Minimal basis sets in calculations of intermolecular interaction energies

Several minimal (7, 3/3) Gaussian basis sets have been used to calculate the energies and some other properties of CH₄ and H₂O. Improved basis sets developed for these molecules have been extended to NH₃ and HF and employed to H₂CO and CH₃OH. Interaction energies between XH_n molecules have been calculated using the old and the new minimal basis sets. The results obtained with the new basis sets are comparable in accuracy to those calculated with significantly more extended basis sets involving polarization functions. Binding energies calculated using the counterpoise method are not much different for the new and the old minimal basis sets, and are likely to be more accurate than the results of much more extended calculations.     

Thermochemical data from ab initio calculations. I. Estimation of SCF energies for augmented basis sets and Hartree–Fock limit energies

A procedure is outlined which allows an estimation of molecular energies both for a finite basis set including polarization functions and for the Hartree–Fock limit. It is shown that the orbital error of a given minimal basis is covered to a certain relatively constant percentage by an augmented basis set calculation. Thus an improvement factor Q_av can be determined by analyzing the corresponding results of small molecules where reasonable estimates of HF limit energies can be taken from the literature. For a combination of Pople's STO -3G and 6-31G* basis sets Q_av turns out to be 0.955.     

Uniform quality gaussian basis sets for molecular calculations,I. C1 hydrocarbons

The optimality of MO basis sets of Gaussian functions, when constructed from AO basis sets optimized for the neutral atom or for atom ions, is investigated. A formal charge parameter Q is defined and used to adjust the AO basis sets to the molecular environment, by virtue of a simple quadratic expression. Calculations on a series of C₁ hydrocarbons (CH₂, CH₃, CH₃⁺, CH₃^?, CH₄) using 3G basis sets indicate considerable variations in the optimum Q value with the molecular species. The proposed method offers a simple alternative technique to a full molecular basis set optimization.     

Basis sets for geometry optimizations of second-row transition metal inorganic and organometallic complexes

Modest-sized basis sets for the second-row transition metal atoms are developed for use in geometry optimization calculations. Our method is patterned after previous work on basis sets for first-row transition metal atoms. The basis sets are constructed from the minimal basis sets of Huzinaga and are augmented with a set of diffuse p and d functions. The exponents of these diffuse functions are chosen to minimize both the difference between the calculated and experimental equilibrium geometries and the total molecular energies for several second-row transition metal inorganic and organon etallic complexes. Slightly smaller basis sets, based on the same Huzinaga minimal sets but augmented with a set of diffuse s and p functions rather than diffuse p and d functions, are also presented. The performance of these basis sets is tested on a wide variety of second-row transition metal inorganic and organometallic complexes and is compared to pseudopotential basis sets incorporating effective core potentials.     

Minimally augmented Karlsruhe basis sets

We propose an extension of the basis sets proposed by Ahlrichs and coworkers at Karlsruhe (these basis sets are designated as the second-generation default or “def2” basis sets in the Turbomole program). The Karlsruhe basis sets are very appealing because they constitute balanced and economical basis sets of graded quality from partially polarized double zeta to heavily polarized quadruple zeta for all elements up to radon (Z = 86). The extension consists of adding a minimal set of diffuse functions to a subset of the elements. This yields basis sets labeled minimally augmented or with “ma” as a prefix. We find that diffuse functions are not quite as important for the def2 basis sets as they are for Pople basis sets, but they are still necessary for good results on barrier heights and electron affinities. We provide assessments and validations of this extension for a variety of data sets and representative cases. We recommend the new ma-TZVP basis set for general-purpose applications of density functional theory.     

A formulation of multiple-reference CI with terms linear in the interelectronic distances. II. An alternative ansatz

An alternative ansatz for r₁₂-MR -CI is given. The final formulas are much more easily obtained than was possible previously. The numerical performance is demonstrated with a model calculation of the ground state of helium using three different Gaussian basis sets (5s, 10s, 16s). With the two largest basis sets, the energies obtained with the new formulas, the formulas of Part I of this series of articles, and the formulas of the original formulation agree within 2 μE_H. Since the new ansatz is much easier to handle mathematically, we recommend its usage for future work. © 1995 John Wiley & Sons, Inc.     

Ab initio calculations on sulfur-containing compounds. I. Uniform quality basis sets for sulfur: Total energies and geometries of H2S

Uniform quality basis sets (UQ-NG ; N=3, 4, 5), with s = p and s ≠ p, and a 6-31 G^* basis set have been optimized for the sulfur atom. These uniform quality basis sets in their uncontracted and contracted forms were used, together with other basis sets reported in the literature (a total of 40 basis sets), to study their accuracy in predicting the bond length and bond angle of H₂S.     

MRD-CI potential surfaces using balanced basis sets. VI. Correlation of bond order with bond function composition for first-row diatomic molecules

This article presents theoretical calculations on bond energies for the first-row diatomics C₂, CN, CO, CF, N₂, NO, NF, O₂, FO, and F₂, which vary in bond order from one to three. The atomic-centered basis functions are systematically augmented with bond functions (BFs), which range in composition from (sp) to 2(spd), to determine the basis set which yields a dissociation energy closest to the experimental D_e. A strong correlation is found to exist between the bond order and the number of BFs required in the optimum basis set. Based on these results, we are able to predict the optimum composition of the BF basis which should be added to a DZP-quality AO basis set for a case in which only the bond order is known. These optimized BF basis sets are shown in the accompanying article to give more accurate potential curves than larger basis sets without bond functions.     

Uniform quality gaussian basis sets for molecular calculations. II. C2 hydrocarbons

This investigation is a continuation of a study on the optimality of MO basis sets of Gaussian functions, when constructed from AO basis sets optimized for the neutral atom or for ions. A formal charge parameter Q is used to adjust AO basis sets to the molecular environment, by virtue of a simple quadratic equation. Calculations are performed on a series of seven C₂ hydrocarbons (C₂H₂, C₂H₄, C₂H₆, C₂H₃⁺ (open), C₂H₃⁺ (bridged), C₂H₅⁺ (bridged), and C₂H₄^? radical anion). A simple rule is formulated to give approximate values of the charge parameter Q.     

The influence of basis sets on wave function tails

Wave function tails are analyzed quantitatively by investigating the dependence of exterior electron density (EED ) on basis sets; the EED is defined as the integrated electron density outside the repulsive molecular surface. Ab initio MO calculations with large scale basis sets were performed to establish the benchmark order of EED values for valence orbitals of some simple molecules. It is found that very popular basis sets, such as 4-31G, which are determined by energy optimization, are inferior in describing the wave function tails to some similar size basis sets, such as MIDI -4, which are obtained by least-squares fit to near Hartree-Fock atomic functions. Further the EED values for atomic 2s functions are shown to be unfavorably smaller than those for atomic 2p functions when the same value is used for the exponent α in the GTO basis sets. This indicates that the frequently used constraint α_s = α_p is not appropriate for describing wave function tails with medium-size basis sets. Deficiencies in the energy-optimized basis sets are found to become more serious for molecules including heavier atoms.     

Optimization of Gaussian basis sets for Dirac-Hartree-Fock calculations

We investigate the optimization of Gaussian basis sets for relativistic calculations within the framework of the restricted Dirac-Hartree-Fock (DHF) method for atoms. We compare results for Rn of nonrelativistic and relativistic basis set optimizations with a finite nuclear-size. Optimization of separate sets for each spin-orbit component shows that the basis set demands for the lower j component are greater than for the higher j component. In particular, the p _1/2 set requires almost as many functions as the s _1/2 set. This implies that for the development of basis sets for heavy atoms, the symmetry type for which a given number of functions is selected should be based on j, not on l, as has been the case in most molecular calculations performed to date.     

Binding energies of hydrogen-bonded clusters from extrapolation-oriented basis sets

The MP2 and CCSD(T) basis set limit binding energies of various hydrogen-bonded clusters were estimated via basis set extrapolation employing the correlation consistent aug-cc-pVDZ and modified aug-cc-pVDZ set containing extra polarization functions from cc-pVTZ set. By adopting the optimal interval for the difference between the cardinal numbers (X) corresponding to two basis sets in the X ⁻³ type extrapolation scheme the estimated binding energies for (H₂O)_n and (HF)_n (n=3−5) are shown to be close to the reference basis set limit values within the error bounds in many cases, manifesting the significance of these basis sets in studying the structures and binding of large hydrogen-bonded clusters.     

A systematic preparation of new contracted Gaussian- type orbital sets. VII. MINI-3, MINI-4, MIDI-3, and MIDI-4 sets for transition metal atoms

Two minimal contracted Gaussian-type orbital (CGTO ) sets are developed for the transition metal atoms. The expansion terms for the first set, MINI -3, are 4, 3, 3, and 3 for s-type CGTO s and others are all three. The abbreviation would be (4333/33/3) where the slash divides symmetry. The expansion terms for the other set, MINI -4, is (4333/43/4). The split-type basis sets, MIDI -3 and MIDI -4, are derived directly from MINI -3 and MINI -4, MINI -3 and MIDI -3 provide the outer-shell orbital energies which are far better than those by single-zeta (SZ ) STO s. MINI -4 and MIDI -4 provide the outer-shell orbital energies which are almost as good as those by double-zeta (DZ ) STO s. The total energies given by the present sets are better than those of SZ except for MINI -3 for Sc and Ti: the energies by MINI -4 and MIDI -4 are only 0.8–1.7 a.u. higher than DZ . The basis sets were tested on the Cu₂ molecule, where a large basis set was also used.     

A method for population and bonding analyses in calculations with extended basis sets

Summary A method for population and bonding analyses in the calculations with extended basis sets is proposed. The definition and evaluation method of the atomic orbitals in molecular environments (AOIMs) are described. It is shown that the AOIMs can be divided into two subsets, the strongly occupied minimal compact subset {AOIM}_B and the very weakly occupied “Rydberg” subset {AOIM}_R, according to the orbital population obtained from Mulliken analysis with AOIMs as basis sets. The viewpoint of “molecular orbitals consisting of minimal atomic orbital sets” can be optimally realized in terms of {AOIM}_B. The Mulliken population based on AOIMs is reasonable and fairly stable to changes of basis sets. The Mayer bond orders calculated based on {AOIM}_B are quite stable to the changes of basis sets; therefore they can be used to measure objectively the contribution of individual atomic orbitals to bonding.     

Cubic-grid Gaussian basis sets for electron scattering calculations. III. Effect of basis-set translation and size on the calculated cross section

Previously developed cubic-grid basis sets of various sizes were used for the calculation of cross sections for elastic and inelastic electron scattering by the He and Ne atoms and the H₂O molecule by the T-matrix expansion method. The aim was to test the invariance of calculated cross sections with respect to the translation of the target molecule and to examine the effect of basis-set size on the results. We also present a simple procedure for accounting for long-range interactions from the part of space that lies outside the volume that contains the cubic-grid basis set. © 1995 John Wiley & Sons, Inc.     

A systematic preparation of new contracted Gaussian-type orbital sets. III. Second-row atoms from Li through ne

Four minimal Gaussian basis sets are generated for the second-row atoms Li through Ne. The first one, MINI-1, consists of a 3-term contraction of primitive Gaussian-type orbitals for 1s, 2s, and 2p atomic orbitals. The convenient shorthand notation would be (3,3) for Li? Be and (3,3/3) for B? Ne. The second one, MINI-2, can be represented by (3,3/4) for B? Ne. In the same way, MINI-3 is described as (4,3) for Li? Be, and MINI-3 and MINI-4 are represented by (4,3/3) and (4,3/4) for B? Ne, respectively. Although the four basis sets are the minimal type, they give the valence shell orbital energies which are close to those of DZ. These four and other sets derived from them are tested for the hetero- and homodiatomic molecules and some organic molecules. They are found to give the orbital energies that agree well with those given by extended calculations. Atomization energies and other spectroscopic constants are also calculated and compared with those of extended calculations. The results clearly indicate that the present basis sets can be used very effectively in the molecular calculations.