Robust and Efficient Auxiliary Density Perturbation Theory Calculations

Exchange-correlation kernel for perturbation dependent auxiliary functions in auxiliary density perturbation theory

CONTEXT

Analytic exchange-correlation kernel formulations are of the outermost importance for density functional theory (DFT) perturbation calculations. In this paper, the working equation for the exchange-correlation kernel of the generalized gradient approximation (GGA) for perturbation dependent auxiliary functions is derived and discussed in the framework of auxiliary density functional theory (ADFT). The presented new formulation is extended to the unrestricted approach, too. A comprehensive discussion of the implementation of the GGA ADFT kernel, using either the native exchange-correlation functional implementations in deMon2k or the ones from the LibXC library, is given. Calculations with analytic exchange-correlation kernels are compared to their finite difference counterparts. The obtained results are in quantitative agreement. Nevertheless, analytic GGA ADFT kernel implementations show substantial improvement in the computational performance. Similar results are reported for analytic second derivatives of effective core potential (ECP) and model core potential (MCP) matrix elements when compared to their finite difference counterparts in molecular frequency analyses.

METHOD

All calculations are performed in the framework of ADFT as implemented in deMon2k. In the ADFT analytic frequency calculations, auxiliary density perturbation theory was used. The underlying two-center exchange-correlation kernel matrix elements are calculated by numerical integration either with analytic or finite difference kernel expressions. Validation calculations are performed with the VWN and PBE functionals employing DFT-optimized DZVP basis sets in conjunction with automatically generated GEN-A2 auxiliary density function sets. In the (Pt3Cu)n cluster benchmark calculations, the RPBE functional was used. For Pt atoms, the quasi-relativistic LANL2DZ effective core potential with the corresponding valence basis set was employed, whereas for Cu atoms, the all-electron DFT-optimized TZVP basis was applied. The auxiliary density was expanded by the automatically generated GEN-A2* auxiliary function set. We run all benchmark calculations in parallel on 24 cores.

Semiempirical Approach to the Fukui Function Analysis of Uric Acid under Different pH Conditions

Analytic Fukui functions calculated at a first-principles level are combined with experimental pKa values and the calculation of tautomerization energies to obtain the effective regioselectivity of uric acid toward electron-transfer reactions under different pH conditions. Second-order electron binding energies are also computed to determine which of the tautomers is more likely to participate in the electron transfer. A comparison of vertical and adiabatic proton detachment energies allows us to conclude that tautomerization is not mediating deprotonation and that two monoanionic species are of comparable relevance. The main difference between these monoanionic species is the ring that has been deprotonated. Both monoanionic species are produced from a single neutral tautomer and mainly produce a single dianionic tautomer. As a method for the analysis of systems affected by pH such as uric acid, we propose to plot condensed Fukui functions versus pH, allowing us to draw the effect of pH on the regioselectivity of electron transfer in a single image.

Efficient implementation of time-dependent auxiliary density functional theory

The random phase approximation of time-dependent auxiliary density functional theory (TDADFT) is rederived from auxiliary density perturbation theory. Our exhaustive validation of TDADFT reveals an upshift of the excitation energies by ∼0.1 eV with respect to standard time-dependent density functional theory. For the computationally efficient implementation of TDADFT, floating point operation optimized three-center electron repulsion integral recurrence relations and their double asymptotic expansions are implemented into the Davidson solver. The computational efficiency of TDADFT is benchmarked with four sets of molecules comprising alkanes, fullerenes, DNA fragments, and zeolites. The results show that TDADFT has a computational scaling between 1.3 and 1.9 with respect to the number of basis functions, which is lower than the scaling of standard time-dependent density functional theory. Due to its computational simplifications, TDADFT is particularly well suited for Born-Oppenheimer molecular dynamics simulations. As illustrative examples, we present the temperature effects on the gas-phase absorption spectra of benzene, naphthalene, and anthracene.

Scalable Molecular GW Calculations: Valence and Core Spectra

We present a scalable implementation of the GW approximation using Gaussian atomic orbitals to study the valence and core ionization spectroscopies of molecules. The implementation of the standard spectral decomposition approach to the screened-Coulomb interaction, as well as a contour-deformation method, is described. We have implemented both of these approaches using the robust variational fitting approximation to the four-center electron repulsion integrals. We have utilized the MINRES solver with the contour-deformation approach to reduce the computational scaling by 1 order of magnitude. A complex heuristic in the quasiparticle equation solver further allows a speed-up of the computation of core and semicore ionization energies. Benchmark tests using the GW100 and CORE65 data sets and the carbon 1s binding energy of the well-studied ethyl trifluoroacetate, or ESCA molecule, were performed to validate the accuracy of our implementation. We also demonstrate and discuss the parallel performance and computational scaling of our implementation using a range of water clusters of increasing size.

Analytic Alchemical Derivatives for the Analysis of Differential Acidity Assisted by the h Function

Analytical calculation of alchemical derivatives based on auxiliary density perturbation theory is described, coded, and validated. For the case where the nucleus is a hydrogen atom and the nuclear charge is changed from 1 to 0, it turns out that a good estimate of the proton binding energies can be obtained very efficiently. First-order results correspond exactly to the molecular electrostatic potential evaluated at the hydrogen nucleus location (removing self-repulsion), in agreement with previously reported extensive studies. Therefore, the second-order results reported here are refinements in accuracy that finally allow a quantitative exploration of differential acidity. Furthermore, the recently reported h function is produced in its analytical form as a byproduct and local descriptor associated with the proton binding energy values found with this approach. In an example application, proton binding energies are computed for a family of imidazolium derivatives to demonstrate the capabilities and the stability of the method with respect to changes in basis set or exchange-correlation functional.

Self-Consistent Auxiliary Density Perturbation Theory

The working equations for the extension of auxiliary density perturbation theory (ADPT) to hybrid functionals, employing the variational fitting of the Fock potential, are derived. The response equations in the resulting self-consistent ADPT (SC-ADPT) are solved iteratively with an adapted Eirola-Nevanlinna algorithm. As a result, a memory and CPU time efficient implementation of perturbation theory free of four-center electron repulsion integrals (ERIs) is obtained. Our validation calculations of SC-ADPT static and dynamic polarizabilities show quantitative agreement with corresponding coupled perturbed Hartree-Fock and Kohn-Sham results employing four-center ERIs. The comparison of SC-ADPT hybrid functional polarizabilities with coupled cluster reference calculations yield semiquantitative agreement. The presented systematic study of the dynamic polarizabilities of oligothiophenes shows that hybrid functionals can overcome the pathological misplacement of excitation poles by the local density and generalized gradient approximations. Good agreement with experimental dynamic polarizabilities for all studied oligothiophenes is achieved with range-separated hybrid functionals in the framework of SC-ADPT.