Construction of basis sets for time-dependent studies

Abstract

The common basis sets constructed for use in electronic structure calculations have been found inadequate for the representation of electrons participating in nonadiabatic time-dependent dynamics calculations. In this paper we outline an approach to construct electronic bases better suited for dynamical processes such as energy deposition and charge transfer in binary collisions of ions, atoms, and molecules. Since electrons of many-atom systems commonly are represented by orbitals formed as linear combinations of atomic orbitals, the focus is on atomic basis sets. The main idea is to construct basis sets that adequately reproduce the first few excitation energies of neutral atoms. In this paper we outline a method for such basis set construction of various levels of accuracy for first-row atoms and give a few illustrative examples.

Time-dependent density functional theory benchmarking for the calculations of atomic spectra: efficiency of exc-ETDZ basis set

“…In fact, we want to compare the efficiency of exc-ETDZ basis set when it is applied with CIS(D) as an illustrative of wave function theory (WFT) methods, and BMK, BH&HLYP and xB97 as three representatives of density functional methods. The atomic spectra at CIS(D)/exc-ETDZ level [25] are collected in Table 1. The overall trends in the calculated first excitation energies in this work together with CIS(D) results are depicted in Fig.…”

“…Augmentation of 6-31G basis by d-type polarization and single set of diffuse s-and p-functions in 6-31?G(d) basis set leads to significant improvement in excited state calculations and diminishes the computed errors by more than five times compared with 6-31G basis set. In fact, basis sets including diffuse functions would certainly modify the TD-DFT estimates of the excitation energy, but we have conserved 6-31G basis set for the sake of comparison between our estimates of excitation energies based on TD-DFT calculations with those reported by Guevara et al [25] at CIS(D) level of theory. Anyway, we will not explain the results of 6-31G basis set throughout the discussion.…”

“…The new orbital exponents of s-and p-orbitals added to 6-31G basis set for constructing exc-ETDZ basis for Li through Ne are, respectively, 0.0163594, 0.0379981, 0.0447004, 0.0523006, 0.0582180, 0.0719134, 0.0265100 and 0.1170 [25]. Only fluorine required an additional d-function with exponent of 0.1170, and neon required the second sp function with exponent of 0.03080 [25].…”

“…All spectrum calculations were carried out using the Gaussian 03 [72] and Gaussian 09 [73] programs. Table 1 specifies eighteen electronic configurations arising from ground and excited states of first-row atoms as well as previous computational [25] and the experimental [71] excitation energies. Table 2 collects the MSE and MUE values for all the tested functionals and basis sets, which are sorted alphabetically for each category of functionals.…”

“…In this respect, Canal Neto et al [24] used the generator coordinate HF method to generate Gaussian basis sets for low-lying excited states of neutral atoms. Recently, Guevara et al [25] provided an approach to construct minimal-accuracy basis sets for the first-row atoms suited for dynamical processes. The constructed basis set, which was labeled by exc-ETDZ, has been claimed to be useful for methods that involve calculation of excited states, such as TD-DFT and configuration interaction with single substitution (CIS) [26] and CIS with perturbative doubles corrections (CIS(D)) [27,28].…”