Gaussian Basis Sets Research Articles

Gaussian Basis Sets for Crystalline Solids: All-Purpose Basis Set Libraries vs System-Specific Optimizations.

It is customary in molecular quantum chemistry to adopt basis set libraries in which the basis sets are classified according to either their size (triple-ζ, quadruple-ζ, ...) and the method/property they are optimal for (correlation-consistent, linear-response, ...) but not according to the chemistry of the system to be studied. In fact the vast majority of molecules is quite homogeneous in terms of density (i.e., atomic distances) and types of bond involved (covalent or dispersive). The situation is not the same for solids, in which the same chemical element can be found having metallic, ionic, covalent, or dispersively bound character in different crystalline forms or compounds, with different packings. This situation calls for a different approach to the choice of basis sets, namely a system-specific optimization of the basis set that requires a practical algorithm that could be used on a routine basis. In this work we develop a basis set optimization method based on an algorithm–similar to the direct inversion in the iterative subspace–that we name BDIIS. The total energy of the system is minimized together with the condition number of the overlap matrix as proposed by VandeVondele et al. [VandeVondele et al. J. Chem. Phys.2007, 227, 114105]. The details of the method are here presented, and its performance in optimizing valence orbitals is shown. As demonstrative systems we consider simple prototypical solids such as diamond, graphene sodium chloride, and LiH, and we show how basis set optimizations have certain advantages also toward the use of large (quadruple-ζ) basis sets in solids, both at the DFT and Hartree–Fock level.

Atoms and molecules in soft confinement potentials

ABSTRACT We present a detailed non-relativistic study of the atoms H, He, C and K and the molecule CH in the centre of a spherical soft confinement potential of the form with stiffness parameter N and confinement radius . The soft confinement potential approaches the hard-wall limit as , giving a more detailed picture of spherical confinement. The confined hydrogen atom is considered as a base model: it is treated numerically to obtain ground- and excited-state energies and nodal positions of the eigenstates to study the convergence towards the hard-wall limit. We also derive some important analytical relations. The use of Gaussian basis sets is analysed. We find that, for increasing stiffness parameter N, the convergence towards the basis-set limit becomes problematic. As an application, we report dipole polarisabilities for different values of N and of hydrogen. For helium, we determine electron correlation effects with varying N and , and discuss the virial theorem for both soft and hard confinements in the limit . For carbon, a change in the orbital population from 2s2p to 2s2 is observed with decreasing , while, for potassium, we observe a change from the S to D ground state at small values. For CH, we show that the one-particle density becomes more spherical with increasing confinement. A possible application of soft confinement to atoms and molecules under high pressure is discussed Prof. Jürgen Gauss observing Schrödinger's cat under quantum confinement.

Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals

A recently developed finite element approach for fully numerical atomic structure calculations [S. Lehtola, Int. J. Quantum Chem. 119, e25945 (2019)] is extended to the description of atoms with spherically symmetric densities via fractionally occupied orbitals. Specialized versions of Hartree-Fock as well as local density and generalized gradient approximation density functionals are developed, allowing extremely rapid calculations at the basis set limit on the ground and low-lying excited states even for heavy atoms. The implementation of range-separation based on the Yukawa or complementary error function (erfc) kernels is also described, allowing complete basis set benchmarks of modern range-separated hybrid functionals with either integer or fractional occupation numbers. Finally, computation of atomic effective potentials at the local density or generalized gradient approximation levels for the superposition of atomic potentials (SAP) approach [S. Lehtola, J. Chem. Theory Comput. 15, 1593 (2019)] that has been shown to be a simple and efficient way to initialize electronic structure calculations is described. The present numerical approach is shown to afford beyond microhartree accuracy with a small number of numerical basis functions, and to reproduce literature results for the ground states of atoms and their cations for $1 \leq Z \leq 86 $. Our results indicate that the literature values deviate by up to 10 {\mu}Eh from the complete basis set limit. The numerical scheme for the erfc kernel is shown to work by comparison to results from large Gaussian basis set calculations from the literature. Spin-restricted ground states are reported for Hartree-Fock and Hartree-Fock-Slater calculations with fractional occupations for $1 \leq Z \leq 118$.

Quantitative electronic stopping power from localized basis set

The electronic stopping power of a swift ion in matter can be obtained from ab initio calculations within time-dependent density functional theory. Most implementations rely today on a plane-wave plus pseudopotential approach, but at the expense of very cumbersome calculations. We show here that localized orbitals, especially with Gaussian-type orbitals, are a valuable alternative. These calculations can yield electronic stopping powers in quantitative agreement with the plane-wave results while maintaining a computational burden that is relatively low. These positive results are possible only when using Gaussian basis sets that were specially designed for the stopping power calculations. With this tool, we investigate the discrepancy between ab initio calculations and experiment at large velocity, the effect of the exchange-correlation functional, and the role of core excitations in the total stopping power. We rule out the widespread centroid path approximation as soon as the core electrons are involved in the process.

Real-space quasi-relativistic quantum chemistry

We present for the first time real-space, arbitrarily-accurate representations of the operators required for up to second-order Douglas-Kroll-Hess (DKH), a model for constructing quasi-relativistic electronic Hamiltonians. The approach can be extended to other operator-based quasi-relativistic models. The representations are in the form of sums of Gaussian functions with positive coefficients and thus enable efficient and numerically-accurate formulations using conventional Gaussian basis sets or other bases such as multiwavelets. The operators are demonstrated with application to hydrogen-like systems using the relativistic-kinematic and first-order DKH Hamiltonians.

Techniques for high-performance construction of Fock matrices.

This paper presents techniques for Fock matrix construction that are designed for high performance on shared and distributed memory parallel computers when using Gaussian basis sets. Four main techniques are considered. (1) To calculate electron repulsion integrals, we demonstrate batching together the calculation of multiple shell quartets of the same angular momentum class so that the calculation of large sets of primitive integrals can be efficiently vectorized. (2) For multithreaded summation of entries into the Fock matrix, we investigate using a combination of atomic operations and thread-local copies of the Fock matrix. (3) For distributed memory parallel computers, we present a globally accessible matrix class for accessing distributed Fock and density matrices. The new matrix class introduces a batched mode for remote memory access that can reduce the synchronization cost. (4) For density fitting, we exploit both symmetry (of the Coulomb and exchange matrices) and sparsity (of 3-index tensors) and give a performance comparison of density fitting and the conventional direct calculation approach. The techniques are implemented in an open-source software library called GTFock.

Polarization consistent basis sets using the projector augmented wave method: a renovation brought by PAW into Gaussian basis sets.

A recently introduced framework incorporating the Projector Augmented Wave method and Gauss-type function (GTF-PAW) [X.-G. Xiong and T. Yanai, J. Chem. Theory Comput., 2017, 13, 3236-3249] opens alternative possibilities for performing low-cost molecular computational chemistry calculations. In this work, we present our first attempt to expand the applicability of this method by developing a family of compact general contracted polarization consistent basis sets (PAW-Ln) as an optimized GTF basis in combination with PAW. The results show that PAW-Ln, despite having small numbers of primitives, can provide not only better performance than effective core potential (ECP) but also good accuracy and desirable systematic convergence compared to larger all-electron basis sets. This demonstrates that GTF-PAW using the PAW-Ln basis sets could be a better alternative to both conventional all-electron- and ECP-based approaches for routine DFT calculations.

Photoionization of H2 using the molecular R-matrix with time approach

SynopsisWe present results of the first calculations using the variational ab initio molecular R-matrix with time approach. We have calculated two and four-photon ionization cross sections for H2 and studied the effects of electron correlation and choice of the Gaussian atomic basis sets. Our results are compared with earlier calculations.

Mixed Ramp-Gaussian Basis Sets for Core-Dependent Properties: STO-RG and STO-R2G for Li-Ne

The traditional Gaussian basis sets used in modern quantum chemistry lack an electron-nuclear cusp, and hence struggle to accurately describe core electron properties. A recently introduced novel type of basis set, mixed ramp-Gaussians, introduce a new primitive function called a ramp function which addresses this issue. This paper introduces three new mixed ramp-Gaussian basis sets - STO-R, STO-RG and STO-R2G, made from a linear combination of ramp and Gaussian primitive functions - which are derived from the single-core-zeta Slater basis sets for the elements Li to Ne. This derivation is done in an analogous fashion to the famous STO-$n$G basis sets. The STO-RG basis functions are found to outperform the STO-3G basis functions and STO-R2G outperforms STO-6G, both in terms of wavefunction fit and other key quantities such as the one-electron energy and the electron-nuclear cusp. The second part of this paper performs preparatory investigations into how standard all-Gaussian basis sets can be converted to ramp-Gaussian basis sets through modifying the core basis functions. Using a test case of the 6-31G basis set for carbon, we determined that the second Gaussian primitive is less important when fitting a ramp-Gaussian core basis function directly to an all-Gaussian core basis function than when fitting to a Slater basis function. Further, we identified the basis sets that are single-core-zeta and thus should be most straightforward to convert to mixed ramp-Gaussian basis sets in the future.

Sampling general distributions with quasi-regular grids: Application to the vibrational spectra calculations.

We introduce a new method for sampling a general multidimensional distribution function Px using a quasiregular grid (QRG) of points xi (i = 1, …, N). This grid is constructed by minimizing a pairwise functional, ∑u(xi, xj) → min, with the short-range pair pseudopotential u(xi, xj), defined locally according to the underlying distribution P(x). While QRGs can be useful in many diverse areas of science, in this paper, we apply them to construct Gaussian basis sets in the context of solving the vibrational Schrödinger equation. Using some 2D and 3D model systems, we demonstrate that the resulting optimized Gaussian basis sets have properties superior to other choices explored previously in the literature.

A generalized any‐particle propagator theory: Calculations of nucleon's binding energies

AbstractGeneralized one‐particle propagator calculations were performed for fermions in atoms: neutrons, protons, and electrons. For this purpose, multicomponent Hartree‐Fock equations were implemented using Gaussian basis sets where, for nucleons, we consider a non‐Coulombic interaction, through a two‐term Yukawa scalar potential and the interaction between electrons and the electrons with positive charge (protons) through a Coulombic potential. The strategy for evaluating the required interaction integrals follows Obara‐Saika and Head‐Gordon recurrence relations combined with the generalized Boys function suggested by Ten‐no. Calculations on the isotopes 2H, 3H, 3He, 4He, 6Li, 6Be, 7Li, and 8Be were realized to test the accuracy of Koopmans' approximation and a second‐order generalized one‐particle propagator. Yukawa potentials were parametrized to reproduce nuclear properties as kinetic energies and radial distributions of density. These potentials produced the reference nuclear Hartree‐Fock calculations on which fully ab initio propagator calculations were performed for these non‐Coulombic potentials. This allowed us to explore the electronic structure of isotopes in an extended nucleus context.

Comparative study of methodologies for calculating metastable states of small to medium-sized molecules.

We present a benchmarking study on the performance of two methods at the forefront of studying electronic metastable states of molecules: the orbital stabilization method and the method of complex absorbing potential augmented Hamiltonians. The performance of the two methods is compared for the calculation of shape resonances in small to medium-sized molecules (up to 15 atoms) at the equation of motion coupled cluster with singles and doubles for the electron attachment level of methodology using even-tempered Gaussian basis sets. The theoretical positions and widths of shape resonances obtained from both methods are compared to the experimentally determined electron affinities and lifetimes. The challenges that accompany the theoretical estimation of resonance positions and widths for medium to large-sized systems with an increase in basis set size are also discussed.

Substitution Effects on the Optoelectronic Properties of Coumarin Derivatives

Coumarin derivatives have gathered major attention largely due to their versatile utility in a wide range of applications. In this framework, we report a comparative computational investigation on the optoelectronic properties of 3-phenylcoumarin and 3-heteroarylcoumarin derivatives established as enzyme inhibitors. Specifically, we concentrate on the variation in the optoelectronic characteristics for the hydroxyl group substitutions within the coumarin moiety. In order to realize our aims, all-electron density functional theory and time dependent density functional theory calculations were performed with a localized Gaussian basis-set matched with a hybrid exchange–correlation functionals. Molecular properties such as highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies, vertical ionization (IEV) and electron affinity energies, absorption spectra, quasi-particle gap, and exciton binding energy values are examined. Furthermore, the influence of solvent on the optical properties of the molecules is considered. We found a good agreement between the experimental (8.72 eV) and calculated (8.71 eV) IEV energy values for coumarin. The computed exciton binding energy of the investigated molecules indicated their potential optoelectronics application.

Ab Initio Many-Body Perturbation Theory Calculations of the Electronic and Optical Properties of Cyclometalated Ir(III) Complexes

Cyclometalated Ir(III) compounds are the preferred choice as organic emitters in organic light-emitting diodes. In practice, the presence of the transition metal surrounded by carefully designed ligands allows fine-tuning of the emission frequency as well as good efficiency of the device. To support the development of new compounds, experimental measurements are generally compared with absorption and emission spectra obtained from ab initio calculations. The standard approach for these calculations is time-dependent density functional theory (TDDFT) with a hybrid exchange-correlation functional like B3LYP. Because of the size of these compounds, the application of more complex quantum chemistry approaches can be challenging. In this work, we used many-body perturbation theory approaches, in particular the GW approximation with the Bethe-Salpeter equation (BSE) implemented in Gaussian basis sets, to calculate the quasiparticle properties and the absorption spectra of six cyclometalated Ir(III) complexes, going beyond TDDFT. In the presented results, we compared standard TDDFT simulations with BSE calculations performed on top of perturbative G0W0 and accounting for eigenvalue self-consistency. Moreover, in order to investigate in detail the effect of the DFT starting point, we concentrated on Ir(ppy)3 and performed GW-BSE simulations starting from different DFT exchange-correlation potentials.

The VN2 negatively charged defect in diamond. A quantum mechanical investigation of the EPR response

The VN2− defect in diamond consists of a vacancy surrounded by two substitutional nitrogen atoms, which lower the local symmetry from Td to C2v. Calculations of the doublet ground state geometry, electronic structure, EPR parameters, and IR spectra of this defect are reported along with a preliminary investigation of the observed optical transition. For the most part our results were obtained using a uniform charge compensated supercell approach together with the B3LYP functional and all-electron Gaussian basis sets designed for the properties studied. In particular, the computed hyperfine and quadrupolar EPR parameters for the carbon and nitrogen atoms adjacent to the vacancy agree very well with the experiments (Fermi contact values are 245 MHz vs 241 for 13C, and 4.1 vs 4.0 for 15N). The accompanying spin distribution may be described as a damped spherical spin wave with little spin density on the nitrogen atoms. IR spectra show some interesting features in the range of approximately 360–1310 cm−1, which are absent in the pristine diamond. Functionals without exact exchange, such as PBE, better reproduce the observed zero phonon line.

Dirac-Fock calculations on molecules in an adaptive multiwavelet basis.

We report the first fully numerical approach for relativistic quantum chemical calculations applicable to molecules. The approach uses an adaptive basis of multiwavelet functions to solve the full four-component Dirac-Coulomb equation to a user-specified accuracy. The accuracy of the code is demonstrated by comparison with ground state energy calculations of atoms performed in GRASP, and the applicability to molecules is shown via ground state calculations of some simple molecules, including water analogs up to H2Po. In the case of molecules, comparison is made with Gaussian basis set calculations in DIRAC.

Graphene and graphene oxide as adsorbents for cadmium and lead heavy metals: A theoretical investigation

The geometrical and electronic parameters for the interaction of two toxic heavy metals, namely: cadmium (Cd) and lead (Pb), on graphene and graphene oxide (GO) surfaces are investigated by using local Gaussian type basis sets and the hybrid PBE0 functional as implemented in the CRYSTAL code. The role of including long-range dispersion (D3) contribution as well as the basis set superposition error (BSSE) on the adsorption process is found to be crucial in the description of such interactions. Generally, Cd and Pb adatoms are found to be adsorbed more strongly on GO rather than pristine graphene due to the incorporation of oxygen functional groups (epoxy and/or hydroxyl) on the surface. Moreover, Pb has interestingly been found to play as an electron donor and to form covalent bonding with the GO surface. Such findings could have an impact in water treatment applications using graphene-based nanomaterials.

Electronic, structural and vibrational properties of calcium monohydride

Thanks to the quantum chemistry approach, a global study has been performed for numerous excited electronic states of calcium monohydride denoted CaH. The CaH molecule is considered as a three effective electrons system. It was treated on the Multireference Configuration Interaction level of theory using the effective core potentials including Core Polarization Potential operator with large Gaussian basis sets. Hence, the Potential Energy Curves (PECs) for 2,4∑+, 2,4∏ and 2,4Δ symmetries have been determined. These curves exhibit an attracted behavior in the avoided crossings region due to the strong interactions between Ca and H. Then, their relative spectroscopic constants have been calculated by solving the vibrational Schrödinger equation using the PECs. Finaly, the vibrational properties and the electric dipole moments of CaH have been investigated and analyzed in detail.

H3 + as a five-body problem described with explicitly correlated Gaussian basis sets.

Various explicitly correlated Gaussian (ECG) basis sets are considered for the solution of the molecular Schrödinger equation with particular attention to the simplest polyatomic system, H3 +. Shortcomings and advantages are discussed for plain ECGs, ECGs with the global vector representation, floating ECGs and their numerical projection, and ECGs with complex parameters. The discussion is accompanied with particle density plots to visualize the observations. In order to be able to use large complex ECG basis sets in molecular calculations, a numerically stable algorithm is developed, the efficiency of which is demonstrated for the lowest rotationally and vibrationally excited states of H2 and H3 +.

A new generation of effective core potentials from correlated calculations: 4s and 4p main group elements and first row additions.

Recently, we developed a new method for generating effective core potentials (ECPs) using valence energy isospectrality with explicitly correlated all-electron (AE) excitations and norm-conservation criteria. We apply this methodology to the 3rd-row main group elements, creating new correlation consistent ECPs (ccECPs) and also deriving additional ECPs to complete the ccECP table for H-Kr. For K and Ca, we develop Ne-core ECPs, and for the 4p main group elements, we construct [Ar]3d10-core potentials. Scalar relativistic effects are included in their construction. Our ccECPs reproduce AE spectra with significantly better accuracy than many existing pseudopotentials and show better overall consistency across multiple properties. The transferability of ccECPs is tested on monohydride and monoxide molecules over a range of molecular geometries. For the constructed ccECPs, we also provide optimized DZ-6Z valence Gaussian basis sets.