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.     

Cooperative effects in extended hydrogen bonded systems involving O?H groups. Ab initio studies of the cyclic S4 water tetramer

The additional energy stabilization due to cooperative effects was calculated in extended hydrogen bonded systems O? H ?O? H ?O? H with unidirectional (homodromic) orientation of the O? H groups. Ab initio restricted Hartree Fock, MP2 and MP3 calculations with geometry optimization and BSSE correction have been performed using the GAUSSIAN 83 program package for the ground states of the linear water dimer with C_s symmetry and the cyclic water tetramer with S₄ symmetry. The latter represents the smallest possible, experimentally observed cooperative structure. A new definition for a cooperativity parameter is proposed. The definition is based on the two-body, non-neighbour interaction energy, plus three- and four-body contributions, including one-body deformation terms in relation to the total interaction energy of the water tetramer. The advantage of this definition is its independence of the reference system, which is necessary in complicated molecular systems with an undefined number of hydrogen bonds, such as disordered or flip-flop systems. According to this definition the energy gain based on cooperativity in the S₄ water tetramer is 29% with the MP3/6-31G** approximation, (30% with HF/4-31G* and 46% with HF/3-21G). The largest contribution of 18% is due to the three-body term on the MP3/6-31G** level, followed by the two-body, non-neighbour term with 11%. The four-body term and the deformation term are in the order of 1% and cancel each other because they have opposite sign.     

Ab initio study of the ground and excited states of HCP and its isomer HPC

The potential energy surface of HCP converting to HPC in its ground electronic state has been investigated with ab initio methods at levels up to MP2/6-311G**//MP4/6-311G** as well as TZV + + ** CASSCF. All geometries are fully optimized and compare favorably to previous theoretical and experimental values. The HCP molecule is predicted to be 85.4 kcal/mol lower in energy than its linear isomer at the-MP2/6-31G*//MP2/6-31G* level. The energy barrier for hydrogen rearrangement is found to be merely 2.3 kcal from the HPC end. CASSCF studies were initiated to clarify the low barrier and lent support to a flat surface as HPC converts to stable, linear HCP at the TZV + + ** level. CASSCF also predicts that HPC is unstable with respect to bending. Harmonic vibrational frequencies for HCP results in 5% accuracy or better. A bent triplet is found to be the lowest excited state using the CASSCF method. © 1993 John Wiley & Sons, Inc.     

Conformational study of the structure of free 12-thiacrown-4 and some of its cation metal complexes

Conformational search of 12-thiacrown-4, 12t4, was performed using the CONFLEX method and the MMFF94S force field whereby 156 conformations were predicted. Optimized geometries of the 156 predicted conformations were calculated at the HF, B3LYP, CAM-B3LYP, M06, M06L, M062x and M06HF levels using the 6-311G** basis set. The correlation energy was recovered at the MP2 level using the same 6-311G** basis set. Optimized geometries at the MP2/6-311G** level and G3MP2 energies were calculated for some of the low energy conformations. The D ₄ conformation was predicted to be the ground state conformation at all levels of theory considered in this work. Comparison between the dihedral angles of the predicted conformations indicated that for the stability of 12t4, a SCCS dihedral angle of 180° requirement is more important than a gauche CSCC dihedral angle requirement. Conformational search was performed also for the 12t4?CAg⁺, Bi³⁺, Cd²⁺, Cu⁺ and Sb³⁺ cation metal complexes using the CONFLEX method and the CAChe-augmented MM3 and MMFF94S force fields. Conformations with relative energies less than 10?kcal/mol at the MP2/6-31+G*//HF/6-31+G* level, with double zeta quality basis set on the metal cations, were considered for computations at the same levels as those used for free 12t4, using also the 6-311G** basis set. The cc-pVTZ-pp basis set was used for the metal cations. The predicted ground state conformations of the 12t4?CAg⁺, Bi³⁺, Cd²⁺, Cu⁺ and Sb³⁺ cation metal complexes are the C ₄, C ₄, C ₄, C _2v and C ₄ conformations, respectively. This is in agreement with the experimental X-ray data for the 12t4?CAg⁺ and Cd²⁺ cation metal complexes, but experimentally by X-ray, the 12t4?CBi³⁺ and Cu⁺ cation metal complexes have C _s and C ₄ structures, respectively.     

Conformational energies and rotational barriers in 3-methyl-1-butene and 1-butene: An ab initio and molecular mechanics study

The calculated result obtained with MM2(87) for the rotation of the isopropyl group in 3-methyl-1-butene is not in agreement with experimental data. In order to reparametrize the C_sp2-C_sp3-C_sp-C_sp3 torsional angle, 3-methyl-1-butene and 1-butene have been studied by molecular mechanics (MM2(87)) and ab initio (MP2/6-31G* and MP3/6-31G*) calculations. The reparametrization of the torsional angle gives calculated results from MM2(87) in agreement with experimental data and ab initio calculations for both 3-methyl-1-butene and 1-butene. The calculated barriers for the rotation of alkyl groups in alkylbenzenes are improved with these new parameters.     

Theoretical studies of structure,stability, and chemical bonding in oxohydride OM4H6 complexes

The results of ab initio RHF/3-21G, RHF/6-31G*, and MP2/6-31G** / / HF/6-31G* calculations for 10 possible configurations of OM₄H₆ molecules (MO · 3MH₂, M = Be, Mg) are reported. Five isomers of OBe₄H₆ and three isomers of OMg₄H₆ have been found within an energy range of ã 15 kcal mol⁻¹. The “lanternlike” C_3v structure is the most favorable one for both complexes. Both molecules OM₄H₆ are stable to decomposition through all of the studied pathways. Chemical bonding in the OM_k polyhedra containing two-, three-and four-coordinated oxygen atoms is discussed. © 1996 John Wiley & Sons, Inc.     

Ab initio potential energy curve for CH bond dissociation in methane

Ab initio calculations on CH₄ → CH₃ + H were performed at the MP4/6-31G** level including all single, double triple and quadruple excitations. Although triple excitations have little effect on the dissociation energy, they are very important in the 2–3 Å range. The potential curve appears to rise more sharply than a Morse curve in this region. Correlation effects are not important for the HCH angle optimization.     

Ab initio study of possible intermediates in the no(4Π) catalyzed geometric isomerizations of olefins

The geometries of acyclic and three-membered ring (nitroxide) H₄C₂NO radicals in their ground ²Π electronic states have been optimized completely at ab initio UHF and ROHF theoretical levels with the STO-3G and the 6-31G** basis sets. The optimizations favour the cyclic nitroxide structure energetically. However ΔE(acyclic - cyclic) at the UHF and ROHF/6-31G** levels are only 3.2 and 1.9 kcal mol^-1, respectively. Incomplete MP2/6-311G** optimizations support these results. The zero-point energy computed at the ROHF/6-31G** level for the nitroxide radical is 2.5 kcal mol^-1 higher than that for the acyclic structure, thus reversing the relative energies by 0.6 kcal mol^-1. The energies of the two radical structures, relative to the sum of those for ethylene and NO, are very close to literature values of the activation energies for the thermal, NO catalyzed geometrical isomerizations of olefins. Thus cyclic nitroxide intermediates may play a role not only in the Hg 6(³P₁) photosensitized, but also in the thermal, NO-catalyzed geometric isomerizations of olefins. Paper dedicated to Professor Otto P. Strausz; presented in part at the 75th Canadian Chemical Congress and Exhibition, Edmonton, May 31 – June 4, 1992.     

Ab initio study of the formation of C3H3+ from the reaction of CH3+ with acetylene

Ab initio molecular orbital theory has been used to study the mechanism of the formation of C₃H₃⁺ from the reaction of CH₃⁺ with acetylene. The highest level geometry optimizations and frequencies were computed at MP2-FC/6-31G**; single point energies of all the critical structures were computed to the MP4-FC/6-31G**//MP2-FC/6-31G** theory level. One of the three alternative transition structures leading to the formation of C₃H₃⁺ gives the cyclopropenyl cation and the other two the propargyl cation. The proportions of C₃H₂D⁺ and C₃HD₂⁺ obtained when CD₃⁺ reacts with acetylene, and the composite nature of the metastable peak observed for the [C₃H₅]⁺→[C₃H₃]⁺ + H₂ fragmentation are explained by assuming a different degree of deuterium scrambling depending on the energy of the system. © 1996 by 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.     

Ab initio molecular orbital calculations for 3,6-dihydro-1,2-dithiin and 3,6-dihydro-1,2-dioxin

Optimized geometries and total energies for the conformers of 3,6-dihydro-1,2-dithiin ( 2 ) and 3,6-dihydro-1,2-dioxin ( 3 ) were calculated at several ab initio MO levels: RHF/3-21G(*), RHF/6-31G*, MP2/6-31G*, and MP2/6-31G*/ /RHF/3-21G(*). For the dioxin, in addition to the above levels the corresponding nonextended basis sets ab initio methods were also carried out. The dithiin results are compared with those of simple disulfanes, HSSH and (CH₃)₂S₂, whose optimized geometries agree closely with the observed structures, which is the gauche (C₂ symmetry). For the disulfanes, the gauche geometries from RHF/3-21G(*) are in good agreement with the observed structure while the RHF/3-21G results best fit the dioxin. Pertinent structural data at the RHF/3-21G(*) for the half-chair (C₂) dithiin are: bond lengths, ? SS? , ? CS? , ? CC?, and ? C?C? , 2.050, 1.817, 1.515, and 1.317 Å, respectively; bond angles, CSS, ?CCS, and C?CS, 98.0, 114.2, and 127.8°, respectively; CSSC dihedral angle of 63.2°; and twist angle of 36.5°. The total energy for half-chair dithiin at MP2/6-31G*//RHF/3-21G(*) is less than the planar (C_2v) and the half-boat (C_s) structures by 69.67 and 29.05 kJ/mol, respectively. The calculated structural data (vs. observed) at RHF/3-21G for the half-chair dioxin are: bond lengths, ? OO? , ? CO? , ? CC?, and C?C, 1.464 (1.463), 1.454, 1.509, and 1.313 Å (1.338 Å), respectively; bond angles, COO, ?CCO, and C?CO, 105.0, 109.8 (110.3), and 120.7° (119.9°), respectively; COOC dihedral angle of 79.7° (80 ± 2°); and twist angle of 39.0 (38.3°). The total energy for half-chair dioxin at MP2/6-31G//RHF/3-21G is less than the planar and the half-boat structures by 70.35 and 42.85 kJ/mol, respectively. The total energies calculated at the extended basis sets (*) ab initio levels for the C₂ symmetry dioxin are much lower than those of the nonextended basis sets. © John Wiley & Sons, Inc.     

Structure of bis(trifluoromethanesulfonyl)imide in inert and protophilic media

According to the data of IR spectroscopy, dielectrometry, and HF/6-31G**, B3LYP/6-311G** quantum chemical calculations bis(trifluoromethanesulfonyl)imide (CF₃SO₂)₂NH in nonpolar medium (CCl₄) exists as an H-complex formed by its molecules in two tautomeric (NH and OH) forms. In a polar medium (CH₂C1₂) linear chain polyassociates with a bifurcate hydrogen bond are formed similar to those existing in the crystal. In the presence of protophilic solvents ion pairs consisting of the protonated molecule of the base and dimeric anion of bis(trifluoromethanesulfonyl)imide are formed.     

Electronic structure of X2 Y3 molecules (X = B, Al, Ga; Y = O,S): A theoretical study

Ab initio molecular orbital and density functional theory calculations on X₂Y₃ (X = B, Al,Ga; Y = O,S) indicate a bent structure withC _2v symmetry to be the preferred arrangement for B₂ O₃, B₂ S₃ and Al₂S₃. In contrast, the linear isomer is favoured for Al₂ O₃ and Ga₂ O₃. These are in agreement with the experimentally observed structures. The electronegativity difference between X and Y, the MO patterns and the ionic nature of the bonding explain variations in the molecular structure. The results from the two theoretical approaches (MP2/6-31G* and Becke3LYP/6-311 +G* level) are comparable.     

Conformers and intramolecular hydrogen bonding of the oxalic acid monomer and its anions

Density functional theory, B3LYP/6‐31G** and B3LYP/6‐311+G(2d,p), and ab initio MP2/6‐31G** calculations have been carried out to investigate the conformers, transition states, and energy barriers of the conformational processes of oxalic acid and its anions. QCISD/6‐31G** geometrical optimization is also performed in the stable forms. Its calculated energy differences between the two most stable conformers are very near to the related observed value at 7.0 kJ/mol. It is found that the structures and relative energies of oxalic acid conformers predicted by these methods show similar results, and that the conformer L1 (C_2h) with the double‐interfunctional‐groups hydrogen bonds is the most stable conformer. The magnitude of hydrogen bond energies depends on the energy differences of various optimized structures. The hydrogen bond energies will be about 32 kJ/mol for interfunctional groups, 17 kJ/mol for weak interfunctional groups, 24 kJ/mol for intra‐COOH in (COOH)₂, and 60 kJ/mol for interfunctional groups in (COOH)COO⁻¹ ion if calculated using the B3LYP/6‐311+G(2d,p) method. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 541–551, 2000     

Infrared predissociation spectroscopy of ammonia cluster cations (NH3)n+ (n=2-4) produced by vacuum-ultraviolet photoionization

Infrared predissociation spectroscopy of vacuum ultraviolet-pumped ion (IRPDS-VUV-PI) is performed on ammonia cluster cations (NH3)n+ (n=2-4) that are produced by VUV photoionization in supersonic jets. The structures of (NH3)2+ and (NH3)4+ are determined through the observation of infrared spectra and vibrational calculations based on ab initio calculations at the MP2/6-31G** and 6-31++G** levels. (NH3)2+ is found to be of the "hydrogen-transferred" form having the (H3N+-...NH2) composition. In contrast, (NH3)4+ exhibits the "head-to-head" dimer cation (H3...NH3+ core structure, where the positive charge is shared between two ammonia molecules in the core, and two other molecules are hydrogen bonded onto the core. An unequivocal assignment of the infrared spectrum of (NH3)3+ has not been achieved, because the presence of two isomeric structures could be suggested by the observed spectrum and theoretical calculations.     

An Ab Initio Study of the Complexes Formed by the Positive Acetylene Ion with the Hydrogen and Nitrogen Molecules and the Argon Atom

The complexes formed by the positive acetylene ion with the hydrogen molecule, the nitrogen molecule, and the argon atom are investigated with ab initio calculations using the 6-311G** and the 6-31+G(2df,2pd) basis sets. MP2/6-311G** energies and optimum geometries are obtained, as well as single-point MP3, MP4, and QCISD(T) energies with the MP2/6-311G** optimized geometries. Single-point calculations are performed with the 6-31+G(2df,2pd) basis set at MP2/6-311G** optimized geometries.     

Ab initio study of hydrogen bonding in the phenol–water system

Three hydrogen-bonded minima on the phenol-water, C₆H₅OH—H₂O, potential energy surface were located with 3–21G and 6–31G** basis sets at both Hartree–Fock and MP2 levels of theory. MP2 binding energies were computed using large “correlation consistent” basis sets that included extra diffuse functions on all atoms. An estimate of the effect of expanding the basis set to the triple-zeta level (multiple f functions on carbon and oxygen and multiple d functions on hydrogen) was derived from calculations on a related prototype system. The best estimates of the electronic binding energies for the three minima are –7.8, –5.0, and –2.0 kcal/mol. The consequences of uncertainties in the geometries and limitations in the level of correlation recovery are analyzed. It is suggested that our best estimates will likely underestimate the complete basis set, full CI values by 0.1–0.3 kcal/mol. Vibrational normal modes were determined for all three minima, including an MP2/6–31G** analysis for the most strongly bound complex. Computational strategies for larger phenol–water complexes are discussed. © John Wiley & Sons, Inc.     

Quantum-Chemical Study of Alkyl Carbenium Ions in 100% Sulfuric Acid

A quantum-chemical study of neutral and protonated monoalkyl sulfates RHSO₄and [RH₂SO₄]⁺(where R = CH₃, C₂H₅, iso-C₃H₇, and tert-C₄H₉) is carried out. Calculations are performed using the Hartree–Fock method in the 6-31G** and 6-31++G** basis sets taking into account electron correlation according to the Müller–Plesset perturbation theory MP2/6-31+G*//6-31+G*. Protonated tert-butyl sulfate was also calculated by the DFT B3LYP/6-31++G** method. It was found that monoalkyl sulfates are covalent compounds, and the complete abstraction of alkyl carbenium ions from them has substantial energy cost: 196.4, 161.7, 150.8 and 136.0 kcal/mol, respectively. Protonated methyl and ethyl sulfates are also covalent compounds according to the calculation. They have lower but still high energies of heterolytic dissociation (65.0 and 33.5 kcal/mol, respectively). The energy of R⁺abstraction from protonated isopropyl sulfate is much lower: 23.6 kcal/mol. The main covalent state and the ion–molecular pair, which is a carbenium ion [C(CH₃)₂H]⁺solvated by the H₂SO₄molecule, have about the same energy. The ground state of protonated tert-butyl sulfate corresponds to the ion–molecular complex [C(CH₃)⁺ ₃H₂SO₄] with still lower energy of carbenium ion [C(CH₃)₃]⁺abstraction, which is equal to 10.0 kcal/mol. Calculation according to the DFT B3LYP/6-31++G** method shows the absence of a minimum for the protonated tert-butyl sulfate with a covalent structure on the potential energy surface.     

Methanediol decomposition mechanisms: A study considering various ab initio approaches

The alternative decomposition reactions CH₂(OH)₂ → CH₂O + H₂O and CH₂(OH)₂ + H₂O → CH₂O + 2H₂O are investigated using the semiempirical PM 3 as well as the ab initio HF /3-21G , HF /6-31G , HF /6-31G **, and MP 2/6-31G ** calculations. Reactants, products, and appropriate transition states are located on corresponding potential energy surfaces and compared with those reported in earlier studies. © 1996 John Wiley & Sons, Inc.     

Steric and Electronic Structure of C6H5XCF3 Molecules (X = O or S): A Quantum-Chemical Study

The potential functions of internal rotation around the Csp ²-X bond in C₆H₅XCF₃ molecules (X = O or S) were obtained by quantum-chemical calculations in the HF/6-31G(d), MP2(f)/6-31G(d), and B3LYP/6-31G(d) approximations. The calculations were performed in the range of torsion angles (angle between the planes of the benzene ring and Csp ²-X-Csp ³ bonds) from 0° to 90° with a 15° step. The barriers to rotation around the Csp ²-X bonds (kJ mol^{- 1}) were evaluated: for C₆H₅XCF₃, 7.60 (HF), 3.04 (MP2), and 1.04 (B3LYP); for C₆H₅XCF₃, 16.57 (HF), 14.67 (MP2), and 8.73 (B3LYP). The geometries (bond angles and bond lengths), Koopmans ionization potentials, and dipole moments of the molecules were calculated. The hybridization, energy, and population of the lone electron pairs of the heteroatoms, and also the energy of their resonance interaction with antibonding orbitals and the natural atomic charges were evaluated using the NBO approach.