The 3-21G(N*) basis set: An economical polarized basis set for ab initio studies on nitrogen-containing molecules

The 3-21G basis set shares with its older cousin, the 4-31G basis set, a tendency to overestimate valence angles at nitrogen atoms and to underestimate seriously barriers to inversion at such atoms. The 6-31G* basis set generally yields greatly improved results in these respects. It is here shown that, for a variety of molecules, supplementation of the 3-21G basis set at three- or two-coordinate nitrogen atoms with a set of six d-functions having exponent 1.0 leads to optimized geometries and inversion barriers at such nitrogen centers in good agreement with results obtained with the 6-31G* basis set. This supplemented basis set, designated as 3-21G(N*), also leads to calculated vibrational frequencies in good agreement with those calculated with the 6-31G* basis set. The 3-21G(N*) basis set offers an economical alternative to the 6-31G* basis set, particularly for molecules containing several first-row atoms other than nitrogen.     

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

The 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.     

Optimum Gaussian basis set for the Bromine atom. Ab initio calculations on the HBr molecule

An optimum (15 ^s 12 ^p 2 ^d ) Gaussian basis set was obtained for the Bromine atom by minimizing the open shell energy functional. In the minimization procedure the method of conjugate gradients was applied. The optimum (15 ^s 12 ^p 2 ^d ) basis set was contracted to an [8 ^s 6 ^p 2 ^d ] “double zeta” quality basis set and this contracted set was tested on the HBr molecule.     

Accurate atomic Gaussian basis functions for second-row atoms: Small split-valence 3-21SP and 4-22SP basis sets

Small split-valence Gaussian 3-21SP and 4-22SP basis sets, previously reported for the first-row atoms [Chem. Phys. Lett., 229 , 151 (1996)], have been extended for the second-row elements of the Periodic Table. The total energies of the ground states of the second-row atoms calculated with the new basis sets are significantly lower than those obtained with the well-known 3-21G (J. Am. Chem. Soc., 104 , 2797 (1982)] and 4-31G [J. Chem. Phys., 56 , 5255 (1972)] basis sets. This is because, as first noted in our previous work for first-row atoms, that the 3-21G and 4-31G basis sets only correspond to a local minimum of the Hartree–Fock energy functional, which is relatively far from its global minimum. The proposed basis sets have been tested by performing geometry optimizations and calculations of normal frequencies in the harmonic approximation of some diatomic and polyatomic molecules at the Hartree–Fock level. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1200–1210     

Optimization of the Lennard-Jones parameters for a combined ab initio quantum mechanical and molecular mechanical potential using the 3-21G basis set

A combined ab initio quantum mechanical and molecular mechanical (AI-QM/MM) potential for use in molecular modeling and simulation has been described. In this article, we summarize a procedure for deriving the empirical parameters embedded in a combined QM/MM model and suggest a set of Lennard-Jones parameters for the combined ab initio 3-21G and MM OPLS-TIP3P (AI-3/MM) potential. Interaction energies and geometrical parameters predicted with the AI-3/MM model for over 80 hydrogen-bonded complexes of organic compounds with water were found to be in good accord with ab initio 6-31G(d) results. We anticipate that the AI-3/MM potential should be reasonable for use in condensed phase simulations. © 1996 by John Wiley & Sons, Inc.     

Efficient diffuse function-augmented basis sets for anion calculations. III. The 3-21+G basis set for first-row elements,Li–F

The relatively small diffuse function-augmented basis set, 3-21+G, is shown to describe anion geometries and proton affinities adequately. The diffuse sp orbital exponents are recommended for general use to augment larger basis sets.     

Performance of revised STO(1M)-3G basis set for prediction of 5-fluorocytosine chemical shifts

Nuclear shieldings and chemical shifts of 5-fluorocytosine (5FC) were predicted in the gas phase and DMSO solution modeled by polarizable continuum model using B3LYP density functional and revised STO(1M)-3G basis set. For comparison, eight arbitrary selected basis sets including STO-3G and medium-size Pople-type and larger dedicated Jensen-type ones were applied. The former basis sets were significantly smaller, but the calculated structural parameters, harmonic vibrational frequencies, were very accurate and close to those obtained with larger, polarization-consistent ones. The predicted ¹³C and ¹H chemical shieldings of 5FC and cytosine, selected as parent molecule, were acceptable (root mean square for ¹³C chemical shifts in DMSO of about 5 ppm and less) though less accurate than those calculated with large basis sets, dedicated for prediction of nuclear magnetic resonance parameters.     

Distributed basis sets of s-type Gaussian functions for molecular electronic structure calculations: Applications of the Gaussian cell model to one-electron polycentric linear molecular systems

A particular formulation of the distributed Gaussian basis-set approach, the extended Gaussian cell model, is applied to the simplest polycentric molecule, the linear H₃²⁺ ion. Calculations of the total energy using two extensions of the original Gaussian cell model are described and results are reported for the ground state and the first excited state. A comparison with recently reported finite element calculations is made for a number of nuclear geometries. © 1996 John Wiley & Sons, Inc.     

Efficiency of numerical basis sets for predicting the binding energies of hydrogen bonded complexes: evidence of small basis set superposition error compared to Gaussian basis sets

Binding energies of selected hydrogen bonded complexes have been calculated within the framework of density functional theory (DFT) method to discuss the efficiency of numerical basis sets implemented in the DFT code DMol3 in comparison with Gaussian basis sets. The corrections of basis set superposition error (BSSE) are evaluated by means of counterpoise method. Two kinds of different numerical basis sets in size are examined; the size of the one is comparable to Gaussian double zeta plus polarization function basis set (DNP), and that of the other is comparable to triple zeta plus double polarization functions basis set (TNDP). We have confirmed that the magnitudes of BSSE in these numerical basis sets are comparative to or smaller than those in Gaussian basis sets whose sizes are much larger than the corresponding numerical basis sets; the BSSE corrections in DNP are less than those in the Gaussian 6-311+G(3df,2pd) basis set, and those in TNDP are comparable to those in the substantially large scale Gaussian basis set aug-cc-pVTZ. The differences in counterpoise corrected binding energies between calculated using DNP and calculated using aug-cc-pVTZ are less than 9 kJ/mol for all of the complexes studied in the present work. The present results have shown that the cost effectiveness in the numerical basis sets in DMol3 is superior to that in Gaussian basis sets in terms of accuracy per computational cost.     

Gaussian basis set of double zeta quality for atoms K through Kr: application in DFT calculations of molecular properties

Contracted basis sets of double zeta (DZ) quality for the atoms from K to Kr are presented. They were determined from fully optimized basis sets of primitive Gaussian-type functions generated in atomic Hartree-Fock calculations. Sets of Gaussian polarization functions optimized at the Möller-Plesset second-order level were added to the DZ basis set. This extends earlier work on segmented contracted DZ basis set for atoms H-Ar. From this set, using the BP86 nonhybrid and B3LYP hybrid functionals, dissociation energy, geometric parameters, harmonic vibrational frequency, and electric dipole moment of a set of molecules were calculated and compared with results obtained with other basis sets and with experimental data reported in the literature. In addition, ⁵⁷Fe and ⁷⁷Se nuclear magnetic resonance chemical shifts in Fe(C₅H₅)₂, H₂Se, and CSe₂ were calculated using density functional theory and gauge-including atomic orbitals and, then, compared with theoretical and experimental values previously published in the literature. Except for chemical shift, one verifies that our results give the best agreement with experimental and benchmark values. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008     

Nucleophilic substitution at sulfonyl sulfur atom: Aminolysis of 1-tosyl-3-methyl imidazolium chloride in aqueous medium.

Kinetics of the reaction of 1-tosyl-3-methyl-imidazolium chloride with various amines were measured to examine the nature of sulfonyl transfer in enzymatic reactions. The activation parameters and the value of the brønsted exponent, β = 0.48, are consistent with a small degree of bonding between the entering amine and the sulfur atom in the transition state. Similarities in the nucleophilic behavior of sulfonyl and carbonyl groups are detected.     

Comparative analysis of a full-electron basis set and pseudopotential for the iodine atom in DFT quantum-chemical calculations of iodine-containing compounds

A systematic study was performed to examine the possibilities of the B3LYP DFT method in a dgdzvp full-electron basis and of the method including a pseudopotential for iodine compounds. The full-electron basis generally gives better agreement for X-I bond lengths and reaction enthalpies of iodination of organic compounds and equally good agreement in calculations of the IR vibrations of the X-I bond length compared with the studies using the pseudopotential. The full-electron basis also allows adequate calculations of the quadrupole coupling constants of iodine atoms and is generally characterized by smaller computing times.     

The sensitivity of B3LYP atomization energies to the basis set and a comparison of basis set requirements for CCSD(T) and B3LYP

The atomization energies of the 55 G2 molecules are computed using the B3LYP approach with a variety of basis sets. The 6–311 + G(3df) basis set is found to yield superior results to those obtained using the augumented-correlation-consistent valence-polarized triple-zeta set. The atomization energy of SO₂ is found to be the most sensitive to basis set and is studied in detail. Including tight d functions is found to be important for obtaining good atomization energies. The results for SO₂ are compared with those obtained using the coupled-cluster singles and doubles approach including a perturbational estimate of the triple excitations.     

The performance of the new 6-31G(##) basis set: molecular structures and vibrational frequencies of transition metal carbonyls

The performance of the newly proposed 6-31G(##) basis set for calculating the equilibrium structure and vibrational frequencies of transition metal carbonyl complexes has been studied at the HF and DFT levels of theory. The 6-31G(##) basis set has been constructed by augmentation of the 6-31G basis set by diffuse and polarization functions, which are generated from the corresponding 6-31G basis AOs response functions obtained in the frame of propagator approach. The predicted values of bond distances and vibrational frequencies for the title compounds are in good agreement with the experimental data. The relative energies and HOMO-LUMO gaps were also estimated for the series of MCO complexes.     

Ab initio calculations of relativistic and electron correlation effects in polyatomics using the universal Gaussian basis set: XeF2

Ab initio accurate all-electron relativistic molecular orbital Dirac–Fock self-consistent field calculations are reported for the linear symmetric XeF₂ molecule at various internuclear distances with our recently developed relativistic universal Gaussian basis set. The nonrelativistic limit Hartree–Fock calculations were also performed for XeF₂ at various internuclear distances. The relativistic correction to the electronic energy of XeF₂ was calculated as ～ ?215 hartrees (?5850 eV) by using the Dirac–Fock method. The dominant magnetic part of the Breit interaction correction to the nonrelativistic interelectron Coulomb repulsion was included in our calculations by both the Dirac–Fock–Breit self-consistent field and perturbation methods. The calculated Breit correction is ～6.5 hartrees (177 eV) for XeF₂. The relativistic Dirac–Fock as well as the nonrelativistic HF wave functions predict XeF₂ to be unbound, due to neglect of electron correlation effects. These effects were incorporated for XeF₂ by using various ab initio post Hartree–Fock methods. The calculated dissociation energy obtained using the MP 2(full) method with our extensive basis set of 313 primitive Gaussians that included d and f polarization functions on Xe and F is 2.77 eV, whereas the experimental dissociation energy is 2.78 eV. The calculated correlation energy is ～ ?2 hartrees (?54 eV) at the predicted internuclear distance of 1.986 Å, which is in excellent agreement with the experimental Xe—F distance of 1.979 Å in XeF₂. In summary, electron correlation effects must be included in accurate ab initio calculations since it has been shown here that their inclusion is crucial for obtaining theoretical dissociation energy (D_e) close to experimental value for XeF₂. Furthermore, relativistic effects have been shown to make an extremely significant contribution to the total energy and orbital binding energies of XeF₂. © 1995 John Wiley & Sons, Inc.     

New scale factors for harmonic vibrational frequencies using the B3LYP density functional method with the triple-zeta basis set 6-311+G(d,p)

We have calculated optimal frequency scaling factors for the B3LYP/ 6-311+G(d,p) method for fundamental vibrational frequencies on the basis of a set of 125 molecules. Using the new scaling factor, the vibrational frequencies calculated with the triple-zeta basis set 6-311+G(d,p) give significantly better accuracy than those calculated with the double-zeta 6-31G(d) basis set. Scale factors were also determined for low-frequency vibrations using the molecular set of 125 molecules and for zero-point energies using a smaller set of 40 molecules. We have studied the effect on the calculated vibrational frequencies for various combinations of diffuse and polarization functions added to the triple-zeta 6-311G basis set. The 6-311+G(d,p) basis set is found to give almost converged frequencies for most molecules, and we conclude that our optimum scaling factors are valid for the basis sets 6-311G(d,p) to 6-311++G(3df,3pd). The new scale factors are 0.9679 for vibrational frequencies, 1.0100 for low-frequency vibrations, and 0.9877 for zero-point vibrational energies.     

The performance of the rapid estimation of basis set error and correlation energy from partial charges method on new molecules of the G3/99 test set

Experimental enthalpies of formation have been approximated using single-point Hartree–Fock (HF)–self-consistent-field (SCF) total energies plus the rapid estimation of basis set error and correlation energy from partial charges (REBECEP) energy corrections. The energy corrections are calculated from the HF–SCF partial atomic charges and optimized atomic energy parameters. The performance of the method was tested on 51 closed-shell neutral molecules (50 molecules from the G3/99 thermochemistry database plus urea, composed of H, C, N, O, and F atoms). The predictive force of the method is demonstrated, because these larger molecules were not used for the optimization of the atomic parameters. We used the earlier RECEP-3 [HF/6-311+G(2d,p)] and REBECEP [HF/6-31G(d)] atomic parameter sets obtained from the G2/97 thermochemistry database (containing small molecules) together with natural population analysis and Mulliken partial charges. The best results were obtained using the natural population analysis charges, although the Mulliken charges also provide useful results. The root-mean-square deviations from the experimental enthalpies of formation for the selected 51 molecules are 1.15, 3.96, and 2.92 kcal/mol for Gaussian-3, B3LYP/6-11+G(3df,2p), and REBECEP (natural population analysis) enthalpies of formation, respectively (the corresponding average absolute deviations are 0.94, 7.09, and 2.27 kcal/mol, respectively). The REBECEP method performs considerably better for the 51 test molecules with a moderate 6-31G(d) basis set than the B3LYP method with a large 6-311+G(3df,2p) basis set. Received: 10 March 2001 / Accepted: 5 July 2001 / Published online: 11 October 2001     

The decomposition of the SCF interaction energy in hydrogen bonded dimers corrected for basis set superposition errors: An examination of the basis set dependence

A systematic examination of the components of the interaction energy, obtained with the Kitaura and Morokuma method, for nine H-bonded dimers without and with counterpoise corrections (CP ) is presented. The nine dimers H_n A …? HBH_m correspond to all the possible combinations of HF, H₂O, and NH₃ as electron donors and electron acceptors. The interaction energy and the corresponding components have been computed over a sizable interval of intermolecular distances with five basis sets (STO -3G, MINI -1, 3-21G, 4-31G, 6-31G**) selected among those most extensively used to study interactions in larger systems. The CP corrections to the ΔE components have been obtained with a method, implemented in our group, which permits assignment to the pertinent components of ΔE of a physically reasonable portion of the CP correction even though different CP corrections are adopted. We examine here three versions of the CP correction, namely, the full CP correction (i.e., the original version of Boys and Bernardi) and CP corrections limited to the virtual space of the partner or to the electron donor only. The resulting data are employed to assess the basis set dependence of several models of hydrogen bonding (the electrostatic model, the semiclassical model, etc.) both with and without CP corrections.