There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The hydrogen bond is the most important of all directional intermolecular interactions. It is operative in determining molecular conformation, molecular aggregation, and the function of a vast number of chemical systems ranging from inorganic to biological. Research into hydrogen bonds experienced a stagnant period in the 1980s, but re-opened around 1990, and has been in rapid development since then. In terms of modern concepts, the hydrogen bond is understood as a very broad phenomenon, and it is accepted that there are open borders to other effects. There are dozens of different types of X-H.A hydrogen bonds that occur commonly in the condensed phases, and in addition there are innumerable less common ones. Dissociation energies span more than two orders of magnitude (about 0.2-40 kcal mol(-1)). Within this range, the nature of the interaction is not constant, but its electrostatic, covalent, and dispersion contributions vary in their relative weights. The hydrogen bond has broad transition regions that merge continuously with the covalent bond, the van der Waals interaction, the ionic interaction, and also the cation-pi interaction. All hydrogen bonds can be considered as incipient proton transfer reactions, and for strong hydrogen bonds, this reaction can be in a very advanced state. In this review, a coherent survey is given on all these matters.

The hydrogen bond in the solid state.

https://www.pci.uni-heidelberg.de/tc/usr/mctdh/lit/rev.pdf

The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets

: The unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio. Harmonic force fields are obtained using Density Functional Theory (DFT), MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set. DFT calculations use the Local Spin Density Approximation (LSDA), BLYP, and Becke3LYP (B3LYP) density functionals. Mid-IR spectra predicted using LSDA, BLYP, and B3LYP force fields are of significantly different quality, the B3LYP force field yielding spectra in clearly superior, and overall excellent, agreement with experiment. The MP2 force field yields spectra in slightly worse agreement with experiment than the B3LYP force field. The SCF force field yields spectra in poor agreement with experiment.The basis set dependence of B3LYP force fields is also explored: the 6-31G* and TZ2P basis sets give very similar results while the 3-21G basis set yields spectra in substantially worse agreements with experiment. jg

Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields

Green fluorescent protein (GFP) from the jellyfish Aequorea victoria and its homologs from diverse marine animals are widely used as universal genetically encoded fluorescent labels. Many laboratories have focused their efforts on identification and development of fluorescent proteins with novel characteristics and enhanced properties, resulting in a powerful toolkit for visualization of structural organization and dynamic processes in living cells and organisms. The diversity of currently available fluorescent proteins covers nearly the entire visible spectrum, providing numerous alternative possibilities for multicolor labeling and studies of protein interactions. Photoactivatable fluorescent proteins enable tracking of photolabeled molecules and cells in space and time and can also be used for super-resolution imaging. Genetically encoded sensors make it possible to monitor the activity of enzymes and the concentrations of various analytes. Fast-maturing fluorescent proteins, cell clocks, and timers further expand the options for real time studies in living tissues. Here we focus on the structure, evolution, and function of GFP-like proteins and their numerous applications for in vivo imaging, with particular attention to recent techniques.

Fluorescent Proteins and Their Applications in Imaging Living Cells and Tissues

Nonadiabatic effects play an important role in many areas of physics and chemistry. The coupling between electrons and nuclei may, for example, lead to the formation of a conical intersection between potential energy surfaces, which provides an efficient pathway for radiationless decay between electronic states. At such intersections the Born-Oppenheimer approximation breaks down, and unexpected dynamical processes result, which can be observed spectroscopically. We review the basic theory required to understand and describe conical, and related, intersections. A simple model is presented, which can be used to classify the different types of intersections known. An example is also given using wavepacket dynamics simulations to demonstrate the prototypical features of how a molecular system passes through a conical intersection.

Beyond Born-Oppenheimer: molecular dynamics through a conical intersection.

/pdf/multidimensional-quantum-dynamics-36abnlpfx5.pdf

Multidimensional Quantum Dynamics

Quantum molecular dynamics describes the time-evolution of a chemical system at the atomic level by directly solving the Schrodinger equation. Time-dependent methods, exemplified by wavepacket propagation, are by now developed to a point where they provide an important insight into the mechanism of many fundamental processes. Of these methods, the most versatile and efficient is probably the multi-configuration time-dependent Hartree (MCTDH) method. The form of the wavefunction used leads to a particularly compact description of the system, and it is possible to run either qualitative, cheap, or accurate, expensive calculations within the same framework. MCTDH has now shown that it is able to treat systems much larger than other wavepacket propagation methods, and benchmark calculations on systems with up to 24 degrees of freedom have been made. In contrast, standard methods can rarely treat more than 4–6 degrees of freedom. In the following, we review the basic theory of MCTDH. Recent advances are included, such as the development of the method for treating the time-evolution of density operators.

Quantum molecular dynamics: propagating wavepackets and density operators using the multiconfiguration time-dependent Hartree method

The molecular dynamics of pyrazine after excitation to the S2 electronic state is investigated using the S2 absorption spectrum as a benchmark. We first present a realistic model Hamiltonian including all 24 vibrational modes of the pyrazine molecule. Using this model, we determined the potential energy surfaces of the lowest two excited states, S1 and S2, which are strongly coupled to each other. We then treated the nuclear motion of all 24 vibrational modes using the multiconfiguration time-dependent Hartree (MCTDH) wave packet propagation method. This method obtains results of good accuracy with acceptable computational effort for such a large system. The calculated spectrum is in good agreement with the experimental one. Furthermore, our results shed light on the role of the 20 modes which are only weakly coupled to the system, and demonstrate that essential physical features, such as symmetries, have to be considered when one wants to treat the molecular dynamics of pyrazine realistically.

Graham A. Worth

Papers

The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets

Beyond Born-Oppenheimer: molecular dynamics through a conical intersection.

Multidimensional Quantum Dynamics

Quantum molecular dynamics: propagating wavepackets and density operators using the multiconfiguration time-dependent Hartree method

Molecular dynamics of pyrazine after excitation to the S2 electronic state using a realistic 24-mode model Hamiltonian