On-the-fly, electric-field-driven, coupled electron-nuclear dynamics

An on-the-fly, electric field driven, coupled electron-nuclear dynamics approach is developed and applied to model the photodissociation of water in the A((1)B1) excited state. In this method, a quantum propagator evolves the photon-induced electronic dynamics in the ultrafast time scale, and a quasi-classical surface hopping approach describes the nuclear dynamics in the slower time scale. In addition, strong system-field interactions are explicitly included in the electronic propagator. This theoretical development enables us to study rapid photon-induced bond dissociation dynamics and demonstrates the partial breakdown of electronic coherence as well as electronic population trapping in the excited state when the molecular vibrations detune the system with respect to the applied field. The method offers a practical way to use on-the-fly dynamics for modeling light-molecule interactions that lead to interesting photochemical events.     

Multistage ab initio quantum wavepacket dynamics for electronic structure and dynamics in open systems: momentum representation, coupled electron-nuclear dynamics, and external fields

We recently proposed a multistage ab initio wavepacket dynamics (MS-AIWD) treatment for the study of delocalized electronic systems as well as electron transport through donor-bridge-acceptor systems such as those found in molecular-wire/electrode networks. In this method, the full donor-bridge-acceptor open system is treated through a rigorous partitioning scheme that utilizes judiciously placed offsetting absorbing and emitting boundary conditions. In this manner, the electronic coupling between the bridge molecule and surrounding electrodes is accounted. Here, we extend MS-AIWD to include the dynamics of open-electronic systems in conjunction with (a) simultaneous treatment of nuclear dynamics and (b) external electromagnetic fields. This generalization is benchmarked through an analysis of wavepackets propagated on a potential modeled on an Al(27) - C(7) - Al(27) nanowire. The wavepacket results are inspected in the momentum representation and the dependence of momentum of the wavepacket as well as its transmission probabilities on the magnitude of external bias are analyzed.     

Electron momentum distributions from valence-bond wave functions

Momentum densities obtained from the Heitler-London (HL) wave functions for diatomic molecules and those from the corresponding valence-bond (VB) wave functions including ionic terms are compared. In each case they shown maxima in the direction perpendicular to the bond. However, the dependence of momentum densities on mutual orientations of the two electronic momenta is quite complex in the latter case. The improvement in the Compton profile on including the ionic terms is illustrated with the example of H₂. The momentum denmsities obtained from the VB wave function constructed from orthogonalized atomic orbitals (OAO) have also been examined. The HL wave function with OAOS leads to the same momentum distribution as the repulsive state HL wave function constructed from overlapping AOS.     

On correlated electron-nuclear dynamics using time-dependent density functional theory

We discuss possibilities and challenges for describing correlated electron and nuclear dynamics within a surface-hopping framework using time-dependent density functional theory (TDDFT) for the electron dynamics. We discuss the recent surface-hopping method proposed by Craig et al. [Phys. Rev. Lett. 95, 163001 (2005)] that is based on Kohn-Sham potential energy surfaces. Limitations of this approach arise due to the Kohn-Sham surfaces generally having different gradients than the true TDDFT-corrected ones. Two mechanisms of the linear response procedure cause this effect: we illustrate these with examples.     

Single particle scattering and momentum distributions in solid hydrogen

The incoherent inelastic neutron scattering function of solid para-hydrogen was recorded. It was shown that at momentum transfers above 5Å⁻¹ the data can be interpreted as recoil spectra from single particle scattering at hydrogen molecules. The evaluation of the momentum distribution and kinetic energy of the scattering particles from such data is discussed.     

Valence-shell momentum distributions and ionization energies of carbon disulfide

Valence-shell binding energy spectra and momentum distributions of CS₂ have been measured using non-coplanar symmetric binary (e,2e) spectroscopy. The present measurements are compared with previously published binding energy spectra calculated using the many body 2ph-TDA Green's function (GF) method and the symmetry-adapted cluster configuration-interaction (SAC CI) method. The measured and the calculated binding energy spectra both show extensive population splittings particularly above 20 eV, confirming a significant breakdown of independent particle ionization picture. A relatively strong-outer valence many-body state at 17.0 eV is shown to be satellite of the (2π₀)^?1 state, in accord with earlier conclusions of photoelectron studies. Momentum distributions measured at several carefully chosen binding energies are compared with the corresponding molecular orbital momentum distributions calculated using small and extended gaussian basis sets. The good qualitative agreement between momentum distributions measured in the inner-valence region wth theoretical 4σ_m and 5σ_g orbital momentum distributions confirms the qualitative predictions of satellite parentages by GF and SAC CI calculations. Momentum and position density contour maps of individual orbitals are used to interpret the shapes and atomic characters of the experimental momentum distributions. Momentum densities of the valence orbitals of CS₂ are compared with those of the respective valence isoelectronic species CO₂     

The nodal structure of the momentum distributions of molecules

The nodal structure of molecular momentum distributions is studied by considering the simplest case of the ground state of the hydrogen molecular ion. By examining the exact expansion of the H₂⁺ momentum distribution, it is shown that an infinite sequence of nodes does exist along the p_z axis (z axis parallel to the bond axis) but not nodal planes perpendicular to the p_z axis (as is found for the simplest LCAO function). The nodes are those points where nonplanar nodal surfaces cross the p_z axis. It is also shown that molecular systems with more than one electron cannot, in the ground state, have nodal surfaces in their momentum distributions. Implications for the directional Compton profiles J( q ) are discussed.     

Charge distributions for molecular dynamics simulations from self-consistent polarization method

Partial atomic charges are important force field parameters. They are usually computed by applying quantum-chemical calculations and the assumed population scheme. In this study polarization consistent scheme of deriving a charge distribution inside solute molecule is proposed. The environment effect is explicitly taken into account by distributing solvent molecules around the solute target. The performed analysis includes a few computational schemes (HF, MP2, B3LYP, and M026X), basis sets (cc-pvnz, n = 2, 3, …, 6), and electrostatically derived charge distributions (KS, CHELP, CHELPG, and HLY). It is demonstrated that the environment effect is very important and cannot be disregarded. The second solvation shell should be included to achieve the charge convergence. Huge corrections to charge distribution are due to induction and dispersion. The B3LYP/cc-pvqz level of theory is recommended for deriving the charges within self-consistent polarization scheme.     

Molecular orbital momentum distributions and binding energies for nitric oxide

Binding energy spectra of the valence electrons of the open shell molecule NO have been obtained up to 55 eV at azimuthal angles of 0° and 7° using binary (e, 2e) spectroscopy at an impact energy of 1200 eV. The momentum distribution has been obtained for the least tightly bound (unpaired) electron, removal of which leads to formation of the X ¹Σ⁺ ground state of NO⁺. Momentum distributions have also been measured at 21.0 and 40.5 eV. The measured momentum distributions are compared with several literature wavefunctions of varying complexity. They are found to be in excellent agreement with those calculated using the natural spin orbital wavefunctions of Kouba and Ohrn.     

Orbital momentum distributions and binding energies for the complete valence shell of molecular chlorine by electron momentum spectroscopy

The complete valence shall binding energy spectrum (10–50 eV) of Cl₂ has been determined using electron momentum (binary (e,2e)) spectroscopy. The inner valence region, corresponding to 4σ_u and 4σ_g ionization, has been measured for the first time and shows extensive splitting of the ionization strength due to electron correlation effects. These measurements are compared with the results of many-body calculations using Green function and CI methods employing unpolarised as well as polarised wavefunctions. Momentum distributions, measured in both the outer and inner valence regions, are compared with calculations using a range of unpolarised and polarised wavefunctions. Computed orbital density maps in momentum and position space for oriented Cl₂ molecules are discussed in comparison with the measured and calculated spherically averaged momentum distributions.     

Regarding the validity of the time-dependent Kohn-Sham approach for electron-nuclear dynamics via trajectory surface hopping

The implementation of fewest-switches surface-hopping (FSSH) within time-dependent Kohn-Sham (TDKS) theory [Phys. Rev. Lett. 95, 163001 (2005)] has allowed us to study successfully excited state dynamics involving many electronic states in a variety of molecular and nanoscale systems, including chromophore-semiconductor interfaces, semiconductor and metallic quantum dots, carbon nanotubes and graphene nanoribbons, etc. At the same time, a concern has been raised that the KS orbital basis used in the calculation provides only approximate potential energy surfaces [J. Chem. Phys. 125, 014110 (2006)]. While this approximation does exist in our method, we show here that FSSH-TDKS is a viable option for computationally efficient calculations in large systems with straightforward excited state dynamics. We demonstrate that the potential energy surfaces and nonadiabatic transition probabilities obtained within the TDKS and linear response (LR) time-dependent density functional theories (TDDFT) agree semiquantitatively for three different systems, including an organic chromophore ligating a transition metal, a quantum dot, and a small molecule. Further, in the latter case the FSSH-TDKS procedure generates results that are in line with FSSH implemented within LR-TDDFT. The FSSH-TDKS approach is successful for several reasons. First, single-particle KS excitations often give a good representation of LR excitations. In this regard, DFT compares favorably with the Hartree-Fock theory, for which LR excitations are typically combinations of multiple single-particle excitations. Second, the majority of the FSSH-TDKS applications have been performed with large systems involving simple excitations types. Excitation of a single electron in such systems creates a relatively small perturbation to the total electron density summed over all electrons, and it has a small effect on the nuclear dynamics compared, for instance, with thermal nuclear fluctuations. In such cases an additional, classical-path approximation can be made. Third, typical observables measured in time-resolved experiments involve averaging over many initial conditions. Such averaging tends to cancel out random errors that may be encountered in individual simulated trajectories. Finally, if the flow of energy between electronic and nuclear subsystems is insignificant, the ad hoc FSSH procedure is not required, and a straightforward mean-field, Ehrenfest approach is sufficient. Then, the KS representation provides rigorously a convenient and efficient basis for numerically solving the TDDFT equations of motion.     

Protein dynamics from a NMR perspective: networks of coupled rotators and fractional Brownian dynamics

Nuclear magnetic resonance (NMR) has proven to be the most valuable tool for investigating internal dynamics of proteins. In this perspective, the interpretation of NMR relaxation data eventually relies on a model of the motions. In this article, we propose to compare two radically different approaches that aim at describing internal dynamics in proteins. It is shown that the correlation functions predicted by a network of coupled rotators can be interpreted in terms of a heuristic approach based on fractional Brownian dynamics for each of the vectors in the network. Our results are interpreted in terms of the probability distributions of relaxation modes in both processes, the median of which turns out to be the relevant quantity for the comparison of both models.     

Determining excitation temperature of fragmented C60 via momentum distributions of fragments

Hot C(60) molecules under nanosecond laser excitation decay by a variety of fragmentation channels. An experimental search has been made to determine the excitation temperature of fragmented C(60)via analyzing the momentum distributions of the prompt ionic fragments C(n)(+) (n ≤ 58). It was found that all the C(60) precursors appearing as these ionic fragments have almost the same temperature and the temperature shows little variation with the laser fluences in our limited range. The results provide a clear evidence that a first-order phase transition in the fragmented C(60) is occurring at this temperature. The value of phase transition temperature is found to be about 6050 ± 250 K, which is in a good agreement with the most recent estimations based on the molecular dynamics simulation. This approach offers an experimental opportunity for studying the fragmentation thermodynamics of more complex polyatomic molecules under excitation temperature determined conditions.     

Vibrational effects on the electron momentum distributions of valence orbitals of formamide

The ionization energy spectra and electron momentum distributions of formamide were investigated using the high-resolution electron momentum spectrometer in combination with high level calculations. The observed ionization energy spectra and electron momentum distributions were interpreted using symmetry adapted cluster-configuration interaction theory, outer valence Green function, and DFT-B3LYP methods. The ordering of 10a(') and 2a(") orbitals of formamide was assigned unambiguously by comparing the experimental electron momentum distributions with the corresponding theoretical results, i.e., 10a(') has a lower binding energy. In addition, it was found that the low-frequency wagging vibration of the amino group at room temperature has noticeable effects on the electron momentum distributions. The equilibrium-nuclear-positions-approximation, which was widely used in electron momentum spectroscopy, is not accurate for formamide molecule. The calculations based on the thermal average can evidently improve the agreement with the experimental momentum distributions.     

Finite-amplitude dynamics of coupled cylindrical menisci

The cylindrical meniscus is a liquid/gas interface of circular-cap cross-section constrained along its axis and bounded by end-planes. The inviscid motions of coupled cylindrical menisci are studied here. Motions result from the competition between inertia and surface tension forces. Restriction to shapes that are of circular-cap cross-section leads to an ordinary differential equation (ode) model, with the advantage that finite-amplitude stability can be examined. The second-order nonlinear ode model has a Hamiltonian structure, showing dynamical behavior like the Duffing-oscillator. The energy landscape has either a single- or double-welled potential depending on the extent of volume overfill. Total liquid volume is a bifurcation parameter, as in the corresponding problem for coupled spherical-cap droplets. Unlike the spherical-cap problem, however, axial disturbances can also destabilize, depending on overfill. For large volumes, previously known axial stability results are applied to find the limit at which axial symmetry is lost and comparison is made to the Plateau-Rayleigh limit.     

Temperature and velocity distributions in an inductively coupled plasma

Computer simulations of inductively coupled plasma discharges (ICP) with flow patterns similar to those found in spectrochemical analysis were reported previously. In this investigation temperature and velocity distributions are measured under conditions which allow direct comparison with computer calculations for pure argon central gas flows without solution aerosols. Based upon these comparisons, a refined ICP gas flow model is proposed and its application provides agreement within experimental error between measured and calculated velocity and temperature profiles in most regions of the discharge.     

Energy level distributions in spectra of coupled harmonic oscillators

The spectral density distribution of a hamiltonian which represents a system of N coupled harmonic oscillators, and hence may approximately describe molecular vibrations in the local mode picture, is analyzed. The spectral density moments are expressed as linear combination of products of coefficients which depend on the molecular structure and of one-particle moments describing individual bonds and interactions between them. Detailed expressions for linear and tetrahedral molecules are analyzed. Moreover, general formulae for matrix elements of powers of momentum in the harmonic oscillator basis are given.