Basis set and correlation effects on computed positive ion hydrogen bond energies of the complexes AHn · AHn + 1+1: AHn = NH3, OH2, and FH

Basis set expansion and correlation effects on computed hydrogen bond energies of the positive ion complexes AH_n · AH_{n + 1}⁺¹, for AH_n = NH₃, OH₂ and FH, have been evaluated. The addition of diffuse functions on nonhydrogen atoms is the single most important enhancement of split-valence plus polarization basis sets for computing hydrogen bond energies. Basis set enhancement effects appear to be additive in these systems. The correlation energy contribution to the stabilization energies of these complexes is significant, with the second order term being the largest term and having a stabilizing effect. The third order term is smaller and of opposite sign, while the fourth order term is smaller yet and stabilizing. As a result, computed MP4 stabilization energies are bracketed by the MP2 and MP3 energies. The overall effect of basis set enhancement is to decrease hydrogen bond energies, whereas the addition of electron correlation increases stabilization energies.     

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.     

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.     

An ab initio study of the structures and enthalpies of the hydrogen-bonded complexes of the acids H2O,H2S,HCN, and HCl with the anions OH−, SH−, CN−, and Cl−

Ab initio calculations at second-order Møller-Plesset perturbation theory with the 6-31 + G(d,p) basis set have been performed to determine the equilibrium structures and energies of a series of negative-ion hydrogen-bonded complexes with H₂O, H₂S, HCN, and HCl as proton donors and OH^–, SH^–, CN^–, and Cl^– as proton acceptors. The computed stabilization enthalpies of these complexes are in agreement to within the experimental error of 1 kcal mol^–1 with the gas-phase hydrogen bond enthalpies, except for HOHOH^–, in which case the difference is 1.8 kcal mol^–1. The structures of these complexes exhibit linear hydrogen bonds and directed lone pairs of electrons except for complexes with H₂O as the proton donor, in which cases the hydrogen bonds deviate slightly from linearity. All of the complexes have equilibrium structures in which the hydrogen-bonded proton is nonsymmetrically bound, although the symmetric structures of HOHOH^– and ClHCl^– are only slightly less bound than the equilibrium structures. MP2/6-31 + G(d,p) hydrogen bond energies calculated at optimized MP2/B-31 + G(d,p) and at optimized HF/6-31G(d) geometries are similar. Using HF/6-31G(d) frequencies to evaluate zero-point and thermal vibrational energies does not introduce significant error into the computed hydrogen bond enthalpies of these complexes provided that the hydrogen-bonded proton is definitely nonsymmetrically bound at both Hartree-Fock and MP2.     

Complexes of ammonia with propane and cyclopropane: electrostatic guidelines for ab initio treatment

A model based on the molecular electrostatic potential (MESP) is employed for the investigation of structures and energies of complexes of ammonia with propane and cyclopropane. The electrostatic model geometries are employed as starting points for an ab initio investigation at the self-consistent field and second-order M?ller-Plesset (MP2) levels. The most stable structures of C₃H₆..NH₃ and C₃H₈..NH₃ complexes have the interaction energies of 10.07 kJ/mol and 8.15 kJ/mol, respectively, at the MP2/6-31G(d,p) level. The energy rank order of the structures is not altered with the use of the 6-31++G(d,p) basis set, and the basis␣set superposition error has little effect. The interaction energy decomposition analysis shows that the electrostatic component is dominant over the other ones. MESP topography thus seems to offer valuable hints for predicting the structures of weakly bonded complexes. Received: 8 July 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

Gradient optimization of polarization exponents inab initio MO calculations on H2SO → HSOH and CH3SH → CH2SH2

Summary Analytical gradients were used to optimize the polarization function exponents in the 6-31G(d) and 6-31G(d, p) basis sets for the reactants, transition structures and products in the reactions H₂SO HSOH and CH₃SH CH₂SH₂. The optimizedd exponents on the heavy atoms change by ±10% in the course of the reactions and depend on the bonding of the heavy atoms. Thep exponents on the hydrogens change by as much as a factor of 5 and depend on the element to which the hydrogen is bonded and its valency. The effect of exponent optimization on the relative energies is small (±3 kcal/mol). With the 6-31G(d, p) basis set, optimization of the polarization exponents can make some of the bonds significantly more polar, as judged by the Mulliken charges.     

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.     

Rivalry between Regium and Hydrogen Bonds Established within Diatomic Coinage Molecules and Lewis Acids/Bases

A theoretical study of the complexes formed by Ag₂ and Cu₂ with different molecules, XH (FH, ClH, OH₂, SH₂, HCN, HNC, HCCH, NH₃ and PH₃) that can act as hydrogen-bond donors (Lewis acids) or regium-bond acceptors (Lewis bases) was carried out at the CCSD(T)/CBS computational level. The heteronuclear diatomic coinage molecules (AuAg, AuCu, and AgCu) have also been considered. With the exception of some of the hydrogen-bonded complexes with FH, the regium-bonded binary complexes are more stable. The AuAg and AuCu molecules show large dipole moments that weaken the regium bond (RB) with Au and favour those through the Ag and Cu atoms, respectively.     

Ab initio molecular-orbital study of the binding of ZnII with SH2 and SH−

This paper reports an ab initio molecular-orbital (MO ) study of binding of SH₂ and SH^? with Zn^II. The mechanism of binding of Zn^II with these ligands is investigated using a detailed analysis of the energy decomposition and of the electronic distribution. The dependence of the results on the choice of the basis set for sulfur (in particular the effect of incorporation of diffuses p and d orbitals) on the geometry of ligand binding, the binding energy, and the proton affinity of SH^? are investigated. Comparison made with the corresponding results concerning the binding of OH₂, OH^?, and NH₃ shows that sulfur binding is less favorable although more covalent. Both sulfur ligands show a marked preference for angular conformations for binding with the metal ion. The effect of Zn^II binding on the ease of deprotonation of H₂S is quite similar to the corresponding effect found earlier for H₂O.     

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.     

Ab initio models for multiple-hydrogen exchange: Comparison of cyclic four- and six-center systems

High-level ab initio calculations {QCISD(T)/6-311 +G**//MP2(fu)/6-31 +G**, with corrections for higher polarization [evaluated at MP2/6-311 +G(3df,2p)] and ΔZPE//MP2(fu)/6-31 +G**, i.e., comparable to Gaussian-2 theory} indicate concerted mechanisms for double- and triple-hydrogen exchange reactions in HF and HCl dimers and trimers, in mixed dimers and trimers containing one NH₃, and in mixed dimers of HF, HCl, and NH₃ with formic acid. All these reactions proceed via cyclic four- or six-center transition structures, the latter being generally more favorable. Calculated activation barriers (ΔH^d? at 0 K, kcal/mol) are 42.3 for (HF)₂, 20.3 for (HF)₃, 41.2 for (HCl)₂, 25.6 for (HCl)₃, 36.0 for NH₃-HF, 10.6 for NH₃(HF)₂, 19.9 for NH₃-HCl, 2.3 for NH₃(HCl)₂, 9.7 for HCO₂H-HF, 7.0 for HCO₂H-HCl, and 11.3, for HCO₂H-NH₃. The barriers are lower for the more ionic systems and when more ion pair character is present. © John Wiley & Sons, Inc.     

An ab initio study of the structure,dissociation energy,and heat of formation of Na2S

The equilibrium geometries and fundamental frequencies of Na₂S are calculated at HF, MP2(FC, FU), and MP3 with the 6–31G(d) basis set and at HF and MP2(FC, FU) with the 6–31G(d) basis set, respectively. The total energy at MP2(FU)/6–31G(d)-optimized geometry is computed at MP4 with 6–311G(d, p), 6–311 + G(d, p), and 6–311G(2df, p), at QCISD(T)/6–311G(d, p), and at MP2/6–311G(3df, 2p) levels, respectively. The dissociation energy, the atomization energy, and the heat of formation for Na₂S are evaluated using the G1 and G2 models. The calculated results indicated that Na₂S in its ground state was a bent structure (C_2v). Electron correlation corrections on the bending angle are very significant. The equilibrium geometrical parameters are R_e(Na-S) = 2.45 Å and ∠Na-S-Na = 111.13° at the MP2(FU)/6–31G(d) level. The theoretically estimated dissociation energy, total atomization energy, and heat of formation are 67.07, 117.55, and 0.35 kcal mol⁻¹, respectively, at 298.15 K. © 1997 John Wiley & Sons, Inc.     

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.     

Supplementary d and f functions in molecular wave functions: Optimum and nonoptimum exponents

Energy optimization calculations have been carried out to determine the variability of optimum p, d, and f polarization function exponents in molecules containing first- and second-row elements and in normal valency and hypercoordinate species. Optimum exponents were determined for single sets of higher-order functions at both Hartree–Fock and correlated (Moller–Plesset) levels of theory using the Dunning–Hay double zeta and the McLean–Chandler triple zeta basis sets. More detailed calculations were used to test the response to nonoptimum d and f function exponents of the total energy, the optimum geometry, and harmonic stretching frequencies. The variability in optimum exponents and the size of the energy penalties incurred by adopting nonoptimum values reduces the utility of standard exponents for p, d, and f polarization functions. © 1993 John Wiley & Sons, Inc.     

Long‐range π‐type hydrogen bond in dimers CH2?HF,CH2O?H2O,and CH2O?NH3

Using four basis bets, (6‐311G(d,p), 6‐31+G(d,p), 6‐31++G(2d,2p), and 6‐311++G(3df,3pd), the optimized structures with all real frequencies were obtained at the MP2 level for the dimers CH₂O? HF, CH₂O? H₂O, CH₂O? NH₃, and CH₂O? CH₄. The structures of CH₂O? HF, CH₂O? H₂O, and CH₂O? NH₃ are cycle‐shaped, which result from the larger bend of σ‐type hydrogen bonds. The bend of σ‐type H‐bond O…H? Y (Y?F, O, N) is illustrated and interpreted by an attractive interaction of a chemically intuitive π‐type hydrogen bond. The π‐type hydrogen bond is the interaction between one of the H atoms of CH₂O and lone pair(s) on the F atom in HF, the O atom in H₂O, or the N atom in NH₃. In contrast with the above three dimers, for CH₂O? CH₄, because there is not a π‐type hydrogen bond to bend its linear hydrogen bond, the structure of CH₂O? CH₄ is noncyclic shaped. The interaction energy of hydrogen bonds and the π‐type H‐bond are calculated and discussed at the CCSD (T)/6‐311++G(3df,3pd) level. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

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.     

Basis set and correlation effects on computed lithium ion affinities of some oxygen and nitrogen bases

Basis set expansion and correlation effects on computed lithium cation affinities have been evaluated for the oxygen and nitrogen bases CH₃OH, H₂CO, CO, CH₃NH₂, CH₂NH, and HCN. The presence of diffuse functions on nonhydrogen atoms is found to be the most important single enhancement of double- and triple-split valence plus polarization basis sets. With the triple-split basis, enhancement effects are nearly additive. Correlation usually decreases computed lithium ion affinities, with the second order Møller-Plesset correlation term being the dominant term.     

Degenerate lithium-hydrogen exchange reactions: Ab initio models for metallation mechanisms involving H2, CH4, NH3, H2O,and HF

Hydrogen exchange reactions between lithium and sodium compounds, MX (M=Li: X=H, CH₃, NH₂, OH, F; M=Na: X=CH₃), and the corresponding hydrides, HX, have been modelled by means of ab initio calculations including electron correlation and zero point energy (ZPE) corrections. Small or no activation barriers (from the initial complexes) are encountered in systems involving lone pairs (10.8, 2.4, 0.0 kcal/mol for X=NH₂, OH, F, respectively). Since the association energies of the initial complexes are much larger (21.0, 20.4, 23.5 kcal/mol, respectively; MP2/6–31+G*/6–31+G* + ZPE), such exchange reactions should occur spontaneously in the gas phase. The methyl systems (X=CH₃) have the largest barriers: 26.7 (M=Li) and 31.7 (M=Na) kcal/mol (MP2/6–31+G*/6–31G* + ZPE), and the initial complexes are only weakly bound. The significance of these systems as models for hydrogen exchange reactions in complexes of electropositive transition metals is discussed. However, the gegenion-free exchange of hydrogen between CH₃ and CH₄ has a much lower, 11.8 kcal/mol barrier (MP2/6–31+G*/6–31+G* + ZPE). All the transition structures are highly ionic (charges on the metals > +0.8). The effect of aggregation has been considered by examining the hydrogen exchange between (LiX)₂ and HX(X=H, CH₃, NH₂, OH). Although these dimer reactions formally involve six, instead of four electrons, no “aromatic” preference is observed.