Combined bond-polarization basis sets for accurate determination of dissociation energies. II. Basis set superposition error as a function of the parent basis set

The effect of the parent basis set on the basis set superposition error caused by bond functions is investigated systematically. An important difference between BSSE at the SCF and correlated levels is pointed out. Three new basis sets are defined, denoted 6-311 + G(d,p)B, 6-311 + G(2d,p)B, and 6-311 + G(2df,p)B. BSSE for the first-row hydrides seems to increase uniformly with increasing atomic number of the central atom. Expansion of the valence part of the basis set from 6-31G to 6-311G, as well as adding f functions, has a significant effect on the BSSE. Additional BSSEs incurred by bond functions are less than or equal to 1 kcal/mol for the 6-311 + G(2df,p)B basis set. For the dissociation energies of the first-row hydride species, agreement with experiment within only a few kcal/mol can be obtained even without resorting to isogyric reaction cycles. For high-quality calculations, adding bond functions seems to have definite advantages over expanding the polarization space beyond the [2d1f] level.     

On the additivity of basis set effects in some simple fluorine containing systems

The reactions F + H₂ → HF + H, HF → H + F, F → F⁺ + e^? and F + e^? → F^? were used as simple test cases to assess the additivity of basis set effects on reaction energetics computed at the MP4 level. The 6-31G and 6-311G basis sets were augmented with 1, 2, and 3 sets of polarization functions, higher angular momentum polarization functions, and diffuse functions (27 basis sets from 6-31Gd, p) to 6-31 ++ G(3df, 3pd) and likewise for the 6-311G series). For both series substantial nonadditivity was found between diffuse functions on the heavy atom and multiple polarization functions (e.g., 6-31 + G(3d, 3p) vs. 6-31 + G(d, p) and 6-31G(3d, 3p)). For the 6-311G series there is an extra nonadditivity between d functions on hydrogen and multiple polarization functions. Provided that these interactions are taken into account, the remaining basis set effects are additive to within ±0.5 kcal/mol for the reactions considered. Large basis set MP4 calculations can also be estimated to within ±0.5 kcal/mol using MP2 calculations, est. E_MP4(6-31 ++ G(3df, 3pd)) ≈ E_MP4(6-31G(d, p)) + E_MP2(6-31 ++ G(3df, 3pd)) – E_MP2(6-31G(d, p)) or E_MP4(6-31 + G(d, p) + E_MP2(6-31 ++ G(3df, 3pd)) – E_MP2(6-31 + G(d, p)) and likewise for the 6-311G series.     

Theoretical study of hydrogen-bonded formaldehyde complexes

The hydrogen-bonded complexes involving formaldehyde and a series of proton donors of varying strengths, have been investigated at different levels of ab initio MO theory. The structures of the studied complexes were SCF optimized at the 6-31G basis set level. The binding energy was estimated employing basis set superposition correction, zero-point vibrations and MP2 correlation contribution at the different basis set: STO-3G; 6-31G; MP2/6-31G; 6-31G**; MP2/6-31G**; 6-311G(2d, 2p) and MP2/6-311G(2d, 2p). Linear relationships were found of the calculated binding energy with: the calculated shift in the carbonyl stretching frequency, the changes in carbonyl bond length and the optimum value of hydrogen-bond distance; furthermore the calculations confirm a parallel trend between the proton-donor ability and the strength of the hydrogen bond.     

An ab initio molecular orbital study of the structures and energies of neutral and charged bimolecular complexes of NH3 with the hydrides AHn (A = N,O, F,P, S,and Cl)

Hartree-Fock 6-31G(d) structures for the neutral, positive ion, and negative ion bimolecular complexes of NH₃ with the first- and second-row hydrides AH_n (AH_n = NH₃, OH₂, FH, PH₃, SH₂, and ClH) have been determined. All of the stable neutral complexes except (NH₃)₂, the positive ion complexes with NH₃ as the proton acceptor, and the negative ion complexes containing first-row anions exhibit conventional hydrogen bonded structures with essentially linear hydrogen bonds and directed lone pairs of electrons. The positive ion complex NH₄⁺ …? OH₂ has the dipole moment vector of H₂O instead of a lone pair directed along the intermolecular line, while the complexes of NH₄⁺ with SH₂, FH, and ClH have structures intermediate between the lone-pair directed and dipole directed forms. The negative ion complexes containing second-row anions have nonlinear hydrogen bonds. The addition of diffuse functions on nonhydrogen atoms to the valence double-split plus polarization 6-31G(d,p) basis set usually decreases the computed stabilization energies of these complexes. Splitting d polarization functions usually destabilizes these complexes, whereas splitting p polarization functions either has no effect or leads to stabilization. The overall effect of augmenting the 6-31G(d,p) basis set with diffuse functions on nonhydrogen atoms and two sets of polarization functions is to lower computed stabilization energies. Electron correlation stabilizes all of these complexes. The second-order Møller–Plesset correlation term is the largest term and always has a stabilizing effect, whereas the third and fourth-order terms are smaller and often of opposite sign. The recommended level of theory for computing the stabilization energies of these complexes is MP2/6-31+G(2d,2p), although MP2/6-31+G(d,p) is appropriate for the negative ion complexes.     

Comparative theoretical and experimental analysis of hydrocarbon σ-radical cations

The structures of σ-radical cations formed by ionization of adamantane, twistane, noradamantane, cubane, 2,4-dehydroadamantane, and protoadamantane were optimized at the B3LYP, B3LYP-D, M06-2X, B3PW91, and MP2 levels of theory using 6-31G(d), 6-311+G(d,p), 6-311+G(3df,2p), cc-PVDZ, and cc-PVTZ basis sets. On the whole, single-configuration approximations consistently describe the structure and transformations of the examined σ-radical cations. The best correlations (r = 0.97–0.98) between the calculated adiabatic ionization potentials and experimental oxidation (anodic) potentials of hydrocarbons were obtained in terms of B3PW91 approximation.     

Proton affinities of molecules containing nitrogen and oxygen: comparing ab initio and semiempirical results to experiments

We report a comparison of theoretical and experimental proton affinities at nitrogen and oxygen sites within a series of small molecules. The calculated proton affinities are determined using the semiempirical methods AM 1, MNDO , and PM 3; the ab initio Hartree–Fock method at the following basis levels: 3-21G //3-21G , 3-21+G //3-21G , 6-31G *//6-31G *, and 6-31+G (d, p)//6-31G *; and Møller–Plesset perturbation calculations: MP 2/6-31G *//6-31G *, MP 3/6-31G *//6-31G *, MP 2/6-31G +(d, p)//6-31G *, MP 3/6-31G +(d, p)//6-31G *, and MP 4(SDTQ )/6-31G +G (d, p)//6-31G *. The semiempirical methods have more nonsystematic scatter from the experimental values, compared to even the minimal 3-21G level ab initio calculations. The thermodynamically corrected 6-31G *//6-31G * proton affinities provide acceptable results compared to experiment, and we see no significant improvement over 6-31G *//6-31G * in the proton affinities with any of the higher-level calculations. © 1992 John Wiley & Sons, Inc.     

Is tetrahedral H42+ a minimum? Anomalous behavior of popular basis sets with the standard p exponents on hydrogen

The nature of the tetrahedral H₄²⁺ stationary point (minimum or triply degenerate saddle) depends remarkably upon the theoretical level employed. Harmonic vibrational analyses with, e.g., the 6-31G** (and 6-31 + +G**) and Dunning's [4s2p1d;2s1p] [D95(d,p)] basis sets using the standard p exponent suggest (erroneously) that the T_d geometry is a minimum at both the HF and MP2 levels. This is not the case at definitive higher levels. The C₃H₄²⁺ structure with an apical H is another example of the failure of the calculations with the 6-31G**, 6-311G**, and D95(d,p) basis sets. Even at MP2/6-31G** and MP2/ cc-pVDZ levels, the C_3v structure has no negative eigenvalues of the Hessian. Actually, this form is a second-order saddle point as shown by the MP2/6-31G** calculation with the optimized exponent. The D_4h methane dication structure is also an example of the misleading performance of the 6-31G** basis set. In all these cases, energy-optimized hydrogen p exponents give the correct results, i.e., those found with more extended treatments. Optimized values of the hydrogen polarization function exponents eliminate these defects in 6-31G** calculations. Species with higher coordinate hydrogens may also be calculated reliably by using more than one set of p functions on hydrogen [e.g., the 6-31G(d,2p) basis set]. Not all cases are critical. A survey of examples, also including some boron compounds, provides calibration. © 1993 John Wiley & Sons, Inc.     

Optical rotation and two chiral C atoms of aliphatic cyclic dipeptides

Accurate geometries structures and total energies have been determined for the conformers of cyclo(L-Pro-Gly), cyclo(L-Ala-L-Ala), and cyclo(L-Pro-Ala) in the gaseous phase, using HF and B3LYP correlation methods at 6−31++G(d), 6−311++G(d, p), 6−311++G(2d, 2p) and aug-cc-pvdz basis sets. High level computations MP2 with 6−311++G(2d, 2p) basis set indicate that the relative stabilities of the available conformers can be determined correctly at the B3LYP/6−311++g(2d, 2p) level of theory. We have also described the implementation of DFT and HF theory for calculations of the optical rotation at 589.3 nm. In L-Ala-L-Ala, and L-Pro-Ala molecules, they have two chiral C (C*), so we discuss the different effect of two chiral C to optical activity of cydo(L-Pro-Gly), cyclo(L-Ala-L-Ala), and cyclo(L-Pro-Ala).     

Substituent effects in second-row molecules: Basis set performance in calculations of normal valency phosphorus and sulfur compounds

Ab inito molecular orbital calculations of the phosphorus- and sulfur-containing series PH₂X, PH₃X⁺, SHX, and SH₂X⁺ (X = H, CH₃, NH₂, OH, F) have been carried out over a range of Gaussian basis sets and the results (optimized geometrical structures, relative energies, and electron distributions) critically compared. As in first-row molecules there are large discrepancies between substituent interaction energies at different basis set levels, particularly in electron-rich molecules; use of basis sets lower than the supplemented 6-31G basis incurs the risk of obtaining substituent stabilizations with large errors, including the wrong sign. Only a small part of the discrepancies is accounted for by structural differences between the optimized geometries. Supplementation of low level basis sets by d functions frequently leads to exaggerated stabilization energies for π-donor substituents. Poor performance also results from the use of split valence basis sets in which the valence shell electron density is too heavily concentrated in diffuse component of the valence shell functions, again likely to occur in electron-rich molecules. Isodesmic reaction energies are much less sensitive to basis set variation, but d function supplementation is necessary to achieve reliable results, suggesting a marginal valence role for d functions, not merely polarization of the bonding density. Optimized molecular geometries are relatively insensitive to basis set and electron population analysis data, for better-than-minimal bases, are uniform to an unexpected degree.     

A study of basis set effects on structures and electronic structures of phosphine oxide and fluorophosphine oxide

A variety of basis sets have been used for geometric and electronic structure studies. Electronic effects were measured using integrated spatial electron populations (ISEP). The two largest basis sets used, 6-31G* and DZ+P, give significantly different results. Use of two d-orbital sets (6-31G*[dd]) or decontraction of the 2sp shell on phosphorus has little further effect. d-Orbitals on oxygen are required for consistent electronic structure results, and d-orbitals on fluorine have a small but significant effect. Use of diffuse functions, required for anions, is not recommended with small basis sets on neutral molecules. Large negative charges (≈?1.5) on oxygen are given by all of the larger basis sets by the ISEP procedure and indicate that the PO bond in these compounds is largely semi-polar. The best simple symbolic representation of phosphine oxide is H₃P⁺? 0^?, rather than H₃P?0.     

Blue‐shifted and red‐shifted hydrogen bonds: Theoretical study of the CH3CHO· · ·HNO complexes

The blue‐shifted and red‐shifted H‐bonds have been studied in complexes CH₃CHO…HNO. At the MP2/6‐31G(d), MP2/6‐31+G(d,p) MP2/6‐311++G(d,p), B3LYP/6‐31G(d), B3LYP/6‐31+G(d,p) and B3LYP/6‐311++G(d,p) levels, the geometric structures and vibrational frequencies of complexes CH₃CHO…HNO are calculated by both standard and CP‐corrected methods, respectively. Complex A exhibits simultaneously red‐shifted C? H…O and blue‐shifted N? H…O H‐bonds. Complex B possesses simultaneously two blue‐shifted H‐bonds: C? H…O and N? H…O. From NBO analysis, it becomes evident that the red‐shifted C? H…O H‐bond can be explained on the basis of the two opposite effects: hyperconjugation and rehybridization. The blue‐shifted C? H…O H‐bond is a result of conjunct C? H bond strengthening effects of the hyperconjugation and the rehybridization due to existence of the significant electron density redistribution effect. For the blue‐shifted N? H…O H‐bonds, the hyperconjugation is inhibited due to existence of the electron density redistribution effect. The large blue shift of the N? H stretching frequency is observed because the rehybridization dominates the hyperconjugation. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Quantum-chemical study on conformations of molecular complexes formed by 2-methyl-1,3,2-dioxaborinane with methylamine

Conformations of 1: 1 molecular complexes of 2-methyl-1,3,2-dioxaborinane with methylamine were studied in terms of restricted Hartree-Fock approximation using STO-3G, 3-21G, and 6-31G(d) bass sets. The results showed possible formation of two types of complexes, one with dative N→B bond, and the other with intermolecular hydrogen bond NH … O. Their relative stability and conformations are determined by both mutual orientation of the components and basis set used.     

Why betaine crystallizes in high local Cs symmetry. An ab initio MO and DFT study of anhydrous betaine and betaine monohydrate

A theoretical study of the structure, charge distribution, rotational barrier and fundamental vibrations of anhydrous betaine (CH₃)₃NCH₂COO (trimethylglycine) was carried out and compared with available experimental data. Calculations were carried out at HF, MP2 and B3LYP levels using a 6-31+G(d,p) basis set. The calculated rotational barrier of the betaine carboxylic group is 40.5 kJ/mol at the MP4(SDQ)/6-311G(d,p)//HF/6-31+G(d,p) level of theory. The rotation of the carboxylic group changes the molecule from a highly symmetric (C _s ) conformation into a twisted conformation resulting in shortening of the molecule by about 50 pm. Natural population analysis (NPA) indicates intramolecular interaction between the carboxylic oxygen and the nearest methyl hydrogens resulting in internal hydrogen bonding. MP4(SDQ)/6-311G(d,p) single-point NPA calculations on a betaine monohydrate model taken from the X-ray geometry show an expected weakening in the internal hydrogen bond. Calculations explain why betaine preferentially crystallizes in high local C _s symmetry. Received: 24 March 1998 / Accepted: 3 September 1998 / Published online: 7 December 1998     

The structure of 1-chlorosilatrane: An ab initio molecular orbital and a density functional theory study

The molecular geometries of the 1-chloro-, 1-fluoro-, 1-methyl-, and 1-hydrogenosilatranes were fully optimized by the restricted Hartree-Fock (HF) method supplemented with 3-21G, 3-21G(d), 6-31G(d), and CEP-31G(d) basis sets; by MP2 calculations using 6-31G(d) and CEP-31G(d) basis sets; and by GGA-DFT calculations using 6-31G(d5) basis set with the aim of locating the positions of the local minima on the energy hypersurface. The HF/6-31G(d) calculations predict long (>254 pm) and the MP2/CEP calculations predicted short (∼225 pm) equilibrium Si(SINGLE BOND)N distances. The present GGA-DFT calculations reproduce the available gas phase experimental Si(SINGLE BOND)N distances correctly. The solid phase experimental results predict that the Si(SINGLE BOND)N distance is shorter in 1-chlorosilatrane than in 1-fluorosilatrane. In this respect the HF results show a strong basis set dependence, the MP2/CEP results contradict the experiment, and the GGA-DFT results in electrolytic medium agree with the experiment. The latter calculations predict that 1-chlorosilatrane is more polarizable than 1-fluorosilatrane and also support a general Si(SINGLE BOND)N distance shortening trend for silatranes during the transition from gas phase to polar liquid or solid phase. The calculations predict that the ethoxy links of the silatrane skeleton are flexible. Consequently, it is difficult to measure experimentally the related bond lengths and bond and torsion angles. This is the probable origin of the surprisingly large differences for the experimental structural parameters. On the basis of experimental analogies, ab initio calculations, and density functional theory (DFT) calculations, a gas phase equilibrium (r_e) geometry is predicted for 1-chlorosilatrane. The semiempirical methods predict a so-called exo minimum (at above 310 pm Si(SINGLE BOND)N distance); however, the ab initio and GGA-DFT calculations suggest that this form is nonexistent. The GGA-DFT geometry optima were characterized by frequency analysis. © 1996 by John Wiley & Sons, Inc.     

Ab initio calculations on sulfur-containing compounds. II. One-electron properties of H2S

Closed-shell RHF one-electron properties are calculated for H₂S using a total of 41 different s, p basis sets and two polarized basis sets (6–31G* and 6–31G**). Total energies and geometries alone are not a comprehensive criteria for selecting the best basis sets. It is shown here that the comparison of a number of one-electron properties can serve as an excellent criteria for testing basis sets. The quality or reliability of a basis set is taken as being its agreement with a large uncontracted s, p basis set (s, p limit).     

Reliability of MEP and MEP-derived properties computed from DFT methods for molecules containing P, S and CL

We present a systematic study on the reliability of different theoretical methods to represent the molecular electrostatic potential (MEP), and MEP-derived properties of prototypical compounds containing phosphorus, sulfur and chlorine. Calculations at the Hartree-Fock and M?ller-Plesset up to fourth-order level of theory, as well as local, non-local and hybrid density functional computations were performed for a representative set of neutral molecules. The study was carried out using different basis sets ranging from the medium-sized 6-31G(d ) to the large 6-31G(2d,2p) basis set, but in some test calculations more extended basis sets were also considered. The analysis of the results was performed discussing separately the effect of the basis set and of the level of theory used to determine the molecular wavefunction on the reliability of the MEP and MEP-derived properties. Received: 4 March 1997 / Accepted: 27 June 1997     

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     

A comparative quantum mechanical study of bond separation energies as a measure of cyclic conjugation

Restricted Hartree-Fock (RHF), second-order Møller-Plesset (MP2), and density functional calculations [using the Becke/Lee-Yang-Parr (B-LYP) exchange/correlation gradient-corrected functionals] employing the 6-311G(d, p) and 6-311 + + G(d, p) basis sets have been carried out to calculate isodesmic bond separation energies for reactions involving a number of representative five- and six-membered ring organic compounds. The MP2 and density functional approaches yield reasonably good energies; the density functional method agrees particularly well with experiment, exhibiting a root-mean-square error of only 2.5 kcal/mol. Ring geometries are calculated satisfactorily in all approaches but are given particularly accurately by the MP2 approach. A comparison of the B-LYP bond separation energies with several other definitions of resonance energy shows that these different approaches correlate with each other in a reasonable fashion. © 1995 John Wiley & Sons, Inc.