Ab Initio Basis Set Research Articles

On the performance of density functional methods for describing atomic populations, dipole moments and infrared intensities

Atomic populations according to the Mulliken, electrostatic, natural population, and atomic polar tensor (APT) definitions were evaluated for first- and second-row compounds using different correlated ab initio techniques, DFT methods, and basis sets. All definitions except Mulliken exhibit modest basis set sensitivity. B3LYP predicts partial charges in agreement with high-level ab initio results. Exact-exchange corrections are more important than gradient corrections for this property. B3LYP with at least sdpf basis sets usually predicts dipole moments and infrared intensities in agreement with more accurate calculations, while semiquantitative IR intensities are obtained even with the modest cc-pVDZ basis set.

Molecular orbital study of the structure and interactions of ylidene rhodanines

Semiempirical (with the AM1 Hamiltonian) and ab initio (mainly with the 6-31G* and LANL2DZ+ +(d,p) basis sets) molecular oribital calculations show the predominant tautomer of gas phase methylidene rhodanine is 2-thioxo-4-thiazolidinone in agreement with earlier work on other types of rhodanines. Inclusion of solvation effects in the AM1 calculations corroborates with this tautomer is also preferred in aqueous solution. Energy-optimized bond lengths and angles show good agreement with those for a crystalline benzylidene rhodanine. The geometry of a hydrogen bonded dimer matches closely the crystalline state arrangement. The two N-H ⋯ O hydrogen bonds that form in the dimer. provide a stabilization energy of about - 10 kcal/mol. The interactions of methylidene rhodanine with a calcium ion are modeled with basis sets as large as LANL2DZ+ +(d,p). The preferred binding site is near the carbonyl oxygen for the neutral rhodanine and near the nitrogen and thione sulfur in a bidentate arrangement for the rhodanine anion. Implications for the interaction of benzylidene rhodanines with various possible protein and metalloprotein receptors are discussed.

A comparison of high-quality ab initio basis sets: the inversion barrier in ammonia

The abilities of several large Gaussian basis sets in conjunction with standard correlation treatments to reproduce the classical barrier to inversion in ammonia are compared and dissected. The basis sets incorporate primitive functions from five different sources. Second- and third-order Møller-Plesset perturbation theory and coupled-cluster methods have been used, with an extrapolation to the correlation limit taken from the literature. Each of the employed sets of primitive sp functions are found to be sufficient for 30 cm −1 accuracy, but only after the inclusion of standard diffuse sp functions on nitrogen. Contraction errors in the basis sets are usually small, generally contributing less than 30 cm −1 to the barrier height but up to 70 cm −1 in some cases. An analysis of the basis set requirements for the accurate computation of core correlation has also been performed. It is found that, for sufficiently large basis sets, liberation of the 1s electrons of nitrogen in the correlated treatments consistently results in reductions of 40–70 cm −1 in the barrier height, even without the addition of core-specific functions to the standard basis sets. The best estimate of the classical inversion barrier in ammonia is 1821 cm −1, with an estimated uncertainty of ±30 cm −1.

Solvent effects on electronic properties, geometries and internal rotation barriers of bithiophenes. An ab initio self-consistent reaction field theoretical study

A self-consistent reaction field (SCRF) theoretical model has been used to simulate the average solvent effects on some π-conjugated organic thiophene dimers. Restricted Hartree-Fock molecular orbital calculations, using ab initio basis sets up to 6–31 + G *, are reported on geometries, total energies and rotational barriers of 2,2′-bithiophene, and its 3,3′- and 3,4′-dimethyl derivatives.

Theoretical study of C 24N 4 molecule

Both ab initio 6-31G, 3-21G and STO-3G basis sets and semiempirical PM3 and AM1 molecular orbital calculations are carried out on the C 24N 4 molecule of the T d symmetry group. Results on the fully optimized structure which constrained T d symmetry, molecular orbitals and vibrational frequency were obtained by both ab initio and semiempirical methods. The binding energy and various thermodynamic properties were also calculated via the PM3 and AM1 semiempirical methods. All the evidence of this work proves that the C 24N 4 molecule is stable and that its four six-membered rings with a remarkable delocalized C…C bond are similar to the related rings in the C 60 buckminsterfullerene structure.

A systematic study on the basis set dependence of the Hartree-Fock, MP2 and CIS harmonic force fields and vibrational frequencies of formaldehyde in comparison with the experimental results

The aim of this work was to find the limits of the vibrational frequency calculations by ab initio methods, in the framework of the harmonic frequency model and so find the possibility of eliminating the scaling of force constants. Therefore the efficiency of the different ab initio methods and basis sets were investigated from the point of view of vibrational frequency calculations. The applied methods were the Hartree-Fock (HF), the Møller-Plessett second-order perturbation (MP2) and the configuration interaction with first excited states (CIS). Sixteen different basis sets were applied from STO-3G to 6–311 + G ∗∗. The model molecule was formaldehyde. Equilibrium configurations and energies, vibrational frequencies and thermodynamic properties were calculated for all 48 cases. The results were compared to the harmonized experimental geometric parameters and the harmonized measured frequencies. According to the comparison the results of the MP2 method were found to be preferable. For good agreements the application of polarization functions, at least on the heavy atoms, is essential. Therefore the MP2/4-31G ∗ is the smallest basis set resulting in reasonable harmonic frequencies without any scaling. The increase in the number of Gaussian functions replacing a Slater-type orbital, the subsequent splitting of the valence orbitals and the addition of polarization functions on the hydrogens improve the agreement. The influence of the diffuse functions is not very large but excluding the CH stretching modes they improve the calculated frequency values in comparison with the harmonized experimental ones. In the case of the CH stretching modes the calculations with the basis set containing only polarization functions yield the best results. The minimal deviations from the harmonized frequencies are in the magnitude of 1 %, and for some normal modes they are smaller than 1 %.

A theoretical investigation of the N-oxide moiety

Molecular orbital calculations were carried out for pyridine-1-oxide and to determine the level of theory required to accurately represent the NO bond. The results clearly show that semi-empirical calculations fail to reproduce experimental values for bond lengths in pyridine-1-oxide. Lower level ab initio basis sets also provided poor results. STO-6-31G ∗∗ does, however provide good agreement with experiment for the NO bond lengths of pyridine-1-oxide.

Ab initio computation of semiempirical π-electron methods. III. The benzene molecule, the zero-differential-overlap approximation, and the transferability of parameters

The correlated, size-extensive ab initio effective valence shell Hamiltonian (ℋν) method is used to compute the true π-electron Hamiltonian of benzene and to use it for testing various assumptions of the Pariser–Parr–Pople (PPP) semiempirical electronic structure method. On one hand, the ab initio ℋν method enables computing the low lying valencelike vertical excitation energies and ionization potentials. For example, the calculated ℋν excitation energies deviate from experiment on average by only 0.28 eV, which compares well with similar correlated ab initio calculations. More remarkably, however, the ℋν method can reproduce the vertical excitation energies on average to 0.35 eV simply by employing valence orbitals constructed from symmetry adapted linear combinations of carbon atom pπ orbitals. Thus the ℋν calculations demonstrate that accurate benzene excitation energies can be obtained using a common set of valence orbitals for every valencelike state and, in fact, for every conjugated hydrocarbon! In addition, the true, correlated benzene π-electron effective integrals are ab initio counterparts of semiempirical parameters and transfer extremely well to other small molecules such as ethylene and cyclo-butadiene. The degree of transferability is improved when increasing the size of the primitive ab initio basis set. An analysis of the ℋν effective integrals demonstrates that the true PPP model can indeed neglect a portion of one- and two-electron parameters which are assumed to be small by the zero differential overlap (ZDO) approximation, since the correlation contributions render some effective integrals negligible. On the other hand, some typically neglected parameters, such as two-electron, three-center interactions, are computed as too large to just neglect. Likewise, the exact π-electron ℋν contains three-electron many-body interactions which are large (greater than 0.1 eV) and thus cannot be explicitly neglected in PPP models.

Ab initio computation of semiempirical π-electron methods. I. Constrained, transferable valence spaces in ℋν calculations

Large basis set ℋν calculations are performed for ethylene, cyclobutadiene, and trans-butadiene in order to examine the accuracy of approximate ℋν calculations specifically designed to reproduce a Pariser–Parr–Pople-like (PPP) semiempirical model from first principles. This is the first ℋν study in which systematic, semiempirical-like approximations to ℋν are examined for their accuracy and basis set dependence in computations of vertical excitation energies and ionization and potentials for large, polyatomic molecules. We focus explicitly on two fundamental semiempirical-like approximations to ab initio ℋν calculations. First, it is shown that ab initio ℋν calculations can produce reasonably accurate vertical excitation energies and ionization potentials for the low-lying valencelike states when using valence orbitals ‘‘constrained’’ to be linear combinations of transferable, carbon atom pπ orbitals. The differences between full ab initio ℋν and constrained ℋν calculations for all states (with one exception each in trans- and cyclobutadiene) range between roughly 0.00 and 0.25 eV for all states and, furthermore, these constrained errors show no basis set dependence. Second, it is shown that the excitation energies and ionization potentials are not influenced significantly by the nonclassical ℋν three- and four-body operators. When neglecting these interactions, errors of only a few tenths of an electron volt are again encountered, and these errors also display no basis set dependence. These conclusions are shown to be consistent with previous ab initio ℋν calculations. Because the three- and four-body ℋν terms are neglected as a leading approximation, the computed oneand two-body empirical parameters which appear in the PPP-like model. The present calculations explain the errors expected to occur in further, approximate ℋν calculations, the states which can be reasonably described with both approximate ℋν calculations and PPP-like models, and the ab initio basis set requirements for future ab initio ℋν studies of these models.

Comparison and Scaling of Hartree-Fock and Density Functional Harmonic Force Fields. 1. Formamide Monomer

We have compared force constants of formamide calculated by a wide range of ab initio quantum chemical methods and basis sets. Force fields calculated by local and gradient-corrected density functional theory (DFT) methods were found to be closer to MP2/6-31G ** values than Hartree-Fock (HF) values. A comparison of calculated frequencies and infrared intensities with experimental values indicated better performance of the DFT methods over HF and even MP2. Several scaling schemes for interaction force constants were evaluated, as well as the effect of the variation of interaction force constants with theoretical method on the calculated frequencies, IR intensities, and normal modes

Frontier orbital energies in quantitative structure-activity relationships: A comparison of quantum chemical methods

The energies of the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) have long been used as descriptors in QSAR (Quantitative Structure-Activity Relationships). It is shown that different quantum chemical methods of calculating these energies yield results which sometimes correlate poorly with each other. This could seriously affect physical interpretation of QSAR equations. A comparison is made between HOMO and LUMO energies and their differences and sums (hardness and electronegativity) calculated by some of the best knownab initio and semi-empirical methods for two series of simple organic molecules. The difference between the HOMO and LUMO energies correlates better between methods than does either alone, and their sum correlates relatively poorly. MINDO/3 (Modified Intermediate Neglect of Differential Overlap, version 3) is the poorest method in terms of correlation with the more extended basis setab initio methods, followed by CNDO (Complete Neglect of Differential Overlap) and INDO (Intermediate Neglect of Differential Overlap). The best semi-empirical methods, in terms of correlation with experiment and the more extended basis setab initio calculations, are MNDO (Modified Neglect of Differential Overlap), AM1 (Austin Model 1) and PM3 (Parametric Method 3). The simplestab initio method, STO-3G, does not agree as well with the extended basis set calculations or with experimental results as the more advanced semi-empirical methods.

Macrocyclic effect and conformational analysis of the mixed-donor macrocycle 12-ane N 2O 2 by means of quantum chemical methods

Minimal GLO basis set ab initio and CNDO/2 calculations have been performed for four possible conformations of 1,7-dioxa-4,10-diazacyclododecane (12-ane N 2O 2) and their Li(I) complexes, using experimental bond lengths and angles. The special complex stability enhancement of cyclic ligands, known as the macrocyclic effect, has also been investigated by comparison with open chain analogues. The results indicate a good agreement between CNDO/2 and ab initio methods in the prediction of the lowest energy conformation of the free ligand, which is the alternate from with torsional angles of 68° and 66°, respectively. For the Li(I) complex, the CNDO/2 method predicts as expected a wrong conformation. The 12-ane N 2O 2/Li(I) complex is more flexible than either tetraaza or tetraoxa analogues. In addition, the lesser flexibility of the ring of the free 12-ane N 2O 2 ligand compared with that of macrocycles with only one sort of donor atom, reflects a higher energy requirement in arranging the donor atoms in a way suitable for complexation, leading to a lower net macrocyclic effect of the ‘mixed-donor’ macrocyclic ligand.

Molecular electrostatic potential of substituted aromatic compounds: Factors affecting the differences between Ab Initio and semiempirical results

AbstractThe molecular electrostatic potential (MEP) distribution of anisole, chlorobenzene, and fluorobenzene obtained from STO‐3G, 3‐21G, and 6‐31G* basis set ab initio and MNDO and AM1 semiempirical wave functions is investigated to explain the differences among the MEP features obtained for polychlorodibenzo‐p‐dioxins. The main topological features as well as the absoltue and relative minima location obtained from ab initio calculations are independent from the choice of the basis set. MNDO calculations are in good agreement with the ab initio ones in the case of anisole and fluorobenzene, while they incorrectly describe the MEP of chlorobenzene. The AM1 fails to localize the absolute minimum of fluorobenzene and does not find the minimum above the chlorobenzene chlorine atom. The poor agreement of both semiempirical methods with ab initio for any kind of chlorinated compounds is confirmed by results obtained for chloreothylene and chloroethane. We hypothesize that the main problem concerning these methods is that they freeze a too large amount of electrons in the atomic core of elements belonging to the second row, which makes for a wrong description of the core–valence electron interactions. Results obtained by modifying the AM1 parameters related to these interactions confirm our hypothesis. © 1992 by John Wiley & Sons, Inc.

Molecular orbital estimates of the structures and internal rotational barriers in 2-fluorotoluene and 2-chlorotoluene

The internal rotational barriers in 2-fluorotoluene and 2-chlrrotoluene are computed with the ab initio basis sets, 6-31G and 6-31G*, as well as by single-point MP2/ / 6-31G* calculations. For the fluoro derivative, good agreement with the barrier from rotational spectra is obtained. The computed barrier for 2-chlorotoluene agrees with that derived from dipolar couplings in solution but is possibly smaller than the value implied by the absence of splittings in its rotational spectrum. The 6-31G* structures are given.

Experimental and theoretical studies of the effects of hydration on proton exchange equilibria

Theoretical calculations with the ab initio molecular orbital STO-3G basis set on the effect of trihydration on the relative acidities of 3- and 4-substituted phenols, 4-substituted quinuclidinium ions and 4-substituted bicyclo [2.2.2]octylammonium ions are reported. These results are contrasted with calculations on non-hydrated species and compared with results in aqueous solution and in the gas phase. Unlike results for smaller molecules such as substituted acetic acids and methylammonium ions, the solvation effects of three molecules of water are far short of that observed in going from the gas phase to aqueous solution. Reasons for this are discussed in the context of solvent attenuation factors for various molecules.

The internal polarization basis set: A note of the force-adaptedab initiocalculation

A new version of the force-adapted ab initio basis set was proposed in this communication based on Nakatsuji’s Family basis set and our previous research. Test examples show that the internal polarization basis set, in which the polarization function is appended in the inner shells, is effective in improving the accuracy of the resultant force as well as in reducing computational efforts.

Ab initio and semiempirical calculations on the tautomeric equilibria of N-unsubstituted and N-substituted benzotriazoles

The geometries, relative stabilities, ionization potentials, and dipole moments for benzotriazole tautomers and their (dimethylamino) methyl derivatives were calculated by PM3, AM1, and MNDO semiempirical methods with full geometry optimization and with an ab initio 3-21G basis set

Theoretical description of the conformation and the tautomerism of progabide

A theoretical description of the conformation and tautomerism of the progabide molecule was performed employing the ab initio STO-3G and 3-21G basis sets and a quantum chemical reaction field model for the consideration of the solvent influence. The calculations indicated a conformation with planar orientation of the A ring and considerable rotation of the B ring with respect to the imine bond as the most stable conformation. The consequences for conformation of hydrogen bond formation and breaking were examined. Predominance of the aromatic tautomer in apolar and the quinonoid tautomer in polar solvents is predicted.

Stability of substituted pyrylium salts and the corresponding 2- H- and 4- H-pyrans

The stabilities of a series of 4-substituted pyrylium salts have been compared with those of the correspondingly substituted benzenes using the ab initio STO-3G basis set. It is shown that marked field and resonance effects operate in the pyrylium salts covering a range of more than 50 kcal mol −1 compared to the benzenes. The corresponding 4- H- and 2- H-pyrans that would be produced by hydride ion attack have also been studied, the 2- H-pyrans usually being the more stable. Similar substituent effects occur in these equilibria. The relative stability of the parent 2- H- and 4- H- pyrans is discussed, the 4- H-pyran being the preferred structure at the STO-3G, 3-21G and 6- 31G ∗ bases.

Conformation of N-acetyl- l-pro- d-ala- N-methyl tripeptide empirical, semi-empirical MO and AB initio MO calculations

Conformational energies of the title peptide calculated by the empirical program packages GROMOS, CHARMM and DISCOVER (the latter two also with the AMBER force field), semiempirical MO scheme AMI, and the ab initio STO-3G basis set are compared. The lowest energies were obtained for either of the C7C7 (axial and equatorial) conformations except by CHARMM with incorporated AMBER force field, by which the βII conformation is preferred. The relative energy differences of these three conformations are within 3–5 kcal mol −1. Energy minimizations of the peptide surrounded by 121 SPC type water molecules give the lowest energy of hydration for the βII bend. The calculated energies are compared with the results of experimental conformational analysis.