Quantum Mechanical Wave Packet Calculations Research Articles

Quantum and quasiclassical dynamics of Coriolis coupling effects and stereodynamics

The dynamics of C + H2 → H + CH reaction is theoretically studied using the quasiclassical trajectory and quantum mechanical wave packet methods. The analysis of reaction probabilities, integral cross sections, and rate coefficients reveal the essential Coriolis coupling effects in the quantum mechanical wave packet calculations. The calculated polarization-dependent differential cross section, P(θr ) and P(ϕr ) show that the j ′ of product rotational angular momentum is not only aligned along the y axis and the direction of the vector x + z , but also strongly oriented along the positive y axis.

Controlling high harmonic generation in diatomic molecules by phase shaped laser pulses

SynopsisIn this work we explore the high-order harmonic generation in the H2+ molecule under the action of phase shaped pulses. To this end, quantum mechanical wavepacket calculations are performed within a collinear model of H2+. We analyze the effect of a chirp to the plateau extension of the HHG spectrum, observing significant differences with respect to the sign of the chirp parameter. This result is found to originate from a subtle electron recollision dynamics within the chirped laser pulses, as substantiated by classsical trajectory calculations. Extension of this work focuses on including the nuclear motion of H2+.

Quantum dynamics on S(1D) + H2 reaction: effect of orientation and rotation

Time-dependent quantum mechanical wave packet calculations have been carried out to study the effect of orientation and rotation of the hydrogen molecule on the reaction S (1D) + H2(X1 Σ + )(v = 0, j = 0–3) → SH(X2 Π) + H(2S) using the double many-body expansion (DMBE)/complete basis set (CBS) potential energy surface (PES) by Song and Varandas [J. Chem. Phys. 130, 134317 (2009)]. Reaction probability and integral cross section values were calculated over a range of collision energy values. The cross section values are compared with the experimental values as well as with the other quantum mechanical results. Our calculation shows that reaction probability values strongly depend on the orientation and rotation of the hydrogen molecule. It was also found that rotational excitation of H2 molecule significantly enhances integral reaction cross section values contrary to earlier reported quasi-classical trajectory calculation results.

Photodissociation of N2O: Triplet states and triplet channel

The role of triplet states in the UV photodissociation of N(2)O is investigated by means of quantum mechanical wave packet calculations. Global potential energy surfaces are calculated for the lowest two (3)A' and the lowest two (3)A'' states at the multi-reference configuration interaction level of electronic structure theory using the augmented valence quadruple zeta atomic basis set. Because of extremely small transition dipole moments with the ground electronic state, excitation of the triplet states has only a marginal effect on the far red tail of the absorption cross section. The calculations do not show any hint of an increased absorption around 280 nm as claimed by early experimental studies. The peak observed in several electron energy loss spectra at 5.4 eV is unambiguously attributed to the lowest triplet state 1(3)A'. Excitation of the 2(1)A' state and subsequent transition to the repulsive branch of the 2(3)A'' state at intermediate NN-O separations, promoted by spin-orbit coupling, is identified as the main pathway to the N(2)((1)Σ(g)(+))+O((3)P) triplet channel. The yield, determined in two-state wave packet calculations employing calculated spin-orbit matrix elements, is 0.002 as compared to 0.005 ± 0.002 measured by Nishida et al. [J. Phys. Chem. A 108, 2451 (2004)].

Photodissociation of N2O: Energy partitioning

The energy partitioning in the UV photodissociation of N(2)O is investigated by means of quantum mechanical wave packet and classical trajectory calculations using recently calculated potential energy surfaces. Vibrational excitation of N(2) is weak at the onset of the absorption spectrum, but becomes stronger with increasing photon energy. Since the NNO equilibrium angles in the ground and the excited state differ by about 70°, the molecule experiences an extraordinarily large torque during fragmentation producing N(2) in very high rotational states. The vibrational and rotational distributions obtained from the quantum mechanical and the classical calculations agree remarkably well. The shape of the rotational distributions is semi-quantitatively explained by a two-dimensional version of the reflection principle. The calculated rotational distribution for excitation with λ = 204 nm and the translational energy distribution for 193 nm agree well with experimental results, except for the tails of the experimental distributions corresponding to excitation of the highest rotational states. Inclusion of nonadiabatic transitions from the excited to the ground electronic state at relatively large N(2)-O separations, studied by trajectory surface hopping, improves the agreement at high j.

The dynamics of the H++ D2reaction: a comparison of quantum mechanical wavepacket, quasi-classical and statistical-quasi-classical results

A detailed study of the proton exchange reaction H(+) + D(2)(v = 0, j = 0) --> HD + D(+) on its ground 1(1)A' potential energy surface has been carried out using 'exact' close-coupled quantum mechanical wavepacket (WP-EQM), quasi-classical trajectory (QCT), and statistical quasi-classical trajectory (SQCT) calculations for a range of collision energies starting from the reaction threshold to 1.3 eV. The WP-EQM calculations include all total angular momenta up to J(max) = 50, and therefore the various dynamical observables are converged up to 0.6 eV. It has been found that it is necessary to include all Coriolis couplings to obtain reliable converged results. Reaction probabilities obtained using the different methods are thoroughly compared as a function of the total energy for a series of J values. Comparisons are also made of total reaction cross sections as function of the collision energy, and rate constants. In addition, opacity functions, integral cross sections (ICS) and differential cross sections (DCS) are presented at 102 meV, 201.3 meV and 524.6 meV collision energy. The agreement between the three sets of results is only qualitative. The QCT calculations fail to describe the overall reactivity and most of the dynamical observables correctly. At low collision energies, the QCT method is plagued by the lack of conservation of zero point energy, whilst at higher collision energies and/or total angular momenta, the appearance of an effective repulsive potential associated with the centrifugal motion "over" the well causes a substantial decrease of the reactivity. In turn, the statistical models overestimate the reactivity over the whole range of collision energies as compared with the WP-EQM method. Specifically, at sufficiently high collision energies the reaction cannot be deemed to be statistical and important dynamical effects seem to be present. In general the WP-EQM results lie in between those obtained using the QCT and SQCT methods. One of the main, unexpected, conclusions of this work is that an accurate description of the reaction and of its various dynamical features requires a computationally expensive, accurate quantum mechanical treatment.

Time-dependent quantum dynamics of the He + H+He reaction

Time-dependent quantum-mechanical wave packet calculations have been carried out to calculate the reaction probabilities and cross sections for the proton transfer reaction, He + H+He → HeH+ + He, in a collision energy range 0.0–0.5 eV. A global analytical potential energy surface developed by Panda and Sathyamurthy (2003 J. Phys. Chem. A 107 7125) has been used for the purpose. The probability curves are characterized by numerous oscillatory structures attributed to the presence of resonances. The calculated reaction probabilities are found to be weakly dependent on vibrational and rotational excitations of the diatom for total angular momentum (J) = 0. For higher J values, rotational excitation results in a decline in probability values for j = 1 followed by enhancements for j = 2 and 3. The oscillations seen in reaction probabilities are not fully washed out in the integral cross sections. The dependence of cross section on initial orientations of the reactants is also studied.

Time-dependent quantum study of the kinetics of the H(2S) + FO(2II) → OH(2II) + F(2P) reaction

Quantum mechanical wave packet calculations are carried out for the H((2)S) + FO((2)II) --> OH((2)II) + F((2)P) reaction on the adiabatic potential energy surface of the ground (3)A'' triplet state. The state-to-state and state-to-all reaction probabilities for total angular momentum J = 0 have been calculated. The probabilities for J > 0 have been estimated from the J = 0 results by using J-shifting approximation based on a capture model. Then, the integral cross sections and initial state-selected rate constants have been calculated. The calculations show that the initial state-selected reaction probabilities are dominated by many sharp peaks. The reaction cross section does not manifest any sharp oscillations and the initial state-selected rate constants are sensitive to the temperature.

Quantum Mechanical Calculations for the H2O + hν → O(1D) + H2 Photodissociation Process

Quantum mechanical wavepacket calculations for the photodissociation of water in the second absorption band are presented. Using O + H2 Jacobi coordinates, partial cross sections for the O(1D) + H2 channel are calculated for different initial rotational states. Conical intersection and Renner-Teller effects are included. The branching ratios for the four accessible dissociation channels at 121.6 nm are in good agreement with experiment (J. Chem. Phys. 1982, 77, 2432). The calculations predict significant rotational and vibrational excitation of the H2 fragments. Photodissociation of ortho and para water produces predominantly, but not exclusively, ortho and para H2 fragments, respectively.

Quasiclassical trajectory study of reactive and dissociative processes in H2+H2: Comparison with quantum-mechanical calculations

Quasiclassical trajectory calculations have been carried out for H(2)(v(1)=high)+H(2)(v(2)=low) collisions within a three degrees of freedom model where five different geometries of the colliding complex were considered. Within this approach, probabilities for different competitive processes are studied: four center reaction, collision induced dissociation, reactive dissociation, and three-body complex formation. The purpose is to compare in detail with equivalent quantum-mechanical wave packet calculations [Bartolomei et al., J. Chem. Phys 122, 064305 (2005)], especially the behavior of the probabilities near reaction thresholds. Quasiclassical calculations compare quite well with the quantum-mechanical ones for collision induced dissociation as well as for the four center reaction, although quantum effects become very important near thresholds, particularly for lower v(1)'s and for the four center process. Less quantitative agreement is found for reactive dissociation and three-body complex formation. It is found that most quantum effects are due to differences between quantum and classical vibrational distributions of H(2)(v(1)=high). Zero point energy violation has been found in the classical reactive-dissociative probabilities. Extension of these findings to full-dimensional treatments is examined.

The photodissociation of hydrogen iodide: Is it adiabatic?

AbstractThe assumption that the photodissociation of HI proceeds adiabatically is re‐examined in the context of recently calculated alignment parameters, a(⟂), for the ground state halogen atoms resulting from photodissociation of the analogous HCl and HBr molecules. The a(⟂) alignment parameters for HCl, HBr, and HI are determined from time‐dependent quantum mechanical wave packet calculations based on the best available ab initio electronic structure for each molecule. The experimental measurement of the alignment of the I(2P3/2) atoms is proposed as a stringent test of whether the photodissociation is adiabatic or involves non‐adiabatic coupling of the A1Π1 and a3Π1 electronic states. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

Photodissociation of HBr. 1. Electronic Structure, Photodissociation Dynamics, and Vector Correlation Coefficients

Ab initio potential energy curves, transition dipole moments, and spin-orbit coupling matrix elements are computed for HBr. These are then used, within the framework of time-dependent quantum-mechanical wave-packet calculations, to study the photodissociation dynamics of the molecule. Total and partial integral cross sections, the branching fraction for the formation of excited-state bromine atoms Br(2P(1/2)), and the lowest order anisotropy parameters, beta, for both ground and excited-state bromine are calculated as a function of photolysis energy and compared to experimental and theoretical data determined previously. Higher order anisotropy parameters are computed for the first time for HBr and compared to recent experimental measurements. A new expression for the Re[a1(3) (parallel, perpendicular)] parameter describing coherent parallel and perpendicular production of ground-state bromine in terms of the dynamical functions is given. Although good agreement is obtained between the theoretical predictions and the experimental measurements, the discrepancies are analyzed to establish how improvements might be achieved. Insight is obtained into the nonadiabatic dynamics by comparing the results of diabatic and fully adiabatic calculations.

Dynamics of (H−,H2) collisions: A time-dependent quantum mechanical investigation on a new ab initio potential energy surface

A global analytical potential energy surface for the ground state of H(3)(-) has been constructed by fitting an analytic function to the ab initio potential energy values computed using coupled cluster singles and doubles with perturbative triples [CCSD(T)] method and Dunning's augmented correlation consistent polarized valence triple zeta basis set. Using this potential energy surface, time-dependent quantum mechanical wave packet calculations were carried out to calculate the reaction probabilities (P(R)) for the exchange reaction H(-)+H(2)(v, j)-->H(2)+H(-), for different initial vibrational (v) and rotational (j) states of H(2), for total angular momentum equal to zero. With increase in v, the number of oscillations in the P(R)(E) plot increases and the oscillations become more pronounced. While P(R) increases with increase in rotational excitation from j=0 to 1, it decreases with further increase in j to 2 over a wide range of energies. In addition, rotational excitation quenches the oscillations in P(R)(E) plots.

The CH+H reaction studied with quantum-mechanical and classical trajectory calculations

The CH+H→C+H2 reaction is studied with quantum-mechanical wave packet calculations and quasiclassical trajectory calculations using a CH2 ground-state potential energy surface. Although quantum tunneling is important for direct hydrogen abstraction, the dominance of the complex formation mechanism ensures the reliability of quasiclassical calculations. Most collisions (≈80%) are nonreactive, because of a too-weak excitation of the CH vibration after a H–CH collision with H approaching CH with HCH angles larger than 60 deg. In this aspect the reaction differs from reactions such as the well-studied O(1D)+H2 reaction, where the H–H vibration in the triatomic complex is strongly excited. Also presented is the rate constant for a temperature range between 50 and 2000 K, obtained from quasiclassical cross-section results for collision energies between 0.0005 and 0.3 eV. The role of the excited triplet and singlet states of CH2 on the reaction dynamics is discussed.

An ab initio study of the photodissociation of HN3 molecules following excitation in the à 1A″ ← X̃ 1A′ absorption system

Ab initio calculations of two-dimensional cuts through the full six-dimensional potential energy surfaces of the ground ( 1A′) and first excited (A 1A″) states of HN3 are reported. Specifically, we have investigated the variation of the potential energy surfaces with respect to simultaneous changes of the H–NNN and HN–NN bond lengths, and to changes of the H–NNN bond length and ∠N–N–N angle. These pairs of co-ordinates were chosen in the light of the deduced importance of each of these motions in interpreting the experimentally observed ultraviolet photochemistry of this molecule. Two-dimensional quantum mechanical wavepacket calculations of the photodissociation dynamics have been carried out using each of these two-dimensional surfaces. These offer strong support to our earlier interpretations (Cook et al., Phys. Chem. Chem. Phys., 1999, 1, 45) regarding the form of the vibrational energy disposal in the N3() products arising via H–NNN bond fission on the A state potential energy surface. They also allow investigation of factors influencing the relative branching into the competing H–NNN and HN–NN bond fission channels on the excited state potential energy surface, and predict relative branching ratios for these two channels, as a function of excitation energy, in reasonable accord with the limited available experimental data.

Toward control of surface reactions with a scanning tunneling microscope. Structure and dynamics of benzene desorption from a silicon surface

A theoretical study of tip-induced desorption of benzene from a Si(100) surface is presented. The energetically forbidden process is triggered by inelastic resonance tunneling mediated by a cationic state of the substrate–adsorbate complex. Potential energy surfaces for the neutral and ionic states are computed within a cluster model. Quantum mechanical time-dependent wave packet calculations are used to explore the desorption dynamics. Extension of the scheme to study the response of different classes of organic adsorbates to tunneling current and to control of other surface reactions with a scanning tunneling microscope is discussed.

S 1 –S 2 vibronic coupling in cis-1,3,5-hexatriene. I. Electronic structure calculations

The estimates for the vertical excitation energy of the 2 1A1 state of cis-1,3,5-hexatriene (CHT) vary considerably and provide a good example of the difficulties that can arise in determining transition energies. The great uncertainty is surprising if one considers that this state has already been characterized by high resolution techniques such as resonance enhanced multiphoton ionization (REMPI) and fluorescence excitation spectroscopy in free jet expansions. A theoretical analysis of this problem is clearly needed and the present work, along with the following paper, represents an effort to investigate the nature of the 2 1A1 and 1 1B1 states of CHT. It is shown that a combination of ab initio electronic structure and quantum-mechanical wave packet calculations is required to systematically approach a question as involved as locating the energetical position of the 2 1A1 level. We characterize the energy dependence of the 1 1A1, 2 1A1, and 1 1B1 states of CHT as a function of the in-plane normal coordinates for small displacements from the ground-state equilibrium geometry employing the single-state multiconfigurational second-order perturbation theory (CASPT2) method. This information constitutes the basis for the construction of diabatic harmonic model potential-energy functions associated with the three electronic states in the Franck–Condon region that is essential for the treatment of nonadiabatic dynamics. Five totally symmetric modes with high Franck–Condon and/or tuning activity are identified. Vibronic interaction between the S1 and S2 states is primarily mediated by four vibrations of b1 symmetry, ν26, ν27, ν30, and ν31. ν30 and ν31 are found to be exceptionally powerful interstate coupling modes and the strong nonadiabatic effects induced by these modes in CHT are mainly responsible for the spectroscopic differences observed for the S1 and S2 states of CHT and trans-1,3,5-hexatriene.

Competition of different ionization pathways in K2 studied by ultrafast pump–probe spectroscopy: A comparison between theory and experiment

We present a comparison of experiment and theory of ultrafast one-color pump–probe multiphoton ionization spectrocopy of K2. The wave packet propagation in the A 1Σu+ state and in the (2) 1Πg Rydberg state is monitored in detail by changing systematically the pump and probe wavelength from 779 nm to 837 nm. The measured total ionization rates as a function of the delay time between pump and probe are shown to depend sensitively on the pump and probe wavelengths used and exhibit drastic changes and a variety of fascinating structures as the direct observation of inward and outward wave packet detection and frequency doubling of the detected wave packet oscillation. The time dependent quantum mechanical wave packet calculations are in excellent agreement with the experimental results and allow a clear interpretation of different ionization pathways and mechanisms observed in the femtosecond ion signal.

Observing the spin of a free electron

Long ago, Bohr, Pauli, and Mott argued that it is not, in principle, possible to measure the spin components of a free electron. One can try to use a Stern-Gerlach type of device, but the finite size of the beam results in an uncertainty of the splitting force that is comparable with the gradient force. The result is that no definite spin measurement can be made. Recently there has been a revival of interest in this problem, and we will present our own analysis and quantum-mechanical wave-packet calculations which suggest that a spin measurement is possible for a careful choice of initial conditions.

The influence of molecular rotation on the direct subsurface absorption of H2 on Pd(111)

Within the generalized gradient approximation (GGA) of density functional theory (DFT) we have calculated a three-dimensional (3D) potential energy surface (PES) including an angular degree of freedom for a H2 molecule interacting with a Pd(111) surface. There is an entrance channel barrier (≈0.09 eV) to both dissociative chemisorption and direct subsurface absorption, but after this barrier is crossed direct subsurface absorption can proceed almost without a barrier. 3D quantum mechanical wave packet calculations incorporating the rotation of H2 in a plane perpendicular to the surface show a large part of the hydrogen going directly subsurface even at low incident kinetic energies. The wave packet calculations also show that in the low energy regime rotation inhibits direct subsurface absorption at low j0 and promotes it at high j0.