Economic Basis Set Research Articles

A New Basis Set for the Calculation of 13C NMR Chemical Shifts within a Non-empirical Correlated Framework.

A new basis set of triple-ζ quality for carbon, 3z-S, is developed and tested at the DFT, MP2, and CCSD(T) levels, taking into account solvent and vibrational corrections for a number of molecules ranging from the smallest fluoromethane, CH3F, to the largest 5,10,15,20-tetraphenylporphyrin, C44H30N4. The proposed highly economical 3z-S basis set has been proven to provide very good accuracy in all examinations, comparable to that of the NMR-oriented Jensen's pcS-2 basis set, which is about 50% larger than 3z-S.

Economical basis sets and their uses in ab initio calculations

In this article, we review a practical and effective scheme proposed by one of the authors for choosing basis sets in ab initio calculations and assess its efficiency in selected applications. In the scheme, we consider the different roles of the particular functions, including the polarization and diffuse functions, adopted in the basis set, as well as the nature and environment of the atom. The number and level of basis functions required to describe an atom should be determined according to its relative order in the periodic table and/or electronegativity. For an atom with a relatively higher electronegativity, larger basis functions including polarization and diffuse functions should be used, while the basis functions for a less electronegative atom or positively charged atom can be reduced and may not adopt any polarization and diffuse functions. For systems involving hydrogen bonding, weak interactions, functional groups, metallic bonding with zero or low‐positive valence, and other sensitive interactions, both the polarization and diffuse functions may need to be used. These economical composite basis sets are applied to a variety of systems, from small to very large compounds. Compared with the calculations required for conventional basis set schemes at different levels, the economical composite basis set can accurately predict the structures and properties of compounds while saving significant CPU. A single‐point calculation using the geometric structure determined using the economical composite basis set can further improve the accuracy of calculating certain properties. © 2014 Wiley Periodicals, Inc.

Core–valence correlation effects in the ground and low-lying excited states of GaN

We present careful analysis of the accuracy of molecular properties of the GaN molecule calculated by the Coupled Cluster CCSD(T) method including the core–valence correlation effects. We demonstrate that calculations of the core–valence correlation effects with basis sets which were optimised considering just valence electrons of the gallium atom lead to unreliable results. Our objective is to find the relation between the accuracy and the oversimplification due to the use of aug-cc-pVXZ basis sets when 3d and eventually also 3s3p electrons are correlated with these basis sets, having in mind calculations of larger systems. We observe the oscillatory behaviour of molecular properties with increasing cardinal basis set number X in the aug-cc-pVXZ series. This is the main deficiency of this more economical basis set. Extrapolation to the complete basis set limit with this series is only possible starting with the aug-cc-pVQZ basis. Regular behaviour with increasing X show results with the aug-cc-pCVXZ series. Reasonable molecular properties are provided by the ANO-RCC basis sets with 3d 104s 24p 1 correlated electrons of Ga.

Computation of large systems with an economic basis set: systems in excited states

An economic basis set for ab initio calculations of systems in excited states has been studied. The economic basis set, in which the polarization functions are applied only to oxygen (O), while the 6-31G basis set is used for carbon (C) and hydrogen (H), is shown to save considerable computing time and to give reliable geometric and frequency measurements. In addition, the economic basis set has been considered for obtaining reliable excitation energies, with the correction factor, using high-level single-point energy calculations. This study is expected to shed light on basis set selection for computations of large systems in excited states.

Computation of large systems with an economic basis set: Structures and reactivity indices of nucleic acid base pairs from density functional theory

We show here that an economic basis set can describe nucleic acid base pairs involving the hydrogen bond interactions in density functional calculations. The economic basis set in which the polarization function is added only to oxygen and nitrogen atoms of strong electronegativity can predict reliable geometric structures and dipole moment of nucleic acid base pairs, comparable to those obtained from the basis set of 6-31G* in B3LYP calculations. Combining single point calculations with the standard basis set on the geometric structures optimized by the economic basis set, the present approach has predicted accurate natural bond orbital charge, binding energy, electronegativity, hardness, softness, and electrophilicity index. The principle for basis selection presented in this study can be regarded as a general guideline in the computation of large biological systems with considerably high accuracy and low computational expense.

Structures and Properties of Silicon Oxide Clusters by Theoretical Investigations

In this paper, we outline our computational work in the area of silicon oxide clusters. To reduce the computational cost, we designed an economic basis set for silicon oxide systems, and reliable structures were obtained by this approach. To reveal the formation mechanism of silicon nanowires, we investigated the structures and properties of silicon suboxide clusters in particular monoxide clusters that play an important role in the oxide-assisted growth. And to improve our understanding of the silicon dioxide clusters and to bridge the gap between gas phase and solid phase silica, we proposed several models based on the two-membered ring (2MR), three-membered ring (3MR), four-membered ring (4MR), the hybrid of the 2MR and 3MR, or the 3MR and 4MR.

COMPUTATION OF LARGE SYSTEMS WITH AN ECONOMIC BASIS SET: AB INITIO CALCULATIONS OF BIOLOGICAL NUCLEIC ACID BASE PAIRS

We show that an economic basis set, in which the polarization functions are considered only for oxygen and nitrogen atoms of strong electronegativity, can be used to determine reliable structures of nucleic acid base pairs. Mulliken charge analysis and the HOMO-LUMO gap in single-point energy calculations using standard basis sets on the geometric structures optimized with the economic basis set found reasonable agreements with the ones of standard calculations. This study is expected to provide a general guideline for basis set selection in the computation of large biological systems being performed with considerable high accuracy, using a low cost computation resource.

Calculation of Electron Detachment Energies for Water Cluster Anions: An Appraisal of Electronic Structure Methods, with Application to (H2O)20- and (H2O)24-

We present benchmark calculations of vertical electron detachment energies (VDEs) for various conformers of (H2O)n-, using both wave function and density functional methods, in sequences of increasingly diffuse Gaussian basis sets. For small clusters (n < or = 6), a systematic examination of VDE convergence reveals that it is possible to converge this quantity to within approximately 0.01 eV of the complete-basis limit, using a highly diffuse but otherwise economical Pople-style basis set of double-zeta quality, with 28 atom-centered basis functions per water molecule. Floating-center basis functions can be useful but are not required to obtain accurate VDEs. Second-order Møller-Plesset perturbation (MP2) theory suffices to obtain VDEs that are within 0.05 eV of the results from both experiment and coupled-cluster theory, and which always err toward underbinding the extra electron. In contrast to these consistent predictions, VDEs calculated using density functional theory (DFT) vary widely, according to the fraction of Hartree-Fock exchange in a given functional. Common functionals such as BLYP and B3LYP overestimate the VDE by 0.2-0.5 eV, whereas a variant of Becke's "half and half" functional is much closer to coupled-cluster predictions. Exploratory calculations for (H2O)20- and (H2O)24- cast considerable doubt on earlier calculations that were used to assign the photoelectron spectra of these species to particular cluster isomers.

Computation of Large Systems with Economic Basis Set: Simulation of Diamond Metallization Using Titanium

Economic basis sets for ab initio calculations of systems involving titanium (Ti) atom have been studied. The basis set in which the polarization and diffuse functions are applied only to Ti and its nearest neighboring atoms is shown to give reliable binding energies and geometries for various carbon-based compounds. Such a basis set is used as the economic basis set for calculations of medium-sized clusters simulating Ti and diamond interactions. For large clusters composed of Ti and C atoms, the more economic basis set 6-31G is considered for obtaining reliable energetics with the correction using high-level single-point energy calculations with 6-31+G*. The approach to determine the economic basis set is expected to be useful for a general system containing transition metal element. With the economic basis sets, simulations of diamond metallization have revealed reasonable behavior of the Ti atomic interaction with diamond film. On the basis of the determined energetics of Ti deposition, the high Ti concentration in CVD diamond after metallization is conjectured to occupy the grain boundaries rather than the bulk of diamond grain. For a Ti atom with high kinetic energy, the Ti atom may penetrate through a diamond (001) surface more easily than through a diamond (111) surface. In the diamond bulk, the Ti atom may energetically favor to substitute a C site more than diffusion.

Computation of large systems with an economic basis set: Ab initio calculations of silicon oxide clusters

Silicon oxide plays an important role in many technological areas. Extensive ab initio calculations for related systems are thus desired but are limited due to the requirement of a huge computation resource. We show here that an economic basis set can be used to determine reliable atomic and electronic structures of the silicon oxide system. Binding energies in a single-point energy calculation using a standard higher-level basis set on the geometric structures optimized with the economic basis set found reasonable agreement with reported ones of high-level calculations. The approach has enabled the computation of silicon oxide clusters as large as 16 atoms being performed with considerably high accuracy using a medium level of computation resources.

Computation of large systems with economic basis set: systems involving weak sodium–organic interaction

We show that an economic basis set can describe systems involving sodium–organic interaction in ab initio calculations. Basis sets, in which the polarization and the diffuse functions are considered only for sodium and atoms of strong electronegativity of various Na-containing weakly bound systems, can predict geometric structures, dipole moments and binding energies with negligible basis set superposition error (BSSE), comparable to those using 6-31+G * in calculations with density functional theory. This study is expected to provide a general guideline for basis set selection in computations of large systems involving metal–organic interaction.

Computation of large systems with an economic basis set: a density functional study on proton-bound carboxylic acid clusters

We show that first-principle calculations with an economic basis set can predict reliable geometric structures and accurate vibrational frequencies for small proton-bound carboxylic acid clusters. This leads to the potential of using limited computational resources to study large molecular systems. Further applications using density functional (DFT) theory on a series of proton-bound formic and acetic acid clusters have found reasonable evaporation energies in comparison with experiments. Our DFT calculations have exactly reproduced the changeover from monomer loss to dimer loss at n=6 found in an experiment for proton-bound formic acid clusters.

The MIDI! basis set for quantum mechanical calculations of molecular geometries and partial charges

We present a series of calculations designed to identify an economical basis set for geometry optimizations and partial charge calculations on medium-size molecules, including neutrals, cations, and anions, with special emphasis on functional groups that are important for biomolecules and drug design. A new combination of valence basis functions and polarization functions, called the MIDI! basis set, is identified as a good compromise of speed and accuracy, yielding excellent geometries and charge balances at a cost that is as affordable as possible for large molecules. The basis set is optimized for molecules containing H, C, N, O, F, P, S, and Cl. Although much smaller than the popular 6-31G* basis set, in direct comparisons it yields more accurate geometries and charges as judged by comparison to MP2/cc-pVDZ calculations.

Theoretical and experimental studies of the triatomic doubly charged ions CO2+2, OCS2+, and CS2+2

The term schemes of the doubly charged ions CO2+2, OCS2+, and CS2+2 have been calculated by the CIPSI method using a new and economical basis set of polarized atomic orbitals and difference orbitals. The calculated energies are compared with existing and new experimental data obtained from Auger spectra, double charge transfer, and photoionization including the PIPICO technique. A complete assignment of the manifolds of singlet states is achieved with good agreement between theory and experiment. Only the lowest doubly charged ion states are well described by simple two-hole configurations, while three-hole one-particle configurations are important at higher energy. It is confirmed that the triplet ground states of these ions are well populated by photoionization, while the excited singlet states are revealed most clearly by the double charge transfer technique.

The 6‐31G++ basis set: An economical basis set for correlated wavefunctions

AbstractThe 6‐31G++ basis set is described. This basis set is very similar to the existing 6‐31G** set but is somewhat smaller through the use of five (rather than six) second‐order Gaussians (d functions) and has polarization function exponents optimized for correlated rather than Hartree–Fock wavefunctions. The performance of 6‐31G++ is compared with that of the 6‐31G** and 6‐31G** basis sets through calculation of the geometries and atomization energies for the set of molecules LiH, FH, H2O, NH3, CH4, N2, CO, HCN, and HCCH.