Combined bond polarization function basis sets for accurate ab initio calculation of the dissociation energies of AHn molecules (A=LI to F)

An alternative route toward developing basis sets for post-Hartree-Fock calculations, the hybrid bond polarization function method, is investigated. Two new basis sets, denoted 6-31G(d, p)+ B and 6-31 + G(d,p)+B, are defined for the first-row hydrides. The dissociation energies of the first-row hydride species in their respective ground states are computed using full fourth-order Møller-Plesset theory, and compared with results obtained with large polarized basis sets containing no bond functions. It is shown that results are competitive even with basis sets as large as 6-311++G(3df,3pd), while computation times are reduced by a factor of 4 to 20. On empirical grounds, the basis set superposition error should be neglected entirely.     

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.     

Ab initio investigation on stability and properties of XYCO... HZ complexes. II: Post hartree-fock studies on H2CO... HF

Ab initio MP2 level of theory in conjunction with three basis sets of a triple-zeta quality was applied to study the molecular geometry and stability of the H₂CO... HF complex. An interaction energy predicted for this system at the highest, MP4(SDTQ)/6-311 + +G(2df, 2pd)//MP2/6-311 + +G(2df, 2pd), level corrected for the BSSE and ZPE contributions amounts to -4.85 kcal/ mol. BSSE contributes significantly to the interaction energies at all applied levels. Reliable MP2/ 6-311 + +G(2df, 2pd) level harmonic vibrational frequencies, IR intensities, and the predicted isotopic shifts upon deuteration and¹⁸O substitution are presented in order to facilitate experimental studies on the IR spectrum of the title complex.     

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.     

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.     

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.     

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.     

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.     

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.     

Coupling between the convergence behavior of basis set and electron correlation: a quantitative study

The coupling between improvement of the basis set and the valence electron correlation method has been studied quantitatively for the total atomization energies (TAEs) of a number of small molecules, using basis sets of up to [7s6p5d4f3g2h/5s4p3d2f1g] quality. Very significant coupling is found to exist. Using a scaled basis set extrapolation beyond [6s5p4d3f2g/ 4s3p2d1f] at the MP2 or CCSD level, mean absolute errors of 0.18 and 0.15 kcal/mol, respectively, can be obtained for the TAEs of a number of small polyatomic molecules, compared to 0.12 kcal/mol using CCSD(T) throughout. Received: 7 February 1997 / Accepted: 6 May 1997     

The basis set dependence of structures and energies of various states of cyclodisiloxane

Several common basis sets, ranging from minimal to double-zeta, are applied to study the neutral singlet and triplet as well as positive- and negative-ion doublet states of cyclodisiloxane. The effect of d-polarization function exponents on the equilibrium geometries and energies is analyzed. The d-type functions seem to be essential in the basis set of silicon, whereas their presence on oxygen is less critical. The optimum exponents (with respect to SCF energy) are determined to be 0.45 for Si and 0.60 for O, very close to those recommended for the 6–31G^** basis set. The best structural predictions are obtained with the 6–31G(2d, p) basis set, which contains two sets of d functions on the heavy atoms. The predicted Si? O bond length is 166 pm; the Si? Si and O? O distances are 237 and 232 pm, respectively, which correspond to an O—Si? O angle of 88.6°. The ground state is found to be a singlet. All higher states have longer Si? O bonds and Si—Si distances, whereas O—O distances are shorter. The energy separation between the singlet and other states is modified by electron correlation (MP treatment) by only a few kcal/mol.     

Comparison of large basis set DFT and MP2 calculations in the study of the barrier for internal rotation of 2,3,5,6‐tetrafluoroanisole

The barrier for internal rotation around the ? OCH₃ bond in 2,3,5,6‐tetrafluoroanisole was calculated using the density functional theory (DFT) and second‐order Møller–Plesset (MP2) methods with Pople's basis sets up to 6‐311++G(3df,2p) and Jensen basis sets up to pc‐3. The results are converged only if fairly large basis sets are used (at least 6‐311++G(3df,2pd) or pc‐2). Both the DFT and MP2 potential energy curves show internal structure. Two minima and three maxima are observed on the curves, arising from the interplay between lone‐pair delocalization and changes in the hybridization around the oxygen atom, together with the attraction between the positively polarized hydrogens in the methyl group and the negatively polarized fluorine atom at the ortho position. These critical points are somehow ironed out by the addition of zero‐point and thermal corrections to the energy curves. At this level, the MP2 method can describe reasonably well the previously determined single‐well experimental rotational barrier, 2.7 ± 2.0 kcal/mol at 298 K, while all DFT methods yield a much smaller result. As observed experimentally, the ? OCH₃ group is perpendicular to the aryl ring in the equilibrium structure, although two very close minima with an intermediate hump at 90° are still observable. The theoretical free energy barrier of rotation at the MP2(full)/pc‐2 level is 2.0 ± 1.0 kcal/mol, in reasonable agreement with the experimental determination. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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.     

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     

Thermochemistry and NBO analysis of peptide bond: Investigation of basis sets and binding energy

Ab initio methods were used to analyze the structure, energetic and binding energy of the five began dipeptides with methionine, Met-Gly, Met-Ala, Met-Ser, Met-Cys, and Met-Thr dipeptides, in gas phase. The structures of the dipetides and involved amino acids in them were optimized by using Hartree-Fock and DFT methods and 3-21G(d), 6-31G(d), 6-311G, 6-311G(d), and 6-311+G(d) basis sets. The effect of basis sets and electron correlations were analyzed with special emphasis on the calculated binding energies and thermodynamic functions. All used methods revealed that Met-Thr has the highest binding energy among all of the five dipeptide molecules. These numerical results suggest that Thr donates the proton easier than other four amino acids and it has the most tendency to join with methionine and it forms the most strong bond with methionine. This fact may be the reason behind the obtained high binding energies for Met-Thr at all levels. From comparison of the values of binding energy for dipeptides in different levels of theory, we could identify that the order of tendency for joint with methionine is Thr > Gly > Ala > Cys > Ser. Also, these data represented that the highest binding energy provide in HF/6-311G level for all of the dipeptides (14.4202, 11.2387, 8.3267, 9.8853, 17.3362 kcal mol⁻¹ for dipeptides 1–5, respectively). Moreover, natural bond orbital (NBO) analysis demonstrated that the effect of basis sets and electron correlations on σ_N1-C2 bonding orbital occupancy is the same as the basis set and electron correlation effects on binding energy of dipeptides in all cases. The obtained results from studying the effect of basis sets and electron correlations on binding energy, NMR and NBO properties showed that the effect of basis sets is almost independent of molecular structure and computational method, while electron correlation effects are relatively dependent to molecular structure and basis set type. In investigating the effect of basis sets and electron correlations on binding properties, the NBO results are in good agreement with the energetic and thermochemistry data at all levels of calculations. The article is published in the original.     

The role of the basis set and the level of quantum mechanical theory in the prediction of the structure and reactivity of cisplatin

In this article, we conducted an extensive ab initio study on the importance of the level of theory and the basis set for theoretical predictions of the structure and reactivity of cisplatin [cis‐diamminedichloroplatinum(II) (cDDP)]. Initially, the role of the basis set for the Pt atom was assessed using 24 different basis sets, including three all‐electron basis sets (ABS). In addition, a modified all‐electron double zeta polarized basis set (mDZP) was proposed by adding a set of diffuse d functions onto the existing DZP basis set. The energy barrier and the rate constant for the first chloride/water exchange ligand process, namely, the aquation reaction, were taken as benchmarks for which reliable experimental data are available. At the B3LYP/mDZP/6‐31+G(d) level (the first basis set is for Pt and the last set is for all of the light atoms), the energy barrier was 22.8 kcal mol^?1, which is in agreement with the average experimental value, 22.9 ± 0.4 kcal mol^?1. For the other accessible ABS (DZP and ADZP), the corresponding values were 15.4 and 24.5 kcal mol^?1, respectively. The ADZP and mDZP are notably similar, raising the importance of diffuse d functions for the prediction of the kinetic properties of cDDP. In this article, we also analyze the ligand basis set and the level of theory effects by considering 36 basis sets at distinct levels of theory, namely, Hartree‐Fock, MP2, and several DFT functionals. From a survey of the data, we recommend the mPW1PW91/mDZP/6‐31+G(d) or B3PW91/mDZP/6‐31+G(d) levels to describe the structure and reactivity of cDDP and its small derivatives. Conversely, for large molecules containing a cisplatin motif (for example, the cDDP‐DNA complex), the lower levels B3LYP/LANL2DZ/6‐31+G(d) and B3LYP/SBKJC‐VDZ/6‐31+G(d) are suggested. At these levels of theory, the predicted energy barrier was 26.0 and 25.9 kcal mol^?1, respectively, which is only 13% higher than the actual value. © 2012 Wiley Periodicals, Inc.     

(Pentafluoruphenyl)xenonium(II) cyanide, isocyanide, and fluoride in dichloromethane: A PCM/DFT study

Calculations by the PCM/B3LYP/6-311G++(3d₅f₇)&;Xe-3-111G(3d₅)PCM/B3LYP/6-311G-(3d₅f₇)&;Xe-3-111G(d₅) method show that, despite the higher electronegativity of the nitrogen atom, the interaction between the CN^? anion and the (pentaphenyl)xenonium(II) cation forms a xenon-carbon bond which is stronger by 6 kcal mol^?1 than the direct ionic bond between CN^? and Xe⁺.     

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.     

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