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In this paper, we report on the performance of various quantum molecu- lar dynamics simulation methods in describing the photo-induced nonadi- abatic dynamics underlying the isomerization process of the retinal chromophore in rhodopsin. We focus on purely quantum vibronic wavepacket techniques and on various trajectory-based schemes, discussing their capability of accurately capture the isomerization process using a two-dimensional two-state model system coupled to an environment of secondary harmonic modes. Numerical results of various algorithms and time-independent grid schemes for the purely quantum approaches are presented, which also serve as benchmark for the trajectory-based calculations. Independent-trajectory and coupled-trajectory methods are compared as well, devoting particular attention to the scaling of their computational cost when increasing the number of degrees of freedom.

International audience; We present a study of the O(3P) + C2H4 scattering reaction, a process that takes place in the interstellar medium and is of relevance in atmospheric chemistry as well. A comprehensive investigation of the electronic properties of the system has been carried out based on multiconfigurational ab initio CASSCF/CASPT2 calculations, using a robust and consistent active space that can deliver accurate potential energy surfaces in the key regions visited by the system. The paper discloses detailed description of the primary reaction pathways and the relevant singlet and triplet excited states at the CASSCF and CASPT2 level, including an accurate description of the critical configurations, such as minima and transition states. The chosen active space and the CASSCF/CASPT2 computational protocol are assessed against coupled-cluster calculations to further check the stability and reliability of the entire multiconfigurational procedure.

We present a quantum dynamics method based on the propagation of interacting quan- tum trajectories to describe both adiabatic and nonadiabatic processes within the same formalism. The idea originates from the work of Poirier [Chem. Phys. 370 4–14 (2010)] and Schiff and Poirier [J. Chem. Phys. 136 031102 (2012)] on quantum dynamics with- out wavefunctions. It consists in determining the quantum force arising in the Bohmian hydrodynamic formulation of quantum dynamics using only information about quan- tum trajectories. The particular time-dependent propagation scheme proposed here results in very stable dynamics. Its performance is discussed by applying the method to analytical potentials in the adiabatic regime, and by combining it with the exact factorization method in the nonadiabatic regime.

Conventional quantum mechanical characterization of photodissociation dynamics is restricted by steep scaling laws with respect to the dimensionality of the system. In this work, we examine the applicability of the multi-configurational time-dependent Hartree (MCTDH) method in treating nonadiabatic photodissociation dynamics in two prototypical systems, taking advantage of its favorable scaling laws. To conform to the sum-of-product form, elements of the ab initio diabatic potential energy matrix (DPEM) are re-expressed using the recently proposed Monte Carlo canonical polyadic decomposition method, with enforcement of proper symmetry. The MCTDH absorption spectra and product branching ratios are shown to compare well with those calculated using conventional grid-based methods, demonstrating its promise for treating high-dimensional nonadiabatic photodissociation problems.

A Smolyak algorithm adapted to system-bath separation is proposed for rigorous quantum simulations. This technique combines a sparse grid method with the system-bath concept in a specific configuration without limitations on the form of the Hamiltonian, thus achieving a highly efficient convergence of the excitation transitions for the "system" part. Our approach provides a general way to overcome the perennial convergence problem for the standard Smolyak algorithm and enables the simulation of floppy molecules with more than a hundred degrees of freedom.The efficiency of the present method is illustrated on the simulation of H$_2$ caged in an sII clathrate hydrate including two kinds of cage modes. The transition energies are converged by increasing the number of normal modes of water molecules. Our results confirm the triplet splittings of both translational and rotational ($j=1$) transitions of the H$_2$ molecule. Furthermore, they show a slight increase of the translational transitions with respect to the ones in a rigid cage., 5 pages, 3 figures

International audience; We present the first use of curvilinear vibrational coordinates, specifically poly-spherical coordinates, in combination with vibrational coupled cluster theory. The polyspherical coordinates are used in the context of both the adaptive density-guided approach to potential energy surface construction and in the subsequent vibrational coupled cluster calculations of anharmonic vibrational states. Results obtained based on the polyspherical coordinate parametrization are compared to results obtained with the use of rectilinear vibrational coordinates, namely normal coordinates and hybrid optimized and localized coordinates for the formaldehyde molecule. This comparison is carried out with the full vibrational configuration interaction model, using the respective fully coupled potential energy surfaces and untruncated kinetic energy operators. The polyspherical coordinates are shown to facilitate an acceleration of convergence for truncated methods, when compared to the use of normal coordinates. We furthermore report on calculations on the hydrogen peroxide molecule in polyspherical coordinate 1 parametrization. The polyspherical vibrational coordinates are shown to perform very well, even for truncated methods, especially when considering the difficulty that rec-tilinear vibrational coordinates can exhibit in treating complicated internal molecular motion.

In order to simplify the numerical solution of the time-dependent or time-independent Schrödinger equations associated with atomic and molecular motions, the use of well-adapted coordinates is essential. Usually, this set of curvilinear coordinates leads to a Hamiltonian operator that is as separable as possible. Although their corresponding kinetic energy operator (KEO) expressions can be derived analytically for small systems or special kinds of coordinates, a numerical and exact approach allows one to compute them in terms of sophisticated curvilinear coordinates. Furthermore, the numerical approach enables one to easily define reduced-dimensionality or constrained models. We present here a recent implementation of this numerical approach that allows nested coordinate transformations, therefore leading to great flexibility in the definition of the curvilinear coordinates. Furthermore, this implementation has no limitations in terms of numbers of atoms or coordinate transformations. The quantum dynamics of the cis–trans photoisomerization of part of the retinal chromophore illustrates the construction of the coordinates and KEO part of a three-dimensional model. This article is part of the theme issue ‘Chemistry without the Born–Oppenheimer approximation’.

The exact factorization of the electron-nuclear wavefunction is applied to the study of the photo- isomerization of a retinal chromophore model. We describe such an ultrafast nonadiabatic process by analyzing the time-dependent potentials of the theory and by mimicking nuclear dynamics with quantum and coupled trajectories. The time-dependent vector and scalar potentials are the signature of the exact factorization, as they guide nuclear dynamics by encoding the complete electronic dynamics and including excited-state effects. Analysis of the potentials is, thus, essential – when possible – to predict the time-dependent behavior of the system of interest. In this work, we employ the exact time-dependent potentials, available for the numerically-exactly solvable model used here, to propagate quantum nuclear trajectories representing the isomerization reaction of the retinal chromophore. The quantum trajectories are the best possible trajectory-based description of the reaction when using the exact-factorization formalism, and thus allow us to assess the performance of the coupled-trajectory, fully approximate, schemes derived from the exact-factorization equations.

International audience; In this work, we present the efficient combination of Smolyak representations with time indepen-dent quantum mechanical approach using absorbing boundary conditions for the cumulative reac-tion probability calculations of a multidimensional reactive scattering problem. Our approach usesboth kinds of Smolyak representations (finite basis and grid) which drastically reduces the size ofthe basis representation for the cumulative reaction operator. The cumulative reaction probabilityis thus obtained by solving the eigenvalue problem within the context of reaction path Hamiltonianusing the compact Smolyak basis combined with an iterative Lanczos algorithm. Benchmark cal-culations are presented for reactive scattering models with a linear reaction coordinate and appliedto a 25D model highlighting the efficiency of the present approach for multidimensional reactiveprocesses.

We present a study of the O(

We study the relaxation process through a conical intersection of a photo-excited retinal chromophore model. The analysis is based on a two-electronic-state two-dimensional Hamiltonian developed by Hahn and Stock [J. Phys. Chem. B 104 1146 (2000)] to reproduce, with a minimal model, the main features of the 11-cis to all-trans isomerization of the retinal of rhodopsin. In particular, we focus on the performance of various trajectory-based schemes to nonadiabatic dynamics, and we compare quantum-classical results to the numerically exact quantum vibronic wavepacket dynamics. The purpose of this work is to investigate, by analyzing electronic and nuclear observables, how the sampling of initial conditions for the trajectories affects the subsequent dynamics.

International audience; We report an in-depth analysis of the photo-induced isomerization of the 2-cis-penta-2,4-dieniminium cation: a minimal model of the 11-cis retinal protonated Schiff base chromophore of the dim-light photoreceptor rhodopsin. Based on recently-developed three-dimensional potentials parametrized on ab initio multi-state multi-con-figurational second-order perturbation theory data, we perform quantum-dynamical studies. In addition, simulations based on various quantum-classical methods, among which Tully surface hopping and the coupled-trajectory approach derived from the exact factorization, allow us to validate their performance against vibronic-wavepacket propagation and, therefore, a purely quantum treatment. Quantum-dynamics results uncover qualitative differences with respect to the two-dimensional Hahn-Stock potentials , widely-used as model potentials for the isomerization of the same chromophore, due to the increased dimensionality and three-mode correlation. Quantum-classical simulations show, instead, that three-dimensional model potentials are capable of capturing a number of features revealed by atomistic simulations and experimental observations. In particular, a recently reported vibrational phase relationship between double-bond torsion and hydrogen-out-of-plane modes critical for rhodopsin isomerization efficiency is correctly reproduced.

International audience; We present a detailed derivation of the generalized coupled-trajectory mixed quantum classical (G-CT-MQC) algorithm based on the exact factorization equations. The ultimate goal is to propose an algorithm that can be employed for molecular dynamics simulations of non-radiative phenomena, as the spin-allowed internal conversions and the spin-forbidden intersystem crossings. Internal conversions are nonadiabatic processes driven by the kinetic coupling between electronic states, whereas intersystem crossings are mediated by the spin-orbit coupling. In the paper we discuss computational issues related to the suitable representation for electronic dynamics and to the different nature of kinetic and spin-orbit coupling. Numerical studies on model systems allow us to test the performance of the G-CT-MQC algorithm in different situations.

International audience; We investigate spin-orbit interactions in ultrafast molecular processes employing the exact factor-ization of the electron-nuclear wavefunction. We revisit the original derivation by including spin-orbitcoupling, and show how the dynamics driven by the time-dependent potential energy surface allevi-ates inconsistencies arising from different electronic representations. We propose a novel trajectory-based scheme to simulate spin-forbidden non-radiative processes, and we show its performance inthe treatment of excited-state dynamics where spin-orbit effects couple different spin multiplets

International audience; In this study, we examine the effect of a flexible description of the clathrate hydrateframework on the translation-rotation (TR) eigenstates of guest molecules such asmolecular hydrogen. Traditionally, the water cage structure is assumed to be rigid,thus ignoring the quantum nature of hydrogen nuclei in the water framework. How-ever, it has been shown that protons in a water molecule possess a marked delocalisedcharacter in many situations, ranging from water clusters to proton transfer in thebulk. In the case of water clathrates, all previous TR bound-state calculations of guestmolecules consider that the caging water molecules are fixed at their equilibrium ge-ometry. Only recently, a static investigation of the role of proton configurations wasperformed by Baˇci ́c and co-workers by sampling a very large number of differentstatic structures of water clathrates.Here, we investigate the importance of the rotational degrees of freedom of the wa-ter cage on the TR levels of guest molecule using an efficient adiabatic decouplingscheme. Our approach combines rigid body Diffusion Monte Carlo calculations forthe description of the rotational degree of freedom of water molecules surroundingthe guest molecular hydrogen to an efficient Smolyak sparse-grid technique for thecalculation of the TR levels. This approach allows us to take into account the highlyanharmonic nature of the rotational water motions in a high-dimensional system.The clathrate-induced splittings of the j= 1 rotational levels are much more sensi-tive to the quantum hydrogen delocalisation than the translational transitions. Thisresults is in good agreement with the previous static study of Baˇci ́c and co-workers.

We report the results of calculations pertaining to the HH intramolecular stretching fundamentals of (p-H

Photodissociation of ozone following absorption of biologically harmful solar ultraviolet radiation is the key mechanism for the life protecting properties of the atmospheric ozone layer. Even though ozone photolysis is described successfully by post-Hartree-Fock theory, it has evaded direct experimental access so far, due to the unavailability of intense ultrashort deep ultraviolet radiation sources. The rapidity of ozone photolysis with predicted values of a few tens of femtoseconds renders both ultrashort pump and probe pulses indispensable to capture this manifestation of ultrafast chemistry. Here, we present the observation of femtosecond time-scale electronic and nuclear dynamics of ozone triggered by \ensuremath{\sim}10-fs, \ensuremath{\sim}2-\textmu{}J deep ultraviolet pulses and, in contrast to conventional attochemistry experiments, probed by extreme ultraviolet isolated pulses. An electronic wave packet is first created. We follow the splitting of the excited B-state related nuclear wave packet into a path leading to molecular fragmentation and an oscillating path, revolving around the Franck-Condon point with 22-fs wave-packet revival time. Full quantum-mechanical ab initio multiconfigurational time-dependent Hartree simulations support this interpretation.

We report the first fully coupled quantum six-dimensional (6D) bound-state calculations of the vibration-translation-rotation eigenstates of a flexible H

We report the first fully coupled quantum six-dimensional (6D) bound-state calculations of the vibration-translation-rotation eigenstates of a flexible H2, HD, and D2 molecule confined inside the small cage of the structure II clathrate hydrate embedded in larger hydrate domains with up to 76 H2O molecules, treated as rigid. Our calculations use a pairwise-additive 6D intermolecular potential energy surface for H2 in the hydrate domain, based on an ab initio 6D H2–H2O pair potential for flexible H2 and rigid H2O. They extend to the first excited (v = 1) vibrational state of H2, along with two isotopologues, providing a direct computation of vibrational frequency shifts. We show that obtaining a converged v = 1 vibrational state of the caged molecule does not require converging the very large number of intermolecular translation-rotation states belonging to the v = 0 manifold up to the energy of the intramolecular stretch fundamental (≈4100 cm−1 for H2). Only a relatively modest-size basis for the intermolecular degrees of freedom is needed to accurately describe the vibrational averaging over the delocalized wave function of the quantum ground state of the system. For the caged H2, our computed fundamental translational excitations, rotational j = 0 → 1 transitions, and frequency shifts of the stretch fundamental are in excellent agreement with recent quantum 5D (rigid H2) results [A. Powers et al., J. Chem. Phys. 148, 144304 (2018)]. Our computed frequency shift of −43 cm−1 for H2 is only 14% away from the experimental value at 20 K.We report the first fully coupled quantum six-dimensional (6D) bound-state calculations of the vibration-translation-rotation eigenstates of a flexible H2, HD, and D2 molecule confined inside the small cage of the structure II clathrate hydrate embedded in larger hydrate domains with up to 76 H2O molecules, treated as rigid. Our calculations use a pairwise-additive 6D intermolecular potential energy surface for H2 in the hydrate domain, based on an ab initio 6D H2–H2O pair potential for flexible H2 and rigid H2O. They extend to the first excited (v = 1) vibrational state of H2, along with two isotopologues, providing a direct computation of vibrational frequency shifts. We show that obtaining a converged v = 1 vibrational state of the caged molecule does not require converging the very large number of intermolecular translation-rotation states belonging to the v = 0 manifold up to the energy of the intramolecular stretch fundamental (≈4100 cm−1 for H2). Only a relatively modest-size basis for the intermol...

A generalized Frenkel-Holstein Hamiltonian is constructed to describe exciton migration in oligo(para-phenylene vinylene) chains, based on excited state electronic structure data for an oligomer comprising 20 monomer units (OPV-20). Time-dependent density functional theory calculations using the ωB97XD hybrid functional are employed in conjunction with a transition density analysis to study the low-lying singlet excitations and demonstrate that these can be characterized to a good approximation as a Frenkel exciton manifold. Based on these findings, we employ the analytic mapping procedure of Binder et al. [J. Chem. Phys. 141, 014101 (2014)] to translate one-dimensional (1D) and two-dimensional (2D) potential energy surface (PES) scans to a fully anharmonic, generalized Frenkel-Holstein (FH) Hamiltonian. A 1D PES scan is carried out for intra-ring quinoid distortion modes, while 2D PES scans are performed for the anharmonically coupled inter-monomer torsional and vinylene bridge bond length alternation modes. The kinetic energy is constructed in curvilinear coordinates by an exact numerical procedure, using the TNUM Fortran code. As a result, a fully molecular-based, generalized FH Hamiltonian is obtained, which is subsequently employed for quantum exciton dynamics simulations, as shown in Paper II [R. Binder and I. Burghardt, J. Chem. Phys. 152, 204120 (2020)].

International audience; Upon UV light absorption, 4-aminobenzonitrile undergoes an ultrafast radiationless decay process from a charge-transfer state to a locally-excited state. This pathway proceeds through an extended seam of conical intersections between the second- and first-excited singlet electronic states. Quantum dynamics simulations show that planar geometries dominate the earlier times (

In quantum dynamics, physically well-adapted curvilinear coordinates are coordinates that lead to a Hamiltonian operator as separable as possible, in order to simplify the resolution of the...

We report on high-dimensional quantum dynamical simulations of torsion-induced exciton migration in a single-chain oligothiophene segment comprising twenty repeat units, using a first-principles parametrized Frenkel J-aggregate Hamiltonian. Starting from an initial inter-ring torsional defect, these simulations provide evidence of an ultrafast two-time scale process at low temperatures, involving exciton-polaron formation within tens of femtoseconds, followed by torsional relaxation on a ~300 femtosecond time scale. The second step is the driving force for exciton migration, as initial conjugation breaks are removed by dynamical planarization. The quantum coherent nature of the elementary exciton migration step is consistent with experimental observations highlighting the correlated and vibrationally coherent nature of the dynamics on ultrafast time scales., 4 pages, 4 figures

International audience; We report a theoretical study of the frequency shift (redshift) of the stretching fundamental transition of an H2 molecule confined inside the small dodecahedral cage of the structure II clathrate hydrate and its dependence on the condensed-phase environment. In order to determine how much the hydrate water molecules beyond the confining small cage contribute to the vibrational frequency shift, quantum five-dimensional (5D) calculations of the coupled translation-rotation eigenstates are performed for H2 in the v=0 and v=1 vibrational states inside spherical clathrate hydrate domains of increasing radius and a growing number of water molecules, ranging from 20 for the isolated small cage to over 1900. In these calculations, both H2 and the water domains are treated as rigid. The 5D intermolecular potential energy surface (PES) of H2 inside a hydrate domain is assumed to be pairwise additive. The H2–H2O pair interaction, represented by the 5D (rigid monomer) PES that depends on the vibrational state of H2, v=0 or v=1, is derived from the high-quality ab initio full-dimensional (9D) PES of the H2–H2O complex [P. Valiron et al., J. Chem. Phys. 129, 134306 (2008)]. The H2 vibrational frequency shift calculated for the largest clathrate domain considered, which mimics the condensed-phase environment, is about 10% larger in magnitude than that obtained by taking into account only the small cage. The calculated splittings of the translational fundamental of H2 change very little with the domain size, unlike the H2 j = 1 rotational splittings that decrease significantly as the domain size increases. The changes in both the vibrational frequency shift and the j = 1 rotational splitting due to the condensed-phase effects arise predominantly from the H2O molecules in the first three complete hydration shells around H2.

Methods for the calculation of vibrational contributions to nonresonant and resonant linear and nonlinear optical properties of molecules are reviewed. Both the Bishop–Kirtman perturbation theory and the finite-field/nuclear relaxation–curvature approach are treated. Emerging methods using variational approaches instead of perturbation theory and the methodology required to employ curvilinear coordinates instead of the more usual normal coordinates are briefly described, too. Finally, methods using a time-dependent approach are also treated.

The primal definition of first-order non-adiabatic couplings among electronic states relies on the knowledge of how electronic wavefunctions vary with nuclear coordinates. However, the non-adiabatic coupling between two electronic states can be obtained in the vicinity of a conical intersection from energies only, as this vector spans the branching plane along which degeneracy is lifted to first order. The gradient difference and derivative coupling are responsible of the two-dimensional cusp of a conical intersection between both potential-energy surfaces and can be identified to the non-trivial eigenvectors of the second derivative of the square energy difference, as first pointed out in Koppel and Schubert [Mol. Phys. 104(5-7), 1069 (2006)]. Such quantities can always be computed in principle for the cost of two numerical Hessians in the worst-case scenario. Analytic-derivative techniques may help in terms of accuracy and efficiency but also raise potential traps due to singularities and ill-defined derivatives at degeneracies. We compare here two approaches, one fully numerical, the other semianalytic, where analytic gradients are available but Hessians are not, and investigate their respective conditions of applicability. Benzene and 3-hydroxychromone are used as illustrative application cases. It is shown that non-adiabatic couplings can thus be estimated with decent accuracy in regions of significant size around conical intersections. This procedure is robust and could be useful in the context of on-the-fly non-adiabatic dynamics or be used for producing model representations of intersecting potential energy surfaces with complete obviation of the electronic wavefunctions.

International audience; The photodynamics of 3-hydroxychromone in its first-excited singlet electronic state (bright state of ππ* character) is investigated with special emphasis given to two types of reaction pathways: the excited-state intramolecular-proton-transfer coordinate and the hydrogen-torsion coordinate linking the excited cis and trans isomers. A newly-found conical intersection with the second-excited singlet electronic state (dark state of nπ* character) is suspected to be, to some extent, the reason for the slower rate constant. This hypothesis based on quantum-chemistry calculations is supported by quantum-dynamics simulations in full dimensionality. They show significant transfer of electronic population and provide consistently a vibronic interpretation for the forbidden band in the UV absorption spectrum.

We report the results of calculations pertaining to the HH intramolecular stretching fundamentals of (p-H2)2 encapsulated in the large cage of structure II clathrate hydrate. The eight-dimensional (8D) quantum treatment assumes rotationless (j = 0) H2 moieties and a rigid clathrate structure but is otherwise fully coupled. The (H2)2-clathrate interaction is constructed in a pairwise-additive fashion, by combining the ab initio H2-H2O pair potential for flexible H2 and rigid H2O [D. Lauvergnat et al., J. Chem. Phys. 150, 154303 (2019)] and the six-dimensional (6D) H2-H2 potential energy surface [R. J. Hinde, J. Chem. Phys. 128, 154308 (2008)]. The calculations are performed by first solving for the eigenstates of a reduced-dimension 6D "intermolecular" Hamiltonian extracted from the full 8D Hamiltonian by taking the H2 moieties to be rigid. An 8D contracted product basis for the solution of the full problem is then constructed from a small number of the lowest-energy 6D intermolecular eigenstates and two discrete variable representations covering the H2-monomer internuclear distances. Converged results are obtained already by including just the two lowest intermolecular eigenstates in the final 8D basis of dimension 128. The two HH vibrational stretching fundamentals are computed for three hydrate domains having an increasing number of H2O molecules. For the largest domain, the two fundamentals are found to be site-split by ∼0.5 cm-1 and to be redshifted by about 24 cm-1 from the free-H2 monomer stretch frequency, in excellent agreement with the experimental value of 26 cm-1. A first-order perturbation theory treatment gives results that are nearly identical to those of the 8D quantum calculations.

International audience; 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.

Recently we reported a series of numerical simulations proving that it is possible in principle to create an electronic wave packet and subsequent electronic motion in a neutral molecule photoexcited by a UV pump pulse within a few femtoseconds. We considered the ozone molecule: for this system the electronic wave packet leads to a dissociation process. In the present work, we investigate more specifically the time-resolved photoelectron angular distribution of the ozone molecule that provides a much more detailed description of the evolution of the electronic wave packet. We thus show that this experimental technique should be able to give access to observing in real time the creation of an electronic wave packet in a neutral molecule and its impact on a chemical process., Accepted in Scientific Report

A new ab initio potential energy surface based on an internally contracted multireference configuration-interaction wave function is constructed for the O2(X 3Σ-g,ν)+O2(X 3Σ-g,ν=0) →O3(X 1A1)+O(3P) reaction with ν>20. The vibrational state-to-state reaction probabilities are calculated with a time independent reactive scattering method. The state selected reactive rate constants calculated with 2D reduced dimensionality theory are very small, suggesting that the reaction of ozone formation is not significant in the O2(X 3Σ-g,ν)+O2(X 3Σ-g,ν=0) collision. © 1998 American Institute of Physics.

For the computation of rovibrational levels and their spectroscopic intensities, the Eckart conditions are essential to achieve the optimal separation between rotation and vibration. Dymarsky and Kudin [J. Chem. Phys. 122, 124103 (2005)] proposed a procedure for a simplified calculation of the Eckart rotation matrix. In the present work, we have adapted their approach to obtain a kinetic energy operator in curvilinear coordinates using a numerical but exact procedure without resorting to finite differences. Furthermore, we have modified this approach for the study of molecular systems with several minima, for which several Eckart reference geometries are required. The HONO molecular system has been used to show the efficiency of our implementation. Using the Eckart conditions with multi-reference geometries allows for a calculation of the rotational levels as well as frequencies and intensities of the infrared spectra of both HONO isomers with a single calculation.

International audience; Full-dimensionality quantum calculations of acetylene–vinylidene isomerization J. Full quantum mechanical calculations of vibrational energies of methane and fluoromethane are carried out using a polyspherical description combining Radau and Jacobi coordinates. The Hamiltonian is built in a potential-optimized discrete variable representation, and vibrational energies are solved using an iterative eigensolver. This new approach can be applied to a large variety of molecules. In particular, we show that it is able to accurately and efficiently compute eigenstates for four different molecules : CH4 , CHD3 , CH2D2 , and CH3F. Very good agreement is obtained with the results reported previously in the literature with different approaches and with experimental data.

International audience; The variational nuclear-motion codes ElVibRot and GENIUSH have been used to compute rotational-vibrational states of the F-(H2O) anion and its deuterated isotopologue, F-(D2O), employing a full-dimensional, semiglobal potential energy surface (PES) called SLBCL, developed as part of this study for the ground electronic state of the complex. The PES is determined from all-electron, explicitly correlated coupled-cluster singles, doubles, and connected triples [CCSD(T)-F12a] computations with an atom-centered, fixed-exponent Gaussian basis set of cc-pCVTZ-F12 quality. The SLBCL PES accurately reproduces the two equivalent minima of the complex, the corresponding transition barrier of C2v point-group symmetry, as well as the proton transfer and the dissociation asymptotes towards the products HF + OH- and F- + H2O, respectively. The code ElVibRot has been updated so that it can use curvilinear internal coordinates corresponding to a reaction path. The variationally computed vibrational energy levels are compared to relevant experimental and previously determined first-principles results. The vibrational states reveal the presence of pronounced anharmonic effects and considerable intermode couplings resulting in strong resonances, involving in particular the HOH bend and ionic OH stretch motions. Tunneling results in particularly significant splittings for F-(H2O); as expected, the splittings are orders of magnitude smaller for the F-(D2O) molecule. The rovibrational energy levels reveal that, despite the large-amplitude vibrational motions, the rotations of F-(H2O) basically follow rigid-rotor characteristics.

International audience; The nonadiabatic dynamics of ethene in its N, V and Z valence states is reinvestigated. Wave packet dynamics initiated by a vertical p !p* excitation is studied and particular emphasis is put on the investigation of the evolution of diabatic and adiabatic state populations. A new algorithm for computing the adiabatic state populations from diabatically represented wavefunctions is discussed and applied here for the first time. We have used the potential model of ethene which was derived by Krawczyk et al. [R.P. Krawczyk, A. Viel, U. Manthe, W. Domcke, Photoinduced dynamics of the valence states of ethene: a six-dimensional potential-energy surface of three electronic states with several conical intersections. J. Chem. Phys. 119 (2003) 1397–1411] and the kinetic energy operator derived by Viel et al. [A. Viel, R.P. Krawczyk, U. Manthe, W. Domcke, Photoinduced dynamics of ethene in the N, V and Z valence states: a sixdimensional nonadiabatic quantum dynamics investigation, J. Chem. Phys. 120 (2004) 11000–11010]. However, a second kinetic energy operator, which is more accurate than the first one, was derived and applied. The results of our calculations are in qualitative agreement with the previous ones of Viel et al., but there are marked quantitative differences. 2007 Elsevier B.V. All rights reserved.

We examine the effect of dissipation on the laser control of a process that transforms a state into a superposed state. We consider a two-dimensional double well of a single potential energy surface. In the context of reactivity, the objective of the control is the localization in a given well, for instance the creation of an enantiomeric form whereas for quantum gates, this control corresponds to one of the transformation of the Hadamard gate. The environment is either modelled by coupling few harmonic oscillators (up to five) to the system or by an effective interaction with an Ohmic bath. In the discrete case, dynamics is carried out exactly by using the coupled harmonic adiabatic channels. In the continuous case, Markovian and non-Markovian dynamics are considered. We compare two laser control strategies: the Stimulated Raman Adiabatic Passage (STIRAP) method and the optimal control theory. Analytical estimations for the control by adiabatic passage in a Markovian environment are also derived.

International audience; A highly correlated approach using curvilinear valence coordinates is applied to calculate the vibrational fundamentals and some combination modes of the formamide molecule with high accuracy. A series of potential energy surfaces (PESs) has been generated by AGAPES, a program for adaptive generation of adiabatic PESs, at various electronic structure qualities until excellent nonaccidental agreement with the experimentally assigned fundamental transitions was reached at the CCSDT(T)-F12a/aug-cc-pVTZ level of theory using the improved relaxation method of the Heidelberg multiconfiguration time-dependent Hartree (MCTDH) package in connection with an exact expression for the kinetic energy in valence coordinates generated by the TANA program. By comparison of the overtone series ν1–3ν1 to experiment, we demonstrate that the known problems concerning the floppy ν1 wagging motion are solved within this approach. The potential energy coupling as well as the vibrational coupling in curvilinear coordinates is discussed together with the efficiency of this approach.

International audience; A study combining accurate quantum chemistry and full-dimensional quantum dynamics is presented to confirm the existence of an ultrafast radiationless decay channel from the charge-transfer state to the locally excited state in 4-aminobenzonitrile. This intramolecular charge-transfer pathway proceeds through a newly found planar conical intersection, and it is shown to be more efficient in the presence of acetonitrile than in the gas phase. Our results are consistent with recent experimental observations. I ntramolecular charge transfer (ICT) in electron donor− acceptor molecules is a process of high interest that has given place to a strong debate over the last decades. A large amount of experimental and theoretical studies have been devoted to this kind of systems, often focused on the aminobenzonitrile family and particularly on the parent system, 4-aminobenzonitrile (ABN), and on its N-dimethyl derivative, DMABN. 1 The small size and simple architecture of ABN and DMABN have made them prototype systems for studying ICT phenomena. They are particularly interesting because, despite their similarity, their luminescent patterns are quite different; while ABN only shows the normal fluorescence band in any environment, DMABN exhibits normal fluorescence in non-polar solvents but dual fluorescence in polar ones. 2,3 This indicates that the different photochemical behaviors are not due to different characters of the electronic states but to changes induced by the polar environment. Despite the large amount of time and effort invested in their study, there is still a very lively controversy involving these systems. It is well-established that the normal band is originated from a locally excited (LE) state, while the anomalous band is due to a charge-transfer (CT) state of high dipole moment that is stabilized in polar solvent environments. The exact structures of the species responsible for the anomalous band and the mechanism that populates them are unclarified questions due to contradictory arguments based on both experimental observations and theoretical calculations, which support different models and hypotheses. Mainly, three models are in the lead of the controversy regarding the structure of the luminescent CT species: the planar ICT model (PICT), 4 the twisted one (TICT), 5 and the partially twisted or pretwisted one (pTICT). 6 It seems sufficiently proved that the PICT and TICT species do in fact correspond to two minimum-energy points of the potential energy surface (PES) of the excited CT state in both ABN and DMABN, but their role in the fluorescence spectra is less clear. A fourth model, the rehybridized ICT (RICT), 7 is thought to be a stable species of a πσ* excited state but is nowadays discarded as a luminescent species. Regarding the ICT mechanism, it is well-established that the initial excitation populates first the S 2 state of CT character. The subsequent sequence of steps along the LE or CT PES until the luminescent species are populated is still under discussion. Computational works indicate the existence of a conical intersection (CI) seam between the LE and CT PES that allows internal conversion to occur over a large range of molecular geometries. 8 Experimental works suggest initial population of the LE state and later equilibration with a CT state. 9 It has even been suggested the involvement of the πσ* state in the early stages of the ICT process, 10 but recent works present arguments to discard this possibility. 11,12 This is in fact a point that deserves to be clarified. Park et al. have published a recent paper reporting a study of highly time-resolved fluorescence spectra (TRFS) over the whole emission region of DMABN in acetonitrile. 13 The precise measurements of this study give information about the dynamics of the ICT process free from the interferences of the

Dynamics of complex molecular systems in generalized coordinates (q,p) using numerical kinetic energy operators is investigated. The kinematical tools necessary for quantum, classical or semiclassical dynamics with or without constraints mainly come from the covariant and contravariant components of the metric tensor and their derivatives up to the second ones. These quantities are computed numerically but without any other approximation than the numerical precision by the code TNUM. This code generates kinetic energy operators in the internal coordinates of the Z-matrix describing the molecular frame geometry in the ab initio quantum chemistry step or in symmetry adapted coordinates [D. Lauvergnat, A. Nauts, J. Chem. Phys. 116 (2002) 8560]. Various reduced dimensionality models can be used in the upgraded code. The interface with an ab initio code is calibrated on a 22-atom system for which a two-dimensional quantum treatment with a constrained Hamiltonian has been carried out previously. The test application concerns the spreading properties of a wave packet in an unstable flat region around a valley ridge inflexion point between two transition states in the Endo-dimerization of cyclopentadiene. We perform here on-the-fly classical or semiclassical dynamics in full or reduced dimensionality.

This paper deals with a cen- tral paradigm of chemistry, the elec- tron-pair bond. Valence bond (VB) theory and electron-localization func- tion (ELF) calculations of 21 single bonds demonstrate that along the two classical bond families of covalent and ionic bonds, there exists a class of charge-shift bonds (CS bonds) in which the fluctuation of the electron pair den- sity plays a dominant role. In VB theory, CS bonding manifests by way of a large covalent-ionic resonance energy, RECS, and in ELF by a depleted basin population with large variances (fluctuations). CS bonding is shown to be a fundamental mechanism that is necessary to satisfy the equilibrium condition, namely the virial ratio of the kinetic and potential energy contribu- tions to the bond energy. The paper de- fines the atomic propensity and territo- ry for CS bonding: Atoms (fragments) that are prone to CS bonding are com- pact electronegative and/or lone-pair- rich species. As such, the territory of CS bonding transcends considerations of static charge distribution, and in- volves: a) homopolar bonds of heteroa- toms with zero static ionicity, b) heter- opolar s and p bonds of the electro- negative and/or electron-pair-rich ele- ments among themselves and to other atoms (e.g., the higher metalloids, Si, Ge, Sn, etc), c) all hypercoordinate molecules. Several experimental mani- festations of charge-shift bonding are discussed, such as depleted bonding density, the rarity of ionic chemistry of silicon in condensed phases, and the high barriers of halogen-transfer reac- tions as compared to hydrogen-trans- fers.

In the present work, we study the vibrational spectrum of ammonia in full dimensionality (6D), with special emphasis on the tunneling splitting. The inversion motion, i.e., the active mode v(2), is indeed relatively well decoupled from the other five inactive modes. Therefore, an adiabatic separation in an active wave function and an inactive one, approximated with a 5D-harmonic basis function, is certainly well adapted to describing this motion. This separation leads to several 1D-effective Hamiltonians for each 5D-harmonic basis function or adiabatic channel. Two models have been tested: the harmonic adiabatic approximation (HADA), when only one channel is used and the coupled HADA (cHADA), when several channels are coupled. In order to get reliable values for tunneling splitting, our calculations have shown that: (i) the calculation of the electronic potential has to be performed with a large atomic basis set (up to quintuple zeta) with a method including core-valence correlation; (ii) the cHADA is required since the HADA overestimates the energy levels. Furthermore, our values for the tunneling splitting are in good agreement with the experimental data of ammonia and several isotopomers. (C) 2004 Elsevier B.V. All rights reserved.

We present a factorization method of the Hamiltonian operator of a triatomic molecular system constrained rigidly and obtain two new classes of exactly solvable potentials. Using some well-known shape invariance potentials, we obtain the spectrum of the non-constrained triatomic molecules for 12 classes of noncentral and separable potentials depending on five or six parameters.

The internal rotation of the methanol molecule is studied in full dimensionality i.e., the 12 coordinates are treated explicitly using an adiabatic separation of the 1D-torsional and the 11D-inactive wave functions. The potential energy surface is calculated with the help of quantum chemistry codes and is expanded in a Taylor series up to the second order along the torsional path. Our main results show that the torsional energy levels of this 1+11D-adiabatic model are noticeably different from those of the 1D-models, whether the zero point energy correction along the path is included or not.

Vibrationally excited N2H+ and N2D+ ions with internal energies of at least 1.3 eV have been produced by electron ionization of a mixture of N2 and H2 (or D2). Their radiative overall lifetime has been determined using the monitor ion technique in a triple cell ICR spectrometer. Theoretical calculation of the vibrational energy levels up to 2.3 eV and of the radiative lifetimes for the fundamental transition of the three normal modes of each isotopomer has been performed in order to help the qualitative analysis of the experimental results. Excitation of ν1 stretching mode is quickly relaxed and is not observed in our experimental conditions. The measured overall lifetimes correspond mainly to excitation of ν2 bending mode. Excitation of the ν3 stretching above v=2 for N2H+ and v=3 for N2D+ seems to be negligible.

A new numerical method for the calculation of parts of the vibrational spectra of polyatomic molecules is presented. In particular, this method accounts for the high-lying floppy states in which the molecule may be delocalized over several isomeric forms. For testing the validity of the method, i.e. for allowing comparisons with reliable results previously obtained, the method is applied to triatomic molecules, namely the molecules isoelectronic to HCN/CNH (HCP, HSiN and HSiP). But the method is obviously designed for larger systems. The potential energy surfaces of the four molecules studied are topologically strongly different, i.e. the repartitions of the minima and the transition states are changing significantly from one another, thus producing different spectral profiles.

Numerical simulations are presented to validate the possible use of cutting-edge attosecond time- resolved photoelectron spectroscopy to observe in real time the creation of an electronic wavepacket and subsequent electronic motion in a neutral molecule photoexcited by a UV pump pulse within a few femtoseconds.

For computational rovibrational spectroscopy the choice of the frame is critical for an approximate separation of overall rotation from internal motions. To minimize the coupling between internal coordinates and rotation, Eckart proposed a condition ["Some studies concerning rotating axes and polyatomic molecules," Phys. Rev. 47, 552-558 (1935)] and a frame that fulfills this condition is hence called an Eckart frame. A method is developed to introduce in a systematic way the Eckart frame for the expression of the kinetic energy operator (KEO) in the polyspherical approach. The computed energy levels of a water molecule are compared with those obtained using a KEO in the standard definition of the Body-fixed frame of the polyspherical approach. The KEO in the Eckart frame leads to a faster convergence especially for large J states and vibrationally excited states. To provide an example with more degrees of freedom, rotational states of the vibrational ground state of the trans nitrous acid (HONO) are also investigated.

To understand the photoreactivity of aminobenzonitrile and benzopyran, their electronic structures and the potential energy landscapes were analyzed at the CASSCF level and models were developed to perform quantum dynamics calculations