowest eigenvalue is computed using a short iterative Lanczos scheme. Two different examples are studied to illustrate the new approach: the calculation of the vibrational states of methyl and acetonitrile. The calculations for methyl employ the single-layer MCTDH approach, a general potential energy surface, and the correlation discrete variable representation. A five-layer MCTDH representation and a sum of product-type Hamiltonian are used in the acetonitrile calculations. Very fast convergence and order of magnitude reductions in the numerical effort compared to the previously used block relaxation scheme are found. Furthermore, a detailed comparison with the results of Avila and Carrington [J. Chem. Phys. 134, 054126 (2011)] for acetonitrile highlights the potential problems of convergence tests for high-dimensional systems.

Resolving the Experimental Photoelectron Spectra of CAl3Si. J Phys Chem A 2024;128:355-369. [PMID: 38189257 DOI: 10.1021/acs.jpca.3c06295] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

The experimental photoelectron spectra concerning the six electronic states of CAl3Si- are resolved through electronic structure calculations and quantum nuclear dynamics in this study. It incorporates a model diabatic Hamiltonian to evaluate the coupling parameters and fit the potential energy curves (PECs). The analysis of these PECs showed us that there are sufficient nonadiabatic effects in the photoelectron spectra through the presence of various conical intersections. Poisson intensity distributions (PIDs) and the wave packet density plots are utilized for assigning the fundamental and first overtone excitations. The nuclear dynamics study is accomplished by employing time-dependent (TD) and time-independent (TI) quantum chemistry methods. Ultimately, our theoretical results concurred well with the experimental findings exhibiting vibronic coupling amidst the nearly positioned electronic states.

Rovibrational states calculations of the H2O-HCN heterodimer with the multiconfiguration time dependent Hartree method

Water and hydrogen cyanide are two of the most common species in space and the atmosphere with the ability of binding to form dimers such as H2O-HCN. In the literature, while calculations characterizing various properties of the H2O-HCN cluster (equilibrium distance, vibrational frequencies and rotational constants) have been done in the past, extensive calculations of the rovibrational states of this system using a reliable quantum dynamical approach have yet to be reported. In this work, we intend to mend that by performing the first calculation of the rovibrational states of the H2O-HCN van der Waals complex on a recently developed potential energy surface. We use the block improved relaxation procedure implemented in the Heidelberg MultiConfiguration Time-Dependent Hartree (MCTDH) package to compute the states of the H2O-HCN isomer, from which we extract the transition frequencies and rotational constants of the complex. We further adapt an approach first suggested by Wang and Carrington-and supported here by analysis routines of the Heidelberg MCTDH package-to properly characterize the computed rovibrational states. The subsequent assignment of rovibrational states was done by theoretical analysis and visual inspection of the wavefunctions. Our simulations provide a Zero Point Energy (ZPE) and intermolecular vibrational frequencies in good agreement with past ab initio calculations. The transition frequencies and rotational constants obtained from our simulations match well with the available experimental data. This work has the broad aim to propose the MCTDH approach as a reliable option to compute and characterize rovibrational states of van der Waals complexes such as the current one.

Accurate Potential Energy Surfaces Using Atom-Centered Potentials and Minimal High-Level Data

We demonstrate that a Δ-density functional theory (Δ-DFT) approach based on atom-centered potentials (ACPs) represents a computationally inexpensive and accurate method for representing potential energy surfaces (PESs) for the HONO and HFCO molecules and vibrational frequencies derived therefrom. Using as few as 100 CCSD(T)-F12a reference energies, ACPs developed for use with B3LYP/def2-TZVPP are shown to produce PESs for HONO and HFCO with mean absolute errors of 27.7 and 5.8 cm-1, respectively. Application of the multiconfigurational time-dependent Hartree (MCTDH) method with ACP-corrected B3LYP/def2-TZVPP PESs produces vibrational frequencies for cis- and trans-HONO with mean absolute percent errors (MAPEs) of 0.8 and 1.1, compared to 0.8 obtained for the two isomers with CCSD(T)-F12a/cc-pVTZ-F12/MCTDH. For HFCO, the vibrational frequencies obtained using the present (Δ-DFT)/MCTDH approach give a MAPE of 0.1, which is the error obtained with CCSD(T)-F12a/cc-pVTZ-F12/MCTDH. The ACP approach is therefore successful in representing a PES calculated at a high level of theory (CCSD(T)-F12a) and a promising method for the development of a general protocol for the representation of accurate molecular PESs and the calculation of molecular properties from them.

Temperature Dependence of the Electronic Absorption Spectrum of NO2

The nitrogen dioxide (NO₂) radical is composed of the two most abundant elements in the atmosphere, where it can be formed in a variety of ways including combustion, detonation of energetic materials, and lightning. Relevant also to smog and ozone cycles, together these processes span a wide range of temperatures. Remarkably, high-resolution NO₂ electronic absorption spectra have only been reported in a narrow range below about 300 K. Previously, we reported [ J. Phys. Chem. A 2021, 125, 5519-5533] the construction of quasi-diabatic potential energy surfaces (PESs) for the lowest four electronic states (X̃, Ã, B̃, and C̃) of NO₂. In addition to three-dimensional PESs based on explicitly correlated MRCI(Q)-F12/VTZ-F12 ab initio data, the geometry dependence of each component of the dipoles and transition dipoles was also mapped into fitted surfaces. The multiconfigurational time-dependent Hartree (MCTDH) method was then used to compute the 0 K electronic absorption spectrum (from the ground rovibrational initial state) employing those energy and transition dipole surfaces. Here, in an extension of that work, we report an investigation into the effects of elevated temperature on the spectrum, considering the effects of the population of rotationally and vibrationally excited initial states. The calculations are complemented by new experimental measurements. Spectral contributions from hundreds of rotational states up to N = 20 and from 200 individually-characterized vibrational states were computed. A spectral simulation tool was developed that enables modeling the spectrum at various temperatures─by weighting individual spectral contributions via the partition function, or for pure excited initial states, which can be probed via transient absorption spectroscopy. We validate these results against experimental absorption spectroscopy data at high temperatures, as well as via a new measurement from the (1,0,1) initial vibrational state.

A theoretical study of vibronic coupling in the photoelectron spectra of Al6N. Phys Chem Chem Phys 2023;25:12990-13003. [PMID: 37165932 DOI: 10.1039/d3cp00836c]

This work emphasizes the appearance of non-adiabatic effects in the photoelectron spectra of Al₆N^-. It includes ab initio electronic structure calculations obtained on the first seven low-lying electronic states of Al₆N^- and a nuclear dynamics study utilizing time-dependent and time-independent quantum chemistry approaches. A model vibronic Hamiltonian is constructed in a diabatic electronic representation to estimate the coupling parameters corresponding to the fifteen vibrational modes of Al₆N^-. Theoretical spectral bands are achieved by employing the vibronic coupling theory followed by reduced dimensional calculations to understand the role of individual vibrational modes in the overall photoelectron spectra. Finally, the theoretically obtained photodetachment spectra show good agreement with the experimental spectra revealing vibronic coupling among the closely spaced spectral bands.

Unraveling the Photoelectron Spectrum of 1-Phospha-2,3,4-triazolate Anion, HCPN3-, A Theoretical Approach

The first five low-lying electronic states of HCPN₃ are probed through extensive ab initio electronic structure and quantum dynamics studies to reproduce the 193 nm photoelectron spectrum. Vibronic Hamiltonian is constructed and availed for time-dependent (TD) and time-independent (TI) quantum dynamical studies. The presence of numerous conical intersections (CIs) and crossings among electronic states yielded interesting nonadiabatic effects in the photoelectron bands of the overall spectrum. Moreover, the theoretical bands corresponding to five electronic states have reproduced all three experimental spectral bands. Among these, the first two bands originated due to a combination of four electronic states as predicted by previous studies. The third band corresponds to the fifth electronic state. The results calculated via TD and TI approaches exhibited satisfying agreement with the experimental results.

The coupling of the hydrated proton to its first solvation shell

The Zundel ([Formula: see text]) and Eigen ([Formula: see text]) cations play an important role as intermediate structures for proton transfer processes in liquid water. In the gas phase they exhibit radically different infrared (IR) spectra. The question arises: is there a least common denominator structure that explains the IR spectra of both, the Zundel and Eigen cations, and hence of the solvated proton? Full dimensional quantum simulations of these protonated cations demonstrate that two dynamical water molecules and an excess proton constitute this fundamental subunit. Embedded in the static environment of the parent Eigen cation, this subunit reproduces the positions and broadenings of its main excess-proton bands. In isolation, its spectrum reverts to the well-known Zundel ion. Hence, the dynamics of this subunit polarized by an environment suffice to explain the spectral signatures and anharmonic couplings of the solvated proton in its first solvation shell.

Multi-state and Multi-mode Vibronic Coupling Effects in the Photoionization Spectroscopy of Acetaldehyde

Multi-state and multi-mode vibronic dynamics in the seven energetically low-lying (X~2A', A~2A″, B~2A', C~2A', D~2A″, E~2A', and F~2A') electronic states of the acetaldehyde radical cation is theoretically studied in this article. Adiabatic energies of these electronic states are calculated by ab initio quantum chemistry methods. A vibronic coupling model of seven electronic states is constructed in a diabatic electronic basis to carry out the first-principles nuclear dynamics study. The vibronic spectrum is calculated and compared with the experimental findings reported in the literature. The progressions of vibrational modes found in the spectrum are assigned. The findings reveal that the X~2A' and F~2A' electronic states are energetically well-separated from the other electronic states and the remaining states (A~2A″ to E~2A') are energetically very close or even quasi-degenerate at the equilibrium geometry of the reference electronic ground state of acetaldehyde. The energetic proximity of A~2A″ to E~2A' electronic states results in multiple multi-state conical intersections. The impact of electronic nonadiabatic interactions due to conical intersections on the vibronic structure of the photoionization band and nonradiative internal conversion dynamics is discussed.

Multilayer Multiconfiguration Time-Dependent Hartree Study on the Mode-/Bond-Specific Quantum Dynamics of Water Dissociation on Cu(111)

In this work, full-dimensional (9D) quantum dynamics calculations on mode-/bond-specific surface scattering of a water molecule on a copper (111) rigid surface are performed through the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. To easily perform the ML-MCTDH calculations on such a triatomic molecule-surface system, we first choose specific Jacobi coordinates as a set of coordinates of water. Next, to efficiently perform the 9D ML-MCTDH wavepacket propagation, the potential energy surface is transferred to a canonical polyadic decomposition form with the aid of a Monte Carlo-based method. Excitation-specific dissociation probabilities of H₂O on Cu(111) are computed, and mode-/bond-specific dynamics are demonstrated by comparison with a probability curve computed for a water molecule in the ground state. The dependence of the dissociation probability of the initial state of H₂O is studied, and it is found that the excitation-specific dissociation probabilities can be divided into three groups. We find that the vibrationally excited states enhance the dissociation reactivity of H₂O, while the rotationally excited states hardly influence it.

Intramolecular Vibrational Redistribution in Formic Acid and its Deuterated Forms

The intramolecular vibrational relaxation dynamics of formic acid and its deuterated isotopologues is simulated on the full-dimensional potential energy surface of Richter and Carbonnière [F. Richter and P. Carbonnière, J. Chem. Phys. 148, 064303 (2018)] using the Heidelberg MCTDH package. We focus on couplings with the torsion vibrational modes close to the trans- cis isomerisation coordinate from the dynamics of artificially excited vibrational mode overtones. The C-O stretch bright vibrational mode is coupled to the out-of-the plane torsion mode in HCOOH, where this coupling could be exploited for laser-induced trans-to- cis isomerisation. Strong isotopic effects are observed: deuteration of the hydroxyl group, i.e., in HCOOD and DCOOD, destroys the C-O stretch to torsion mode coupling whereas in DCOOH, little to no effect is observed.

Unraveling the Origin of Symmetry Breaking in H2 O@C60 Endofullerene Through Quantum Computations

We explore the origin of the anomalous splitting of the 101 levels reported experimentally for the H2 O@C60 endofullerene, in order to give some insight about the physical interpretations of the symmetry breaking observed. We performed fully-coupled quantum computations within the multiconfiguration time-dependent Hartree approach employing a rigorous procedure to handle such computationally challenging problems. We introduce two competing physical models, and discuss the observed unconventional quantum patterns in terms of anisotropy in the interfullerene interactions, caused by the change in the off-center position of the encapsulated water molecules inside the cage or the uniaxial C60 -cage distortion, arising from noncovalent bonding upon water's encapsulation, or exohedral fullerene perturbations. Our results show that both scenarios could reproduce the experimentally observed rotational degeneracy pattern, although quantitative agreement with the available experimental rotational levels splitting value has been achieved by the model that considers an uniaxial elongation of the C60 -cage. Such finding supports that the observed symmetry breaking could be mainly caused by the distortion of the fullerene cage. However, as nuclear quantum treatments rely on the underlying interactions, a decisive conclusion hinges on the availability of their improved description, taken into account both endofullerene and exohedral environments, from forthcoming highly demanding electronic structure many-body interaction studies.

Adaptive Fitting of Potential Energy Surfaces of Small to Medium-Sized Molecules in Sum-of-Product Form: Application to Vibrational Spectroscopy

A semi-automatic sampling and fitting procedure for generating sum-of-product (Born-Oppenheimer) potential energy surfaces based on a high-dimensional model representation is presented. The adaptive sampling procedure and subsequent fitting relies on energies only and can be used for re-fitting existing analytic potential energy surfaces in sum-of-product form or for direct fits from ab initio computa- tions. The method is tested by fitting ground electronic state potential energy surfaces for small to medium sized semi-rigid molecules, i.e., HFCO, HONO, and HCOOH, based upon ab initio computations at the CCSD(T)-F12/cc-pVTZ-F12 or MP2/aug-cc-pVTZ levels of theory. Vibrational eigenstates are computed using block improved relaxation in the Heidelberg MCTDH package and compared to available experimental and theoretical data. The new potential energy surfaces are compared to the best ones currently available for these molecules, in terms of accuracy, including of resulting vibrational states, required numbers of sampling points, and number of fitting parameters. The present procedure leads to compact expansions and scales well with the number of dimensions for simple potentials such as single or double wells.

The Jahn-Teller and pseudo-Jahn-Teller effects in propyne radical cation

The Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) effects in the X 2E, A 2E and B 2A1 electronic states of propyne radical cation are investigated with the aid of ab initio...

Computational vibrational spectroscopy of molecule-surface interactions: what is still difficult and what can be done about it

Interactions of molecules with solid surfaces are responsible for key functionalities for a range of currently actively pursued technologies, including heterogeneous catalysis for synthesis or decomposition of molecules, sensitization, surface...

Encapsulation of a Water Molecule inside C60 Fullerene: The Impact of Confinement on Quantum Features

We introduce an efficient quantum fully coupled computational scheme within the multiconfiguration time-dependent Hartree (MCTDH) approach to handle the otherwise extremely costly computations of translational-rotational-vibrational states and energies of light-molecule endofullenes. Quantum calculations on energy levels are reported for a water molecule inside C60 fullerene by means of such a systematic approach that includes all nine degrees of freedom of H2O@C60 and does not consider restrictions above them. The potential energy operator is represented as a sum of natural potentials employing the n-mode expansion, along with the exact kinetic energy operator, by introducing a set of Radau internal coordinates for the H2O molecule. On the basis of the present rigorous computations, various aspects of the quantized intermolecular dynamics upon confinement of H2O@C60 are discussed, such as the rotational energy level splitting and the significant frequency shifts of the encapsulated water molecule vibrations. The impact of water encapsulation on quantum features is explored, and insights into the nature of the underlying forces are provided, highlighting the importance of a reliable first-principles description of the guest-host interactions.

The Low-Lying Electronic States of NO2: Potential Energy and Dipole Surfaces, Bound States, and Electronic Absorption Spectrum

Nitrogen dioxide, NO₂, is a free radical composed of the two most abundant elements in Earth's atmosphere, nitrogen and oxygen, and is relevant to atmospheric and combustion chemistry. The electronic structure of even its lowest-lying states is remarkably complex, with various conical intersections and Renner-Teller pairings, giving rise to complex and perturbed vibronic states. Here we report some analysis of the 18 molecular states of doublet spin-multiplicity formed by combining ground-state N(⁴S_u) and O(³P_g) atoms. Three-dimensional potential energy surfaces were fit at the MRCI(Q)-F12/VTZ-F12 level, describing the lowest four (X̃, Ã, B̃, and C̃) electronic states. A properties-based diabatization procedure was applied to accommodate the intersections, producing energies in a quasidiabatic representation and yielding couplings that were also fit into surfaces. The low-lying vibrational levels on the ground X̃ state were computed and compared with experimental measurements. Compared to experiment, the lowest 125 calculated vibrational levels (up to 8500 cm^-1 above the zero-point energy) have a root-mean-squared error of 16.5 cm^-1. In addition, dipole moments for each of the lowest four electronic states-and the transition dipoles between them-were also computed and fit. With the coupled energy and dipole surfaces, the electronic spectrum was calculated in absolute intensity and compared with experimental measurements. Detailed structure in the experimental spectrum was successfully reproduced, and the total integrated intensity matches experiment to an accuracy of ∼1.5% with no empirical adjustments.

Comparison of the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method and the density matrix renormalization group (DMRG) for ground state properties of linear rotor chains

We demonstrate the applicability of the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method to the problem of computing ground states of one-dimensional chains of linear rotors with dipolar interactions. Specifically, we successfully obtain energies, entanglement entropies, and orientational correlations that are in agreement with the Density Matrix Renormalization Group (DMRG), which has been previously used for this system. We find that the entropies calculated by ML-MCTDH for larger system sizes contain nonmonotonicity, as expected in the vicinity of a second-order quantum phase transition between ordered and disordered rotor states. We observe that this effect remains when all couplings besides nearest-neighbor are omitted from the Hamiltonian, which suggests that it is not sensitive to the rate of decay of the interactions. In contrast to DMRG, which is tailored to the one-dimensional case, ML-MCTDH (as implemented in the Heidelberg MCTDH package) requires more computational time and memory, although the requirements are still within reach of commodity hardware. The numerical convergence and computational demand of two practical implementations of ML-MCTDH and DMRG are presented in detail for various combinations of system parameters.

High-Dimensional Quantum Dynamics Study on Excitation-Specific Surface Scattering Including Lattice Effects of a Five-Atom Surface Cell

In this work, high-dimensional (21D) quantum dynamics calculations on the mode-specific surface scattering of a carbon monoxide molecule on a copper(100) surface with lattice effects of a five-atom surface cell are performed through the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. We employ a surface model in which five surface atoms near the impact site are treated as fully flexible quantum particles, while all other more distant atoms are kept at fixed locations. To efficiently perform the 21D ML-MCTDH wave packet propagation, the potential energy surface is transferred to a canonical polyadic decomposition form with the aid of a Monte Carlo-based method. Excitation-specific sticking probabilities of CO on Cu(100) are computed, and lattice effects caused by the flexible surface atoms are demonstrated by comparison with sticking probabilities computed for a rigid surface. The dependence of the sticking probability of the initial state of the system is studied, and it is found that the sticking probability is reduced when the surface atom on the impact site is initially vibrationally excited.

Vibronic coupling in the first six electronic states of pentafluorobenzene radical cation: Radiative emission and nonradiative decay

Nuclear dynamics in the first six vibronically coupled electronic states of pentafluorobenzene radical cation is studied with the aid of the standard vibronic coupling theory and quantum dynamical methods. A model 6 × 6 vibronic Hamiltonian is constructed in a diabatic electronic basis using symmetry selection rules and a Taylor expansion of the elements of the electronic Hamiltonian in terms of the normal coordinate of vibrational modes. Extensive ab initio quantum chemistry calculations are carried out for the adiabatic electronic energies to establish the diabatic potential energy surfaces and their coupling surfaces. Both time-independent and time-dependent quantum mechanical methods are employed to perform nuclear dynamics calculations. The vibronic spectrum of the electronic states is calculated, assigned, and compared with the available experimental results. Internal conversion dynamics of electronic states is examined to assess the impact of various couplings on the nuclear dynamics. The impact of increasing fluorination of the parent benzene radical cation on its radiative emission is examined and discussed.

“Inverted” CO molecules on NaCl(100): a quantum mechanical study

Inverted (“O-down”) CO adsorbates on NaCl(100), recently observed experimentally after IR vibrational excitation (Lau et al., Science, 2020, 367, 175–178), are characterized using periodic DFT and a quantum mechanical description of vibrations.

A general automatic method for optimal construction of matrix product operators using bipartite graph theory

Constructing matrix product operators (MPOs) is at the core of the modern density matrix renormalization group (DMRG) and its time dependent formulation. For the DMRG to be conveniently used in different problems described by different Hamiltonians, in this work, we propose a new generic algorithm to construct the MPO of an arbitrary operator with a sum-of-products form based on the bipartite graph theory. We show that the method has the following advantages: (i) it is automatic in that only the definition of the operator is required; (ii) it is symbolic thus free of any numerical error; (iii) the complementary operator technique can be fully employed so that the resulting MPO is globally optimal for any given order of degrees of freedom; and (iv) the symmetry of the system could be fully employed to reduce the dimension of MPO. To demonstrate the effectiveness of the new algorithm, the MPOs of Hamiltonians ranging from the prototypical spin-boson model and the Holstein model to the more complicated ab initio electronic Hamiltonian and the anharmonic vibrational Hamiltonian with the sextic force field are constructed. It is found that for the former three cases, our automatic algorithm can reproduce exactly the same MPOs as the optimally hand-crafted ones already known in the literature.

Rationalization of photo-detachment spectra of the indenyl anion (C9H7-) from the perspective of vibronic coupling theory

The nuclear dynamics of the low-lying first four electronic states of the prototypical indenyl radical is investigated based on first principles calculations to rationalize the experimental vibronic structure of the radical. The study is performed following both time-dependent and time-independent quantum-chemistry approaches using a model diabatic Hamiltonian. The construction of model Hamiltonians is based on the fits of the adiabatic energies calculated from the electronic structure method. The analyses of the static and dynamics results of the present study corroborate the experimental findings regarding the shape of the spectrum, vibrational progressions and the lifetime of the excited state. Finally, the present theoretical investigations suggest that the electronic non-adiabatic effect is extremely important for a detailed study of the vibronic structure and the electronic relaxation mechanism of the low-lying electronic states of the indenyl radical.

The smallest proton-bound dimer H5+: theoretical progress

The protonated hydrogen dimer, H5+, is the smallest system including proton transfer, and has been of long-standing interest since its first laboratory observation in 1962. H5+ and its isotopologues are the intermediate complexes in deuterium fractionation reactions, and are of central importance in molecular astrophysics. The recently recorded infrared spectra of both H5+ and D5+ reveal a rich vibrational dynamics of the cations, which presents a challenge for standard theoretical approaches. Although H5+ is a four-electron ion, which makes highly accurate electronic structure calculations tractable, the construction of ab initio-based potential energy and dipole moment surfaces has proved a hard task. In the same vein, the difficulties in treating the nuclear motion could also become cumbersome due to their high dimensionality, floppiness and/or symmetry. These systems are prototypical examples for studying large-amplitude motions, as they are highly delocalized, interconverting between equivalent minima through internal rotation and proton transfer motions requiring state-of-the-art treatments. Recent advances in the computational vibrational spectroscopy of the H5+ cation and its isotopologues are reported from full quantum spectral simulations, providing important information in a rigorous manner, and open perspectives for further future investigations. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.

A generalized vibronic-coupling Hamiltonian for molecules without symmetry: Application to the photoisomerization of benzopyran

We present a model for the lowest two potential energy surfaces (PESs) that describe the photoinduced ring-opening reaction of benzopyran taken as a model compound to study the photochromic ring-opening reaction of indolinobenzospiropyran and its evolution toward its open-chain analog. The PESs are expressed in terms of three effective rectilinear coordinates. One corresponds to the direction between the equilibrium geometry in the electronic ground state, referred to as the Franck-Condon geometry, and the minimum of conical intersection (CI), while the other two span the two-dimensional branching space at the CI. The model correctly reproduces the topography of the PESs. The ab initio calculations are performed with the extended multiconfiguration quasidegenerate perturbation theory at second order method. We demonstrate that accounting for electron dynamic correlation drastically changes the global energy landscape since some zwitterionic states become strongly stabilized. Quantum dynamics calculations using this PES model produce an absorption spectrum that matches the experimental one to a good accuracy.

Fully Coupled Quantum Treatment of Nanoconfined Systems: A Water Molecule inside a Fullerene C60

We implemented a systematic procedure for treating the quantal rotations by including all translational and vibrational degrees of freedom for any triatomic bent molecule in any embedded or confined environment, within the MCTDH framework. Fully coupled quantum treatments were employed to investigate unconventional properties in nanoconfined molecular systems. In this way, we facilitate a complete theoretical analysis of the underlying dynamics that enables us to compute the energy levels and the nuclear spin isomers of a single water molecule trapped in a C₆₀ fullerene cage. The key point lies in the full 9D description of both nuclear and electronic degrees of freedom, as well as a reliable representation of the guest-host interaction. The presence of occluded impurities or inhomogeneities due to noncovalent interactions in the interfullerene environment could modify aspects of the potential, causing significant coupling between otherwise uncoupled modes. Using specific n-mode model potentials, we obtained splitting patterns that confirm the effects of symmetry breaking observed by experiments in the ground ortho-H₂O state. Further, our investigation reveals that the first rotationally excited states of the encapsulated ortho- and para-H₂O have also raised their 3-fold degeneracy. In view of the complexity of the problem, our results highlight the importance of accurate and computational demanding approaches for building up predictive models for such nanoconfined molecules.

Imaging large amplitude out-of-plane motion in photoexcited pentafluorobenzene using time-resolved photoelectron spectroscopy: a computational study

Excited-state dynamics of pentafluorobenzene is studied in detail for a quartic vibronic coupling model including the six b1 vibrational modes of the molecule and the two lowest excited electronic states. The study analyzes the influence of the large-amplitude out-of-plane vibrational motion on the electronic dynamics and extends to the simulation of the emerging time-resolved photoelectron spectra. The mapping of coherent non-separable electron-nuclear motion into oscillatory photoelectron signals is discussed.

Isotope effects on the resonance interactions and vibrational quantum dynamics of fluoroform 12,13CHF3

We report a comparison of the analysis of the low energy spectrum of ¹³CHF₃ and ¹²CHF₃ from the THz (FIR) range to the ν₁ fundamental at high resolution (δ[small nu, Greek, tilde] < 0.001 cm^-1 or otherwise Doppler limited) on the basis of FTIR spectra taken both with ordinary light sources and with the synchrotron radiation from the Swiss Light Source. Several vibrational levels are accurately determined including, in particular, the 2ν₄ CH-bending overtone and the ν₁ CH-stretching fundamental of ¹³CHF₃. Comparison of experimental results with those from accurate full dimensional vibrational calculations allows for a study of the time-dependent quantum dynamics of intramolecular vibrational redistribution (IVR) in the CH chromophore both on short time scales (fs) and longer time scales (ps) when coupling to the lower frequency modes becomes important and where the ¹²C/¹³C isotope effects are very large.