On the properties of a primitive semiclassical surface hopping propagator for nonadiabatic quantum dynamics

A previously developed nonadiabatic semiclassical surface hopping propagator [M. F. Herman J. Chem. Phys. 103, 8081 (1995)] is further studied. The propagator has been shown to satisfy the time-dependent Schrodinger equation (TDSE) through order h, and the O(h2) terms are treated as small errors, consistent with standard semiclassical analysis. Energy is conserved at each hopping point and the change in momentum accompanying each hop is parallel to the direction of the nonadiabatic coupling vector resulting in both transmission and reflection types of hops. Quantum mechanical analysis and numerical calculations presented in this paper show that the h2 terms involving the interstate coupling functions have significant effects on the quantum transition probabilities. Motivated by these data, the h2 terms are analyzed for the nonadiabatic semiclassical propagator. It is shown that the propagator can satisfy the TDSE for multidimensional systems by including another type of nonclassical trajectories that reflect on the same surfaces. This h2 analysis gives three conditions for these three types of trajectories so that their coefficients are uniquely determined. Besides the nonadiabatic semiclassical propagator, a numerically useful quantum propagator in the adiabatic representation is developed to describe nonadiabatic transitions.     

Nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method revisited: applications to Tully's three model systems

The nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method for nonadiabatic problems is reformulated. The method has the same spirit as Tully's surface hopping technique [J. Chem. Phys. 93, 1061 (1990)] and almost keeps the same structure as the original single-surface HK SC-IVR method except that trajectories can hop to other surfaces according to the hopping probabilities and phases, which can be easily integrated along the paths. The method is based on a rather general nonadiabatic semiclassical surface hopping theory developed by Herman [J. Chem. Phys. 103, 8081 (1995)], which has been shown to be accurate to the first order in h and through all the orders of the nonadiabatic coupling amplitude. Our simulation studies on the three model systems suggested by Tully demonstrate that this method is practical and capable of describing nonadiabatic quantum dynamics for various coupling situations in very good agreement with benchmark calculations.     

Ultrafast strong field quantum control on K2 dimers

In this theoretical wave packet study, we demonstrate efficient strong field quantum control by Selective Population of Dressed States (SPODS) on K₂ dimers. Shaped femtosecond pulses are used to switch population transfer among different final states with high selectivity and almost unit efficiency. The physical mechanism of this ultrafast molecular strong field control scenario is analyzed in analogy to the interpretation of recent experimental studies of SPODS on atoms. Criteria for the design of SPODS-pulses are presented along with experimental signatures for the observation of SPODS on molecules.     

Interpretation of the vibrational relaxation of H2 in H2 within the semiclassical effective mass approach

The temperature dependence of the rate coefficients for vibrational relaxation of H2 in neat H2 is interpreted within the semiclassical effective mass approach. Across the temperature range of 80-3000 K, the experimental rate coefficients vary by five orders of magnitude and fall onto a strongly nonlinear Landau-Teller plot. This behavior is explained by the nonclassical nature of the energy release and by a substantial participation of rotation of the colliding partners in inducing the vibrational transition. A single fitting parameter, the optimal reduced mass, permits one to represent the temperature dependence of the rate coefficient within a factor of 2. This parameter is found to be close to that obtained from a simple model suggested by Sewell et al. [J. Chem. Phys. 99, 2567 (1993)].     

A new method for the determination of free L-carnitine in serum samples based on high field single quantum coherence filtering 1H-NMR spectroscopy

The rapid and accurate determination of specific metabolites present in biofluids is a very demanding task which is essential in both medicine and chemistry. l-carnitine (3-hydroxy-4-N-trimethylammonium butyrate) is an important metabolite which participates in a series of biological paths and therefore its determination is of diagnostic importance. A single quantum coherence filtering ¹H NMR methodology was used for the accurate and rapid determination of l-carnitine in human serum samples. The methodology is based on spectral simplification, and specifically on the distinction of the N-methyl proton signal of l-carnitine that is greatly overlapped in the ¹H-NMR spectrum of serum. The quantitative results provided by the proposed method are in excellent agreement with those obtained by the enzymatic method, which is widely used. The proposed method is rapid (~20 min of experimental time), selective, sensitive, and has good analytical characteristics (accuracy, reproducibility). Selected protein precipitation methods were also investigated and sample pretreatment with EtOH is suggested.     

Application of the finite element method to time-dependent quantum mechanics: II. H 2 + in a laser field

A finite element method in Cartesian coordinates in three dimensions is described to solve the time-dependent Schrödinger equation for H ₂ ⁺ in the presence of time-dependent electromagnetic fields. The ionization rates, nonlinear optical polarizabilities and harmonic generation spectrum of H ₂ ⁺ have been calculated for field directions parallel or perpendicular to the hydrogen molecule ion axis. Comparisons of the present numerical results with previously published calculations show that the finite element method reproduces perturbative results and can treat nonperturbativity arbitrary intense short pulses as it includes automatically both bound and continuum electronic states.     

Electronic energy functionals: Levy–Lieb principle within the ground state path integral quantum Monte Carlo

We propose a theoretical/computational protocol based on the use of the Ground State Path Integral Quantum Monte Carlo for the calculation of the kinetic and Coulomb energy density for a system of N interacting electrons in an external potential. The idea is based on the derivation of the energy densities via the (N ? 1)‐conditional probability density within the framework of the Levy–Lieb constrained search principle. The consequences for the development of energy functionals within the context of density functional theory are discussed. We propose also the possibility of going beyond the energy densities and extend this idea to a computational procedure where the (N ? 1)‐conditional probability is an implicit functional of the electron density, independently from the external potential. In principle, such a procedure paves the way for an on‐the‐fly determination of the energy functional for any system. © 2012 Wiley Periodicals, Inc.     

Hierarchical modeling N2 adsorption on the surface of and within a C60 crystal: from quantum mechanics to molecular simulation

The adsorption of N(2) on the surface of, and within, a C(60) face-centered cubic crystal has been studied using a hierarchical approach. First, an ab initio potential between N(2) and C(60) is obtained from a recently developed quantum mechanical hybrid method, and then the adsorption behavior is predicted using Monte Carlo simulation. On the crystal surface, N(2) adsorption isotherm at 77.3 K is of type II. The adsorption simulated with the ab initio potential is slightly greater than that with the empirical Steele potential derived from experimental N(2) adsorption on planar graphite, and both are in fairly good agreement with measured results. With increasing pressure, N(2) molecules are found to sequentially occupy three favorable sites: the octahedral sites, the tetrahedral sites, and the top of C(60) molecules. Finally multiple layers form and wetting occurs as the bulk N(2) saturation pressure is reached. The isosteric heat of adsorption exhibits two maxima and finally approaches the enthalpy of vaporization of bulk N(2). Within the crystal, the N(2) adsorption isotherm at 77.3 K is of type I, and the use of ab initio potential leads to significantly greater adsorption than the Steele potential. N(2) molecules are observed to intercalate only the octahedral sites, and the isosteric heat of adsorption is nearly a constant. As in our previous work of N(2) and O(2) adsorption in the C(168) schwarzite (Jiang et al. J. Phys. Chem. B 2004, 108, 9852), this work demonstrates the importance of an accurate adsorbate-adsorbent interaction potential in the determination of gas adsorption behavior.     

Excited state dynamics with the direct trajectory surface hopping method: azobenzene and its derivatives as a case study

We review the recent studies of the photoisomerization dynamics of azobenzene and its derivatives by surface hopping simulations based on semiempirical potential energy surfaces. We examine the ability of semiclassical methods to predict the excited state dynamics and to reproduce transient spectroscopic signals that constitute the most direct experimental evidence in this field. We show that the available simulation methods yield a deep insight into the mechanism of photochemical reactions and excited state decay, and a fairly good quantitative agreement with experimental findings. Probably the most important technical improvements we can envisage concern the surface hopping algorithm and the usage of ab initio data in the simulation of transient spectra. Concerning azobenzene, our results show that the isomerization mechanism is torsion of the N=N double bond, both by n → π* and by π → π* excitation. The influence of the solvent and the findings of some recent femtochemistry experiments deserve further work to be fully interpreted.     

Vibrational energy relaxation rates of H2 and D2 in liquid argon via the linearized semiclassical method

The vibrational energy relaxation (VER) rates for H2 and D2 in liquid argon (T=152 K, rho=1.45x1022 cm-3) are calculated using the linearized semiclassical (LSC) method (J. Phys. Chem. 2003, 107, 9059, 9070). The calculation is based on Fermi's golden rule. The VER rate constant is expressed in terms of the quantum-mechanical force-force correlation function, which is then estimated using the LSC method. A local harmonic approximation (LHA) is employed in order to compute the multidimensional Wigner integrals underlying the LSC approximation. The H2-Ar and D2-Ar interactions are described by the three-body potential of Bissonette et al. (J. Phys. Chem. A 1996, 105, 2639). The LHA-LSC-based VER rate constants for both D2 and H2 are found to be about 2-3 orders of magnitude slower than those obtained experimentally. However, their ratio agrees quantitatively with the corresponding experimental result. In contrast, the classical VER rate constants are found to be 8-9 orders of magnitude slower than those obtained experimentally, and their ratio is found to be qualitatively different from the corresponding experimental result.     

Minima hopping: an efficient search method for the global minimum of the potential energy surface of complex molecular systems

A method is presented that can find the global minimum of very complex condensed matter systems. It is based on the simple principle of exploring the configurational space as fast as possible and of avoiding revisiting known parts of this space. Even though it is not a genetic algorithm, it is not based on thermodynamics. The efficiency of the method depends strongly on the type of moves that are used to hop into new local minima. Moves that find low-barrier escape-paths out of the present minimum generally lead into low energy minima.     

Insights in quantum dynamical effects in the infrared spectroscopy of liquid water from a semiclassical study with an ab initio-based flexible and polarizable force field

The dynamical properties of liquid water play an important role in many processes in nature. In this paper, we focus on the infrared (IR) absorption spectrum of liquid water based on the linearized semiclassical initial value representation (LSC-IVR) with the local Gaussian approximation (LGA) [J. Liu and W. H. Miller, J. Chem. Phys. 131, 074113 (2009)] and an ab initio based, flexible, polarizable Thole-type model (TTM3-F) [G. S. Fanourgakis and S. S. Xantheas, J. Chem. Phys. 128, 074506 (2008)]. Although the LSC-IVR (LGA) gives the exact result for the isolated three-dimensional shifted harmonic stretching model, it yields a blueshifted peak position for the more realistic anharmonic stretching potential. By using the short-time information of the LSC-IVR correlation function; however, it is shown how one can obtain more accurate results for the position of the stretching peak. Due to the physical decay in the condensed phase system, the LSC-IVR (LGA) is a good and practical approximate quantum approach for the IR spectrum of liquid water. The present results offer valuable insight into future attempts to improve the accuracy of the TTM3-F potential or other ab initio-based models in reproducing the IR spectrum of liquid water.     

Simulation of vibrational dephasing of I(2) in solid Kr using the semiclassical Liouville method

In this paper, we present simulations of the decay of quantum coherence between vibrational states of I(2) in its ground (X) electronic state embedded in a cryogenic Kr matrix. We employ a numerical method based on the semiclassical limit of the quantum Liouville equation, which allows the simulation of the evolution and decay of quantum vibrational coherence using classical trajectories and ensemble averaging. The vibrational level-dependent interaction of the I(2)(X) oscillator with the rare-gas environment is modeled using a recently developed method for constructing state-dependent many-body potentials for quantum vibrations in a many-body classical environment [J. M. Riga, E. Fredj, and C. C. Martens, J. Chem. Phys. 122, 174107 (2005)]. The vibrational dephasing rates gamma(0n) for coherences prepared between the ground vibrational state mid R:0 and excited vibrational state mid R:n are calculated as a function of n and lattice temperature T. Excellent agreement with recent experiments performed by Karavitis et al. [Phys. Chem. Chem. Phys. 7, 791 (2005)] is obtained.     

Electric field effects in sodium bis(2-ethylhexyl)sulfosuccinate water-in-oil microemulsions: field-induced percolation and dynamics of structural changes

We investigate the effect of high electric fields on the percolation behaviour of sodium bis(2-ethylhexyl)sulfosuccinate water-in-oil microemulsions in the L₂ phase and examine the existence of critical fields as a function of droplet radius and droplet concentration. It is shown that there is no direct correlation with critical fields as discussed for electrorheological fluids. Very low critical fields are found in certain ranges of droplet radii. Clustering of droplets with material exchange may be postulated under these conditions. Received: 29 July 1999/Accepted: 8 February 2000     

Bichromatically driven double well: parametric perspective of the strong field control landscape reveals the influence of chaotic states

The aim of this work is to understand the influence of chaotic states in control problems involving strong fields. Towards this end, we numerically construct and study the strong field control landscape of a bichromatically driven double well. A novel measure based on correlating the overlap intensities between Floquet states and an initial phase space coherent state with the parametric motion of the quasienergies is used to construct and interpret the landscape features. "Walls" of no control, which are robust under variations of the relative phase between the fields, are seen on the control landscape and associated with multilevel interactions involving chaotic Floquet states.     

The three-dimensional nonadiabatic dynamics calculation of DH(2)(+) and HD(2)(+) systems by using the trajectory surface hopping method based on the Zhu-Nakamura theory

A theoretical investigation on the nonadiabatic processes of the full three-dimensional D(+)+H(2) and H(+)+D(2) reaction systems has been performed by using trajectory surface hopping (TSH) method based on the Zhu-Nakamura (ZN) theory. This ZN-TSH method refers to not only classically allowed hops but also classically forbidden hops. The potential energy surface constructed by Kamisaka et al. is employed in the calculation. A new iterative method is proposed to yield the two-dimensional seam surface from the topography of the adiabatic potential surfaces, in which the inconvenience of directly solving the first-order partial differential equation is avoided. The cross sections of these two systems are calculated for three competing channels of the reactive charge transfer, the nonreactive charge transfer, and the reactive noncharge transfer, for ground rovibrational state of H(2) or D(2). Also, this study provides reaction probabilities of these three processes for the total angular momentum J=0 and ground initial vibrational state of H(2) or D(2). The calculated results from ZN-TSH method are in good agreement with the exact quantum calculations and the experimental measurements.     

The triplet channel in the photodissociation of ozone in the Hartley band: classical trajectory surface hopping analysis

The triplet channel in the photodissociation of ozone in the Hartley band, O3 + hv-->O(3P) + O2(3sigma), is investigated by means of a classical trajectory surface hopping method using ab initio diabatic potential energy surfaces for the B and the R states. Because of the strong recoil in the R state along the breaking O-O bond, O2(3sigma) is produced with a high rotational energy. The nonadiabatic transition probability depends markedly on the coordinate along the crossing seam. As a consequence a unique correlation is found between the internuclear geometry at the crossing and the final vibrational state of O2(3sigma). The calculated distribution of the translational energy is in good accord with the measured distribution.     

A surface hopping method for chemical reaction dynamics in solution described by diabatic representation: an analysis of tunneling and thermal activation

We present a surface hopping method for chemical reaction in solution based on diabatic representation, where quantum mechanical time evolution of the vibrational state of the reacting nuclei as well as the reaction-related electronic state of the system are traced simultaneously together with the classical motion of the solvent. The method is effective in describing the system where decoherence between reactant and product states is rapid. The diabatic representation can also give a clear picture for the reaction mechanism, e.g., thermal activation mechanism and a tunneling one. An idea of molecular orbital theory has been applied to evaluate the solvent contribution to the electronic coupling which determines the rate of reactive transition between the reactant and product potential surfaces. We applied the method to a model system which can describe complex chemical reaction of the real system. Two numerical examples are presented in order to demonstrate the applicability of the present method, where the first example traces a chemical reaction proceeded by thermal activation mechanism and the second examines tunneling mechanism mimicking a proton transfer reaction.