Slater Basis Sets Research Articles

Kohn-Sham Density in a Slater Orbital Basis Set.

Finite, atom-centered Slater basis sets are used to determine approximate Kohn-Sham molecular orbitals. This is achieved by minimizing the kinetic energy plus the sum-squared difference between the Kohn-Sham density and the full configuration interaction density. As a result of the finite basis, a weight factor is introduced to balance the two minimization components. Results herein show that this can be done systematically, without sensitive dependence on the choice of scaling factor. In addition, the algorithm is applied to the LiH diatomic for fractional electron counts, where stretching the bond introduces significant reorganization of the electron density. The analysis will show the correct KS orbital structure and reveal the effects of correlation and electron locality on the KS solutions.

Computational Prediction of Graphdiyne-Supported Three-Atom Single-Cluster Catalysts

Computational Prediction of Graphdiyne-Supported Three-Atom Single-Cluster Catalysts

Spin–orbit coupling matrix elements from the explicitly connected expressions of the response functions within the coupled-cluster theory

In this work, we present a coupled cluster-based approach to the computation of the spin–orbit coupling matrix elements. The working expressions are derived from the quadratic response function with the coupled-cluster parametrisation, using the auxiliary excitation operator S. Systematic approximations are proposed with the CCSD and CC3 levels of theory. The new method is tested by computing lifetimes of several electronic states of Ca, Sr and Ba atoms, with Gaussian and Slater basis sets. The results are compared with available theoretical and experimental data.

Superatomic Signature and Reactivity of Silver Clusters with Oxygen: Double Magic Ag 17 – with Geometric and Electronic Shell Closure

Understanding the stability and reactivity of silver clusters toward oxygen provides insights to design new materials of coinage metals with atomic precision. Herein, we report a systematic study o...

Accurate atomic momentum integrals and Compton profiles

Analytical expressions for integrals involving momentum density have been developed, and an algorithm for the efficient computation of Compton profiles (CPs) based in those equations is reported. The performance of the algorithm is tested by computing the CPs of atoms from helium to xenon for a wide range of incident photon energies. Calculations have been made at Hartree–Fock level (HF), using three different Slater basis sets, showing a good agreement with the experimental results.

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.

Comparison of Standard Functionals to Calculate the Properties of Molecules at the Variational Limit

B1LYP, B1PW91, B3LYP, BHandH, BHandHLYP, BLYP, BP, CAMY-B3LYP, HTBS, KMLYP, LCYBLYP, LCY-BP86, LCY-PBE, LDA, M06, M06-2X, M06-HF, M06L, mPBE, mPW, MPW1K, MPW1PW, O3LYP, OLYP, OPBE, OPBE0, PBE, PBE0, PBEsol, PW91, revPBE, revTPSS, RPBE, TPSS, TPSSH, X3LYP, and HF methods are used to calculate the electron energy Eel of the reference GeO and C2H6 compounds in Slater basis sets QZ4P, aug-TZ2P, and TZ2P, as well as DZ for C2H6. The Eel values are recalculated into the bond breaking enthalpy D0(Ge–O) and formation enthalpy ΔfH2980 of ethane, and calculation errors for Eel are obtained at the variation limit. The ADF program settings are chosen so that they make it possible to attribute these Eel errors to the structure of DFT functionals. The dependence of the Eel values on the type (size) of the basis set is studied. It is demonstrated that when Eel is calculated for GeO, the optimum combination is DFT/TZ2P, where DFT = LCY-BLYP, LCY-BP86, LCY-PBE, CAMYB3LYP; for C2H6 it is DFT/TZ2P, where DFT = PBE0, M06, mPBE, OLYP. Errors in the calculation of the geometric parameters are studied.

DFT computational correlations on conformational barriers of Zn2+ and Ni2+ chiral meso-(α,β-unsaturated)- porphyrins.

Correlations between DFT and experimental measurements on Zn2+ and Ni2+ chiral meso-(α,β-unsaturated)- porphyrins were performed using Kohn-Sham methodology. The exchange-correlation Becke88-Perdew86 functional was used in conjunction with double-zeta Slater basis sets. An accurate description of the electronic processes depending on the metal ion (Zn, Ni) or ligand (perilaldehyde and myrtenal) was made, confirming experimental results in terms of structural and electronic modifications. Moreover, this theoretical study provides a stronger knowledge and interpretation of the dynamical conformational features of the free base, Zn and Ni structures. Fundamental links between the central metallic atom and distortions of the porphyrinic core and ligands were demonstrated, in agreement with experimental data. We observed that the core in ZnPeriP and ZnMyrtP species is almost flat, in comparison with the Ni porphyrinic core, which appeared much more distorted. The type of distortion differs between PeriP and MyrtP ligands, with a combined saddled-ruffled characteristic with the former and a pronounced ruffled twisting for the latter. Finally, conformational energy barriers were extracted by spinning one of the arms in steps of 20° in a 360° dihedral angle. The resulted conformational barriers for NiPeriP or NiMyrtP are lower in energy than for ZnPeriP or ZnMyrtP, in agreement with experimental data.

DFT study of Zn2+ and Ni2+ BCP8 bridled porphyrins: Theoretical correlations

DFT investigations on M-BCP8 (M=Zn, Ni) bridled chiral porphyrins were performed. The conformational flexibility depending on the metal ion, the environment, or the electronic redox state was analysed in the framework of Kohn–Sham formalism, within a Generalized Gradient functional, namely GGA-PBE, corroborated with triple-zeta Slater basis sets. Correlations between the metal ion size and the deformation of the porphyrinic core highlight a more pronounced deformation for Ni2+-BCP8 than for Zn2+-BCP8, suggesting that the short distances in Ni-N porphyrins are responsible for the ruffling of the porphyrinic core, whereas the Zn2+ ion being larger, fits better in the cavity and does not impose any strong deformation. Description of the most stable atropoisomer was proved in agreement with experimental NMR and X-ray measurements. The free base and the Zn2+ complex exhibit a preferential αααα conformation in solution, while for Ni2+ analogue, the atropisomer was 100% αβαβ. In the case of ZnBCP-8 the main atropoisomer is changing in comparison with the crystal data, obtaining in dichloromethane and nitrobenzene a more stable Zn open conformation but in equilibrium with the closed conformation. Stabilization due to solvation was investigated, explaining the difference of behaviour observed for ZnBCP-8. The effect of supramolecular aggregation observed experimentally was theoretically investigated in terms of dimer formation. We also calculated the BSSE errors and even the thermodynamic entropy and ZPE parameters that can eventually influence the αβαβ/αααα equilibriums.

R-matrix calculation of bound and resonant states of BeH

Bound and resonant states of BeH are studied using the diatomic UK molecular R-matrix codes together with a Slater basis set for the BeH+ target states. Bound and resonant states of BeH are determined from an e-BeH+ collisional calculation. The calculations are repeated for 40 internuclear distances in the range 1.5–6.0 a0 to yield bound state and resonance curves for BeH. Additionally, we also obtain the resonance widths in the range of the inter-nuclear distances considered. The data obtained may be useful for modeling various e-BeH+ collision-induced processes, particularly dissociative recombination and dissociative excitation.

Nuclear cusp conditions and their fulfillment in molecular calculations with SLATER basis sets

A short revision of the main antecedents on the nuclear cusp conditions is followed by a derivation of the general expressions of the conditions which must be accomplished by wave functions and densities. It is stressed that in case of the molecular densities, besides Kato's cusp condition, there are also simple cusp conditions for the three dipole‐type terms of the densities but not for terms of order higher than dipole. The degree of fulfillment of standard atomic and molecular calculations with Slater basis sets is tested, concluding that errors of spherical terms usually affect the third or fourth significant figures, being smaller as nuclear charges increase, and the errors of dipole‐type components are greater than those of the spherical terms. In practice, improvements in the computational method or in the basis set do not guarantee a better fulfillment of the cusp conditions. Hydrogen is a special case which can yield poor results. © 2014 Wiley Periodicals, Inc.

Multipole moments from the partition–expansion method

Analytical expressions for the atomic multipole moments defined from the partition–expansion method are reported for both Gaussian and Slater basis sets. In case of Gaussian functions, two algorithms are presented and examined. The first one gives expressions in terms of generalized overlap integrals whose master formulas are derived here with the aid of the shift-operator technique. The second uses translation methods, which lead to integrals involving Gaussian and Bessel functions, which are also known. For Slater basis sets, an algorithm based on translation methods is reported. In this algorithm, atomic multipoles are expressed in terms of integrals involving Macdonald functions, which have been solved in previous works. The accuracy of these procedures is tested and their efficiency illustrated with practical applications, including the computation of the full molecular electrostatic potential (not only the long-range) in large systems.

Improved partition–expansion of two‐center distributions involving slater functions

The calculation of the electronic structure of large systems is facilitated by the substitution of the two-center distributions by their projections on auxiliary basis sets of one-center functions. An alternative is the partition-expansion method in which one first decides what part of the distribution is assigned to each center, and next expands each part in spherical harmonics times radial factors. The method is exact, requires neither auxiliary basis sets nor projections, and can be applied to Gaussian and Slater basis sets. Two improvements in the partition-expansion method for Slater functions are reported: general expressions valid for arbitrary quantum numbers are derived and the efficiency of the procedure is increased giving analytical solutions to integrals previously computed by numerical quadrature. The efficiency of the new version is assessed in several molecules and the advantages over the projection methods are pointed out.

Performance assessment of density functional theory-based models using orbital momentum distributions

The performance of a number of established and widely used density functional theory (DFT) methods (B3LYP, Bhandh, BP86, PW91, Vosko, Wilk, and Nusair (VWN), LB94, PBe0, statistical average of orbital potentials (SAOP) and X3LYP) and the Hartree–Fock (HF) method has been assessed using the 7σ orbital momentum distributions (MDs) of nitrous oxide (N2O). The DFT methods are combined with a number of Gaussian basis sets as well as even-tempered Slater basis sets. Orbital MDs of N2O are compared with experimental measurement of the same orbital from electron momentum spectroscopy. This study reveals information regarding the performance of (a) the DFT methods and their long-range behaviour, (b) Gaussian and Slater basis set contributions to this orbital, (c) combinations (i.e. the models) of the DFT methods and basis sets and (d) the entire region of chemical significance of the orbital. In general, for any given method, it is found that Slater basis sets achieve better overall agreement with experiment than Gaussian basis sets. Dunning's aug-cc-pVTZ basis set achieves the best performance for the MDs for this orbital among the Gaussian basis sets. The B3LYP and BP86 models exhibit similar overall performance to more recent models such as X3LYP and SAOP. This study also demonstrates that the particular combination of density functional method and basis set employed have a significant effect on the quality of the calculated orbitals.

Finite-size scaling for quantum criticality using the finite-element method

Finite size scaling for the Schrödinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite-element method was shown to be a powerful numerical method for ab initio electronic-structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite-element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, local density approximation, and an "exact" formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems.

Predicting the UV spectrum of polyoxometalates by TD‐DFT

UV absorption spectra of the Lindqvist polyoxometalate [W(6)O(19)](2-) were predicted by relativistic time-dependent density functional theory with several combinations of density functional and basis set. Hybrid functionals with frozen-core Slater basis sets were found to provide the best agreement with experiment while keeping reasonable computational demand. The approach was extended to [W(10)O(32)](4-) and [PW(12)O(40)](3-), suggesting that it can be applied to the polyoxometalates family.

The two faces of static correlation

Restricted Hartree-Fock (RHF) and UHF wavefunctions for beryllium-like ions with nuclear charge 3 ≤ Z ≤ 5 are found using a near-complete Slater basis set. The triplet (RHF → UHF) instability and correlation energy are investigated as a function of Z and we find that the instability vanishes for Z > 4.5. We reproduce this surprising behavior using a minimal-basis model and, by comparing with the stretched H(2) molecule, conclude that "static" (also known as nondynamical, near-degeneracy, first-order, or strong) correlation comes in two flavors: one that can be captured by UHF and another that cannot. In the former (Type A), there is an "absolute near-degeneracy"; in the latter (Type B), there is a "relative near-degeneracy." This dichotomy clarifies discussions of static correlation effects.

Benchmark all-electron ab initio quantum Monte Carlo calculations for small molecules

We study the efficiency, precision and accuracy of all-electron variational and diffusion quantum Monte Carlo calculations using Slater basis sets. Starting from wave functions generated by Hartree-Fock and density functional theory, we describe an algorithm to enforce the electron-nucleus cusp condition by linear projection. For the 55 molecules in the G2 set, the diffusion quantum Monte Carlo calculations recovers an average of 95% of the correlation energy and reproduces bond energies to a mean absolute deviation of 3.2 kcal/mol. Comparing the individual total energies with essentially exact values, we investigate the error cancellation in atomization and chemical reaction path energies, giving additional insight into the sizes of nodal surface errors.

Invariant atomic orbitals by radial moment analysis of accurate molecular orbitals

Radial moment analysis of accurate molecular orbitals in extended Slater basis sets reveals approximately invariant atomic orbitals. These atomic orbitals are very similar to the solutions of the Hartree-Fock equations for the free atoms, but small, and possibly significant, regular differences are found. These atomic orbitals provide a suitable standard set of atomic orbitals for semiempirical molecular calculations, and provide theoretical support for the concept of atomic orbitals in molecules. Orbitals for first- and second-row elements and hydrogen are presented. Hydrogen is unique in showing an appreciable variation depending on the atom to which it is bonded.

Electron-nucleus cusp correction and forces in quantum Monte Carlo

A simple method is presented which ensures the electron-nucleus cusp condition is satisfied by the Slater-Jastrow wavefunctions commonly employed in quantum Monte Carlo simulations. The method is applied in variational energy calculations of the neon atom and a selection of molecules using both Gaussian and Slater basis sets. In addition, we discuss the relationship between the electron-nucleus cusps and the variance of forces, and investigate the sensitivity of forces to the quality of the cusps for various diatomic molecules.