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.     

Does CH prefer a C2v rather than a Cs structure?

The closely related C_s ( 1 ) and C_2v ( 3 ) structures of CH have been reinvestigated at many ab initio levels using MP2/6-31G** and MP2/6-311 + + G(2df, 2pd) geometries. The largest basis sets employed were 6-311G(3df, 2p), 6-311 + + G(3df, 3pd), and the Dunning “correlation consistent” polarized triple-split valence basis set (cc-pVTZ). Electron correlation was probed at the MP4 level, but the QCISD method was also used with the largest basis sets. While electron correlation favors 3 over 1 by about 2 kcal/mol, the correlated relative energies with all basis sets employed range from 0.36–1.03 kcal/mol in favor of 1 . The best estimate of this difference, 0.86 kcal/mol, is essentially identical with the (scaled) zero-point energy difference, 0.84 kcal/mol, favoring 3 over 1 . These results indicate that 1 and 3 have almost exactly the same energy at 0 K. Our best value for the dissociation energy of CH is 42.0 kcal/mol [QCISD(T)/6-311 + + G(3df, 3pd)//MP2(fu)/6-311 + + G(2df, 2pd), corrected to 298 K], which agrees very well with the experimental value. © 1992 by John Wiley & Sons, Inc.     

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.     

Thermodynamic functions of lactams in the ideal gas state

Thermodynamic functions (enthalpy, entropy, free energy, and heat capacity) of azacycloalkan-2-ones with ring sizes n = 4–8 in the ideal gas state are calculated by means of quantum chemistry and statistical physics, using an anharmonic approximation in the range of 298–1500 K with allowance for all known conformers and optical isomers. Equilibrium structures and total energies of lactams are calculated using the B3LYP/6-311++G(3df, 3pd), B3LYP/aug-cc-pVQZ, and MP2/6-311++G(3df, 3pd) methods, and the anharmonic frequencies of the fundamental vibrations of all the investigated structures were found via B3LYP/6-311++G(3df, 3pd).     

Potential Energy Surface of Cooperative Proton Tunneling in the C2H+ 3 Cation

The nine-dimensional potential energy surface for proton tunneling in the nonrigid C₂H⁺ ₃ cation was constructed from quantum-chemical data [MP4SDQ(T)/6-311++G(3df,3pd)] on the equilibrium geometry, energy, frequencies, and eigenvectors of the normal vibrations at the stationary points and transition states using the theory of isodynamic symmetry groups along the tunneling path.     

Theoretical prediction of the contact distance dependence of the electron transfer reactivity of the ClO/ClO− coupling system

On the basis of the structures and properties of the ClO/ClO^? system obtained at the density functional theory (DFT) (UB3LYP) level, employing the 6‐311+G(3df) standard basis set, the electron transfer reactivity of this system is investigated. The results indicate that there are five possible stable coupling complexes that correspond to the generous minima on the global potential energy surfaces (PES). The most stable coupling complex is planar EC4, in which there is a O? O linkage with two trans‐Cl atoms. Their stabilization energies are calculated to be 20.57 (EC1: C₁), 20.54 (EC2: C₂, ²B), 20.69 (EC3: C₁), 20.70 (EC4: C_s, ²A′), and 20.69 (EC.5: C_2h, ²B_u) kcal/mol at the B3LYP/6‐311+G(3df) level; with the correction of the basis set superposition error (BSSE), the stability order of these encounter complexes is EC4 > EC.5 > EC3 > EC1 > EC2. Based on the five encounter complexes, five coupling modes are designed for the study of the electron transfer reactivity of this system. The dissociation energy curves at the activated states and the corresponding activation energies of these five coupling modes are obtained and are compared at the B3LYP/6‐311+G(3df) and MP2/6‐311+G* levels. The inapplicability of DFT methods has also been discussed in this article in predicting the energy curves, especially with a long contact distance, in which DFT methods give the abnormal behavior for the dissociations of the complexes caused by the “inverse symmetry breaking” problem. On the basis of the golden rule of the time‐dependent perturbation theory, the electron transfer reactivity and the contact distance dependence of the various electron transfer kinetics parameters (e.g., activation energy, coupling matrix element) have been analyzed at the UMP2(full)/6‐311+G* level. The electron transfer can take place over a range of contact distances, but the most effective coupling distance corresponds to only a small range. The coupling orientation analyses also indicate that the most favorable coupling mode to the electron transfer does not always correspond to the most stable encounter complex mechanism. Some highly energetic coupling modes are more favorable for the electron transfer. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Correlated one‐electron wave functions

Using four basis sets, 6‐311G(d,p), 6‐31+G(d,p), 6‐311++G(2d,2p), and 6‐311++G(3df,3pd), the optimized structures with all real frequencies were obtained at the MP2 level for 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 acidic 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. By contrast with above the 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 a 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     

Electron affinities of metals computed by density functional theory and ab initio methods

An extensive computational study of the meal electron affinity was performed using the ab initio and density functional theory (DFT) methods. HF, MP2, MP3, MP4, QCISD, and QCISD(T) was used as computational methods, while the hybrid, local, and nonlocal DFT methods with the LYP, P86, PW91, and VWN correlation functionals were used. Two basis sets, one small and applicable to almost all metals (LanL2DZ) and one large [6-311 + + G(3df, 3 pd)] used only for small metals, were employed. The computed results were compared with the experimental data and the capabilities of the DFT methods to perform this study were discussed. © 1997 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     

Potential energy curves and calculations of spectroscopic constants for the ground state of AlC and AlN

The density functional theory method with B3LYP/6-311++G(df,pd), B3LYP/6-311++G(2df, 2pd), and B3LYP/6-311++G(3df,3pd) basis sets is used to compute the geometrics and single point energy of aluminum carbide (AlC) and aluminium nitride (AlN) in their ground state. The Level 8.0 program is used to calculate spectroscopic constants and fit the energy potential curves. The effect of a basis set on the spectroscopic constants is discussed. The results show that the calculated potential curve matches well with the Level 8.0 fitting curve, and the calculated values of spectroscopic constants become more reliable with the improvement of the quality of basis sets. The spectroscopic constants are in good agreement with the existing experimental and theoretical values. For the first time, the reliable anharmonicity constant data of AlC are reported, which agrees so well with the experimental value.     

DFT investigation of the mechanism of CH2CO + O(3P) reaction

A detailed theoretical survey of the potential energy surface (PES) for the CH₂CO + O(³P) reaction is carried out at the QCISD(T)/6‐311+G(3df,2p)//B3LYP/6‐311+G(d,p) level. The geometries, vibrational frequencies, and energies of all stationary points involved in the reaction are calculated at the B3LYP/6‐311+G(d,p) level. More accurate energy information is provided by single‐point calculations at the QCISD(T)/6‐311+G(3df,2p) level. Relationships of the reactants, transition states, intermediates, and products are confirmed by the intrinsic reaction coordinate (IRC) calculations. The results suggest that P1(CH₂+CO₂) is the most important product. This study presents highlights of the mechanism of the title reaction. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

HCN exchange on [Cu(HCN)4]+: a quantum chemical investigation

Density functional (B3LYP, B3PW91, X3LYP, BP86, PBEPBE, PW91PW91, and M06) and ab initio (MP2, MP4sdq, CCSD, and CCSD(T)) calculations with extended basis sets (6-311+G**, TZVP, LANL2DZ+p, and SDD+p, the latter including extra polarization and diffuse functions) indicate that HCN exchange on [Cu(HCN)₄]⁺ proceeds via an associative interchange (I_a) mechanism and a D_3h transition structure {[Cu(HCN)₅]⁺}^?. The activation barrier, relative to the model complex [Cu(HCN)₄]⁺·HCN, varies modestly, depending on the computational level. Typical values are 8.0?kcal?M^?1 (B3LYP/6-311+G**), 6.0?kcal?M^?1 (M06/6-311+G**), and 4.8?kcal?M^?1 (CCSD(T)/6-311+G**//MP2(full)/6-311+G**). Inclusion of an implicit solvent model (B3LYP(CPCM)/6-311+G**) leads to an activation barrier of 5.8?kcal?mol^?1. Comparison of the HCN exchange mechanisms on [Li(HCN)₄]⁺ (limiting associative, A) and [Cu(HCN)₄]⁺ (associative interchange, I_a) reveals that π back donation in the equatorial Cu–N bonds in the transition state determines the mechanism.     

Regioselectivity in cycloaddition reaction between phosphaacetylene and diazomethane: An ab initio study

The [3 + 2] cycloaddition reaction of phosphaacetylene with diazomethane was investigated by means of high level ab initio calculations. It was deduced that the aromatic diazaphosphole is formed via a nonaromatic intermediate. The regiospecificity of the reaction is thus determined by the energy difference between the two transition states that lead to the two possible regioisomeric intermediates. Of the transition states in the concerted pathways, the one leading to the regioisomer with two PC bonds ( 3 ) was found to be more stable at all the levels of theory investigated, including coupled-cluster singles doubles (CCSD)(T)/6-311 + G^*//Møller-Plessett(MP)2/6-311 + G^* (+ basis set superposition, BSSE, correction). The energy difference between the two transition states, however, is always less than 2 kcal/mol. When the free energies in the two reactions are calculated by use of the harmonic frequencies, the energy separation between the two transition structures remains practically unchanged. The free energy of activation ΔG^† was 21 kcal/mol at the CCSD(T)/6-311 + G^* level of theory and use of the MP2/6-31 + G^* frequencies. At the MP2 level, a rather stable complex is obtained in the initial phase of the reaction. However, the stability of the complexes decreases at the CCSD(T) level, and application of the BSSE correction results in unstable complexes. © 1997 by John Wiley & Sons, Inc.     

Ab initio study on the reaction mechanism of ozone with bromine atom

Ab initio calculations of the potential energy surface (PES) for the Br+O₃ reaction have been performed using the MP2, CCSD(T), and QCISD(T) methods with 6‐31G(d), 6‐311G(d), and 6‐311+G(3df). The reaction begins with a transition state (TS) when the Br atom attacks a terminal oxygen of ozone, producing an intermediate, the bromine trioxide (M), which immediately dissociates to BrO+O₂. The geometry optimizations of the reactants, products, and intermediate and transition states are carried out at the MP2/6‐31G(d) level. The reaction potential barrier is 3.09 kcal/mol at the CCSD(T)/6‐311+G(3df)//MP2 level, which shows that the bromine atom trends intensively to react with the ozone. The comparison of the Br+O₃ reaction with the F+O₃ and Cl+O₃ reactions indicates that the reactions of ozone with the halogen atoms have the similar reaction mechanism. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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.     

Post-Hartree-Fock and DFT level studies on the Cl2CO …︁ Cl2 complex: Accurate molecular parameters,harmonic vibrational frequencies,and interaction energies

The Cl₂CO …︁ Cl₂ complex was studied using ab initio post-Hartree-Fock theory at the MP2 and MP4 levels and, for comparison, the DFT method with 6-311G(2d), 6-311 + G(2d), and Sadlej's medium-size polarized (MSPBS) basis sets. A potential energy search recovered a planar minimum-energy structure characterized by a bent conformation. For this weakly bound complex, the interaction energy corrected for the basis set superposition error amounted to − 0.88, − 1.09, − 1.43, and − 0.38 kcal/mol at the MP4(SDTQ)/6-311G(2d), MP4(SDTQ)/6-311 + G(2d), MP4(SDTQ)/MSPBS, and DFT(Becke3LYP)/6-311 + G(2d) levels of theory, respectively. Two highly symmetrical forms, linear and T-shaped, correspond to transition-state conformers. The analysis of harmonic vibrational frequencies and potential energy distribution was performed at the MP2 and DFT levels with the 6-311 + G(2d) basis set. © 1996 John Wiley & Sons, Inc.     

Hydrogen bond effects on the fundamental vibration frequencies of pyridine

The IR band structure and intensities, as well as normal vibration frequencies, are calculated by the density functional method using the Becke exchange functional and the Lee-Yang-Parr (B3LYP) correlation functional with the 6-311+G(d, p) basis set for pyridine and water molecules and for 1:1 and 1:2 hydrogen-bonded complexes (pyridine...H₂O and pyridine...D₂O). The structures of the hydrogen-bonded complexes are established. The characteristicity of the fundamental vibration frequencies and absolute IR intensities of pyridine in its hydrogen-bonded complexes is analyzed. The solvent effect is investigated within the framework of the self-consistent reactive field (SCRF) model. The thermodynamic characteristics of complexation are calculated using the modified G1, G2, and G2(MP2) models and the B3LYP/6-311+G(d, p) theoretical method including the basis set superposition error (BSSE).Original Russian Text Copyright © 2004 by K. V. Berezin, V. V. Nechaev, and S. N. ZotovTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 3, pp. 412–418, May–June, 2004.     

Complexation of Phenol and Thiophenol by Amine N‐Oxides: Isothermal Titration Calorimetry and ab Initio Calculations

To develop a new solvent‐impregnated resin (SIR) system for removal of phenols from water, the complex formation of dimethyldodecylamine N‐oxide (DMDAO), trioctylamine N‐oxide (TOAO), and tris(2‐ethylhexyl)amine N‐oxide (TEHAO) with phenol (PhOH) and thiophenol (PhSH) is studied. To this end we use isothermal titration calorimetry (ITC) and quantum chemical modeling (on B3LYP/6‐311G(d,p)‐optimized geometries: B3LYP/6‐311+G(d,p), B3LYP/6‐311++G(2d,2p), MP2/6‐311+G(d,p), and spin component scaled (SCS) MP2/6‐311+G(d,p); M06‐2X/6‐311+G(d,p)//M06‐2X/6‐311G(d,p), MP2 with an extrapolation to the complete basis set limit (MP2/CBS), as well as CBS‐Q). The complexes are analyzed in terms of structural (e.g., bond lengths) and electronic elements (e.g., charges). Furthermore, complexation and solvent effects (in benzene, toluene, and mesitylene) are investigated by ITC measurements, yielding binding constants K, enthalpies ΔH⁰, Gibbs fre energies ΔG⁰, and entropies ΔS⁰ of complex formation, and stoichiometry N. The ITC measurements revealed strong 1:1 complex formation between both DMDAO–PhOH and TOAO–PhOH. The binding constant (K=1.7–5.7×10⁴ M ^?1) drops markedly when water‐saturated toluene was used (K=5.8×10³ M ^?1), and π–π interaction with the solvent is shown to be relevant. Quantum mechanical modeling confirms formation of stable 1:1 complexes with linear hydrogen bonds that weaken on attachment of electron‐withdrawing groups to the amine N‐oxide moiety. Modeling also showed that complexes with PhSH are much weaker than those with PhOH, and in fact too weak for ITC determination. CBS‐Q incorrectly predicts equal or even higher binding enthalpies for PhSH than for PhOH, which invalidates it as a benchmark for other calculations. Data from the straightforward SCS‐MP2 method without counterpoise correction show very good agreement with the MP2/CBS values.     

Theoretical study of the gas‐phase SN2 reactions of X− with CH3OY (X,Y = Cl,Br, I)

The gas‐phase nucleophilic substitution reactions at saturated oxygen X^? + CH₃OY (X, Y = Cl, Br, I) have been investigated at the level of CCSD(T)/6‐311+G(2df,p)//B3LYP/6‐311+G(2df,p). The calculated results indicate that X^? preferably attacks oxygen atom of CH₃OY via a S_N2 pathway. The central barriers and overall barriers are respectively in good agreement with both the predictions of Marcus equation and its modification, respectively. Central barrier heights (ΔH and ΔH) correlate well with the charges (Q) of the leaving groups (Y), Wiberg bond orders (BO) and the elongation of the bonds (O? Y and O? X) in the transition structures. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

HNO(H<Subscript>2</Subscript>O)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1–4) clusters: a theoretical study

The geometrical structure, binding energy, and vibrational spectra of small clusters of nitrosyl hydride (HNO) and water molecules, HNO(H₂O) _n , where (n = 1–4), have been investigated at the MP2 level of theory, using 6-311++G(2d,2p) basis set. We located three dimers, six trimers, nine tetramers, and three pentamers at the MP2/6-311++G(2d,2p) computational level. Particular attention is given to existence and magnitude of NH···O blue-shifting hydrogen bonds. Blue shifts of the NH stretching frequency upon complex formation in the ranges between 28 and 151 cm⁻¹ is predicted. Cooperative effect in terms of stabilization energy along with the many-body interaction energies analysis was performed for the studied clusters. The Atoms in Molecules (AIM) theory was also applied to explain the nature of the complexes.