Time-dependent Quantum Mechanical Methods Research Articles

Vibronic dynamics in the low-lying coupled electronic states of methyl cyanide radical cation

Static and dynamic aspects of the Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) interactions between the ground and first excited electronic states of the methyl cyanide radical cation are theoretically investigated here. The latter involves construction of a theoretical model by ab initio computation of electronic potential energy surfaces and their coupling surfaces and simulation of the nuclear dynamics employing time-independent and time-dependent quantum mechanical methods. The present system represents yet another example belonging to the ( E + A) ⊗ e JT–PJT family, with common JT and PJT active degenerate (e) vibrational modes. The theoretical results are found to be in very good accord with the recent experimental data revealing that the JT interactions are particularly weak in the ground X ∼ 2 E electronic manifold of methyl cyanide radical cation, On the other hand, the PJT interactions of this ground electronic manifold with the first excited A ∼ 2 A 1 electronic state of the radical cation are stronger which cause an increase of the spectral line density. The effect of deuteration on the JT–PJT dynamics of the methyl cyanide radical cation is also discussed.

Differential and Integral Cross Sections for the H + O2 → OH + O Combustion Reaction

We present accurate differential and integral cross sections for the H + O2 --> OH + O reaction obtained on a newly developed ab initio potential energy surface using time-independent and time-dependent quantum mechanical methods. The product angular distributions near the reaction threshold show pronounced forward and backward peaks, reflecting the complex-forming mechanism. However, the asymmetry of these peaks suggests certain nonstatistical behaviors, presumably due to some relatively short-lived resonances. The integral cross section increases monotonically with the collision energy above a reaction threshold.

Excited state properties of sizable molecules in solution: from structure to reactivity

We review some recent advances in quantum mechanical methods devised specifically for the study of excited electronic state of large size molecules in solution. The adopted theoretical/computational framework is rooted in the density functional theory (DFT) and its time-dependent extension (TD-DFT) for the characterization of ground and excited states, in the polarizable continuum model (PCM) for the treatment of bulk solvent effects, and in time-dependent quantum mechanical methods for chemical dynamics. Selected applications to the simulation of absorption spectra, to the interpretation of time-resolved experiments, and to the computation of dissociative electron transfer rates are presented and discussed.

Acetylene adsorption on Si(1 0 0): A study of the role of surface steps

The focus of this study is on the adsorption of organic molecules onto steps on Si(1 0 0) and acetylene has been chosen as a show-case example. The study is based on a time-dependent quantum mechanical method and is divided into two parts. The first part has a methodological meaning and illustrates the dynamical events occurring when the molecule impinges onto the flat Si(1 0 0) surface. The second part analyzes preferred adsorption sites at steps, which are evaluated under stationary conditions from the minimization of the total energy. Adsorption–desorption events at those sites are analyzed considering temperature-activated motions obtained from the time-dependent representation. The simulation method is based on two Hamiltonians, i.e., semiempirical Hartree–Fock and Density Functional, and uses a cluster to model the exposed surface. Divergences and similarities of the properties of steps with respect to properties of the flat surface, as reported in the literature or obtained from this study, are analyzed and discussed.

Acetylene adsorption onto Si(1 0 0): a study of adsorption dynamics and of surface steps

In this study the interactions of organic molecules with the silicon surface are considered. The purpose is either to achieve some methodological advantages in a time-dependent quantum mechanical representation of adsorption or to describe effects of the surface structure so far absent from the literature. The acetylene molecule is used as a show-case example and the study is divided into two parts. The first part deals with the dynamical aspects of adsorption. A time-dependent quantum mechanical method with a semi-empirical Hamiltonian is presented and its results are compared with the ones in the literature. The second part analyzes the functionality of a surface containing steps. In these calculations acetylene is deposited onto the steps of a silicon surface vicinal to (1 0 0) and the optimal configuration of the system is evaluated under stationary conditions from the minimization of the total energy. The simulation method is based on two Hamiltonians, i.e. semiempirical Hartree–Fock and density functional, and uses a cluster to model the exposed surface.

Collision energy dependence of the HD(nu' = 2) product rotational distribution of the H + D2 reaction in the range 1.30-1.89 eV.

An experimental and theoretical investigation of the collision energy dependence of the HD(nu' = 2,j') rotational product state distribution for the H + D2 reaction in the collision energy range of Ecol = 1.30-1.89 eV has been carried out. Theoretical results based on time-dependent and time-independent quantum mechanical methods agree nearly perfectly with each other, and the agreement with the experiment is good at low collision energies and very good at high collision energies. This behavior is in marked contrast to a previous report on the HD(nu' = 3,j') product state rotational distribution [Pomerantz et al., J. Chem. Phys. 120, 3244 (2004)] where a systematic difference between experiment and theory was observed, especially at the highest collision energies. The reason for this different behavior is not yet understood. In addition, this study employs Doppler-free spectroscopy to resolve an ambiguity in the E, F-X resonantly enhanced multiphoton ionization transition originating from the HD(nu' = 2,j' = 1) state, which is found to be caused by an accidental blending with the transition coming from the HD(nu' = 1,j' = 14) state.

Theoretical prediction on vibrational spectra of [Ar?Ar-H

Centrosymmetric linear [Ar-H-Ar]+ and asymmetric linear [Ar---Ar-H]+ are two stable configurations of [Ar2H]+. Based on the global potential energy surface of [Ar2H]+ provided by our group recently, we calculated the vibrational spectra of [Ar---Ar-H]+ with total angular momentum J = 0 by time-dependent quantum mechanical method, and the influence of quantum tunneling effect on vibrational spectra was found. With the help of the observation on the eigenstate functions and the modified potential energy surface, assignments were made to the spectra. The strong coupling between the excited bending mode of [Ar-H-Ar]+ and the vibrational states of [Ar---Ar-H]+ was discussed.

A quantum wave packet study of three-dimensional inelastic scattering: He—H2

A time-dependent quantum mechanical method has been described to calculate the state-to-state inelastic scattering probabilities for three-dimensional atom—diatom inelastic scattering at the zero total angular momentum. The method utilizes the potentially optimized discrete variable representation (DVR) technique for operating a diatomic Hamiltonian on the wave function and avoids the necessity of repeating many Fourier transformations for this operation. The method has been applied to the He + H2(v,j)→ He + H2(v′,j′) inelastic scattering problem.

The Chebyshev propagator for quantum systems

This paper provides an overview of some recent developments in quantum dynamic and spectroscopic calculations using the Chebyshev progagator. It is shown that the Chebyshev operator (Tk(Ĥ)) can be considered as a discrete cosine type propagator (cos(KΘ^)), in Which the angle operator (Θ^ = arccos Ĥ) is a single-valued mapping of the scaled Hamiltonian (Ĥ) and the order (k) is an effective time. Properties in the angle domain (thus in energy domain) can be obtained from those in the order domain via a cosine Fourier transform. The equivalence and parallelism between the order-angle formulation and the time-energy formulation allow one to transplant existing time-dependent quantum mechanical methods. Compared with the time propagator, the Chebyshev propagator has a number of numerical advantages. Because of its polynomial form, the action of the Chebyshev propagator can be evaluated exactly except for roundoff errors. The three-term recursion formula for Chebyshev polynomials is stable and requires minimal memory. The discretization error in time propagation can be avoided because the Chebyshev propagator is naturally disrcrete. Additional computational savings over the time propagation are possible because the Chebyshev wave packet can be propagated in the real space. Various applications of the Chebyshev propagator are discussed.

Quantum mechanical and semiclassical studies of N+N2 collisions and their application to thermalization of fast N atoms

Energy loss of fast N(4S) atoms in a bath gas of N2 molecules is investigated taking into account elastic and inelastic collisions. Quantum mechanical calculations using a vibrationally close-coupled rotationally sudden approach are performed to obtain the elastic scattering cross sections. Inelastic cross sections involving ro-vibrational transitions of the molecules are determined from a quantum-classical approach in which the vibrational motion of the molecule is treated by the time-dependent quantum mechanical method and the remaining degrees of freedom described by classical mechanics. The computed angular and energy resolved cross sections are used to construct the Boltzmann kernel for energy relaxation of fast N(4S) atoms from which the parameters governing the thermalization are readily extracted.

Multidimensional propagator scheme for explicitly time-dependent Hamiltonians: applications to the multiphoton dissociation dynamics of the HCN molecule

A new multidimensional time-dependent quantum mechanical method is proposed for studying the evolution of explicitly time-dependent Hamiltonians. A propagator is constructed by making use of multidimensional Floquet states. Model applications to the problem of the dissociation of a triatomic molecule (restricted to collinear geometry) in strong laser fields, particularly multimode dissociation dynamics, are encouraging.

A theoretical study of the high-order harmonics of a 200 nm laser from H2 and HeH+

Using a time-dependent quantum mechanical method, based on the evolution of the electron density in real time, a theoretical study is made of the high harmonic generation in H2 and HeH+, corresponding to a 200 nm laser. For H2, four laser intensities in the range 1013–1016 W cm−2 are employed while only one intensity (≈ 1016 W cm−2) is employed for HeH+. Up to the 45th order (4.44 nm) harmonic for H2 and the 53rd order (3.77 nm) harmonic in HeH+ are predicted. For H2, increase in laser intensity I does not change the structure of the high harmonic spectrum but increases the yield of each harmonic according to a fractional law of I1.5. Polar molecules/molecular ions might serve as excellent sources for higher harmonics, the yield and order of the harmonic increasing with increasing mass, ionization potential and polarizability.

A theoretical study of the high-order harmonics of a 200 nm laser from H 2 and HeH +

Using a time-dependent quantum mechanical method, based on the evolution of the electron density in real time, a theoretical study is made of the high harmonic generation in H 2 and HeH +, corresponding to a 200 nm laser. For H 2, four laser intensities in the range 10 13–10 16 W cm −2 are employed while only one intensity (≈ 10 16 W cm −2) is employed for HeH +. Up to the 45th order (4.44 nm) harmonic for H 2 and the 53rd order (3.77 nm) harmonic in HeH + are predicted. For H 2, increase in laser intensity I does not change the structure of the high harmonic spectrum but increases the yield of each harmonic according to a fractional law of I 1.5. Polar molecules/molecular ions might serve as excellent sources for higher harmonics, the yield and order of the harmonic increasing with increasing mass, ionization potential and polarizability.

Molecular Collision Dynamics on Several Electronic States

A time-dependent quantum mechanical method for propagating the wave function on several electronic states is discussed for the polyatomic case and illustrated by the quenching collision of a Na (3p 2P) atom by H2. The specification of method is governed by the need to have a clear physical interpretation of the results, by the recognition that the motion on a given electronic state can often (but not always) be well approximated by classical mechanics, and by the need for a computational procedure that is simple enough to handle polyatomic systems. These desiderata are realized by the spawning technique which is discussed in detail. One more feature of the method is that it allows for a smooth interface with the methodologies of quantum chemistry so that the electronic structure problem can be solved simultaneously with the time propagation of the nuclear dynamics. The method is derived from a variational principle and so can yield quantum mechanically numerically converged results. The parameters that go...

Quantum mechanical three-dimensional wavepacket study of the Li+HF→LiF+H reaction

A three-dimensional time-dependent quantum mechanical wavepacket method is used to calculate the state-to-state reaction probabilities at zero total angular momentum for the Li + HF → LiF +H reaction. Reaction probabilities starting from several different initial HF vibrational–rotational states (v=0,j=0,1,2) and going to all possible open channels are computed over a wide range of energies. A single computation of the wavepacket dynamics yields reaction probabilities from a specific initial quantum state of the reactants to all possible final states over a wide range of energies. The energy dependence of the reaction probabilities shows a broad background structure on which resonances of varying widths are superimposed. Sharp resonance features seem to dominate particularly at low product translational energies. There are marked changes in the energy dependence of the reaction probabilities for different initial or final diatom rotational quantum numbers, but it is noticeable that, for both reactants and products, odd and even rotational quantum numbers give rise to similar features. Our results clearly identify some resonance features which are present in the reaction probability plots for all product and initial states, though they appear in the form of sharp peaks in some plots and sharp dips in others. We speculate that these features arise from reactive scattering resonances which serve to redistribute the flux preferentially to particular product quantum states. The present calculations extend to higher energies than previously published time-independent reactive scattering calculations for this system.

Theoretical study of vibrational excitation of ammonia scattered from Cu

Abstract A time-dependent quantum-mechanical method is used to study the vibrational excitation of ammonia scattered from the Cu(111) surface. The two-dimensional model includes the translational coordinate and the umbrella vibrational coordinate of ammonia. Empirical potential energy surfaces are used in the calculation. It is found that the vibrational excitation probabilities of the scattered NH 3 increase linearly with the normal incident kinetic energy above the excitation threshold. However, the vibration-translation correlation for the ND 3 deviates somewhat from linearity. A much larger overall vibrational inelasticity is found for the deuterated isotope, which is attributed to its heavier mass and lower vibrational frequency. The mechanism for vibrational excitation is analyzed by the scattering of single channel wave packets. It is shown that vibrational excitation occurs almost exclusively for the initially nitrogen-up wave packet. Our theoretical results are in reasonably good agreement with experimental observations, in support for an electronically adiabatic, translational-to-vibrational energy transfer mechanism.

Three-Dimensional Time-Dependent Wavepacket Calculation of the Transition State Resonances for MuH2 and MuD2: Resonance Energies and Widths

The transition state resonances of Mu + H2 and Mu + D2 collisions are investigated on the accurate DMBE potential energy surface for H3 using a three-dimensional (3D) time-dependent quantum-mechanical method for total angular momentum J = 0. The discrete variable representation−finite basis representation (DVR−FBR) transform method is used to describe the dynamics in the bending coordinate, while the two stretching coordinates are treated by a sine fast Fourier transform (FFT) technique. The time propagation of the wavepacket is carried out using the Feit−Fleck split operator algorithm. For both systems, the progressions of the resonance states in 3D are the same as in 2D. Compared with the 2D results, their lifetimes tend to be shorter.

Resonance Raman intensity analysis of polyatomic molecules

A time-dependent quantum mechanical (TDQM) method of wavepacket propagation in computing resonance Raman intensities for polyatomic systems, has been developed and demonstrated by applying it tocis-stilbene andtrans-azobenzene. In the case of the former, Raman excitation profiles (REPs) for the various vibrational modes have also been computed. It is observed that the calculated absorption spectrum and the REPs compare very well with the experimental results. A comparison of these results with those of the often semiclassical approach reveals that the TDQM method can be used to study polyatomic systems with as much ease as the semiclassical wavepacket method.

The Role of Nonadiabatic Coupling in Bond-Selective Dissociations: Two-Dimensional Model Calculations

Abstract The photodissociation dynamics of the model CH2XY (X and Y are halogen atoms) molecule was studied using a time-dependent quantum mechanical method in two dimensions. Simple functional forms were employed as two diabatic potential energy surfaces which correspond to the excited states of C–X (n–σ*) and C–Y (n–σ*). Bond selectivity in the photodissociation is quantitatively examined in terms of the coupling strength between the two surfaces. A method to predict the bond selectivity in the photodissociations is also discussed on the basis of the results of ab initio molecular orbital calculations.

A comparison of time-dependent and time-independent quantum reactive scattering—Li+HF→LiF+H model calculations

Reactive scattering probabilities are computed over a wide range of collision energies for a model system based on the Li+HF→LiF+H reaction using both grid based time-dependent and time-independent quantum mechanical methods. The computations are carried out using a fixed Li–F–H angle which is chosen to be that at which the barrier to the chemical reaction is lowest. The calculated reaction probabilities for this system display many sharp features as a function of energy which are ascribed to scattering resonances. The time-independent calculations have been carried out on a very dense energy grid, thus permitting detailed comparison between time-independent and time-dependent methods (in the latter case, a single computation of the wave packet dynamics provides information on the energy dependence over a given energy range). The results show that the time-dependent calculations are capable of reproducing even the sharpest resonance features computed using the time-independent method. The time-dependent techniques are conceptually very simple and therefore easily implemented. The results presented also demonstrate that the grid based time-dependent quantum mechanical methods used here are able to describe threshold energy dependence of reaction probabilities where the exit channel kinetic energy is effectively zero. The nature of some of the resonance structures are investigated by computing the time-independent continuum wave functions at the ‘‘resonance’’ energies thus mapping out the nodal structure of the wave functions. The good agreement between time-independent and time-dependent methods is shown to be maintained when a centrifugal barrier is added to the potential to simulate the effect of nonzero orbital angular momentum.