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     

Locally dense basis sets for chemical shift calculations

Calculations of chemical shifts have been carried out using “locally dense” basis sets for the resonant atom of interest, and smaller, attenuated sets on other atoms in the molecule. For carbon, calculations involving a 6-311G(d) triply split valence set with polarization on the resonant atom and 3-21G atomic bases on other heavy atoms result in good agreement with experiment, and are virtually identical to those found employing the larger basis on all atoms. For species such as nitrogen, oxygen, and fluorine where standard balanced basis sets do not agree well with experiment, use of attenuated sets fail as well. The use of locally dense basis sets permits calculations previously impractical, and the successful application to carbon suggests that the chemical shift is most dependent on the local basis set, and less so on whether or not a balanced or unbalanced calculation is being carried out.     

Theoretical study of some 1,3-substituted (1,3-diketonato)borondifluorides. Potential energy curve relevant to the barrier crossing reaction

Ab initio Hartree-Fock calculations utilising STO-3G, 3-21G^* and 6-31G^* basis sets have been performed on three neutral and highly polar molecules, (diformylmethine)borondifluoride, (acetylacetonato)borondifluoride and (dibenzylmethine) borondifluoride. The calculated and experimental structures are well correlated when using the HF/3-21G^* basis set, except for the structure parameters involving the boron atom. The HF/6-31G^* basis set does not improve the accuracy in structure calculations. The conformational analysis is in agreement with the experimentally observed C_2v symmetrical structures, where the boron atom is tetrahedrally coordinated. The calculations support a one-dimensional ground state barrier crossing reaction for (dibenzylmethine)borondifluoride, where the phenyl torsion is the most likely reaction coordinate. Both HF/6-31G^* calculations and the second-order Møller-Plesset correction with the 3-21G^* basis set suggest an activation energy of the ground state reaction of about 30 kJ mol⁻¹. The ground state barrier crossing reaction kinetics is evaluated by the Kramers theory. The calculated ground state parameters relevant to the barrier crossing reaction are compared with the experimentally observed excited state values.     

Electron momentum spectroscopy of CF2Cl2: experimental and theoretical momentum profiles for outer valence orbitals

Electron momentum distributions for outer valence orbitals of CF2Cl2 have been obtained by (e,2e) electron momentum spectroscopy at an incident energy of 1200 eV + binding energy. The experimental electron momentum profiles are compared with Hartree-Fock and density functional theory (DFT) calculations using B3LYP hybrid functional with the 6-31G and 6-311+G* basis sets. Generally, the shapes of the experimental momentum profiles are well reproduced by DFT calculations using larger basis sets 6-311 + G*. An attempt has been made to clarify the ordering of the outer valence orbitals, which have been in controversy, by comparing experimental results with B3LYP/6-311 + G* calculations.     

The electronic structure of small sodium clusters

Ab initio molecular orbital calculations using the STO3-21G basis set has been carried out for the cluster series Na _n ⁺ , Na _n , and Na _n ^– (wheren=2–7). The basis set is shown to be reliable compared with more extensive basis sets at the Hartree-Fock level. Thirty-one optimized structures are reported and discussed, many of which (especially for the anions) have not been considered. The STO3-21G//STO3-21G calculations suggest that for most of the species the optimum geometries are planar. In particular, the optimized structures for the anionic species should provide a starting point for more sophisticated configuration interaction calculations.     

Acetamide, a challenge to theory and experiment? On the molecular structure, conformation, potential to internal rotation of the methyl group and force fields of free acetamide as studied by quantum chemical calculations

The molecular geometry has been optimized without any constraints using different basis sets and levels of theory as: Hartree-Fock with basis sets 6–31+G**, 6–311++G**, cc-pVTZ and aug-cc-pVTZ, MP2 with basis sets 6–311++G** and cc-pVTZ, MP3 with basis set 6–311++G**, and density functional theory with basis sets 6–311++G** and cc-pVTZ. Small basis sets up to 6-31G predict the syn conformation of the methyl group to be the most stable conformation. Larger basis sets predict an unsymmetrical conformation with one of the H atoms perpendicular to the amide skeleton or an anti-like conformation. Dunnings correlation consistent polarized valence triple zeta, cc-pVTZ, basis set including MP2 predict two conformations, one perpendicular and one anti to be the most stable. The DFT calculations predict anti-like conformations. The most accurate calculations predict anti-like conformations which have not been predicted previously. The vibrational frequencies have been calculated for several basis sets and compared to the observed frequencies. The wagging frequency of the NH₂ is very dependent on the basis sets and levels of theory. Most calculations predict a planar NH₂ group in agreement with experiment. A scaled molecular force field has been determined by fitting the calculated frequencies to the observed ones for the perpendicular conformation using MP2/cc-pVTZ. The barrier heights for the methyl group have been calculated. The rotational constants, I_A + I_B − I_C values and dipole moments are compared with experimental values.     

Energetics of reactions involving radical species in solution: Calculation of relative electrode potentials for nitroimidazoles using density functional and continuum methods

Nonlocal density functional calculations and a semiempirical modified Born method for computing free energies of hydration were used to calculate the electrode potentials for a series of nitroimidazoles to a mean accuracy of about 80 mV. The density functional calculations used the nonlocal Becke '88 functional for exchange and either the nonlocal Lee-Yang-Parr or the local Vosko-Wilk-Nusair functionals for correlation and were performed at the HF/3-21G geometry. The most suitable geometry for these calculations was determined from a survey of various semiempirical, Hartree-Fock (HF) and density functional methods, with a variety of basis sets. The HF/3-21G method was found to yield a very favorable compromise between speed and accuracy in the determination of the geometry of 2-nitroimidazole, but the small basis set density functional calculations performed very badly. Density functional atom-optimized basis sets were found to give better overall results than traditional Pople-type basis sets. The free energy of hydration calculations employed the AM1 SM2 method. Both the gas-phase energies and the free energies of hydration made a significant contribution to the computed electrode potential. Indeed, an inverse relationship was found between the gas-phase electron affinity and the difference in free energy of hydration between the neutral nitroimidazole and its radical anion. The protocol established here may be useful for investigating novel bioreductive agents. © 1996 John Wiley & Sons, Inc.     

Nonempirical calculations of potential-energy surfaces for nucleophilic addition of H− and F− to an acetylene molecule

The minimal energy paths for the nucleophilic addition of a hydride ion (H^–) and a fluoride ion (F^–) to a molecule of acetylene (A) have been calculated with the use of 3–21++G and 3–21+G double basis sets in the framework of the Hartree-Fock-Roothaan method. The values of the total energies of the reactants, transition states, and products have been refined by means of calculations with more complete basis sets [6–31++G// 3–21++G and 6–31++G*//3–21++G for reaction (1); 6–31+G*//3–21+G and 6–31++G**//3–21+G for reaction (2)] and by taking into account the correlation energy for reaction (1) in the framework of the SCEP/6–31++*//3–21++G method. It has been established that the activation energy of reaction (2) is 15.94 kJ/mole lower than that for reaction (1), that reaction (1) is exothermic, and that the enthalpy change accompanying reaction (2) is close to zero. The character of the distribution of the electron density along the minimal energy paths of both reactions has been analyzed, and the differences appearing as a result of the replacement of the soft nucleophile H^– by the harder nucleophile F^– have been ascertained. The results of the calculations have been compared with the results available in the literature for reaction (1).Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 25, No. 2, pp. 149–155, March–April, 1989.     

Comparison of the use of the MNDO and MINDO/3 methods with ab initio methods to study tautomerism in histamine, 2- and 4-methylhistamine

The semiempirical MNDO and MINDO/3 methods are used to study the various tautomeric forms of histamine, 2-methylhistamine, and 4-methylhistamine. Comparisons of the optimized structures and tautomerization energies are made with values obtained from ab initio Hartree-Fock calculations using the 3-21G and STO-3G basis sets. Based on these results and previous comparisons of STO-3G results with x-ray structures, the present results indicate that while there are some differences in the values of the structural parameters, the changes in structure upon tautomerization and/or protonation are very similar. Further analysis of the MNDO and MINDO/3 structures by means of their utilization in 3-21G and STO-3G calculations indicates that either of these semiempirical methods provides reliable values for the structural parameters. Both methods give good qualitative agreement with the ab initio calculations for the relative energies of the various tautomers in the three compounds. In these studies the MNDO method appears to give better quantitative agreement with the 3-21G and STO-3G results than the MINDO/3 method.     

Vibrational absorption intensities in chemical analysis—VIII. Dimethyl sulphide

The structure and electric dipole moment of dimethyl sulphide have been calculated with a variety of basis sets. It is shown that the force fields computed with the 3-21G, 3-21G and 6-311G** bases are very similar after scaling. The vibrational assignments are discussed. The force field is compared with that of trimethyl phosphine. There is an excellent accord for the CH stretching modes, but the ab initio calculations indicate that the X-C/X-C (X = S,P) interaction terms have opposite signs. This appears to be incompatible with the experimental data. Effective atomic charges and atomic polar tensors (APT) are computed with the above bases and also with bond centred sp functions added to the 3-21G* basis. It is shown that the APT are much more sensitive to the basis set than are the effective atomic charges. The effects of the lone pair electrons on the bond electrical properties are much less than with oxy-ethers, though the overall perturbation of the sulphur atom on the intensities is greater. A number of inadequacies of the SCF calculations are identified.     

An SCF and CI Study of the 1,3 Shift in the HX?CHY⇌XCH?YH Isoelectronic Series: X,YCH2, NH,and O

Ab initio molecular orbital calculations at SCF level with the 3-21G, 6-31G, and 6-31G** basis sets and CI level with the 6-31G basis set have been carried out for an isoelectronic series HX? CH?Y and X?CH? YH, where X, Y can be CH₂, NH, and O. Optimized structures (3-21G and 6-31G**) for both tautomers and the 1,3 hydrogen shift transition states are reported. The relative stabilities of the isomers and the barriers of the 1,3 shift are discussed in terms of proton affinities and bond orders. It is shown that both the relative stabilities of the tautomers and the relative barrier heights can be explained qualitatively using simple proton affinity arguments and that the barrier heights are quantitatively related to bond orders.     

Theoretical studies on pteridines. 2. Geometries,tautomer, ionization and reduction energies of substrates and inhibitors of dihydrofolate reductase

Ab initio SCF calculations with STO-3G and 3-21G basis sets are reported for approximately 85 pteridines of interest to the study of the reaction and inhibition mechanisms of dihydrofolate reductase. These include tautomeric, protonated, deprotonated, reduced and 6-substituted forms of the 2-amino-4-oxo- and 2,4-diamino-pteridines, many of which are not easily amenable to experimental investigation. Full geometry optimizations at the SCF/STO-3G level for 30 such pteridines have been performed. A step-wise computational protocol designed to identify the minimum level of theory necessary for reliable prediction of relative tautomer, reduction and ionization energies has been developed in an effort to minimize the cost of calculations for this reasonably large N-heterobicylic system. In general, SCF/STO-3G results were found to be inadequate while SCF/3-21G results obtained with STO-3G optimized geometries agreed with all available experimental evidence with the exception of the relative acidity of 6-methyl-7,8-dihydropterin. Correlation graphs relating experimental pK_a's to the calculated ionization energies are presented: these are of potential predictive value. An analysis is given of the importance of resonance substructures, such as the guanidinium and extended-guanidinium groups, in stabilizing some preferred tautomeric and ionized forms, and in explaining the observed geometry changes.     

Reduced-size polarized basis sets for calculations of molecular electric properties. II. Simulation of the Raman spectra

The accuracies of the calculated vibrational frequencies and Raman intensities given by two new, highly compact Pol-type basis sets, Z2PolX and Z3PolX, have been determined and compared to the 6-31G(d), PolX, and aug-cc-pVTZ basis sets. Calculation of accurate Raman intensities has previously required large basis sets, but the ZmPolX basis sets are smaller even than PolX, which are the most compact basis sets able to calculate accurate Raman intensities. For the largest compound studied, C5H10O2, Z3PolX required more than an order of magnitude less CPU time than PolX, which has been shown to be 10 times faster than aug-cc-pVTZ. Two sets of test molecules were studied: one was a series of small molecules for which experimental values for absolute Raman activities were available; the second was a series of medium-sized molecules (mainly common organic solvents) where only relative Raman band intensities were available. The accuracies of the Raman intensities given by both of the ZmPolX basis sets were good compared to those of the PolX and aug-cc-pVTZ sets, and much better than the 6-31G(d) values. The errors in even unscaled frequency values <2000 cm(-1) were also acceptable and were slightly lower for Z3PolX than Z2PolX (30 cm(-1) vs. 48 cm(-1)). The combination of good intensity and frequency data meant that for the medium-sized organic molecules there was a close correspondence between the simulated Raman spectra and experimental data, and that the observed bands could easily be assigned on the basis of these calculations. Achieving this level of accuracy in the simulations at modest computational cost should now allow computational methods to be combined with experimental Raman studies much more widely than is currently the case.     

An ab initio study of intermolecular hydrogen bonding between small peptide fragments

Several small peptide fragments are investigated with ab initio (Hartree-Fock) calculations, using Gaussian basis sets. Complexation energies, net atomic charges, and optimum geometries are obtained. The geometries predicted by the STO -6G, and 6–31G* basis sets are quite similar, whereas the binding energies obtaiend by the 6–31G calculations are higher than those obtained with STO -6G and 6–31G* basis sets.     

Theoretically Calculated Deformation Density of Small Molecules

Analysis of the theoretical electron deformation density based on EHMO and ab initio calculations has been applied to the simple molecules F₂, H₂O and SO₂ The effects from varied basis sets for such deformation density were sought. The accumulation of electron density between the bonded atoms calculated from EHMO and ab initio methods with STO-3G is generally under-estimated. Such phenomena are significantly improved by using split-valence basis sets e.g. 3–21G and 4–31G. The addition of d polarization functions is apparently important for the sulfur atom in sulfur-related bonding. 3–21G or 3–21G^* basis sets were found to provide not only valuable deformation density distributions of molecules but also comparable orbital energy states with respect to the experimental values.     

The ring-opening of an unsymmetrical tetrahedral intermediate - 2-hydroxy-1,3-oxathiolane

Ab initio calculations were performed on 2-hydroxy-1,3-oxathiolane: and the two products of its breakdown: Complete geometry optimizations were performed at minimal (STO-3G) and split-valence (3-21G) basis set levels. In addition, a single point calculation was performed at 6-31G* level withd orbitals added on sulfur only. The conformation of the oxathiolane intermediate and its stability relative to the breakdown products was investigated. The STO-3G basis set gave an envelope form while 3-21G gave the twist form of the five-membered ring as the most stable. For all three basis sets the ester product was more stable than thioester.