The MCTDH method has been used successfully to treat the non-adiabatic dynamics of a number of systems. These are hard problems due to the number of modes that need to be included in a calculation, and the strong coupling between the nuclear and electronic motion at conical intersections connecting electronic states in these systems. In this review, an overview of the basic theory of the method is given highlighting how it is able to treat larger systems than other quantum dynamics methods. The vibronic coupling model Hamiltonian is also described, which provides a good starting point for the description of these systems. Examples of calculations made and systems treated are given. Finally, a development of the basic MCTDH method in which some of the usual time-dependent basis functions are replaced by Gaussian wavepackets is outlined. This method promises not only to treat larger systems, but to provide a consistent quantum–semiclassical framework.

Using the MCTDH wavepacket propagation method to describe multimode non-adiabatic dynamics

This review covers the multiconfiguration time-dependent Hartree (MCTDH) method, which is a powerful and general algorithm for solving the timedependent Schr¨ odinger equation. The formal derivation is discussed as well as applications of the method. Recent extensions of MCTDH are treated in brief, namely, MCTDHB and MCTDHF, for treating identical particles (bosons and fermions), and the very powerful multilayer (ML-MCTDH) formalism. Compact representations of potential energy surfaces (PESs) are also discussed, as the representation of a PES becomes a major bottleneck when going to larger systems (nine or more dimensions) while employing a full-dimensional, complicated, and nonseparable PES. As applications of MCTDH, we discuss the calculation of photoionization and photoexcitation spectra of the vibronically coupled systems butatriene and pyrazine, respectively, and the infra-red spectrum of the Zundel cation (protonated water dimer) H5O + . C � 2011 John Wiley & Sons, Ltd.

Studying molecular quantum dynamics with the multiconfiguration time-dependent Hartree method

Despite impressive advances of computational spectroscopy, a robust and user-friendly multi-frequency virtual spectrometer is not yet available. This contribution summarises ongoing efforts in our research group toward the implementation and validation of such a tool with special reference to the building blocks of biomolecules in their natural environment. Our integrated computational tool allows the computation of several kinds of spectra, including vibrational (e.g. IR, VCD), electronic (e.g. absorption, emission, ECD) as well as magnetic resonance (e.g. ESR, NMR) for both closed- and open-shell systems in vacuo and in condensed phases, and includes facilities for drawing, comparing, and modifying all the computed spectra. A number of test cases involving a combination of different spectroscopic ranges will be discussed in order to point out strengths, limitations, and ongoing developments of our research plan.

Implementation and validation of a multi-purpose virtual spectrometer for large systems in complex environments

Singlet fission is a photophysical process in molecules and molecular aggregates, in which a singlet exciton generated by irradiation splits into two triplet excitons. Recently, singlet fission has attracted a great deal of attention from the viewpoint of applications in organic photovoltaic cells, where singlet fission has a possibility of improving the photoelectric conversion efficiency. Although singlet fission was first observed about 50 years ago in anthracene crystals, and the mechanism has been investigated in detail for a small number of molecular systems such as tetracene and pentacene crystals, the relationships between molecular or crystal structures and singlet fission efficiency are yet to be precisely clarified. Thus, molecular structure – singlet fission relationships and molecular or crystal design guidelines for efficient singlet fission are intensely desired for realizing efficient photovoltaic energy conversion, and experimental and theoretical investigations advance rapidly. We introduce three investigation steps, which are based on bottom-up theoretical modeling from a molecule to a molecular aggregate or crystal. The modelling involves energy level matching at the molecular level, electronic coupling at the aggregate level, and singlet fission dynamics including exciton–phonon (vibronic) coupling, by emphasizing the importance of interplay between each step. From the modelling, we present several design guidelines for efficient singlet fission, which is together with practical molecular structures, chemical modifications and molecular configurations.

Molecular design for efficient singlet fission

Alternating short and long bond length (ABL) distortions observed within the ring structures of molecular metal oxide anions or polyoxometalates (POMs) are reminiscent of the cooperative linear ABL distortions in perovskite d0 metal oxides. We show herein that these distortions have a common origin: a pseudo Jahn−Teller (PJT) vibronic instability. Four POM structural types with different MnOn ring sizes are investigated herein using density functional theoretical methods: Lindqvist [M6O19]q− (n = 4), Keggin α-[XM12O40]q− (n = 6), Wells−Dawson α-[X2M18O62]q− (n = 8), and Preyssler [(Na)P5W30O110]14− (n = 10), where M = MoVI and WVI and X = SiIV, GeIV, PV, AsV, SVI, and SeVI. Chirality is induced within the latter three structural types by the ABL ring distortions. The calculations confirm the PJT vibronic origin of the ABL distortions with good agreement between calculated geometries and published single-crystal X-ray diffraction data. Both theory and experiment show that the vibronic interaction and disto...

On the origin of alternating bond distortions and the emergence of chirality in polyoxometalate anions.

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‘ ‘, and 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], ...

Multimode Jahn-Teller and pseudo-Jahn-Teller interactions in the cyclopropane radical cation: complex vibronic spectra and nonradiative decay dynamics.

The static and dynamic aspects of (E x e)-Jahn-Teller (JT) interactions in the electronic ground state (X 2 E') of the cyclopropane radical cation are investigated with the aid of an ab initio based quantum dynamical approach. The valence photoelectron spectrum of cyclopropane pertinent to an ionization to the X 2 E' electronic manifold of its radical cation is calculated and compared with the most recent experimental recording of Holland and co-workers using He I and synchrotron radiation as excitation sources [J. Electron Spectrosc. Relat. Phenom. 2002, 57, 125]. A model diabatic Hamiltonian up to a quadratic vibronic coupling scheme and ab initio calculated coupling parameters are employed in the quantum dynamical simulations. Despite some minor details, the theoretical results are in good accord with the observed bimodal shape of the photoelectron band. The observed splitting of the maxima of ∼0.78 eV in the bimodal profile compares well with our theoretical value of ∼0.76 eV. A strong first-order JT activity of the degenerate vibrational modes is discovered, which results in the distinct twin structure of the photoelectron band, indicating transitions to both the sheets of the so-called Mexican hat potential energy surface of the X 2 E' electronic ground state of the radical cation. Two Condon active (A' 1 ) and three JT active (E') vibrational modes are found to contribute mostly to the nuclear dynamics in this electronic manifold. The low-energy progression in the photoelectron band is found to be mainly caused by the degenerate CH 2 wagging and ring deformation modes. While the linear vibronic coupling scheme overestimates the observed spacing in the low-energy progressions, it leads to a very good agreement with the overall shape of the observed band. The effect of quadratic coupling terms of the Hamiltonian on this low-energy progression is also discussed.

Theoretical Investigation of Jahn−Teller Dynamics in the 2E‘ Electronic Ground State of the Cyclopropane Radical Cation

Photodetachment spectroscopy of phenide anion C6H5- is theoretically studied with the aid of electronic structure calculations and quantum dynamical simulations of nuclear motion. The theoretical results are compared with the available experimental data. The vibronic structure of the first, second, and third photoelectron bands associated with the ground X 2A1 and low-lying excited A 2B1 and B 2A2 electronic states of the phenyl radical C6H5 is examined at length. While the X state of the radical is energetically well separated and its interaction is found to be rather weak with the rest, the A and B electronic states are found to be only approximately 0.57 eV apart in energy at the vertical configuration. Low-energy conical intersections between the latter two states are discovered and their impact on the nuclear dynamics underlying the second and third photoelectron bands is delineated. The nuclear dynamics in the X state solely proceeds through the adiabatic path and the theoretically calculated vibrational level structure of this state compares well with the experimental result. Two Condon active totally symmetric (a1) vibrational modes of ring deformation type form the most dominant progression in the first photoelectron band. The existing ambiguity in the assignment of these two vibrational modes is resolved here. The A-B conical intersections drive the nuclear dynamics via nonadiabatic paths, and as a result the second and third photoelectron bands overlap and particularly the third band due to the B state of C6H5 becomes highly diffused and structureless. Experimental photodetachment spectroscopy results are not available for these bands. However, the second band has been detected in electronic absorption spectroscopy measurements. The present theoretical results are compared with these absorption spectroscopy data to establish the nonadiabatic interactions between the A and B electronic states of C6H5.

Vibronic interactions in the photodetachment spectroscopy of phenide anion.

We report a theoretical account on the static and dynamic aspects of the Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) interactions in the ground and first excited electronic states of the ethane radical cation. The findings are compared with the experimental photoionization spectrum of ethane. The present theoretical approach is based on a model diabatic Hamiltonian and with the parameters derived from ab initio calculations. The optimized geometry of ethane in its electronic ground state (A1g1) revealed an equilibrium staggered conformation belonging to the D3d symmetry point group. At the vertical configuration, the ethane radical cation belongs to this symmetry point group. The ground and low-lying electronic states of this radical cation are of Eg2, A1g2, Eu2, and A2u2 symmetries. Elementary symmetry selection rule suggests that the degenerate electronic states of the radical cation are prone to the JT distortion when perturbed along the degenerate vibrational modes of eg symmetry. The A1g2 state is ...

Exploring the Jahn-Teller and pseudo-Jahn-Teller conical intersections in the ethane radical cation.

Multimode Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) coupling effects in the photoelectron spectrum of ethane are theoretically investigated. In this article, we focus on the vibronic structure of the second excited B ∼ 2 E u electronic manifold of the ethane radical cation which reveals an asymmetric band in the 14.5–16.5 eV ionization energy range in the experimental recordings. Ionization of an electron from the third occupied 1eu molecular orbital of ethane produces the radical cation in the degenerate B ∼ 2 E u electronic manifold, which is prone to the JT instability when distorted along the degenerate eg vibrational modes. The theoretical formalism employed here is based on a model diabatic Hamiltonian and a quadratic vibronic coupling scheme with the parameters derived from ab initio electronic structure calculations. The photoelectron band is calculated by carrying out quantum dynamical simulations in the coupled manifold of electronic states. The B ∼ 2 E u electronic manifold of the radical cation is estimated to be ∼2.75 eV and ∼2.40 eV above its X ∼ 2 E g and the A ∼ 2 A 1 g electronic states, respectively. The symmetry selection rule suggests PJT coupling of these electronic states along the vibrational modes of eg/eu symmetry. The quadratic JT spectrum simulated within the B ∼ 2 E u electronic manifold shows two maxima at ∼ 14.96 eV and ∼15.76 eV which are attributed to the two JT split adiabatic sheets of this electronic manifold. This is in good accord with their position observed at ∼15.0 eV and ∼15.8 eV, respectively, in the experimental recording. The diffuse structure of the overall band can be accounted to a large extent by considering the A ∼ 2 A 1 g - B ∼ 2 E u PJT interactions. The overall shape of the theoretical band agrees very well with the experimental results. Further refinement of the theoretical results may be accomplished by including X ∼ 2 E g - A ∼ 2 A 1 g - B ∼ 2 E u PJT interactions in the theoretical model. Importance of the latter vibronic interactions is also discussed in the text.

T. S. Venkatesan

Papers

Multimode Jahn-Teller and pseudo-Jahn-Teller interactions in the cyclopropane radical cation: complex vibronic spectra and nonradiative decay dynamics.

Theoretical Investigation of Jahn−Teller Dynamics in the 2E‘ Electronic Ground State of the Cyclopropane Radical Cation

Vibronic interactions in the photodetachment spectroscopy of phenide anion.

Exploring the Jahn-Teller and pseudo-Jahn-Teller conical intersections in the ethane radical cation.

Multistate and multimode vibronic dynamics: The Jahn–Teller and pseudo-Jahn–Teller effects in the ethane radical cation