Dario Rocca

Turbo charging time-dependent density-functional theory with Lanczos chains

We introduce a new implementation of time-dependent density-functional theory which allows the entire spectrum of a molecule or extended system to be computed with a numerical effort comparable to that of a single standard ground-state calculation. This method is particularly well suited for large systems and/or large basis sets, such as plane waves or real-space grids. By using a superoperator formulation of linearized time-dependent density-functional theory, we first represent the dynamical polarizability of an interacting-electron system as an off-diagonal matrix element of the resolvent of the Liouvillian superoperator. One-electron operators and density matrices are treated using a representation borrowed from time-independent density-functional perturbation theory, which permits us to avoid the calculation of unoccupied Kohn-Sham orbitals. The resolvent of the Liouvillian is evaluated through a newly developed algorithm based on the nonsymmetric Lanczos method. Each step of the Lanczos recursion essentially requires twice as many operations as a single step of the iterative diagonalization of the unperturbed Kohn-Sham Hamiltonian. Suitable extrapolation of the Lanczos coefficients allows for a dramatic reduction of the number of Lanczos steps necessary to obtain well converged spectra, bringing such number down to hundreds (or a few thousands, at worst) in typical plane-wave pseudopotential applications. The resulting numerical workload is only a few times larger than that needed by a ground-state Kohn-Sham calculation for a same system. Our method is demonstrated with the calculation of the spectra of benzene, C(60) fullerene, and of chlorophyll a.

Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods

We report a systematic study of the weak chemical bond between two benzene molecules. We first show that it is possible to obtain a very good description of the C(2) dimer and the benzene molecule by using pseudopotentials for the chemically inert 1s electrons and a resonating valence bond wave function as a variational ansatz, expanded on a relatively small Gaussian basis set. We employ an improved version of the stochastic reconfiguration technique to optimize the many-body wave function, which is the starting point for highly accurate simulations based on the lattice regularized diffusion Monte Carlo method. This projection technique provides a rigorous variational upper bound for the total energy, even in the presence of pseudopotentials, and substantially improves the accuracy of the trial wave function, which already yields a large fraction of the dynamical and nondynamical electron correlation. We show that the energy dispersion of two benzene molecules in the parallel displaced geometry is significantly deeper than the face-to-face configuration. However, contrary to previous studies based on post-Hartree-Fock methods, the binding energy remains weak ( approximately 2 kcal/mol) also in this geometry, and its value is in agreement with the most accurate and recent experimental findings [H. Krause et al., Chem. Phys. Lett. 184, 411 (1991)].

Ab initio calculations of optical absorption spectra: Solution of the Bethe–Salpeter equation within density matrix perturbation theory

We describe an ab initio approach to compute the optical absorption spectra of molecules and solids, 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. This procedure is equivalent to solving the statically screened 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. In this way, full absorption spectra may be obtained with a computational workload comparable to ground state Hartree-Fock calculations. We present results for small molecules, for the spectra of a 1 nm Si cluster in a wide energy range (20 eV), and for a dipeptide exhibiting charge transfer excitations.

turboTDDFT – A code for the simulation of molecular spectra using the Liouville–Lanczos approach to time-dependent density-functional perturbation theory☆

We introduce turboTDDFT, an implementation of the Liouville-Lanczos approach to linearized time-dependent density-functional theory, designed to simulate the optical spectra of molecular systems made of up to several hundred atoms. turboTDDFT is open-source software distributed under the terms of the GPL as a component of Quantum ESPRESSO. As with other components, turboTDDFT is optimized to run on a variety of di erent platforms, from laptops to massively parallel architectures, using native mathematical libraries (LAPACK and FFTW) and a hierarchy of custom parallelization layers built on top of MPI.

A block variational procedure for the iterative diagonalization of non-Hermitian random-phase approximation matrices

We present a technique for the iterative diagonalization of random-phase approximation (RPA) matrices, which are encountered in the framework of time-dependent density-functional theory (TDDFT) and the Bethe-Salpeter equation. The non-Hermitian character of these matrices does not permit a straightforward application of standard iterative techniques used, i.e., for the diagonalization of ground state Hamiltonians. We first introduce a new block variational principle for RPA matrices. We then develop an algorithm for the simultaneous calculation of multiple eigenvalues and eigenvectors, with convergence and stability properties similar to techniques used to iteratively diagonalize Hermitian matrices. The algorithm is validated for simple systems (Na(2) and Na(4)) and then used to compute multiple low-lying TDDFT excitation energies of the benzene molecule.

Molecular design of photoactive acenes for organic photovoltaics

Absorption spectra of n-acenes (n from 2 to 6, for naphthalene, anthracene, tetracene, pentacene, and hexacene, respectively) have been calculated using a newly developed code based on time-dependent density-functional theory. Our calculations show that absorption spectra and charge carrier mobility of acenes not only depend on the molecular identity but also on the molecular packing. By designing the interaction between metal substrates and the first layer of acene molecules, they can be packed in a face-to-face fashion instead of the conventional herringbone (face-to-edge) arrangement. Acenes in the cofacial packing would increase the pi-orbital overlap and thus enhance the charge mobility by maximizing electronic coupling between adjacent molecules. Absorption spectra of cofacially packed acenes have a better overlap with the solar spectrum, which allows harvesting more of the solar energy from red photons.