Electronic Potential Energy Surfaces Research Articles

Novel potential energy surface-based quantum dynamics of ion–molecule reaction **Project supported by the National Natural Science Foundation of China (Grant Nos. 11674198 and 11304185).

According to a novel electronic ground-state potential energy surface of , we calculate the reaction probabilities and the integral cross section for the titled reaction by the Chebyshev wave packet propagation method. The reaction probabilities in a collision-energy range of 0.0 eV–1.0 eV show an oscillatory structure for the reaction due to the existence of the potential well. Compared with the results of Martínez et al., the present integral cross section is large, which is in line with experimental data.

Quasi-classical dynamics investigations of the F + D 2 O → DF + OD reaction on a full dimensional accurate potential energy surface

Abstract The influence of vibrational excitations in the fully deuterated water (D2O) reactant on the reaction with the fluorine atom (F) is investigated using the full-dimensional quasi-classical trajectory method on an accurate ground electronic state potential energy surface. The results show that the reactant vibrational excitation in each mode of D2O has very complicated effect on the reactivity. At low collision energy, excitations in all three modes are more effective than collision energy in promoting the reaction, and their efficacies follow this order: symmetric stretching mode > anti-symmetric stretching mode > bending mode. At high collision energies, the efficacies of the bending and the anti-symmetric stretching modes are similar to or slightly less than collision energy, while the symmetric stretching mode is significantly less effective than collision energy. These intricate mode specificities in the F + D2O → DF + OD reaction cannot be rationalized by the sudden vector projection model due to much denser density of states and faster intramolecular vibrational relaxation rate in D2O than in H2O.

Non-adiabatic quantum reactive scattering in hyperspherical coordinates.

A new electronically non-adiabatic quantum reactive scattering methodology is presented based on a time-independent coupled channel formalism and the adiabatically adjusting principal axis hyperspherical coordinates of T Pack and Parker [J. Chem. Phys. 87, 3888 (1987)]. The methodology computes the full state-to-state scattering matrix for A + B2(v, j) ↔ AB(v', j') + B and A + AB(v, j) → A + AB(v', j') reactions that involve two coupled electronic states which exhibit a conical intersection. The methodology accurately treats all six degrees of freedom relative to the center-of-mass which includes non-zero total angular momentum J and identical particle exchange symmetry. The new methodology is applied to the ultracold hydrogen exchange reaction for which large geometric phase effects have been recently reported [B. K. Kendrick et al., Phys. Rev. Lett. 115, 153201 (2015)]. Rate coefficients for the H/D + HD(v = 4, j = 0) → H/D + HD(v', j') reactions are reported for collision energies between 1 μK and 100 K (total energy ≈1.9 eV). A new diabatic potential energy matrix is developed based on the Boothroyd, Keogh, Martin, and Peterson (BKMP2) and double many body expansion plus single-polynomial (DSP) adiabatic potential energy surfaces for the ground and first excited electronic states of H3, respectively. The rate coefficients computed using the new non-adiabatic methodology and diabatic potential matrix reproduce the recently reported rates that include the geometric phase and are computed using a single adiabatic ground electronic state potential energy surface (BKMP2). The dramatic enhancement and suppression of the ultracold rates due to the geometric phase are confirmed as well as its effects on several shape resonances near 1 K. The results reported here represent the first fully non-adiabatic quantum reactive scattering calculation for an ultracold reaction and validate the importance of the geometric phase on the Wigner threshold behavior.

Nonadiabatic Dynamics via the Symmetrical Quasi-Classical Method in the Presence of Anharmonicity.

The symmetrical quasi-classical (SQC) method recently proposed by Miller and Cotton allows one to simulate nonadiabatic dynamics based on an algorithm with classical-like scaling with respect to system size. This is made possible by casting the electronic degrees of freedom in terms of mapping variables that can be propagated in a classical-like manner. While SQC was shown to be rather accurate when applied to benchmark models with harmonic electronic potential energy surfaces, it was also found to become inaccurate and to suffer numerical instabilities when applied to anharmonic systems. In this paper, we propose an extended SQC (E-SQC) methodology for overcoming those discrepancies by describing the anharmonic nuclear modes, which are coupled to the electronic degrees of freedom, in terms of classical-like mapping variables. The accuracy of E-SQC relative to standard SQC is demonstrated on benchmark models with quartic and Morse potential energy surfaces.

Electronic field emission models beyond the Fowler-Nordheim one

We propose several quantum mechanical models to describe electronic field emission from first principles. These models allow us to correlate quantitatively the electronic emission current with the electrode surface details at the atomic scale. They all rely on electronic potential energy surfaces obtained from three dimensional density functional theory calculations. They differ by the various quantum mechanical methods (exact or perturbative, time dependent or time independent), which are used to describe tunneling through the electronic potential energy barrier. Comparison of these models between them and with the standard Fowler-Nordheim one in the context of one dimensional tunneling allows us to assess the impact on the accuracy of the computed current of the approximations made in each model. Among these methods, the time dependent perturbative one provides a well-balanced trade-off between accuracy and computational cost.

Sub-500 fs electronically nonadiabatic chemical dynamics of energetic molecules from the S1 excited state: Ab initio multiple spawning study.

Energetic materials store a large amount of chemical energy. Different ignition processes, including laser ignition and shock or compression wave, initiate the energy release process by first promoting energetic molecules to the electronically excited states. This is why a full understanding of initial steps of the chemical dynamics of energetic molecules from the excited electronic states is highly desirable. In general, conical intersection (CI), which is the crossing point of multidimensional electronic potential energy surfaces, is well established as a controlling factor in the initial steps of chemical dynamics of energetic molecules following their electronic excitations. In this article, we have presented different aspects of the ultrafast unimolecular relaxation dynamics of energetic molecules through CIs. For this task, we have employed ab initio multiple spawning (AIMS) simulation using the complete active space self-consistent field (CASSCF) electronic wavefunction and frozen Gaussian-based nuclear wavefunction. The AIMS simulation results collectively reveal that the ultrafast relaxation step of the best energetic molecules (which are known to exhibit very good detonation properties) is completed in less than 500 fs. Many, however, exhibit sub-50 fs dynamics. For example, nitro-containing molecules (including C-NO2, N-NO2, and O-NO2 active moieties) relax back to the ground state in approximately 40 fs through similar (S1/S0)CI conical intersections. The N3-based energetic molecule undergoes the N2 elimination process in 40 fs through the (S1/S0)CI conical intersection. Nitramine-Fe complexes exhibit sub-50 fs Fe-O and N-O bond dissociation through the respective (S1/S0)CI conical intersection. On the other hand, tetrazine-N-oxides, which are known to exhibit better detonation properties than tetrazines, undergo internal conversion in a 400-fs time scale, while the relaxation time of tetrazine is very long (about 100 ns). Many other characteristics of sub-500 fs nonadiabatic decay of energetic molecules are discussed. In the end, many unresolved issues associated with the ultrafast nonadiabatic chemical dynamics of energetic molecules are presented.

Kinetics studies of the F + HCl → HF + Cl reaction on an accurate potential energy surface

A full-dimensional electronic ground state potential energy surface for the hydrogen abstraction reaction F + HCl → HF + Cl is developed by using the permutation invariant polynomial neural network approach based on 6509 points computed at the level of CCSD(T)-F12a/AVTZ. Spin-orbit correction is also taken into account at the complete active space self-consistent field level. Theoretical thermal rate coefficients determined by the ring polymer molecular dynamics (RPMD) approach agree well with experiment, validating the accuracy of the PES. Kinetic isotope effect is also investigated.

Relevance of the Nuclear Quantum Effects on the Proton/Deuteron Transmission through Hexagonal Boron Nitride and Graphene Monolayers

According to recent experiments, atomically thin hexagonal boron nitride and graphene are permeable to protons and deuterons (and not to other atomic species), and the experimental estimates of the activation energy are lower than the theoretical values by about 0.5 eV for the isolated proton–membrane transfer model. Our analysis of the electronic potential energy surfaces along the normal to the transmission direction, obtained using correlated electronic structure methods, suggests that the aqueous environment is essential to stabilize the proton transmission, as opposed to the hydrogen atom. Therefore, the process is examined within a molecular model of H2O–H(D)+–material–H2O. Exact quantum-mechanical scattering calculations are performed to assess the relevance of the nuclear quantum effects, such as tunneling factors and the kinetic isotope effect (KIE). Deuteration is found to affect the thermal reaction rate constants (KIE of 3–4 for hexagonal boron nitride and 20–30 for the graphene) and to effect...

Simulating Coherent Multidimensional Spectroscopy of Nonadiabatic Molecular Processes: From the Infrared to the X-ray Regime.

Crossings of electronic potential energy surfaces in nuclear configuration space, known as conical intersections, determine the rates and outcomes of a large class of photochemical molecular processes. Much theoretical progress has been made in computing strongly coupled electronic and nuclear motions at different levels, but how to incorporate them in different spectroscopic signals and the approximations involved are less established. This will be the focus of the present review. We survey a wide range of time-resolved spectroscopic techniques which span from the infrared to the X-ray regimes and can be used for probing the nonadiabatic dynamics in the vicinity of conical intersections. Transient electronic and vibrational probes and their theoretical signal calculations are classified by their information content. This includes transient vibrational spectroscopic methods (transient infrared and femtosecond off-resonant stimulated Raman), resonant electronic probes (transient absorption and photoelectron spectroscopy), and novel stimulated X-ray Raman techniques. Along with the precise definition of what to calculate for predicting the various signals, we outline a toolbox of protocols for their simulation.

Geometric Phase Effects in Nonadiabatic Dynamics near Conical Intersections

Dynamical consideration that goes beyond the common Born-Oppenheimer approximation (BOA) becomes necessary when energy differences between electronic potential energy surfaces become small or vanish. One of the typical scenarios of the BOA breakdown in molecules beyond diatomics is a conical intersection (CI) of electronic potential energy surfaces. CIs provide an efficient mechanism for radiationless electronic transitions: acting as "funnels" for the nuclear wave function, they enable rapid conversion of the excessive electronic energy into the nuclear motion. In addition, CIs introduce nontrivial geometric phases (GPs) for both electronic and nuclear wave functions. These phases manifest themselves in change of the wave function signs if one considers an evolution of the system around the CI. This sign change is independent of the shape of the encircling contour and thus has a topological character. How these extra phases affect nonadiabatic dynamics is the main question that is addressed in this Account. We start by considering the simplest model providing the CI topology: two-dimensional two-state linear vibronic coupling model. Selecting this model instead of a real molecule has the advantage that various dynamical regimes can be easily modeled in the model by varying parameters, whereas any fixed molecule provides the system specific behavior that may not be very illustrative. After demonstrating when GP effects are important and how they modify the dynamics for two sets of initial conditions (starting from the ground and excited electronic states), we give examples of molecular systems where the described GP effects are crucial for adequate description of nonadiabatic dynamics. Interestingly, although the GP has a topological character, the extent to which accounting for GPs affect nuclear dynamics profoundly depends on topography of potential energy surfaces. Understanding an extent of changes introduced by the GP in chemical dynamics poses a problem of capturing GP effects by approximate methods of simulating nonadiabatic dynamics that can go beyond simple models. We assess the performance of both fully quantum (wave packet dynamics) and quantum-classical (surface-hopping, Ehrenfest, and quantum-classical Liouville equation) approaches in various cases where GP effects are important. It has been identified that the key to success in approximate methods is a method organization that prevents the quantum nuclear kinetic energy operator to act directly on adiabatic electronic wave functions.

Effects of zero point vibration on the reaction dynamics of water dimer cations following ionization.

Reactions of water dimer cation (H2O)2+ following ionization have been investigated by means of a direct ab initio molecular dynamics method. In particular, the effects of zero point vibration and zero point energy (ZPE) on the reaction mechanism were considered in this work. Trajectories were run on two electronic potential energy surfaces (PESs) of (H2O)2+: ground state (2 A″-like state) and the first excited state (2 A'-like state). All trajectories on the ground-state PES lead to the proton-transferred product: H2 O+ (Wd)-H2 O(Wa) → OH(Wd)-H3 O+ (Wa), where Wd and Wa refer to the proton donor and acceptor water molecules, respectively. Time of proton transfer (PT) varied widely from 15 to 40 fs (average time of PT = 30.9 fs). The trajectories on the excited-state PES gave two products: an intermediate complex with a face-to-face structure (H2 O-OH2 )+ and a PT product. However, the proton was transferred to the opposite direction, and the reverse PT was found on the excited-state PES: H2 O(Wd)-H2 O+ (Wa) → H3 O+ (Wd)-OH(Wa). This difference occurred because the ionizing water molecule in the dimer switched between the ground and excited states. The reaction mechanism of (H2O)2+ and the effects of ZPE are discussed on the basis of the results. © 2017 Wiley Periodicals, Inc.

Effects of Cr-doping on the adsorption and dissociation of S, SO, and SO2 on Ni(111) surfaces.

Nickel-based alloys are widely applied materials in high-temperature applications because they exhibit superior corrosion resistance and mechanical properties. The effects of sulfur, which is invariably present in industrial atmospheres, on the early stages of oxidation of Ni-based surfaces are not well understood. Here we use density functional theory to investigate the interactions of sulfur, SO, and SO2 with the Ni(111) and Cr-doped Ni(111) surface and elucidate their electronic interactions and potential energy surfaces. The results show that Cr doping of the Ni(111) surface increases the adsorption energies of sulfur, oxygen on the sulfur pre-adsorbed condition, SO and SO2. Further, this increase positively correlates with Cr concentration on top of the Ni(111) surface, although sulfur does not have any preferential interaction with Cr. This explains why Cr doping has little effect on the activation energy of sulfur for the most preferable diffusion path. Nevertheless, the increase in adsorption energies indicates a strong interaction with Cr-doped surfaces, which is due to the Cr-enhanced charge transfer to sulfur adsorbates. The existence of pre-adsorbed sulfur is shown to have a destabilizing effect on the oxygen interactions with the surfaces. Our results show that Cr doping helps to stabilize the protective oxide scale on Ni(111) surfaces and enhances its corrosion resistance.

Ionization, negative ion formation, elastic scattering and spin exchange in H + H collisions at low- to intermediate-energies

A new, two-electron transition mechanism is identified that provides the dominant pathway for negative ion formation in 1–20 keV H + H collisions revealed by use of the so-called ‘hidden crossings’ theoretical framework. This transition is made via a branch point between sheets of the complex, quasi-molecular, electronic potential energy surface for singlet states. Good agreement between measurements and the theoretically predicted cross sections is obtained. This mechanism also provides a pathway for ionization in this energy range adding to that previously identified (Bent et al 1998 J. Chem. Phys. 108 1459) involving hidden crossings among the triplet quasi-molecular states, improving the agreement of the resulting theoretical predictions with measurements between 2 and 20 keV. Also improving agreement with measurements is the addition of the effect of Rosenthal oscillations that are superposed upon the ionization and negative ion formation cross sections. We note that in addition to fundamental new insight provided by these calculations, the resulting data support modeling of hydrogen gases and plasmas such as in astrophysical environments and terrestrial laboratory experiments. Further supporting such needs for H + H collision data, we have also created a new and more comprehensive data set that significantly updates previous work (Krstic and Schultz 1999 J. Phys. B: At. Mol. Opt. Phys. 32 3485 and references therein) of elastic scattering and spin exchange integral and differential cross sections.

Cavity Born-Oppenheimer Approximation for Correlated Electron-Nuclear-Photon Systems.

In this work, we illustrate the recently introduced concept of the cavity Born–Oppenheimer approximation [Flick et al. PNAS2017, 10.1073/pnas.1615509114] for correlated electron–nuclear-photon problems in detail. We demonstrate how an expansion in terms of conditional electronic and photon-nuclear wave functions accurately describes eigenstates of strongly correlated light-matter systems. For a GaAs quantum ring model in resonance with a photon mode we highlight how the ground-state electronic potential-energy surface changes the usual harmonic potential of the free photon mode to a dressed mode with a double-well structure. This change is accompanied by a splitting of the electronic ground-state density. For a model where the photon mode is in resonance with a vibrational transition, we observe in the excited-state electronic potential-energy surface a splitting from a single minimum to a double minimum. Furthermore, for a time-dependent setup, we show how the dynamics in correlated light-matter systems can be understood in terms of population transfer between potential energy surfaces. This work at the interface of quantum chemistry and quantum optics paves the way for the full ab initio description of matter-photon systems.

Molecular plasmonics: The role of rovibrational molecular states in exciton-plasmon materials under strong-coupling conditions

We extend the model of exciton-plasmon materials to include a ro-vibrational structure of molecules using wave-packet propagations on electronic potential energy surfaces. The new model replaces conventional two-level emitters with more complex molecules allowing to examine the influence of alignment and vibrational dynamics on strong coupling with surface plasmon-polaritons. We apply the model to a hybrid system comprising a thin layer of molecules placed on top of a periodic array of slits. Rigorous simulations are performed for two types of molecular systems described by vibrational bound-bound and bound-continuum electronic transitions. Calculations reveal new features in transmission, reflection and absorption spectra including the observation of significantly higher values of the Rabi splitting and vibrational patterns clearly seen in the corresponding spectra. We also examine the influence of anisotropic initial conditions on optical properties of hybrid materials demonstrating that the optical response of the system is significantly affected by an initial pre-alignment of the molecules. Our work demonstrates that pre-aligned molecules could serve as an efficient probe for the sub-diffraction characterization of the near-field near metal interfaces.

Nuclear quantum effects on adsorption of H2 and isotopologues on metal ions

The nuclear quantum effects on the zero-point energy (ZPE), influencing adsorption of H2 and isotopologues on metal ions, are examined using normal mode analysis of ab initio electronic structure results for complexes with 17 metal cations. The lightest metallic nuclei, Li and Be, are found to be the most ‘quantum’. The largest selectivity in adsorption is predicted for Cu, Ni and Co ions. Analysis of the nuclear wavepacket dynamics on the ground state electronic potential energy surfaces (PES) performed for complexes of Li+ and Cu+2 with H2/D2/HD shows that the PES anharmonicity changes the ZPE by up to 9%.

A diabatic electronic state system to describe the internal conversion of azulene.

A diabatic system of two electronic potential energy surfaces as well as the coupling between them is presented. The system is to be used to study the dynamics of the S1 → S0 internal conversion of azulene and is based on single point calculations of the minima of the two surfaces and a dipole-quadrupole (DQ) diabatization. Based on this, a couple of harmonic diabatic surfaces together with a linear coupling surface have been devised. Some preliminary dynamics results are shown.

Stueckelberg Oscillations in a Two‐State Two‐Path Model of a Conical Intersection

AbstractThe two‐state two‐path model is introduced as a minimized model to describe the quantum dynamics of an electronic wave packet in the vicinity of a conical intersection. It involves two electronic potential energy surfaces each of which hosts a pair of quasi‐classical trajectories over which the wave packet is assumed to be delocalized. When both trajectories evolve dynamically either diabatically or adiabatically, the full wave packet dynamics shows only features of the dynamics around avoided level crossings in the vicinity of the conical intersection. When one trajectory evolves adiabatically whereas the other trajectory follows a diabatic evolution, quantum mechanical interference of the wave packet components on each path generates Stueckelberg oscillations in the transition probability. These are surprisingly robust against a dissipative environment and, thus, should be a marker for conical intersections.

Intramolecular Singlet Fission in Quinoidal Bi- and Tetrathiophenes: A Comparative Study of Low-Lying Excited Electronic States and Potential Energy Surfaces.

Quinoidal bithiophene has recently been introduced ( Varnavski, O. et al. J. Phys. Chem. Lett. 2015 , 6 , 1375 - 1384 ) as a very promising isolated organic compound for intramolecular singlet fission (iSF) with an outstanding SF quantum yield of ≈180%. In contrast, another recent study ( Ren, L. et al. J. Am. Chem. Soc. 2015 , 137 , 11294 - 11302 ) revealed that quinoidal tetrathiophenes have no activity in the iSF process and are strong fluorophores instead, with measured fluorescent quantum yields up to 53.1%. Using DFT and TD-DFT methods, the authors of the second contribution attributed the marked differences between these compounds to faster reverse T2 → S1 intersystem crossing processes in the tetrathiophenes. To address this unprecedented discrepancy, quinoidal bithiophene and tetrathiophene compounds and their derivatives are carefully examined using the CASPT2 technique. Theoretical evidence is provided through detailed investigation of CASPT2 potential energy surfaces of different singlet and triplet states involved in the iSF process. Through comparison of the CASPT2 results with the CASSCF and RAS-2SF data, it is found that the dynamic electron correlation present in the CASPT2 method plays a crucial role for correct description of the multiexciton nature of the triplet pair 1[TT] state in quinoidal bi- and tetrathiophenes. Effects of substitution and structural modification on iSF activity of these compounds are also examined using the CASPT2 method where the obtained results are in accordance with previous experimental predictions. These results contribute to a better understanding of the iSF mechanism in quinoidal systems which could be relevant for designing new iSF active compounds.

On the Jahn–Teller effect in the [formula omitted] electronic ground state of CH3F+

In view of recent experimental and theoretical developments, we revisit our earlier theoretical studies (Mahapatra et al., 2004, 2005) on the Jahn–Teller effect in the degenerate X∼2E electronic ground state of CH3F+. The electronic potential energy surfaces and the coupling surfaces are re-calculated employing state-of-the-art ab initio quantum chemistry methods. The vibronic Hamiltonian, constructed with the aid of multimode vibronic coupling theory and symmetry selection rules, is systematically extended to higher order in the Taylor series expansion and the parameters are carefully revised in the present study. First principles quantum dynamics study is carried out to calculate the vibronic eigenvalue spectrum of this degenerate electronic state of CH3F+. The vibronic energy levels are assigned and compared with the experimental pulsed-field-ionization zero-electron-kinetic energy (PFI-ZEKE) and one photon ZEKE spectra of CH3F+ and also with the earlier theoretical results reported in the literature.