Atomic and molecular intracules for excited states

Intracules in position space, momentum space and phase space have been calculated for low-lying excited states of the He atom, Be atom, formaldehyde and butadiene. The phase-space intracules (Wigner intracules) provide significantly more information than the position- and momentum-space intracules, particularly for the Be atom. Exchange effects are investigated through the differences between corresponding singlet and triplet states.This work was supported by the Engineering and Physical Sciences Research Council through the award of an Advanced Research Fellowship (GR/R77636) to NAB and a Joint Research Equipment Initiative grant (GR/R62052)

Structure and bonding in ionized water clusters

The structure and bonding in ionized water clusters, (H_2O)n+(n = 3–9), has been studied using the basin hopping search algorithm in combination with quantum chemical calculations. Initially candidate low energy isomers are generated using basin hopping in conjunction with density functional theory. Subsequently, the structures and energies are refined using second order Moller-Plesset perturbation theory and coupled cluster theory, respectively. The lowest energy isomers are found to involve proton transfer to give H_3O+ and a OH radical, which are more stable than isomers containing the hemibonded hydrazine-like fragment (H_2O-OH_2), with the calculated infrared spectra consistent with experimental data. For (H_2O)_9^+ the observation of a new structural motif comprising proton transfer to form H_3O^+ and OH, but with the OH radical involved in hemibonding to another water molecule is discussed

Structural optimization of molecular clusters with density functional theory combined with basin hopping

Identifying the energy minima of molecular clusters is a challenging problem. Traditionally, search algorithms such as simulated annealing, genetic algorithms, or basin hopping are usually used in conjunction with empirical force fields. We have implemented a basin hopping search algorithm combined with density functional theory to enable the optimization of molecular clusters without the need for empirical force fields. This approach can be applied to systems where empirical potentials are not available or may not be sufficiently accurate. We illustrate the effectiveness of the method with studies on water, methanol, and water + methanol clusters as well as protonated water and methanol clusters at the B3LYP+D/6-31+G* level of theory. A new lowest energy structure for H+(H2O)7 is predicted at the B3LYP+D/6-31+G* level. In all of the protonated mixed water and methanol clusters, we find that H+ prefers to combine with methanol rather than water in the lowest-energy structures

The effect of basis set and exchange-correlation functional on time-dependent density functional theory calculations within the Tamm-Dancoff approximation of the X-ray emission spectroscopy of transition metal complexes

The simulation of X-ray emission spectra of transition metal complexes with time- dependent density functional theory (TDDFT) is investigated. X-ray emission spectra can be computed within TDDFT in conjunction with the Tamm-Dancoff approximation by using a reference determinant with a vacancy in the relevant core orbital, and these calculations can be performed using the frozen orbital approxi- mation or with the relaxation of the orbitals of the intermediate core-ionised state included. Both standard exchange-correlation functionals and functionals specifically designed for X-ray emission spectroscopy are studied, and it is shown that the computed spectral band profiles are sensitive to the exchange-correlation functional used. The computed intensities of the spectral bands can be rationalised by consid- ering the metal p orbital character of the valence molecular orbitals. To compute X-ray emission spectra with the correct energy scale allowing a direct comparison with experiment requires the relaxation of the core-ionised state to be included and the use of specifically designed functionals with increased amounts of Hartree-Fock exchange in conjunction with high quality basis sets. A range-corrected functional with increased Hartree-Fock exchange in the short range provides transition energies close to experiment and spectral band profiles that have a similar accuracy to those from standard functionals

Structural optimization of molecular clusters with density functional theory combined with basin hopping

Identifying the energy minima of molecular clusters is a challenging problem. Traditionally, search algorithms such as simulated annealing, genetic algorithms, or basin hopping are usually used in conjunction with empirical force fields. We have implemented a basin hopping search algorithm combined with density functional theory to enable the optimization of molecular clusters without the need for empirical force fields. This approach can be applied to systems where empirical potentials are not available or may not be sufficiently accurate. We illustrate the effectiveness of the method with studies on water, methanol, and water + methanol clusters as well as protonated water and methanol clusters at the B3LYP+D/6-31+G* level of theory. A new lowest energy structure for H+(H2O)7 is predicted at the B3LYP+D/6-31+G* level. In all of the protonated mixed water and methanol clusters, we find that H+ prefers to combine with methanol rather than water in the lowest-energy structures

Density Functional Theory Calculations of Core–Electron Binding Energies at the K-Edge of Heavier Elements

The capability to determine core–electron binding energies (CEBEs) is vital in the analysis of X-ray photoelectron spectroscopy, and the continued development of light sources has made inner shell spectroscopy of heavier elements increasingly accessible. Density functional theory is widely used to determine CEBEs of lighter elements (boron–fluorine). It is shown that good performance of exchange-correlation functionals for these elements does not necessarily translate to the calculation of CEBEs for the heavier elements from the next row of the periodic table, and in general, larger errors are observed. Two strategies are explored that improve the accuracy of the calculated CEBEs. The first is to apply element and functional dependent energy corrections, and the second is a reparametrization of a short-range corrected functional. This functional is able to reproduce experimental phosphorus and sulfur K-edge CEBEs with an average error of 0.15 eV demonstrating the importance of reducing the self-interaction error associated with the core electrons and represents progress toward a density functional theory calculation that performs equally well for ionization at the K-edge of all elements

Vibrational Analysis of Carbon Nanotube Based Nanomechanical Resonators

A vibrational analysis of three types of carbonnanotube based nanomechanical resonator is presented. Harmonic vibrational frequencies and the associated normal modes are evaluated through diagonalisation of the full mass-weighted hessian matrix where a very large mass is assigned to the suitable carbon atoms to represent the constraints arising as a consequence of the different resonator configurations. The vibrational frequencies are determined for carbon nanotubes of different dimensions, and the response of the resonators to an applied mass is studied. For the flexural modes which are relevant for mass-sensing resonator devices, the calculations show the resonant frequency to increase as the tube diameter increases. For the longest nanotubes studied, the frequencies for cantilever and bridged resonators are very similar, and double-walled nanotubes have resonant frequencies that lie between the frequencies of the component single-walled nanotubes. The vibrational modes for a shuttle resonator have also been determined, and the lowest frequency mode was found to correspond to the relative rotation of the nanotubes with frequencies in the range 70 -- 120 GHz. The calculations predict a sensitivity of up to 1030 Hz/g although the response of the flexural modes of suspended nanotubes is dependent on the location of the adsorbed mass, while the response based upon the relative rotational motion in double-walled nanotubes is independent of the position of the adsorbed mass

Computational study of the structure and electronic circular dichroism spectroscopy of blue copper proteins

The calculation of the electronic circular dichroism (CD) spectra of the oxidised form of the blue copper proteins plastocyanin and cucumber basic protein and the relationship between the observed spectral features and the structure of the active site of the protein is investigated. Excitation energies and transition strengths are computed using multi reference configuration interaction, and it is shown that computed spectra based on coordinates from the crystal structure or a single structure optimised in quantum mechanics/molecular mechanics (QM/MM) or ligand field molecular mechanics (LFMM) are qualitatively incorrect. In particular, the rotational strength of the ligand to metal charge transfer band is predicted to be too small or have the incorrect sign. By considering calculations on active site models with modified structures it is shown that the intensity of this band is sensitive to the non-planarity of the histidine and cysteine ligands coordinated to copper. Calculation of the ultraviolet absorption and CD spectra based upon averaging over many structures drawn from a LFMM molecular dynamics simulation are in good agreement with experiment, and superior to analogous calculations based upon structures from a classical molecular dynamics simulation. This provides evidence that the LFMM force field provides an accurate description of the molecular dynamics of these proteins

Reactivity of the O2+·(H2O)n and NO+·(H2O)n cluster ions in the D-region of the ionosphere

The protonated water clusters present in the D-region of the ionosphere have been postulated to be formed from cluster ions such as O2+·(H2O)n and NO+·(H2O)n, although the detailed mechanism of the underlying reactions is not understood. Second order Møller–Plesset perturbation theory based Born–Oppenheimer ab initio molecular dynamics (AIMD) simulations of the reactions of the O2+·(H2O)n and NO+·(H2O)n cluster ions to form protonated water clusters reveal different mechanisms for the O2+ and NO+ based ions. AIMD simulations of O2+·(H2O)n=2–5 with initial velocities of the atoms sampled from the Maxwell–Boltzmann distribution at 220 K show that following charge transfer, a reaction to form a protonated water cluster and OH occurs rapidly where the neutral O2 molecule is just a spectator. In contrast, the reaction of NO+·(H2O)n=4,5 has been hypothesised to involve an intracluster reaction, but no reaction is observed in AIMD simulations using thermal initial velocities. However, it is shown that reactions to form protonated water clusters do occur in simulations when a water molecule collides with a NO+·(H2O)4 cluster