Examining solvent effects on the ultrafast dynamics of catechol.

We consider the effect of a polar, hydrogen bond accepting, solvent environment on the excited state decay of catechol following excitation to its first excited singlet state (S1). A comparison of Fourier transform infrared spectroscopy and explicit-solvent ab initio frequency prediction suggests that 5 mM catechol in acetonitrile is both nonaggregated and in its "closed" conformation, contrary to what has been previously proposed. Using ultrafast transient absorption spectroscopy, we then demonstrate the effects of aggregation on the photoexcited S1 lifetime: at 5 mM catechol (nonaggregated) in acetonitrile, the S1 lifetime is 713 ps. In contrast at 75 mM catechol in acetonitrile, the S1 lifetime increases to 1700 ps. We attribute this difference to aggregation effects on the excited-state landscape. This work has shown that explicit-solvent methodology is key when calculating the vibrational frequencies of molecules in a strongly interacting solvent. Combining this with highly complementary steady-state and transient absorption spectroscopy enables us to gain key dynamical insights into how a prominent eumelanin building block behaves when in polar, hydrogen bond accepting solvents both as a monomer and as an aggregated species.

Determination of Secondary Species in Solution through Pump-Selective Transient Absorption Spectroscopy and Explicit-Solvent TDDFT.

The measured electronic excitations of a given species in solution are often a composite of the electronic excitations of various equilibrium species of that molecule. It is common for a proportion of a species to deprotonate in solution, or form a tautomeric equilibrium, producing new peaks corresponding to the electronic excitations of the new species. One prominent example is alizarin in methanol, which at different temperatures, and in solutions with differing pH, has an isosbestic point between the two dominant excitations at 435 and 540 nm. The peak at 435 nm has been attributed to alizarin; the peak at 540 nm, however, more likely results from a species in equilibrium with alizarin. In this work, we were able to use both experimental and computational techniques to selectively examine electronic properties of both alizarin and its secondary species in equilibrium. This was achieved through use of transient electronic absorption spectroscopy, following selective photoexcitation of a specific species in equilibrium. The resulting transient electronic absorption spectra were compared to the known transient absorption spectra of potential secondary equilibrium species. The ground state absorption spectra associated with each species in equilibrium were predicted using linear-scaling time-dependent density functional theory with an explicitly modeled solvent and compared to the experimental result. This evidence from both techniques combines to suggest that the excitation at 540 nm arises from a specific monoanionic form of alizarin.

Implicit and explicit host effects on excitons in pentacene derivatives.

An ab initio study of the effects of implicit and explicit hosts on the excited state properties of pentacene and its nitrogen-based derivatives has been performed using ground state density functional theory (DFT), time-dependent DFT, and ΔSCF. We observe a significant solvatochromic redshift in the excitation energy of the lowest singlet state (S1) of pentacene from inclusion in a p-terphenyl host compared to vacuum; for an explicit host consisting of six nearest neighbour p-terphenyls, we obtain a redshift of 65 meV while a conductor-like polarisable continuum model (CPCM) yields a 78 meV redshift. Comparison is made between the excitonic properties of pentacene and four of its nitrogen-based analogs, 1,8-, 2,9-, 5,12-, and 6,13-diazapentacene with the latter found to be the most distinct due to local distortions in the ground state electronic structure. We observe that a CPCM is insufficient to fully understand the impact of the host due to the presence of a mild charge-transfer (CT) coupling between the chromophore and neighbouring p-terphenyls, a phenomenon which can only be captured using an explicit model. The strength of this CT interaction increases as the nitrogens are brought closer to the central acene ring of pentacene.

Predicting solvatochromic shifts and colours of a solvated organic dye: The example of nile red.

The solvatochromic shift, as well as the change in colour of the simple organic dye nile red, is studied in two polar and two non-polar solvents in the context of large-scale time-dependent density-functional theory (TDDFT) calculations treating large parts of the solvent environment from first principles. We show that an explicit solvent representation is vital to resolve absorption peak shifts between nile red in n-hexane and toluene, as well as acetone and ethanol. The origin of the failure of implicit solvent models for these solvents is identified as being due to the strong solute-solvent interactions in form of π-stacking and hydrogen bonding in the case of toluene and ethanol. We furthermore demonstrate that the failures of the computationally inexpensive Perdew-Burke-Ernzerhof (PBE) functional in describing some features of the excited state potential energy surface of the S1 state of nile red can be corrected for in a straightforward fashion, relying only on a small number of calculations making use of more sophisticated range-separated hybrid functionals. The resulting solvatochromic shifts and predicted colours are in excellent agreement with experiment, showing the computational approach outlined in this work to yield very robust predictions of optical properties of dyes in solution.

Simulation of electron energy loss spectra of nanomaterials with linear-scaling density functional theory.

Experimental techniques for electron energy loss spectroscopy (EELS) combine high energy resolution with high spatial resolution. They are therefore powerful tools for investigating the local electronic structure of complex systems such as nanostructures, interfaces and even individual defects. Interpretation of experimental electron energy loss spectra is often challenging and can require theoretical modelling of candidate structures, which themselves may be large and complex, beyond the capabilities of traditional cubic-scaling density functional theory. In this work, we present functionality to compute electron energy loss spectra within the onetep linear-scaling density functional theory code. We first demonstrate that simulated spectra agree with those computed using conventional plane wave pseudopotential methods to a high degree of precision. The ability of onetep to tackle large problems is then exploited to investigate convergence of spectra with respect to supercell size. Finally, we apply the novel functionality to a study of the electron energy loss spectra of defects on the (1 0 1) surface of an anatase slab and determine concentrations of defects which might be experimentally detectable.

Solvent Effects on Electronic Excitations of an Organic Chromophore.

In this work we study the solvatochromic shift of a selected low-energy excited state of alizarin in water by using a linear-scaling implementation of large-scale time-dependent density functional theory (TDDFT). While alizarin, a small organic dye, is chosen as a simple example of solute-solvent interactions, the findings presented here have wider ramifications for the realistic modeling of dyes, paints, and pigment-protein complexes. We find that about 380 molecules of explicit water need to be considered in order to yield an accurate representation of the solute-solvent interaction and a reliable solvatochromic shift. By using a novel method of constraining the TDDFT excitation vector, we confirm that the origin of the slow convergence of the solvatochromic shift with system size is due to two different effects. The first factor is a strong redshift of the excitation due to an explicit delocalization of a small fraction of the electron and the hole from the alizarin onto the water, which is mainly confined to within a distance of 7 Å from the alizarin molecule. The second factor can be identified as long-range electrostatic influences of water molecules beyond the 7 Å region on the ground-state properties of alizarin. We also show that these electrostatic influences are not well reproduced by a QM/MM model, suggesting that full QM studies of relatively large systems may be necessary in order to obtain reliable results.

The potential of imogolite nanotubes as (co-)photocatalysts: a linear-scaling density functional theory study.

We report a linear-scaling density functional theory (DFT) study of the structure, wall-polarization absolute band-alignment and optical absorption of several, recently synthesized, open-ended imogolite (Imo) nanotubes (NTs), namely single-walled (SW) aluminosilicate (AlSi), SW aluminogermanate (AlGe), SW methylated aluminosilicate (AlSi-Me), and double-walled (DW) AlGe NTs. Simulations with three different semi-local and dispersion-corrected DFT-functionals reveal that the NT wall-polarization can be increased by nearly a factor of four going from SW-AlSi-Me to DW-AlGe. Absolute vacuum alignment of the NT electronic bands and comparison with those of rutile and anatase TiO2 suggest that the NTs may exhibit marked propensity to both photo-reduction and hole-scavenging. Characterization of the NTs' band-separation and optical properties reveal the occurrence of (near-)UV inside-outside charge-transfer excitations, which may be effective for electron-hole separation and enhanced photocatalytic activity. Finally, the effects of the NTs' wall-polarization on the absolute alignment of electron and hole acceptor states of interacting water (H2O) molecules are quantified and discussed.

Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: Obtaining efficiency and accuracy with in situ optimised local orbitals.

We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on a small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.

Identifying and tracing potential energy surfaces of electronic excitations with specific character via their transition origins: application to oxirane.

We show that the transition origins of electronic excitations identified by quantified natural transition orbital (QNTO) analysis can be employed to connect potential energy surfaces (PESs) according to their character across a wide range of molecular geometries. This is achieved by locating the switching of transition origins of adiabatic potential surfaces as the geometry changes. The transition vectors for analysing transition origins are provided by linear response time-dependent density functional theory (TDDFT) calculations under the Tamm-Dancoff approximation. We study the photochemical CO ring opening of oxirane as an example and show that the results corroborate the traditional Gomer-Noyes mechanism derived experimentally. The knowledge of specific states for the reaction also agrees well with that given by previous theoretical work using TDDFT surface-hopping dynamics that was validated by high-quality quantum Monte Carlo calculations. We also show that QNTO can be useful for considerably larger and more complex systems: by projecting the excitations to those of a reference oxirane molecule, the approach is able to identify and analyse specific excitations of a trans-2,3-diphenyloxirane molecule.

Mapping functional groups on oxidised multi-walled carbon nanotubes at the nanometre scale.

Despite voluminous research on the acid oxidation of carbon nanotubes (CNTs), there is a distinct lack of experimental results showing distributions of functional groups at the nanometre length scale. Here, functional peaks have been mapped across individual multi-walled CNTs with low-dose, monochromated electron energy-loss spectroscopy (EELS) in the scanning transmission electron microscope (STEM). Density functional theory simulations show that the EELS features are consistent with oxygenated functional groups, most likely carboxyl moieties.

Linear-scaling time-dependent density-functional theory in the linear response formalism.

We present an implementation of time-dependent density-functional theory (TDDFT) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures. The method avoids any explicit reference to canonical representations of either occupied or virtual Kohn-Sham states and thus achieves linear-scaling computational effort with system size. In contrast to conventional localised orbital formulations, where a single set of localised functions is used to span the occupied and unoccupied state manifold, we make use of two sets of in situ optimised localised orbitals, one for the occupied and one for the unoccupied space. This double representation approach avoids known problems of spanning the space of unoccupied Kohn-Sham states with a minimal set of localised orbitals optimised for the occupied space, while the in situ optimisation procedure allows for efficient calculations with a minimal number of functions. The method is applied to a number of medium sized organic molecules and a good agreement with traditional TDDFT methods is observed. Furthermore, linear scaling of computational cost with system size is demonstrated on (10,0) carbon nanotubes of different lengths.

Linear-scaling density-functional simulations of charged point defects in Al2O3 using hierarchical sparse matrix algebra.

We present calculations of formation energies of defects in an ionic solid (Al(2)O(3)) extrapolated to the dilute limit, corresponding to a simulation cell of infinite size. The large-scale calculations required for this extrapolation are enabled by developments in the approach to parallel sparse matrix algebra operations, which are central to linear-scaling density-functional theory calculations. The computational cost of manipulating sparse matrices, whose sizes are determined by the large number of basis functions present, is greatly improved with this new approach. We present details of the sparse algebra scheme implemented in the ONETEP code using hierarchical sparsity patterns, and demonstrate its use in calculations on a wide range of systems, involving thousands of atoms on hundreds to thousands of parallel processes.

Accurate and efficient method for the treatment of exchange in a plane-wave basis.

We describe an accurate and efficient extension of Chawla and Voth's [J. Chem. Phys. 108, 4697 (1998)] plane-wave based algorithm for calculating exchange energies, exchange energy densities, and exchange energy gradients with respect to wave-function parameters in systems of electrons subject to periodic boundary conditions. The theory and numerical results show that the computational effort scales almost linearly with the number of plane waves and quadratically with the number of k vectors. To obtain high accuracy with relatively few k vectors, we use an adaptation of Gygi and Baldereschi's [Phys. Rev. B 34, 4405 (1986)] method for reducing Brillouin-zone integration errors.