Gaussian basis density functional theory for systems periodic in two or three dimensions: Energy and forces

Optimization of atomic density-fitting basis functions for molecular two-electron integral approximations

A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the product densities, modeling their contribution to the exchange and second-order correlation energy, and a simple weighted error measure is minimized. Generally contracted Gaussian auxiliary basis sets are optimized to match the wavefunction basis sets [D. N. Laikov, Theor. Chem. Acc. 138, 40 (2019)] for all 102 elements in a scalar-relativistic approximation [D. N. Laikov, J. Chem. Phys. 150, 061103 (2019)].

Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Stress tensor

A full implementation of the analytical stress tensor for periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. It is the extension of the implementation of analytical energy gradients (Lazarski et al., Journal of Computational Chemistry 2016, 37, 2518-2526) to the stress tensor for the purpose of optimization of lattice vectors. Its key component is the efficient calculation of the Coulomb contribution by combining density fitting approximation and continuous fast multipole method. For the exchange-correlation (XC) part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097-3104) is extended to XC weight derivatives and stress tensor. The computational efficiency and favorable scaling behavior of the stress tensor implementation are demonstrated for various model systems. The overall computational effort for energy gradient and stress tensor for the largest systems investigated is shown to be at most two and a half times the computational effort for the Kohn-Sham matrix formation. © 2019 Wiley Periodicals, Inc.

Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients

A full implementation of analytical energy gradients for molecular and periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. Its key component is a combination of density fitting (DF) approximation and continuous fast multipole method (CFMM) that allows for an efficient calculation of the Coulomb energy gradient. For exchange-correlation part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097) is extended to energy gradients. Computational efficiency and asymptotic O(N) scaling behavior of the implementation is demonstrated for various molecular and periodic model systems, with the largest unit cell of hematite containing 640 atoms and 19,072 basis functions. The overall computational effort of energy gradient is comparable to that of the Kohn-Sham matrix formation. © 2016 Wiley Periodicals, Inc.

Density Functional Theory for Molecular and Periodic Systems Using Density Fitting and Continuous Fast Multipole Methods

An implementation of Kohn-Sham density functional theory within the TURBOMOLE program package with Gaussian-type orbitals (GTO) as basis functions is reported that treats molecular and periodic systems of any dimensionality on an equal footing. Its key component is a combination of density fitting/resolution of identity (DF) approximation and continuous fast multipole method (CFMM) applied for the electronic Coulomb term. This DF-CFMM scheme operates entirely in the direct space and partitions Coulomb interactions into far-field part evaluated using multipole expansions and near-field contribution calculated employing density fitting. Computational efficiency and favorable scaling behavior of our implementation approaching O(N) for the formation of Kohn-Sham matrix is demonstrated for various molecular and periodic systems including three-dimensional models with unit cells containing up to 640 atoms and 19072 GTO basis functions.

Theoretical and experimental investigations on the photoconductivity and nonlinear optical properties of donor–acceptor π conjugated copolymer, poly(2,5-(3,4-ethylenedioxythiophene)-alt-2,7-(9,9-dioctylfluorene))

A new donor–acceptor copolymer, poly(2,5-(3,4-ethylenedioxythiophene)-alt-2,7-(9,9-dioctylfluorene) copolymer with high optical limiting efficiency (0.47 GW cm⁻²) and photoconductivity (at 75 V μm⁻¹, the photosensitivity was 289 742).

Resolution of identity approximation for the Coulomb term in molecular and periodic systems

A new formulation of resolution of identity approximation for the Coulomb term is presented, which uses atom-centered basis and auxiliary basis functions and treats molecular and periodic systems of any dimensionality on an equal footing. It relies on the decomposition of an auxiliary charge density into charged and chargeless components. Applying the Coulomb metric under periodic boundary conditions constrains the explicit form of the charged part. The chargeless component is determined variationally and converged Coulomb lattice sums needed for its determination are obtained using chargeless linear combinations of auxiliary basis functions. The lattice sums are partitioned in near- and far-field portions which are treated through an analytical integration scheme employing two- and three-center electron repulsion integrals and multipole expansions, respectively, operating exclusively in real space. Our preliminary implementation within the TURBOMOLE program package demonstrates consistent accuracy of the method across molecular and periodic systems. Using common auxiliary basis sets the errors of the approximation are small, in average about 20 muhartree per atom, for both molecular and periodic systems.

Scalar relativistic all-electron density functional calculations on periodic systems

Scalar relativistic effects are included in periodic boundary conditions calculations with Gaussian orbitals. This approach is based on the third-order Douglas-Kroll-Hess approximation, allowing the treatment of all electrons on an equal footing. With this methodology, we are able to perform relativistic all-electron density functional calculations using the traditional local spin-density and generalized gradient approximations (GGA), as well as meta-GGA and hybrid density functionals. We present benchmark results for the bulk metals Pd, Ag, Pt, and Au, and the large band gap semiconductors AgF and AgCl.

Models for the treatment of crystalline solids and surfaces

Crystalline solids and surfaces have become a subject of growing interest. The difficulty of a comprehensive description of a variety of phenomena by a single method has led to the development of many models. These models can be classified as nonperiodic and periodic models. The former include free clusters, saturated clusters, and embedded clusters. The latter two models serve to remove the boundary effects of the free clusters. No perfect avoidance of such effects can be achieved in this way. The cyclic cluster model overcomes this difficulty in a natural way. It is periodic with a finite periodicity. An embedding can take into account a long-range effect in ionic crystals. Previous periodic approaches relied on the large unit cell model, which is related to the supercell approach. For perfect crystals the conventional unit cell approach is a well-known standard. However, its disadvantage is the unphysical periodicity of defects, which is avoided in the cyclic cluster model. The present article presents a description of these models together with selective applications to solid-state systems and surfaces.

Structure and conformational behavior of biopolymers by density functional calculations employing periodic boundary conditions. I. The case of polyglycine, polyalanine, and poly-alpha-aminoisobutyric acid in vacuo

Fully quantum mechanical calculations exploiting periodic boundary conditions (PBC) have been applied to the study of four different regular structures (alpha- and 3(10)-helix, fully extended and repeated gamma-turns) of the infinite polypeptides of glycine, alanine, and alpha-aminoisobutyric acid (Aib) in vacuo. alpha-Helix is predicted to be the most stable conformer for polyalanine and polyglycine, being stabilized over the 3(10)-helix mainly by more favorable dipole-dipole interactions. Contrary to previous suggestions, steric effects and hydrogen-bond strengths are comparable for both helix structures. 3(10)-Helix is preferred for poly-Aib, since in this case alpha-helix is strongly distorted due to unfavorable intrachain repulsions. Extended structures and repeated gamma-turns are much less stable than helix structures for all of the polypeptides examined, mainly due to the absence of favorable long-range interactions. The optimized geometries are in good agreement with the available experimental data and reveal a remarkable dependence on the nature of the residue forming the polypeptides; at the same time the electronic and structural parameters of each residue strongly depend on the secondary structure of the polypeptides.