turboTDDFT 2.0—Hybrid functionals and new algorithms within time-dependent density-functional perturbation theory

Abstract

We present a new release of the turboTDDFT code featuring an implementation of hybrid functionals, a recently introduced pseudo-Hermitian variant of the Liouville-Lanczos approach to time-dependent density-functional perturbation theory, and a newly developed Davidson-like algorithm to compute selected interior eigen-values/vectors of the Liouvillian super-operator. Our implementation is thoroughly validated against benchmark calculations performed on the cyanin (C 21 O 11 H 21 ) molecule using the Gaussian 09 and turboTDDFT 1.0 codes. External routines/libraries: turboTDDFT 2.0 is a tightly integrated component of the Quantum ESPRESSO distribution and requires the standard libraries linked by it: BLAS, LAPACK, FFTW, MPI. Nature of problem: Calculation of the optical absorption spectra of molecular systems. Solution method: Electronic excited states are addressed by linearized time-dependent density-functional theory within the plane-wave pseudo-potential method. The dynamical polarizability can be computed in terms of the resolvent of the Liouvillian super-operator, using a pseudo-Hermitian variant of the Lanczos recursion scheme. As an alternative, individual eigenvalues of the Liouvillian can be computed via a newly introduced variant of the Davidson method. In both cases, hybrid functionals can now be used. Restrictions: Spin-restricted formalism. Linear-response regime. Adiabatic XC kernels only. Hybrid functional are only accessible using norm-conserving pseudo-potentials. Unusual features: No virtual orbitals are used, nor even calculated. Within the Lanczos method a single recursion gives access to the whole optical spectrum; when computing individual excitations usinf the Davidson method, interior eigenvalues can be easily targeted.

Generalization of Dielectric-Dependent Hybrid Functionals to Finite Systems

“…The improvement of the accuracy of adiabatic timedependent density functional theory is an area of active research in condensed matter physics and physical chemistry [59,[82][83][84][85][86][87]; hence, we explored the application of Eq. (10) to time-dependent density functional theory (TDSX), and we show below that the SX functional can correctly reproduce not only ionization energies and fundamental gaps but also optical gaps.…”

“…We note that the evaluation of empty electronic states is not necessary in TDDFT calculations, when following the procedure of Ref. [59].…”

“…The fundamental gaps of the Si nanoparticles and the vertical ionization potentials of Thiel's test set were obtained in the same way. Absorption properties (i.e., optical gaps) of the Thiel's test set were instead computed using time-dependent density functional theory, as implemented in Quantum ESPRESSO in the turboTDDFT code [59]. We used the latter code to solve the TDDFT equations in the adiabatic approximation, where the exchange-correlation potential was described by the functional of Eq.…”

Communication: A novel implementation to compute MP2 correlation energies without basis set superposition errors and complete basis set extrapolation

“…Improved efficiency without loss of accuracy might be reached by decreasing the kinetic energy cut-off used to evaluate the exchange term. 46,47 Since PWs are intrinsically characterized by periodic boundary conditions, our methodology is suitable for generalization to treat periodic solids, 31 and this will be considered in future extensions of our approach.…”

How Adsorption Onto TiO2 Modifies the Properties of Multiswitchable DTE Systems: Theoretical Insights

“…[63][64][65][66] An effective diagonalization tool, the Lanczos approach has applications ranging from vibrational structure theory to damped couple cluster electronic 5 response theory, and is necessary when employing large basis sets such as plane waves in order to avoid the prohibitive inversion of L. [67][68][69] . Unlike conventional spectral calculations, the Lanczos approach enables access to the entire absorption spectrum at a reasonable computing cost, at the expense of being unable to resolve individual excitation states.…”