Time-dependent Hartree Scheme Research Articles

Photophysics of barrelene: The Jahn-Teller and pseudo-Jahn-Teller effects

The static and dynamic aspects of Jahn-Teller(JT) and pseudo-Jahn-Teller(PJT) interactions between ground (X˜2A2′) and first three excited electronic states (A˜2E′, B˜2E″ and C˜2A′1 ) of bicyclo- [2,2,2]-octa-2,5,7-triene (barrelene) radical cation (Bl+) are theoretically investigated here. This belongs to the (E + E) ⊗ e and (E + A) ⊗ e JT-PJT class of compounds as described by the symmetry of the electronic states and the molecular point group. The complex vibronic dynamics on the coupled electronic states of the cation is simulated by both time-independent and time-dependent wave packet propagation method using multi configuration time-dependent Hartree scheme. The JT effects in the A˜ and B˜ electronic states and the PJT coupling between the B˜ and C˜ electronic states of Bl+ are found very strong. The final theoretical results are compared with the experimental results.

Ab initio quantum study of UV absorption spectra of cis- and trans-hexatriene

The vibronic structure of the UV-absorption spectra of cis- and trans-hexatriene is revisited in a comparative theoretical investigation. The multidimensional potential energy surfaces of the relevant 1A1 (1Ag) and 1B2 (1Bu) electronic states are obtained from CASPT2 and MRCI ab initio calculations using carefully chosen CAS-spaces. These provide the basis for subsequent wavepacket dynamical calculations for the coupled electronic states carried out with the multiconfiguration time-dependent Hartree scheme. The experimental spectra in the ∼5eV energy range are well reproduced for both isomers. The influence of the various degrees of freedom is assessed by comparing the results for different dimensionalities of the calculations. The implications of these findings for the photophysical properties (fluorescence dynamics) are discussed.

Thermal flux based analysis of state-to-state reaction probabilities

Flux correlation functions facilitate rigorous quantum mechanical calculations of reaction rates and initial state-selected reaction probabilities. Combined with an efficient multi-dimensional wave packet propagation employing the multi-configurational time-dependent Hartree scheme, polyatomic reactions can be accurately studied. Very recently, the approach has been generalized to the treatment of fully resolved state-to-state reaction probabilities. The generalized flux correlation function employed utilizes two flux operators corresponding to a dividing surface located in the transition state region and two additional dividing surfaces located in the reactant and product asymptotic areas. The present work provides further analysis of this generalized flux correlation function. It studies state-to-state reaction probabilities of the D + H2(ν, j) → HD(ν′, j′) + H reaction for J = 0 and investigates the contributions of the different thermal flux eigenstate pairs, which correspond to vibrational states of the activated complex.

Quantum grow—A quantum dynamics sampling approach for growing potential energy surfaces and nonadiabatic couplings

A quantum sampling algorithm for the interpolation of diabatic potential energy matrices by the Grow method is introduced. The new procedure benefits from penetration of the wave packet into classically forbidden regions, and the accurate quantum mechanical description of nonadiabatic transitions. The increased complexity associated with running quantum dynamics is reduced by using approximate low order expansions of the nuclear wave function within a Multi-configuration time-dependent Hartree scheme during the Grow process. The sampling algorithm is formulated and applied for three representative test cases, demonstrating the recovery of analytic potentials by the interpolated ones, and the convergence of a dynamic observable.

Photoionization-induced dynamics of the ammonia cation studied by wave packet calculations using curvilinear coordinates

The determination of the photoelectron spectrum of NH 3 and of the internal conversion dynamics of NH 3 + recently published [A. Viel, W. Eisfeld, S. Neumann, W. Domcke, U. Manthe, J. Chem. Phys. 124 (2006) 214306] is complemented by the investigation of the effect of the vibrational angular momenta couplings on the dynamics. The multi-configurational time-dependent Hartree method is used to propagate a wave packet on the analytical anharmonic six-dimensional three-sheeted potential energy surface for the ground and first excited states of the ammonia cation. Curvilinear coordinates and the associated quasi-exact kinetic energy operator suitable for the multi-configurational time-dependent Hartree scheme are employed. A non-negligible effect of the use of Cartesian normal modes instead of the curvilinear coordinates is observed on the low energy part of the photoelectron spectrum. However, the three different time scales found in the dynamical calculations for the second absorption band are very similar regardless of the use of either normal modes or curvilinear coordinates.

Multimode Jahn−Teller and Pseudo-Jahn−Teller Interactions in the Cyclopropane Radical Cation: Complex Vibronic Spectra and Nonradiative Decay Dynamics

The complex vibronic spectra and the nonradiative decay dynamics of the cyclopropane radical cation (CP+) are simulated theoretically with the aid of a time-dependent wave packet propagation approach using the multireference time-dependent Hartree scheme. The theoretical results are compared with the experimental photoelectron spectrum of cyclopropane. The ground and first excited electronic states of CP+ are of X2E' and A2E'' type, respectively. Each of these degenerate electronic states undergoes Jahn-Teller (JT) splitting when the radical cation is distorted along the degenerate vibrational modes of e' symmetry. The JT split components of these two electronic states can also undergo pseudo-Jahn-Teller (PJT)-type crossings via the vibrational modes of e'', a1'' and a2'' symmetries. These lead to the possibility of multiple multidimensional conical intersections and highly nonadiabatic nuclear motions in these coupled manifolds of electronic states. In a previous publication [J. Phys. Chem. A 2004, 108, 2256], we investigated the JT interactions alone in the X2E' ground electronic manifold of CP+. In the present work, the JT interactions in the A2E'' electronic manifold are treated, and our previous work is extended by considering the coupling between the X2E' and A2E'' electronic states of CP+. The nuclear dynamics in this coupled manifold of two JT split doubly degenerate electronic states is simulated by considering fourteen active and most relevant vibrational degrees of freedom. The vibronic level spectra and the ultrafast nonradiative decay of the excited cationic states are examined and are related to the highly complex entanglement of electronic and nuclear degrees of freedom in this prototypical molecular system.

Quantum mechanical calculation of the OH+HCl→H2O+Cl reaction rate: Full-dimensional accurate, centrifugal sudden, and J-shifting results

Full-dimensional quantum calculations for the thermal rate constant of the OH+HCl→H2O+Cl reaction rigorously accounting for the total angular momentum are presented in this work. The dynamics calculation is performed on the Clary, Hernández, and Nyman potential energy surface and employs the flux correlation function formalism and the multiconfigurational time-dependent Hartree scheme. Comparison of the theoretical k(T) values with experiment reveals deficiencies of the potential energy surface. In order to test the validity of different approximations often imposed on the overall rotation, quantum dynamics simulations have also been carried out within the coupled states (CS) and J-shifting approximations. No significant discrepancies are found between CS and accurate results as was to be expected from previous experience. In contrast to previous results for the OH+H2 reaction, the J-shifting approximation yields a reasonable agreement as well.

Reaction cross sections for the H+D2(ν=1)→HD+D and D+H2(ν=1)→DH+H systems. A multiconfiguration time-dependent Hartree (MCTDH) wave packet propagation study

Cumulative initial-state-selected reaction cross sections of the H+D2 and D+H2 systems are computed for collision energies up to 1.6 eV and initial vibrational and rotational quantum numbers ν0=1 and j0=0–4. The Boothroyd–Keogh–Martin–Peterson (BKMP2) potential energy surface is taken as interaction potential. For comparison the Liu–Siegbahn–Truhlar–Horowitz (LSTH) potential energy surface is also considered, however, for j0=0 only. The cross sections are computed by propagating wave packets employing the multiconfiguration time-dependent Hartree scheme. The reactive flux, which determines the integral cross section, is evaluated through the interaction of the wave packet with a complex absorbing potential. A new approach of J-interpolation for the reaction probabilities has been developed. This approach allows to skip about every second of the individual propagations. The presence of weak oscillations appearing in the total integral cross sections has been observed. As in our previous calculations [J. Phys. Chem. 105, 2604 (2001)] on ν0=0, we attribute them to transition state resonances associated with excitations of the bending motion. Some of the present results are compared with previous results obtained by using the coupled states approximation.

On the Effect of Initial Rotation on Reactivity. A Multi-Configuration Time-Dependent Hartree (MCTDH) Wave Packet Propagation Study on the H + D2 and D + H2 Reactive Scattering Systems

Cumulative initial-state-selected reaction cross sections of the H + D2 and D + H2 systems are analyzed for collision energies up to 1.3 eV. Initial states of the diatom with rotational quantum numbers j0 = 0−4 and vibrational quantum number v0 = 0 are considered. The Liu−Siegbahn−Truhlar−Horowitz (LSTH) potential energy surface is taken as interaction potential. The geometric phase is ignored but no further (nonnumerical) approximations are made. The cross sections are computed by propagating wave packets employing the multiconfiguration time-dependent Hartree scheme. The reactive flux, which determines the integral cross section, is evaluated through the interaction of the wave packet with a complex absorbing potential. The initial-state-selected integral cross sections, σj0(E), in particular those for j0= 0, show weak oscillations, which we attribute to transition state resonances associated with excitations of the bending motion. Some of the present results are discussed in comparison with results obtained by using the coupled states approximation.

Efficiently computing bound-state spectra: A hybrid approach of the multi-configuration time-dependent Hartree and filter-diagonalization methods

We present a new approach for determining bound-state spectra of molecules or clusters. In our approach a wave packet propagation is performed, which exploits the efficiency of the multi-configuration time-dependent Hartree scheme, to produce an autocorrelation function. From this, an accurate spectrum is extracted employing the filter-diagonalization procedure. The accuracy of this hybrid method is demonstrated by applying it to the spectrum of carbon dioxide. Compared with the filter-diagonalization scheme based on a numerically exact wave packet propagation and with a matrix diagonalization using the Lanczos algorithm, our approach turns out to be more efficient. The method can easily be generalized to the treatment of resonant states.

Circular dichroism of helical polymers: a short-wavelength formulation

Linear response theory and a time-dependent Hartree scheme that includes static field effects are used to formulate the induced transverse current for a dilute isotropic system of helical polymers for which absorption occurs at wavelengths that are much larger than the spatial extent of each polarizable unit making up the system but no necessarily larger than the dimensions of the system

Linear response theory of dye–polymer complex circular dichroism

A linear response theory for the circular dichroism of dye–polymer complexes is presented. The time dependent Hartree approximation is employed and the effect of electrostatic fields is included in an approximate manner. Periodic boundary conditions are used to describe the polymer which may have several chromophores per repeating unit and any number of bound dye molecules. A partitioning technique is used to obtain the two components of the circular dichroism, that of the dye aggregate which is shifted due to dye–polymer interaction. The induced circular dichroism predicted by a less accurate scheme, a matrix approach, is shown for a typical case to be at least 24% less intense than that predicted by the time dependent Hartree scheme.

Circular dichroism of unordered polymers: Extended time dependent Hartree theory for polypeptides

Equations describing circular dichroism (CD) and optical rotatory dispersion (ORD) of a system of unordered polymers in solution are derived via a linear response method in terms of exact states of the system. Origin dependent extrinsic magnetic moment operators are not used. After a multipole expansion of the induced transverse current and a long wavelength expansion of the susceptibilities, the equation of motion of the radiation field’s average vector potential is solved and a definition of the refractive index provides an account of CD−ORD. It is shown that the contribution to the current by the susceptibility characterizing induced electric dipole polarization through intrinsic magnetic dipolar coupling with the curl of the radiation field is identical to the contribution by the susceptibility characterizing induced magnetic dipole polarization through electric dipolar coupling with the radiation field only for isotropic media. Approximate polypeptide susceptibilities are obtained by an extension of the time dependent Hartree scheme. The extension is shown to be necessary when electric and nπ* magnetic dipole transitions are degenerate or near degenerate, for which anomalous dispersion arises and rotational strength is not conserved. The resulting susceptibilities are obtained from the solution to a normal mode problem. The normal modes are determined not only by electric dipolar coupling but also by the coupling of electric quadrupoles with others and with electric dipoles. The time dependent Hartree scheme is then on a comparable level with the matrix scheme, and the two methods are discussed.

Atomic Response Function

The response function of atoms is derived approximately within the framework of the time-dependent Hartree scheme for external fields of wavelength large compared to atomic dimensions. Solutions of the resulting dispersion equation correspond to new resonances of atoms. The theory is discussed in terms of the properties of the differential oscillator-strength distribution, or photoabsorption cross section, for the Hartree model and for the statistical model of the atom. An illustrative calculation in the statistical approximation exhibits qualitatively the conditions for the occurrence of these resonances.