The fundamental problem faced in quantum chemistry is the calculation of molecular properties, which are of practical importance in fields ranging from materials science to biochemistry. Within chemical precision, the total energy of a molecule as well as most other properties, can be calculated by solving the Schrödinger equation. However, the computational resources required to obtain exact solutions on a conventional computer generally increase exponentially with the number of atoms involved 1,2 . This renders such calculations intractable for all but the smallest of systems. Recently, an efficient algorithm has been proposed enabling a quantum computer to overcome this problem by achieving only a polynomial resource scaling with system size 2,3,4 . Such a tool would therefore provide an extremely powerful tool for new science and technology. Here we present a photonic implementation for the smallest problem: obtaining the energies of H 2 , the hydrogen molecule in a minimal basis. We perform a key algorithmic step-the iterative phase estimation algorithm 5,6,7,8 -in full, achieving a high level of precision and robustness to error. We implement other algorithmic steps with assistance from a classical computer and explain how this non-scalable approach could be avoided. Finally, we provide new theoretical results which lay the foundations for the next generation of simulation experiments using quantum computers. We have made early experimental progress towards the long-term goal of exploiting quantum information to speed up quantum chemistry calculations.Experimentalists are just beginning to command the level of control over quantum systems required to explore their information processing capabilities. An important long-term application is to simulate and calculate properties of other many-body quantum systems. Pioneering experiments were first performed using nuclear-magnetic-resonance-based systems to simulate quantum oscillators 9 , leading up to recent simulations of a pairing Hamiltonian 7,10 . Very recently the phase transitions of a two-spin quantum magnet were simulated 11 using an ion-trap system. Here we simulate a quantum chemical system and calculate its energy spectrum, using a photonic system. Molecular energies are represented as the eigenvalues of an associated time-independent HamiltonianĤ and can be efficiently obtained to fixed accuracy, using a quantum algorithm with three distinct steps 6 : encoding a molecular wavefunction into qubits; simulating its time evolution using quantum logic gates; and extracting the approximate energy using the phase estimation algorithm 3,12 . The latter is a general-purpose quantum algorithm for evaluating the eigenvalues of arbitrary Hermitian or unitary operators. The algorithm estimates the phase, φ, accumulated by a molecular eigenstate, |Ψ , under the action of the time-evolution operator,Û =e −iĤt/ , i.e.,where E is the energy eigenvalue of |Ψ . Therefore, estimating the phase for each eigenstate amounts to estimating the eigenvalues of the Hamiltonia...

Melanins are pigmentary macromolecules found throughout the biosphere that, in the 1970s, were discovered to conduct electricity and display bistable switching. Since then, it has been widely believed that melanins are naturally occurring amorphous organic semiconductors. Here, we report electrical conductivity, muon spin relaxation, and electron paramagnetic resonance measurements of melanin as the environmental humidity is varied. We show that hydration of melanin shifts the comproportionation equilibrium so as to dope electrons and protons into the system. This equilibrium defines the relative proportions of hydroxyquinone, semiquinone, and quinone species in the macromolecule. As such, the mechanism explains why melanin at neutral pH only conducts when "wet" and suggests that both carriers play a role in the conductivity. Understanding that melanin is an electronic-ionic hybrid conductor rather than an amorphous organic semiconductor opens exciting possibilities for bioelectronic applications such as ion-toelectron transduction given its biocompatibility.bioelectronics | electrical properties | biomacromolecules | ionic conduction T he melanins are responsible for multiple critical functions in humans such as photoprotection and free radical scavenging (1). These molecules are also found in the substantia nigra of the human brain stem where their exact biological role is unknown; however, it has been speculated that neuromelanin may be involved in neural transmission (2). Melanin phototoxicity is also implicated in deadly melanoma skin cancer (3, 4). Despite decades of intense studies across biology, chemistry, and physics, the full details of the structure and functions of the melanins are still not clearly understood. Eumelanin, the major component in human skin pigment is viewed as the archetypal "true" melanin (here we adopt the standard nomenclature in which the terms "eumelanin" and "melanin" are used interchangeably). Eumelanin is composed of aggregated oligomeric and polymeric species based upon the indolic monomers 5,6-dihydroxyindole (DHI) and 5,6-dihydroxyindole-2-carboxylic acid (DHICA) and their various redox forms (1). These monomers are randomly cross-linked to form planar sheets, stacked via aromatic π-interactions and with varying conjugation length and character (5, 6, 7). For many years, melanins were considered as extended linear homo-or heteropolymers with a conjugated backbone (8). However, this view no longer has any credence and the disordered 2D protomolecular sheet model is now widely accepted. This sheet model has quite profound implications for the treatment of melanins within a conventional polymer framework, and many of the standard methods and theories for probing structure property relationships in macromolecules are inadequate or simply do not apply.Two properties of melanin have particularly intrigued physicists and chemists for decades: (i) Melanins are electrical conductors showing photoconductivity in the solid state; and (ii) melanins are black with broad featureless opt...

We review the interplay of frustration and strong electronic correlations in quasi-two-dimensional organic charge transfer salts, such as (BEDT-TTF) 2 X and EtnMe 4−n P n[Pd(dmit) 2 ] 2 . These two forces drive a range of exotic phases including spin liquids, valence bond crystals, pseudogapped metals, and unconventional superconductivity. Of particular interest is that in several materials with increasing pressure there is a first-order transition from a spin liquid Mott insulating state to a superconducting state. Experiments on these materials raise a number of profound questions about the quantum behaviour of frustrated systems, particularly the intimate connection between spin liquids and superconductivity. Insights into these questions have come from a wide range of theoretical techniques including first principles electronic structure, quantum many-body theory and quantum field theory. In this review we introduce some of the basic ideas of the field by discussing a simple frustrated Heisenberg model with four spins. We then describe the key experimental results, emphasizing that for two materials, κ-(BEDT-TTF) 2 Cu 2 -(CN) 3 and EtMe 3 Sb[Pd(dmit) 2 ] 2 , there is strong evidence for a spin liquid ground state, and for another, EtMe 3 P[Pd(dmit) 2 ] 2 , there is evidence of a valence bond crystal ground state. We review theoretical attempts to explain these phenomena, arguing that they can be captured by a Hubbard model on the anisotropic triangular lattice at half filling, and that Resonating Valence Bond (RVB) wavefunctions capture most of the essential physics. We review evidence that this Hubbard model can have a spin liquid ground state for a range of parameters that are realistic for the relevant materials. In particular, spatial anisotropy and ring exchange are key to destabilising magnetic order. We conclude by summarising the progress made thus far and identifying some of the key questions still to be answered. (S,S13,S24)= J J' J J J 1 2 3 4

We review the role of strong electronic correlations in quasi-twodimensional organic charge transfer salts such as (BEDT-TTF)2X, (BETS)2Y and β ′ -[Pd(dmit)2]2Z. We begin by defining minimal models for these materials. It is necessary to identify two classes of material: the first class is strongly dimerised and is described by a half-filled Hubbard model; the second class is not strongly dimerised and is described by a quarter filled extended Hubbard model. We argue that these models capture the essential physics of these materials. We explore the phase diagram of the half-filled quasi-two-dimensional organic charge transfer salts, focusing on the metallic and superconducting phases. We review work showing that the metallic phase, which has both Fermi liquid and 'bad metal' regimes, is described both quantitatively and qualitatively by dynamical mean field theory (DMFT). The phenomenology of the superconducting state is still a matter of contention. We critically review the experimental situation, focusing on the key experimental results that may distinguish between rival theories of superconductivity, particularly probes of the pairing symmetry and measurements of the superfluid stiffness. We then discuss some strongly correlated theories of superconductivity, in particular, the resonating valence bond (RVB) theory of superconductivity. We conclude by discussing some of the major challenges currently facing the field. These include: parameterising minimal models; the evidence for a pseudogap from nuclear magnetic resonance (NMR) experiments; superconductors with low critical temperatures and extremely small superfluid stiffnesses; the possible spin-liquid states in κ-(ET)2Cu2(CN)3 and β ′ -[Pd(dmit)2]2Z; and the need for high quality large single crystals.

Discoveries of ratios whose values are constant within broad classes of materials have led to many deep physical insights. The Kadowaki-Woods ratio (KWR) 1,2 compares the temperature dependence of a metals resistivity to that of its heat capacity; thereby probing the relationship between the electronelectron scattering rate and the renormalisation of the electron mass. However, the KWR takes very different values in different materials 3,4 . Here we introduce a ratio, closely related to the KWR, that includes the effects of carrier density and spatial dimensionality and takes the same (predicted) value in organic charge transfer salts, transition metal oxides, heavy fermions and transition metalsdespite the numerator and denominator varying by ten orders of magnitude.Hence, in these materials, the same emergent physics is responsible for the mass enhancement and the quadratic temperature dependence of the resistivity and no exotic explanations of their KWRs are required.In a Fermi liquid the temperature dependence of the electronic contribution to the heat capacity is linear, i.e., C el (T ) = γT . Another prediction of Fermi liquid theory 5 is that, at low temperatures, the resistivity varies as ρ(T ) = ρ 0 + AT 2 . This is observed experimentally when electron-electron scattering, which gives rise to the quadratic term, dominates over electron-phonon scattering.Rice observed 1 that in the transition metals A/γ 2 ≈ a T M = 0.4 µΩ cm mol 2 K 2 /J 2 (Fig. 1), even though γ 2 varies by an order of magnitude across the materials he studied. Later, Kadowaki and Woods 2 found that in many heavy fermion compounds A/γ 2 ≈ a HF = 10 µΩ cm mol 2 K 2 /J 2 (Fig. 1), despite the large mass renormalisation which causes γ 2 to vary by more than two orders of magnitude in these materials. Because of this remarkable

Melanin, the human skin pigment, is found everywhere in nature. Recently it has gained significant attention for its potential bioelectronic properties. However, there remain significant obstacles in realizing its electronic potential, in particular, the identity of the solid-state free radical in eumelanin, which has been implicated in charge transport. We have therefore undertaken a hydration-controlled continuous-wave electron paramagnetic resonance study on solid-state eumelanin. Herein we show that the EPR signal from solid-state eumelanin arises predominantly from a carbon-centered radical but with an additional semiquinone free radical component. Furthermore, the spin densities of both of these radicals can be manipulated using water and pH. In the case of the semiquinone radical, the comproportionation reaction governs the pH- and hydration-dependent behavior. In contrast, the mechanism underlying the carbon-centered radical's pH- and hydration-dependent behavior is not clear; consequently, we have proposed a new destacking model in which the intermolecular structure of melanin is disordered due to π-π destacking, brought about by the addition of water or increased pH, which increases the proportion of semiquinone radicals via the comproportionation reaction.

We study the excited states of two iridium(III) complexes with potential applications in organic light-emitting diodes: fac-tris(2-phenylpyridyl)iridium(III) [Ir(ppy)(3)] and fac-tris(1-methyl-5-phenyl-3-n-propyl-[1,2,4]triazolyl)iridium(III) [Ir(ptz)(3)]. Herein we report calculations of the excited states of these complexes from time-dependent density functional theory (TDDFT) with the zeroth-order regular approximation (ZORA). We show that results from the one-component formulation of ZORA, with spin-orbit coupling included perturbatively, accurately reproduce both the results of the two-component calculations and previously published experimental absorption spectra of the complexes. We are able to trace the effects of both scalar relativistic correction and spin-orbit coupling on the low-energy excitations and radiative lifetimes of these complexes. In particular, we show that there is an indirect relativistic stabilisation of the metal-to-ligand charge transfer (MLCT) states. This is important because it means that indirect relativistic effects increase the degree to which SOC can hybridise singlet and triplet states and hence plays an important role in determining the optical properties of these complexes. We find that these two compounds are remarkably similar in these respects, despite Ir(ppy)(3) and Ir(ptz)(3) emitting green and blue light respectively. However, we predict that these two complexes will show marked differences in their magnetic circular dichroism (MCD) spectra.

We present a resonating-valence-bond theory of superconductivity for the Hubbard-Heisenberg model on an anisotropic triangular lattice. Our calculations are consistent with the observed phase diagram of the half-filled layered organic superconductors, such as the beta, beta', kappa, and lambda phases of (BEDT-TTF)2X [bis(ethylenedithio)tetrathiafulvalene] and (BETS)2X [bis(ethylenedithio)tetraselenafulvalene]. We find a first order transition from a Mott insulator to a dx2-y2 superconductor with a small superfluid stiffness and a pseudogap with dx2-y2 symmetry.