The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or "Boys orbitals" as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices.

Maximally-localized Wannier Functions: Theory and Applications

We present a method for determining the free-energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting cases. Convergence and errors can be rigorously and easily controlled. The parameters of the simulation can be tuned so as to focus the computational effort only on the physically relevant regions of the order parameter space. The algorithm is tested on the reconstruction of an alanine dipeptide free-energy landscape.

Well-tempered metadynamics: a smoothly converging and tunable free-energy method.

: 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

Over the past three decades a new spectroscopic technique with unique possibilities has emerged. Based on coherent and time-resolved detection of the electric field of ultrashort radiation bursts in the far-infrared, this technique has become known as terahertz time-domain spectroscopy (THz-TDS). In this review article the authors describe the technique in its various implementations for static and time-resolved spectroscopy, and illustrate the performance of the technique with recent examples from solid-state physics and physical chemistry as well as aqueous chemistry. Examples from other fields of research, where THz spectroscopic techniques have proven to be useful research tools, and the potential for industrial applications of THz spectroscopic and imaging techniques are discussed.

Terahertz spectroscopy and imaging – Modern techniques and applications

PLUMED: a portable plugin for free-energy calculations with molecular dynamics

The potential of mean force of interacting aromatic amino acids is calculated using molecular dynamics simulations. The free energy surface is determined in order to study stacking and T-shape competition for phenylalanine−phenylalanine (Phe−Phe), phenylalanine−tyrosine (Phe−Tyr), and tyrosine−tyrosine (Tyr−Tyr) complexes in vacuo, water, carbon tetrachloride, and methanol. Stacked structures are favored in all solvents with the exception of the Tyr−Tyr complex in carbon tetrachloride, where T-shaped structures are also important. The effect of anchoring the two α-carbons (Cα) at selected distances is investigated. We find that short and large Cα−Cα distances favor stacked and T-shaped structures, respectively. We analyze a set of 2396 protein structures resolved experimentally. Comparison of theoretical free energies for the complexes to the experimental analogue shows that Tyr−Tyr interaction occurs mainly at the protein surface, while Phe−Tyr and Phe−Phe interactions are more frequent in the hydrophobi...

Stacking and T-shape competition in aromatic-aromatic amino acid interactions.

Success in designing and tailoring solid-state reactions depends on the knowledge of the mechanisms regulating the reactivity at the microscopic level In spite of several attempts to rationalize the reactivity of crystals1,2,3,4,5, the question of the existence of a critical distance for a reaction to occur remains unsolved In this framework, the role of lattice phonons, which continuously tune the relative distance and orientation of the molecules, is still not fully understood Here, we show that at the onset of the transformation of crystalline benzene to an amorphous hydrogenated carbon the intermolecular C–C distance is always the same (about 26 A) once collective motions are taken into account, and it is independent of the pressure and temperature conditions This conclusion is supported by first-principles molecular-dynamics simulations This is a clear demonstration of the role of lattice phonons in driving the reactivity in the crystalline phase by fine-tuning of the nearest-neighbour distances The knowledge of the critical C–C distance can be crucial in planning solid-state reactions at moderate pressure

Triggering dynamics of the high-pressure benzene amorphization.

1 Lattice Dynamics.- 1.1 Introduction.- 1.2 The Dynamical Equations in Cartesian Coordinates.- 1.3 Dispersion Curves. Acoustic and Optical Modes.- 1.4 Invariance Conditions.- 1.5 Molecular Coordinates.- 1.6 The Dynamical Equations in Molecular Coordinates.- 2 Symmetry.- 2.1 Space Group Symmetry.- 2.2 Irreducible Representations of the Translational Group.- 2.3 Irreducible Representations of the Space Groups.- 2.4 Time Reversal.- 2.5 Symmetry of the Dynamical Matrix.- 2.6 Symmetry Properties of Vibrational States.- 2.7 Selection Rules.- 3 Intermolecular Potentials.- 3.1 The Crystal Potential.- 3.2 The Intramolecular Potential.- 3.3 The Intermolecular Potential.- 3.4 Intermolecular Force Constants.- 3.5 Lattice Sums and Ewald's Method.- 2.6 Calculation of Phonon Frequencies.- 4 Anharmonic Interactions.- 4.1 Introduction.- 4.2 The Crystal Hamiltonian.- 4.3 Quantum Field Treatment of Phonons.- 4.4 The Hamiltonian Renormalization Procedure.- 4.5 The Self-Consistent Phonon Method.- 4.6 The Method of the Green's Functions.- 4.7 Thermal Strain.- 4.8 Anharmonic Calculations.- 5 Two-Phonon Spectra of Molecular Crystals.- 5.1 Introduction.- 5.2 General Considerations.- 5.3 Two-phonon Density of States.- 5.4 Two-phonon Absorption Coefficients.- 6 Infrared and Raman Intensities in Molecular Crystals.- 6.1 Introduction.- 6.2 Historical Survey.- 6.3 Electrostatic Model of Infrared and Raman Intensities of Molecular Crystals.

Lattice Dynamics of Molecular Crystals

A Car–Parrinello molecular dynamics simulation has been performed on fully deuterated liquid methanol. The results are compared with the latest available experimental and theoretical data. It is shown that the liquid is aggregated in chains of hydrogen bonded molecules. The structure of the aggregates is characterized and it is found that the dynamics includes a fast and a slow regime. The weak H bond formed by the methyl group hydrogens and oxygen atom of surrounding molecules has been characterized. The importance of inductive effects is shown and discussed in terms of maximally localized Wannier function centers. Special attention is devoted to clarify how the molecular dipole moment depends on the number of H bonds formed by each molecule. The IR spectrum is computed and analyzed in terms of H-bond interactions. Insights on the short time dynamics and on the H-bond network are illustrated.

Hydrogen bond dynamics in liquid methanol

Using an improved DFT calculation of the vibrational frequencies based on the B3-LYP functional and the 6-31G* basis set, the infrared, Raman, neutron inelastic and luminescence spectra of C60 are ...

Vincenzo Schettino

Papers

Stacking and T-shape competition in aromatic-aromatic amino acid interactions.

Triggering dynamics of the high-pressure benzene amorphization.

Lattice Dynamics of Molecular Crystals

Hydrogen bond dynamics in liquid methanol

The Vibrational Spectrum of fullerene C60