Ab-initio calculations of Many-Body effects in liquids: the electronic excitations of water (original) (raw)
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Theoretical Characterisation of the Electronic Excitation in Liquid Water
ChemPhysChem, 2005
Because of its central role in basically all aspects of science, water is certainly one of the most extensively investigated substances, from a theoretical point of view. Many properties have been, in fact, theoretically addressed both in the isolated and condensed phases. Nevertheless, many aspects are still not completely understood and represent the focus of active theoretical interest. Among them, one of the most appealing is certainly the understanding of the electronic properties, in particular the photoabsorption features, in condensed phase. Liquid water experimentally shows, under ambient conditions, the 0-1 absorption maximum at 147 nm, that is, 88 kJ mol À1 shifted toward the blue with respect to the corresponding absorption in vacuum. This blue-shift is known to be more pronounced in ice than in liquid water, and it is also present in small water clusters. From these observations, it is well-established that such a blue-shift is to be mainly ascribed to the short contacts of the excited molecule with its solvation shell (the water dipole moment undergoes an inversion upon 0-1 excitation ). However, only a few theoretical studies have been so far devoted to modelling water photoabsorption in the condensed phase. The computational methods available nowadays are, in fact, able to provide extremely accurate information about the photoexcitation of isolated molecules. However, there are still many difficulties in modelling the same phenomenon in the condensed phase. The inclusion of electronic degrees of freedom (necessary for studying an electronic excitation) into a simulation of a large number of molecules (necessary for a reliable modelling of a condensed phase) is, in fact, still challenging from a computational point of view. In this context, we recently proposed a theoretical computational approach, the perturbed matrix method (PMM), whose main computational feature is the possibility of including, into a classical simulation algorithm, electronic degrees of freedom. In a number [a] M.
Insights into the ultraviolet spectrum of liquid water from model calculations
Journal of Chemical …, 2010
With a view toward a better molecular level understanding of the effects of hydrogen bonding on the ultraviolet absorption spectrum of liquid water, benchmark electronic structure calculations using high level wave function based methods and systematically enlarged basis sets are reported for excitation energies and oscillator strengths of valence excited states in the equilibrium water monomer and dimer and in a selection of liquid-like dimer structures. Analysis of the electron density redistribution associated with the two lowest valence excitations of the water dimer shows that these are usually localized on one or the other monomer, although valence hole delocalization can occur for certain relative orientations of the water molecules. The lowest excited state is mostly associated with the hydrogen bond donor and the significantly higher energy second excited state mostly with the acceptor. The magnitude of the lowest excitation energies is strongly dependent on where the valence hole is created, and only to a lesser degree on the perturbation of the excited electron density distribution by the neighboring water molecule. These results suggest that the lowest excitation energies in clusters and liquid water can be associated with broken acceptor hydrogen bonds, which provide energetically favorable locations for the formation of a valence hole. Higher valence excited states of the dimer typically involve delocalization of the valence hole and/or delocalization of the excited electron and/or charge transfer. Two of the higher valence excited states that involve delocalized valence holes always have particularly large oscillator strengths. Due to the pervasive delocalization and charge transfer, it is suggested that most condensed phase water valence excitations intimately involve more than one water molecule and, as a consequence, will not be adequately described by models based on perturbation of free water monomer states. The benchmark calculations are further used to evaluate a series of representative semilocal, global hybrid, and range separated hybrid functionals used in efficient time-dependent density functional methods. It is shown that such an evaluation is only meaningful when comparison is made at or near the complete basis set limit of the wave function based reference method. A functional is found that quantitatively describes the two lowest excitations of water dimer and also provides a semiquantitative description of the higher energy valence excited states. This functional is recommended for use in further studies on the absorption spectrum of large water clusters and of condensed phase water.
Electronic excitations: density-functional versus many-body Green’s-function approaches
Reviews of Modern Physics, 2002
Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green's-function equations, starting with a one-electron propagator and considering the electron-hole Green's function for the response. Key ingredients are the electron's self-energy ⌺ and the electron-hole interaction. A good approximation for ⌺ is obtained with Hedin's GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of ⌺. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.
Time-dependent density functional theory TD-DFT calculations of the electronic response of molecular and bulk liquid water based on a very accurate orbital-dependent ground-state exchange-correlation potential, the statistical average of model orbital potentials SAOP, and on the adiabatic local density approximation ALDA for the exchange-correlation kernel are described. The quality of the calculated excitation energies, both in the molecule and in the liquid, is assessed by comparison to hybrid TD-DFT calculations and experimental data. A combination of classical molecular dynamics simulations and TD-DFT calculations sampling several disordered configurations of a small liquid sample is then used to simulate the optical absorption spectrum in the region of 0–15 eV. The resulting room-temperature absorption profile is discussed in connection with previous TD-DFT calculations as well as with results from Green’s function theory and experiment.
Ab initio Electronic Structure of Liquid Water
Physical review letters, 2016
Self-consistent GW calculations with efficient vertex corrections are employed to determine the electronic structure of liquid water. Nuclear quantum effects are taken into account through ab initio path-integral molecular dynamics simulations. We reveal a sizable band-gap renormalization of up to 0.7 eV due to hydrogen-bond quantum fluctuations. Our calculations lead to a band gap of 8.9 eV, in accord with the experimental estimate. We further resolve the ambiguities in the band-edge positions of liquid water. The valence-band maximum and the conduction-band minimum are found at -9.4 and -0.5 eV with respect to the vacuum level, respectively.
2011
We present an approach to compute optical absorption spectra from first principles, which is suitable for the study of large systems and gives access to spectra within a wide energy range. In this approach, the quantum Liouville equation is solved iteratively within first order perturbation theory, with a Hamiltonian containing a static self-energy operator [1]. This is equivalent to solving the Bethe-Salpeter equation. Explicit calculations of single particle excited states and inversion of dielectric matrices are avoided using techniques based on Density Functional Perturbation Theory [1,2]. The calculation and inclusion of GW quasi-particle corrections within this framework are discussed. The efficiency and accuracy of our approach are demonstrated by computing optical spectra of solids, nanostructures and dipeptide molecules exhibiting charge transfer excitations. [4pt] [1] D.Rocca, D.Lu and G.Galli, J. Chem. Phys. 133, 164109 (2010). [0pt] [2] H. Wilson, F. Gygi and G. Galli, Phys. Rev. B , 78, 113303, (2008).
Optical spectra from molecules to crystals: Insight from many-body perturbation theory
Physical Review B, 2015
Time-dependent density-functional theory (TDDFT) is successful in describing excitation energies of finite systems, already in its most simple form, the adiabatic local-density approximation (ALDA). By confronting TDDFT with many-body perturbation theory, we clarify when and why this method can be trusted for molecular materials, where many-body effects can be crucial. We show that ALDA provides accurate results for excitations with mainly single-particle character. Conversely, when electron-hole correlations as well as local-field effects become decisive, only a many-body approach can quantitatively predict absorption features.
The Journal of Chemical Physics, 2008
In a recent paper ͓Aschi et al., ChemPhysChem 6, 53 ͑2005͔͒, we characterized, by means of theoretical-computational procedures, the electronic excitation of water along the typical liquid state isochore ͑55.32 mol/ l͒ for a large range of temperature. In that paper we were able to accurately reproduce the experimental absorption maximum at room temperature and to provide a detailed description of the temperature dependence of the excitation spectrum along the isochore. In a recent experimental work by Marin et al. ͓J. Chem. Phys. 125, 104314 ͑2006͔͒, water electronic excitation energy was carefully analyzed in a broad range of density and temperature, finding a remarkable agreement of the temperature behavior of the experimental data with our theoretical results. Here, by means of the same theoretical-computational procedures ͑molecular dynamics simulations and the perturbed matrix method͒, we investigate water electronic absorption exactly in the same density-temperature range used in the experimental work, hence, now considering also the absorption density dependence. Our results point out that, ͑1͒ for all the densities and temperatures investigated, our calculated absorption spectra are in very good agreement with the experimental ones and ͑2͒ the gradual maxima redshift observed increasing the temperature or decreasing the density has to be ascribed to a real shift of the lowest X → A electronic transition, supporting the conclusions of Marin et al.
Molecular electronic excitations calculated from a solid-state approach: Methodology and numerics
Physical Review B, 2005
We investigate the applicability and accuracy of a solid-state approach, which was developed originally for the relatively homogeneous electron gas, to describe electronic single-particle and electron-hole pair excitations in molecules. Thereby we start from the determination of the molecular ground state within the local density functional theory using repeated supercells and pseudopotentials for the electron-ion interaction. The electronic spectra are obtained from the Green's function formalism. The exchange-correlation self-energy ⌺ is linearly expanded in the screened Coulomb interaction, i.e., the GW approximation is used. Optical spectra are obtained from the Bethe-Salpeter equation for the irreducible polarization propagator. The numerical implementation and possible pitfalls of this methodology are discussed using silane, disilane, and water molecules as examples. In particular the influence of the dynamics of the screening, the supercell size, and the number of empty states are studied. The resulting single-and two-particle excitation energies are compared with experiment and previous theoretical work.
2019
We present the open-source VOTCA-XTP software for the calculation of the excited-state electronic structure of molecules using many-body Green’s functions theory in the GW approximation with the Bethe–Salpeter Equation (BSE). This work provides a summary of the underlying theory and discusses details of its implementation based on Gaussian orbitals, including, i.a., resolution-of-identity techniques, different approaches to the frequency integration of the self-energy or acceleration by offloading compute-intensive matrix operations using GPUs in a hybrid OpenMP/Cuda scheme. A distinctive feature of VOTCA-XTP is the capability to couple the calculation of electronic excitations to a classical polarizable environment on atomistic level in a coupled quantum- and molecular-mechanics (QM/MM) scheme, where a complex morphology can be imported from Molecular Dynamics simulations. The capabilities and limitations of the GW -BSE implementation are illustrated with two examples. First, we st...