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An examination is made of how nuclear motion ought to be considered in solutions to the eigenvalue problem for the full Coulomb Hamiltonian and the role played by the usual clamped-nuclei electronic Hamiltonian in the construction of such solutions., SCOPUS: ar.j, info:eu-repo/semantics/published

We review theoretical methods which can be used for the simulation of time-dependent electronic and nuclear dynamics of gas-phase molecules beyond the Born-Oppenheimer approximation. We concentrate on methods which allow for a description of extensive electronic excitation and ionization. Particular emphasis is placed on the extended multiconfiguration time-dependent Hartree-Fock (Ex-MCTDHF) method. We provide a derivation of the equations of motion of the Ex-MCTDHF method, and discuss its advantages and disadvantages over the methods based on the Born-Huang expansion.

We show that two-particle interferences can be used to probe the nuclear motion in a doubly-excited hydrogen molecule. The dissociation of molecular hydrogen by electron impact involves several decay channels, associated to different molecular rotational states, which produce quantum interferences in the detection of the atomic fragments. Thanks to the correlations between the angular momentum and vibrational states of the molecule, the fragments arising from each dissociation channel carry out a phase-shift which is a signature of the molecule rotation. These phase-shifts, which cannot be observed in a single-atom detection scheme, may be witnessed in realistic experimental conditions in a time-of-flight coincidence measurement. We analyse the interferences arising from the two lowest-energy rotational states of a para-hydrogen molecule. Our result shows the relevance of two-fragments correlations to track the molecular rotation., 5 pages, 3 Figures. Submitted

Journal of electron spectroscopy and related phenomena 204, 237 - 244 (2015). doi:10.1016/j.elspec.2015.06.012, Interatomic Coulombic decay (ICD) is a decay mechanism occurring in loosely bound matter, e.g. in systems bound by van der Waals-forces or hydrogen bonds. In many such cases the decay time is similar to the time scale of nuclear motion during the decay. As the efficiency of ICD strongly depends on the internuclear distance of the atoms or molecules involved in the decay, an overall non-trivial temporal decay behavior arises. The progress of examining the time-domain aspects of interatomic Coulombic decay is summarized in this short topical review with a special emphasis on experiments that are now feasible due to the developments of free-electron lasers., Published by Elsevier, New York, NY [u.a.]

We study strong-field molecular ionization as a function of pulse duration. Experimental measurements of the photoelectron yield for a number of molecules reveal competition between different ionization continua (cationic states) which depends strongly on pulse duration. Surprisingly, in the limit of short pulse duration, we find that a single ionic continuum dominates the yield, whereas multiple continua are produced for longer pulses. Using calculations which take vibrational dynamics into account, we interpret our results in terms of nuclear motion and non-adiabatic dynamics during the ionization process.

G of KRb molecule are obtained. " The spectroscopic parameters De, Re, Be, xe, xexe, xeye, etc. are determined. " The obtained vibrational energy levels correspond with the experimental data. graphical abstract The potential energy curves (PECs) of the ground state X 1 R + and two low-lying excited states 1 3 R + and 1 3 G of KRb molecule have been calculated using the multireference configuration interaction method and the effective core potential basis set. The PECs are fitted into analytical potential energy functions (APEFs) using the Morse long-range potential. The spectroscopic parameters for the states are determined using the analytical derivatives of APEFs. The vibrational energy levels have been calculated by solving the radial Schrodinger equation of nuclear motion based on the APEFs, and compared with the theoretical

Chemical Physics In most chemical reactions, electrons move earlier and faster than nuclei. It is therefore common to model reactions by using potential energy surfaces that depict nuclear motion in a particular electronic state. However, in certain cases, two such surfaces connect in a conical intersection that mingles ultrafast electronic and nuclear rearrangements. Yang et al. used electron diffraction to obtain time-resolved images of CF3I molecules traversing a conical intersection in the course of photolytic cleavage of the C–I bond (see the Perspective by Fielding). Science , this issue p. [64][1]; see also p. [30][2] [1]: /lookup/doi/10.1126/science.aat0049 [2]: /lookup/doi/10.1126/science.aat6002

We extend the broadened classical master equation (bCME) approach [W. Dou and J. E. Subotnik, J. Chem. Phys. 144, 024116 (2016)] to the case of two electrodes, such that we may now calculate non-equilibrium transport properties when molecules come near metal surfaces and there is both strong electron-nuclear and strong metal-molecule coupling. By comparing against a numerically exact solution, we show that the bCME usually works very well, provided that the temperature is high enough that a classical treatment of nuclear motion is valid. Finally, in the low temperature (quantum) regime, we suggest a means to incorporate broadening effects in the quantum master equation (QME). This bQME works well for fairly low temperatures.

A procedure, based on Rayleigh-Schrodinger perturbation theory, for obtaining vibrational, rotational, and temperature-dependent Compton profiles and profile anisotropies is presented and applied to H2 to test its validity. The computed vibrational-rotational dependence is found to agree well with the results of Smith et al. who obtained vibrational-rotational profiles for H2 by numerically integrating the Schrodinger equation for nuclear motion. The procedure is used to obtain vibrational, rotational, and temperature-dependent profiles and anisotropies for some alkali halide molecules. It is found that the vibrational and temperature dependence of the parallel-perpendicular anisotropies in these molecules is substantial.

Out-of-plane nuclear motion stimulated in the core-excited state and symmetry breaking due to this nuclear motion have been investigated for B Is excitation in the BF3 molecule by a combination of three different experimental methods: angle-resolved ion-yield spectroscopy, vibrationally resolved resonant Auger electron spectroscopy and quadruple-ion coincidence momentum-imaging technique. (C) 2002 Elsevier Science B.V. All rights reserved.

Vibrationally resolved molecular frame photoelectron angular distributions (MFPADs) of fixed-in-space molecules have been evaluated for diatomic and polyatomic molecules. Calculations have been performed by using an extension of the static-exchange density functional theory formerly developed by P. Decleva [1] and coworkers and extended in order to include the nuclear motion in the Born-Oppenheimer approximation. The method proved to be very accurate for diatomic molecules [2, 3, 5], particularly at high energy of the photoelectron. In this work, we present the results obtained for the inner shell photoionization of C2H2, NH3, CH4, CF4, BF3 and SF6.

arXiv:1403.5408, Using time dependent density functional theory (TDDFT) we examine the energy, angular and time-resolved photoelectron spectra (TRPES) of ethylene in a pump-probe setup. To simulate TRPES we expose ethylene to an ultraviolet (UV) femtosecond pump pulse, followed by a time delayed extreme ultraviolet (XUV) probe pulse. Studying the photoemission spectra as a function of this delay provides us direct access to the dynamic evolution of the molecule’s electronic levels. Further, by including the nuclei's motion, we provide direct chemical insight into the chemical reactivity of ethylene. These results show how angular and energy resolved TRPES could be used to directly probe electron and nucleus dynamics in molecules., We acknowledge financial support from the European Research Council Advanced Grant DYNamo (ERC-2010-AdG-267374), Spanish Grants (FIS2010-21282-C02-01 and PIB2010US-00652), Grupos Consolidados UPV/EHU del Gobierno Vasco (IT-578-13) and Ikerbasque. A. Crawford-Uranga also acknowledges financial support from the Departamento de Educación, Política Lingüistica y Cultura del Gobierno Vasco (BFI-2011-26) and DIPC. D. J. Mowbray acknowledges financial support from the Spanish “Juan de la Cierva” program (JCI-2010-08156).

The rovibrational spectrum of H 3 + has been analyzed by taking into account that non-adiabatic couplings can be simulated by using atomic masses for vibrational and nuclear masses for rotational motion. This results in computed transition frequencies that reproduce experiment in most cases by a factor of 10 better than the original results including only adiabatic corrections. The deviation from experiment is in the range of a few hundredths of a wavenumber.

A vibration–rotation Hamiltonian for a symmetric triatomic molecule, based upon a stretch–bender reference frame has been derived. This frame is chosen so that as the molecule bends the reference geometry follows the minimum in the potential energy surface, thus minimizing the size of the displacements required to reach the instantaneous axis geometry. This may be regarded as an extension of methods based upon the rigid–bender reference frame approach developed by Hougen, Bunker, and Johns [J. Mol. Spectrosc. 34, 136 (1970)]. This new stretch–bender Hamiltonian is combined with the Barrow, Dixon, and Duxbury [Mol. Phys. 27, 1217 (1974)] and the Jungen and Merer [Mol. Phys. 40, 25 (1980)] methods of solving the Renner–Teller coupling problem in which molecules execute large amplitude nuclear motion, producing a compact method for the variational calculation of the energies of such a system. The a 1A1 and b 1B1 states of the methylene radical, CH2, are used to demonstrate the use of this method for the ana...

The short-time vibrational wave packet motion in a molecule with several vibrational degrees of freedom shows oscillatory behavior with the characteristic vibrational periods. For long times revivals will occur, i.e., the wave packet restores its initial form. For small vibrational coupling the revival times in the single modes are approximately those of the uncoupled nuclear motion. The fact that the revivals with respect to the single degrees of freedom occur at different times can be used to control the branching ratio between reaction channels by short-pulse electronic excitation at different times. A model of the HOD molecule is used to demonstrate this general scenario.

A spectrum of the hot water molecule has been recorded in emission at a temperature of 1000°C in the region 900 cm −1 to 2000 cm −1 . A total of 4381 lines were observed; 1750 are assigned, mostly to the ν 2 , 2ν 2 − ν 2 , 3ν 2 − 2ν 2 , 4ν 2 − 3ν 2 , and 5ν 2 − 4ν 2 bands. The 5ν 2 − 4ν 2 band has been seen for the first time and the rotational analysis of the other hot bands has been extended to high J and K a values. The assignment of transitions involving previously unobserved levels was achieved using high accuracy ab initio electronic structure calculations, an ab initio adiabatic correction to this potential, and variational nuclear motion calculations of the spectra. The band origin of 5ν 2 is determined to be 7542.39 cm −1 ± 0.05 cm −1 , significantly different from the value obtained from the “dark state” perturbative treatment.

We highlight the effect of the nuclear motion on the control scheme and in particular on the oscillating dipole.

Exact thresholds for electron stimulated desorption of neutral particles from ices of Ar, N 2 , CO, O 2 , and NO are measured and assigned to electronic transitions. Based on these threshold data, microscopic processes that convert electronic energy into nuclear motion are discussed.

Measurements result in effective, usually temperature-dependent structural parameters of molecules, and never directly in equilibrium structures, which are theoretical constructs. A recent high-accuracy semiglobal potential energy surface of the electronic ground state of the ammonia molecule, called NH3-Y2010 (J. Mol. Spectrosc. 2011, 268, 123), which exhibits mass-independent equilibrium NH bond length and a HNH bond angle of 1.0109 Å and 106.75°, respectively, is employed together with the variational nuclear motion code GENIUSH (J. Chem. Phys. 2009, 130, 134112; 2011, 134, 074105) to determine directly measurable, effective structural parameters of the (14)NH(3) and (14)ND(3) molecules. The effective r(g)- and r(a)-type NH(ND) distances determined at 300 K are 1.0307(1.0254) and 1.0256(1.0217) Å, respectively, with an estimated accuracy of 2 × 10(-4) Å. The effective θ(g) HNH and DND bond angles at 300 K are 106.91° and 106.85°, respectively. The root-mean-square amplitudes of vibration, l(g), for the NH(ND) distances at 300 K are 0.073(0.062) Å. These structural parameters confirm the less accurate results of a room-temperature gas-electron-diffraction study (J. Chem. Phys. 1968, 49, 2488, all data in Å): r(g)(NH) = 1.030(2), l(g)(NH) = 0.073(2), r(g)(ND) = 1.027(3), and l(g)(ND) = 0.061(2). The computed difference in the r(g,T)(NH) bond lengths of the two spin isomers (ortho and para forms) of (14)NH(3) is 3 × 10(-5) Å at 0 K, the difference diminishes at temperatures of about 30-50 K.

The geometrical structure of linear chains is discussed with reference to procedures for treating both electronic and nuclear motion and illustrated with reference to recent density functional calculations.

An improved Born-Oppenheimer formalism, which was recently proposed in order to eliminate the inconsistency of the usual approach, is applied to diatomic and polyatomic molecules to gauge, in general terms, the modifications in the electronic structure due to nuclear motion. Whenever the concept of molecular shape is significant (the nuclear movement being restricted to small changes from an equilibrium geometry), it is appropriate to speak of an electronic structure independently of the nuclear movement. The same applies to wave-packet descriptions of this movement. The situation is different, however, for excited vibrational states.

The results of pure ab initio calculations of the hyperfine coupling constants for the vibronic levels of the 2Πu(X2A1, A2B1) system of the BH2 molecule are presented. Computations are performed for various isotopomers of BH2 in the energy range 0-15 000 cm−1.The study shows that even for the lowest vibronic states reliable hfcc′s can be obtained only if the nuclear motion is taken into account. Comparisons with NH2 and CH+2 are made.

The leading nonadiabatic corrections to rovibrational levels of a diatomic molecule are expressed in terms of three functions of internuclear distance: corrections to the adiabatic potential, the effective nuclear mass, and the effective moment of inertia. The resulting radial Schr\"odinger equation for nuclear motion is solved numerically yielding accurate nonadiabatic energies for all rovibrational levels of H$_2$ molecule in excellent agreement with previous calculations by Wolniewicz., Comment: 14 pages

A simple formula is obtained for coupling electrons in a complex system to the electromagnetic field. It includes the effect of intra-atomic excitations and nuclear motion, and can be applied in. e.g., first-principles-based simulations of the coupled dynamics of electrons and nuclei in materials and molecules responding to ultrashort laser pulses. Some additional aspects of nonadiabatic dynamical simulations are also discussed, including the potential of "reduced Ehrenfest'" simulations for treating problems where standard Ehrenfest simulations will fail., Comment: 6 pages, Physical Review B

The partition of a molecule in different regions where virial relations are fulfilled has been proved in the literature to be a fruitful scheme for the description of molecular properties. However, the conceptual importance of this approach is somewhat diminished by the fact that nuclei are considered to occupy successive fixed positions. We show that this restriction can in fact be relaxed when such partitions of molecules are considered. The conditions that density functions must fulfill on the surfaces of such regions, when the nuclear motion is taken into account, are found. Using these conditions, we have examined general cases where the nuclear motion may introduce important modifications of the surfaces defined by the usual condition of zero flux on the one-particle density corresponding to the fixed nuclei model. Finally a further generalization is introduced by considering partitions of subsystems of particles of the system.

To compare aspects of theoretical and experimental models of molecules, we employ the results of quantum-chemical calculations on diazomethane and six structural isomers with formula H2CN2; significant deficiencies of both models impede comparison between a calculated value of a property and a corresponding value deduced from experiment

We report a new dynamic two-center interference effect in high-harmonic generation from ${\mathrm{H}}_{2}$, in which the attosecond nuclear motion of ${\mathrm{H}}_{2}^{+}$ initiated at ionization causes interference to be observed at lower harmonic orders than would be the case for static nuclei. To enable this measurement we utilize a recently developed technique for probing the attosecond nuclear dynamics of small molecules. The experimental results are reproduced by a theoretical analysis based upon the strong-field approximation which incorporates the temporally dependent two-center interference term.

We discuss the implementation (https://commons.lbl.gov/display/csd/LBNL-AMO-MCTDHF) of Multiconfiguration Time-Dependent Hartree-Fock for polyatomic molecules using a Cartesian product grid of sinc basis functions, and present absorption cross sections and other results calculated with it.

We have measured and explained a new mechanism of molecular ionization near the appearance intensity that produces a sequence of peaks in the nuclear kinetic energy spectrum separated by the photon energy. Our interpretation is based on an internally consistent model for the nuclear motion during an intense laser pulse. Within this model, the same concepts and language can be used for both dissociation and ionization, leading to a more unified understanding of the dynamics.

The R-matrix method is used to calculate dissociative excitation cross sections for the four lowest-lying electronically excited states of H2O in the energy range 5-15 eV. For the first time calculations are performed taking into account the nuclear motion by means of an adaptation of the adiabatic nuclei approximation. Cross sections are compared with previous and new fixed-nuclei results and also experiments. Resonance positions and widths are calculated for different geometries of the water molecule.

The potential energy curves (PECs) of X2Σ+ and A2Π states of the CN molecule have been calculated with the multi-reference configuration interaction method and the aug-cc-pwCV5Z basis set. Based on the PECs, all of the vibrational and rotational levels of the 13C14N molecule are obtained by solving the Schrodinger equation of the molecular nuclear motion. The spectroscopic parameters are determined by fitting the Dunham coefficients with the levels. Both the levels and the spectroscopic parameters are in good qualitative agreement with the experimental data available. The analytical potential energy functions are also deduced from the calculated PECs. The present results can provide a helpful reference for future spectroscopy experiments or dynamical calculations of the molecule.

In this survey we will discuss the evolution of core-excited states of adsorbed molecules. The chapter will be organised as follows. After giving a short introduction (Sect. 5.1), we will start with a discussion of the primary core- excitation process (Sect. 5.2); followed by a brief review of results on decay dynamics (Sect. 5.3); finally we will touch on the question of core-excitation- induced dissociation and desorption (Sect. 5.4).

This lecture will focus upon the recombination of electrons with molecular ions, since the interaction between electronic and nuclear motion is an important feature of molecular processes and condensed matter physics, but is not present in the recombination of electons with atomic ions. Two processes will be considered, dissodative recombination, $$\text{e + AB}^\text{ + } \to \text{AB}^{\text{**}} \to \text{A} + \text{B}$$ (1) which has recently been reviewed by Mitchell (1990), and three body-recombination $$\text{e + AB}^\text{ + } \to \text{C} \to \text{AB + C}$$ (2) where the third body C could be an electron or another molecule.

Based on the potential energy function which considers the nuclear motion and isotopic effect of DTO (X1A1), the atomic and molecular reactive collision for O+DT has been studied by Monte-Carlo quasi-classical trajectory approach. It is shown that the reaction O+DT→DTO with a long-lived complex compound has no threshold energy at low collision energy, which agrees with the potential surface. When the collision energy is higher than 209.2 kJ·mol-1, the interchange reactions will start and then increase until DTO molecules are decomposed completely into D, T, O with the collision energy increasing. The interchange reactions O+DT(0, 0)→OD+T and O+DT (0, 0)→OT+D have corresponding threshold energies. The trajectories and collision section of interchange reactions show asymmetrical distribution which corresponds to the potential surface.

The last decade has seen significant advances in our understanding of small, in particular triatomic, molecules and clusters. It is now poss­ible to use high-resolution spectroscopic data to obtain detailed and accu­rate potential energy surfaces of atom-diatom Van der Waals systems by successive refinement of a parameterised potential function. The chapter by Hutson in this book gives a discussion of these methods.

The Born-Oppenheimer approximation, which states that electronic and nuclear motion can be treated separately in quantum mechanical calculations, is a key simplifying step in quantum mechanics that underlies the way we think about molecules. But does it really hold in all bimolecular reactions? In his Perspective, Manolopoulos compares the theoretical study of Alexander et al. with earlier experimental work on the reaction of chlorine with molecular hydrogen to form hydrochloric acid. According to theory, all is well for the Born-Oppenheimer approximation but the experiments suggest otherwise. It remains to be seen how the discrepancy will be resolved.

Using a 6 fs optical pulse we have impulsively excited the entire manifold of Franck-Condon-connected vibronic levels for the S 0 to S 1 transition in an organic dye in solution. Periodic perturbations to the absorption spectrum are observed as a consequence of the nuclear motion brought about by the coherent excitation of the manifold of vibrational levels.

The processes of vibrational excitation and dissociative attachment in low-energy electron collisions with HCl molecule are considered. TheR matrix theory of these processes incorporating nuclear dynamics is developed. The input data of the theory are characteristics of the systeme-HCl calculated in the fixed-nuclei approximation. The comparison with experimental data and other theories is given. It is shown that the account of the nuclear motion leads to the significant increase of the vibrational excitation cross sections near threshold. However, in the present variant of the theory, the cross sections for the excitation of the first level are essentially lower than the experimental ones. The dissociative attachment cross sections are in good agreement with the experiment.

A quasi-relativistic Hamiltonian for an atom and a molecule is constructed. The Foldy-Wouthuysen transformation is applied to the Hamiltonian. Consequently, extra terms from interactions between the electronic motion and the nuclear magnetic field contributing to the Darwin term and the spin-orbit coupling are derived explicitly. Moreover, the coupling between nuclear motion and the spin of the electron is obtained.

The Green's function for the nuclear motion of a diatomic molecule in the quasi-classical approximation has been found taking into account the nonadiabatic coupling of two-electron terms. The Green's function obtained permits the resonant multiphoton transitions to be calculated effectively in molecules under nonadiabatic conditions.

Magnetic susceptibilities of V(CO) 6 in the solid state were determined in the temperature range 4.2–300°K. A theoretical interpretation is proposed: above 66°K, V(CO) 6 is octahedral but the 2 T 2g ground term strongly couples with the nuclear motion. Below 66°K, both axial distortion and magnetic exchange interaction between pairs of molecules appear. The parameters corresponding to this interpretation are calculated by looking for the best fit between experimental and theoretical temperature dependences of paramagnetism.

The far ultraviolet absorption edges of H2, HD, and D2 have been studied under high resolution and the different limits corresponding to absorption from different lower state rotational levels have been observed. The sharpness of the limits for low, as compared to those for high J values, shows that the upper electronic state (which in all probability is the C 1 Π u state) has no potential maximum which might have falsified the values of the dissociation limit. From the precisely measured edges new values for the dissociation energies of H2, HD, and D2 have been determined which are D 0 0 ( H 2 ) = 36113.0 ± 0.3 cm −1 , D 0 0 ( HD ) = 36399 ·9 ± 1 ·0 cm −1 , D 0 0 ( D 2 ) = 36743.6 ± 0.5 cm −1 . If B′ 1 Σ u rather than C 1 Π u is the upper state of the continuum these values would have to be raised by 0.6 cm−1. The zero-point energies of the three molecules have been determined from the most recent data in the literature including the correction term Y00 due to the finer interaction of vibration and rotation. The addition of these zero-point energies to the D 0 0 gives independent De values for the three molecules. A slight difference between De(H2) and De(D2) has been found which is ascribed to an electronic isotope effect caused by a difference in the effect of nuclear motion in the molecule from that in the separated atoms. The magnitude of the effect is in agreement with predictions by Van Vleck. After correction for this effect one obtains the dissociation energy for infinite mass D e ( ∞ H 2 ) = 38287.0 ± 0.8 cm − , a value that agrees extremely well with Kolos and Roothaan's recent theoretical value.

The interaction between diatomic molecules at finite temperatures is analysed with respect to their translational, rotational and vibrational motion. At low temperatures quantum diffraction phenomena associated with these motions affect the intermolecular potential. These effects disappear when the temperature rises to high values compared to some characteristic temperatures found for each of the three types of motion. In this limit it is a reasonable approximation to consider the intermolecular potential as a suitable average over all possible configurations of the nuclei of the molecules.

The results of numerical calculations of the vibrational energy levels of the H2 molecule in the ground electronic state are presented. These were obtained by solving the Schrödinger equation for the nuclear motion using the adiabatic potential calculated by Kolos and Wolniewicz (1965). In agreement with experiment, it was found that H2 has 15 vibrational levels in the ground state. The vibrational transition frequencies agree with the experimental ones (Herzberg and Howe 1959) to better than one part in a thousand. For the lower levels, the remaining discrepancies can be accounted for using Van Vleck's (1936) estimate of the nonadiabatic frequency shifts. Results of similar calculations for D2 and T2 are also given.